This project is to develop new mathematical methods to better model the loop regions of proteins. Loop regions lack secondary structure and predicting their 3-dimensional conformation from amino acid sequences is one of the main challenges in the study of protein structure and function. Loops are often the sites of the biological mechanisms of action of a protein. Learning these biological mechanisms requires mathematical and computational methods that can sample these conformations efficiently. Due to their inherent flexibility, loop regions may assume a vast variety of shapes and discovering the biologically relevant conformations of low free energy by purely random search can be prohibitive. The discovery and efficient incorporation of appropriate constraints can dramatically reduce the conformational search problem and make it tractable to computation. The Coutsias and Dill groups have published collaboratively on these problems for ten years and contributed some of the current state-of-the-art methods to various software. Here it is proposed: (1) to generalize current state of the art methods for imposing loop closure constraints to treat arbitrary steric and other physical or geometrical constraints in a unified formalism;(2) to develop the mathematics more deeply, relating the numerical analysis of constrained loop closure algorithms to the underlying algebraic and geometric properties of multivariate polynomial systems;(3) to combine our static constraint methods with Gaussian Net dynamics methods to treat dynamics efficiently too;(4) to further increase the efficiencies and coverings through the development of novel concerted move sets combined with a deeper understanding of the topological and geometrical properties of constrained conformation spaces, and (5) to apply them to several biologically important loop modeling problems. If successful, the methods developed in this project will be useful for better understanding biological mechanisms of action and for computational drug discovery, where ligand binding to a protein often depends on its interactions with loops.

Public Health Relevance

Reliable computer determination of the structures of loops in proteins has enormous practical applications: It enables not only prediction of loop conformations controlling biological processes - such as antigen recognition, signal transduction, and enzyme active site gating - but also reengineering of loops at critical locations in proteins for new functions.

National Institute of Health (NIH)
National Institute of General Medical Sciences (NIGMS)
Research Project (R01)
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Special Emphasis Panel (ZGM1-CBCB-5 (BM))
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Smith, Ward
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University of New Mexico
Biostatistics & Other Math Sci
Schools of Arts and Sciences
United States
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Hauser, Kevin; He, Yiqing; Garcia-Diaz, Miguel et al. (2017) Characterization of Biomolecular Helices and Their Complementarity Using Geometric Analysis. J Chem Inf Model 57:864-874
Bhardwaj, Gaurav; Mulligan, Vikram Khipple; Bahl, Christopher D et al. (2016) Accurate de novo design of hyperstable constrained peptides. Nature 538:329-335
Hauser, Kevin; Essuman, Bernard; He, Yiqing et al. (2016) A human transcription factor in search mode. Nucleic Acids Res 44:63-74
Lewis, Robert H; Coutsias, Evangelos A (2016) Flexibility of Bricard's linkages and other structures via resultants and computer algebra. Math Comput Simul 125:152-167
Coutsias, Evangelos A; Lexa, Katrina W; Wester, Michael J et al. (2016) Exhaustive Conformational Sampling of Complex Fused Ring Macrocycles Using Inverse Kinematics. J Chem Theory Comput 12:4674-87
Perez, Alberto; Morrone, Joseph A; Simmerling, Carlos et al. (2016) Advances in free-energy-based simulations of protein folding and ligand binding. Curr Opin Struct Biol 36:25-31
Perez, Alberto; Morrone, Joseph A; Brini, Emiliano et al. (2016) Blind protein structure prediction using accelerated free-energy simulations. Sci Adv 2:e1601274
MacCallum, Justin L; Perez, Alberto; Dill, Ken A (2015) Determining protein structures by combining semireliable data with atomistic physical models by Bayesian inference. Proc Natl Acad Sci U S A 112:6985-90
Perez, Alberto; MacCallum, Justin L; Brini, Emiliano et al. (2015) Grid-based backbone correction to the ff12SB protein force field for implicit-solvent simulations. J Chem Theory Comput 11:4770-9
Perez, Alberto; MacCallum, Justin L; Dill, Ken A (2015) Accelerating molecular simulations of proteins using Bayesian inference on weak information. Proc Natl Acad Sci U S A 112:11846-51

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