title: A computational method for the investigation of multistable systems and its application to genetic switches.
abstract: Genetic 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.
  
  
  
  Here 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.
  
  
  
  Our 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.
authors.affiliation: Department of Cell and Developmental Biology, University College London, Gower Street, London, WC1E 6BT, UK.
authors.forename: Miriam
authors.initials: M
authors.lastname: Leon
authors.affiliation: Department of Cell and Developmental Biology, University College London, Gower Street, London, WC1E 6BT, UK.
authors.forename: Mae L
authors.initials: ML
authors.lastname: Woods
authors.affiliation: Department of Cell and Developmental Biology, University College London, Gower Street, London, WC1E 6BT, UK.
authors.forename: Alex J H
authors.initials: AJ
authors.lastname: Fedorec
authors.affiliation: Department of Cell and Developmental Biology, University College London, Gower Street, London, WC1E 6BT, UK. christopher.barnes@ucl.ac.uk.|Department of Genetics, Evolution and Environment, University College London, Gower Street, London, WC1E 6BT, UK. christopher.barnes@ucl.ac.uk.
authors.forename: Chris P
authors.identifier: 0000-0002-9459-1395
authors.initials: CP
authors.lastname: Barnes
mesh_terms: D019295:Computational Biology / Q000379:methods*; D053263:Gene Regulatory Networks; D009010:Monte Carlo Method; D013269:Stochastic Processes; D058615:Synthetic Biology
keywords: Design of genetic circuits; Genetic switches; Sequential Monte Carlo