Tunable Stochastic State Switching in 2D MoS2 Nanomechanical Resonators with Nonlinear Mode Coupling and Internal Resonance.

Coupled nanomechanical resonators have unveiled fascinating physical phenomena, including phonon-cavity coupling, coupled energy decay pathway, avoided crossing, and internal resonance. Despite these discoveries, the mechanisms and control techniques of nonlinear mode coupling phenomena with internal resonances require further exploration. Here, we report on the observation of stochastic switching between the two resonance states with coupled 1:1 internal resonance, for resonant two-dimensional (2D) molybdenum disulfide (MoS2) nanoelectromechanical systems (NEMS), which is directly driven to the critical coupling regime without parametric pumping. We further demonstrate that the probability of state switching is linearly tunable from ∼0% to ∼100% by varying the driving voltage. Furthermore, we gradually increase the white noise amplitude and show that the probability of obtaining the higher-energy state decreases, and the stochastic switching phenomenon eventually disappears. The results provide insights into the dynamics of coupled NEMS resonators and open up new possibilities for sensing and stochastic computing.

Effects of stochastic forces on the nonlinear behaviour of a silicon nitride membrane nanoelectromechanical resonator.

In this work, we present the effects of stochastic force generated by white noise on the nonlinear dynamics of a circular silicon nitride membrane. By tuning the membrane to the Duffing nonlinear region, detected signals switching between low- and high-amplitudes have been observed. They are generated by noise-assisted random jumps between bistable states at room temperature and exhibit high sensitivity to the driving frequency. Through artificially heating different mechanical vibration modes by external input of white noise, the switching rate exhibits exponential dependence on the effective temperature and follows with Kramer's law. Furthermore, both the measured switching rate and activation energy exhibit sensitivity to the width of the hysteresis window in nonlinear response and the driving force, which is in qualitative agreement with the theoretical descriptions. Besides, white noise-induced hysteresis window squeezing and bifurcation point shifting have also been observed, which are attributed to the stochastic force modulation of the spring constant of the membrane. These studies are carried out in an all-electric operating scheme at room temperature, paving the way for the exploration of probability distribution-based functional elements that can be massively integrated on-chip.

Spiracular fluttering decouples oxygen uptake and water loss: a stochastic PDE model of respiratory water loss in insects.

In insect respiration, oxygen from the air diffuses through a branching system of air-filled tubes to the cells of the body and carbon dioxide produced in cellular respiration diffuses out. The tracheal system has a very large surface area, so water loss is a potential threat and the question of how insects regulate oxygen uptake and water loss has been an important issue in insect physiology for the past century. The tracheal system starts at spiracles on the surface of the body that insects can open and close, and three phases are observed experimentally, open or closed for relatively long periods of time and opening and closing rapidly, which is called fluttering. In previous work we have shown that during this flutter phase, no matter how small the percentage of time that the spiracles are open, the insect can absorb almost as much oxygen as if the spiracle were always open, if the insect flutters fast enough. This left open the question of water loss during the flutter phase, which is the question addressed in this paper. We formulate a stochastic diffusion-convection model for the concentration of water vapor in the tracheae. Mathematical analysis of the model yields an explicit formula for water loss as a function of six non-dimensional parameters and we use experimental data from various insects to show that, for parameters in the physiological ranges, water loss during the flutter phase is approximately proportional to the percentage of time open. This means that the insect can solve the oxygen uptake versus water loss problem by choosing to have their spiracles open a small percentage of time during the flutter phase and fluttering rapidly.

Asynchronous Stabilization for Two Classes of Stochastic Switching Systems with Applications on Servo Motors.

This paper addresses the asynchronous stabilization problem of two typical stochastic switching systems, i.e., dual switching systems and semi-Markov jump systems. By dual switching, it means that the systems contain both deterministic and stochastic switching dynamics. New stability criteria are firstly proposed for these two switched systems, which can well handle the asynchronous phenomenon. The conditional expectation of Lyapunov functions is allowed to increase during some unmatched interval to reduce the conservatism. Next, we present numerically testable asynchronous controller design methods for the dual switching systems. The proposed method is suitable for the situation where the asynchronous modes come from both inaccurate mode detection and time varying delay. Meanwhile, the transition probabilities are both uncertain and partly accessible. Finally, novel asynchronous controller design methods are proposed for the semi-Markov jump systems. The sojourn time of the semi-Markov jump systems can have both lower and upper bounds, which could be more practical than previous scenarios. Examples are utilized to demonstrate the effectiveness of the proposed methods.

On the fitness of informative cues in complex environments.

To be able to deal with uncertainty is of primary importance to most living organisms. When cues provide information about the state of the environment, organisms can use them to respond flexibly. Life forms have evolved complex adaptations and sensory mechanisms to use these environmental cues and extract valuable information about the environment. Previous work has shown a theoretical limit to the amount of fitness benefit possible to be extracted from the cues. We show that the previously used information theoretical approaches can be generalised to scenarios involving any potential relationship between the number of possible phenotypes and environmental states. Such cases are relevant when physiological constraints or complex ecological scenarios lead to the number of environmental states exceeding potential phenotypes. We illustrate cases in which these scenarios can emerge: along environmental gradients, such as geographical transects or complex environments, where organisms adopt different bet-hedging strategies, switching stochastically between phenotypes or developing intermediate ones. In conclusion, we develop an information-theoretic extensible approach for investigating and quantifying fitness in ecological studies.

High-Frequency Stochastic Switching of Graphene Resonators Near Room Temperature.

Stochastic switching between the two bistable states of a strongly driven mechanical resonator enables detection of weak signals based on probability distributions, in a manner that mimics biological systems. However, conventional silicon resonators at the microscale require a large amount of fluctuation power to achieve a switching rate in the order of a few hertz. Here, we employ graphene membrane resonators of atomic thickness to achieve a stochastic switching rate of 4.1 kHz, which is 100 times faster than current state-of-the-art. The (effective) temperature of the fluctuations is approximately 400 K, which is 3000 times lower than the state-of-the-art. This shows that these membranes are potentially useful to transduce weak signals in the audible frequency domain. Furthermore, we perform numerical simulations to understand the transition dynamics of the resonator and use analytical expressions to investigate the relevant scaling parameters that allow high-frequency, low-temperature stochastic switching to be achieved in mechanical resonators.

Shortsighted Evolution Constrains the Efficacy of Long-Term Bet Hedging.

To survive unpredictable environmental change, many organisms adopt bet-hedging strategies that are initially costly but provide a long-term fitness benefit. The temporal extent of these deferred fitness benefits determines whether bet-hedging organisms can survive long enough to realize them. In this article, we examine a model of microbial bet hedging in which there are two paths to extinction: unpredictable environmental change and demographic stochasticity. In temporally correlated environments, these drivers of extinction select for different switching strategies. Rapid phenotype switching ensures survival in the face of unpredictable environmental change, while slower-switching organisms become extinct. However, when both switching strategies are present in the same population, then demographic stochasticity-enforced by a limited population size-leads to extinction of the faster-switching organism. As a result, we find a novel form of evolutionary suicide whereby selection in a fluctuating environment can favor bet-hedging strategies that ultimately increase the risk of extinction. Population structures with multiple subpopulations and dispersal can reduce the risk of extinction from unpredictable environmental change and shift the balance so as to facilitate the evolution of slower-switching organisms.

A Simplified model of mutually inhibitory sleep-active and wake-active neuronal populations employing a noise-based switching mechanism.

Infant rats switch randomly between the sleeping and waking states; during early infancy (up to postnatal day 8), sleep and wake bouts are random, brief (with means on the order of several seconds) and exponentially distributed, with the length of a particular bout independent of the length of prior bouts. As the rat ages during this early period, mean sleep and wake bout lengths gradually increase, though sleep and wake bouts remain exponentially distributed. Additionally, sleep and wake bouts are regulated independently of each other - alterations in the development of sleep (wake) bouts has no impact on the regulation wake (sleep) bouts. Sleep and wake bout behavior is associated with the activity of mutually inhibitory sleep-active and wake-active brainstem populations. In this work, I employ a simplified biophysical model of two mutually inhibitory populations consisting of ten integrate-and-fire neurons each and a noise-based switching mechanism. I show that such a noise-based switching mechanism naturally accounts for the experimentally observed features of sleep-wake switching during early infancy - random alternating activity bouts occur as a consequence of noise (provided inhibition is strong relative to excitation), bout durations are exponential (due to a lack of memory within the system), and cross-population inhibition or intrapopulation excitatory coupling provide mechanisms for changing and independently regulated sleep and wake bout means.

Bet-hedging in stochastically switching environments.

We investigate the evolution of bet-hedging in a population that experiences a stochastically switching environment by means of adaptive dynamics. The aim is to extend known results to the situation at hand, and to deepen the understanding of the range of validity of these results. We find three different types of evolutionarily stable strategies (ESSs) depending on the frequency at which the environment changes: for a rapid change, a monomorphic phenotype adapted to the mean environment; for an intermediate range, a bimorphic bet-hedging phenotype; for slowly changing environments, a monomorphic phenotype adapted to the current environment. While the last result is only obtained by means of heuristic arguments and simulations, the first two results are based on the analysis of Lyapunov exponents for stochastically switching systems.

Dynamics of Amino Acid Metabolism, Gene Expression, and Circulomics in a Recombinant Chinese Hamster Ovary Cell Line Adapted to Moderate and High Levels of Extracellular Lactate.

The accumulation of metabolic wastes in cell cultures can diminish product quality, reduce productivity, and trigger apoptosis. The limitation or removal of unintended waste products from Chinese hamster ovary (CHO) cell cultures has been attempted through multiple process and genetic engineering avenues with varied levels of success. One study demonstrated a simple method to reduce lactate and ammonia production in CHO cells with adaptation to extracellular lactate; however, the mechanism behind adaptation was not certain. To address this profound gap, this study characterizes the phenotype of a recombinant CHO K-1 cell line that was gradually adapted to moderate and high levels of extracellular lactate and examines the genomic content and role of extrachromosomal circular DNA (eccDNA) and gene expression on the adaptation process. More than 500 genes were observed on eccDNAs. Notably, more than 1000 genes were observed to be differentially expressed at different levels of lactate adaptation, while only 137 genes were found to be differentially expressed between unadapted cells and cells adapted to grow in high levels of lactate; this suggests stochastic switching as a potential stress adaptation mechanism in CHO cells. Further, these data suggest alanine biosynthesis as a potential stress-mitigation mechanism for excess lactate in CHO cells.

Stochastic switching of delayed feedback suppresses oscillations in genetic regulatory systems.

Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates the effect of delayed feedback. To do so, we consider a hybrid model where stochastic delays evolve by a continuous-time Markov chain, and between switching events, the system of interest evolves via a deterministic delay equation. Our main contribution is the calculation of an effective delay equation in the fast switching limit. This effective equation maintains the influence of all subsystem delays and cannot be replaced with a single effective delay. To illustrate the relevance of this calculation, we investigate a simple model of stochastically switching delayed feedback motivated by gene regulation. We show that sufficiently fast switching between two oscillatory subsystems can yield stable dynamics.

Evolutionary Rescue Through Partly Heritable Phenotypic Variability.

Environmental variation is commonplace, but unpredictable. Populations that encounter a deleterious environment can sometimes avoid extinction by rapid evolutionary adaptation. Phenotypic variability, whereby a single genotype can express multiple different phenotypes, might play an important role in rescuing such populations from extinction. This type of evolutionary bet-hedging need not confer a direct benefit to a single individual, but it may increase the chance of long-term survival of a lineage. Here, we develop a population genetic model to explore how partly heritable phenotypic variability influences the probability of evolutionary rescue and the mean duration of population persistence in changing environments. We find that the probability of population persistence depends nonmonotonically on the degree of phenotypic heritability between generations: some heritability can help avert extinction, but too much heritability removes any benefit of phenotypic variability. Partly heritable phenotypic variation is particularly advantageous when it extends the persistence time of a declining population and thereby increases the chance of rescue via beneficial mutations at linked loci. We discuss the implications of these results in the context of therapies designed to eradicate populations of pathogens or aberrant cellular lineages.

Courting disaster: How diversification rate affects fitness under risk.

Life is full of risk. To deal with this uncertainty, many organisms have evolved bet-hedging strategies that spread risk through phenotypic diversification. These rates of diversification can vary by orders of magnitude in different species. Here we examine how key characteristics of risk and organismal ecology affect the fitness consequences of variation in diversification rate. We find that rapid diversification is strongly favored when the risk faced has a wide spatial extent, with a single disaster affecting a large fraction of the population. This advantage is especially great in small populations subject to frequent disaster. In contrast, when risk is correlated through time, slow diversification is favored because it allows adaptive tracking of disasters that tend to occur in series. Naturally evolved diversification mechanisms in diverse organisms facing a broad array of environmental risks largely support these results. The theory presented in this article provides a testable ecological hypothesis to explain the prevalence of slow stochastic switching among microbes and rapid, within-clutch diversification strategies among plants and animals.

The evolution of phenotypic switching in subdivided populations.

Stochastic switching is an example of phenotypic bet hedging, where offspring can express a phenotype different from that of their parents. Phenotypic switching is well documented in viruses, yeast, and bacteria and has been extensively studied when the selection pressures vary through time. However, there has been little work on the evolution of phenotypic switching under both spatially and temporally fluctuating selection pressures. Here we use a population genetic model to explore the interaction of temporal and spatial variation in determining the evolutionary dynamics of phenotypic switching. We find that the stable switching rate is mainly determined by the rate of environmental change and the migration rate. This stable rate is also a decreasing function of the recombination rate, although this is a weaker effect than those of either the period of environmental change or the migration rate. This study highlights the interplay of spatial and temporal environmental variability, offering new insights into how migration can influence the evolution of phenotypic switching rates, mutation rates, or other sources of phenotypic variation.