Speed-Dependent Cellular Decision Making in Nonequilibrium Genetic Circuits

Despite being governed by the principles of nonequilibrium transitions, gene expression dynamics underlying cell fate decision is poorly understood. In particular, the effect of signaling speed on cellular decision making is still unclear. Here we show that the decision between alternative cell fates, in a structurally symmetric circuit, can be biased depending on the speed at which the system is forced to go through the decision point. The circuit consists of two mutually inhibiting and self-activating genes, forced by two external signals with identical stationary values but different transient times. Under these conditions, slow passage through the decision point leads to a consistently biased decision due to the transient signaling asymmetry, whereas fast passage reduces and eventually eliminates the switch imbalance. The effect is robust to noise and shows that dynamic bifurcations, well known in nonequilibrium physics, are important for the control of genetic circuits

Paradigmatic integrated signaling–transcriptional circuit switch.

<p>(A) Schematic representation: Nodes represent proteins, regulated by protein kinases with concentrations and , where and stand for transcription factors that can be phosporylated to generate and . Black lines represent transcriptional interactions, while grey lines stand for protein-protein interactions. (B) Time evolution of the input signals (black) and (grey), with . In this work is considered to have a rising time smaller than . (C) Amplitude of the transient asymmetry between signals . Here the maximal asymmetry is (see also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032779#pone-0032779-t001" target="_blank">Table 1</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032779#s4" target="_blank">Methods</a>).</p

Asymmetric decision under fluctuations.

<p>(A) Typical time series of and for two input signals that grow at different speeds. (B) Initial and final distribution functions of values for 1000 cells. (C) Dependence of the fraction of cells that end up in the high branch, on the speed of the transition (measured by ) for different values of the maximum asymmetry (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032779#pone-0032779-g001" target="_blank">Fig. 1C</a>). For all curves in (A), (B) and (C) with exception of plot (ii), (iii) and (iv), the underlying equations are Eqs. (1) to (4) with . Also shown in (C) for are the ratios for an extended version of the system of Eqs. (1) to (4) with noisy dynamics (dashed dark blue line, no symbols (iv)) and without noise (solid light blue line, no symbols (iii)) (see also Eqs. (6) to (9) in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032779#s4" target="_blank">Methods</a>). We also tested the effects of fluctuations in phosphorylation reactions, i.e. (see (C), dashed light blue line, no symbols (ii)) for the extended system of equations (Eqs. (6) to (9)) with noisy dynamics. Parameters for (A), (B) and (C) (i) are those of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032779#pone-0032779-g001" target="_blank">Fig. 1</a> and for all curves (see also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032779#pone-0032779-t001" target="_blank">Table 1</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032779#s4" target="_blank">Methods</a>). Parameters for (C) (ii), (iii) and (iv) are and (see also Eqs. (6) to (9)). For all curves and where fluctuations are considered .</p

Parameters in the decision genetic switch with external stimulation model.

<p>Parameters used in Eqs. (1) to (4) and their respective interpretation and values. See also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032779#pone.0032779-Guantes1" target="_blank">[7]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032779#pone.0032779-Andrecut1" target="_blank">[15]</a>.</p