Chapter 8 – Theoretical Biophysics  317

New molecular simulation tools have also been adapted to addressing biological questions

from nonbiological roots. For example, the Ising model of quantum statistical mechanics was

developed to account for emergent properties of ferromagnetism. Here it can also be used to

explain several emergent biological properties, such as modeling phase transition behaviors.

Powerful as they are, however, computer simulations of molecular behavior are only as

good as the fundamental data and the models that go into them. It often pays to take a step

back from the simulation results of all the different tools developed to really see if simulation

predictions make intuitive sense or not. In fact, a core feature to molecular simulations is the

ultimate need for “validation” by experimental tools. That is, when novel emergent behaviors

are predicted from simulation, then it is often prudent to view them with a slightly cynical

eye until experiments have really supported these theoretical findings.

8.2.1  GENERAL PRINCIPLES OF MD

A significant point to note concerning the structure of biomolecules determined using

conventional structural biology tools (see Chapter 5), including not just proteins but also

sugars and nucleic acids, is that biomolecules in a live cell in general have a highly dynamic

structure, which is not adequately rendered in the pages of a typical biochemistry textbook.

Ensemble-​average structural determination methods of NMR, x-​ray crystallography, and

EM all produce experimental outputs that are biased toward the least dynamic structures.

These investigations are also often performed using high local concentrations of the biomol­

ecule in question far in excess to those found in the live cell that may result in tightly packed

conformations (such as crystals) that do not exist naturally. However, the largest mean

average signal measured is related to the most stable state that may not necessarily be the

most probabilistic state in the functioning cell. Also, thermal fluctuations of the biomolecules

due to the bombardment by surrounding water solvent molecules may result in considerable

variability around a mean-​average structure. Similarly, different dissolved ions can result in

important differences in structural conformations that are often not recorded using standard

structural biology tools.

MD can model the effects of attractive and repulsive forces due to ions and water

molecules and of thermal fluctuations. The essence of MD is to theoretically determine

the force F experienced by each molecule in the system being simulated in very small time

intervals, typically around 1 fs (i.e., 10⁻¹⁵ s), starting from a predetermined set of atomic

obtained from atomistic level structural biology of usually either x-​ray diffraction, NMR (see

Chapter 5), or sometimes homology modeling (discussed later in this chapter). Often, these

starting structures can be further optimized initially using the energy minimization methods

of MS simulations. After setting appropriate boundary conditions of system temperature and

pressure, and the presence of any walls and external forces, the initial velocities of all atoms

in the system are set. If the ith atom from a total of n has a velocity of magnitude Vi and mass

mi, then, at a system temperature T, the equipartition theorem (see Chapter 2) indicates, in

the very simplest ideal gas approximation of noninteracting atoms, that

(8.1)

3

2

2

1

2

nk T

m v

i

n

i

i

B

=

=^∑

The variation of individual atomic speeds in this crude ideal gas model is characterized by the

Maxwell–​Boltzmann distribution, such that the probability p(vx,i) of atom i having a speed vx

parallel to the x-​axis is given by

(8.2)

p v

m v

k T

m v

k T

m

k T

x i

i

x i

i

n

i

x i

i

,

,

,

(

) ⁼

−(

)

−(

)

=

=

∑

exp

/

exp

/

e

B

B

B

2

1

2

2

2

2π

xp

/

exp

/

B

−(

)

=

−(

)

m v

k T

v

i

x i

v

x i

v

,

,

2

2

2

2

2

1

2

2

πσ

πσ