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(1) Computer simulations on Graphics Processing Units (GPUs): Molecular simulations are indispensable for the theoretical exploration of condensed phase systems. However, theoretical modeling of the hydrophobic bond formation and rupture under experimental force loads, used in dynamic force spectroscopy measurements, is challenging even for distributed computing systems. For example, to obtain a single trajectory of a C16H34–C16H34 bond rupture and formation in reasonable CPU time (3-7 days) using all-atom MD simulations with explicit solvent, we employed tens of thousand times faster pulling speed, compared to the experimental value (current all-atom MD simulations are limited to 10-100 nanosecond duration). Unfortunately, we did not expect (neither could we predict) that under these force loads the hydrophobic bonds become very unstable. As a result, this affects greatly resolution of distributions of the rupture forces and lifetimes of single C16H34–C16H34 bonds, obtained from MD simulations, that cannot be compared directly with experimental data. In addition, the entire theoretical analysis and modeling of water structure around hydrophobic solutes loses its interpreting capacity. To overcome this problem, we have adapted Graphics Processing Units (GPUs) that are used as performance accelerators in diverse scientific applications. Modern GPUs have evolved into highly parallel, multithreaded processors, which employ IEEE floating point arithmetic. Massive multithreading, fast context switching, and high bandwidth shared memory enable GPUs to tolerate latencies, and run many cores simultaneously. Because on a GPU more transistors are devoted to performing actual calculations, rather than to cache memory and flow control (as on a CPU), GPUs are capable of performing many arithmetic operations simultaneously. Also, CUDA, a parallel computing environment (extension of C), provides a high level software platform and allows one to define kernels that are executed in parallel by many independent threads. We believe that the use of GPUs will enable us to simulate 10-100 times longer trajectories of the C16H34–C16H34 bond rupture and formation using 10-100 times slower pulling speeds. This will enable us to resolve better the kinetics and thermodynamics of the formation and force-induced rupture of hydrophobic bonds. Unfortunately, CPU-based methods cannot be easily translated to GPUs due to fundamental differences in processor and memory architecture. To overcome this limitation, in the first year of this project, we have developed (i) several GPU-based implementations of efficient pseudorandom number generators and (ii) accurate numerical integration schemes for GPU-based molecular simulations.

(2) Pseudo-random number generators (PRNGs): In the first year of this project, we have created optimized, easy to use GPU-based software for all-atom MD simulations in explicit water. MD simulations require a reliable source of pseudorandom numbers. Unfortunately, PRNGs used on CPUs, such as ran2, cannot be adapted to a GPU due to large memory needed for ran2 invocation. While there exist stand alone GPU implementations of good quality PRNGs, in a MD simulation run a PRNG should be incorporated into the program kernel to generate many random numbers. None of the existing programs for a GPU use fast PRNGs of proven statistical quality. The KISS generator (OpenMM project) offers ~80% of the performance of the Hybrid Taus generator and only ~40% of the performance of the Mersenne Twister generator. We have created CUDA-based implementations of high quality PRNGs that have been incorporated into a standard CUDA code. To minimize the amount of memory used to store the current state of the PRNG and the number of read/write operations for a large system (104-105 particles), we have adapted a single PRNG that generates one sequence of random numbers in all threads, and have implemented PRNGs of very high statistical quality: Mersenne Twister MT19937, Twisted GFSR (TT800), and Mersenne Twister MT11213.

(3) Numerical integration schemes: In all-atom MD simulations, the dynamics of the particle is obtained by propagating the particle coordinate dR/dt=V and velocity dV/dt=ξV+f(R), where f(R) is the molecular force. Because GPUs allow one to run longer MD trajectories with hundreds of million iterations, there is a question of numerical accuracy of an integration protocol. The use of symplectic algorithms guarantee that despite the truncation error the Hamiltonian shows limited secular errors growing in time. We have developed and tested GPU-based implementations of numerical integration schemes integrators, such as velocity Verlet algorithm, symplectic low order scheme, symplectic high order algorithm, Bruenger-Brooks-Karplus algorithm, and fourth order Hamiltonian Runge-Kutta scheme, and their higher order versions. These algorithms will be used to develop GPU-based implementations of all-atom MD simulations in explicit and implicit water.

(4) In the second year of this project, the optimized CUDA code will be used to carry out the proposed research activities. These include Specific Aim 1 – Mapping the free energy landscape for the hydrophobic bond rupture, and Specific Aim 2 – Probing the dependence of hydration barrier on the hydrodynamic bond size and direction of stretching force.

(5) Since GPU-based calculations are 10-50 times faster than some of the heavily optimized CPU-based methods, they represent one of the major directions of development in petascale computing. The long-range goals of my career are (i) to create optimized implementations for molecular simulations on alternative computing systems that (ii) will reduce the time-to-solution of today's challenging scientific applications. In addition, I thrive (iii) to generate a synergy between mentoring, teaching, and research where the study of fundamental chemical processes motivates learning, and where scholarly activities enhance the creativity needed for the design of advanced computational models and development of novel theoretical approaches to interpret experimental data.

(6) Gradiate Student: During the first year of this project, Mr. Artem Zhmurov - a chemistry graduate (PhD) student working in my research group, has received advanced training in programming on alternative GPU-based computing platforms using CUDA language (Compute Unified Device Architecture), and knowledge necessary for the CUDA based software development of all-atom MD implementations with implicit and explicit water on single and multiple GPUs (PRNGs, numerical integration schemes, force-field realization).