Chapter 8 – Theoretical Biophysics  319

The force is obtained by calculating the grad of the potential energy function U that

underlies the summed attractive and repulsive forces. No external applied forces are involved

in standard MD simulations; in other words, there is no external energy input into the system,

and so the system is in a state of thermodynamic equilibrium.

Most potential energy models used, whether quantum or classical in nature, in practice

require some level of approximation during the simulation process and so are often referred

to as pseudopotentials or effective potentials. However, important differences exist between

MD methods depending on the length and time scales of the simulations, the nature of the

force fields used, and whether surrounding solvent water molecules are included or not.

8.2.2  CLASSICAL MD SIMULATIONS

Although the forces on single molecules ultimately have a quantum mechanical (QM)

origin—​all biology in this sense one could argue is QM in nature—​it is very hard to find

even approximate solutions to Schrödinger’s equation for anything but a maximum of a few

atoms, let alone the ~10²³ found in one mole of biological matter. The range of less straight­

forward quantum effects in biological systems, such as entanglement, quantum coher­

ence, and quantum superposition, are discussed in Chapter 9. However, in the following

section of this chapter, we discuss specific QM methods for MD simulations. But, for many

applications, classical MD simulations, also known as simply molecular mechanics (MM),

FIGURE 8.1  Molecular dynamics simulations (MDS). Simplified schematic of the general

algorithm for performing MDS.