To avoid having to do an exhaustive search on all single stuck at faults, we LY450139, VX-702 perform an All SAT on the circuit S where we constrain the output to be not Z0. We now form a new CNF S1 S C1 C2. The result ing All SAT on S1 is a list of all non redundant single stuck at faults and their faulty output. These faults are flagged for drug simulation using any of the next three cases.
The results from this case can also be used immedi ately in several ways. For example, this method classifies for each single stuck at fault whether it is redundant or non redundant. That is, any fault which is redundant does not produce an incorrect output, and can be ignored from a therapy standpoint. In a second example, the faulty output from the stuck at model can be com pared to a previously measured output from expression data, in order to identify which genes are potentially faulty. This information can be used to target genes for potential drug development, avoiding genes that are untestable. Case 2 Fault rectification with fewest drugs In the presence of a particular fault, the problem is determining whether a selection of drugs can rectify the circuit, i. e. change the faulty output to the correct out put. If this is not possible, we want to obtain the best or closest output to the correct output, by using drugs. To do this, we guide the WPMS solver by assign ing weights to the output states. For example, in the GF network used in our experiments, the fault free output Z0 is assigned the highest weight and remaining output states are assigned decreasing weights based on increasing Hamming distance from the fault free output. We assume that faulty states that have a larger Hamming distance have a more pronounced cancer proliferative effect. Additionally, the selection of drugs to achieve the best output should use the least number of drugs to mini mize the side effects on the patient. To incorporate this in the WPMS solver, each drug that is not selected is given a weight of 1. The GF network example has 6 drugs, thus if no drugs are selected, then the cumulative drug weight is 6. Likewise, if all drugs are selected, the drug weight is 0. Note that the output and drug weights are assigned in such a way as to avoid the situation where a less desirable output is chosen over a higher weight output with more drugs. We assume that from a clinical standpoint, the priority is to first produce the best possible output, and secondarily to use the fewest drugs required for that output.
All faulty circuits with non redundant faults from Case 1 are augmented with the output and drug weights and simulated using WPMS. The WPMS solver will implicitly and deterministically find the assignment of drugs that achieves the best possible output and with the fewest drugs. The output values, selected drugs, and highest weight of the fault drug circuits are recorded and com pared with the drug free circuits. An immediate result from this method is that a fault where the fault drug cir cuit which obtains its best output with zero drugs is in fact an untestable fault, wherein no drug combination can improve the output.