Combinatorial Toolbox for Protein Sequence Design and Landscape Analysis in the Grand Canonical Model

TL;DR

This paper introduces a combinatorial toolbox based on linear programming and network flow techniques for analyzing protein landscapes and designing sequences within the Grand Canonical model, expanding previous methods and uncovering new structure-function insights.

Contribution

The paper develops a versatile combinatorial toolbox that broadens the scope of computational techniques for protein landscape analysis and sequence design in the Grand Canonical model.

Findings

Efficient algorithms for protein sequence design and landscape analysis.

Hardness results for certain computational problems in the model.

Discovery of novel relationships between native 3D structures and the Grand Canonical model.

Abstract

In modern biology, one of the most important research problems is to understand how protein sequences fold into their native 3D structures. To investigate this problem at a high level, one wishes to analyze the protein landscapes, i.e., the structures of the space of all protein sequences and their native 3D structures. Perhaps the most basic computational problem at this level is to take a target 3D structure as input and design a fittest protein sequence with respect to one or more fitness functions of the target 3D structure. We develop a toolbox of combinatorial techniques for protein landscape analysis in the Grand Canonical model of Sun, Brem, Chan, and Dill. The toolbox is based on linear programming, network flow, and a linear-size representation of all minimum cuts of a network. It not only substantially expands the network flow technique for protein sequence design in Kleinberg's seminal work but also is applicable to a considerably broader collection of computational problems than those considered by Kleinberg. We have used this toolbox to obtain a number of efficient algorithms and hardness results. We have further used the algorithms to analyze 3D structures drawn from the Protein Data Bank and have discovered some novel relationships between such native 3D structures and the Grand Canonical model.