A computational method for the investigation of multistable systems and its application to genetic switches

Abstract

BackgroundGenetic switches exhibit multistability, form the basis of epigenetic memory, and are found in natural decision making systems, such as cell fate determination in developmental pathways. Synthetic genetic switches can be used for recording the presence of different environmental signals, for changing phenotype using synthetic inputs and as building blocks for higher-level sequential logic circuits. Understanding how multistable switches can be constructed and how they function within larger biological systems is therefore key to synthetic biology.ResultsHere we present a new computational tool, called StabilityFinder, that takes advantage of sequential Monte Carlo methods to identify regions of parameter space capable of producing multistable behaviour, while handling uncertainty in biochemical rate constants and initial conditions. The algorithm works by clustering trajectories in phase space, and iteratively minimizing a distance metric. Here we examine a collection of models of genetic switches, ranging from the deterministic Gardner toggle switch to stochastic models containing different positive feedback connections. We uncover the design principles behind making bistable, tristable and quadristable switches, and find that rate of gene expression is a key parameter. We demonstrate the ability of the framework to examine more complex systems and examine the design principles of a three gene switch. Our framework allows us to relax the assumptions that are often used in genetic switch models and we show that more complex abstractions are still capable of multistable behaviour.ConclusionsOur results suggest many ways in which genetic switches can be enhanced and offer designs for the construction of novel switches. Our analysis also highlights subtle changes in correlation of experimentally tunable parameters that can lead to bifurcations in deterministic and stochastic systems. Overall we demonstrate that StabilityFinder will be a valuable tool in the future design and construction of novel gene networks.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-016-0375-z) contains supplementary material, which is available to authorized users.

Multistability in cellular differentiation enabled by a network of three mutually repressing master regulators

“…In the Waddington landscape perspective, these three 'double positive' states can lie between two terminal 'single positive' states and can promote trans-differentiation among them (Fig 10). A previous modeling effort also suggested these possible six states for a toggle triad [16]; our approach through RACIPE enables two additional insights: a) a higher relative frequency of 'single positive' states as compared to the 'double positive' ones, and b) increase in 'double positive' states in presence of self-activation.…”

“…This 'intermediate' progenitor state is often 'metastable' and can differentiate to one of the two relatively more stable terminal states [2]. However, the dynamics of networks giving rise to three distinct states with a common progenitor have not been relatively as well-studied [16], despite instances of such decision-making seen in differentiation of CD4 expressing T-cells [17,18].…”

Automated design of synthetic microbial communities

“…Approximate Bayesian computation with sequential Monte Carlo sampling (ABC SMC) is a model selection and parameterisation method that has been applied to synthetic biology systems [33]. We have previously used ABC SMC to identify robust genetic oscillators in two and three-gene networks [34], and to identify parameter regions that give rise to multistable genetic switches [35]. ABC SMC also allows us to derive design principles that are key to producing the desired behaviour [34,35].…”

Computational study of parameter sensitivity in DevR regulated gene expression

“…Role of parameter robustness has also been investigated in neurogenic network [10]. A Monte Carlo based computation tool has been developed to identify regions of parameter space that can generate multi-stable states while taking into account fluctuations in parameter space and initial conditions [11].…”