Statistical weight matrix

US model can be combined with the Monte Carlo simulation approach to calculate a r range of properties them is available from the simple matrix multiplication method. 2 RIS Monte Carlo method the statistical weight matrices are used to generate chain irmadons with a probability distribution that is implied in their statistical weights. 

In the RIS model for PE described by Abe et al. [143], the conformational partition function, Z, of the unperturbed chain with n bonds is formulated using a well-known statistical weight matrix for bond i, Uj, that is usually written in a 3 x 3 form. 

A perfectly analogous procedure can be performed for the RIS model on the 2nnd lattice, using an expression for Z developed with the statistical weight matrix in Eq. (4.4) or (4.5) [153]. The replacement for Eq. (4.6) becomes ... 

Collect the statistical weights into statistical weight matrices (of dimension Vj.j X v , where v,- is the number of rotational isomeric states of bond i), one per skeletal bond subject to conformational change, indexing rows and columns of the matrices with the RIS of the bond. The generic statistical weight matrix for bond i is termed U,-. 

M Values for the interdiad statistical weight matrix, Up, in which all first-order interactions are included, are given in the original paper. Table VI. 

For CH2-CH2-CH2 (ethylene) bond pairs, the statistical weight matrix is designated Ue. 

The statistical weight matrix for bond i in branch j is denoted by jUj. Matrices are given as... 

For molecules limited to one helical sequence, the basic statistical weight matrix used is given by ... 

In order to calculate the partition function and molecular averages, a 4x4 statistical weight matrix for the fth residue is formulated to correlate the states of residues i-1, i, and / + 1 of the polymer chain ... 

By choosing the c state as a standard state, the number of statistical weights is reduced to three (relative to that of the c state), viz. vs,i > and vh,l - Hence, the 3x3 matrix for the nearest-neighbor interaction model can be written as ... 

Here, the subscript i is placed on the matrix instead of on the individual statistical weights, and /designates the species of amino acid in the rth residue of the protein. 

The statistical weight matrix U used for an amino acid residue is given by U... 

Application of matrix methods to partially helical homopolypeptides is most easily achieved by using a 2 x 2 statistical weight matrix A. 

Matrix schemes which assign end effects to each end of a helical segment are also proposed. A 3 x3 statistical weight matrix B using this weighting scheme is used here. Row index states of amino acid residues i-1 and /, while columns index states of amino acid residues i and /+ 1. 

Helix-probability profiles are calculated using the method of Zlmm and Bragg. A 3 x3 statistical weight matrix is formulated ... 

The states potentially available to each residue are denoted c, h, and h. States denoted by h differ from those denoted by h in that they merit an additional weighting factor that arises from helix-helix Interaction In the cross-linked dimer. For a single chain, a 3 x 3 matrix U S,n9 e Is used in which rows index the states of residue i-1 and i, while columns index the states of residues / and/ + 1. The order of indexing is etc or h), he, hh. The required statistical weight matrices for the A Bj pair are of dimensions 10 x 10 and are of different formulation depending upon whether ix (see below). For indexing, see original paper. 

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