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  • 1
    facet.materialart.
    Unknown
    Publication Date: 2019-10-24
    Keywords: ddc:000
    Language: German
    Type: annualzib , doc-type:report
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  • 2
    Publication Date: 2014-02-26
    Description: We propose a variant of the control reduced interior point method for the solution of state constrained problems. We show convergence of the corresponding interior point pathfollowing algorithm in function space. Morever, we provide error bounds for the iterates.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 3
    Publication Date: 2014-02-26
    Description: This paper aims at presenting the complex coupled network of the human menstrual cycle to the interested community. Beyond the presently popular smaller models, where important network components arise only as extremely simplified source terms, we add: the GnRH pulse generator in the hypothalamus, receptor binding, and the biosynthesis in the ovaries. Simulation and parameter identification are left to a forthcoming paper.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 4
    Publication Date: 2014-02-26
    Description: This work explores two applications of a classical result on the continuity of Nemyckii operators to optimal control with PDEs. First, we present an alternative approach to the analysis of Newton's method for function space problems involving semi-smooth Nemyckii operators. A concise proof for superlinear convergence is presented, and sharpened bounds on the rate of convergence are derived. Second, we derive second order sufficient conditions for problems, where the underlying PDE has poor regularity properties. We point out that the analytical structure in both topics is essentially the same.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 5
    Publication Date: 2014-02-26
    Description: In this paper, we study the efficiency of Nash equilibria for a sequence of nonatomic routing games. We assume that the games are played consecutively in time in an online fashion: by the time of playing game $i$, future games $i+1,\dots,n$ are not known, and, once players of game $i$ are in equilibrium, their corresponding strategies and costs remain fixed. Given a sequence of games, the cost for the sequence of Nash equilibria is defined as the sum of the cost of each game. We analyze the efficiency of a sequence of Nash equilibria in terms of competitive analysis arising in the online optimization field. Our main result states that the online algorithm $\sl {SeqNash}$ consisting of the sequence of Nash equilibria is $\frac{4n}{2+n}$-competitive for affine linear latency functions. For $n=1$, this result contains the bound on the price of anarchy of $\frac{4}{3}$ for affine linear latency functions of Roughgarden and Tardos [2002] as a special case. Furthermore, we analyze a problem variant with a modified cost function that reflects the total congestion cost, when all games have been played. In this case, we prove an upper bound of $\frac{4n}{2+n}$ on the competitive ratio of $\sl {SeqNash}$. We further prove a lower bound of $\frac{3n-2}{n}$ of $\sl {SeqNash}$ showing that for $n=2$ our upper bound is tight.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 6
    Publication Date: 2016-06-09
    Description: To approximate convolutions which occur in evolution equations with memory terms, a variable-stepsize algorithm is presented for which advancing $N$ steps requires only $O(N\log N)$ operations and $O(\log N)$ active memory, in place of $O(N^2)$ operations and $O(N)$ memory for a direct implementation. A basic feature of the fast algorithm is the reduction, via contour integral representations, to differential equations which are solved numerically with adaptive step sizes. Rather than the kernel itself, its Laplace transform is used in the algorithm. The algorithm is illustrated on three examples: a blow-up example originating from a Schrödinger equation with concentrated nonlinearity, chemical reactions with inhibited diffusion, and viscoelasticity with a fractional order constitutive law.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 7
    Publication Date: 2020-11-13
    Description: This paper deals with MIP-based primal heuristics to be used within a branch-and-cut approach for solving multi-layer telecommunication network design problems. Based on a mixed-integer programming formulation for two network layers, we present three heuristics for solving important subproblems, two of which solve a sub-MIP. On multi-layer planning instances with many parallel logical links, we show the effectiveness of our heuristics in finding good solutions early in the branch-and-cut search tree.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 8
    Publication Date: 2019-05-10
    Description: The dynamics of ventricular fibrillation caused by irregular excitation is simulated in the frame of the monodomain model with an action potential model due to Aliev-Panfilov for a human 3D geometry. The numerical solution of this multiscale reaction-diffusion problem is attacked by algorithms which are fully adaptive in both space and time (code library {\sc Kardos}). The obtained results clearly demonstrate an accurate resolution of the cardiac potential during the excitation and the plateau phases (in the regular cycle) as well as after a reentrant excitation (in the irregular cycle).
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 9
    Publication Date: 2020-12-15
    Description: The topic of this paper are integer programming models in which a subset of 0/1-variables encode a partitioning of a set of objects into disjoint subsets. Such models can be surprisingly hard to solve by branch-and-cut algorithms if the permutation of the subsets of the partition is irrelevant. This kind of symmetry unnecessarily blows up the branch-and-cut tree. We present a general tool, called orbitopal fixing, for enhancing the capabilities of branch-and-cut algorithms in solving this kind of symmetric integer programming models. We devise a linear time algorithm that, applied at each node of the branch-and-cut tree, removes redundant parts of the tree produced by the above mentioned permutations. The method relies on certain polyhedra, called orbitopes, which have been investigated in (Kaibel and Pfetsch (2006)). However, it does not add inequalities to the model, and thus, it does not increase the difficulty of solving the linear programming relaxations. We demonstrate the computational power of orbitopal fixing at the example of a graph partitioning problem motivated from frequency planning in mobile telecommunication networks.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 10
    Publication Date: 2014-11-10
    Description: In this paper, we discuss the relation of unsplittable shortest path routing (USPR) to other routing schemes and study the approximability of three USPR network planning problems. Given a digraph $D=(V,A)$ and a set $K$ of directed commodities, an USPR is a set of flow paths $\Phi_{(s,t)}$, $(s,t)\in K$, such that there exists a metric $\lambda=(\lambda_a)\in \mathbb{Z}^A_+$ with respect to which each $\Phi_{(s,t)}$ is the unique shortest $(s,t)$-path. In the \textsc{Min-Con-USPR} problem, we seek for an USPR that minimizes the maximum congestion over all arcs. We show that this problem is hard to approximate within a factor of $\mathcal{O}(|V|^{1-\epsilon})$, but easily approximable within min$(|A|,|K|)$ in general and within $\mathcal{O}(1)$ if the underlying graph is an undirected cycle or a bidirected ring. We also construct examples where the minimum congestion that can be obtained by USPR is a factor of $\Omega(|V|^2)$ larger than that achievable by unsplittable flow routing or by shortest multi-path routing, and a factor of $\Omega(|V|)$ larger than by unsplittable source-invariant routing. In the CAP-USPR problem, we seek for a minimum cost installation of integer arc capacities that admit an USPR of the given commodities. We prove that this problem is $\mathcal{NP}$-hard to approximate within $2-\epsilon$ (even in the undirected case), and we devise approximation algorithms for various special cases. The fixed charge network design problem \textsc{Cap-USPR}, where the task is to find a minimum cost subgraph of $D$ whose fixed arc capacities admit an USPR of the commodities, is shown to be $\mathcal{NPO}$-complete. All three problems are of great practical interest in the planning of telecommunication networks that are based on shortest path routing protocols. Our results indicate that they are harder than the corresponding unsplittable flow or shortest multi-path routing problems.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 11
    Publication Date: 2014-11-11
    Description: In this paper, we investigate the connection availabilities for the new protection scheme Demand-wise Shared Protection (DSP) and describe an appropriate approach for their computation. The exemplary case study on two realistic network scenarios shows that in most cases the availabilities for DSP are comparable with that for 1+1 path protection and better than in case of shared path protection.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 12
    Publication Date: 2016-06-30
    Description: THESEUS, the ZIB threading environment, is a parallel implementation of a protein threading based on a multi-queued branch-and-bound optimal search algorithm to find the best sequence-to-structure alignment through a library of template structures. THESEUS uses a template core model based on secondary structure definition and a scoring function based on knowledge-based potentials reflecting pairwise interactions and the chemical environment, as well as pseudo energies for homology detection, loop alignment, and secondary structure matching. The threading core is implemented in C++ as a SPMD parallization architecture using MPI for communication. The environment is designed for generic testing of different scoring functions, e.g. different secondary structure prediction terms, different scoring matrices and information derived from multiple sequence alignments. A validaton of the structure prediction results has been done on the basis of standard threading benchmark sets. THESEUS successfully participated in the 6th Critical Assessment of Techniques for Protein Structure Prediction (CASP) 2004.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 13
    Publication Date: 2014-02-26
    Description: We consider a multi-queue multi-server system with $n$ servers (processors) and $m$ queues. At the system there arrives a stationary and ergodic stream of $m$ different types of requests with service requirements which are served according to the following $k$-limited head of the line processor sharing discipline: The first $k$ requests at the head of the $m$ queues are served in processor sharing by the $n$ processors, where each request may receive at most the capacity of one processor. By means of sample path analysis and Loynes' monotonicity method, a stationary and ergodic state process is constructed, and a necessary as well as a sufficient condition for the stability of the $m$ separate queues are given, which are tight within the class of all stationary ergodic inputs. These conditions lead to tight necessary and sufficient conditions for the whole system, also in case of permanent customers, generalizing an earlier result by the authors for the case of $n$=$k$=1.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 14
    Publication Date: 2014-02-26
    Description: In order to compute the thermodynamic weights of the different metastable conformations of a molecule, we want to approximate the molecule's Boltzmann distribution in a reasonable time. This is an essential issue in computational drug design. The energy landscape of active biomolecules is generally very rough with a lot of high barriers and low regions. Many of the algorithms that perform such samplings (e.g. the hybrid Monte Carlo method) have difficulties with such landscapes. They are trapped in low-energy regions for a very long time and cannot overcome high barriers. Moving from one low-energy region to another is a very rare event. For these reasons, the distribution of the generated sampling points converges very slowly against the thermodynamically correct distribution of the molecule. The idea of ConfJump is to use $a~priori$ knowledge of the localization of low-energy regions to enhance the sampling with artificial jumps between these low-energy regions. The artificial jumps are combined with the hybrid Monte Carlo method. This allows the computation of some dynamical properties of the molecule. In ConfJump, the detailed balance condition is satisfied and the mathematically correct molecular distribution is sampled.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 15
    Publication Date: 2020-02-11
    Description: "`Volkssport Sudoku"' titelt der Stern in seiner Ausgabe vom 24. Mai2006. In der Tat traut sich derzeit kaum noch eine Zeitung, ohne Sudoku zu erscheinen. Die Begeisterung am Lösen dieser Zahlenrätsel offenbart eine unvermutete Freude am algorithmischen Arbeiten. Mathematisch kann man Sudokus als lineare diophantische Gleichungssysteme mit Nichtnegativitätsbedingungen formulieren. Solche ganzzahligen linearen Programme sind die wichtigsten Modellierungswerkzeuge in zahlreichen Anwendungsgebieten wie z.B. der Optimierung von Telekommunikations- und Verkehrsnetzen. Moderne Verfahren zur Lösung dieser Optimierungsprobleme sind durch Sudokus allerdings deutlich weniger zu beeindrucken als Zeitungsleser.
    Keywords: ddc:000
    Language: German
    Type: reportzib , doc-type:preprint
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  • 16
    Publication Date: 2020-02-11
    Description: This article surveys mathematical models and methods used for physical PCB layout, i.e., component placement and wire routing. The main concepts are briefly described together with relevant references.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 17
    Publication Date: 2020-12-15
    Description: We study online multicommodity minimum cost routing problems in networks, where commodities have to be routed sequentially. Arcs are equipped with load dependent price functions defining the routing weights. We discuss an online algorithm that routes each commodity by minimizing a convex cost function that depends on the demands that are previously routed. We present a competitive analysis of this algorithm showing that for affine linear price functions this algorithm is $4K/2+K$-competitive, where $K$ is the number of commodities. For the parallel arc case this algorithm is optimal. Without restrictions on the price functions and network, no algorithm is competitive. Finally, we investigate a variant in which the demands have to be routed unsplittably.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 18
    Publication Date: 2021-03-16
    Description: Perfect graphs constitute a well-studied graph class with a rich structure, reflected by many characterizations w.r.t different concepts. Perfect graphs are, e.g., characterized as precisely those graphs $G$ where the stable set polytope STAB$(G)$ coincides with the clique constraint stable set polytope QSTAB$(G)$. For all imperfect graphs STAB$(G) \subset$ QSTAB$(G)$ holds and, therefore, it is natural to measure imperfection in terms of the difference between STAB$(G)$ and QSTAB$(G)$. Several concepts have been developed in this direction, for instance the dilation ratio of STAB$(G)$ and QSTAB$(G)$ which is equivalent to the imperfection ratio imp$(G)$ of $G$. To determine imp$(G)$, both knowledge on the facets of STAB$(G)$ and the extreme points of QSTAB$(G)$ is required. The anti-blocking theory of polyhedra yields all {\em dominating} extreme points of QSTAB$(G)$, provided a complete description of the facets of STAB$(\overline G)$ is known. As this is typically not the case, we extend the result on anti-blocking polyhedra to a {\em complete} characterization of the extreme points of QSTAB$(G)$ by establishing a 1-1 correspondence to the facet-defining subgraphs of $\overline G$. We discuss several consequences, in particular, we give alternative proofs of several famous results.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 19
    Publication Date: 2014-11-10
    Description: We give experimental and theoretical results on the problem of computing the treewidth of a graph by exact exponential time algorithms using exponential space or using only polynomial space. We first report on an implementation of a dynamic programming algorithm for computing the treewidth of a graph with running time $O^\ast(2^n)$. This algorithm is based on the old dynamic programming method introduced by Held and Karp for the {\sc Tra veling Salesman} problem. We use some optimizations that do not affect the worst case running time but improve on the running time on actual instances and can be seen to be practical for small instances. However, our experiments show that the space use d by the algorithm is an important factor to what input sizes the algorithm is effective. For this purpose, we settle the problem of computing treewidth under the restriction that the space used is only polynomial. In this direction we give a simple $O^\ast(4^n)$ al gorithm that requires {\em polynomial} space. We also show that with a more complicated algorithm, using balanced separators, {\sc Treewidth} can be computed in $O^\ast(2.9512^n)$ time and polynomial space.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 20
    Publication Date: 2014-03-10
    Description: The dynamic behavior of molecules can often be described by Markov processes. From computational molecular simulations one can derive transition rates or transition probabilities between subsets of the discretized conformational space. On the basis of this dynamic information, the spatial subsets are combined into a small number of so-called metastable molecular conformations. This is done by clustering methods like the Robust Perron Cluster Analysis (PCCA+). Up to now it is an open question how this coarse graining in space can be transformed to a coarse graining of the Markov chain while preserving the essential dynamic information. In the following article we aim at a consistent coarse graining of transition probabilities or rates on the basis of metastable conformations such that important physical and mathematical relations are preserved. This approach is new because PCCA+ computes molecular conformations as linear combinations of the dominant eigenvectors of the transition matrix which does not hold for other clustering methods.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 21
    Publication Date: 2014-02-26
    Description: Das deutschsprachige Bibliothekswesen verfügt mit den \glqq Regeln für den Schlagwortkatalog \grqq (RSWK) unter Verwendung der \glqq Schlagwortnormdatei \grqq (SWD) über ein Instrumentarium, welches zusammen mit einem \glqq Faceted Browsing \grqq das bisher bestehende Angebot für ein Information Retrieval optimal ergänzen kann. Die Verbindung zwischen Standardvokabular (SWD) und Kettenbildung (RSWK) einerseits und eine nach Facetten-Eigenschaften gegliederte Navigation andererseits unterstützt bestmöglich eine inhaltlich bezogene Recherche. Die Stärken und Schwächen der RSWK/SWD werden erörtert und auch Klassifikationen (DDC und RVK) als mögliche Facetten diskutiert.
    Keywords: ddc:000
    Language: German
    Type: reportzib , doc-type:preprint
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  • 22
    Publication Date: 2016-06-09
    Keywords: ddc:000
    Language: English
    Type: masterthesis , doc-type:masterThesis
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  • 23
    Publication Date: 2022-03-14
    Description: A lot of problems arising in Combinatorial Optimization and Operations Research can be formulated as Mixed Integer Programs (MIP). Although MIP-solving is an NP-hard optimization problem, many practically relevant instances can be solved in reasonable time. In modern MIP-solvers like the branch-cut-and-price-framework SCIP, primal heuristics play a major role in finding and improving feasible solutions at the early steps of the solution process. This helps to reduce the overall computational effort, guides the remaining search process, and proves the feasibility of the MIP model. Furthermore, a heuristic solution with a small gap to optimality often is sufficient in practice. We investigate 16 different heuristics, all of which are available in SCIP. Four of them arise from the literature of the last decade, nine are specific implementations of general heuristic ideas, three have been newly developed. We present an improved version of the feasibility pump heuristic by Fischetti et al., which in experiments produced solutions with only a third of the optimality gap compared to the original version. Furthermore, we introduce two new Large Neighborhood Search (LNS) heuristics. Crossover is an LNS improvement heuristic making use of similarities of diverse MIP solutions to generate new incumbent solutions. RENS is an LNS rounding heuristic which evaluates the space of all possible roundings of a fractional LP-solution. This heuristic makes it possible to determine whether a point can be rounded to an integer solution and which is the best possible rounding. We conclude with a computational comparison of all described heuristics. It points out that a single heuristic on its own has only a slight impact on the overall performance of SCIP, but the combination of all of them reduces the running time by a factor of two compared to a version without any heuristics.
    Keywords: ddc:000
    Language: English
    Type: masterthesis , doc-type:masterThesis
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  • 24
    Publication Date: 2014-02-26
    Description: We present a finite volume method for the solution of the two-dimensional Poisson equation $ \nabla\cdot( \beta( {\mbox{\boldmath $x$}}) \nabla u({\mbox{\boldmath $x$}})) = f(\mbox{\boldmath $x$}) $ with variable, discontinuous coefficients and solution discontinuities on irregular domains. The method uses bilinear ansatz functions on Cartesian grids for the solution $u({\mbox{\boldmath $x$})$ resulting in a compact nine-point stencil. The resulting linear problem has been solved with a standard multigrid solver. Singularities associated with vanishing partial volumes of intersected grid cells or the dual bilinear ansatz itself are removed by a two-step asymptotic approach. The method achieves second order of accuracy in the $L^\infty$ and $L^2$ norm.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 25
    Publication Date: 2014-11-11
    Description: In this article we aim at an efficient sampling of the stationary distribution of dynamical systems in the presence of metastabilities. In the past decade many sophisticated algorithms have been inven ted in this field. We do not want to simply add a further one. We address the problem that one has applied a sampling algorithm for a dynamical system many times. This leads to different samplings which more or less represent the stationary distribution partially very well, but which are still far away from ergodicity or from the global stationary distribution. We will show how these samplings can be joined together in order to get one global sampling of the stationary distribution.
    Keywords: ddc:000
    Language: English
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  • 26
    Publication Date: 2014-02-26
    Description: The concept of jump system, introduced by Buchet and Cunningham (1995), is a set of integer points with a certain exchange property. In this paper, we discuss several linear and convex optimization problems on jump systems and show that these problems can be solved in polynomial time under the assumption that a membership oracle for a jump system is available. We firstly present a polynomial-time implementation of the greedy algorithm for the minimization of a linear function. We then consider the minimization of a separable-convex function on a jump system, and propose the first polynomial-time algorithm for this problem. The algorithm is based on the domain reduction approach developed in Shioura (1998). We finally consider the concept of M-convex functions on constant-parity jump systems which has been recently proposed by Murota (2006). It is shown that the minimization of an M-convex function can be solved in polynomial time by the domain reduction approach.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 27
    Publication Date: 2020-12-15
    Description: We introduce orbitopes as the convex hulls of 0/1-matrices that are lexicographically maximal subject to a group acting on the columns. Special cases are packing and partitioning orbitopes, which arise from restrictions to matrices with at most or exactly one 1-entry in each row, respectively. The goal of investigating these polytopes is to gain insight into ways of breaking certain symmetries in integer programs by adding constraints, e.g., for a well-known formulation of the graph coloring problem. We provide a thorough polyhedral investigation of packing and partitioning orbitopes for the cases in which the group acting on the columns is the cyclic group or the symmetric group. Our main results are complete linear inequality descriptions of these polytopes by facet-defining inequalities. For the cyclic group case, the descriptions turn out to be totally unimodular, while for the symmetric group case, both the description and the proof are more involved. The associated separation problems can be solved in linear time.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 28
    Publication Date: 2014-11-21
    Description: The standard computational methods for computing the optimal value functions of Markov Decision Problems (MDP) require the exploration of the entire state space. This is practically infeasible for applications with huge numbers of states as they arise, e.\,g., from modeling the decisions in online optimization problems by MDPs. Exploiting column generation techniques, we propose and apply an LP-based method to determine an $\varepsilon$-approximation of the optimal value function at a given state by inspecting only states in a small neighborhood. In the context of online optimization problems, we use these methods in order to evaluate the quality of concrete policies with respect to given initial states. Moreover, the tools can also be used to obtain evidence of the impact of single decisions. This way, they can be utilized in the design of policies.
    Keywords: ddc:000
    Language: English
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  • 29
    Publication Date: 2014-11-21
    Description: Wir beschäftigen uns mit dem Problem der Betriebsplanung von Laserschweißrobotern im Karosseriebau. Gegeben ist eine Menge von Schweißnähten, die innerhalb einer Fertigungszelle an einem Karosserieteil gefertigt werden müssen. Die Schweißnähte werden durch mehrere parallel betriebene Roboter bearbeitet. Die Aufgabe besteht darin, für jeden Roboter eine Reihenfolge und eine zeitliche Koordinierung seiner Bewegungen zu finden, so dass alle Schweißnähte innerhalb der Taktzeit der Fertigungszelle bearbeitet werden und so wenig Laserquellen wie möglich eingesetzt werden. Dabei müssen einige Nebenbedingungen berücksichtigt werden. Für dieses spezielle Schweißproblem haben wir eine Formulierung als gemischt-ganzzahliges lineares Programm entwickelt, welches sich für die untersuchten praktischen Fälle sehr schnell lösen lässt.
    Keywords: ddc:000
    Language: German
    Type: reportzib , doc-type:preprint
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  • 30
    Publication Date: 2021-08-05
    Description: Modern applications of mathematical programming must take into account a multitude of technical details, business demands, and legal requirements. Teaching the mathematical modeling of such issues and their interrelations requires real-world examples that are well beyond the toy sizes that can be tackled with the student editions of most commercial software packages. We present a new tool, which is freely available for academic use including complete source code. It consists of an algebraic modeling language and a linear mixed integer programming solver. The performance and features of the tool are in the range of current state-of-the-art commercial tools, though not in all aspects as good as the best ones. Our tool does allow the execution and analysis of large real-world instances in the classroom and can therefore enhance the teaching of problem solving issues. Teaching experience has been gathered and practical usability was tested in classes at several universities and a two week intensive block course at TU Berlin. The feedback from students and teachers has been very positive.
    Keywords: ddc:000
    Language: English
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  • 31
    Publication Date: 2014-11-21
    Description: The Bottleneck Shortest Path Problem is a basic problem in network optimization. The goal is to determine the limiting capacity of any path between two specified vertices of the network. This is equivalent to determining the unsplittable maximum flow between the two vertices. In this note we analyze the complexity of the problem, its relation to the Shortest Path Problem, and the impact of the underlying machine/computation model.
    Keywords: ddc:000
    Language: English
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  • 32
    Publication Date: 2014-02-26
    Description: We introduce a new and rich class of graph coloring manifolds via the Hom complex construction of Lov\´{a}sz. The class comprises examples of Stiefel manifolds, series of spheres and products of spheres, cubical surfaces, as well as examples of Seifert manifolds. Asymptotically, graph coloring manifolds provide examples of highly connected, highly symmetric manifolds.
    Keywords: ddc:000
    Language: English
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  • 33
    Publication Date: 2014-02-26
    Description: We give coordinate-minimal geometric realizations in general position for 17 of the 20 vertex-minimal triangulations of the orientable surface of genus 3 in the 5x5x5-cube.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 34
    Publication Date: 2014-02-26
    Description: Biochemical interactions are determined by the 3D-structure of the involved components - thus the identification of conformations is a key for many applications in rational drug design. {\sf ConFlow} is a new multilevel approach to conformational analysis with main focus on completeness in investigation of conformational space. In contrast to known conformational analysis, the starting point for design is a space-based description of conformational areas. A tight integration of sampling and analysis leads to an identification of conformational areas simultaneously during sampling. An incremental decomposition of high-dimensional conformational space is used to guide the analysis. A new concept for the description of conformations and their path connected components based on convex hulls and {\em Hypercubes}is developed. The first results of the {\sf ConFlow} application constitute a 'proof of concept' and are further more highly encouraging. In comparison to conventional industrial applications, {\sf ConFlow} achieves higher accuracy and a specified degree of completeness with comparable effort.
    Keywords: ddc:000
    Language: English
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  • 35
    Publication Date: 2014-02-26
    Description: We consider linear inverse problems where the solution is assumed to fulfill some general homogeneous convex constraint. We develop an algorithm that amounts to a projected Landweber iteration and that provides and iterative approach to the solution of this inverse problem. For relatively moderate assumptions on the constraint we can always prove weak convergence of the iterative scheme. In certain cases, i.e. for special families of convex constraints, weak convergence implies norm convergence. The presented approach covers a wide range of problems, e.g. Besov- or BV-restoration for which we present also numerical experiments in the context of image processing.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 36
    Publication Date: 2014-03-10
    Description: Whenever the invariant stationary density of metastable dynamical systems decomposes into almost invariant partial densities, its computation as eigenvector of some transition probability matrix is an ill-conditioned problem. In order to avoid this computational difficulty, we suggest to apply an aggregation/disaggregation method which only addresses wellconditioned sub-problems and thus results in a stable algorithm. In contrast to existing methods, the aggregation step is done via a sampling algorithm which covers only small patches of the sampling space. Finally, the theoretical analysis is illustrated by two biomolecular examples.
    Keywords: ddc:000
    Language: English
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  • 37
    Publication Date: 2016-02-29
    Description: \noindent We give a partial description of the $(s,t)-p$-path polytope of a directed graph $D$ which is the convex hull of the incidence vectors of simple directed $(s,t)$-paths in $D$ of length $p$. First, we point out how the $(s,t)-p$-path polytope is located in the family of path and cycle polyhedra. Next, we give some classes of valid inequalities which are very similar to inequalities which are valid for the $p$-cycle polytope, that is, the convex hull of the incidence vectors of simple cycles of length $p$ in $D$. We give necessary and sufficient conditions for these inequalities to be facet defining. Furthermore, we consider a class of inequalities that has been identifie d to be valid for $(s,t)$-paths of cardinality at most $p$. Finally, we transfer the results to related polytopes, in particular, the undirected counterpart of the $(s,t)-p$-path polytope.
    Keywords: ddc:000
    Language: English
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  • 38
    Publication Date: 2020-11-13
    Description: The numerical integration of dynamical contact problems often leads to instabilities at contact boundaries caused by the non-penetration condition between bodies in contact. Even a recent energy dissipative modification due to Kane et al. (1999), which discretizes the non-penetration constraints implicitly, is not able to circumvent artificial oscillations. For this reason, the present paper suggests a contact stabilization which avoids artificial oscillations at contact interfaces and is also energy dissipative. The key idea of this contact stabilization is an additional $L^2$-projection at contact interfaces, which can easily be added to any existing time integration scheme. In case of a lumped mass matrix, this projection can be carried out completely locally, thus creating only negligible additional numerical cost. For the new scheme, an elementary analysis is given, which is confirmed by numerical findings in an illustrative test example (Hertzian two body contact).
    Keywords: ddc:000
    Language: English
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  • 39
    Publication Date: 2016-06-30
    Keywords: ddc:000
    Language: German
    Type: masterthesis , doc-type:masterThesis
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  • 40
    Publication Date: 2014-02-26
    Description: We discuss different approaches for the enumeration of triangulated surfaces. In particular, we enumerate all triangulated surfaces with 9 and 10 vertices. We also show how geometric realizations of orientable surfaces with few vertices can be obtained by choosing coordinates randomly.
    Keywords: ddc:000
    Language: English
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  • 41
    Publication Date: 2014-02-26
    Description: The concept of L##-convexity is introduced by Fujishige--Murota (2000) as a discrete convexity for functions defined over the integer lattice. The main aim of this note is to understand the difference of the two algorithms for L##-convex function minimization: Murota's steepest descent algorithm (2003) and Kolmogorov's primal algorithm (2005).
    Keywords: ddc:000
    Language: English
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  • 42
    Publication Date: 2014-02-26
    Description: In this survey on combinatorial properties of triangulated manifolds we discuss various lower bounds on the number of vertices of simplicial and combinatorial manifolds. Moreover, we give a list of all known examples of vertex-minimal triangulations.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 43
    Publication Date: 2020-02-11
    Description: This paper concerns the problem of operating a landside container exchange area that is serviced by multiple semi-automated rail mounted gantry cranes (RMGs) that are moving on a single bi-directional traveling lane. Such a facility is being built by Patrick Corporation at the Port Botany terminal in Sydney. The gantry cranes are a scarce resource and handle the bulk of container movements. Thus, they require a sophisticated analysis to achieve near optimal utilization. We present a three stage algorithm to manage the container exchange facility, including the scheduling of cranes, the control of associated short-term container stacking, and the allocation of delivery locations for trucks and other container transporters. The key components of our approach are a time scale decomposition, whereby an integer program controls decisions across a long time horizon to produce a balanced plan that is fed to a series of short time scale online subproblems, and a highly efficient space-time divisioning of short term storage areas. A computational evaluation shows that our heuristic can find effective solutions for the planning problem; on real-world data it yields a solution at most~8\% above a lower bound on optimal RMG utilization.
    Keywords: ddc:000
    Language: English
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  • 44
    Publication Date: 2014-02-26
    Description: We describe an algorithm for the enumeration of (candidates of) vertex-transitive combinatorial $d$-manifolds. With an implementation of our algorithm, we determine, up to combinatorial equivalence, all combinatorial manifolds with a vertex-transitive automorphism group on $n\leq 13$ vertices. With the exception of actions of groups of small order, the enumeration is extended to 14 and 15 vertices.
    Keywords: ddc:000
    Language: English
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  • 45
    Publication Date: 2014-02-26
    Description: We give coordinate-minimal geometric realizations in general position of all 865 vertex-minimal triangulations of the orientable surface of genus 2 in the 4x4x4-cube.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 46
    Publication Date: 2014-02-26
    Description: We give a complete enumeration of combinatorial 3-manifolds with 10 vertices: There are precisely 247882 triangulated 3-spheres with 10 vertices as well as 518 vertex-minimal triangulations of the sphere product $S^2 x S^1$ and 615 triangulations of the twisted sphere product $S^2 \underline{x} S^1$. An analysis of the 3-spheres with up to 10 vertices shows that all these spheres are shellable, but that there are 29 vertex-minimal non-shellable 3-balls with 9 vertices.
    Keywords: ddc:000
    Language: English
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  • 47
    Publication Date: 2019-05-10
    Description: Adaptive numerical methods in time and space are introduced and studied for linear poroelastic models in two and three space dimensions. We present equivalent models for linear poroelasticity and choose both the {\em displacement--pressure} and the {\em stress--pressure} formulation for our computations. Their discretizations are provided by means of linearly implicit schemes in time and linear finite elements in space. Our concept of adaptivity opens a way to a fast and reliable simulation of different loading cases defined by corresponding boundary conditions. We present some examples using our code {\sf Kardos} and show that the method works efficiently. In particular, it could be used in the simulation of some bone healing models.
    Keywords: ddc:000
    Language: English
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  • 48
    Publication Date: 2016-06-30
    Description: During the last few years more and more functionalities of RNA have been discovered that were previously thought of being carried out by proteins alone. One of the most striking discoveries was the de tection of microRNAs, a class of noncoding RNAs that play an important role in post-transcriptional gene regulation. Large-scale analyses are needed for the still increasingly growing amount of sequen ce data derived from new experimental technologies. In this paper we present a framework for the detection of the distinctive precursor structure of microRNAS that is based on the well-known Smith-Wat erman algorithm and various filtering steps. We conducted experiments on real genomic data and we found several new putative hits for microRNA precursor structures.
    Keywords: ddc:000
    Language: English
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  • 49
    Publication Date: 2014-02-26
    Description: Wir erleben zu Beginn des aufkommenden Informationszeitalters mit dem Siegeszug von Google und anderen Internet-Technologien einen Wandel im Verhalten von Wissenschaftlern und Studenten, der mit dem Einsatz von {\sl Google Scholar} und {\sl Google Book Search} einen Paradigmenwechsel für Bibliotheken und Informationsversorger gleichkommt. Der Artikel untersucht die technischen Hintergründe für den Erfolg dieser besonderen Art des Information Retrievals: Fulltext Indexing und Citation Ranking als besondere Form des Information Minig. Er diskutiert Stärken und auch Schwächen des Google-Ansatzes. Der Autor stellt sich auch der Frage, unter welchen Bedingungen es möglich ist, ein zu {\sl Google Scholar} und der {\sl Google Book Search} konkurrenzfähiges Retrieval in der Landschaft der Bibliotheken und Bibliotheksverbünde zu entrichten. Die These ist, dass dieses unter Einsatz des {\sl Open Source} Indexierers {\sl Lucene} und des Web-Robots {\sl Nutch} möglich ist. Bibliotheken können durch gezielten Einsatz solcher Internet-Technologien dem Nutzer die Leistungen, welche Google uns mit seinen Tools im {\sl Visible Web} und mit Referenzen auf {\sl Citations} in der Welt der Literatur zur Verfügung stellt, in vergleichbarer Art auch für ihre eigenen durch Lizenzen geschützten digitalen Journale und ihre speziellen lokal verfügbaren Ressourcen, auf die Internet-Suchmaschinen keine Zugriff haben, anbieten. Es besteht die Hoffnung, dass Nutzer dann nicht - wie in einer kürzlichen Studie des OCLC konstatiert - überwiegend im Internet verbleiben, sondern bei ihrer Suche auch den Weg zu den Angeboten der örtlichen Bibliothek attraktiv finden.
    Keywords: ddc:000
    Language: German
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  • 50
    Publication Date: 2014-02-26
    Description: We consider a system where the arrivals form a Poisson process and the required service times of the requests are exponentially distributed. According to the generalized processor sharing discipline, each request in the system receives a fraction of the capacity of one processor which depends on the actual number of requests in the system. We derive systems of ordinary differential equations for the LST and for the moments of the conditional waiting time of a request with given required service time as well as a stable and fast recursive algorithm for the LST of the second moment of the conditional waiting time, which in particular yields the second moment of the unconditional waiting time. Moreover, asymptotically tight upper bounds for the moments of the conditional waiting time are given. The presented numerical results for the first two moments of the sojourn times in the $M/M/m-PS$ system show that the proposed algorithms work well.
    Keywords: ddc:000
    Language: English
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  • 51
    Publication Date: 2022-07-07
    Description: We present a domain decomposition approach for the computation of the electromagnetic field within periodic structures. We use a Schwarz method with transparent boundary conditions at the interfaces of the domains. Transparent boundary conditions are approximated by the perfectly matched layer method (PML). To cope with Wood anomalies appearing in periodic structures an adaptive strategy to determine optimal PML parameters is developed. We focus on the application to typical EUV lithography line masks. Light propagation within the multi-layer stack of the EUV mask is treated analytically. This results in a drastic reduction of the computational costs and allows for the simulation of next generation lithography masks on a standard personal computer.
    Keywords: ddc:000
    Language: English
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  • 52
    Electronic Resource
    Electronic Resource
    Springer
    European archives of psychiatry and clinical neuroscience 220 (1975), S. 347-360 
    ISSN: 1433-8491
    Keywords: Genetics ; Twins ; Adoptions ; Behaviour Disorder ; Affective Disorder, Unipolar and Bipolar
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary The methods and results of some recent family, twin and adoption studies of childhood behaviour disorders, crime, alcoholism, psychopathic personality and neurosis are briefly described. The data of Slater (1938) on the parents and children of manic-depressives are reanalysed. Bipolar affective illnesses were more frequent in the families of bipolar than unipolar probands. There was no support for sex-linked inheritance in either group or for further genetic subdivision of the unipolar group according to age of onset or alcoholic or psychopathic family history. It is suggested that for the time being we may have to be satisfied with three broad and aetiologically overlapping clinical types of depression: bipolar, unipolar and reactive.
    Type of Medium: Electronic Resource
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  • 53
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 14 (1975), S. 1841-1846 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The conformational phase diagram of poly(L-lysine) (4.6 × 10-4 M, residue) in sodium dodecyl sulfate (1.6 × 10-2 M) solution was constructed from circular dichroism results at various temperatures and pH's. Poly(L-lysine)-sodium dodecyl sulfate complexes undergo a β-helix transition upon raising the pH of the solution. The transition pH tends to shift downward at elevated temperatures. No helix-β transition can be detected for poly(L-lysine) in sodium dodecyl sulfate solution (pH 〉 11) even after 1-hr heating at 70°C. This is in marked contrast with uncharged poly(L-lysine) solution without sodium dodecyl sulfate, which is converted into the β-form upon mild heating of the solution above 50°C.
    Additional Material: 3 Ill.
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  • 54
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 14 (1975), S. 1885-1903 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A normal coordinate analysis of V-amylose has been performed for an isolated 61 helical chain. Negligible splitting from interactions of vibrations of successive residues is expected between A and E vibrational species due to the large size of the monomer unit. As a result, calculation of only the totally symmetric A modes represents an adequate approximation to the vibrational spectrum of helical polysaccharides. Using this method together with a valence force field we have obtained good agreement between the observed and calculated frequencies. In addition, the computed potential energy distribution and Cartesian displacement coordinates match previous experimental assignments, based on deuterium exchange. The analysis also supports the proposed mechanism for conversion of V-amylose to the more extended B-form. This conversion results in an observed frequency shift for the Raman line at 946 cm-1 which is predicted by the calculations.
    Additional Material: 6 Ill.
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  • 55
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 14 (1975), S. 2025-2033 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The circular dichroism of Ac-(Ala)x-OMe and H-Lys-(Lys)x-OH with x = 1, 2, 3, and 4 has been measured in aqueous solutions. The oligomers with x = 4 show similar circular dichroism spectra in water when the lysyl amino groups are protonated, and they respond in similar fashion to heating and to sodium perchlorate. Both oligomers at 15°C exhibit a positive circular dichroism band at 217-218 nm, which is eliminated by the isothermal addition of 4 M sodium perchlorate or by heating. The positive circular dichroism of the lysine oligomer is also eliminated when the pH is elevated to deprotonate the amino groups. Positive circular dichroism is still observed for Ac-(Ala)4-OMe at elevated pH. Circular dichroism spectra have been estimated for poly(L-alanine) and poly(L-lysine) as statistical coils under the above conditions, based on the trends established with the oligomers. Poly(L-lysine) and poly(L-alanine) are predicted to exhibit similar circular dichroism behavior in aqueous solution so long as the lysyl amino groups are protonated. The circular dichroism of the statistical coil of poly(L-lysine), but not poly(L-alanine), is predicted to change when the pH is elevated sufficiently to deprotonate the lysyl amino groups. These results suggest that the unionized lysyl side chains participate in interactions that are not available to poly(L-alanine). Hydrophobic interactions may occur between the unionized lysyl side chains. Protonation of the lysyl amino groups is proposed to disrupt these interactions, causing poly(L-alanine) and protonated poly(L-lysine) to have similar circular dichroism properties.
    Additional Material: 4 Ill.
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  • 56
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Synthesis of nonapeptide hydrazide (sequence 93-101), [Thr107]-decapeptide (sequence 99-108), [Thr107]-tridecapeptide (sequence 96-108), [Thr107]-hexadecapeptide (sequence 93-108), [Thr107]-heptacosapeptide (sequence 82-108), and Nα-benzyloxycarbonyl-[Thr107]-dotetracontapeptide (sequence 67-108) of the proposed primary structure of baker's yeast iso-1-cytochrome c are described. Evidence is presented to indicate that these materials are sequentially homogeneous.
    Additional Material: 4 Ill.
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  • 57
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 14 (1975), S. 2115-2135 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Poly-β-benzyl-L-aspartate (poly[Asp(OBzl)]) forms either a lefthanded α-helix, β-sheet, ω-helix, or random coil under appropriate conditions. In this paper the Raman spectra of the above poly[Asp(OBzl)] conformations are compared. The Raman active amide I line shifts from 1663 cm-1 to 1679 cm-1 upon thermal conversion of poly[Asp(OBzl)] from the α-helical to β-sheet conformation while an intense line appearing at 890 cm-1 in the spectrum of the α-helix decreases in intensity. The 890 cm-1 line also displays weak intensity when the polymer is dissolved in chloroform-dichloroacetic acid solution and therefore is converted to the random coil. This line probably arises from a skeletal vibration and is expected to be conformationally sensitive. Similar behavior in the intensity of skeletal vibrations is discussed for other polypeptides undergoing conformational transitions.The Raman spectra of two cross-β-sheet copolypeptides, poly(Ala-Gly) and poly(Ser-Gly), are examined. These sequential polypeptides are model compounds for the crystalline regions of Bombyx mori silk fibroin which forms an extensive β-sheet structure. The amide I, III, and skeletal vibrations appeared in the Raman spectra of these polypeptides at the frequencies and intensities associated with β-sheet homopolypeptides. Since the sequential copolypeptides are intermediate in complexity between the homopolypeptides and the proteins, these results indicate that Raman structure-frequency correlations obtained from homopolypeptide studies can now be applied to protein spectra with greater confidence.The perturbation scheme developed by Krimm and Abe for explaining the frequency splitting of the amide I vibrations in β-sheet polyglycine is applied to poly(L-valine), poly-(Ala-Gly), poly(Ser-Gly), and poly[Asp(OBzl)]. The value of the “unperturbed” frequency, V0, for poly[Asp(OBzl)] was significantly greater than the corresponding values for the other polypeptides. A structural origin for this difference may be displacement of adjacent hydrogen-bonded chains relative to the standard β-sheet conformation.
    Additional Material: 7 Ill.
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  • 58
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 14 (1975) 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 59
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Circular dichroism studies on synthetic peptides related to the C-terminal region of yeast iso-1-cytochrome c were carried out and compared with conformational studies on horse cytochrome c fragments. Evidence is presented for a weaker predisposition for ordered structure in the former peptides when compared with the corresponding region in horse cytochrome c. These findings agree with theoretical predictions and with observations that yeast and other mammalian type cytochromes c differ in several minor respects.
    Additional Material: 11 Ill.
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  • 60
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 14 (1975), S. 2107-2114 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A polarimetric electric-field-jump relaxation apparatus is described and used to determine the relaxation spectrum for the helix-coil transition of poly(α,L-glutamic acid) in water at 24°C. A maximum relaxation time of 1.7 μc occurs at the transition midpoint (pH = 5.9) yielding a rate constant for helical growth of 6 × 107 sec-1.
    Additional Material: 2 Ill.
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  • 61
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 14 (1975), S. 2181-2195 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Mixtures of a weak polybase (polyethylenimine) and a weak polyacid acrylamide-acrylic acid copolymer in aqueous solutions at several ionic strengths and polymer concentrations are studied potentiometrically. When the concentrations of the polyethylenimine and acrylamide-acrylic acid copolymer charges are not too different, phase separation into two liquid phases (“complex coacervation”) is observed. In the pH region where no phase separation occurs, potentiometric titrations are performed on mixtures of both polymers. From the titrations of polyethylenimine solutions, acrylamide-acrylic acid copolymer solutions, and the mixtures, the free energy of interaction has been evaluated according to the theory of Litan. The dependence of the free energy of interaction on pH, polymer concentrations, and ionic strength is explained quantitatively with a model of cooperative electrostatic physical association.
    Additional Material: 6 Ill.
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  • 62
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The problem of deducing the DNA structure with correct base pairing and specific symmetry is formulated in the form of algebraic equations. In this way the number of independent variables determining double-helix conformation can be reduced from six to four. The effectiveness of the method is illustrated by the computations for A-DNA and B-DNA. The method allows one to predict all possible conformations of the complementary nucleic acids.
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  • 63
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    Biopolymers 14 (1975), S. 2211-2230 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The synthesis and characterization of a series of sequential polypeptides with the repeating sequences Aze-Pro-Aze, Pro-Aze-Pro, Pro-Aze-Gly, Aze-Pro-Gly, Ala-Aze-Gly, Aze-Ala-Gly, and Pro-Pro-Gly are reported. The polymers were prepared by the active ester method, using the p-nitrophenyl, pentachlorophenyl, and N-hydroxysuccinimide esters as the polymerizable tripeptide derivatives. Except for poly(Ala-Aze-Gly) obtained via the N-hydroxysuccinimide ester, all polymers were isolated in good yields and have weight-average molecular weights in the range 10,000-30,000. The molecular weights have been determined by applying the calibrated gel chromatography system described by Fairweather et al. [J. Chromatogr. (1972) 67, 157] and by viscometry. All di- and tripeptide intermediates were chemically and optically pure.
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  • 64
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    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Synthetic regular polytripeptides of the type (Gly-R2-R3) where R2, R3, or both, are imino acids have been widely studied as model compounds for collagen. One such polytripeptide is poly(Gly-Pro-Hyp), since triplets with this sequence constitute about 10% of collagen. Recently, a new model has been proposed for this polytripeptide in which one of the three peptide bonds in the tripeptide unit is in the cis conformation, and the γ-hydroxyl group of hydroxyproline forms a direct interchain hydrogen bond within the triple helix. We have confirmed this structure by model building using computer techniques, and the helical parameters obtained by us are close to the experimentally observed values. The model is also found to be comparable in stability with other models from energy considerations.
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  • 65
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Several globular proteins have values of the Scheraga-Mandelkern β parameter significantly below the theoretical minimum value, β0 = 2.112 × 106, for an impermeable sphere. Using the Felderhof-Deutch generalization of the Debye-Bueche-Brinkman theory of hydrodynamics of porous spheres, we have shown that values of β slightly below this supposed minimum are theoretically expected. A porous sphere of uniform density has a minimum β of 2.084 × 106 at a Debye shielding ratio of 6.5, corresponding, for example, to a sphere radius of 11 Å and an inverse hydrodynamic shielding length of 0.6 Å-1, values not far from those of small proteins. A two-layer porous sphere model gives similar results. Although this is the first theoretical explanation of values of β below β0, the theory is incomplete since β values as low as 2.03 × 106 are observed.
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  • 66
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    Biopolymers 14 (1975), S. 2489-2506 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: NMR measurements of poly(γ-benzyl-L-glutamate) are reported in several different strengths of magnetic field to determine the relaxation time of the helix-coil transition. Nmr spectra of various samples had line shapes varying from the double to single, depending on the extent of the polydispersity of the sample. This result indicated that the correct line shape of a polypeptide is obscured in the overlapping of multipeaks, which are due to the heterogeneity of the molecular weight in the sample. Thus, the conventional line-shape analysis could not be applied to the kinetic study of the helix-coil transition of polypeptides without consideration of this polydispersity effect on the line shape.To overcome this difficulty, we measured linewidths of nmr spectra for fairly monodisperse samples, using various nmr spectrometers, having field strengths from 60 to 220 MHz. The results were analyzed by a quadratic equation, which involves an additional term proportional to the frequency difference of two sites. The equation differs from the conventional quadratic equation, usually utilized in the case of the fast-exchange limit, only in this additional term. This modification is required to evaluate correctly the unusual broadening of the linewidth resulting from the polydispersity effect and to determine the relaxation time reflected in nmr.Nmr spectra of three samples (DP-35, 85, and 250) were measured by 220-, 100-, and 60-MHz spectrometers in trifluoroacetic acid/chloroform at 28°C and linewidths were analyzed. Relaxation times of the helix-coil transition obtained at the transition midpoint are 2.5 × 10-4, 7 × 10-4, and 1.1 × 10-3 sec, for DP-35, 85, and 250, respectively.
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  • 67
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    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Theoretical expressions are derived for the change in the polarized components of the fluorescence, resulting from the orientation of a rigid molecule bearing a chromophore with arbitrary angles for the absorption and transition moments \documentclass{article}\pagestyle{empty}\begin{document}$ \vec \mu _a $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ \vec \mu _e $\end{document} with respect to the molecular axis. The break in the symmetry relation HV = VH is related to the tilt angle between \documentclass{article}\pagestyle{empty}\begin{document}$ \vec \mu _a $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ \vec \mu _e $\end{document}. The theory is applied to a sonicated DNA-2-hydroxy-4,4′-diamidinostilbene complex, in the blue and red emission bands of this peculiar dye. Simultaneous measurements of linear dichroism and fluorescence lead to the determination of an angle of 47° between a fluorescent bound dye and the DNA axis, with no difference for the blue- and red-emitting species, but confirm the presence of nonfluorescent bound dye in a more perpendicular arrangement.
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  • 68
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    Biopolymers 14 (1975), S. 2613-2623 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The translational drag, rotational drag, and intrinsic viscosity of spherical multisubunit structures have been calculated analytically using the Felderhof-Deutch theory of polymer frictional properties. The structures considered were hollow shells, spheres with uniform subunit density, and spheres covered with a subunit layer of different density. Changes in the transport coefficients resulting from the random removal of subunits and from the variation of subunit size are calculated. For the case of the shell, the results agree with the numerical computations of Bloomfield, Dalton, and Van Holde [Biopolymers 5, 135, 149 (1967)].
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  • 69
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Interactions of glutaraldehyde with either n-butylamine, poly(α,L-lysine), or collagen resulted in a fast release of protons in dilute aqueous solutions at various pH values, followed by much slower changes. The latter reactions, which extended over hours and days, were followed spectrophotometrically and revealed the formation of distinct absorption bands in the visible and near-ultraviolet regions in all the above systems. The visible-range bands disappeared upon treatment with sodium borohydride. A qualitative relationship between oxygen uptake by the system n-butylamine-glutaraldehyde and the slow formation of colored products has been established, while the chemical nature of the reaction products has not been determined.Sedimentation velocity, viscosity, and optical rotation measurements on the products of interaction between poly(L-lysine) and glutaraldehyde in aqueous solution indicated large conformational changes in the polyamino acid present in excess (in residues) over the dialdehyde. In particular, the intrinsic viscosity dropped considerably after interaction, indicating intramolecular crosslinking. At molar ratios of 1:1 between polylsine residues and aldehyde groups, intermolecular crosslinking of polylysine was obtained at pH 8.6.Electron microscopic examinations of collagen samples treated by glutaraldehyde at various pH values indicated changes from unordered to more ordered structures upon treatment with glutaraldehyde, in particular at pH 10.The present structural and optical investigations are considered to be relevant to tanning processes of hides and to fixation procedures.
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  • 70
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    Biopolymers 14 (1975), S. 2625-2637 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In order to obtain a molecular picture of the A and B forms of a DNA subunit, potential energy calculations have been made for dGpdC with C(3′)-endo and C(2′)-endo [or C(3′)-exo] sugar puckerings. These are compared with results for GpC. The global minima for dGpdC and GpC are almost identical. They are like A-form duplex DNA and RNA, respectively, with bases anti, the ω′, ω angle pair near 300°, 280°, and sugar pucker C(3′)-endo. For dGpdC, a B-form helical conformer, with sugar pucker C(2′)-endo and ω′ = 257°, ω = 298°, is found only 0.4 kcal/mol above the global minimum. A second low-energy conformation (2.3 kcal/mol) has ω′ = 263°, ω = 158° and ψ near 180°. This has dihedral angles like the original Watson-Crick model of the double helix. In contrast, for GpC, the C(2′)-endo B form is 6.9 kcal/mol above the global minimum. These theoretical results are consistent with experimental studies on DNA and RNA fibers. DNA fibers exist in both A and B forms, while RNA fibers generally assume only the A form. A low-energy conformation unlike the A or B forms was found for both dGpdC and GpC when the sugars were C(3′)-endo. This conformation - ω′,ω near 20°,80° - was not observed for C(2′)-endo dGpdC. Energy surface maps in the ω′,ω plane showed that C(2′)-endo dGpdC has one low-energy valley. It is in the B-form helical region (ω′ ∼ 260°, ω ∼ 300). When the sugar pucker is C(3′)-endo, dGpdC has two low-energy regions: the A-form helical region and the region with the minimum at ω′ = 16°, ω = 85°.
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  • 71
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    Biopolymers 14 (1975), S. 319-334 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The properties of apomyoglobin were examined in aqueous solutions and various helix- and random-coil-forming solvents by solvent perturbation, optical rotation, circular dichroism, and viscosity measurements. The solvent perturbation data obtained in neutral aqueous solutions suggest 25-40% exposure of the two tryptophyl residues and 50-60% exposure of the three tyrosyls. The estimates of burial of these groups are in the ranges expected for myoglobin based on its X-ray structure. In the helicogenic alcohols, methanol, ethanol, 2-chloroethanol, trifluoroethanol, and 1-propyl alcohol, as well as in acidic solutions, 8 M urea and 6M guanidine hydrochloride, essentially all the tryptophyl and tyrosyl residues are found to be exposed to solvent based on this method. Analysis of the ORD and CD data indicates that in the alcohols the α-helix content of apomyoglobin has in most cases changed from 58-59% to about 80-95%. Analysis of the intrinsic viscosity data based on the equations of Simha and Kirkwood and Auer indicates that the polypeptide chain in these solvents has the dimensions of fully extended α-helical rods, with lengths of 221-251 Å and mean diameters of 12.8-13.6 Å. It is concluded that apomyoglobin in the various alcohols must have an extended but somewhat irregular rodlike structure, having a few bend or irregular sequences between the α-helical segments due largely to the presence of the four proline residues, 37, 88, 100, and 120 in the amino acid sequence.
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  • 72
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    Biopolymers 14 (1975), S. 335-351 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The fluorescence parameters, lifetime, relative quantum yield, maximum and mean wavelength, half-width, and polarization, of bovine serum albumin (BSA) were measured at 15°C in aqueous solutions containing varying concentrations of different chemical perturbants, glycerol, Cu2+ ions, guanidine hydrochloride, and urea. By considering a quenching mechanism as being either dynamic or static, depending upon whether the quenching is or is not accompanied by a change in the fluorescence lifetime, we were able to correlate the changes produced in the various fluorescence parameters by the different chemical perturbants with changes in macromolecular structure as the concentration of perturbant was gradually increased. The addition of glycerol and of Cu2+ ions indicated that in aqueous BSA both tryptophan residues are below the surface of the macromolecule, out of contact with solvent water, and, as a consequence, they are statically quenched. “Ultra-Pure” guanidine hydrochloride at 2.4 M or more caused a drastic conformation change, which resulted in the emergence of a visible tyrosine peak at 304 nm in the BSA fluorescence spectrum when either 260- or 270-nm excitation was employed. With the same excitation, the enhancement of BSA tyrosine fluorescence by 6-8 M ultra-pure urea produced only a shoulder near 304 nm in the BSA fluorescence spectrum. We have introduced the use of a new relative quantum yield for protein fluorescence, q′, referenced to the quantum yield of unquenched free tryptophan, which eliminates the quenching action of water from the reference.
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  • 73
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    Biopolymers 14 (1975), S. 409-417 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The storage and loss shear moduli, G′ and G″, have been measured for dilute solutions of unaggregated and aggregated tobacco mosaic virus samples in glycerol-water mixtures, by the Birnboim-Schrag multiple-lumped resonator modified for use with aqueous solvents. The frequency range was 100-5800 Hz, the concentration range 0.6-2.1 × 10-3 g/ml, and the temperatures 25.0° and 37.8°C. The number-average and weight-average molecular weights of the aggregated sample were estimated as 1.4 and 2.0 × 108, respectively, from electron microscopy. The extrapolated intrinsic moduli [G′] and [G″] were compared with the predictions of the Kirkwood-Auer theory for rigid rodlike molecules. For the unaggregated sample, the frequency dependence of [G′] and [G″] agreed well with the theory assuming the intrinsic viscosity to be 27 ml/g, though the asymptotic limit of [G′]M/RT at higher frequencies was slightly larger than the theoretical value of 3/5. For the aggregated sample, the data agreed with theory for rigid rods as modified to account for molecular-weight distribution.
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  • 74
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    Biopolymers 14 (1975), S. 1109-1114 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 6 Ill.
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  • 75
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    Biopolymers 14 (1975) 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 76
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    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Manning's and Scatchard's models for the description of ion-polyelectrolyte interactions are compared in the case of linear polyelectrolytes and bivalent counterions, where “condensation” of the counterions is known to occur for certain concentration ratios of the two species in solution. This comparison leads to the definition of certain conditions on Scatchard's parameters for a precise structural interpretation of Scatchard's plots to be valid. Experimental data obtained with both models are compared and found in good agreement under such conditions.
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  • 77
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    Biopolymers 14 (1975), S. 1121-1132 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Semi-empirical energy calculations for an internal Pro-Pro dimer are presented that take into account the nature of the flexibility of the proline ring due to its puckering. Calculations show that three stable conformations are available for the dimer: the cis (ω = 0°, ψ = 160°); the trans (ω = 180°, ψ = 160°, also referred to as trans′); and the cis′ (ω = 180°, ψ = -40°) conformations. The best conformational pathways between these stable conformations are determined. Calculations also show that the barrier for cis′-trans′ conversion is of the same order of magnitude as that for cis-trans conversion.
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  • 78
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    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Using the free energy difference between double-helix and random-coil forms of DNA as a measure of the stability of the double helix, we calculate the dependence of the stability on excess univalent cation concentration and on polynucleotide phosphate concentration, both as functions of the equivalent ratio r of divalent cation-to-phosphate concentrations. The theoretical tool is merely to compare the free energy of one polyelectrolyte solution, characterized by the polyelectrolyte linear charge density, with the free energy of another, characterized by a different value of the charge density. It is assumed only that the charge density of the double helix is greater than that of the coil form. The calculation represents the only molecular theory given to date (for r ≠ O) for these aspects of helix stability.We find that, as excess univalent cation concentration increases, the helix stability increases if r is small but decreases if r is large (i.e., of the order of unity). Moreover, as the concentration of nucleotide phosphate increases, the helix stability does not change for small values of r but increases for large values. For both effects, a continuous transition as a function of r bridges the low-r and high-r behaviour.
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  • 79
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    Biopolymers 14 (1975), S. 1423-1435 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The association of chloroform-soluble derivatives of uracil and adenine has been examined in chloroform solution in the presence of dissolved water. Analysis by infrared spectroscopy shows that complex formation still occurs in these conditions, and that the extent of association is substantially unchanged by the presence of water. Evidence is presented for the coexistence of two kinds of base pair (involving, respectively, the C2 and C4 carbonyl groups of the pyrimidine) in the solutions, and for some displacement in their relative balance by the added water. The binding of water to the C2 and C4 carbonyl groups can be separately observed in both the free uracil derivative and its 1:1 complex with 9-ethyladenine. Little or no competition has been found to occur between the formation of base pairs and binding of water to the bases, as judged by measurements of water solubility in chloroform solutions of the bases individually and in 1:1 mixtures. The evidence suggests that this phenomenon can be largely explained by the formation of double hydrogen bonds by the uracil carbonyl groups. Taken together with recent published observations, the results indicate that hydrogen bonding may make a much greater energetic contribution to conformational stability of biopolymers in aqueous solution that has been supposed.
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  • 80
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    Biopolymers 14 (1975), S. 1437-1446 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: By use of a polycondensation procedure free of racemization, stereoregular polymethionines have been synthesized from C-activated D-methionyl-L-methionine and L-methionyl-D-methionyl-L-methionine.The poly(D-methionyl-L-methionine) and poly(L-methionyl-D-methionyl-L-methionine) so prepared are soluble in chloroform and can be purified through dissolution in this solvent and precipitation by ligroin.Poly(D-Met-L-Met)which is obtained in a 25% yield, is about 5000 in average molecular weight. It has no discernible optical activity when examined between 400 and 600 nm in a trifluoroacetic acid solution.Poly(L-Met-D-Met-L-Met) (40% yield, M. W. = 10,000) is an optically active polymer. [α]43624 ≈ + 170° for a chloroformic solution (c = 0.2 CHCl3).
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  • 81
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    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 82
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    Biopolymers 14 (1975) 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 83
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    Biopolymers 14 (1975), S. 1581-1595 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The structure of β-chitin has been refined by rigid-body least-squares methods, based on the intensity data for highly crystalline specimens from the pogonophore Oligobrachia ivanovi. The structure consists of an array of poly-N-acetyl-D-glucosamine chains all having the same sense, which are linked together in sheets by N—H … O=C hydrogen bonding of the amide groups. In addition to the O-3′—H … O-5 intramolecular hydrogen bond, analogous to that in cellulose, the CH2OH side chain forms an intrasheet hydrogen bond to the carbonyl oxygen on the next chain. This structure shows considerably better agreement between observed and calculated intensities than that possessing an intersheet hydrogen bond, as had been proposed previously. The structure is consistent with the swelling properties of β-chitin and can also be seen to be analogous to that of native cellulose.
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  • 84
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    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Conformational analysis of N-methylamide of pyroglutamic acid has been performed by theoretical energy calculations and experimental physical techniques, namely, laser Raman spectroscopy and depolarized Rayleigh scattering. The two theoretically predicted conformations are evidenced in crystalline state (ψ1 = +169°) and in aqueous solution (ψ1 ≃ -20°). This study confirms the interest of a careful vibrational analysis of peptides and N-deuterated derivatives for providing an estimate of the dihedral angle ψ. The relationship between amide III frequency and ψ values is emphasized.
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  • 85
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    Biopolymers 14 (1975), S. 1553-1563 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The adsorption of globular proteins at solid/liquid or liquid/liquid interfaces provides evidence of unfolded molecular conformation. Proteins with high apolar character are strongly unfolded, while those with high polar character are generally incompletely unfolded. Structural changes of globular proteins at adsorption on mercury electrodes were studied by ac polarography and capacity-time curves. The surface area per molecule of nine globular proteins was determined from the adsorption kinetics at the dropping mercury electrode. For all the proteins investigated, this value was greater than the maximal molecular cross section of the native proteins. The surface area was about 19 Å2 per amino acid residue, which coincides with the value for unfolded proteins at the water/air interface. Differences between dropping mercury electrode and hanging drop mercury electrode occurred only with lysozyme and phosphorylase; for the other proteins, the structure of the adsorption layer was independent of the time of interaction at the electrode. Since not all of the reducible groups of the adsorbed proteins come into contact with the electrode, the flattening should be incomplete.
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  • 86
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    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Classical potential energy calculations have been made for the ribodinucleoside monophosphates ApA, CpC, GpG, and UpU. Van der Waal's, electrostatic, and torsional contributions to the energy were calculated, and the energy was minimized with the seven backbone conformational angles as simultaneously variable parameters. At the global minimum, ApA and CpC have conformations like double helical RNA: the angles ω′ and ω are g-g-, the sugar pucker is C3′-endo, and the bases are anti. GpG and UpU, on the other hand, have the ω′,ω angle pair g-t at the global minimum, and for GpG the bases are syn. Energy contour maps for ω′ and ω show two broad, low energy regions for ApA, CpC, and UpU: one is g-g-, and the second encompasses g-t and g+g+ within a single lowenergy contour. The two regions are connected by a path at 10-13 kcal./mole. For GpG, with bases syn, however, only a small low-energy region at g-t is found. The helical ‘A’ RNA conformation is 8.5 kcal/mole higher for this molecule. Thus, the base composition is shown to influence the conformations adopted by dinucleoside phosphates. Comparison of calculations with experimetal data, where available, show good agreement.
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  • 87
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    Biopolymers 14 (1975), S. 1615-1622 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The far infrared spectra of poly(L-proline) I (190-35 cm-1) and II (400-35 cm-1) were obtained in the solid state at both 300° and 110°K. A significant difference in the region below 100 cm-1 was observed. A very intense band located at 60 cm-1 in the infrared spectrum of form II has no counterpart in form I. This indicates the sensitivity of low-frequency vibrations to the difference in conformation assumed by both forms in the solid state.Additional bands observed in this study are correlated with ir and Raman data previously reported and tentative assignments are made using the results of normal mode calculations (in the single-chain approximation) which have been reported.
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  • 88
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    Biopolymers 14 (1975), S. 1623-1631 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Potentiometric titrations of poly(S-carboxymethyl-L-cysteine) and poly(S-carboxy-ethyl-L-cysteine) were carried out in aqueous sodium chloride solutions and in water. For samples of both polymers of high molecular weight, a new pattern was observed concerning the change of titration curve with time; the β-coil transition became sharper and the transition free energy increased by about 100 cal mole-1 as the equilibrium was approached. This suggests that equilibrium data were not obtained in most previous studies on the titration involving the β-coil transition. It also shows that the reversbility is not necessarily sufficient to confirm the equilibrium. Another pattern, which was previously observed, was also confirmed with a low molecular weight sample of poly(S-carboxymethytl-L-cysteine). The titration curves were shown to be insensitive to polymer concentration, even when aggregation or phase separation was present. The validity of the Gouy model to describe the titration curve of the β-structure was found to depend on molecular weight as well as on the nature of the side chain.
    Additional Material: 5 Ill.
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  • 89
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    New York : Wiley-Blackwell
    Biopolymers 14 (1975), S. 1651-1666 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Three kinds of fluorescence enhancement result from the interaction of 2-p-toluidinylnaphthalene-6-sulfonate and calf-skin collagen. They are negatively cooperative, independent, and highly cooperative fluorescence enhancement. In the independent region at pH 3.7, the binding number is about 36 moles of 2-p-toluidinylnaphthalene-6-sulfonate per mole of tropocollagen with a binding constant of 2.0 × 104 M-1; with ΔG = -5.7 kcal/mole, ΔH = -4.0 kcal/mole, and ΔS = 6 e.u. The pH dependence of fluorescence of native collagen shows that the deprotonated forms of the β and γ carboxyl groups of aspartic and glutamic acid decrease the intensity, possibly by charge repulsion of the negatively charged sulfonate group of 2-p-toluidinylnaphthalene-6-sulfonate. The positive charge of lysine is found to be unimportant in the interaction of 2-p-toluidinylnaphthalene-6-sulfonate with collagen. Fluorescence enhancement is caused mainly by the hydrophobic interactions of 2-p-toluidinylnaphthalene-6-sulfonate and collagen. Salt bridge formation between basic and acidic side chains in very low salt concentration may be detectable by 2-p-toluidinylnaphthalene-6-sulfonate fluorescence.
    Additional Material: 9 Ill.
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  • 90
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A series of copolymers of L-lysine and L-valine [poly(L-lysinef L-valine100-f)] containing 0-13% L-valine have been studied, in 0.10M KF solution, using potentiometric titration and circular dichroism spectroscopy. Incorporation of increasing amounts of valine into the copolymers favors β-sheet formation over α-helix formation at high pH and room temperature. The titrations were analyzed using the method of Zimm and Rice and the partial free energy (ΔG0cβ) for the coil-to-β-sheet transition for valine is estimated at 900 cal/mole at 25°C. From the temperature dependence of the free energy, the partial enthalpy, ΔH0cβ, and entropy, ΔS0cβ, of the transition for valine is estimated to be 854 cal/mole and 6.0 e.u., respectively. The corresponding partial thermodynamic parameters for L-lysine are in agreement with published results. The fraction of β-sheet versus pH has been calculated for poly(L-lysine86.8 L-valine13.2) at 25.0°C using the titration data; data obtained from circular dichroism spectroscopy for the same copolymer are in good accord. It is concluded from these results that L-valine is a very strong β-sheet forming amino acid. Furthermore, these results indicate that the Zimm-Rice method is applicable to transitions between the coil and β-sheet states for a polypeptide containing two different residues.
    Additional Material: 7 Ill.
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  • 91
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    New York : Wiley-Blackwell
    Biopolymers 14 (1975), S. 1667-1684 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Conformational analysis of double-stranded helical polynucleotides was carried out in terms of internal and external parameters, using semiempirical energy potential functions. The results obtained show that the structures proposed on the basis of the X-ray analysis for A-DNA and RNA's are almost identical to those corresponding to the conformational energy minima, whereas that proposed for B-DNA still appears to suffer from conformational strains. On the other hand, the B-DNA structure theoretically predicted is stabilized by both van der Waals energy and possible specific interactions with water molecules and counterions. This may explain the stability of the B form with respect to the A form at high relative humidity and ion strength. A possible role of the A + T fraction in stabilizing the B-type DNA emerges in connection with its preferential ability to bind ions. This agrees with the results on the crystalline structures of GpC and ApU. For RNA's, the occurrence of only A-type structures is explained as being due to the C(3′)-endo puckering of ribose in a double helix.
    Additional Material: 13 Ill.
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  • 92
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 14 (1975), S. 1685-1700 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A very general approach to the chemical equilibria between many interacting molecules during sedimentation (boundary, band, or active enzyme) taking into account boundary conditions, cell geometry, equilibrium constants, diffusion, enzyme kinetics, etc., is presented. Through a Fortran program, the method has been applied to two very simple but typical cases. With only minor adjustments, the method presented here for sedimentation studies can be extended to all sorts of problems in which “pools” of various species are interacting with each other.
    Additional Material: 3 Ill.
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  • 93
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    New York : Wiley-Blackwell
    Biopolymers 14 (1975), S. 1769-1772 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 2 Ill.
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  • 94
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    New York : Wiley-Blackwell
    Biopolymers 14 (1975), S. 1717-1738 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The theoretical study of the cooperative binding of a small ligand to a linear homopolymer is extended to systems in which two different complexes can form. The binding isotherms are derived under the assumption that the cooperative interactions exist only between molecules belonging to the same type of binding mode and are limited to nearest neighbors (Ising model). The binding to a single-stranded chain is first considered and two extreme cases are studied: (1) the two complexes can form independently from each other (model of independent classes of binding sites); (2) only one class of binding site exists, each possessing two different states of complexation (three-state model).Binding to a double-helical chain is also considered. Three simple types of competition between the different modes of binding are distinguished. The corresponding models are defined as: (1) the model of independent classes of binding sites; (2) the model of monoexclusive interactions between the different kinds of complexes (the symmetric and asymmetric cases are both considered); (3) the model of biexclusive interactions. The comparative study of the different cases shows that the binding isotherms are very similar at large polymer-to-ligand concentration ratios, while they can be very different at low polymer-to-ligand ratios. This can be used to obtain information on the mechanism of dye binding to nucleic acids by equilibrium studies as shown in a subsequent paper.
    Additional Material: 11 Ill.
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  • 95
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The infrared spectra of poly(L-valine)'s with varying degrees of polymerization have been investigated, as well as copolymers of L-alanine and L-valine. The spectra of nujol mulls of various molecular-weight poly(L-valine)'s, isolated directly from the polymerization media, as well as spectra of these same samples after treatment with strong acid, are recorded. In the 700-250-cm-1 region, bands at 543 and 414 cm-1 are found to increase with increasing degree of polymerization in the nujol mulls, but are missing in the acid-treated samples. These bands are assigned to the L-valine residues with an β-helixlike local conformation. It is inferred that the polymerization proceeds initially in the β form, and after a critical degree of polymerization the chains adopt an appreciable amount of an α-helixlike local conformation.
    Additional Material: 7 Ill.
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  • 96
    Electronic Resource
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    New York : Wiley-Blackwell
    Biopolymers 14 (1975), S. 1811-1826 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Fluorescent probe analysis of purified elastin using 1-anilinonaphthalene-8-sulfonate has been used to investigate reversible structural changes that accompany stretching of this rubberlike protein. There is a specific binding of 1-anilinonaphthalene-8-sulfonate to elastin with a single dye molecule attached per 74,000 molecular-weight protein subunit. When labeled elastin is stretched, the intensity of the 1-anilinonaphthalene-8-sulfonate fluorescence decreases reversibly, and this decrease appears to be linked to an increase in the environmental polarity in the immediate vicinity of the bound dye molecule. The results of experiments carried out in H2O and D2O indicate that this polarity change is due to an increase in the exposure of the 1-anilinonaphthalene-8-sulfonate to water as the hydrophobic interior of the protein subunit is unfolded during stretching. The data are consistent with the proposal that the elastin network is a two-phase system of hydrophobic protein globules surrounded by free solvent spaces.
    Additional Material: 6 Ill.
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  • 97
    Electronic Resource
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    New York : Wiley-Blackwell
    Biopolymers 14 (1975), S. 1847-1861 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Optical rotatory dispersion (ORD) and circular dichroism (CD) spectra of single- and multistranded polyribonucleotides undergo extensive changes on binding of the silver ion. These changes are consistent with the proposition that Ag(I) binds to the heterocyclic bases and not to the phosphate groups of polynucleotides. ORD and CD of silver complexes of poly(A)·poly(U) and double-helical rice dwarf viral RNA display negative Cotton effects when there is more than one Ag(I) per two nucleotide residues in solution. These observations suggest a significant distortion of the double-helical conformation as a result of Ag(I) binding. Silver(I) binding sites of pyrimidine polynucleotides are apparently saturated when there is one Ag(I) per two nucleotide residues and those of purine polynucleotides at one Ag(I) per nucleotide in solution. These data are consistent with the supposition that some Ag(I) binding sites exist on the pyrimidine ring and additional sites on the imidazole ring of polynucleotides. The sedimentation coefficient of poly(A) increases by severalfold when one Ag(I) is present per nucleotide residue. Silver(I) may introduce intra- and interstrand cross-links (through bidentate chelates) in single-stranded polynucleotides, resulting in structures with high sedimentation coefficients. Among the polynucleotides studied, poly(U) was an exception. Silver(I) did not affect the optical properties (absorbance, ORD, and CD) of poly(U) at neutral pH.
    Additional Material: 4 Ill.
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  • 98
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    New York : Wiley-Blackwell
    Biopolymers 14 (1975), S. 1915-1932 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A method for estimating the zero shear rate viscosity for dilute solutions of rigid macromolecules with complex configurations is proposed; this method is based on the macromolecular kinetic theory of Curtiss, Bird, and Hassager. Macromolecular models constructed from a collection of spheres, cylindrical rods, circular discs, and parallelepipeds with arbitrary dimensions and relative orientations can be easily handled by this method. Comparison with available experimental data for several biopolymers shows excellent agreement. As an application to this method, we investigate the effect of surface roughness on the intrinsic viscosity of spherical particles.
    Additional Material: 9 Ill.
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  • 99
    Electronic Resource
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    New York : Wiley-Blackwell
    Biopolymers 14 (1975), S. 1991-1993 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 1 Tab.
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  • 100
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 14 (1975), S. 1933-1949 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Analysis of the time decay of fluorescence of 1-anilino-naphthalene-8-sulfonate bound to phosphorylase b reveals the presence of two components with different decay times. In glycylglycine buffer, pH 7.0, the addition of the activators AMP or IMP, or the conversion to phosphorylase a results in a preferential decrease in the amplitude of the component of longer decay time, arising probably from a preferential dissociation of 1-anilino-naphthalene-8-sulfonate from the corresponding site as a consequence of a change in molecular state.
    Additional Material: 6 Ill.
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