Intrinsic noise profoundly alters the dynamics and steady state of morphogen-controlled bistable genetic switches

During tissue development, patterns of gene expression determine the spatial arrangement of cell types. In many cases, gradients of secreted signaling molecules - morphogens - guide this process. The continuous positional information provided by the gradient is converted into discrete cell types by the downstream transcriptional network that responds to the morphogen. A mechanism commonly used to implement a sharp transition between two adjacent cell fates is the genetic toggle switch, composed of cross-repressing transcriptional determinants. Previous analyses emphasize the steady state output of these mechanisms. Here, we explore the dynamics of the toggle switch and use exact numerical simulations of the kinetic reactions, the Chemical Langevin Equation, and Minimum Action Path theory to establish a framework for studying the effect of gene expression noise on patterning time and boundary position. This provides insight into the time scale, gene expression trajectories and directionality of stochastic switching events between cell states. Taking gene expression noise into account predicts that the final boundary position of a morphogen-induced toggle switch, although robust to changes in the details of the noise, is distinct from that of the deterministic system. Moreover, stochastic switching introduces differences in patterning time along the morphogen gradient that result in a patterning wave propagating away from the morphogen source. The velocity of this wave is influenced by noise; the wave sharpens and slows as it advances and may never reach steady state in a biologically relevant time. This could explain experimentally observed dynamics of pattern formation. Together the analysis reveals the importance of dynamical transients for understanding morphogen-driven transcriptional networks and indicates that gene expression noise can qualitatively alter developmental patterning

Noise control and utility: From regulatory network to spatial patterning

Stochasticity (or noise) at cellular and molecular levels has been observed extensively as a universal feature for living systems. However, how living systems deal with noise while performing desirable biological functions remains a major mystery. Regulatory network configurations, such as their topology and timescale, are shown to be critical in attenuating noise, and noise is also found to facilitate cell fate decision. Here we review major recent findings on noise attenuation through regulatory control, the benefit of noise via noise-induced cellular plasticity during developmental patterning, and summarize key principles underlying noise control

Non-equilibrium phase transitions in biomolecular signal transduction

We study a mechanism for reliable switching in biomolecular signal-transduction cascades. Steady bistable states are created by system-size cooperative effects in populations of proteins, in spite of the fact that the phosphorylation-state transitions of any molecule, by means of which the switch is implemented, are highly stochastic. The emergence of switching is a nonequilibrium phase transition in an energetically driven, dissipative system described by a master equation. We use operator and functional integral methods from reaction-diffusion theory to solve for the phase structure, noise spectrum, and escape trajectories and first-passage times of a class of minimal models of switches, showing how all critical properties for switch behavior can be computed within a unified framework

A Dynamic Analysis of Moving Average Rules

The use of various moving average rules remains popular with financial market practitioners. These rules have recently become the focus of empirical studies. However there have been very few studies on the analysis of financial market dynamics resulting from the fact that some agents engage in such strategies. In this paper we seek to fill this gap in the literature by proposing a dynamic financial market model in which demand for traded assets has both a fundamentalist and a chartist component. The chartist demand is governed by the difference between a long run and a short run moving average. Both types of traders are boundedly rational in the sense that, based on a certain fitness measure, traders switch from a strategy with low fitness to the one with high fitness. We characterise first the stability and bifurcation properties of the underlying deterministic model via the reaction coefficient of the fundamentalists, the extrapolation rate of the chartists and the lag lengths used for moving averages. By increasing the switching intensity, we then examine various rational routes to randomness for different, but fixed, long run moving averages. The price dynamics of the moving average rule is also examined and it is found that an increase of the window length of the long moving average can destabilize an otherwise stable system, leading to more complicated, even chaotic behaviour. The analysis of the corresponding stochastic model is able to explain various market price phenomena, including market crashes, price switching between different levels and price resistance.moving averages; fundamentalis; trend followers; stability; bifurcation; volatility clustering

Almost Sure Stabilization for Adaptive Controls of Regime-switching LQ Systems with A Hidden Markov Chain

This work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown Markov chain. The control system displays continuous dynamics represented by differential equations and discrete events given by a hidden Markov chain. Different from previous work on stabilization of adaptive controlled systems with a hidden Markov chain, where average criteria were considered, this work focuses on the almost sure stabilization or sample path stabilization of the underlying processes. Under simple conditions, it is shown that as long as the feedback controls have linear growth in the continuous component, the resulting process is regular. Moreover, by appropriate choice of the Lyapunov functions, it is shown that the adaptive system is stabilizable almost surely. As a by-product, it is also established that the controlled process is positive recurrent

Low-lying bifurcations in cavity quantum electrodynamics

The interplay of quantum fluctuations with nonlinear dynamics is a central topic in the study of open quantum systems, connected to fundamental issues (such as decoherence and the quantum-classical transition) and practical applications (such as coherent information processing and the development of mesoscopic sensors/amplifiers). With this context in mind, we here present a computational study of some elementary bifurcations that occur in a driven and damped cavity quantum electrodynamics (cavity QED) model at low intracavity photon number. In particular, we utilize the single-atom cavity QED Master Equation and associated Stochastic Schrodinger Equations to characterize the equilibrium distribution and dynamical behavior of the quantized intracavity optical field in parameter regimes near points in the semiclassical (mean-field, Maxwell-Bloch) bifurcation set. Our numerical results show that the semiclassical limit sets are qualitatively preserved in the quantum stationary states, although quantum fluctuations apparently induce phase diffusion within periodic orbits and stochastic transitions between attractors. We restrict our attention to an experimentally realistic parameter regime.Comment: 13 pages, 10 figures, submitted to PR

A neuromorphic systems approach to in-memory computing with non-ideal memristive devices: From mitigation to exploitation

Memristive devices represent a promising technology for building neuromorphic electronic systems. In addition to their compactness and non-volatility features, they are characterized by computationally relevant physical properties, such as state-dependence, non-linear conductance changes, and intrinsic variability in both their switching threshold and conductance values, that make them ideal devices for emulating the bio-physics of real synapses. In this paper we present a spiking neural network architecture that supports the use of memristive devices as synaptic elements, and propose mixed-signal analog-digital interfacing circuits which mitigate the effect of variability in their conductance values and exploit their variability in the switching threshold, for implementing stochastic learning. The effect of device variability is mitigated by using pairs of memristive devices configured in a complementary push-pull mechanism and interfaced to a current-mode normalizer circuit. The stochastic learning mechanism is obtained by mapping the desired change in synaptic weight into a corresponding switching probability that is derived from the intrinsic stochastic behavior of memristive devices. We demonstrate the features of the CMOS circuits and apply the architecture proposed to a standard neural network hand-written digit classification benchmark based on the MNIST data-set. We evaluate the performance of the approach proposed on this benchmark using behavioral-level spiking neural network simulation, showing both the effect of the reduction in conductance variability produced by the current-mode normalizer circuit, and the increase in performance as a function of the number of memristive devices used in each synapse.Comment: 13 pages, 12 figures, accepted for Faraday Discussion

A Dynamic Analysis of Moving Average Rules

The use of various moving average rules remains popular with financial market practitioners. These rules have recently become the focus of a number empirical studies, but there have been very few studies of financial market models where some agents employ technical trading rules also used in practice. In this paper we propose a dynamic financial market model in which demand for traded assets has both a fundamentalist and a chartist component. The chartist demand is governed by the difference between current price and a (long run) moving average. Both types of traders are boundedly rational in the sense that, based on a fitness measure such as realized capital gains, traders switch from a strategy with low fitness to the one with high fitness. We characterize the stability and bifurcation properties of the underlying deterministic model via the reaction coefficient of the fundamentalists, the extrapolation rate of the chartists and the lag lengths used for the moving averages. By increasing the intensity of choice to switching strategies, we then examine various rational routes to randomness for different moving average rules. The price dynamics of the moving average rule is also examined and one of our main findings is that an increase of the window length of the moving average rule can destabilize an otherwise stable system, leading to more complicated, even chaotic behaviour. The analysis of the corresponding stochastic model is able to explain various market price phenomena, including temporary bubbles, sudden market crashes, price resistance and price switching between different levels.