Linear and Nonlinear Regression for Combinatorial Optimization Problem of Multiple Transgenesis

Abstract

Combinatorial optimization problem is a difficult class of problems from which to obtain exact solutions, but such problems often arise in biotechnology, for example, it is often necessary to find optimal combinations of genes in transgenics to improve production of a useful compound by microorganisms. In the cases of 20 candidate genes for introduction into cells, the number of possible combinations of introduced genes is approximately 106. Testing all of their combinations by experimental observation is impossible practically. A few combinations are observed experimentally for large numbers of possible combinations generally. We tested two methods for the prediction of effects of transgenes: multivariate linear regression and the RBF (Radial Basis Function) network, with a simulated and an unpublished experimentally observed dataset of transgenic yeast. Results show that RBF network can detect a special gene (introduced gene) at the five percent significance level when the gene causes production values that are 1.5 times greater than other genes for the simulated dataset. Prediction by RBF network causes over-learning for larger numbers of learning data, however, it is superior than that by the linear regression model at the best condition.