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  • 1
    Electronic Resource
    Electronic Resource
    [s.l.] : Nature Publishing Group
    Nature 249 (1974), S. 490-491 
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] The rapid development in the techniques of manufacturing synthetic enzyme membranes6 provides a new tool for demonstrating the existence of hysteretic phenomena which do not occur as a result of structural changes in a system. The idea is based on studies by chemical engineers in which cooperative ...
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 0301-4622
    Keywords: Artificial membrane ; Donnan layer ; Membrane potential
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Biology , Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 7 (1979), S. 41-56 
    ISSN: 1432-1416
    Keywords: Immobilized enzyme systems ; Diffusion-reaction ; Hysteresis, oscillations ; Pattern formation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Summary Hysteresis, oscillations, and pattern formation in realistic biochemical systems governed by P.D.E.s are considered from both numerical and mathematical points of view. Analysis of multiple steady states in the case of hysteresis, and bifurcation theory in the cases of oscillations and pattern formation, account for the observed numerical results. The possibility to realize these systems experimentally is their main interest, thus bringing further arguments in favor of theories explaining basic biological phenomena by diffusion and reaction.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Applied mathematics & optimization 1 (1975), S. 222-285 
    ISSN: 1432-0606
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Abstract Immobilized enzyme systems are systems where enzyme(s) (catalyst(s) of biochemical reaction(s)) is (are) distributed inside an artificial membrane. They are governed by the coupling between diffusion and reaction, and the typical equation describing such a system is∂s/∂t−∂ 2s/∂x2+σs/(1+s) = 0, s = s(x,t) denoting the substrate concentration. In a first part are described several enzyme systems, together with their (partial differential) equations. A second part is devoted to the mathematical methods used to prove existence and uniqueness of a solution for these equations. In the third part, are given the numerical methods used to get an approximate solution. The last part deals with some open loop control problems in these biochemical systems. Existence of an optimal control is proved, the cost function gradient is found using the adjoint state and the steepest descent algorithm is used.
    Notes: Resume Les systèmes à enzymes immobilisées sont des systèmes où des enzymes (catalyseurs de réactions biochimiques) sont distribués à l'intérieur d'une membrane artificielle. Ils sont gouvernés par le couplage entre diffusion et réaction et l'équation typique décrivant un tel système est∂s/∂t−∂ 2s/∂x2+σs/(1+s) = 0, s = s(x,t) étant la concentration du substrat. Dans une première partie sont décrits plusieurs systèmes enzymatiques, ainsi que leurs équations (aux dérivées partielles). Une seconde partie est consacrée aux méthodes mathématiques utilisées pour démontrer l'existence et l'unicité d'une solution pour ces équations. Dans la troisième partie sont données les méthodes numériques utilisées pour obtenir une solution approchée. La dernière partie traite de problèmes de contrôle en boucle ouverte dans ces systèmes biochimiques. L'existence d'un contrôle optimal est démontrée, le gradient de la fonction coût est trouvé en utilisant l'état adjoint et l'algorithme de “steepest descent” est utilisé.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 12 (1973), S. 43-52 
    ISSN: 1573-2878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The aim of this paper is to show that the simple gradient method is efficient when applied to the optimal control of a distributed parameter system. The system is a model of a biological membrane (with enzymes), and the problem is to approach a desired flux of substrate entering the membrane by acting on an inhibitor's concentration at the boundary of the membrane.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Acta applicandae mathematicae 1 (1983), S. 263-279 
    ISSN: 1572-9036
    Keywords: 34C ; 34D ; 65N ; 65P ; 92 ; numerical methods ; bifurcation theory ; enzyme kinetics ; morphogenesis ; Galerkin method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper deals with the use of the Galerkin approximation for calculating branches of steady-state solutions. It is motivated by the analysis of a reaction-diffusion system modeled by a pair of nonlinear partial differential equations on a two-dimensional domain. The goal is to check the possibility of closed loops emerging from a ‘trivial’ branch. This issue is of importance in recent theories on morphogenesis in embryos (Kauffman et al. [3]). Numerical methods for continuing Galerkin approximations of the steady states give arcs of stable or unstable solutions. The numerical results are in agreement with the predictions of Brezzi et al. [6–8]. In particular, bifurcations from the trivial steady-state or symmetry-breaking bifurcations remain bifurcations for the approximate problem. The whole connected set of solutions thus obtained gives new insight into the behavior of solutions to reaction-diffusion equations and strongly advocates Kauffman's theory.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 21 (1979), S. 1239-1249 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: In a fermentation process, the establishment of gas mass balances provides valuable information and allows both measurements concerning the characteristics of the biomass itself and the monitoring of a cultivation process. If the quantity and oxidation level of substances excreted into the fermentation broth are known or constant, the yield factor and the dry cell-weight production are stoichiometrically related to the quantity of CO2 evolved and to the quantity of O2 consumed. Where frequent measurements of both yield factor and dry cell-weight production are desirable or where rapid adjustment of the parameters is necessary, on-line identification of these parameters is required, An algorithm allowing the identification of the specific growth rate is presented. Moreover, this technique allows one to estimate the percent protein in the biomass during continuous culture.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 16 (1974), S. 315-332 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The kinetic behavior of water insoluble enzyme columns was studied using the hydrolysis of GPNA (N-glutaryl-L-phenylalanine-p-nitroanilide) by α-chymotrypsin as a model. Thermal denaturation of soluble and insoluble enzyme was compared in a batch reactor and in a tubular reactor. Convection of metabolites, enzyme reaction, diffusion of metabolites across porous particles and the kinetic behavior of a water insoluble enzyme column were tested.The respective and mutual effects of the first two phenomena were comprehensively analyzed for both stationary state and transient conditions. When the ingoing substrate concentration was varying with time, convection-reaction equations were solved by digital computation. The possible effects of diffusion limitations and unstirred layers are discussed.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 25 (1983), S. 845-855 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A numerical treatment of the signal produced by an electrode onto which an artificial enzyme membrane is mounted can give the concentration of the substrate (glucose, saccharose, lactose, amino acids, etc.) in solution. In the example of a glucose analyzer, in which glucose oxidase catalyzes the oxidation of glucose, the computer receives pO2 level data from the electrode and calculates the glucose concentration. The transient electrode signal, measured as the enzyme membrane is exposed to a solution of glucose, is least-square approximated by a third-degree polynomial whose slope at inflection point is characteristic of the external glucose concentration. A calibration procedure provides a cubic spline approximation of glucose concentration as a function of slope, thus enabling automatic measurement of samples. The computer performs the calculations, and actuates valves for air rinsing, introduction of the sample, and water rinsing.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 129-139 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a method of identification of material behaviour parameters. The method is applied to a simple example: the identification of orthotropic parameters using a plate bending test. A number of results are presented concerning the choice of numerical algorithm, the experimental protocole (number and locations of test points, loading) and the sensitivity of the method on experimental errors.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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