The prediction of molecular conformation.

Although the art of predicting molecular conformation has not yet reached maturity, it is no longer in its infancy. On the one hand, model-building techniques taking account of van der Waals’ radii and hydrogen bonding have been used to interpret ambiguous experimental data, leading Pauling & Corey to the a-helix and B-pleated sheet, and Watson & Crick to the double helix of DNA. On the other hand, the need to locate properly the structure of least free energy (properly including kinetic as well as potential energy, quantization, vibrational entropy and solvent effects) has long been recognized. The theoretical principles required were identified early in the twentieth century. All that limits the general application of these principles is the amount of computer power available. Thus approaches to the calculation of structure are primarily concerned with the development of rapid methods of calculation. and the choices of assumptions, approximations, and constraints. so that interesting problems are tractable in reasonable computer time. There are several possible approaches: the choice is dictated by the specific problem of interest. If one wishes to compare the potential energies of a molecule in different conformations, i.e. for different rigid configurations of nuclei, then the ‘state’ of-the-art’ calculation is the ab initio quantum mechanical approach. Kinetic energy is included, but only in relation to electron motion. This approach is said to be free of ad hoc parameters. It exploits the variation pr inciplewhich is to say that all electron configurations are possible-to find the most probable we change the configuration to locate that of least energy. Clearly, the way in which the electron distribution is modelled must be flexible enough to allow this, though the more flexible the model, the more computation time is required. Generally, one starts from a description of atomic orbitals as a sum of two or more Gaussian or Slater-type functions. each of varying height and spread. The more such functions used per orbital, the greater the flexibility and the better the result. Such extended basis set calculations, with as many functions as seem to give reasonable convergence (to a single answer) with increasing numbers of functions, have been applied by us to protein and nucleic acid fragments (Robson et al.. 1978: Hillier & Robson, 1979: Platt et al., 1981; Platt & Robson. 1982): each conformation of a molecule of about 20 atoms takes roughly 1 h of computing time, and increases rapidly as the number of orbitals increases. If one wishes instead to take account of the kinetic energy of the nuclei, either to study conformational transitions and modes of vibration or to give a more complete account of the free energy at equilibrium, one uses Molecular Dynamics (MD) (Alder & Wainwright, 1959; McCammon et al., 1976). which is another state-of-the-art calculation. Starting at a particular conformation and scaling the nuclear velocities to accord with the required temperature of the system, one calculates a ‘genuine’ time course of events by applying Newton’s Laws of Motion to the nuclei. Clearly, many conformations must be explored and the potential energy, and hence forces. cannot be calculated directly by quantum-mechanical methods. Indeed, no account is given of quantization, not even of bond vibrations. Instead, potential energy functions are used, which are simple analytical functions of the distance between pairs of atoms and the types of atom (e.g. sp2 oxygen, sp3 carbon). The total energy of any configuration of the system is the sum over these pairwise interactions. Even so, it may take several hours of computer time to simulate a real process lasting IO-’Os or less. A related and somewhat cheaper approach is Monte Carlo (MC) (Metropolis et al., 1963; Premilat & Maigret, 1976). which neglects kinetic energy and can only be applied to equilibrium situations. Because of this neglect, however, conformations can be changed at will, without regard to conservation of momenta. Nonetheless, injudicious sampling of conformations would introduce a bias into the estimates of average properties which are the goal ofthis approach. As ‘Monte Carlo’ implies, this is overcome by sampling at random, until the average properties of interest converge. Nevertheless a known type of bias must be introduced, since convergence would otherwise take too long, but its effects can, and must be, abstracted later. The various types of Monte Carlo procedures are characterized by the nature of this bias: the best known is that of Metropolis et al. (1953) (see also Finney, 1982). This approach is particularly popular for treating the solvent environment, and even infinite solutions can be modelled by surrounding each solute by, say, 350 water molecules moving in a kind of ‘crystal unit cell’ to avoid surface effects as in a droplet of solution. In such a study (Hagler et al., 1980) more than 20h of computer time may be required to obtain the free energy and average conformation of the system for one solute conformer. If, as for a globular-protein-water system, the average conformation of the solute protein is also believed to be the most likely conformation, one can ‘simply’ minimize the potential energy as a function of conformation. A minimum in the potential energy generally corresponds to a minimum in free energy, and a minimum of low potential energy is generally a minimum of low free energy, but the conformations of lowest free energy and lowest potential energy may differ drastically due to entropy effects. Fortunately, having identified lowpotentid-energy minima, the associated free energy is fairly readily estimated (Hagler ef al., 1979). The problem is still non-trivial for, say, a globular protein, because of the existence of multiple local minima; one assumes that only the lower energy minima are of interest. By using a number of approximations and techniques for circumventing shallow local minima (Robson & Osguthorpe, 1979; Platt & Robson. 1982), a small protein may cost an hour or so of computer time. This still