Noise-induced transitions in gene circuits: A perturbative approach for slow noise.

We consider a generic class of gene circuits affected by nonlinear extrinsic noise. To address this nonlinearity we introduce a general perturbative methodology based on assuming timescale separation between noise and gene dynamics, with fluctuations exhibiting a large but finite correlation time. We apply this methodology to the case of the toggle switch, and by considering biologically relevant log-normal fluctuations, we find that the system exhibits noise-induced transitions.

Effect of decreasing population growth-rate on deforestation and population sustainability.

We consider the effect of non-constant parameters on the human-forest interaction logistic model coupled with human technological growth introduced in [1]. In recent years in fact, a decrease in human population growth rate has emerged which can be measured to about 1.7% drop per year since 1960 value, which coincides with latest UN projections for next decades up to year 2100 [2].

Effect of Ergodic and Non-Ergodic Fluctuations on a Charge Diffusing in a Stochastic Magnetic Field.

In this paper, we study the basic problem of a charged particle in a stochastic magnetic field. We consider dichotomous fluctuations of the magnetic field where the sojourn time in one of the two states are distributed according to a given waiting-time distribution either with Poisson or non-Poisson statistics, including as well the case of distributions with diverging mean time between changes of the field, corresponding to an ergodicity breaking condition. We provide analytical and numerical results for all cases evaluating the average and the second moment of the position and velocity of the particle.

Bimodality in gene expression without feedback: from Gaussian white noise to log-normal coloured noise.

Extrinsic noise-induced transitions to bimodal dynamics have been largely investigated in a variety of chemical, physical, and biological systems. In the standard approach in physical and chemical systems, the key properties that make these systems mathematically tractable are that the noise appears linearly in the dynamical equations, and it is assumed Gaussian and white. In biology, the Gaussian approximation has been successful in specific systems, but the relevant noise being usually non-Gaussian, non-white, and nonlinear poses serious limitations to its general applicability.

Deforestation and world population sustainability: a quantitative analysis.

In this paper we afford a quantitative analysis of the sustainability of current world population growth in relation to the parallel deforestation process adopting a statistical point of view. We consider a simplified model based on a stochastic growth process driven by a continuous time random walk, which depicts the technological evolution of human kind, in conjunction with a deterministic generalised logistic model for humans-forest interaction and we evaluate the probability of avoiding the self-destruction of our civilisation. Based on the current resource consumption rates and best estimate of technological rate growth our study shows that we have very low probability, less than 10% in most optimistic estimate, to survive without facing a catastrophic collapse.

An ongoing role for Wnt signaling in differentiating melanocytes in vivo.

A role for Wnt signaling in melanocyte specification from neural crest is conserved across vertebrates, but possible ongoing roles in melanocyte differentiation have received little attention. Using a systems biology approach to investigate the gene regulatory network underlying stable melanocyte differentiation in zebrafish highlighted a requirement for a positive-feedback loop involving the melanocyte master regulator Mitfa. Here, we test the hypothesis that Wnt signaling contributes to that positive feedback.

Know the Single-Receptor Sensing Limit? Think Again.

How cells reliably infer information about their environment is a fundamentally important question. While sensing and signaling generally start with cell-surface receptors, the degree of accuracy with which a cell can measure external ligand concentration with even the simplest device-a single receptor-is surprisingly hard to pin down. Recent studies provide conflicting results for the fundamental physical limits.

Information transfer through a signaling module with feedback: A perturbative approach.

Signal transduction in biological cells is effected by signaling pathways that typically include multiple feedback loops. Here we analyze information transfer through a prototypical signaling module with biochemical feedback. The module switches stochastically between an inactive and active state; the input to the module governs the activation rate while the output (i.

Accurate encoding and decoding by single cells: amplitude versus frequency modulation.

Cells sense external concentrations and, via biochemical signaling, respond by regulating the expression of target proteins. Both in signaling networks and gene regulation there are two main mechanisms by which the concentration can be encoded internally: amplitude modulation (AM), where the absolute concentration of an internal signaling molecule encodes the stimulus, and frequency modulation (FM), where the period between successive bursts represents the stimulus. Although both mechanisms have been observed in biological systems, the question of when it is beneficial for cells to use either AM or FM is largely unanswered.

Memory improves precision of cell sensing in fluctuating environments.

Biological cells are often found to sense their chemical environment near the single-molecule detection limit. Surprisingly, this precision is higher than simple estimates of the fundamental physical limit, hinting towards active sensing strategies. In this work, we analyse the effect of cell memory, e.

Dynamics of natural killer cell receptor revealed by quantitative analysis of photoswitchable protein.

Natural Killer (NK) cell activation is dynamically regulated by numerous activating and inhibitory surface receptors that accumulate at the immune synapse. Quantitative analysis of receptor dynamics has been limited by methodologies that rely on indirect measurements such as fluorescence recovery after photobleaching. Here, we report an apparently novel approach to study how proteins traffic to and from the immune synapse using NK cell receptors tagged with the photoswitchable fluorescent protein tdEosFP, which can be irreversibly photoswitched from a green to red fluorescent state by ultraviolet light.

Transmission of information between complex systems: 1/f resonance.

We study the transport of information between two complex systems with similar properties. Both systems generate non-Poisson renewal fluctuations with a power-law spectrum 1/f(3-μ), the case μ=2 corresponding to ideal 1/f noise. We denote by μ(S) and μ(P) the power-law indexes of the system of interest S and the perturbing system P, respectively.

Optimal receptor-cluster size determined by intrinsic and extrinsic noise.

Biological cells sense external chemical stimuli in their environment using cell-surface receptors. To increase the sensitivity of sensing, receptors often cluster. This process occurs most noticeably in bacterial chemotaxis, a paradigm for sensing and signaling in general.

Increased accuracy of ligand sensing by receptor diffusion on cell surface.

The physical limit with which a cell senses external ligand concentration corresponds to the perfect absorber, where all ligand particles are absorbed and overcounting of same ligand particles does not occur. Here, we analyze how the lateral diffusion of receptors on the cell membrane affects the accuracy of sensing ligand concentration. Specifically, we connect our modeling to neurotransmission in neural synapses where the diffusion of glutamate receptors is already known to refresh synaptic connections.

Beyond the death of linear response: 1/f optimal information transport.

Nonergodic renewal processes have recently been shown by several authors to be insensitive to periodic perturbations, thereby apparently sanctioning the death of linear response, a building block of nonequilibrium statistical physics. We show that it is possible to go beyond the "death of linear response" and establish a permanent correlation between an external stimulus and the response of a complex network generating nonergodic renewal processes, by taking as stimulus a similar nonergodic process. The ideal condition of 1/f noise corresponds to a singularity that is expected to be relevant in several experimental conditions.

Increased accuracy of ligand sensing by receptor internalization.

Many types of cells can sense external ligand concentrations with cell-surface receptors at extremely high accuracy. Interestingly, ligand-bound receptors are often internalized, a process also known as receptor-mediated endocytosis. While internalization is involved in a vast number of important functions for the life of a cell, it was recently also suggested to increase the accuracy of sensing ligand as the overcounting of the same ligand molecules is reduced.

Memory effects in the two-level model for glasses.

We study an ensemble of two-level systems interacting with a thermal bath. This is a well-known model for glasses. The origin of memory effects in this model is a quasistationary but nonequilibrium state of a single two-level system, which is realized due to a finite-rate cooling and slow thermally activated relaxation.

Correlation function and generalized master equation of arbitrary age.

We study a two-state statistical process with a non-Poisson distribution of sojourn times. In accordance with earlier work, we find that this process is characterized by aging and we study three different ways to define the correlation function of arbitrary age of the corresponding dichotomous fluctuation. These three methods yield exact expressions, thus coinciding with the recent result by Godrèche and Luck [J.

Aging and rejuvenation with fractional derivatives.

We discuss a dynamic procedure that makes fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment, and divergent second moment, namely, with the power index mu in the interval 2 View Article and Find Full Text PDF

Absorption and emission in the non-Poissonian case.

This Letter addresses the challenging problems posed to the Kubo-Anderson (KA) theory by the discovery of intermittent resonant fluorescence with a nonexponential distribution of waiting times. We show how to extend the KA theory from aged to aging systems, aging for a very extended time period or even forever, being a crucial consequence of non-Poisson statistics.

Generalized master equation via aging continuous-time random walks.

We discuss the problem of the equivalence between continuous-time random walk (CTRW) and generalized master equation (GME). The walker, making instantaneous jumps from one site of the lattice to another, resides in each site for extended times. The sojourn times have a distribution density psi(t) that is assumed to be an inverse power law with the power index micro.