316 8.2  Molecular Simulation Methods

Theoretical biophysics approaches can be extended much further than this, into smaller and

larger length and time scales to those described earlier, and these are discussed in Chapter 9.

We can broadly divide theoretical biophysics into continuum level analysis and discrete

level approaches. Continuum approaches are largely those of pencil and paper (or pen, or

quill) that enable exact mathematical solutions to be derived often involving complex differ­

ential and integral calculus approaches and include analysis of systems using, for example,

reaction–​diffusion kinetics, biopolymer physics modeling, fluid dynamics methods, and also

classical mechanics. Discrete approaches carve up the dimensions of space and time into

incrementally small chunks, for example, to probe small increments in time to explore how

a system evolves stochastically and/​or to divide a complex structure up into small length

scale units to make them tractable in terms of mathematical analysis. Following calculations

performed on these incremental units of space or time, then each can be linked together

using advanced in silico (i.e., computational) tools. Nontrivial challenges lie at the interface

between continuum and discrete modeling, namely, how to link the two regimes. A related

issue is how to model low copy number systems using continuum approaches, for example,

at some threshold concentration level, there may simply not be any biomolecule in a given

region of space in a cell at a given time.

The in silico tools include a valuable range of simulation techniques spanning length and

time scales from atomistic simulations through to molecular dynamics simulations (MDS).

Varying degrees of coarse-​graining enable larger time and length scales to be explored.

Computational discretization can also be applied to biomechanical systems, for example, to

use finite element analysis (FEA). A significant number of computational techniques have

also been developed for image analysis.

8.2  MOLECULAR SIMULATION METHODS

Theoretical biophysics tools that generate positional data of molecules in a biological system

are broadly divided into molecular statics (MS) and molecular dynamics (MD) simulation

methods. MS algorithms utilize energy minimization of the potential energy associated

with forces of attraction and repulsion on each molecule in the system and estimate its

local minimum to find the zero force equilibrium positions (note that the molecular simula­

tion community use the phrase force field in reference to a specific type of potential energy

function). MS simulations have applications in nonbiological analysis of nanomaterials; how­

ever, since they convey only static equilibrium positions of molecules, they offer no obvious

advantage to high-​precision structural biology tools and are likely to be less valuable due to

approximations made to the actual potential energy experienced by each molecule. Also,

this static equilibrium view of structure can be misleading since, in practice, there is vari­

ability around an average state due to thermal fluctuations in the constituent atoms as well

as surrounding water solvent molecules, in addition to quantum effects such as tunneling-​

mediated fluctuations around the zero-​point energy state. For example, local molecular

fluctuations of single atoms and side groups occur over length scales <0.5 nm over a wide

time scale of ~10⁻¹⁵ to 0.1 s. Longer length scale rigid-​body motions of up to ~1 nm for struc­

tural domains/​motifs in a molecule occur over ~1 ns up to ~1 s, and larger scales motions

>1 nm, such as protein unfolding events binding/​unbinding of ligands to receptors, occur

over time scales of ~100 ns up to thousands of seconds.

Measuring the evolution of molecular positions with time, as occurs in MD, is valuable

in terms of generating biological insight. MD has a wide range of biophysical applications

including simulating the folding and unfolding of certain biomolecules and their general sta­

bility, especially of proteins, the operation of ion channels, in the dynamics of phospholipid

membranes, and the binding of molecules to recognition sites (e.g., ligand molecules binding

to receptor complexes), in the intermediate steps involved in enzyme-​catalyzed reactions,

and in drug design for rationalizing the design of new pharmacological compounds (a form

of in silico drug design; see Chapter 9). MD is still a relatively young discipline in biophysics,

with the first publication of an MD-​simulated biological process being only as far back as

1975. That was on the folding of a protein called “pancreatic trypsin inhibitor” known to

inhibit an enzyme called trypsin (Levitt and Warshel, 1975).