Artificial neural network prediction of tetragonal lysozyme face growth rates

To predict unknown growth rates for the tetragonal lysozyme (110) crystal face, an artificial neural network (ANN) is designed and tested using five input variables (including protein and salt concentration, temperature, initial crystal size and angle of the (110) crystal face to the vertical). The ANN shows ninety percent prediction success for the entire data set of face growth rates, compared to a multidimensional linear regression which shows a maximum correlation coefficient, R = 0.768. In this case, using the number of categories criterion (NCC) for the standard multiple regression, traditional statistical methods can distinguish fewer than 2 categories (high and low growth rates) and cannot group or cluster the data to give more refined partitions. A non-linear surface requires at least 3 categories (high, low, and medium growth rates) to define its curvature. The outcome of the neural net, on the other hand, shows that a complex, multimodal surface (> 2000 measurements) can be reduced to a smaller, more manageable subset (< 150 significant training points) of best and worst growth conditions. The isocontours for best temperature and protein concentration values for lysozyme growth have a complex saddle, the geometrical structure of which would elude a simple experimental design based on usual gradient descent methods for finding optimum. These results suggest that a more complete optimization plan, comparable in sophistication to the protein folding optimization itself, may be required to define a global summit on the crystallization surface. Criteria for producing a general optimization strategy for protein crystallization are critically discussed and recommendations for building such an experimental design program based on neural networks are briefly put forward.