Discrete Molecular Dynamics Simulation of Biomolecules - Computational Modeling of Biological Systems - page 56

function, it is exactly these details that are of the highest interest and utility. MD
simulations allow for the generation of experimentally testable hypotheses, and
experiments play an essential role in validating simulation methodology.
The first MD simulation of a fluid system was reported by Alder and Wainwright
in 1957 [ 7 ]. In a hard sphere fluid system, the authors found evidence of a
solid-fluid phase transition that had not been observed in previous Monte Carlo
simulations. The subject of hard sphere simulations falls in the general category
of discrete potential MD (DMD), which is also called event-driven molecular
dynamics, discontinuous molecular dynamics, or discrete molecular dynamics.
The DMD methodology is continuously under development for hard-sphere and
polymer systems [ 8 - 15 ], and has recently seen an increase in applications for
studying biomolecules [ 16 - 22 ]. The development of continuous potentials for MD
simulations has facilitated the inclusion of detailed aspects of atomic interactions
[ 23 , 24 ], which is the most common form of MD in current practice. Since the
publication of the first MD simulation of bovine pancreatic trypsin inhibitor (BPTI)
in 1977 [ 25 ], the application of MD simulations to study the structure, dynamics,
and function of biomolecules has been increasing steadily. However, the time scales
currently accessible in MD simulations are typically 10-100 ns, which restrict
their application to many biological processes with large time and length scales
(e.g., protein folding occurs in milliseconds to seconds). Even utilizing worldwide
computing resources [ 26 ] or specialized high-performance computers dedicated
to MD simulations (such as Anton [ 27 , 28 ]), the time scale reached by MD is
still in the range of microseconds. Conversely, with the recent development of
DMD for biological systems, including the DMD force field [ 21 ], all-atom protein
models [ 29 - 31 ], and hydrogen bond modeling [ 18 ], DMD simulations of realistic
biomolecular systems can reach microsecond time scales on personal computers.
All-atom DMD simulations have been applied to study protein folding [ 21 , 30 ],
protein design [ 32 , 33 ], protein structure optimization [ 34 ], and post-translational
modification of proteins [ 35 ]. In this chapter, we focus on DMD simulations of
biomolecules. We briefly discuss the DMD algorithm and recent optimization
approaches, important developments of DMD methodology for biomolecules, and
several applications of all-atom DMD for biomolecules.

2 Discrete Molecular Dynamics

2.1 Algorithm

DMD simulations are based on pairwise interaction potentials that are discontinuous
functions of the interatomic distance, r (Fig. 1 ). We assign for each atom a specific
type—A, B, C, :::—that determines its interaction with other atoms. The interaction
potential between two atoms i (type A) and j (type B) is characterized by distances
r AB min <r AB 1 <r AB 2::: <r AB k::: <r AB max ,wherer AB min corresponds to the