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  • 1990-1994  (3,239)
  • 1890-1899
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  • 1850-1859
  • 1830-1839
  • 1994  (1,879)
  • 1990  (1,360)
  • Biochemistry and Biotechnology  (1,769)
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  • Mathematics and Statistics  (244)
Material
Years
  • 1990-1994  (3,239)
  • 1890-1899
  • 1880-1889
  • 1850-1859
  • 1830-1839
Year
  • 1
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1-9 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Let f(u) be twice continuously differentiable on [0, c]) for some constant c such that f(0) 〉 0,f′ ≥ 0,f″ ≥ 0, and limu→cf(u) = ∞. Also, let χ(S) be the characteristic function of the set S. This article studies all solutions u with non-negative ut, in the region where u 〈 c and with continuous ux for the problem: uxx - ut = - f(u)χ({u 〈 c}), 0 〈 x 〈 a, 0 〈 t 〈 ∞, subject to zero initial and first boundary conditions. For any length a larger than the critical length, it is shown that if ∫0cf(u) du 〈 ∞, then as t tends to infinity, all solutions tend to the unique steady-state profile U(x), which can be computed by a derived formula; furthermore, increasing the length a increases the interval where U(x) ≡ c by the same amount. For illustration, examples are given.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 71-76 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we construct two approximating sequences for heteroclinic solution to a scalar ODE. These sequences do not ‘intersect’ and bound a unique real solution from below and above, thus enabling us to estimate this solution with any accuracy.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 95-105 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper is concerned with the question of necessary and sufficient conditions to find a vector field V∊ Γ(TM) solving the equation div V = Φ under inhomogeneous boundary conditions V|∂M = Z|∂M with Z∊ Γ (TM) An existence and regularity result is given for an arbitrary Riemannian manifold with boundary, M. The proof is based on the Hodge theory of differential forms.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 107-113 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: For the theory of boundary value problems in linear elasticity, it is of crucial importance that the space of vector-valued L2-functions whose symmetrized Jacobians are square-integrable should be compactly embedded in L2. For regions with the cone property this is usually achieved by combining Korn's inequalities and Rellich's selection theorem. We shall show that in a class of less regular regions Korn's second inequality fails whereas the desired compact embedding still holds true.
    Type of Medium: Electronic Resource
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  • 6
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 171-188 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This article deals with flow phenomena in liquid crystal materials. The model that I analyse is that due to Ericksen for liquid crystals with variable degree of orientation. One of the goals is understanding the role of the order parameter in the model. I examine the multiplicity of solutions, phases, that occur in shear flow regimes and analyse their stability under physically realistic conditions. In particular, I show that ellipticity of the linearized system of governing equations is a consequence of the Clausius-Duhem inequality.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 8
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    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 229-238 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We show how saddle point techniques can be used to obtain new results for general resonance problems of the type considered by Landesman and Lazer.
    Type of Medium: Electronic Resource
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  • 9
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 269-291 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In an exterior domain Ω⊂∝n, n ≥ 2, we consider the generalized Stokes resolvent problem in Lq-space where the divergence g = div u and inhomogeneous boundary values u = ψ with zero flux ∫∂Ωψ·N do = 0 may be prescribed. A crucial step in our approach is to find and to analyse the right space for the divergence g. We prove existence, uniqueness and a priori estimates of the solution and get new results for the divergence problem. Further, we consider the non-stationary Stokes system with non-homogeneous divergence and boundary values and prove estimates of the solution in L5(0, T;Lq(Ω)) for 1 〈 s, q 〈 ∞.
    Type of Medium: Electronic Resource
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  • 10
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    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 377-393 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The evolution model of a microstructure described as appropriately generalized Young measures, which was developed in [11], is discretized here by means of a suitably adapted finite element method. The convergence of the approximate solutions is proved, and a one-dimensional example is treated to discuss some implementation experience and to show some illustrative results.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 11
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 12
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 451-476 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we show the existence of a weak solution of the boundary value problem for the time dependent Vlasov-Poisson system. First, we regularize the system in order to apply a fixed-point theorem. Then we pass to the limit using an energy estimate.
    Type of Medium: Electronic Resource
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  • 13
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    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 509-524 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider a two-dimensional parabolic system with general competitive interactions as a two-player game with conflicting objectives and with controls on the inhomogencous (source) terms. We show the existence of an optimal solution of the game as the saddle point of a suitable objective functional.
    Type of Medium: Electronic Resource
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  • 14
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 15
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    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 613-641 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study here the Landau-Maxwell system in its classical form. We prove the local existence of weak solution with initial data of unrestricted size. The main tools consist of an approximation method and a regularity result for velocity averages of solutions of some general linear transport equations.
    Type of Medium: Electronic Resource
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  • 16
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 17
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 681-695 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove using the Faedo-Galerkin method the existence of a generalized solution of an initial-boundary value problem for the non-linear evolution equation0 ≤ Q ≤ 2, in a cylinder QT = Ω × (0, T), where T u = yuxx + uyy is the Tricomi operator and l(u) a special differential operator of first order. We then show that the approximate generalized solution of problem (*) converges to the approximate generalized solution of the corresponding stationary boundary value problem as t → ∞.
    Type of Medium: Electronic Resource
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  • 18
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 765-785 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study a non-linear problem in pressure saturation modelling of a free boundary problem, arising in self-lubricating bearings, with Neumann boundary conditions for the pressure and a non-local constraint on the saturation variable, which indeed is a Lagrange multiplier. We prove an existence theorem by introducing an artificial time dependence and using the pseudo-characteristics discretization method and semi-coercive variational inequalities.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 19
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 837-854 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove existence and uniqueness theorems for weak solutions of equations describing stationary isothermic motion of a mixture of two viscous incompressible fluids with asymmetric stress tensor, in a bounded subset of ∝3. The model of the flow we consider here assumes that some of coefficients characterizing isotropic properties of the fluid equal zero.
    Type of Medium: Electronic Resource
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  • 20
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 943-952 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, two different control problems with state constraints for shape memory alloys are considered: in the non-isothermal case, we study boundary control problems, and in the isothermal situation, a dynamical shape optimization problem is considered. In both cases, the transverse displacement is the constrained state variable. The first-order conditions of optimality are derived.
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  • 21
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 971-987 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We give a thorough quantitative error analysis for the effect of coefficient idealization on solutions of linear elliptic boundary value problems. The a posteriori error estimate is derived by a tactful application of the duality theory in convex analysis. The estimate involves an auxiliary function subject to certain constraint. We discuss in detail the selection of a good auxiliary function for various cases. Numerical examples show the effectiveness of our a posteriori error estimate.
    Additional Material: 1 Ill.
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  • 22
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1045-1052 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study positive solutions u to Δu + f(u) = 0 in Ω, u = 0 on ∂Ω, and we address the following question: If Ω is a small perturbation of a ball, is u a small perturbation of a radially symmetric function? We prove two theorems which give an affirmative answer under different assumptions on the non-linearity f and on the topologies in which perturbations are considered.
    Type of Medium: Electronic Resource
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  • 23
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1071-1087 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we present the asymptotic analysis of the linear Boltzmann equation for neutrons with a small positive parameter ∊ related to the mean free path, based upon the Chapman-Enskog procedure of the kinetic theory. We prove that if proper initial conditions derived by considering initial layer solutions are used, the diffusion equation gives the uniform approximation to the neutron density function with the O(∊2) accuracy.
    Type of Medium: Electronic Resource
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  • 24
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 551-575 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The positive vertical equilibrium profiles of a phytoplankton population growing in a vertical test tube under controlled experimental conditions (temperature, salinity, light intensity at the top surface) for nutrients are discussed with reference to their stability properties for arbitrary positive initial values of the biomass concentration along the tube. Two different approaches are followed. First a stability result is established in the Sobolev norm H2 by estimating the norms of the perturbations recursively in successive subintervals of suitably small amplitude. The second approach provides stability in the sense of the uniform convergence as a corollary of a stability theorem for a rather general class of integro-differential equations.
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  • 25
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1129-1140 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The problem of stability of stationary solutions of the Vlasov-Poisson system has received a lot of attention in the physics literature, both in the stellar dynamics and the plasma physics cases. The energy-Casimir method has been used to prove non-linear stability for various conservative systems, but no rigorous application to the Vlasov-Poisson system has been given yet. We employ this method to prove non-linear stability of stationary solutions for the plasma physics case in three geometrically different settings.
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  • 26
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 339-347 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper presents a mapping approach for the construction of exact solutions to the combined KdV and mKdV equation. There exist two types of soliton solutions which will reduce back to those of the KdV and mKdV equations in some appropriate limits. Four types of the general cnoidal wave solutions are also obtained.
    Type of Medium: Electronic Resource
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  • 27
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 431-450 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We continue the study of general interface problems. We prove regularity and asymptotics of solutions in usual Sobolev spaces for non-constant coefficients operators. We also give the stabilization procedure when unstable decompositions appear near a critical angle.
    Additional Material: 18 Ill.
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  • 28
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 477-486 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove the global existence of analytic solutions to the non-linear viscoelastic equations of the following type: \documentclass{article}\pagestyle{empty}\begin{document}$$ u_n \, = \,\phi \,(\,||\,\nabla _x \,u\,||^2)\Delta u\, + \,\Psi \,(||\,D_x^\beta \,1\,u\,||^2,\,.\,.\,.\,\,||\,D_{x^N }^\beta \,||)\,\Delta u_t $$\end{document} where φ and ψ are continuous and non-negative functions satisfying some additional conditions. The method of the analytic energy estimates is used.
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  • 29
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 30
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 933-942 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We investigate the effect of temperature dependence of the viscosity on the stability of the adiabatic shearing flows of an incompressible Newtonian viscous fluid between two parallel plates. When the viscosity strongly decreases with temperature, the shearing flow caused by a steady motion of the upper plate (steady shearing) becomes unstable, while the shearing flow caused by a time-dependent body force is found to be stable.
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  • 31
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994) 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 32
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1005-1016 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A constructive method for obtaining subsolutions and supersolutions to the Cauchy problem for systems of parabolic equations is discussed. Applications of the method to Fujita-type systems are considered leading to global existence and finite time blow-up results.
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  • 33
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1053-1070 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The existence of global in space variables solutions for a class of non-linear subelliptic evolution operators is proved. A Cauchy problem and an initial-boundary value problem are considered using the contraction theorem and Galerkin methods.
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  • 34
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    Mathematical Methods in the Applied Sciences 17 (1994), S. 1089-1114 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper deals with bimetal problems of thermoelastostatics. By means of an explicit particular solution a reduction to problems of elastostatics is given. An indirect boundary integral method is applied for solving the traction boundary value problem. The solution is represented by a potential of single layer type having Green's contact tensor as the kernel. Thus, from the first the transmission conditions are satisfied. The Fredholm property of the boundary integral operator as well as the asymptotics of the potential density at an interface corner depend on the symbol of a Mellin convolution operator. The singular functions at corners can be obtained by calculating the potential for terms in the asymptotic expansion of the density.
    Additional Material: 7 Ill.
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  • 35
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    Mathematical Methods in the Applied Sciences 17 (1994), S. 1115-1127 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The problem of determining the Stokes flow of a micropolar fluid exterior to several closed surfaces but contained by an exterior contour that encloses all the interior surfaces, is formulated as a system of linear Fredholm integral equations of the second kind. These integral equations are obtained when the velocity and microrotation vector fields are represented by a double-layer potential with unknown density, and certain singular solutions of the Stokes' micropolar equations. This double-layer potential is defined over the union of all the surfaces involved including the exterior contour. The singularities, corresponding to a concentrated force and concentrated couple located within each interior surface, give rise to force and torque whose magnitudes are linearly dependent on the unknown density of the double layer. It is shown that the system possesses a unique continuous solution when the boundaries are Lyapunov surfaces and the boundary data is continuous.
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  • 36
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    Mathematical Methods in the Applied Sciences 17 (1994), S. 1213-1230 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The eigenfunction expansion theorem and its application to the scattering operator and the scattering matrix is extended to Schrödinger operators with measure potentials with unbounded support on ∝n that are known to generate wave operators that are strongly complete. Analyticity conditions of the eigenfunctions and the scattering matrix are presented.
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  • 37
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    Mathematical Methods in the Applied Sciences 17 (1994), S. 395-429 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study transmission problems for elliptic operators of order 2m with general boundary and interface conditions, introducing new covering conditions. This allows to prove solvability, regularity and asymptotics of solutions in weighted Sobolev spaces. We give some numerical examples for the location of the singular exponents.
    Additional Material: 18 Ill.
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  • 38
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1017-1043 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We generalize spherical harmonics expansions of scalar functions to expansions of alternating differential forms (‘q-forms’). To this end we develop a calculus for the use of spherical co-ordinates for q-forms and determine the eigen-q-forms of the Beltrami-operator on SN-1 which replace the classical spherical harmonics. We characterize and classify homogeneous q-forms u which satisfy Δu = 0 on ∝N﹨{0} and determine Fredholm properties, kernel and range of the exterior derivative d acting in weighted Lp-spaces of q-forms (generalizing results of McOwen for the scalar Laplacian). These techniques and results are necessary prerequisites for the discussion of the low-frequency behaviour in exterior boundary value problems for systems occurring in electromagnetism and isotropic elasticity.
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  • 39
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    Mathematical Methods in the Applied Sciences 17 (1994), S. 1141-1164 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider wave propagation in a cone shaped unbounded domain which contains an inhomogeneous medium with non-smooth coefficients. Existence and completeness of the wave operators are proved in the case of local perturbations of the domain and the coefficients.
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  • 40
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    Mathematical Methods in the Applied Sciences 17 (1994), S. 1193-1212 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study a collisionless transport model for electrons in a semiconductor, and we perform an asymptotic analysis for low temperatures or large applied biases. We derive analytic relations for the built-in potential and for the current which flows through the structure.
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  • 41
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    Mathematical Methods in the Applied Sciences 17 (1994), S. 11-20 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The physical model for penetrative convection in porous media is here considered to study the effects of variation of the source parameters on the flow. In this note we study the continuous dependence upon the heat supply and the body force of the classical solutions to the initial-boundary value problem of a heat conducting fluid through a porous solid, both for the (well-posed) forward problem and for the (improperly posed) backward in time one. For the former problem we obtain a result of continuous dependence with respect to the L2 norm; while for the latter we prove a result of Hölder continuity in a suitably constrained class of solutions.
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  • 42
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    Mathematical Methods in the Applied Sciences 17 (1994), S. 21-39 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study some boundary value problems on two-dimensional polygonal topological networks, where on each face, the considered operator is the biharmonic operator. The transmission conditions we impose along the edges are inspired by the models introduced by H. Le Dret [13] and Destuynder and Nevers [9]. The boundary conditions on the external edges are the classical ones. This class of problem contains the boundary value problems for the biharmonic equation in a plane polygon (see [3, 11, 12, 18]). Conforming to the classical results cited above, we prove that the weak solution of our problem admits a decomposition into a regular part and a singular part, the latter being a linear combination of singular functions depending on the domain and the considered boundary value problem. Finally, we give the exact formula for the coefficients of these singularities.
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  • 43
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    Mathematical Methods in the Applied Sciences 17 (1994), S. 115-154 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the propagation of linear waves, generated by a compactly supported time-harmonic force distribution, in an infinite string under the assumption that the material properties are p1-periodic for x 〉 a and p2-periodic for x 〈 - a. As has been pointed out in two preceding papers devoted to related configurations ([4], [5]), the combination of a time-periodic force and a periodic spatial structure may lead to resonance phenomena. We show that the present configuration also permits resonances of orders t and t1/2 for a discrete set of frequencies. The occurrence of resonances is closely related to the presence of non-trivial solutions of the corresponding time-independent homogeneous problem which satisfy certain asymptotic properties (‘standing waves’).
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  • 44
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    Mathematical Methods in the Applied Sciences 17 (1994), S. 155-169 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper is concerned with some qualitative analysis for a coupled system of five reaction-diffusion equations which arises from a physiology model. The uniform boundedness of the time-dependent solution is obtained under various boundary conditions. Sufficient conditions are also given to ensure the asymptotic stability of the non-negative steady-state solutions under Dirichlet or Robin boundary condition for each component. Under homogeneous Neumann boundary condition for some components the time-dependent solution is proven to converge to a constant steady state determined by the initial functions.
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  • 45
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    Mathematical Methods in the Applied Sciences 17 (1994), S. 189-207 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Perturbation of a single-degree-of-freedom conservative oscillator leads to the emergence and vanishing of periodic solutions and to various types of self-excited oscillations. Using techniques from dynamical systems theory, in particular a certain Poincaré map, we establish the presence of Hopf bifurcations, various types of homoclinic bifurcations and saddle-node bifurcations of the associated Poincaré map. The corresponding bifurcation sets in parameter space are computed explicitly by perturbation methods. The theory is applied to the generalized van der Pol and the generalized Rayleigh oscillator, and to the case of a non-linear spring attached to a conveyor belt.
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  • 46
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    Mathematical Methods in the Applied Sciences 17 (1994), S. 293-303 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the inverse electromagnetic scattering problem for an inhomogeneity of compact support with constant permittivity Colton and Päivärinta suggested an optimization scheme which yields a numerical method for determining the refractive index if the far-field data of the scattering problem is known [1]. We prove the denseness of the Cauchy data to certain interior transmission problems and conclude that the infimum of the optimization scheme is zero even if the permittivity varies. Before proving the denseness result, we investigate a boundary value problem which is needed to prove the denseness result.
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  • 47
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove the correctness of a principle of linearization in the investigation of the uniform asymptotic stability of a sufficiently smooth, but generally non-steady, solution of the Navier-Stokes equations for compressible fluids in the case of a constant temperature.
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  • 48
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    Mathematical Methods in the Applied Sciences 17 (1994), S. 349-376 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove global existence and uniqueness of classical solutions of the Wigner-Poisson and Schrödinger-Poisson systems of equations for both repulsive and attractive potentials. In the repulsive case, we prove decay estimates for the particle density, the potential and the solutions.
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  • 49
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    Mathematical Methods in the Applied Sciences 17 (1994), S. 487-508 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper is devoted to a posteriori quantitative analysis for errors caused by linearization of non-linear elliptic boundary value problems and their finite element realizations. We employ duality theory in convex analysis to derive computable bounds on the difference between the solution of a non-linear problem and the solution of the linearized problem, by using the solution of the linearized problem only. We also derive computable bounds on differences between finite element solutions of the nonlinear problem and finite element solutions of the linearized problem, by using finite element solutions of the linearized problem only. Numerical experiments show that our a posteriori error bounds are efficient.
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  • 50
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    Mathematical Methods in the Applied Sciences 17 (1994), S. 901-918 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The dynamic thermoelastic impact of two rods is modelled by a coupled system of two quasivariational inequalities and two equalities that reflect a bilateral contact condition and a radiation condition for the temperatures. The existence of a weak solution is established using a penalization method that employs Galerkin approximations and a priori estimates.
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  • 51
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    Proteins: Structure, Function, and Genetics 18 (1994), S. 205-215 
    ISSN: 0887-3585
    Keywords: peptide folding ; disulfide framework ; insect toxins ; NMR ; distance geometry ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: An analysis of the sequences of scyllatoxin and charybdotoxin suggested that it would be possible to design a core peptide sequence which would still fold to give the β-hairpin and helix seen in the toxins, but which would eliminate one disulfide and connecting residues. The core sequence was modeled, then synthesized and purified. The cysteines oxidize in air to give the same disulfide pairings as seen in the parent toxins as the major product. The three-dimensional structure of the core sequence peptide, termed Max, was determined using proton NMR spectroscopy and found to be identical in secondary structure to the toxins. However differences were found in the relative orientation of the β-hairpin and helix. The use of this structural motif, found in many insect toxins, as a disulfide framework for exploring sequence/structure/activity relationships is discussed. © 1994 John Wiley & Sons, Inc.
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  • 52
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    Proteins: Structure, Function, and Genetics 18 (1994), S. 246-253 
    ISSN: 0887-3585
    Keywords: microcalorimetry ; heat capacity ; enthalpy ; hydrogen bonding ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: The energetics of ubiquitin unfolding have been studied using differential scanning microcalorimetry. For the first time it has been shown directly that the enthalpy of protein unfolding is a nonlinear function of temperature. Thermodynamic parameters of ubiquitin unfolding were correlated with the structure of the protein. The enthalpy of hydrogen bonding in ubiquitin was calculated and compared to that obtained for other proteins. It appears that the energy of hydrogen bonding correlates with the average length of the hydrogen bond in a given protein structure. © 1994 John Wiley & Sons, Inc.
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  • 53
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    Proteins: Structure, Function, and Genetics 18 (1994), S. 262-266 
    ISSN: 0887-3585
    Keywords: protein structure prediction ; protein stability ; hydrogen bond ; β-sheet ; amino acid propensity ; steric effect ; hydrogen exchange ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Amino acid side chains can enhance peptide group hydrogen bond strength in protein structures by obstructing the competing hydrogen bond to solvent in the unfolded state. Available data indicate that the steric blocking effect contributes an average of 0.5 kJ per residue to protein hydrogen bond strength and accounts for the intrinsic α-sheet propensities of the amino acids. In available data for helical models, the contribution to α-helix propensities is obscured especially by large context-dependent effects. These issues are all related by a common side chain-dependent steric clash which disfavors peptide to water H-bond formation, peptide to catalyst complexation in hydrogen exchange reactions (Bai et al., Proteins 17:75-86, 1993), and peptide to peptide H-bonding in the helical main chain conformation (Creamer and Rose, Proc. Natl. Acad. Sci. U.S.A. 89:5937-5941, 1992) but not in α-strands. © 1994 John Wiley & Sons, Inc.
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  • 54
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    Proteins: Structure, Function, and Genetics 18 (1994), S. 281-294 
    ISSN: 0887-3585
    Keywords: membrane ; protein ; structure ; prediction ; G-protein coupled receptor ; rhodopsin ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Integral membrane proteins (of the α-helical class) are of central importance in a wide variety of vital cellular functions. Despite considerable effort on methods to predict the location of the helices, little attention has been directed toward developing an automatic method to pack the helices together. In principle, the prediction of membrane proteins should be easier than the prediction of globular proteins: there is only one type of secondary structure and all helices pack with a common alignment across the membrane. This allows all possible structures to be represented on a simple lattice and exhaustively enumerated. Prediction success lies not in generating many possible folds but in recognizing which corresponds to the native. Our evaluation of each fold is based on how well the exposed surface predicted from a multiple sequence alignment fits its allocated position. Just as exposure to solvent in globular proteins can be predicted from sequence variation, so exposure to lipid can be recognized by variable-hydrophobic (variphobic) positions. Application to both bacteriorhodopsin and the eukaryotic rhodopsin/opsin families revealed that the angular size of the lipid-exposed faces must be predicted accurately to allow selection of the correct fold. With the inherent uncertainties in helix prediction and parameter choice, this accuracy could not be guaranteed but the correct fold was typically found in the top six candidates. Our method provides the first completely automatic method that can proceed from a scan of the protein sequence databanks to a predicted three-dimensional structure with no intervention required from the investigator. Within the limited domain of the seven helix bundle proteins, a good chance can be given of selecting the correct structure. However, the limited number of sequences available with a corresponding known structure makes further characterization of the method difficult. © 1994 John Wiley & Sons, Inc.
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  • 55
    ISSN: 0887-3585
    Keywords: triglyceride lipase ; proenzyme ; molecular replacement ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: A neutral lipase from the filamentous fungus Rhizopus delemar has been crystallized in both its proenzyme and mature forms. Although the latter crystallizes readily and produces a variety of crystal forms, only one was found to be suitable for X-ray studies. It is monoclinic (C2, a = 92.8 Å, b = 128.9 Å, c = 78.3 Å, β = 135.8) with two molecules in the asymmetric unit related by a noncrystallographic diad. The prolipase crystals are orthorhombic (P212121, with a = 79.8 Å, b = 115.2 Å, c = 73.0 Å) and also contain a pair of molecules in the asymmetric unit. Initial results of molecular replacement calculations using the refined coordinates of the related lipase from Rhizomucor miehei identified the correct orientations and positions of the protein molecules in the unit cells of crystals of both proenzyme and the mature form. © 1994 John Wiley & Sons, Inc.
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  • 56
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    Proteins: Structure, Function, and Genetics 18 (1994), S. 309-317 
    ISSN: 0887-3585
    Keywords: protein structure prediction ; predicted contact maps ; correlated mutations ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: The maintenance of protein function and structure constrains the evolution of amino acid sequences. This fact can be exploited to interpret correlated mutations observed in a sequence family as an indication of probable physical contact in three dimensions. Here we present a simple and general method to analyze correlations in mutational behavior between different positions in a multiple sequence alignment. We then use these correlations to predict contact maps for each of 11 protein families and compare the result with the contacts determined by crystallography. For the most strongly correlated residue pairs predicted to be in contact, the prediction accuracy ranges from 37 to 68% and the improvement ratio relative to a random prediction from 1.4 to 5.1. Predicted contact maps can be used as input for the calculation of protein tertiary structure, either from sequence information alone or in combination with experimental information. © 1994 John Wiley & Sons, Inc.
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  • 57
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    Proteins: Structure, Function, and Genetics 18 (1994), S. 324-337 
    ISSN: 0887-3585
    Keywords: protein structure ; secondary structure ; peptide geometry ; Ramachandran plot ; β-turns ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: The polypeptide of a protein molecule can be considered as a chain of Cα atoms linked by pseudobonds between the Cα atoms of successive amino acid residues. This paper presents an analysis of the angle and dihedral angles made by these pseudobonds in protein structures determined at high resolution by X-ray crystallography. This analysis reveals a strong correlation between Cα geometry and the protein fold. The regular features of protein secondary structure such as α-helix and α-sheet are very clearly defined. In addition, it is possible to identify with some confidence the discrete populations of particular conformations of α-turn. Comparison with the traditional Ramachandran type of plot demonstrates that an analysis of protein structure on the basis of Cα geometry provides a richer description of protein conformation. In addition, the characteristics of this geometry could be a useful guide in model building of protein structure. © 1994 John Wiley & Sons, Inc.
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  • 58
    ISSN: 0887-3585
    Keywords: X-ray crystallography ; extracellular matrix ; multiwavelength anomalous diffraction (MAD) ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Crystals of a fragment of human fibronectin encompassing the 7th through the RGD-containing 10th type III repeats (FN7-10) have been produced with protein expressed in E. coli. The crystals are monoclinic with one molecule in the asymmetric unit and diffract to beyond 2.0 Å Bragg spacings. A mutant FN7-10 was produced in which three methionines, in addition to the single native methionine already present, have been introduced by site-directed mutagenesis. Diffraction-quality crystals of this mutant protein have been grown in which methionine was replaced with selenomethionine. The introduction of methionine by site-directed mutagenesis to allow phasing from selenomethionyl-substituted crystals is shown to be feasible by this example and is proposed as a general approach to solving the crystallographic phase problem. Strategies for selecting propitious sites for methionine mutations are discussed. © 1994 Wiley-Liss, Inc.
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  • 59
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    Proteins: Structure, Function, and Genetics 19 (1994), S. 55-72 
    ISSN: 0887-3585
    Keywords: secondary structure prediction ; prediction of secondary structure class ; prediction of secondary structure content ; evolutionary information ; multiple alignment profiles ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Using evolutionary information contained in multiple sequence alignments as input to neural networks, secondary structure can be predicted at significantly increased accuracy. Here, we extend our previous three-level system of neural networks by using additional input information derived from multiple alignments. Using a position-specific conservation weight as part of the input increases performance. Using the number of insertions and deletions reduces the tendency for overprediction and increases overall accuracy. Addition of the global amino acid content yields a further improvement, mainly in predicting structural class. The final network system has a sustained overall accuracy of 71.6% in a multiple cross-validation test on 126 unique protein chains. A test on a new set of 124 recently solved protein structures that have no significant sequence similarity to the learning set confirms the high level of accuracy. The average cross-validated accuracy for all 250 sequence-unique chains is above 72%. Using various data sets, the method is compared to alternative prediction methods, some of which also use multiple alignments: the performance advantage of the network system is at least 6 percentage points in three-state accuracy. In addition, the network estimates secondary structure content from multiple sequence alignments about as well as circular dichroism spectroscopy on a single protein and classifies 75% of the 250 proteins correctly into one of four protein structural classes. Of particular practical importance is the definition of a position-specific reliability index. For 40% of all residues the method has a sustained three-state accuracy of 88%, as high as the overall average for homology modelling. A further strength of the method is greatly increased accuracy in predicting the placement of secondary structure segments. © 1994 Wiley-Liss, Inc.
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  • 60
    ISSN: 0887-3585
    Keywords: endonuclease overexpression ; crystallization ; X-ray diffraction ; protein-DNA complex ; Type II restriction enzyme ; vapor diffusion ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: We have overexpressed the type II restriction endonuclease PvuII (R.PvuII) in E. coli, prepared large amounts of the homogeneous enzyme, and crystallized it with an oligonucleotide carrying a PvuII recognition site. The cocrystals are orthorhombic space group P212121 with cell constants a = 95.8 Å, b = 86.3 Å, c = 48.5 Å, and diffract X-rays to at least 2.7 Å. There is a complex of two protein subunits and one oligonucleotide duplex in the asymmetric unit. © 1994 Wiley-Liss, Inc.
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  • 61
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    Proteins: Structure, Function, and Genetics 19 (1994) 
    ISSN: 0887-3585
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
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  • 62
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    Proteins: Structure, Function, and Genetics 19 (1994), S. 80-83 
    ISSN: 0887-3585
    Keywords: maize protein ; crystals ; X-ray diffraction ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Phospholipid transfer protein from maize seedlings has been crystallized using trisodium citrate as precipitant. The crystal belongs to the orthorhombic space group P212121 with unit cell dimensions of a = 24.46 Å, b = 49.97 Å, and c = 69.99 Å. The presence of one molecule in the asymmetric unit gives a crystal volume per protein mass (Vm) of 2.36 Å 3/Da and a solvent content of 48% by volume. The X-ray diffraction pattern extends at least to 1.6 Å Bragg spacing when exposed to both CuKα and synchrotron X-rays. A set of X-ray data to approximately 1.9 Å Bragg spacing has been collected from a native crystal. © 1994 Wiley-Liss, Inc.
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  • 63
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    Proteins: Structure, Function, and Genetics 19 (1994), S. 85-97 
    ISSN: 0887-3585
    Keywords: protein conformation ; secondary structure ; protein folding ; helix stability ; helix formation ; conformational entropy ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Much effort has been invested in seeking to understand the thermodynamic basis of helix stability in both peptides and proteins. Recently, several groups have measured the helix-forming propensities of individual residues (Lyu, P. C., Liff, M. I., Marky, L. A., Kallenbach, N. R. Science 250:669-673, 1990; O'Neil, K. T., DeGrado, W. F. Science 250:646-651, 1990; Padmanabhan, S., Marqusee, S., Ridgeway, T., Laue, T. M., Baldwin, R. L. Nature (London) 344:268-270, 1990). Using Monte Carlo computer simulations, we tested the hypothesis that these differences in measured helix-forming propensity are due primarily to loss of side chain conformational entropy upon helix formation (Creamer, T. P., Rose, G. D. Proc. Natl. Acad. Sci. U.S.A. 89:5937-5941, 1992). Our previous study employed a rigid helix backbone, which is here generalized to a completely flexible helix model in order to ensure that earlier results were not a methodological artifact. Using this flexible model, side chain rotamer distributions and entropy losses are calculated and shown to agree with those obtained earlier. We note that the side chain conformational entropy calculated for Trp in our previous study was in error; a corrected value is presented. Extending earlier work, calculated entropy losses are found to correlate strongly with recent helix propensity scales derived from substitutions made within protein helices (Horovitz, A., Matthews, J. M., Fersht, A. R. J. Mol. Biol. 227:560-568, 1992; Blaber, M., Zhang, X.-J., Matthews, B. M. Science 260:1637-1640, 1993). In contrast, little correlation is found between these helix propensity scales and the accessible surface area buried upon formation of a model polyalanyl α-helix. Taken in sum, our results indicate that loss of side chain entropy is a major determinant of the helix-forming tendency of residues in both peptide and protein helices. © 1994 Wiley-Liss, Inc.
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  • 64
    ISSN: 0887-3585
    Keywords: crystallography ; hydroxamate ; high resolution ; metalloproteinase ; zinc ; X-ray ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: The X-ray crystal structure of a 19 kDa active fragment of human fibroblast collagenase has been determined by the multiple isomorphous replacement method and refined at 1.56 Å resolution to an R-factor of 17.4%. The current structure includes a bound hydroxamate inhibitor, 88 waters and three metal atoms (two zincs and a calcium). The overall topology of the enzyme, comprised of a five stranded β-sheet and three α-helices, is similar to the thermolysin-like metalloproteinases. There are some important differences between the collagenase and thermolysin families of enzymes. The active site zinc ligands are all histidines (His-218, His-222, and His-228). The presence of a second zinc ion in a structural role is a unique feature of the matrix metalloproteinases. The binding properties of the active site cleft are more dependent on the main chain conformation of the enzyme (and substrate) compared with thermolysin. A mechanism of action for peptide cleavage similar to that of thermolysin is proposed for fibroblast collagenase. © 1994 Wiley-Liss, Inc.
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  • 65
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    Proteins: Structure, Function, and Genetics 19 (1994), S. 110-119 
    ISSN: 0887-3585
    Keywords: folding intermediate ; urea denaturation ; stopped-flow circular dichroism ; molten globule ; hemindicyanide ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: The refolding kinetics of horse cyanometmyoglobin induced by concentration jump of urea was investigated by five optical probe stopped-flow methods: absorption at 422 nm, tryptophyl fluorescence at around 340 nm, circular dichroism (CD) at 222 nm, CD at 260 nm, and CD at 422 nm. In the refolding process, we detected three phases with rate constants of 〉 1 × 102 s-1, (4.5-9.3) S-1, and (2-5) × 10-3 s-1. In the fastest phase, a substantial amount of secondary structure (40%) is formed within the dead time of the CD stopped-flow apparatus (10.7 ms). The kinetic intermediate populated in the fastest phase is shown to capture a hemindicyanide, suggesting that a “heme pocket precursor” recognized by hemindicyanide must be constructed within the dead time. In the middle phase, most of secondary and tertiary structures, especially around the captured hemindicyanide, have been constructed. In the slowest phase, we detected a minor structural rearrangement accompanying the ligand-exchange reaction in the fifth coordination of ferric iron. We present a possible model for the refolding process of myoglobin in the presence of the heme group. © 1994 Wiley-Liss, Inc.
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  • 66
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    Proteins: Structure, Function, and Genetics 19 (1994), S. 120-131 
    ISSN: 0887-3585
    Keywords: enzymes ; protein immobilization ; microcalorimetry ; protein melting domains ; protein DSC ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Ribonuclease A has been immobilized on silica beads through glutaraldeyde-mediated chemical coupling in order to improve the stability of the protein against thermal denaturation. The thermodynamic and binding properties of the immobilized enzyme have been studied and compared with those of the free enzyme. The parameters describing the binding of the inhibitor 3′ -CMP (Ka and ΔH) as monitored by spectrophotometry and calorimetry were not significantly affected after immobilization. Conversely both the stability and unfolding mechanism drastically changed. Thermodynamic analysis of the DSC data suggests that uncoupling of protein domains has occurred as a consequence of the immobilization. The two state approximation of the protein unfolding process is not longer valid for the immobilized RNase. Protein stability strongly depends on the hydrophobicity properties of the support surface as well as on the presence of the inhibitor and pH. For example, after immobilization on a highly hydrophobic surface, the enzyme is partially in the unfolded state. The binding of a ligand is able to reorganize the protein structure into a native-like conformation. The refolding rates are different for the two protein domains and vary as a function of pH and presence of the inhibitor 3′-CMP. © 1994 Wiley-Liss, Inc.
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  • 67
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    Proteins: Structure, Function, and Genetics 19 (1994), S. 73-76 
    ISSN: 0887-3585
    Keywords: molecular recognition ; protein assembly ; protein folding ; protein interactions ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Recent advances in the measurement and theory of “hydration” interactions between biomolecules provide a basis on which to formulate mechanisms of biomolecular recognition. In this paper we have developed a mathematical formalism for analyzing specificity encoded in dynamic distributions of surface polar groups, a formalism that incorporates newly recognized properties of directly measured “hydration” forces. As expected, attraction between surfaces requires complementary patterns of surface polar groups. In contrast to usual expectations, thermal motion can create these complementary surface configurations. We have demonstrated that assembly can occur with an increase in conformational entropy of polar residues. Elevated temperature then facilitates recognition rather than hinders it. This mechanism might underlie some temperature-favored assembly reactions common in biological systems that are usually associated with the “hydrophobic effect” only. © 1994 Wiley-Liss, Inc.
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  • 68
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    Proteins: Structure, Function, and Genetics 20 (1994), S. 174-184 
    ISSN: 0887-3585
    Keywords: coiled-coils ; keratin ; intermediate filament proteins ; link segments ; heptad phasing ; computer modeling ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Structural discontinuities have previously been identified in four regions of the coiled-coil rod domain structure present in intermediate filament (IF) protein molecules. These include a point at which a phase shift occurs in the heptad periodicity characteristic of the sequence of polar and apolar residues in α-helical coiled-coils, and three links that lack a heptad substructure. We have studied these regions by computer-based molecular modeling and comparative sequence analysis and conclude that the phasing discontinuity can be accommodated without significant distortion of the overall double-helical chain conformation; the L2 link has a similar conformation in all different types of IF molecules, a favorable conformation being one in which the two strands wrap tightly around each other; the L12 links vary in length between different IF types but contain important sequence similarities suggestive of a partial β structure; the L1 links show larger variations in length, a lower degree of similarity, and probably diverse structures. Variations in the overall charges of the different links suggest that ionic interactions may playa significant role in filament assembly. The results also have general significance for other α-fibrous proteins in which either the characteristic heptad phasing undergoes a discontinuity or where a short non-coiled-coil sequence occurs within a coiled-coil rod domain structure. © 1994 Wiley-Liss, Inc.
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  • 69
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    Proteins: Structure, Function, and Genetics 20 (1994), S. 191-196 
    ISSN: 0887-3585
    Keywords: human Clara cell 10-kDa protein ; X-ray diffraction ; phospholipase A2 inhibitor ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Crystals of recombinant human Clara cell 10-kDa protein were grown both from ammonium sulfate and polyethylene glycol (PEG) solutions. Crystals grown from ammonium sulfate solution have been characterized by X-ray diffraction studies as monoclinic with the space group C2 and lattice constants a = 69.2 Å, b = 83.0 Å, c = 58.3 Å, and β = 99.7°. The monoclinic crystals diffract to beyond 2.5 Å. Some of the crystals grown from PEG were of a similar habit to those grown from ammonium sulfate, but others were triclinic with the space group P1 and cell constants a = 40.3 Å, b = 46.3 Å, c = 51.3 Å, α = 117.7°, β = 102.3°, and γ = 71.4°. These crystals diffract to beyond 3.2 Å. © 1994 Wiley-Liss, Inc.
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  • 70
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    Proteins: Structure, Function, and Genetics 20 (1994), S. 185-190 
    ISSN: 0887-3585
    Keywords: heme ; secondary structure ; conformation ; hemopexin ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Hemopexin is a serum glyco-protein that binds heme with the highest known affinity of any characterized heme-binding protein and plays an important role in receptormediated cellular heme uptake. Complete understanding of the function of hemopexin will require the elucidation of its molecular structure. Previous analysis of the secondary structure of hemopexin by far-UV circular dichroism (CD) failed due to the unusual positive ellipticity of this protein at 233 nm. In this paper, we present an examination of the structure of hemopexin by both Fourier-transform infrared (FTIR) and circular dichroism spectroscopy. Our studies show that hemopexin contains about 55% β-structure, 15% α-helix, and 20% turns. The two isolated structural domains of hemopexin each have secondary structures similar to hemopexin. Although there are significant tertiary conformational changes indicated by the CD spectra, the overall secondary structure of hemopexin is not affected by binding heme. However, moderate changes in secondary structure do occur when the heme-binding domain of hemopexin associates with heme. In spite of the exceptionally tight binding at neutral pH, heme is released from the bis-histidyl heme-hemopexin complex at pH 5.0. Under this acidic condition, hemopexin maintains the same overall secondary structure as the native protein and is able to resume the heme-binding function and the native structure of the hemeprotein (as indicated by the CD spectra) when returned to neutral pH. We propose that the state of hemopexin identified in vitro at pH 5.0 resembles that of this protein in the acidic environment of the endosomes in vivo when hemopexin releases heme during receptor-mediated endocytosis. © 1994 Wiley-Liss, Inc.
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  • 71
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    Proteins: Structure, Function, and Genetics 20 (1994) 
    ISSN: 0887-3585
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
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  • 72
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    Proteins: Structure, Function, and Genetics 20 (1994), S. 197-201 
    ISSN: 0887-3585
    Keywords: cytochrome P450 ; erythromycin ; P450eryF ; crystallization ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Cytochrome P450eryF was overexpressed in Escherichia coli and purified in high yield. Crystals of the protein in the presence of the substrate, 6-deoxyerythronolide B, have been obtained by the hanging drop vapor diffusion method, using polyethylene glycol 4000 as a precipitant. The crystals belong to the orthorhombic space group P212121 with unit cell dimensions of a = 54.16 Å, b = 79.67 Å, and c = 99.48 Å and one molecule per asymmetric unit. A complete native data set has been collected to a resolution of 2.1 Å, and anomalous dispersion difference Patterson maps have revealed the location of the single heme iron atom. © 1994 Wiley-Liss, Inc.
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  • 73
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    Proteins: Structure, Function, and Genetics 20 (1994), S. 203-215 
    ISSN: 0887-3585
    Keywords: SH3 ; Abl ; molecular modeling ; homology modeling ; molecular dynamics ; protein structure prediction ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: A tertiary structure model of the Abl-SH3 domain is predicted by using homology modeling techniques coupled to molecular dynamics simulations. Two template proteins were used, Fyn-SH3 and Spc-SH3. The refined model was extensively checked for errors using criteria based on stereochemistry, packing, solvation free-energy, accessible surface areas, and contact analyses. The different checking methods do not totally agree, as each one evaluates a different characteristic of protein structures. Several zones of the protein are more susceptible to incorporating errors. These include residues 13, 15, 35, 39, 45, 46, 50, and 60. An interesting finding is that the measurement of the Cα chirality correlated well with the rest of the criteria, suggesting that this parameter might be a good indicator of correct local conformation. Deviations of more than 4 degrees may be indicative of poor local structure. © 1994 Wiley-Liss, Inc.
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  • 74
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    Proteins: Structure, Function, and Genetics 18 (1994), S. 81-93 
    ISSN: 0887-3585
    Keywords: serine carboxypeptidase ; protein modeling ; mutation analysis ; comparative modeling ; cathepsin A ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: The deficiency of the lysosomal protective protein/carboxypeptidase L (CARB L) causes the lysosomal storage disorder, galactosialidosis, characterized by neuraminidase and β-galactosidase deficiencies in patients' cells. The three enzymes form a complex inside the lysosome, and the neuraminidase and β-galactosidase deficiencies are secondary to CARB L deficiency. Sequence similarity and common enzymological properties suggest that the protomeric tertiary structure of CARB L is conserved within a family of serine carboxypeptidases which includes the yeast carboxypeptidase Y, killer expression I gene product and several plant carboxypeptidases. We used this homology to build a model of the CARB L structure based on the recently published X-ray atomic coordinates of the wheat carboxypeptidase II (CPDW-II) which shares 32% primary structure identity with CARB L. Small insertions and deletions were accommodated into the model structure by energy minimization using the DREIDING II force field. The Cα atomic-coordinates of the final CARB L model have a RMS shift of 1.01 Å compared to the corresponding conserved residues in the CPDW-II template structure. The correct orientation of the homologous catalytic triad residues Ser150, His429 and Asp392, the potential energy calculations and the distribution of hydrophobic and hydrophillic residues in the structure all support the validity of the CARB L model. Most missense mutations identified in galactosialidosis patients were located in secondary structural elements except for the Tyr211→Asn mutation which is in a loop. The other mutant residues have their side chains deeply buried in the central β-sheet of the model structure except for the Phe412→Val mutation which is located in the dimer interface. The predicted effects of specific mutations on CARB L structural stability correlates well with recently published transient expression studies of mutant CARB L (Shimmoto, M. et al., J. Clin. Invest., 91:2393-2399, 1993). © 1994 John Wiley & Sons, Inc.
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  • 75
    ISSN: 0887-3585
    Keywords: cell multipole method ; Newton-Euler inverse mass operator ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Two new methods developed for molecular dynamics simulations of very large proteins are applied to a series of proteins ranging up to the protein capsid of tomato bushy stunt virus (TBSV).For molecular dynamics of very large proteins and polymers, it is useful to carry out the dynamics using internal coordinates (say, torsions only) rather than Cartesian coordinates. This allows larger time steps, eliminates problems with the classical description of high energy modes, and focuses on the important degrees of freedom. The resulting equation of motion has the form where for T is the vector of generalized forces, M(θ) is the moments of inertia tensor, is the vector of torsions, and C is a vector containing Coriolis forces and nonbond forces. The problem is that to calculate the acceleration vector from M, C, and Trequires inverting. M(θ), an order N3calculation. Since the number of degrees of freedom might be 300,000 for a million atom system, solving these equations every time step is impractical, restricting internal coordinate methods to small systems. The new method, Newton-Euler Inverse Mass Operator (NEIMO) dynamics, constructs the torsional accelerations vector directly by an order N process, allowing internal-coordinate dynamics to be solved for super larger (million atom) systems, The first use of the NEIMO method for molecular dynamics of proteins is presented here.A second serious difficulty for large proteins is calculation of the nonbond forces. We report here the first application to proteins of the new Cell Multipole Method (CMM) to evaluate the Coulomb and van der Waals interactions. The cost of CMM scales linearly with the number of particles while retaining an accuracy significantly better than standard non bond methods (involving cutoffs).Results for NEIMO and CMM are given for simulations of a wide range of peptide and protein systems, including the protein capsid of TBSV with 488,000 atoms. The computational times for NEIMO and CMM are demonstrated to scale linearly with size. With NEIMO the dynamics time steps can be as large as 20 fs (for small peptides), much larger than possible with standard Cartesian coordinate dynamics.For TBSV we considered both the normal form and the high pH form, in which the Ca2+ ions are removed. These calculations lead to a contraction of the protein for both forms (probably because of ignoring the RNA core not observed in the X-ray). © 1994 Wiley-Liss, Inc.
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  • 76
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    Proteins: Structure, Function, and Genetics 20 (1994), S. 68-84 
    ISSN: 0887-3585
    Keywords: side chain conformation ; protein folding ; protein binding ; helix formation ; helix stability ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Theoretical estimations of changes in side chain configurational entropy are essential for understanding the different contributions to the overall thermodynamic behavior of important biological processes like folding and binding. The configurational entropy of any given side chain in any particular protein can be evaluated from the complete energy profile of the side chain. Calculations of the energy profiles can be performed using the side chain single bond dihedrals as the only independent variables as long as the structures at each value of the dihedrals are allowed to relax through small changes in the valence bond angles. The probabilities of different side chain conformers obtained from these energy profiles are very similar to the conformer populations obtained by analysis of side chain preferences in the proteins of the Protein Data Bank. Also, side chain conformational entropies obtained from the energy profiles agree extremely well with those obtained from the Protein Data Bank conformer populations. Changes in side chain configurational entropy in binding and folding can be computed as differences in conformational entropy because, in most cases, the frequency of the rotational oscillation around the energy minimum of any given conformer does not appear to change significantly in the reaction. Changes of side chain conformational entropy calculated in this way were compared with experimental values. The only available experimental data-the effect of side chain substitution on the stability of α-helices-were used for this comparison. The experimental values were corrected to subtract the solvent contributions. This comparison yields an excellent agreement between calculated and experimental values, validating not only the theoretical estimates but also the separability of the entropic contributions into configurational terms and solvation related terms. © 1994 Wiley-Liss, Inc.
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  • 77
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    Keywords: X-ray diffraction ; aspartic protease ; AIDS ; recombinant protein ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: For therapeutically relevant targets, the evaluation of enzymes in complex with their inhibitors by cocrystallization and high resolution structural analysis has become a vital component of structure-driven drug design and development. Two approaches, hanging drop vapor diffusion and a novel microtube batch method, were utilized in parallel to grow crystals of recombinant HIV -2 protease and recombinant human renin in complex with inhibitors. In the case of HIV -2 protease in complex with a reduced amide inhibitor, crystallization was achieved only by the microbatch method. In the case of human renin, the addition of precipitant was required for crystal growth. The microbatch method described here is a useful supplementary or alternative approach for screening parameters and generating crystals suitable for high resolution structural analysis. © 1994 Wiley-Liss, Inc.
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  • 78
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    Proteins: Structure, Function, and Genetics 20 (1994), S. 124-138 
    ISSN: 0887-3585
    Keywords: leghemoglobin ; hydrophobic ; interactions ; hydrophobicity ; protein folding ; structure prediction ; protein dynamics ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: The essential features of the in vitro refolding of myoglobin are expressed in a solvable physical model. Alpha helices are taken as the fundamental collective coordinates of the system, while the refolding is assumed to be mainly driven by solvent-induced hydrophobic forces. A quantitative model of these forces is developed and compared with experimental and theoretical results. The model is then tested by being employed in a simulation scheme designed to mimic solvent effects. Realistic dynamic trajectories of myoglobin are shown as it folds from an extended conformation to a close approximation of the native state. Various suggestive features of the process are discussed. The tenets of the model are further tested by folding the single-chain plant protein leghemoglobin. © 1994 Wiley-Liss, Inc.
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  • 79
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    Proteins: Structure, Function, and Genetics 18 (1994), S. 19-33 
    ISSN: 0887-3585
    Keywords: Discover program ; protein dynamics ; computer simulation ; protein motions ; counterions ; dielectric ; protein electrostatics ; aqueous simulation ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: In this report we examine several solvent models for use in molecular dynamics simulations of protein molecules with the Discover program from Biosym Technologies. Our goal was to find a solvent system which strikes a reasonable balance among theoretical rigor, computational efficiency, and experimental reality. We chose phage T4 lysozyme as our model protein and analyzed 14 simulations using different solvent models. We tested both implicit and explicit solvent models using either a linear distance-dependent dielectric or a constant dielectric. Use of a linear distance-dependent dielectric with implicit solvent significantly diminished atomic fluctuations in the protein and kept the protein close to the starting crystal structure. In systems using a constant dielectric and explicit solvent, atomic fluctuations were much greater and the protein was able to sample a larger portion of conformational space. A series of nonbonded cutoff distances (9.0, 11.5, 15.0, 20.0 Å) using both abrupt and smooth truncation of the nonbonded cutoff distances were tested. The method of dual cutoffs was also tested. We found that a minimum nonbonded cutoff distance of 15.0 Å was needed in order to properly couple solvent and solute. Distances shorter than 15.0 Å resulted in a significant temperature gradient between the solvent and solute. In all trajectories using the proprietary Discover switching function, we found significant denaturation in the protein backbone; we were able to run successful trajectories only in those simulations that used no switching function. We were able to significantly reduce the computational burden by using dual cutoffs and still calculate a quality trajectory. In this method, we found that an outer cutoff distance of 15.0 Å and an inner cutoff distance of 11.5 worked well. While a 10 Å shell of explicit water yielded the best results, a 6 A shell of water yielded satisfactory results with nearly a 40% reduction in computational cost. © 1994 John Wiley & Sons, Inc.
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  • 80
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    Proteins: Structure, Function, and Genetics 18 (1994), S. 94-101 
    ISSN: 0887-3585
    Keywords: surface representation ; molecular recognition ; protein docking ; surface triangulation ; molecular graphics ; molecular visualization ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: We have defined a molecular surface representation that describes precisely and concisely the complete molecular surface. The representation consists of a limited number of critical points disposed at key locations over the surface. These points adequately represent the shape and the important characteristics of the surface, despite the fact that they are modest in number. We expect the representation to be useful in areas such as molecular recognition and visualization. In particular, using this representation, we are able to achieve accurate and efficient protein-protein and protein-small molecule docking. © 1994 John Wiley & Sons, Inc.
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  • 81
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    Proteins: Structure, Function, and Genetics 18 (1994), S. 390-393 
    ISSN: 0887-3585
    Keywords: protein crystallization ; enzyme copurification ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: An unknown protein crystallized from a lobster muscle preparation in which arginine kinase was the majority component. It was identified as enolase by peptide sequencing and activity testing, and a SIRAS electron density map showed its three-dimensional structure to be very similar to that of yeast enolase. © 1994 John Wiley & Sons, Inc.
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  • 82
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    Proteins: Structure, Function, and Genetics 19 (1994), S. 302-309 
    ISSN: 0887-3585
    Keywords: dinuclear copper site ; hemocyanin ; oxygen binding ; allosteric regulation ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: The X-ray structure of an oxygenated hemocyanin molecule, subunit II of Limulus polyphemus hemocyanin, was determined at 2.4 Å resolution and refined to a crystallographic R-factor of 17.1%. The 73-kDa subunit crystallizes with the symmetry of the space group R32 with one subunit per asymmetric unit forming hexamers with 32 point group symmetry. Molecular oxygen is bound to a dinuclear copper center in the protein's second domain, symmetrically between and equidistant from the two copper atoms. The copper-copper distance in oxygenated Limulus hemocyanin is 3.6 ± 0.2 Å, which is surprisingly 1 Å less than that seen previously in deoxygenated Limulus polyphemus subunit II hemocyanin (Hazes et al., Protein Sci. 2:597, 1993). Away from the oxygen binding sites, the tertiary and quaternary structures of oxygenated and deoxygenated Limulus subunit II hemocyanins are quite similar. A major difference in tertiary structures is seen, however, when the Limulus structures are compared with deoxygenated Panulirus interruptus hemocyanin (Volbeda, A., Hol, W. G. J. J. Mol. Biol. 209:249, 1989) where the position of domain 1 is rotated by 8° with respect to domains 2 and 3. We postulate this rotation plays an important role in cooperativity and regulation of oxygen affinity in all arthropod hemocyanins. © 1994 Wiley-Liss, Inc.
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  • 83
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    Proteins: Structure, Function, and Genetics 20 (1994), S. 216-226 
    ISSN: 0887-3585
    Keywords: evolutionary information ; multiple alignments ; neural networks ; protein structure prediction ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Currently, the prediction of three-dimensional (3D) protein structure from sequence alone is an exceedingly difficult task. As an intermediate step, a much simpler task has been pursued extensively: predicting 1D strings of secondary structure. Here, we present an analysis of another 1D projection from 3D structure: the relative solvent accessibility of each residue. We show that solvent accessibility is less conserved in 3D homologues than is secondary structure, and hence is predicted less accurately from automatic homology modeling; the correlation coefficient of relative solvent accessibility between 3D homologues is only 0.77, and the average accuracy of predictions based on sequence alignments is only 0.68. The latter number provides an effective upper limit on the accuracy of predicting accessibility from sequence when homology modeling is not possible. We introduce a neural network system that predicts relative solvent accessibility (projected onto ten discrete states) using evolutionary profiles of amino acid substitutions derived from multiple sequence alignments. Evaluated in a cross-validation test on 238 unique proteins, the correlation between predicted and observed relative accessibility is 0.54. Interpreted in terms of a three-state (buried, intermediate, exposed) description of relative accessibility, the fraction of correctly predicted residue states is about 58%. In absolute terms this accuracy appears poor, but given the relatively low conservation of accessibility in 3D families, the network system is not far from its likely optimal performance. The most reliably predicted fraction of the residues (50%) is predicted as accurately as by automatic homology modeling. Prediction is best for buried residues, e.g., 86% of the completely buried sites are correctly predicted as having 0% relative accessibility. © 1994 Wiley-Liss, Inc.
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  • 84
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    Proteins: Structure, Function, and Genetics 20 (1994), S. 248-258 
    ISSN: 0887-3585
    Keywords: molecular dynamics ; trp-repressor ; ligand ; domain ; dynamic cross-correlation ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Molecular dynamics simulations of the apo- and holo-forms of thetrp-repressor protein were performed under extensively solvated conditions in order to elucidate their dynamic structures and ligand-protein interactions. The root mean square fluctuations calculated from the trajectories agreed with those calculated from X-ray temperature factors. Distance, distance fluctuation, and dynamic cross-correlation maps were drawn to provide information on the dynamic structures and communications among the domains. A three-domain format has been proposed for the crystal structure (Zhang et at., Nature 327:591-597, 1987) namely, helices A-C and F of both subunits make up a central core, and D and E of each subunit forms a DNA binding head. The results of the simulations were mostly consistent with the three-domain format. However, helix F was more flexible and freer than other parts of the central core. The turn DE, the helix-turn-helix DNA binding motif, was free from interactions and correlations with other domains in both forms of the repressor. A comparison of the simulations of the aporepressor and holorepressor showed that tryptophan binding made the DNA-binding helix D more flexible but helix F less flexible. Several amino acid residues in contact with the bound tryptophan were identified as making concerted motions with it. Interaction energies between the corepressor and the amino acid residues of the protein were analyzed; the results were mostly consistent with the mutational experiments. © 1994 Wiley-Liss, Inc.
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  • 85
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    Proteins: Structure, Function, and Genetics 18 (1994), S. 68-80 
    ISSN: 0887-3585
    Keywords: staphylococcal nuclease ; nonproductive substrate binding to ; subsites of ; active site mutants of ; oligonucleotide binding to ; Ca2+ binding to ; Mn2+ binding to ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: By a combination of NMR docking and model building, the substrate binding site on staphylococcal nuclease was found to accommodate a trinucleotide and to consist of three subsites, each interacting with a single nucleotidyl unit of DNA. Binding of the essential Ca2+ activator and substrate cleavage occur between subsites 1 and 2. Hence, catalytically productive binding would span subsites 1 and 2 while nonproductive binding would span subsites 2 and 3. Lys-49 is near subsite 1, and Lys-84 and Tyr-115 interact with substrates at sub site 3 [Weber, D. J., Gittis, A. G., Mullen, G. P., Abeygunawardana, C., Lattman, E. E., Mildvan, A. S. Proteins 13:275-287, 1992]. The proposed locations of these subsites were independently tested by the effects of the K49A, K84A, and Y115A mutations of staphylococcal nuclease on the binding of Mn2+, Ca2+, and the dinucleotide and trinucleotide substrates, 5′-pdTdA, dTdA, and dTdAdG. These three mutants have previously been shown to be fully active and to have CD and 2D NMR spectra very similar to those of the wild-type enzyme (Chuang, W.-J., Weber, D. J., Gittis, A. G., Mildvan, A. S. Proteins 17:36-48, 1993). All three mutant enzymes and their pdTdA and dTdA complexes (but not their dTdAdG complex) bind Mn2+ and Ca2+ more weakly than the wild-type enzyme by factors ranging from 2 to 11. The presence of a terminal phosphate as in 5′-pdTdA raises the affinity of the substrate for staphylococcal nuclease and its three mutants by two orders of magnitude and for the corresponding enzyme-metal complexes by three to four orders of magnitude, suggesting that the terminal phosphate is coordinated by the enzyme-bound divalent cation. Such complexation would result in the nonproductive binding of 5′-pdTdA at subsites 2 and 3. Accordingly, the K84A and Y115A mutations significantly weaken the binding of 5′-pdTdA and its metal to staphylococcal nuclease by factors of 2.2 to 37.8, while the K49A mutation has much smaller or no effect. Such nonproductive binding explains the low activity of staphylococcal nuclease with small substrates, especially those With a terminal phosphate. Similarly, the K84A and Y115A mutations weaken the binding of dTdA and its metal complexes to the enzyme by factors of 3.4 to 13.1 while the K49A mutation has smaller effects indicating significant nonproductive binding of dTdA. The trinucleotide dTdAdG binds more tightly to wild-type and mutant staphylococcal nuclease and to its metal complexes than does the dinucleotide dTdA by factors of 2.4 to 12.2, reflecting the occupancy of an additional subsite. Predominantly productive binding of dTdAdG is indicated by the 1.7- to 8.3-fold lower affinities of the K49A, K84A, and Y115A mutants for the trinucleotide and its metal complexes. The largest effects on dTdAdG binding are seen with the Y115A mutation presumably reflecting the dual role of Tyr-115 both in donating a hydrogen bond to a phosphodiester oxygen between subsites 2 and 3 and in stacking onto the guanine base at subsite 3. © 1994 John Wiley & Sons, Inc.
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  • 86
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    Proteins: Structure, Function, and Genetics 18 (1994), S. i 
    ISSN: 0887-3585
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
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  • 87
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    Proteins: Structure, Function, and Genetics 18 (1994), S. 8-18 
    ISSN: 0887-3585
    Keywords: docking algorithm ; antigen-antibody complex ; epitope ; influenza virus hemagglutinin ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: An automatic docking algorithm has been applied to the modeling of the complex between hemagglutinin from influenza virus and the Fab fragment of a monoclonal antibody raised against this antigen. We have introduced here the use of biochemical information provided by mutants of hemagglutinin. The docking procedure finds a small number of candidate solutions where three sites of escape mutations are buried and form hydrogen bonds in the interface. The localization of the epitope is improved by additional biochemical data about mutants that do not affect antibody binding. Five candidate solutions with low energy, reasonably well-packed interfaces, and six to ten hydrogen bonds are compatible with mutant information. One of the five stands out as generally better than the others from these points of views. © 1994 John Wiley & Sons, Inc.
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  • 88
    ISSN: 0887-3585
    Keywords: α-helix capping ; α-helix initiation ; α-helix termination ; synthetic peptides ; protein folding ; circular dichroism ; 1H nmr ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: A significant fraction of the amino acids in proteins are alpha helical in conformation. Alpha helices in globular proteins are short, with an average length of about twelve residues, so that residues at the ends of helices make up an important fraction of all helical residues. In the middle of a helix, H-bonds connect the NH and CO groups of each residue to partners four residues along the chain. At the ends of a helix, the H-bond potential of the main chain remains unfulfilled, and helix capping interactions involving bonds from polar side chains to the NH or CO of the backbone have been proposed and detected. In a study of synthetic helical peptides, we have found that the sequence Ser-Glu-Asp-Glu stabilizes the alpha helix in a series of helical peptides with consensus sequences. Following the report by Harper and Rose, which identifies SerXaaXaaGlu as a member of a class of common motifs at the N termini of alpha helices in proteins that they refer to as “capping boxes,” we have reexamined the side chain-main chain interactions in a varient sequence using 1H NMR, and find that the postulated reciprocal side chain-backbone bonding between the first Ser and last Glu side chains and their peptide NH partners can be resolved: Deletion of two residues N terminal to the Ser-Glu-Asp-Glu sequence in these peptides has no effect on the initiation of helical structure, as defined by two-dimensional (2D) NMR experiments on this variant. Thus the capping box sequence Ser-Glu-Asp-Glu inhibits N terminal fraying of the N terminus of alpha helix in these peptides, and shows the side chain-main chain interactions proposed by Harper and Rose. It thus acts as a helix initiating signal. Since normal a helix cannot propagate beyond the N terminus of this structure, the box acts as a termination signal in this direction as well. © 1994 John Wiley & Sons, Inc.
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  • 89
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    Proteins: Structure, Function, and Genetics 20 (1994), S. 149-166 
    ISSN: 0887-3585
    Keywords: crystal structure ; cold adaption ; catalytic efficiency ; protein stability ; anionic ; ectotherm ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: The crystal structure of an anionic form of salmon trypsin has been determined at 1.82 Å resolution. We report the first structure of a trypsin from a phoikilothermic organism in a detailed comparison to mammalian trypsins in order to look for structural rationalizations for the cold-adaption features of salmon trypsin. This form of salmon trypsin (T II) comprises 222 residues, and is homologous to bovine trypsin (BT) in about 65% of the primary structure. The tertiary structures are similar, with an overall displacement in main chain atomic positions between salmon trypsin and various crystal structures of bovine trypsin of about 0.8 Å. Intramolecular hydrogen bonds and hydrophobic interactions are compared and discussed in order to estimate possible differences in molecular flexibility which might explain the higher catalytic efficiency and lower thermostability of salmon trypsin compared to bovine trypsin. No overall differences in intramolecular interactions are detected between the two structures, but there are differences in certain regions of the structures which may explain some of the observed differences in physical properties. The distribution of charged residues is different in the two trypsins, and the impact this might have on substrate affinity has been discussed. © 1994 Wiley-Liss, Inc.
    Additional Material: 10 Ill.
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  • 90
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    Proteins: Structure, Function, and Genetics 18 (1994), S. 34-48 
    ISSN: 0887-3585
    Keywords: normal mode refinement ; correlation function ; intra- and intermolecular correlation ; higher order scattering ; human lysozyme ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: We have developed theoretical models for analysis of X-ray diffuse scattering from protein crystals. A series of models are proposed to be used for experimental data with different degrees of precision. First, we propose the normal mode model, where conformational dynamics of a protein is assumed to occur mostly in a limited conformational subspace spanned by a small number of low-frequency normal modes in the protein. When high precision data are available, variances and covariances of the normal mode variables can be determined from experimental data using this model. For experimental data with lower degrees of precision, we introduce a series of simpler models. These models express the covariance matrix using relatively simple empirical correlation functions by assuming the correlation between a pair of atoms to be isotropic. As an application of these simpler models, we calculate diffuse-scattering patterns from a human lysozyme crystal to examine how each adjustable parameter in the models affects general features of the resulting patterns. The results of the calculation are summarized as follows. (1) The higher order scattering makes a significant contribution at high resolutions. (2) The resulting simulated patterns are sensitive to changes in correlation lengths of about 1 Å, as well as to changes of the functional form of the correlation function. (3) But only the “average” value of the intra- and intermolecular correlation lengths seems to determine the gross features of the pattern. (4) The effect of the atom-dependent amplitude of fluctuations is difficult to observe. © 1994 John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
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  • 91
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    Proteins: Structure, Function, and Genetics 18 (1994), S. 186-197 
    ISSN: 0887-3585
    Keywords: carboxypeptidas ; molecular dynamics ; enzymatic mechanisms ; peptidase mechanism ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: An MD simulation of the system carboxypeptidase A (CPA) with the tetrapeptide Val-Leu-Phe-Phe has been performed in order to learn about the substrate disposition just prior to nucleophilic attack. We have explored the model in which the substrate does not substitute the zinc-coordinated water (the “water” mechanism). The simulations do suggest as feasible that the Zn-OH2 group performs a nucleophilic attack on the Phe-Phe peptidic bond. We have also investigated the model in which the carbonyl oxygen displaces the zinc-coordinated water. In this case the substrate and Glu-270 orient themselves to allow an anhydride intermediate during the peptidic bond cleavage (the “anhydride” mechanism). Based on the results of the simulations, both “water” and “anhydride” mechanisms are structurally feasible, although the former model seems more probable on chemical grounds. © 1994 John Wiley & Sons, Inc.
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  • 92
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    Proteins: Structure, Function, and Genetics 18 (1994), S. 174-185 
    ISSN: 0887-3585
    Keywords: computer modeling ; protein structure prediction ; α-carbons ; structure evaluation ; molecular dynamics ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Generation of full protein coordinates from limited information, e.g., the Cα coordinates, is an important step in protein homology modeling and structure determination, and molecular dynamics (MD) simulations may prove to be important in this task. We describe a new method, in which the protein backbone is built quickly in a rather crude way and then refined by minimization techniques. Subsequently, the side chains are positioned using extensive MD calculations. The method is tested on two proteins, and results compared to proteins constructed using two other MD-based methods. In the first method, we supplemented an existing backbone building method with a new procedure to add side chains. The second one largely consists of available methodology. The constructed proteins are compared to the corresponding X-ray structures, which became available during this study, and they are in good agreement (backbone RMS values of 0.5-0.7 Å, and all-atom RMS values of 1.5-1.9 Å). This comparative study indicates that extensive MD simulations are able, to some extent, to generate details of the native protein structure, and may contribute to the development of a standardized methodology to predict reliably (parts of) protein structures when only partial coordinate data are available. © 1994 John Wiley & Sons, Inc.
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  • 93
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    Proteins: Structure, Function, and Genetics 18 (1994), S. i 
    ISSN: 0887-3585
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
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  • 94
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    Proteins: Structure, Function, and Genetics 19 (1994), S. 150-157 
    ISSN: 0887-3585
    Keywords: X-ray crystallography ; membrane protein ; ion channels ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Crystals of the channel-forming domain of colicin E1 from E. coli were grown by vapor diffusion at pH 6.4 and higher pH values. Cleavage of the colicin molecule with trypsin or thermolysin produced two of the pore-forming polypeptides used in these experiments. The third polypeptide was purified from a constructed plasmid that overexpresses only the C-terminal domain of colicin E1. Polypeptide crystals are tetragonal with space group I4, have one monomer in the asymmetric unit, and diffract to 2.2-2.4 Å. Unit cell parameters for the tryptic and thermolytic polypeptides are a = 102.9 Å and c = 35.6 Å. Crystals of the overexpressed polypeptide have unit cell parameters of a =87.2 Å and c =59.1 Å. The crystals were characterized by precession photography, and native data sets of each channel-forming fragment were collected on a Siemens-Nicolet area detector. The crystallization and characterization of these polypeptides are the first steps in the structure determination of the channel-forming domain of colicin E1. © 1994 Wiley-Liss, Inc.
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  • 95
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    Proteins: Structure, Function, and Genetics 20 (1994), S. 356-366 
    ISSN: 0887-3585
    Keywords: NMR ; structure determination ; coiled coil ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: We have determined the structure in solution of a homodimeric protein that is a precursor to the locust neuropeptide adipokinetic hormone I using nuclear magnetic resonance spectroscopy. This precursor, called P1, is comprised of two 41 residue strands joined by a single inter-chain disulphide at Cys39. We have also determined the structure of an end product of P1 processing, called APRP1; this is a homodimer comprised of residues 14-41 of PI. Nuclear Overhauser Effect (nOe) data indicate that in both P1 and APRP1, residues 22-37 (numbered with respect to P1) form pairs of α-helices, with no evidence for any other secondary structure. © 1994 Wiley-Liss, Inc.
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  • 96
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    Proteins: Structure, Function, and Genetics 19 (1994), S. 174-182 
    ISSN: 0887-3585
    Keywords: molecular dynamics ; docking ; computer simulation ; substrate docking ; immunoglobulin ; rational drug design ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: A simple method is described to perform docking of subtrates to proteins or probes to receptor molecules by a modification of molecular dynamics simulations. The method consists of a separation of the center-of-mass motion of the substrate from its internal and rotational motions, and a separate coupling to different thermal baths for both types of motion of the substrate and for the motion of the receptor. Thus the temperatures and the time constants of coupling to the baths can be arbitrarily varied for these three types of motion, allowing either a frozen or a flexible receptor and allowing control of search rate without disturbance of internal structure. In addition, an extra repulsive term between substrate and protein was applied to smooth the interaction. The method was applied to a model substrate docking onto a model surface, and to the docking of phosphocholine onto immunoglobulin McPC603, in both cases with a frozen receptor. Using transrational temperatures of the substrate in the range of 1300-1700 K and room temperature for the internal degrees of freedom of the substrate, an efficient nontrapping exploratory search (“helicopter view”) is obtained, which visits the correct binding sites. Low energy conformations can then be further investigated by separate search or by dynamic simulated annealing. In both cases the correct minima were identified. The possibility to work with flexible receptors is discussed. © 1994 Wiley-Liss, Inc.
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  • 97
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    Proteins: Structure, Function, and Genetics 19 (1994), S. 222-229 
    ISSN: 0887-3585
    Keywords: protein electrostatics ; energy calculations ; ion pairs ; Monte-Carlo simulations ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: A model approach is suggested to estimate the degree of spatial optimization of the electrostatic interactions in protein molecules. The method is tested on a set of 44 globular proteins, representative of the available crystallographic data. The theoretical model is based on macroscopic computation of the contribution of charge-charge interactions to the electrostatic term of the free energy for the native proteins and for a big number of virtual structures with randomly distributed on protein surface charge consetellations (generated by a Monte-Carlo technique). The statistical probability of occurrence of random structures with electrostatic energies lower than the energy of the native protein is suggested as a criterion for spatial optimization of the electrostatic interactions. The results support the hypothesis that the folding process optimizes the stabilizing effect of electrostatic interactions, but to very different degree for different proteins. A parallel analysis of ion pairs shows that the optimization of the electrostatic term in globular proteins has increasingly gone in the direction of rejecting the repulsive short contacts between charges of equal sign than of creating of more salt bridges (in comparison with the statistically expected number of shortrange ion pairs in the simulated random structures). It is observed that the decrease in the spatial optimization of the electrostatic interactions is usually compensated for by an appearance of disulfide bridges in the covalent structure of the examined proteins. © 1994 Wiley-Liss, Inc.
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  • 98
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    Proteins: Structure, Function, and Genetics 19 (1994), S. 244-255 
    ISSN: 0887-3585
    Keywords: energy minimization ; rotamers ; automaton ; de novo design ; sequence prediction ; side-chain conformation prediction ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Globular proteins have high packing densities as a result of residue side chains in the core achieving a tight, complementary packing. The internal packing is considered the main determinant of native protein structure. From that point of view, we present here a method of energy minimization using an automata network to predict a set of amino acid sequences and their side-chain conformations from a desired backbone geometry for de novo design of proteins. Using discrete side-chain conformations, that is, rotamers, the sequence generation problem from a given backbone geometry becomes one of combinatorial problems. We focused on the residues composing the interior core region and predicted a set of amino acid Sequences and their side-chain conformations only from a given backbone geometry. The kinds of residues were restricted to six hydrophobic amino acids (Ala, Ile, Met, Leu, Phe, and Val) because the core regions are almost always composed of hydrophobic residues. The obtained sequences were well packed as was the native sequence. The method can be used for automated sequence generation in the de novo design of proteins. © 1994 Wiley-Liss, Inc.
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  • 99
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    Proteins: Structure, Function, and Genetics 19 (1994), S. 256-268 
    ISSN: 0887-3585
    Keywords: unfolding ; solvation ; contact maps ; protein design ; structural domains ; normal modes ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: General patterns of protein structural organization have emerged from studies of hundreds of structures elucidated by X-ray crystallography and nuclear magnetic resonance. Structural units are commonly identified by visual inspection of molecular models using qualitative criteria. Here, we propose an algorithm for identification of structural units by objective, quantitative criteria based on atomic interactions. The underlying physical concept is maximal interactions within each unit and minimal interaction between units (domains). In a simple harmonic approximation, interdomain dynamics is determined by the strength of the interface and the distribution of masses. The most likely domain decomposition involves units with the most correlated motion, or largest interdomain fluctuation time. The decomposition of a convoluted 3-D structure is complicated by the possibility that the chain can cross over several times between units. Grouping the residues by solving an eigenvalue problem for the contact matrix reduces the problem to a one-dimensional search for all reasonable trial bisections. Recursive bisection yields a tree of putative folding units. Simple physical criteria are used to identify units that could exist by themselves. The units so defined closely correspond to crystallographers' notion of structural domains. The results are useful for the analysis of folding principles, for modular protein design and for protein engineering. © 1994 Wiley-Liss, Inc.
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  • 100
    ISSN: 0887-3585
    Keywords: acyl-CoA dehydrogenase ; bifunctional enzyme ; charge-transfer complex ; clostridial metabolism ; FAD, x-ray diffraction ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: The bifunctional flavoenzyme 5-hydroxyvaleryl-CoA dehydratase/ dehydrogenase has been crystallized from solutions containing ammonium sulfate (form I) or polyethylene glycol (form II) as precipitant. In both cases, the crystals grew in the monoclinic space group C2. The unit cell dimensions for form I crystals were determined as a = 162.8 Å, b = 71.8 Å, c = 83.5 Å, β = 109.1°. Corresponding values for form II crystals were a = 161.2 Å, b = 71.6 Å, c = 82.2 Å, β = 109.3°. In both cases most probably there are two monomers per asymmetric unit. The crystals diffract to about 2 Å resolution and are rather stable in the X-ray beam. © 1994 Wiley-Liss, Inc.
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