The More the Merrier?

The trade-off between traits in life-history strategies has been widely studied for sexual and parthenogenetic organisms, but relatively little is known about the reproduction strategies of asexual animals. Here, we investigate clonal reproduction in the freshwater planarian Schmidtea mediterranea, an important model organism for regeneration and stem cell research. We find that these flatworms adopt a randomized reproduction strategy that comprises both asymmetric binary fission and fragmentation (generation of multiple offspring during a reproduction cycle). Fragmentation in planarians has primarily been regarded as an abnormal behavior in the past; using a large-scale experimental approach, we now show that about one third of the reproduction events in S. mediterranea are fragmentations, implying that fragmentation is part of their normal reproductive behavior. Our analysis further suggests that certain characteristic aspects of the reproduction statistics can be explained in terms of a maximum relative entropy principle.     

Effect of noise and perturbations on limit cycle systems

This paper demonstrates that the influence of noise and of external perturbations on a nonlinear oscillator can vary strongly along the limit cycle and upon transition from limit cycle to stationary point behaviour. For this purpose we consider the role of noise on the Bonhoeffer-van der Pol model in a range of control parameters where the model exhibits a limit cycle, but the parameters are close to values corresponding to a stable stationary point. Our analysis is based on the van Kampen approximation for solutions of the Fokker-Planck equation in the limit of weak noise. We investigate first separately the effect of noise on motion tangential and normal to the limit cycle. The key result is that noise induces diffusion-like spread along the limit cycle, but quasistationary behaviour normal to the limit cycle. We then describe the coupled motion and show that noise acting in the normal direction can strongly enhance diffusion along the limit cycle. We finally argue that the variability of the system's response to noise can be exploited in populations of nonlinear oscillators in that weak coupling can induce synchronization as long as the single oscillators operate in a regime close to the transition between oscillatory and excitatory modes.     

Intrinsic noise and division cycle effects on an abstract biological oscillator

Oscillatory dynamics are common in biological pathways, emerging from the coupling of positive and negative feedback loops. Due to the small numbers of molecules typically contained in cellular volumes, stochastic effects may play an important role in system behavior. Thus, for moderate noise strengths, stochasticity has been shown to enhance signal-to-noise ratios or even induce oscillations in a class of phenomena referred to as "stochastic resonance" and "coherence resonance," respectively. Furthermore, the biological oscillators are subject to influences from the division cycle of the cell. In this paper we consider a biologically relevant oscillator and investigate the effect of intrinsic noise as well as division cycle which encompasses the processes of growth, DNA duplication, and cell division. We first construct a minimal reaction network which can oscillate in the presence of large or negligible timescale separation. We then derive corresponding deterministic and stochastic models and compare their dynamical behaviors with respect to (i) the extent of the parameter space where each model can exhibit oscillatory behavior and (ii) the oscillation characteristics, namely, the amplitude and the period. We further incorporate division cycle effects on both models and investigate the effect of growth rate on system behavior. Our results show that in the presence but not in the absence of large timescale separation, coherence resonance effects result in extending the oscillatory region and lowering the period for the stochastic model. When the division cycle is taken into account, the oscillatory region of the deterministic model is shown to extend or shrink for moderate or high growth rates, respectively. Further, under the influence of the division cycle, the stochastic model can oscillate for parameter sets for which the deterministic model does not. The division cycle is also found to be able to resonate with the oscillator, thereby enhancing oscillation robustness. The results of this study can give valuable insight into the complex interplay between oscillatory intracellular dynamics and various noise sources, stemming from gene expression, cell growth, and division.     

Determinism,noise, and spurious estimations in a generalised model of population growth

We study a generalised model of population growth in which the state variable is population growth rate instead of population size. Stochastic parametric perturbations, modelling phenotypic variability, lead to a Langevin system with two sources of multiplicative noise. The stationary probability distributions have two characteristic power-law scales. Numerical simulations show that noise suppresses the explosion of the growth rate which occurs in the deterministic counterpart. Instead, in different parameter regimes populations will grow with “anomalous” stochastic rates and (i) stabilise at “random carrying capacities”, or (ii) go extinct in random times. Using logistic fits to reconstruct the simulated data, we find that even highly significant estimations do not recover or reflect information about the deterministic part of the process. Therefore, the logistic interpretation is not biologically meaningful. These results have implications for distinct model-aided calculations in biological situations because these kinds of estimations could lead to spurious conclusions.     

Evolutionary Game Dynamics in a Fitness-Dependent Wright-FisherProcess with Noise

Evolutionary game dynamics in finite size populations can be described by a fitness-dependent Wright-Fisher process. We consider symmetric 2$\times $2 games in a well-mixed population. In our model, two parameters to describe the level of player's rationality and noise intensity in environment are introduced. In contrast with the fixation probability method that used in a noiseless case, the introducing of the noise intensity parameter makes the process an ergodic Markov process and based on the limit distribution of the process, we can analysis the evolutionary stable strategy (ESS) of the games. We illustrate the effects of the two parameters on the ESS of games using the Prisoner's dilemma games (PDG) and the snowdrift games (SG). We also compare the ESS of our model with that of the replicator dynamics in infinite size populations. The results are determined by simulation experiments.     

Effects of channel noise on firing coherence of small-world Hodgkin-Huxley neuronal networks

We investigate the effects of channel noise on firing coherence of Watts-Strogatz small-world networks consisting of biophysically realistic HH neurons having a fraction of blocked voltage-gated sodium and potassium ion channels embedded in their neuronal membranes. The intensity of channel noise is determined by the number of non-blocked ion channels, which depends on the fraction of working ion channels and the membrane patch size with the assumption of homogeneous ion channel density. We find that firing coherence of the neuronal network can be either enhanced or reduced depending on the source of channel noise. As shown in this paper, sodium channel noise reduces firing coherence of neuronal networks; in contrast, potassium channel noise enhances it. Furthermore, compared with potassium channel noise, sodium channel noise plays a dominant role in affecting firing coherence of the neuronal network. Moreover, we declare that the observed phenomena are independent of the rewiring probability.     

Mdm2生成速率调控的p53-Mdm2振子的全局动力学和稳定性

肿瘤抑制蛋白p53的动力学在一定程度上可以决定DNA损伤后的细胞命运.p53的动力学行为与p53信号通路中p53-Mdm2振子模块密切相关.然而,p53的负调控子Mdm2的生成速率的增加使其在一些癌细胞中过表达.因此探讨Mdm2生成速率对p53动力学的影响有重要意义.同时,PDCD5作为p53的激活子也调控p53的表达.因此,本文针对PDCD5调控的p53-Mdm2振子模型,通过分岔分析获得了Mdm2生成速率所调控的p53的单稳态、振荡以及单稳态与振荡共存的动力学行为,且稳定性通过能量面进行了分析.此外,噪声强度对p53动力学的稳定性有重要的影响.因此,针对p53的振荡行为,探讨了噪声强度对势垒高度和周期的影响.本文所获得的结果对理解DNA损伤后的p53信号通路调控起到一定的指导作用.     

Rate coding model for discrimination of simple tones in the presence of noise

The predictions of a rate coding model for frequency and amplitude jnd's in the presence of noise are presented for a 1-kHz, 100-ms tone. The model for the neural response incorporates physiological data on dynamic range distribution and rate suppression. A central processor is assumed to estimate the tone frequency, or amplitude, from the tone-evoked rate increment profile. This central processor acts like an ideal detector with respect to the neural noise. The effects of the neural noise as well as the signal variability on the discrimination performance level are evaluated, and the signal variability is found to be significant. The combined effect of threshold distribution, rate suppression, and signal variability make the jnd's practically invariant with noise level, in accordance with published psychophysical data. The values of the frequency jnd at high signal-to-noise ratio, however, are borderline in their consistency with the data. A more obvious discrepancy exists between the model and the psychophysical data regarding the ratio of frequency to amplitude Weber fractions, which can be resolved only by modifying the model auditory filters to be five times sharper than those measured in cats.     

Relevance of multiple quasiparticle tunneling between edge states at nu=p/(2np+1)

We present an explanation for the anomalous behavior in tunneling conductance and noise through a point contact between edge states in the Jain series nu=p/(2np+1), for extremely weak backscattering and low temperatures [Y. C. Chung, M. Heiblum, and V. Umansky, Phys. Rev. Lett. 91, 216804 (2003)10.1103/PhysRevLett.91.216804]. We consider edge states with neutral modes propagating at finite velocity, and we show that the activation of their dynamics causes the unexpected change in the temperature power law of the conductance. Even more importantly, we demonstrate that multiple-quasiparticle tunneling at low energies becomes the most relevant process. This result will be used to explain the experimental data on current noise where tunneling particles have a charge that can reach p times the single-quasiparticle charge. In this Letter, we analyze the conductance and the shot noise to substantiate quantitatively the proposed scenario.     

Model of evolution with sexual and non-sexual reproduction

Using a previously introduced model (Refs. [9, 10]) of biological evolution, we study the role of the reproduction pattern on the fate of an evolving population. Each individual is under the selectional pressure from the environment and random harmful mutations. The habitat (“climate") is changing periodically. Evolution of populations following three reproduction patterns are compared - an asexual one (without recombination) and two with recombination - asexual (meiotic parthenogenesis) and sexual. We show, via Monte-Carlo simulations, that sexual reproduction leads to a better adaptation to the environment, slightly better survival rates for the individuals and higher probability that the population will not become extinct in difficult external conditions. The benefits of sexual reproduction are enhanced by higher birth rates and lower mutation rates. In the case of low birth rates and high mutation rates there is a small preference for the meiotic parthenogenesis. Received 9 August 1999     

Analysis of noise-induced bimodality in a Michaelis–Menten single-step enzymatic cycle

In this paper we study noise-induced bimodality in a specific circuit with many biological implications, namely a single-step enzymatic cycle described by Michaelis–Menten equations. We study the biological feasibility of this phenomenon, which allows for switch-like behavior in response to graded stimuli, considering a small and discrete number of molecules involved in the circuit, and we characterize the conditions necessary for it. We show that intrinsic noise (due to the stochastic character of the Master Equation approach) of a one-dimensional substrate reaction is not sufficient to achieve bimodality, then we characterize analytically the necessary conditions on enzyme number fluctuations. We implement numerically two model circuits that show bimodality over different parameter windows, that depend critically on system size as predicted by our results, providing hints about how such a phenomenon could be exploited in real biological systems.     

Experimental analysis of mode-hopping in bulk semiconductor lasers

In this work we experimentally study mode-hopping in bulk semiconductor lasers. This stochastic process is ruled by Kramers statistics with a decay rate depending on the laser parameters of the temperature of the substrate and the pumping current. For a general combination of these parameters the average residence times in the two active modes are not equal, resulting in an asymmetric probability distribution for the modal intensities. We show that, by choosing an appropriate path in the parameter space, we can vary the residence times of the two modes while holding their ratio constant. Along this path, the shape of modal intensities distributions are constant up to a scaling factor which is a function of the laser parameters. Then, the system can be described by a single Langevin equation. The effect of adding noise to the pumping current is also investigated. PACS 42.65.Sf; 42.55.Sa; 42.50.-p     

Sinusoidal and noise maskers in simultaneous and forward masking

We compare psychophysical tuning curves obtained with sinusoidal and narrow-band (50-Hz wide) noise maskers in both simultaneous and forward masking. In one experiment, we examine the effects of different combinations of duration and intensity of the 1-kHz sinusoidal signal. In a second experiment, we compare tuning curves obtained with a sinusoidal signal to those obtained with a noise signal. In both experiments, a narrow-band noise is a more effective simultaneous masker than a sinusoid for masker frequencies near the signal frequency. We argue that this is probably due to the use of different detection cues in the presence of sinusoidal and noise maskers, and that the greater masking produced by the noise is not simply due to its greater variability. As observed in other studies, tuning curves are narrower in forward masking than in simultaneous masking.     

Implications of Noise on Neural Correlates of Consciousness: A Computational Analysis of Stochastic Systems of Mutually Connected Processes

Random fluctuations in neuronal processes may contribute to variability in perception and increase the information capacity of neuronal networks. Various sources of random processes have been characterized in the nervous system on different levels. However, in the context of neural correlates of consciousness, the robustness of mechanisms of conscious perception against inherent noise in neural dynamical systems is poorly understood. In this paper, a stochastic model is developed to study the implications of noise on dynamical systems that mimic neural correlates of consciousness. We computed power spectral densities and spectral entropy values for dynamical systems that contain a number of mutually connected processes. Interestingly, we found that spectral entropy decreases linearly as the number of processes within the system doubles. Further, power spectral density frequencies shift to higher values as system size increases, revealing an increasing impact of negative feedback loops and regulations on the dynamics of larger systems. Overall, our stochastic modeling and analysis results reveal that large dynamical systems of mutually connected and negatively regulated processes are more robust against inherent noise than small systems.     

一种矢量水听器基阵模拟器的设计

矢量水听器的每个阵元同时测量声场中声矢量和质点振速的3个分量,相对于声压水听器阵来说,矢量阵获取声场中更多的信息。利用矢量阵所获得速度场的信息可以去除目标方位估计中的 180°模糊。模拟器可以模拟实际海洋环境中目标的辐射特性和噪声特性,应用模拟器可以有效地缩短声纳的研制周期。本文提出一种矢量水听器基阵模拟器的设计方案,该方案解决了矢量阵中宽带信号的90°移相问题、时延精确控制问题和宽带噪声的谱状控制问题。     

Dynamical Behavior of an Epidemic Model

It is known that natural systems are undeniably subject to random fluctuations, arising from either environmental variability or internal effects. In this paper, a spatial version of an epidemic model which contains some important factors, such as noise on the infective and diffusion processes on both the susceptible and infective, is investigated. From the numerical results, we know that noise can induce instability and enhance the oscillation of the species density and the cooperation between noise and diffusion gives rise to the appearance of a rich transport phenomenology. Our results show that noise can play a prominent role in the spatial epidemic model.     

Theoretical study of mesoscopic stochastic mechanism and effects of finite size on cell cycle of fission yeast

Based on a deterministic cell cycle model, the mesoscopic stochastic differential equations are theoretically derived from the biochemical reactions. The effects of the finite cell size on the cell cycle regulation in the wild type and wee1^-cdc25Δ double mutant type are numerically studied by virtue of the chemical Langevin equations. (i) When the system is driven only by the internal noise, our numerical results are in qualitative agreement well with some experimental observations and data. (ii) A parameter, which is sensitive to two resettings of M-phase promoting factor to G₂, is treated as a stochastic variable, and the system driven only by the external noise for double mutant type is investigated. (iii) When the system is driven by both the internal and external noise, a simple discussion about the combined effect for double mutant type is given. Our results imply some experimental results would be explained by introducing the appropriate internal or external noise into the cell cycle system.     

Delay control of coherence resonance in type-I excitable dynamics

We consider a simple paradigmatic system of type-I excitability subject to noise and time-delayed feedback. This system is governed by a global bifurcation, namely a saddle-node bifurcation on a limit cycle. In the absence of noise, delay can induce complex dynamics including multiple stable and unstable periodic orbits. Random fluctuations result in coherence resonance in dependence on the noise strength. We show that this effect can be enhanced by delayed feedback control with suitably chosen feedback strength and time delay.