Exploration of the relationship between topology and designability of conformations

Abstract

Protein structures are evolutionarily more conserved than sequences, and sequences with very low sequence identity frequently share the same fold. This leads to the concept of protein designability. Some folds are more designable and lots of sequences can assume that fold. Elucidating the relationship between protein sequence and the three-dimensional (3D) structure that the sequence folds into is an important problem in computational structural biology. Lattice models have been utilized in numerous studies to model protein folds and predict the designability of certain folds. In this study, all possible compact conformations within a set of two-dimensional and 3D lattice spaces are explored. Complementary interaction graphs are then generated for each conformation and are described using a set of graph features. The full HP sequence space for each lattice model is generated and contact energies are calculated by threading each sequence onto all the possible conformations. Unique conformation giving minimum energy is identified for each sequence and the number of sequences folding to each conformation (designability) is obtained. Machine learning algorithms are used to predict the designability of each conformation. We find that the highly designable structures can be distinguished from other non-designable conformations based on certain graphical geometric features of the interactions. This finding confirms the fact that the topology of a conformation is an important determinant of the extent of its designability and suggests that the interactions themselves are important for determining the designability.

Local motifs in proteins combine to generate global functional moves

“…The extent of designability of conformations of proteins is intimately linked to their topology [1]. Topology of folded proteins is deduced from three-dimensional all-atom structures, expressing them as a reduced set of nodes interacting via links.…”

Predicting Designability of Small Proteins from Graph Features of Contact Maps

“…In other words, the topology of each structure and its interaction network were described using graph features. The graph features used in this analysis were the same features used in our earlier study with the lattice models (Leelananda et al, 2011). Fifteen graph features (or protein conformation interaction graph invariants) were used in this analysis (Fig.…”

“…In our earlier study performed on lattice proteins, all possible compact conformations within a set of 2D and 3D lattice spaces were explored, and we found that complementary interaction graph features can be used to predict protein designabilities (Leelananda et al, 2011). It was suggested that the topologies of lattice conformations are important determinants of the extent of their designability.…”

“…obtained when ranges were predicted instead of the exact numerical designabilities as shown in our previous study using lattice models (Leelananda et al, 2011). The number of sequences folding to a particular conformation is given by N s , and this is also designated as the designability of that structure.…”

Protein sequence-structure relationships

“…In Chapter 2, work on the designability of two-dimensional (2D) and threedimensional (3D) lattice models is discussed. Section 2.1 is based on a published article (Leelananda et al, 2011b). Here, graph features of contact maps are employed to describe the topology of lattice models, and the relationship between these features and the designability of models is explored.…”