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The stochastic behavior of a molecular switching circuit with feedback.

ABSTRACT: BACKGROUND: Using a statistical physics approach, we study the stochastic switching behavior of a model circuit of multisite phosphorylation and dephosphorylation with feedback. The circuit consists of a kinase and phosphatase acting on multiple sites of a substrate that, contingent on its modification state, catalyzes its own phosphorylation and, in a symmetric scenario, dephosphorylation. The symmetric case is viewed as a cartoon of conflicting feedback that could result from antagonistic pathways impinging on the state of a shared component. RESULTS: Multisite phosphorylation is sufficient for bistable behavior under feedback even when catalysis is linear in substrate concentration, which is the case we consider. We compute the phase diagram, fluctuation spectrum and large-deviation properties related to switch memory within a statistical mechanics framework. Bistability occurs as either a first-order or second-order non-equilibrium phase transition, depending on the network symmetries and the ratio of phosphatase to kinase numbers. In the second-order case, the circuit never leaves the bistable regime upon increasing the number of substrate molecules at constant kinase to phosphatase ratio. CONCLUSION: The number of substrate molecules is a key parameter controlling both the onset of the bistable regime, fluctuation intensity, and the residence time in a switched state. The relevance of the concept of memory depends on the degree of switch symmetry, as memory presupposes information to be remembered, which is highest for equal residence times in the switched states.

SUBMITTER: Krishnamurthy S

PROVIDER: S-EPMC1904185 | biostudies-literature | 2007

REPOSITORIES: biostudies-literature

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The stochastic behavior of a molecular switching circuit with feedback.

Krishnamurthy Supriya S Smith Eric E Krakauer David D Fontana Walter W

Biology direct 20070531

<h4>Background</h4>Using a statistical physics approach, we study the stochastic switching behavior of a model circuit of multisite phosphorylation and dephosphorylation with feedback. The circuit consists of a kinase and phosphatase acting on multiple sites of a substrate that, contingent on its modification state, catalyzes its own phosphorylation and, in a symmetric scenario, dephosphorylation. The symmetric case is viewed as a cartoon of conflicting feedback that could result from antagonist ...[more]

PMID: 17540019

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Project description:Eukaryotic transcriptional networks are often large and contain several levels of feedback regulation. Many of these networks have the ability to generate and maintain several distinct transcriptional states across multiple cell divisions and to switch between them. In certain instances, switching between cell states is stochastic, occurring in a small subset of cells of an isogenic population in a seemingly homogenous environment. Given the scarcity and unpredictability of switching in these cases, investigating the determining molecular events is challenging. White-opaque switching in the fungal species Candida albicans is an example of stably inherited cell states that are determined by a complex transcriptional network and can serve as an experimentally accessible model system to study characteristics important for stochastic cell fate switching in eukaryotes. In standard lab media, genetically identical cells maintain their cellular identity (either "white" or "opaque") through thousands of cell divisions, and switching between the states is rare and stochastic. By isolating populations of white or opaque cells, previous studies have elucidated the many differences between the 2 stable cell states and identified a set of transcriptional regulators needed for cell type switching and maintenance of the 2 cell types. Yet, little is known about the molecular events that determine the rare, stochastic switching events that occur in single cells. We use microfluidics combined with fluorescent reporters to directly observe rare switching events between the white and opaque states. We investigate the stochastic nature of switching by beginning with white cells and monitoring the activation of Wor1, a master regulator and marker for the opaque state, in single cells and throughout cell pedigrees. Our results indicate that switching requires 2 stochastic steps; first an event occurs that predisposes a lineage of cells to switch. In the second step, some, but not all, of those predisposed cells rapidly express high levels of Wor1 and commit to the opaque state. To further understand the rapid rise in Wor1, we used a synthetic inducible system in Saccharomyces cerevisiae into which a controllable C. albicans Wor1 and a reporter for its transcriptional control region have been introduced. We document that Wor1 positive autoregulation is highly cooperative (Hill coefficient > 3), leading to rapid activation and producing an "all or none" rather than a graded response. Taken together, our results suggest that reaching a threshold level of a master regulator is sufficient to drive cell type switching in single cells and that an earlier molecular event increases the probability of reaching that threshold in certain small lineages of cells. Quantitative molecular analysis of the white-opaque circuit can serve as a model for the general understanding of complex circuits.

Project description:Within an isogenic population, even in the same extracellular environment, individual cells can exhibit various phenotypic states. The exact role of stochastic gene-state switching regulating the transition among these phenotypic states in a single cell is not fully understood, especially in the presence of positive feedback. Recent high-precision single-cell measurements showed that, at least in bacteria, switching in gene states is slow relative to the typical rates of active transcription and translation. Hence using the lac operon as an archetype, in such a region of operon-state switching, we present a fluctuating-rate model for this classical gene regulation module, incorporating the more realistic operon-state switching mechanism that was recently elucidated. We found that the positive feedback mechanism induces bistability (referred to as deterministic bistability), and that the parameter range for its occurrence is significantly broadened by stochastic operon-state switching. We further show that in the absence of positive feedback, operon-state switching must be extremely slow to trigger bistability by itself. However, in the presence of positive feedback, which stabilizes the induced state, the relatively slow operon-state switching kinetics within the physiological region are sufficient to stabilize the uninduced state, together generating a broadened parameter region of bistability (referred to as stochastic bistability). We illustrate the opposite phenotype-transition rate dependence upon the operon-state switching rates in the two types of bistability, with the aid of a recently proposed rate formula for fluctuating-rate models. The rate formula also predicts a maximal transition rate in the intermediate region of operon-state switching, which is validated by numerical simulations in our model. Overall, our findings suggest a biological function of transcriptional "variations" among genetically identical cells, for the emergence of bistability and transition between phenotypic states.

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The stochastic behavior of a molecular switching circuit with feedback.

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The stochastic behavior of a molecular switching circuit with feedback.

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