the motion over the next time step determined and so on. This process allows ‘uphill’motion over the energy
surface, and barriers between minima may be overcome, depending on their height relative to the simula-
tion temperature (Figure 11.20b).
As well as a method for helping to locate the global energy minimum, molecular dynamics simulations
can be regarded as a better representation of the physical state of the system – as a dynamic molecule that, at
normal temperatures, does not have a single ‘frozen’conformation. Rather the method samples a range of
configurations, not just oscillating about the global minimum, but perhaps also significantly occupying other
local energy minimum conformations. The flexibility of DNA can be considerable (Figure 11.21), and this is
an important aspect of its function and recognition properties that often cannot be fully appreciated from
crystallographic and (to a lesser extent) NMR data. The main limitation of molecular dynamics simulations
is the timescale that is accessible. In order for the calculations predicting the trajectory of the molecule to be
accurate, the time-step between which the forces acting on the system are recalculated must be very small –
of the order of a femtosecond. Each calculation is computationally expensive and so current computer
power typically limits such simulations to the order of a few tens of nanoseconds at best, which may take
months to run. On this timescale, only quite modest motions of DNA can be observed directly: oscillations
of small groups of atoms and localised bending and twisting motions. Many more biologically interesting
conformational motions of DNA, for example winding and unwinding of the double helix and base-pair
opening, only happen on the microsecond timescale or more slowly.
The basic output from a molecular dynamics simulation is a trajectory, i.e.the predicted behaviour of a
single molecule as a function of time. However, the individual ‘snapshots’ from a molecular dynamics
simulation can alternatively be regarded as a Boltzmann-weighted ensemble of structures from which
thermodynamic quantities may be calculated. Modelling methods based on this approach are particularly
valuable in that they provide a link between the microscopic behaviour of individual molecules – easy to
simulate but difficult to observe experimentally – and the macroscopic properties of the system, which are
much easier to measure, but can be difficult to interpret in terms of atomic-scale features. Molecular
dynamics simulations of DNA have become increasingly sophisticated over the last few years^53 and are
applied to a rapidly increasing volume of DNA structures and sequences.^54
11.7.3 Mesoscopic Modelling
As indicated above, atomic-scale modelling, where each atom is represented by a sphere and each bond by a
spring, does have some serious limitations. Current computer power limits the size of the molecules that may
be studied this way to the order of a few thousand atoms (e.g.up to perhaps 200 base pairs) and, if one is
interested in dynamics, to timescales of the order of a few tens of nanoseconds. To probe other sizes and
timescales, modellers must adopt mesoscopic modellingmethods, in which, for example a length of DNA
is treated as a uniform elastic rod, or as a set of disks (each representing a base or base pair) connected to
its neighbours by springs. These approaches are particularly used at present to study DNA supercoiling
and packaging.
454 Chapter 11
Figure 11.21 Snapshots taken from a short (120 ps) molecular dynamics simulation of a 126 base-pair DNA
micro-circle, illustrating its conformational flexibility