A Language for Modeling and Optimizing Experimental Biological Protocols

Automation is becoming ubiquitous in all laboratory activities, moving towards precisely defined and codified laboratory protocols. However, the integration between laboratory protocols and mathematical models is still lacking. Models describe physical processes, while protocols define the steps carried out during an experiment: neither cover the domain of the other, although they both attempt to characterize the same phenomena. We should ideally start from an integrated description of both the model and the steps carried out to test it, to concurrently analyze uncertainties in model parameters, equipment tolerances, and data collection. To this end, we present a language to model and optimize experimental biochemical protocols that facilitates such an integrated description, and that can be combined with experimental data. We provide probabilistic semantics for our language in terms of Gaussian processes (GPs) based on the linear noise approximation (LNA) that formally characterizes the uncertainties in the data collection, the underlying model, and the protocol operations. In a set of case studies, we illustrate how the resulting framework allows for automated analysis and optimization of experimental protocols, including Gibson assembly protocols.

Eco-evolutionary dynamics of a population with randomly switching carrying capacity

Environmental variability greatly influences the eco-evolutionary dynamics of a population, i.e. it affects how its size and composition evolve. Here, we study a well-mixed population of finite and fluctuating size whose growth is limited by a randomly switching carrying capacity. This models the environmental fluctuations between states of resources abundance and scarcity. The population consists of two strains, one growing slightly faster than the other, competing under two scenarios: one in which competition is solely for resources, and one in which the slow (cooperating) strain produces a public good (PG) that benefits also the fast (free-riding) strain. We investigate how the coupling of demographic and environmental (external) noise affects the population's eco-evolutionary dynamics. By analytical and computational means, we study the correlations between the population size and its composition, and discuss the social-dilemma-like ‘eco-evolutionary game’ characterizing the PG production. We determine in what conditions it is best to produce a PG; when cooperating is beneficial but outcompeted by free riding, and when the PG production is detrimental for cooperators. Within a linear noise approximation to populations of varying size, we also accurately analyse the coupled effects of demographic and environmental noise on the size distribution.

Stationary Equations for Non-Markovian Biochemical Systems

We develop a new approach for stochastic analysis of biochemical reaction systems with arbitrary distributions of waiting times between reaction events. Specifically, we derive a stationary generalized chemical master equation for a non-Markovian reaction network. Importantly, this equation allows to transform the original non-Markovian problem into a Markovian one by introducing a mean reaction propensity function for every reaction in the network. Furthermore, we derive a stationary generalized linear noise approximation for the non-Markovian system, which is convenient to the direct estimation of the stationary noise in state variables. These derived equations can have broad applications, and exemplars of two representative non-Markovian models provide evidence of their applicability.