Regulatory networks of integer nonlinear programming(RNINLP): A model to analyze gene regulatory networks of breast cancer metastasis

There are more and more data from Human Genome Project that we need better methods to deal with. Some mathematical models have been presented to analyze gene regulatory networks, such as Boolean networks Bayesian networks, differential equation, weight matrices, etc. Some of the models could describe some rules of the genetic regulatory relations properly, such as Bayesian networks, differential equation, but the rest did not work very well. It is thus necessary to consider some new mathematical models to estimate the gene regulatory relations according to some experimental data. Here we have utilized the entropy information from gene data of breast cancer metastasis to get the weights of all the genes, and set up a RNINLP model in which minimum error is regarded as objective function to search for the regulatory relation in the genes, and then sieved regulatory genes by coefficient correlation model. Using the programs of LINGO8.0 and MATLAB7.0, we got a gene regulatory network of the 27 genes related to the breast cancer metastasis. We found that there were 25 pairs of genes exiting regulatory relation and 11 pairs of genes being mutual promotion effect. RNINLP utilizes almost all the information of the data, so it can describe the regulatory relation of genes with coefficient correlation model, and the model can be extended to even more complicated gene regulatory networks.