R-RESPA

Reversible Reference System Propagator Algorithms (r-RESPA) 299... 

Another immediate application of r-RESPA is to the case when the force can be subdivided into a short range part and a long range part. One way for effectuating this break up is to introduce a switching function, s x) that is unity at short inter-particle separations and 0 at large inter-particle separations. We introduced this strategy in our earlier non-reversible RESPA paper [15] where we expressed the total force as. 

Reversible Reference System Propagator Algorithms (r-RESPA) 307 Thus the propagator in Eq. (27) produces the following dynamics algorithm ... 

Fig. 1. CPU times (in hours) for 1 ps MD runs for various proteins using three different methods, direct velocity Verlet with a time-step 0.5 fs, r-RESPA with direct evaluation of electrostatic forces and an overall time-step of 4.0 fs, and r-RESPA/TFMM with an overall time-step 4.0 fs (combination of (2,2,2,2) in force breakup).The energy conservation parameter log AE for the three methods are comparable. The CPU time (hours) is for RISC6000 /MODEL 590 computer.

Since many systems of interest in chemistry have intrinsic multiple time scales it is important to use integrators that deal efficiently with the multiple time scale problem. Since our multiple time step algorithm, the so-called reversible Reference System Propagator Algorithm (r-RESPA) [17, 24, 18, 26] is time reversible and symplectic, they are very useful in combination with HMC for constant temperature simulations of large protein systems. 

This article is organized as follows Sect. 2 explains why it seems important to use symplectic integrators. Sect. 3 describes the Verlet-I/r-RESPA impulse MTS method, Sect. 4 presents the 5 femtosecond time step barrier. Sect. 5 introduce a possible solution termed the mollified impulse method (MOLLY), and Sect. 6 gives the results of preliminary numerical tests with MOLLY. 

The idea is illustrated by Fig. 1. These equations constitute a readily understandable and concise representation of the widely used Verlet-I/r-RESPA impulse MTS method. The method was described first in [8, 9] but tested... 

In the r-RESPA method this operator is decomposed into two or more parts, for example... 

The underlying theory of r-RESPA is somewhat involved, but the final result and const quent implementation is actually rather straightforward, being very closely related to th velocity Verlet integration scheme. For our four-way decomposition the algorithm woul... 

Constant temperatnre is maintained by Nose-Hoover thermostat and the equations of motion were integrated using the two time scale r-RESPA with a large time step of 2 fs and a small time step of 0.2 fs. Equilibration using these initial configurations was then carried out for at least 2 ns before beginning any produc-... 

The problem can further be reduced to two aspects the frequency and computational cost of force calculations. Force calculations, the centres of every MD timestep, range from being very costly to prohibitively costly. The approaches that are currently being pursued in order to solve this problem are quite numerous and include techniques such as the use of multiple timestep methods(r-RESPA) [4], resonance free multiple timestep methods (iso-NHC-RESPA) [5,6], using coarse grained models [3], and other novel approaches. 

Significant Speedups in Simulations of Large Systems via r-RESPA... 

Since its inception, r-RESPA has proven to be indispensable for molecular dynamics simulations of large systems. Using r-RESPA to break down the force calculations into different time scales has given rise to the ability to take significantly larger fundamental time steps without suffering a decrease in the energy conservation of the simulation. 

Table 1. Energy Conservation and CPU times for six (6) simulations of HlV-1-Protease with Saquinivir in solution with different levels of r-RESPA being implemented...

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