Biomedical Engineering Reference
In-Depth Information
4.4
Chapter Summary
In this chapter, we have presented a method for inferring and ranking predictors from
normalized continuous gene expression data using Zhegalkin functions. Our algo-
rithm explores all possible predictor combinations for a target gene, and measures the
error of each predictor based on its best fitting Boolean logic function (represented as
a Zhegalkin function) using the gene expression data (linear or sigmoid representa-
tion). The predictors are then ranked by error to determine a list of top predictors for
the target gene, from which a single predictor can be chosen, or can be used to guide
future expression measurement experiments. We validate our Zhegalkin predictor
inference method on synthetic data from the mutated mammalian network and show
how results can be used to rank and select predictors for genes. We also demonstrate
our method on actual data from the melanoma network (Table 4.27 , 4.28 , 4.29 ).
Additionally, the ranked list can be used to improve predictor set inference (see
Chap. 2) by assigning weights to predictors relative to the MSE. The SAT formulation
can be modified to a Weighted Partial Max-SAT (WPMS) formulation to select
predictors that satisfy GRN constraints as well as minimize the overall MSE weights.
The work presented in this and preceding chapters have focused on inferring the
GRN using logic synthesis tools. An accurate representation of the GRN is necessary
to understand how genes are regulated in a system, how regulation can fail leading
to disease, and more importantly, how to control the GRN to treat the disease. In the
next chapter, we look at applying logic synthesis to the problem of GRN control. In
particular, cancer is described using the stuck-at fault model, and weighted partial
Max-SAT algorithms based on ATPG techniques are used to determine optimum
drug selection for cancer therapy.
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