Conceived and designed the experiments: AK AZ JK JGO. Performed the experiments: AK AZ JK JGO. Analyzed the data: AK AZ JK JGO. Wrote the paper: AK AZ JK JGO.
The authors have declared that no competing interests exist.
Many cellular processes require decision making mechanisms, which must act reliably even in the unavoidable presence of substantial amounts of noise. However, the multistable genetic switches that underlie most decision-making processes are dominated by fluctuations that can induce random jumps between alternative cellular states. Here we show, via theoretical modeling of a population of noise-driven bistable genetic switches, that reliable timing of decision-making processes can be accomplished for large enough population sizes, as long as cells are globally coupled by chemical means. In the light of these results, we conjecture that cell proliferation, in the presence of cell–cell communication, could provide a mechanism for reliable decision making in the presence of noise, by triggering cellular transitions only when the whole cell population reaches a certain size. In other words, the summation performed by the cell population would average out the noise and reduce its detrimental impact.
Genetically identical cells may exhibit diverse phenotypic states even under almost identical environmental conditions. An extreme example of this fact is provided by genetic switches, which can operate in one of two or more states that coexist. Such genetic switching is the basis of many cellular decision-making processes, including differentiation, whereby cells change their state when driven sufficiently beyond a certain threshold. A driving source for such processes might be in the form of environmental signals. However, switching can also occur cell-autonomously, when driven by stochastic fluctuations that unavoidably affect cellular behavior. In fact, noise is ubiquitous in gene expression
Here we study the possibility that cell–cell coupling can provide a mechanism for enhancing the reliability of cellular decision making due to noise. Such a constructive role of coupling has already been discussed in the context of genetic oscillations in multicellular clocks
The mechanism outlined above requires a means of cell–cell communication in the growing cellular population. Eukaryotic cells, specially those forming part of multicellular organisms, have multiple ways to communicate; here we concentrate, for the sake of simplicity, on prokaryotic cells. Bacteria, for instance, have a mechanism of chemical communication
Here we study how the interplay between noise, population growth and cell–cell coupling controls the dynamical behavior of a population of coupled genetic relaxators. These genetic circuits can exhibit bistable or oscillatory behavior when in isolation. Our results indicate that cell growth leads to reduction of noise (see also
We consider a model, proposed in Ref.
Mutually repressing genes
The time evolution of the proteins involved in the genetic circuit represented in
The parameters α1 and α2 determine the expression strength of the toggle switch genes, while α3 represents the activation of
First we analyze the situation in which the circuits operate in a bistable regime. This means that, in the unrealistic assumption that noise is not present, the concentrations of the observed proteins have one of two possible values. Noise, however, induces frequent jumps between the two stable concentration levels
The dynamics of
We note that coupling in this system does not produce synchronization of the toggle switch dynamics because it acts incoherently with respect to it (compare the type of regulation of promoters
The previous results show that in a population of bistable switches under the influence of noise, robust decisions cannot be made unless the noise levels are reduced sufficiently so that fluctuations cannot induce jumps between both states, which can be accomplished by increasing the size of the cell population in the presence of cell–cell coupling. We can therefore envision a mechanism in which decisions are timed to occur only when the population reaches a critical size, below which noise is too large for a stable response to develop. We emphasize here that such a mechanism does not require a deterministic transition in the steady-state behavior of the system (something which quorum sensing can achieve), but only a control of the noise level via the system size. Therefore, the metabolic load in each cell would be comparable before and after the decision has been made.
In order to model this timing mechanism, we represent cell growth in a simplified way: after a given time period
The cell cycle duration is
To quantify how the decision-making dynamics changes as the population size increases, we define an order parameter,
We can also compute the fraction of cells that jump at least once in each cell division round considered. This is depicted in the bottom right panel of
We will now demonstrate that the phenomenon described in the previous paragraphs is a generic property of the interplay between noise and cell–cell communication. To that end, let us consider the case in which cells are originally (in the absence of noise) in an oscillatory regime (the
The concentration
As we have seen, oscillation death would allow decision making to occur even when the intrinsic dynamics of the cells is oscillatory. Noise, however, destroys this effect. On the other hand, in the light of the results presented in the previous section, we can expect inter-cell coupling to reduce the detrimental effect of noise and lead to robust decision making. In order to show this effect, we model again population growth by doubling the number of cells after a fixed cell cycle time
The cell cycle duration is here
Moreover, we quantify once again the restoration of bistability by computing the average number of jumps per cell and cell cycle. This is shown in the bottom left panel of
Interestingly, the top panel of
Therefore, the emergence of synchronous oscillations in a population of coupled genetic circuits
The seeming paradox of how cells can operate reliably in presence of noise is being increasingly recognized recently. Specific gene-regulatory networks have been proposed to filter transcriptional noise so as to allow, e.g., coordinated developmental decisions to take place
Here we have assumed that the signaling autoinducer molecules diffuse very fast in the extracellular medium. Hence, coupling is global throughout the cell population and the resulting clusters do not reflect any spatial distribution. On the other hand, a limited diffusion range of the autoinducer would lead to a short-range, local coupling between the cells, which would in turn provide a patterning mechanism driven by the formation of spatial clusters. Programmed pattern formation driven by finite autoinducer diffusion has already been demonstrated in a synthetic gene-regulatory circuit in
Cell–cell communication has already been used to program a particular cellular process, namely cell death, in
A second effect of the intercell coupling discussed above, is the possibility that coupled genetic oscillators exhibit a phenomenon known as
Noise-reduction due to coupling has already been discussed in a biological context, mainly in the framework of neuronal dynamics. In that context, noise due to either (i) the random opening of ion channels