Algorithmic Challenges in Structural Molecular Biology and Proteomics

Abstract

This paper reviews our research in computational biology and chemistry. Some of the most challenging and influential opportunities for Physical Geometric Algorithms (PGA) arise in developing and applying information technology to understand the molecular machinery of the cell. Our recent work (e.g., [1-20]) shows that many PGA techniques may be fruitfully applied to the challenges of computational molecular biology. PGA research may lead to computer systems and algorithms that are useful in structural molecular biology, proteomics, and rational drug design.Concomitantly, a wealth of interesting computational problems arise in proposed methods for discovering new pharmaceuticals. I'll briefly discuss some recent results from my lab, including new algorithms for interpreting X-ray crystallography [14,17,16] and NMR (nuclear magnetic resonance) data [3,9,6,19,10,5,7,18,4], disease classification using mass spectrometry of human serum [12], and protein redesign [13]. Our algorithms have recently been used, respectively, to reveal the enzymatic architecture of organisms high on the CDC bioterrorism watch-list [17,16], for probabilistic cancer classification from human peripheral blood [12], and to redesign an antibioticproducing enzyme to bind a novel substrate [13]. I'll overview these projects, and highlight some of the algorithmic and computational challenges.

BWM*: A Novel, Provable, Ensemble-Based Dynamic Programming Algorithm for Sparse Approximations of Computational Protein Design

“…observed, low-energy discrete conformations called rotamers (Lovell et al, 2000;Donald, 2011). Given a branch-decomposition of branch-width w for an n-residue design with at most q rotamers per residue, our algorithm computes the corresponding GMEC, called the sparse GMEC, in O(nw 2 q 3 2 w ) time and O(nq 3 2 w ) space, and enumerates each additional conformation in merely O(n log q) time and O(n) space.…”

“…Several protein design algorithms have successfully predicted protein sequences that fold and bind the desired target in vitro (Frey et al, 2010;Roberts et al, 2012;Rudicell et al, 2014;Stevens et al, 2006;Georgiev et al, 2012;Georgiev and Donald, 2007;Georgiev et al, 2014;Donald, 2011), and even in vivo (Reeve et al, 2015;Roberts et al, 2012;Rudicell et al, 2014;Georgiev et al, 2012;Georgiev et al, 2014;Donald, 2011). However, protein design is NP-hard (Kingsford et al, 2005), making algorithms that guarantee optimality expensive for larger designs where many residues are allowed to mutate simultaneously.…”

“…However, protein design is NP-hard (Kingsford et al, 2005), making algorithms that guarantee optimality expensive for larger designs where many residues are allowed to mutate simultaneously. Therefore, researchers have developed tractable approximations of the protein design problem to obtain provably good approximate solutions (Leach and Lemon, 1998;Roberts et al, 2012;Chen et al, 2009;Lilien et al, 2005;Georgiev and Donald, 2007;Donald, 2011, Smadbeck et al, 2014, or employed heuristic approaches to rapidly generate candidate solutions (Lee and Subbiah, 1991;Kuhlman and Baker, 2000;Jones, 1994;Desjarlais and Handel, 1995;Koehl and Delarue, 1994;Jiang et al, 2000;Donald, 2011). Heuristic sampling of sequences quickly generates locally optimal candidate sequences, whereas provable algorithms are guaranteed to return the global minimum energy conformation (GMEC).…”

Computational Protein Design Using AND/OR Branch-and-Bound Search

“…In practice, we often require the design algorithm to output the k best conformations within a given energy cutoff ∆ [7]. In the BnB framework, this can be done easily by running the BnB search k times and remove the optimal conformations found in the preceding rounds from the search space.…”

“…Unfortunately, these heuristic methods can be trapped into local minima and may lead to poor quality of the final solution. On the other hand, several exact and provable search algorithms which guarantee to find the GMEC solution have been proposed, such as Dead-End Elimination (DEE) [6], A* search [21,22,7,35], tree decomposition [32], branch-and-bound (BnB) search [14,31,3], and BnB-based linear integer programming [1,18].…”