Statistical physics of a model binary genetic switch with linear feedback

Visco, Paolo; Allen, Rosalind J.; Evans, Martin R.

doi:10.1103/physreve.79.031923

Cited by 13 publications

(15 citation statements)

References 42 publications

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“…[28] for the generating function of the distribution of mRNA transcribed by an on-off gene (i.e., ignoring protein synthesis and regulation). Similar results utilizing generating function methods that involve F have been obtained for a variety of linear feedback regulation models [2][3][4][5]. For p = 0, we notice that there is a solution of the form y(t) = F (a, b, t) provided that c = 0.…”

Section: A Wkb Approximationsupporting

confidence: 77%

Bistable switching asymptotics for the self regulating gene

Newby¹

2015

J. Phys. A: Math. Theor.

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A simple stochastic model of a self regulating gene that displays bistable switching is analyzed. While on, a gene transcribes mRNA at a constant rate. Transcription factors can bind to the DNA and affect the gene's transcription rate. Before an mRNA is degraded, it synthesizes protein, which in turn regulates gene activity by influencing the activity of transcription factors. Protein is slowly removed from the system through degradation. Depending on how the protein regulates gene activity, the protein concentration can exhibit noise induced bistable switching. An asymptotic approximation of the mean switching rate is derived that includes the pre exponential factor, which improves upon a previously reported logarithmically accurate approximation. With the improved accuracy, a uniformly accurate approximation of the stationary probability density, describing the gene, mRNA copy number, and protein concentration is also obtained.

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Section: A Wkb Approximationsupporting

confidence: 77%

Bistable switching asymptotics for the self regulating gene

Newby¹

2015

J. Phys. A: Math. Theor.

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“…This equation is similar to those found in (20,21) and the steady-state distribution can be solved via a generating function approach (see SI Text).…”

Section: Characterization Of the Network's Steady-state Propertiesmentioning

confidence: 93%

Energetic costs of cellular computation

Mehta

Schwab

2012

Proc. Natl. Acad. Sci. U.S.A.

206

256

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Cells often perform computations in order to respond to environmental cues. A simple example is the classic problem, first considered by Berg and Purcell, of determining the concentration of a chemical ligand in the surrounding media. On general theoretical grounds, it is expected that such computations require cells to consume energy. In particular, Landauer's principle states that energy must be consumed in order to erase the memory of past observations. Here, we explicitly calculate the energetic cost of steady-state computation of ligand concentration for a simple two-component cellular network that implements a noisy version of the Berg-Purcell strategy. We show that learning about external concentrations necessitates the breaking of detailed balance and consumption of energy, with greater learning requiring more energy. Our calculations suggest that the energetic costs of cellular computation may be an important constraint on networks designed to function in resource poor environments, such as the spore germination networks of bacteria.T he relationship between information and thermodynamics remains an active area of research despite decades of study (1-4). An important implication of the recent experimental confirmation of Landauer's principle, relating the erasure of information to thermodynamic irreversibility, is that any irreversible computing device must necessarily consume energy (2, 3). The generality of Landauer's argument suggests that it is true regardless of how the computation is implemented. A particularly interesting class of examples relevant to systems biology and biophysics is that of intracellular biochemical networks that compute information about the external environment. These biochemical networks are ubiquitous in biology, ranging from the quorumsensing and chemotaxis networks in single-cell organisms to networks that detect hormones and other signaling factors in higher organisms.A fundamental issue is the relationship between the information processing capabilities of these biochemical networks and their energetic costs (5-8). It is known that energetic costs place important constraints on the design of physical computing devices as well as on neural computing architectures in the brain and retina (9-11), suggesting that these constraints may also influence the design of cellular computing networks.The best studied example of a cellular computation is the estimation of the steady-state concentration of a chemical ligand in the surrounding environment (12)(13)(14). This problem was first considered in the seminal paper by Berg and Purcell who showed that the information a cell can acquire about its environment is fundamentally limited by stochastic fluctuations in the occupancy of the membrane-bound receptor proteins that detect the ligand (12). In particular, they considered the case of a cellular receptor that binds ligands with a concentration-dependent rate k off 4 and unbinds particles at a uniform rate k off 4 (see Fig. 1). They argued that cells could estimate the ambient che...

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“…that our rare event is a Poisson process). This is not always the case [104,105]. It remains to be seen whether FFS-like methods can be devised for non-Poissonian rare event problems.…”

Section: Challenges and Future Directionsmentioning

confidence: 99%

Forward flux sampling for rare event simulations

Allen

Valeriani

Wolde

2009

J. Phys.: Condens. Matter

423

447

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Abstract. Rare events are ubiquitous in many different fields, yet they are notoriously difficult to simulate because few, if any, events are observed in a conventional simulation run. Over the past several decades, specialised simulation methods have been developed to overcome this problem. We review one recentlydeveloped class of such methods, known as Forward Flux Sampling. Forward Flux Sampling uses a series of interfaces between the initial and final states to calculate rate constants and generate transition paths, for rare events in equilibrium or nonequilibrium systems with stochastic dynamics. This review draws together a number of recent advances, summarises several applications of the method and highlights challenges that remain to be overcome.

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Statistical physics of a model binary genetic switch with linear feedback

Cited by 13 publications

References 42 publications

Bistable switching asymptotics for the self regulating gene

Bistable switching asymptotics for the self regulating gene

Energetic costs of cellular computation

Forward flux sampling for rare event simulations

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