User:Narges.sharif/Graphical Models for Protein Structure

Graphical Models have become powerful frameworks for Protein structure prediction, Protein-protein interaction and Free energy calculations for Protein Structures. Using a graphical model to represent the protein structure allows us to solve many problems including secondary structure prediction, protein protein interactions, protein-drug interaction, and free energy calculations.

There are two main approaches to use Graphical Models in Protein Structure Modeling. First approach uses Discrete variables for representing coordinates or Dihedral angles of the protein structure. The variables are originally all continuous values, to transform them into discrete values, a discretization process is typically applied. Second approach uses Continuous variables for the coordinates or Dihedral angles.

Discrete Graphical Models for Protein Structure

Markov random field, also known as undirected graphical model is a common representation for this problem. Given an undirected graph G = (V, E), a set of random variables X = (X_v)_v ∈ V indexed by V form a Markov random field with respect to G if they satisfy the following equivalent Markov properties:

Pairwise Markov property: Any two non-adjacent variables are conditionally independent given all other variables:

$X_{u}\perp \!\!\!\perp X_{v}|X_{V\setminus \{u,v\}}\quad {\text{if }}\{u,v\}\notin E$

In the Discrete model, the continuous variables are discretized into a set of favorable discrete values. If the variables of choice are dihedral angles, the discretization is typically done by mapping each value to the corresponding Rotamer conformation.

Model

Let X = {X_b, X_s} be the random variables representing the entire protein structure. X_b can be represented by a set of 3-d coordinates of the backbone atoms, or equivalently, by a sequence of bond lengths and dihedral angles.

The probability of a particular conformation x can then be written as

$p(X=x|\Theta )=p(X_{b}=x_{b})p(X_{s}=x_{s}|X_{b},\Theta )$

External links

• example.com