Evolutionary Systems Biology integration of multi-level CTMC interaction models of biochemistry and cancer cell growth using Evolvix.

While biochemistry evidently affects the growth rate of cells, many biochemists routinely ignore population variation, just like population geneticists usually ignore causal details of biochemistry that underpin a change in growth rate caused by a mutation. A true EvoSysBio integration requires an explicit mechanism for how molecular reaction rates affect the reproduction rates that determine the fitness of an organism. Here we simulate a very simple and completely explicit Continuous-Time Markov Chain (CTMC) model of cancer cells whose growth rate is affected by the biochemical equilibrium between two molecular complexes. Approximately 70% of breast cancers are of a type that overexpress Estrogen Receptor-alpha (ERα). Cell growth in this type of cancer is inhibited by hormonal therapies that antagonize ERα function as a transcription factor. ERα is encoded by the ESR1 gene, which itself is a target of ERα mediated transcription. When activated by estrogen, ERα binds to the ESR1 promoter, repressing new synthesis of ERα protein. Estrogen binding also induces pathways that lead to degradation of ERα protein. This negative feedback loop is finely tuned to natural levels of estrogen and results in natural levels of growth. In breast cancer, the system is thrown off its natural course such that increased levels of ERα induce levels of cell growth that can lead to cancer. Thus, both genetic changes to the ESR1 promoter, ERα protein degradation, and biochemical changes in estrogen metabolism can effectively cause changes in cell growth rates, which can be seen as the ‘fitness’ of a cancer cell. Predicting cancer cell growth in this system raises a conceptual multi-level simulation problem, because the molecular aspects of this model need to compute the biochemistry in a way that influences growth rates at the cellular level, without resetting growth at each cell division. We present progress towards addressing this simulation challenge in pure mass-action models, which we implemented using the Evolvix model description language. We found that such models can be constructed in more than one way. We explored some candidate model properties that could aid efforts to develop abstractions for more efficiently simulating the common multi-level modeling problems behind many important biological questions. These efforts are ongoing and aim to find efficient ways of encoding and exploring such models in silico. In particular, we are investigating how architecting a new compiler for a general-purpose programming language for biology could improve the efficiency of analyzing the dynamic multi-level simulation scenarios that characterize many questions in EvoSysBio. Progress can be followed at http://evolvix.org.