Genotype-to-Phenotype Research Strategies

Standard (logistic) regression connects genotype with phenotype in a direct way, thus greatly simplifying biology. In fact, genes code for proteins or RNA ("gene products") which may interact in a variety of ways and influence the phenotype only after a cascade of intermediate steps. Molecular-genetic Neural Networks (NNs) generalize standard regression analysis in a very natural way by (1) implementing multistage gene products through one or more intermediate "layer(s)", and (2) allowing for (linear/nonlinear) interactions between genes and between gene products [e.g., Freeman and Skapura 1991].

Molecular-Genetic Neural Networks

It is the advantage of NNs that the specific knowledge about the cascade of intermediate steps, which ultimately lead from genotype to phenotype, can be incomplete or even unknown ("hidden layers"). In this case, the model’s gene product layers lack direct interpretation and act in the sense of a "black box" [Lee 2004]. However, the influence of each single gene on the phenotype, as well as the interactions between genes, can always be quantified and detailed through analysis of the weight matrices of the fitted model. In the simplest form, molecular-genetic NNs connect each gene with its gene product, while these gene products contribute to a one-dimensional phenotype, for example, IgM level or time to response to treatment. Interactions between gene products are modeled explicitly by implementing one or more gene product layers. Also, the model can easily be modified to meet the specific requirements of multidimensional phenotypes, for example, the various forms of syndrome patterns underlying major depression, schizophrenia or bipolar illness.

Backpropagation Algorithm

NN connects the "neurons" of input and output layers via one or more "hidden" layers. All outputs are computed using sigmoid thresholding of the scalar product of the corresponding weight and input vectors. Outputs at stage "s" are connected to each input of stage "s+1". NN connections are realized through (1) weight matrices and (2) model fitting algorithms minimizing an error function in the weight space (goodness of fit). The most popular fitting strategy, the backpropagation algorithm, looks for the minimum of the error function using the method of gradient descent. The basic algorithm is:

Selecting an Initial Configuration

In principal, NNs may be used for selecting genes (SNPs) out of a pool of candidates. The computational burden of such an approach can become unrealistic for larger data sets, in particular when reproducibility has to be tested through k-fold cross-validation. On the other hand, molecular-genetic NNs possess a sufficient performance when an initial gene configuration is available —either through a priori knowledge or derived through other methods— so that the initial configuration can be optimized by systematically adding or removing genes.

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