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Lifson–Roig Model
In polymer science, the Lifson–Roig model is a helix-coil transition model applied to the alpha helix-random coil transition of polypeptides; it is a refinement of the Zimm–Bragg model that recognizes that a polypeptide alpha helix is only stabilized by a hydrogen bond only once three consecutive residues have adopted the helical conformation. To consider three consecutive residues each with two states (helix and coil), the Lifson–Roig model uses a 4x4 transfer matrix instead of the 2x2 transfer matrix of the Zimm–Bragg model, which considers only two consecutive residues. However, the simple nature of the coil state allows this to be reduced to a 3x3 matrix for most applications. The Zimm–Bragg and Lifson–Roig models are but the first two in a series of analogous transfer-matrix methods in polymer science that have also been applied to nucleic acids and branched polymers. The transfer-matrix approach is especially elegant for homopolymers, since the statistical mecha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polymer Science
Polymer science or macromolecular science is a subfield of materials science concerned with polymers, primarily synthetic polymers such as plastics and elastomers. The field of polymer science includes researchers in multiple disciplines including chemistry, physics, and engineering. Subdisciplines This science comprises three main sub-disciplines: * Polymer chemistry or macromolecular chemistry is concerned with the chemical synthesis and chemical properties of polymers. * Polymer physics is concerned with the physical properties of polymer materials and engineering applications. Specifically, it seeks to present the mechanical, thermal, electronic and optical properties of polymers with respect to the underlying physics governing a polymer microstructure. Despite originating as an application of statistical physics to chain structures, polymer physics has now evolved into a discipline in its own right. * Polymer characterization is concerned with the analysis of chemical str ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nucleation
In thermodynamics, nucleation is the first step in the formation of either a new thermodynamic phase or structure via self-assembly or self-organization within a substance or mixture. Nucleation is typically defined to be the process that determines how long an observer has to wait before the new phase or self-organized structure appears. For example, if a volume of water is cooled (at atmospheric pressure) below 0°C, it will tend to freeze into ice, but volumes of water cooled only a few degrees below 0°C often stay completely free of ice for long periods (supercooling). At these conditions, nucleation of ice is either slow or does not occur at all. However, at lower temperatures nucleation is fast, and ice crystals appear after little or no delay. Nucleation is a common mechanism which generates first-order phase transitions, and it is the start of the process of forming a new thermodynamic phase. In contrast, new phases at continuous phase transitions start to form immedi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polymer Physics
Polymer physics is the field of physics that studies polymers, their fluctuations, mechanical properties, as well as the kinetics of reactions involving degradation and polymerisation of polymers and monomers respectively.P. Flory, ''Principles of Polymer Chemistry'', Cornell University Press, 1953. .Pierre Gilles De Gennes, ''Scaling Concepts in Polymer Physics'' CORNELL UNIVERSITY PRESS Ithaca and London, 1979M. Doi and S. F. Edwards, ''The Theory of Polymer Dynamics'' Oxford University Inc NY, 1986 While it focuses on the perspective of condensed matter physics, polymer physics is originally a branch of statistical physics. Polymer physics and polymer chemistry are also related with the field of polymer science, where this is considered the applicative part of polymers. Polymers are large molecules and thus are very complicated for solving using a deterministic method. Yet, statistical approaches can yield results and are often pertinent, since large polymers (i.e., polymers wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tertiary Structure
Protein tertiary structure is the three dimensional shape of a protein. The tertiary structure will have a single polypeptide chain "backbone" with one or more protein secondary structures, the protein domains. Amino acid side chains may interact and bond in a number of ways. The interactions and bonds of side chains within a particular protein determine its tertiary structure. The protein tertiary structure is defined by its atomic coordinates. These coordinates may refer either to a protein domain or to the entire tertiary structure.Branden C. and Tooze J. "Introduction to Protein Structure" Garland Publishing, New York. 1990 and 1991. A number of tertiary structures may fold into a quaternary structure.Kyte, J. "Structure in Protein Chemistry." Garland Publishing, New York. 1995. History The science of the tertiary structure of proteins has progressed from one of hypothesis to one of detailed definition. Although Emil Fischer had suggested proteins were made of polypept ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pi Helix
A pi helix (or π-helix) is a type of secondary structure found in proteins. Discovered by crystallographer Barbara Low in 1952 and once thought to be rare, short π-helices are found in 15% of known protein structures and are believed to be an evolutionary adaptation derived by the insertion of a single amino acid into an α-helix. Because such insertions are highly destabilizing, the formation of π-helices would tend to be selected against unless it provided some functional advantage to the protein. π-helices therefore are typically found near functional sites of proteins. Standard structure The amino acids in a standard π-helix are arranged in a right-handed helical structure. Each amino acid corresponds to an 87° turn in the helix (i.e., the helix has 4.1 residues per turn), and a translation of along the helical axis. Most importantly, the N-H group of an amino acid forms a hydrogen bond with the C=O group of the amino acid ''five'' residues earlier; this repeated ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
310 Helix
A 310 helix is a type of secondary structure found in proteins and polypeptides. Of the numerous protein secondary structures present, the 310-helix is the fourth most common type observed; following α-helices, β-sheets and reverse turns. 310-helices constitute nearly 10–15% of all helices in protein secondary structures, and are typically observed as extensions of α-helices found at either their N- or C- termini. Because of the α-helices tendency to consistently fold and unfold, it has been proposed that the 310-helix serves as an intermediary conformation of sorts, and provides insight into the initiation of α-helix folding. Discovery Max Perutz, the head of the Medical Research Council Laboratory of Molecular Biology at the University of Cambridge, wrote the first paper documenting the elusive 310-helix. Together with Lawrence Bragg and John Kendrew, Perutz published an exploration of polypeptide chain configurations in 1950, based on cues from noncrystalline diff ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coordinate Vector
In linear algebra, a coordinate vector is a representation of a vector as an ordered list of numbers (a tuple) that describes the vector in terms of a particular ordered basis. An easy example may be a position such as (5, 2, 1) in a 3-dimensional Cartesian coordinate system with the basis as the axes of this system. Coordinates are always specified relative to an ordered basis. Bases and their associated coordinate representations let one realize vector spaces and linear transformations concretely as column vectors, row vectors, and matrices; hence, they are useful in calculations. The idea of a coordinate vector can also be used for infinite-dimensional vector spaces, as addressed below. Definition Let ''V'' be a vector space of dimension ''n'' over a field ''F'' and let : B = \ be an ordered basis for ''V''. Then for every v \in V there is a unique linear combination of the basis vectors that equals '' v '': : v = \alpha _1 b_1 + \alpha _2 b_2 + \cdots + \alpha _n b_n . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partition Function (statistical Mechanics)
In physics, a partition function describes the statistical properties of a system in thermodynamic equilibrium. Partition functions are functions of the thermodynamic state variables, such as the temperature and volume. Most of the aggregate thermodynamic variables of the system, such as the total energy, free energy, entropy, and pressure, can be expressed in terms of the partition function or its derivatives. The partition function is dimensionless. Each partition function is constructed to represent a particular statistical ensemble (which, in turn, corresponds to a particular free energy). The most common statistical ensembles have named partition functions. The canonical partition function applies to a canonical ensemble, in which the system is allowed to exchange heat with the environment at fixed temperature, volume, and number of particles. The grand canonical partition function applies to a grand canonical ensemble, in which the system can exchange both heat and p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transfer-matrix Method
In statistical mechanics, the transfer-matrix method is a Mathematical physics, mathematical technique which is used to write the Partition function (mathematics), partition function into a simpler form. It was introduced in 1941 by Hans Kramers and Gregory Wannier. In many one dimensional Lattice model (physics), lattice models, the partition function is first written as an ''n''-fold summation over each possible Microstate (statistical mechanics), microstate, and also contains an additional summation of each component's contribution to the energy of the system within each microstate. Overview Higher dimensional models contain even more summations. For systems with more than a few particles, such expressions can quickly become too complex to work out directly, even by computer. Instead, the partition function can be rewritten in an equivalent way. The basic idea is to write the partition function (mathematics), partition function in the form : \mathcal = \mathbf_0 \cdot \left ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Weight
In statistical mechanics, multiplicity (also called statistical weight) refers to the number of microstates corresponding to a particular macrostate of a thermodynamic system. Commonly denoted \Omega, it is related to the configuration entropy of an isolated system via Boltzmann's entropy formula S = k_\text \log \Omega, where S is the entropy and k_\text = 1.38\cdot 10^ \, \mathrm is Boltzmann's constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant .... Example: the two-state paramagnet A simplified model of the two-state paramagnet provides an example of the process of calculating the multiplicity of particular macrostate. This model consists of a system of N microscopic dipoles \mu which may either be aligned or anti-aligned with an externally applied magnetic field B. Let ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eigenanalysis
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by \lambda, is the factor by which the eigenvector is scaled. Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated. Formal definition If is a linear transformation from a vector space over a field into itself and is a nonzero vector in , then is an eigenvector of if is a scalar multiple of . This can be written as T(\mathbf) = \lambda \mathbf, where is a scalar in , known as the eigenvalue, characteristic value, or characteristic root ass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
