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Lecture

Polymer Conformation: Beyond the Freely Jointed Chain

In course

PHYS-441: Statistical physics of biomacromolecules

Biological macromolecules such as DNA, RNA, proteins and cytoskeletal filaments are polymers. As such, they share a set of properties that are common to any polymer, which are the focus of this course. Details about the protein folding problem will be cove ...

Description

This lecture delves into the exploration of polymer conformation beyond the Freely Jointed Chain model, introducing the Kratky-Porod model. The instructor discusses the implications of introducing realistic local rigidity terms, the continuum limit, and the importance of correlations in determining the polymer's behavior. The lecture also covers the rescaling argument, the persistence length, and the impact of rigidity on the polymer's mechanical properties.

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Related concepts (32)

Correlation

In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve.

Branching (polymer chemistry)

In polymer chemistry, branching is the regular or irregular attachment of side chains to a polymer's backbone chain. It occurs by the replacement of a substituent (e.g. a hydrogen atom) on a monomer subunit by another covalently-bonded chain of that polymer; or, in the case of a graft copolymer, by a chain of another type. Branched polymers have more compact and symmetrical molecular conformations, and exhibit intra-heterogeneous dynamical behavior with respect to the unbranched polymers.

Pearson correlation coefficient

In statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations.

3D modeling

In 3D computer graphics, 3D modeling is the process of developing a mathematical coordinate-based representation of any surface of an object (inanimate or living) in three dimensions via specialized software by manipulating edges, vertices, and polygons in a simulated 3D space. Three-dimensional (3D) models represent a physical body using a collection of points in 3D space, connected by various geometric entities such as triangles, lines, curved surfaces, etc.

Ising model

The Ising model (ˈiːzɪŋ) (or Lenz-Ising model or Ising-Lenz model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic "spins" that can be in one of two states (+1 or −1). The spins are arranged in a graph, usually a lattice (where the local structure repeats periodically in all directions), allowing each spin to interact with its neighbors.

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