title: Analytic framework for a stochastic binary biological switch.
abstract: We propose and solve analytically a stochastic model for the dynamics of a binary biological switch, defined as a DNA unit with two mutually exclusive configurations, each one triggering the expression of a different gene. Such a device has the potential to be used as a memory unit for biological computing systems designed to operate in noisy environments. We discuss a recent implementation of this switch in living cells, the recombinase addressable data (RAD) module. In order to understand the behavior of a RAD module we compute the exact time-dependent joint distribution of the two expressed genes starting in one state and evolving to another asymptotic state. We consider two operating regimes of the RAD module, a fast and a slow stochastic switching regime. The fast regime is aggregative and produces unimodal distributions, whereas the slow regime is separative and produces bimodal distributions. Both regimes can serve to prepare pure memory states when all cells are expressing the same gene. The slow regime can also separate mixed states by producing two subpopulations, each one expressing a different gene. Compared to the genetic toggle switch based on positive feedback, the RAD module ensures more rapid memory operations for the same quality of the separation between binary states. Our model provides a simplified phenomenological framework for studying RAD memory devices and our analytic solution can be further used to clarify theoretical concepts in biocomputation and for optimal design in synthetic biology.
authors.affiliation: Departamento de Matemática Aplicada, Universidade de São Paulo, São Paulo, Brazil.
authors.forename: Guilherme C P
authors.initials: GC
authors.lastname: Innocentini
authors.affiliation: CBS, CNRS UMR 5048 - UM - INSERM U 1054, Montpellier, France.
authors.forename: Sarah
authors.initials: S
authors.lastname: Guiziou
authors.affiliation: CBS, CNRS UMR 5048 - UM - INSERM U 1054, Montpellier, France.
authors.forename: Jerome
authors.initials: J
authors.lastname: Bonnet
authors.affiliation: DIMNP, UMR CNRS 5235, University of Montpellier, Montpellier, France.
authors.forename: Ovidiu
authors.initials: O
authors.lastname: Radulescu
mesh_terms: D015870:Gene Expression / Q000235:genetics; D008957:Models, Genetic; D013269:Stochastic Processes; D058615:Synthetic Biology