Decoding algorithms in pooling designs with inhibitors and error-tolerance

Pooled screening for synergistic interactions subject to blocking and noise

The complex molecular networks in the cell can give rise to surprising interactions: gene deletions that are synthetically lethal, gene overexpressions that promote stemness or differentiation, synergistic drug interactions that heighten potency. Yet, the number of actual interactions is dwarfed by the number of potential interactions, and discovering them remains a major problem. Pooled screening, in which multiple factors are simultaneously tested for possible interactions, has the potential to increase the efficiency of searching for interactions among a large set of factors. However, pooling also carries with it the risk of masking genuine interactions due to antagonistic influence from other factors in the pool. Here, we explore several theoretical models of pooled screening, allowing for synergy and antagonism between factors, noisy measurements, and other forms of uncertainty. We investigate randomized sequential designs, deriving formulae for the expected number of tests that need to be performed to discover a synergistic interaction, and the optimal size of pools to test. We find that even in the presence of significant antagonistic interactions and testing noise, randomized pooled designs can significantly outperform exhaustive testing of all possible combinations. We also find that testing noise does not affect optimal pool size, and that mitigating noise by a selective approach to retesting outperforms naive replication of all tests. Finally, we show that a Bayesian approach can be used to handle uncertainty in problem parameters, such as the extent of synergistic and antagonistic interactions, resulting in schedules for adapting pool size during the course of testing.

Nonadaptive algorithms for threshold group testing with inhibitors and error-tolerance

A group test gives a positive (negative) outcome if it contains at least u (at most l) positive items, and an arbitrary outcome if the number of positive items is between thresholds l and u. This problem introduced by Damaschke is called threshold group testing. It is a generalization of classical group testing. Chen and Fu extended this problem to the error-tolerant version and first proposed efficient nonadaptive algorithms. In this article, we extend threshold group testing to the k-inhibitors model in which a test has a positive outcome if it contains at least u positives and at most k-1 inhibitors. By using (d + k - l, u; 2e + 1]-disjunct matrix we provide nonadaptive algorithms for the threshold group testing model with k-inhibitors and at most e-erroneous outcomes. The decoding complexity is O(n(u+k) log n) for fixed parameters (d, u, l, k, e).