Synthesis of biological models from mutation experiments

Executable biology presents new challenges to formal methods. This paper addresses two problems that cell biologists face when developing formally analyzable models. First, we show how to automatically synthesize a concurrent in-silico model for cell development given in-vivo experiments of how particular mutations influence the experiment outcome. The problem of synthesis under mutations is unique because mutations may produce non-deterministic outcomes (presumably by introducing races between competing signaling pathways in the cells) and the synthesized model must be able to replay all these outcomes in order to faithfully describe the modeled cellular processes. In contrast, a "regular" concurrent program is correct if it picks any outcome allowed by the non-deterministic specification. We developed synthesis algorithms and synthesized a model of cell fate determination of the earthworm C. elegans. A version of this model previously took systems biologists months to develop. Second, we address the problem of under-constrained specifications that arise due to incomplete sets of mutation experiments. Under-constrained specifications give rise to distinct models, each explaining the same phenomenon differently. Addressing the ambiguity of specifications corresponds to analyzing the space of plausible models. We develop algorithms for detecting ambiguity in specifications, i.e., whether there exist alternative models that would produce different fates on some unperformed experiment, and for removing redundancy from specifications, i.e., computing minimal non-ambiguous specifications. Additionally, we develop a modeling language and embed it into Scala. We describe how this language design and embedding allows us to build an efficient synthesizer. For our C. elegans case study, we infer two observationally equivalent models expressing different biological hypotheses through different protein interactions. One of these hypotheses was previously unknown to biologists.