Time-Trimming Tricks for Dynamic Ways & Means Simulations: Splitting Force Updates to Reduce Computational Work

of balancing a larger step size with lower resolution As one of the largest group of supercomputer consumaccuracy. That is, with decreased intervals of molecular ers, macromolecular modelers are always scrambling observations (force update frequency), the resolution of for more computer time. With the goal of gaining insights some fast processes might have to be sacrificed. Aninto a variety of biological processes, scientists are also other obstacle is practical: the more sophisticated algocontinuously trimming down algorithmic cost. This rithms, such as those described below, are not trivial economizing of code performance time while maximizto incorporate in the context of large programs, since ing the resulting biological information can be pursued evaluations of the total force depend on many program by using sophisticated mathematical and computer sciunits. This makes the application of new integrators for ence machinery where available (e.g., for fast electroMD more complex than fast schemes for electrostatics static summations [1] or nonbonded-list manipulations), summations. by approximating where possible (e.g., continuum solIn the evolution of certain physical systems—motion vation [2], conformational path estimates [3]), or any of planets or flow of compound concentrations in chemicombination of the above. cal reactions—the effect of the fast processes on the Though a variety of simulation techniques are availglobal motion is negligible. In biomolecular systems, able (see Figure 1), the molecular dynamics (MD) apunfortunately for algorithm developers, vibrational modes proach tops the list in popularity because of its physical are intricately coupled: thus, fast small-amplitude moappeal and biological connection. Namely, the trajectortions can trigger a cascade of events that culminate in ies showing the evolution in time and space of molecular large-scale global rearrangements. This intricate couconformations follow classical physics; this allows kipling limits the traditional mathematical machinery availnetic processes to be followed in detail, linking and able for MD integration and compels algorithm developexpanding upon experimental observations. MD’s popers to seek inventive, tailored approaches (see Figure ularity would be overwhelming if the technique’s compu1). Still, against these challenges, mathematicians and tational demands, and hence biological scope, were not other computational scientists have labored in the past so limited for large systems. This limitation stems from decade to understand the numerical limitations of MD the numerical stability requirement, which restricts the integration, devise clever schemes, and design aptimestep size used for integrating the equations of moproaches departing from accurate motion-following that tion to a relatively small value (e.g., 1 fs). This timestep instead yield greater overall information on the large size implies one million or more steps for simulating a thermally accessible configuration space of macromolemere nanosecond in the life of a biomolecule; this numcules [8, 7, 9, 10]. ber already translates to days or months of computing Following a historical perspective of method developtime, even on state-of-the-art platforms [4], since each ment, we sketch the mathematical machinery for the step typically requires at least one expensive force evalpromising integration approach termed “force splitting” uation. (In empirical molecular force fields, the force or “multiple timesteps” (MTS). We describe the associis defined as the negative gradient of the total energy ated difficulties in standard MTS implementations (reso[enthalpy], which is expressed as a sum of harmonic nance artifacts), outline how they can be overcome at bond length and bond angle expressions, trigonometric the cost of augmenting the underlying Hamiltonian (as torsion terms, nonbonded Coulomb and van der Waals in the LN approach [6, 11]), and illustrate how these components, and other terms.) methods can be evaluated and used to study large bioCertainly, code parallelization on multiple-processor logical systems. We conclude by outlining some outmachines shaves off computing clock time, as demonstanding problems that remain, such as the efficient strated by the longest simulation to date, 1 s, for a implementation of MTS schemes in combination with villin headpiece, achieved in 4 months of dedicated CPU Ewald summations and in applications to various thertime on 256 processors of a Cray T3D/E [5], or by IBM’s modynamic ensembles. ambitious announcement to fold proteins by 2005 on