or unstable structures. Molecular modelling also provides a method to relate the structural, dynamic and
thermodynamic properties of nucleic acids to underlying theories of the physical processes that drive
structure, bonding and recognition.
11.7.1 Molecular Mechanics and Energy Minimisation
Crick and Watson’s model of the DNA duplex was constructed of wired-up physical shapes, but modern
modelling is carried out almost exclusively through computational techniques. In theory, the most accurate
predictions of molecular structure can come from quantum mechanical calculations, which treat the electronic
structure of molecules in detail and from first principles. But despite the continuing rapid increase in computer
power, the size of nucleic structures that are most often of interest precludes their day-to-day use. Instead,
the most commonly used method is molecular mechanics.
Individual atoms are considered as spheres, and the bonds that connect them as springs. A set of equations,
called a force field, determine how the energy of the system varies as bonds stretch or compress, bond angles
vary or torsions rotate. Other terms in the equations describe the energetic consequences of nonbonded
(van der Waals and electrostatic) interactions between atoms. A computer can then calculate the energy of the
system as a function of the atomic coordinates. This gives rise to the idea of an energy surface(Figure 11.20a)
and the simplest application of molecular mechanics, which is energy minimisation.
The ‘true’ structure of the molecule corresponds to a situation in which there is no net force acting on
any atom, i.e.to a point on this surface with zero slope. Starting from an arbitrary initial guess for this true
structure, the process of energy minimisation involves calculation of the forces and moving ‘downhill’ on
this surface until a minimum is reached. However, the figure illustrates the important point that for most
rather complex biomolecular structures, the energy surface has many minima. The real molecule is
expected to adopt the global minimum energy conformation, but energy minimisation may only lead to a
local minimum and thus predict an incorrect structure for the molecule. Because of the complexity of real
energy surfaces, the process of searching for the true global energy minimum conformation can be very
difficult and time-consuming, since there is no way of being absolutely sure that the global minimum has
been found until the entire energy surface is examined.
11.7.2 Molecular Dynamics
One of the most widely used methods to try and overcome the problem of obtaining the global energy min-
imum of a structure is molecular dynamics. In this computer simulation method, masses and velocities,
representative of a particular temperature, are assigned to each atom in some starting conformation. Using the
solution of Newton’s equations of motion, the conformation of the system at some later time-point is pre-
dicted. The forces acting on each atom, and thus the velocities, are then recalculated at this new conformation,
Physical and Structural Techniques Applied to Nucleic Acids 453
Figure 11.20 Each configuration of a molecule has an associated energy. In energy minimisation (a), different initial
guesses (•) for the true structure may be optimised to local () rather than the global (*) energy
minimum. Using molecular dynamics (b) the global energy minimum may be more reliably identified