Deterministic and stochastic population-level simulations of an artificial lac operon genetic network.

Michail Stamatakis,Kyriacos Zygourakis

doi:10.1186/1471-2105-12-301

Abstract

BackgroundThe lac operon genetic switch is considered as a paradigm of genetic regulation. This system has a positive feedback loop due to the LacY permease boosting its own production by the facilitated transport of inducer into the cell and the subsequent de-repression of the lac operon genes. Previously, we have investigated the effect of stochasticity in an artificial lac operon network at the single cell level by comparing corresponding deterministic and stochastic kinetic models.ResultsThis work focuses on the dynamics of cell populations by incorporating the above kinetic scheme into two Monte Carlo (MC) simulation frameworks. The first MC framework assumes stochastic reaction occurrence, accounts for stochastic DNA duplication, division and partitioning and tracks all daughter cells to obtain the statistics of the entire cell population. In order to better understand how stochastic effects shape cell population distributions, we develop a second framework that assumes deterministic reaction dynamics. By comparing the predictions of the two frameworks, we conclude that stochasticity can create or destroy bimodality, and may enhance phenotypic heterogeneity.ConclusionsOur results show how various sources of stochasticity act in synergy with the positive feedback architecture, thereby shaping the behavior at the cell population level. Further, the insights obtained from the present study allow us to construct simpler and less computationally intensive models that can closely approximate the dynamics of heterogeneous cell populations.

Highlights

The lac operon genetic switch is considered as a paradigm of genetic regulation
The insights provided from the new study allow us to construct simpler and less computationally intensive models that can closely approximate the dynamics of heterogeneous cell populations
Population Model with Stochastic Reaction Dynamics In an earlier study [10], we presented the formulation of a cell population master equation (CPME) that describes cell population dynamics and takes into account the major sources of heterogeneity: stochasticity of intracellular reactions, DNA-duplication, cell division, and random partitioning of species contents into the two daughter cells

Summary

Introduction

The lac operon genetic switch is considered as a paradigm of genetic regulation. This system has a positive feedback loop due to the LacY permease boosting its own production by the facilitated transport of inducer into the cell and the subsequent de-repression of the lac operon genes. Several experimental studies of this system over the past several decades have elucidated the underlying biomolecular interactions and a plethora of mathematical models have integrated the complex interplays of the key biochemical species in order to predict the behavior of the system [see, for example, [2]] Most of these models, pertain to the single cell behavior [see, for example the models reviewed in [3]] with a limited number of studies focusing on cell populations, or taking comparative approaches. A stochastic single cell model was developed by transforming the phenomenological deterministic rates into propensities The latter transformation is not unique, contrary to the case of a mechanistic model where the reaction rate expressions are derived on the basis of statistical mechanical assumptions [see for instance chapter X in ref. The Vilar et al models do not appear to account for the dilution of the concentrations due to cellular growth [9], for cell division and for stochastic partitioning or DNA duplication effects, which are important sources of extrinsic noise [10,11,12]

Methods

Results

Conclusion