Additional Research Paper

Protofold II: Enhanced Model and Implementation for Kinetostatic Protein Folding1

[+] Author and Article Information
Pouya Tavousi

Kinematics Design Laboratory,
Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: pouya.tavousi@engr.uconn.edu

Morad Behandish

Computational Design Laboratory,
Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: m.behandish@engr.uconn.edu

Horea T. Ilieş

Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: ilies@engr.uconn.edu

Kazem Kazerounian

Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: kazem@engr.uconn.edu

Manuscript received September 8, 2015; final manuscript received January 29, 2016; published online March 22, 2016. Assoc. Editor: Abraham Quan Wang.

J. Nanotechnol. Eng. Med 6(3), 034601 (Mar 22, 2016) (24 pages) Paper No: NANO-15-1074; doi: 10.1115/1.4032759 History: Received September 08, 2015; Revised January 29, 2016

A reliable prediction of three-dimensional (3D) protein structures from sequence data remains a big challenge due to both theoretical and computational difficulties. We have previously shown that our kinetostatic compliance method (KCM) implemented into the Protofold package can overcome some of the key difficulties faced by other de novo structure prediction methods, such as the very small time steps required by the molecular dynamics (MD) approaches or the very large number of samples needed by the Monte Carlo (MC) sampling techniques. In this paper, we improve the free energy formulation used in Protofold by including the typically underrated entropic effects, imparted due to differences in hydrophobicity of the chemical groups, which dominate the folding of most water-soluble proteins. In addition to the model enhancement, we revisit the numerical implementation by redesigning the algorithms and introducing efficient data structures that reduce the expected complexity from quadratic to linear. Moreover, we develop and optimize parallel implementations of the algorithms on both central and graphics processing units (CPU/GPU) achieving speed-ups up to two orders of magnitude on the GPU. Our simulations are consistent with the general behavior observed in the folding process in aqueous solvent, confirming the effectiveness of model improvements. We report on the folding process at multiple levels, namely, the formation of secondary structural elements and tertiary interactions between secondary elements or across larger domains. We also observe significant enhancements in running times that make the folding simulation tractable for large molecules.

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Fig. 1

The polypeptide chain is modeled as a kinematic linkage, in which the peptide planes are assumed to be rigid

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Fig. 2

The solvent-accessible and -excluded surfaces

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Fig. 3

The forces on each link are converted into an equivalent set of joint torques on the preceding joints in the chain

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Fig. 4

Atom centers are hashed into a 3D grid, and the neighbors are selected within a cutoff distance

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Fig. 5

The main process flowchart of Protofold II

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Fig. 6

Thread execution model on the CPU

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Fig. 7

Thread execution model on the GPU

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Fig. 11

Free energy variations during folding of a 15-residue polyalanine chain into a right-handed α-helix in vacuum (top) and in water (bottom) using Protofold II

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Fig. 12

The Ramachandran plots for the energy variations of a pair of Ala residues in vacuum (i.e., without solvation effects) (left) and in water (i.e., with solvation effects) (right) using Protofold II

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Fig. 13

The Ramachandran plots for the folded backbone conformation of 2000 10 - to 20-residue polyalanine chains in vacuum (i.e., without solvation effects) (top) and in water (i.e., with solvation effects) (bottom) starting from random initial conditions −90 deg≤ϕi0,ψi0≤+90 deg using Protofold II

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Fig. 14

The effect of 3D hashing on the force computation times of a 60-residue polyalanine chain with and without solvation effects (on C-1)

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Fig. 15

Sequential running times for electrostatic, van der Waals, and solvation forces, and CPU-parallel running times of the latter for a 1200-residue polypeptide chain (on C-1)

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Fig. 16

CPU- and GPU-parallel running times (top) and speed-ups (bottom) with and without memory optimization for polypeptide chains of various lengths (on C-1)

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Fig. 17

CPU- and GPU-parallel running times (top) and speed-ups (bottom) with memory optimization on two GPUs for polypeptide chains of various lengths (on C-2)

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Fig. 18

Myoglobin (PDB: 1TES) hinged at Asp-21 and Gly-125 for variations in ϕ21,ϕ125 (left) and ψ21,ψ125 (right)

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Fig. 19

Intramolecular versus total (i.e., solvation included) free energy landscape for Myoglobin (PDB: 1TES) in the vicinity of the native conformation versus variations in (ϕ21,ψ21) (left) and (ϕ125,ψ125) (right)

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Fig. 20

Troponin-C (PDB: 2JNF) hinged at Thr-24 and Asp-145 for variations in ϕ24,ϕ145 (left) and ψ24,ψ145 (right)

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Fig. 21

Intramolecular versus total (i.e., solvation included) free energy landscape for Troponin-C (PDB: 2JNF) in the vicinity of the native conformation versus variations in (ϕ24,ψ24) (left) and (ϕ145,ψ145) (right)

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Fig. 22

PDB: 1GCS hinged at Ile-81 for variations in ϕ81 and ψ81, one at a time

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Fig. 23

Energy variations for PDB: 1GCS versus changes in ϕ81 for fixed native ψ81

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Fig. 24

Energy variations for PDB: 1GCS versus changes in ψ81 for fixed native ϕ81




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