The increasing use of computers in pharmaceutics was the topic of a science symposium, held on September 13. It was chaired by Professor Ray Rowe, the Conference Science Chairman
The increase in the use of computers in pharmaceutics was largely a consequence of the increase in computer power, which had been exponential over the past 40 years, Professor ROWE said. Memory capacity had increased by a factor of 109 over this period, and the operational speed had increased by the same amount. The cost per arithmetical operation had correspondingly decreased by the same factor, and there seemed to be no end in sight to this continual improvement. One result was that computational tasks that were unthinkable as recently as 10 years ago were now an everyday occurrence.
The first presentation was an account of the use of computation in the field of crystallisation, with particular reference to the problems generated by the existence of polymeric forms.
Dr FRANK LEUSEN (Molecular Simulations Ltd, Cambridge) pointed out that polymorphs of drug substances could be the cause of expensive delays in development, and could also cause regulatory difficulties as their differing solubilities could alter therapeutic performance. For example, he said, there were 36 known polymorphic forms of chocolate, only one of which, form 5, was the edible variety, as its melting-point was just below physiological temperature. When its temperature in storage was inadvertently raised, perhaps by being left in a hot car, and then subsequently lowered, a characteristic white bloom or spots could appear: this indicated that polymorph 6 had been formed. Polymorph 6 had a melting point slightly higher than body temperature, and so had a much less pleasant, waxy feel in the mouth.
More seriously from a pharmaceutical viewpoint, the author described a range of computer-driven methods of finding the stable crystal lattice arrangements of a given compound once its molecular structure was known. These included both the normal stable form and, in addition, any possible polymorphs. Four routes existed from the molecular structure to the lattice arrangement, depending upon the physical form of the new substance. The most straightforward case was when a reasonably good quality single crystal could be made. An X-ray diffraction pattern could be obtained and compared with the patterns synthesised by a computer program that generated a vast number of structures and found the best fit between the calculated and known experimental patterns.
This was a highly automated, rapid and successful method, but very often the required crystal could not be made: what was available might effectively only be a powder, and X-ray powder diffraction was not as informative as diffraction from a good crystal.
The author's second and third methods were dependent on whether the powder data were, of their kind, of high or low quality. High quality powder patterns could be handled by a software package called Powdersolve, which produced an adequate structure by using lattice energy calculations as a supplement. Low quality patterns were still of value, as they could be used to select the best candidate from a range of structures that the computations suggested.
The fourth method was to calculate the crystal structure ab initio which, at present, was only possible for comparatively small, rigid, non-ionic molecules. For all the methods, the computation time increased dramatically with the number of degrees of freedom of the molecule. Glutamic acid, for example, had 10 degrees of freedom, which was the total of the internal flexural and rotational motions available to its molecule, which gave a calculation time of three minutes. For cimetidine, with 14, the time increased to 220 minutes, and for a compound with 18 degrees of freedom, it reached 11,400 minutes.
The prediction of the existence of polymorphs, as opposed to the most stable structure, was more difficult. Effectively, it involved exploring a heavily populated space of possible structures. Luckily, most organic compounds tended to crystallise in only a few of the possible space groups: 75 per cent were in the most popular five groups, and 95 per cent fell into the top 15. The principal difficulty was to decide the order in which the postulated structures should be placed with regard to their energy, because there could be several with similar values so that the differences between them were approaching the limits of discrimination of the method.
The second presentation was about the topic of crystal engineering, and was also largely concerned with the problem of polymorphism. Professor ROGER DAVEY (chemical engineering department, UMIST, Manchester) moved away from the computational aspects of crystal structure to give an account of the rather strange behaviour of the two main polymorphs of 2,6-dihydroxybenzoic acid. One of the polymorphs was deposited from solutions in toluene, and the other from solutions in chloroform, and, in addition, one form appeared when a beaker-sized apparatus was used, and the other when the container was a 20-litre crystallisation vessel.
The compound had one carboxyl group and two hydroxyls, and two conformations. In form 1, the carboxyl group was free, while the hydroxyls were loosely bound and the resulting compound tending to form dimers that packed in a herring-bone fashion. This form was the product of crystallisation from toluene. In form 2, the carboxyl group and one of the hydroxyls were bound, while the other hydroxyl was free, resulting in the molecules then tending to associate in long chains linked by weak bonds. The X-ray diffraction patterns of the two forms were very different, as would be expected.
With regard to solvent interactions, computer calculations showed that form 1, the dimer, would be expected to be more soluble in toluene and the chain form, form 2, in chloroform. This was established by finding the 4kcal interaction surface between the molecule and the solvent. In addition, the behaviour of the UV extinction coefficient in toluene was fairly regular, with Beer's law being obeyed up to quite high concentrations, whereas in chloroform there was a fall, then a rise, then another fall, indicating that chloroform, with its rather acidic proton, solvated the dimers.
When carrying out a crystallisation, form 1 would usually come out of solution first, and then be gradually replaced by form 2, which was the more stable polymorph. When performed in a 100ml beaker, the transformation, which occured by a gradual redissolution and second deposition, took about 20 minutes. When the process was scaled up to a size of 20L, the same transformation took 20 hours. The explanation for this was that the magnetic stirrer used in the beaker was quite a good grinding mill, so that the tiny crystals of form 2 that grew on the surface of the crystals of form 1 were knocked off and became nuclei for the direct further deposition of form 2 from the mother liquor. The impeller of the larger vessel, being centrally located and not touching the vessel base, did not remove the small crystals from the larger, and so the transformation time was almost two orders of magnitude longer.
The properties of solid materials were obviously a function of the arrangement of the molecules on the crystal lattice and the forces between them. Professor PETER YORK (University of Bradford) spoke about prediction of parameters such as surface polarity when a crystal was fractured, and mechanical properties, such as elasticity and plasticity, that were of importance in the secondary processing of bulk materials, for example, milling and dissolution behaviour.
For any material, as its particle size was reduced, there would be a critical diameter below which the particles would no longer break, but would undergo plastic deformation. (This diameter was about 15 micro-metres for propranolol hydrochloride, 20 to 25 for lactose, and as much as 1,000 for polymers.)
An important quantity for any crystalline material was the attachment energy, which was the energy released (per mole) when a fresh layer of the appropriate molecules were added to a crystal plane. Such energies could be calculated from the lattice structure and the intermolecular forces, and the plane for which the attachment energy was the smallest should be the predominating fracture plane. The functional chemical groups exposed would be those at the break, and they could be examined by inverse phase chromatography, in which the milled product was the stationary phase, and various probe substances of different polarity were passed through the packed bed, their residence times indicating the character of the surface produced by fracture.
A computational approach to the elastic constants of crystals, which underlie Young's modulus, and to their cohesive energy densities, which related to indentation hardness, had also proved fruitful, particularly in the field of tableting. It was possible, from the crystal structure and a knowledge of the force field of the molecules, to form a compliance matrix and to calculate its second derivatives. This gave the components of the required stress-strain relationships for the solid. Such calculations had been performed for aspirin, carbamazepine and sulphathiazoles I and III.
The final presentation of the symposium was given by Professor ROWE (Zeneca Pharmaceuticals, Macclesfield; University of Bradford and Conference Science Chairman), who described several uses of computation in the field of dosage form design, notably tablets, which were currently the administration route for 48 per cent of the therapeutic drug usage in the UK.
By means of a triangular diagram, he illustrated the mixture of data, theory, judgment, understanding, experience and heuristics that together made up the art and science of formulation, and that, when taken up into the vast memory and processing capability of modern computers, constituted an expert system.
Several such systems existed that, when fed with details of the physical and chemical properties of a new drug and the proposed excipients, generated a formulation as good as any produced by a human formulator. While the expert system was good for the suggestion of an initial formulation, the neural network was better for their modelling, and for extremely data-rich situations. Such a network emulated the learning mechanism that was thought to take place in animals: the computer provided a first layer of simulated neurones that were fed with initial data, with each datum being loaded with its own weighting factor to reflect the importance assigned to it. The neurones then fired and provided the input to a second layer, the members of which fired when they received a sufficiently large input from those in the first layer. The connections between the neurones changed progressively according to the amount of traffic on each particular pathway and according to the output produced at any given time being satisfactory.
The system gradually evolved into one that had gained the capability of designing formulations, and two or three neuronal layers were usually enough. Indeed, the system could be so effective that, if run for a long period, it could become overtrained, and, although very good within its original sphere in which it had memorised all the data, it lost its capability to be in any degree innovative.
A further use of computers was in the modelling of a compaction operation, using a finite-element method in which the particles to be compacted and the die in which the process was to be carried out were covered with a set of points, all joined by lines to form a network. As the punch descended, the computer allowed each small element to deform according to its own appropriate elastic or plastic properties and to the local stress pattern that had arisen as a result of the stepwise calculations that had already been made. The examples shown included hard particles that were deformable with difficulty, brittle particles that would fracture, and soft particles that would deform to fill the voids between particles of other types. All started out spherical, in a more or less regular packing, and ended up as simulated compressed tablets; the various modes of deformation had given useful information on the manufacture of real tablets.
In response to questions, Professor Rowe indicated that the expert system and the neural network had been tested on just about all the excipients that one might come across, and that the tablet simulation program had not yet completed its testing: its simulation results were still undergoing review.