Design principles of a genetic alarm clock.

Jaroslav Albert,Marianne Rooman

doi:10.1371/journal.pone.0047256

Abstract

Turning genes on and off is a mechanism by which cells and tissues make phenotypic decisions. Gene network motifs capable of supporting two or more steady states and thereby providing cells with a plurality of possible phenotypes are referred to as genetic switches. Modeled on the bases of naturally occurring genetic networks, synthetic biologists have successfully constructed artificial switches, thus opening a door to new possibilities for improvement of the known, but also the design of new synthetic genetic circuits. One of many obstacles to overcome in such efforts is to understand and hence control intrinsic noise which is inherent in all biological systems. For some motifs the noise is negligible; for others, fluctuations in the particle number can be comparable to its average. Due to their slowed dynamics, motifs with positive autoregulation tend to be highly sensitive to fluctuations of their chemical environment and are in general very noisy, especially during transition (switching). In this article we use stochastic simulations (Gillespie algorithm) to model such a system, in particular a simple bistable motif consisting of a single gene with positive autoregulation. Due to cooperativety, the dynamical behavior of this kind of motif is reminiscent of an alarm clock – the gene is (nearly) silent for some time after it is turned on and becomes active very suddenly. We investigate how these sudden transitions are affected by noise and show that under certain conditions accurate timing can be achieved. We also examine how promoter complexity influences the accuracy of this timing mechanism.

Highlights

Genetic circuits bear resemblance to human-made (e. g. electrical) circuits, in that both types perform a specific function or functions and are optimized to be robust against stochastic fluctuations and, in the former case, genetic mutations
The proteins encoded by a gene themselves regulate their production rate; they are referred to as transcription factors (TF)
The degradation term is linearly dependent on y, whereas the rate of production is generally a more complicated function of y, e. g. a Hill function, f (y)~yn=(kzyn), where k is called the Hill coefficient and is related to y1=2, the TF concentration at which f ~1=2; n is the Hill exponent, an integer determined by the promoter complexity

Summary

Introduction

Genetic circuits bear resemblance to human-made (e. g. electrical) circuits, in that both types perform a specific function or functions and are optimized to be robust against stochastic fluctuations and, in the former case, genetic mutations. Network motifs with positive autoregulation have been studied extensively [7,8,9,10] and their functions are well-known: (i) they slow the response time to stimuli, (ii) they increase the intrinsic noise and variability among a cell population, and (iii) those capable of supporting more than one steady state can function as bistable switches In some cases these functions work together as, for example, during an epigenic differentiation where the intrinsic noise can trigger a random transition from low to high protein concentration, giving rise to two different populations of cells [11,12,13]. Due to greater degree of freedom and parameter space, circuits comprised of several genes tend to be more robust against external fluctuations and genetic mutations Somewhere between this practical drawback and functional advantage lies an optimal design for generating controlled delayed responses. To narrow the focus of our study, we set out to answer these three specific questions: (i) Is accurate switching at all possible in this type of system? (ii) What effects, if any, does the length of the delay have on this accuracy? (iii) What are the conditions under which this accuracy is possible?

Results

Discussion

Materials and Methods