Role Of Time Delay Research Articles

The role of time delay in adaptive cellular negative feedback systems

Adaptation in cellular systems is often mediated by negative feedbacks, which usually come with certain time delays causing several characteristic response patterns including an overdamped response, damped or sustained oscillations. Here, we analyse generic two-dimensional delay differential equations with delayed negative feedback describing the dynamics of biochemical adaptive signal-response networks. We derive explicit thresholds and boundaries showing how time delay determines characteristic response patterns of these networks. Applying our theoretical analyses to concrete data we show that adaptation to osmotic stress in yeast is optimal in the sense of minimizing adaptation time without causing oscillatory behaviour, i.e., a critically damped response. In addition, our framework demonstrates that a slight increase of time delay in the NF-κB system might induce a switch from damped to sustained oscillatory behaviour. Thus, we demonstrate how delay differential equations can be used to explicitly study the delay in biochemical negative feedback systems. Our analysis also provides insight into how time delay may tune biological signal-response patterns and control the systems behaviour.

Competitive Dynamics in Intellectual Property Risk

This paper examines the role of time delays on the path dependency of corporate growth with a focus on intellectual property in technology intensive industries and proposes a methodology for assessment of competitive risks.

The Roles of Time Delay and Colored Noises on the Interspike Intervals of Calcium Spikes

In view of the same time delay in active and passive transport processes with colored noises of intracellular Ca^(2+), the interspike intervals (ISI) of calcium spikes of the intracellular calcium oscillation (ICO) are investigated by means of a second-order algorithm for the stochastic simulation of colored noises. Because the ICO exhibits anti-synchronous oscillation, thus we respectively compute the average ISI and its standard deviation (SD) of calcium spikes in the cytosol and endoplasmic reticulum (ER) with different time delays and strengths of colored noises. The results indicate that: (i) the average ISI are equal for the cytosol and ER, and have linear growth as the time delay prolongs. (ii) The average ISI firstly increases then remains steady as the colored noises strengthen. (iii) However, both SDs vs. time delay show that coherence resonance occurs.

Modelling and Analysis of miRNA Regulation

MiRNA regulation is involved in many important biological processes such as cell proliferation, apoptosis and metabolism. Computational predictions of miRNA targets suggest that up 30 % of human proteins coding genes may be regulated by miRNAs. This makes miRNAs one of the most abundant classes of regulatory genes in humans. In the present paper we develop a time delay model of a feedback system regulated via miRNA. The model resulted in three DDEs with three discrete time delays. Since this system is a classical case study, covering several essential features of miRNA and genetic regulatory mechanisms, general conclusions about design principles and role of time delays in the stability of gene circuits can be suggested. The basic view that time delays are a key factor in the dynamic behaviour of the system was confirmed by the analytical calculations and numerical simulations.

Effect of Delay on the Synchronization of Weakly Coupled Neurons via Inhibitory Chemical Synapses

Inhibitory chemical coupling connections are ubiquitous in neuronal system. In this paper, we first reduce the complex neuronal dynamics to a simple phase model by means of phase-model reduction method. Then we examine the roles of time delays extensively on the synchronization properties by bifurcation analysis and numerical simulation. Finally, we identify the existence and the stability of various phase-locked states. Along with the expected phase and anti-phase synchronization regimes, we find the emergent phenomena that significantly influence the synchronization behavior.

Effect of Delay on the Synchronization of Weakly Coupled Neurons via Inhibitory Chemical Synapses

Inhibitory chemical coupling connections are ubiquitous in neuronal system. In this paper, we first reduce the complex neuronal dynamics to a simple phase model by means of phase-model reduction method. Then we examine the roles of time delays extensively on the synchronization properties by bifurcation analysis and numerical simulation. Finally, we identify the existence and the stability of various phase-locked states. Along with the expected phase and anti-phase synchronization regimes, we find the emergent phenomena that significantly influence the synchronization behavior.

Reverse resonance and stochastic resonance in intracellular calcium oscillations

The roles of time delay on the coherence resonance are investigated in the intracellular calcium oscillation system described by the processes of active and passive transport of intracellular Ca2+ driven by colored noises. From the numerical simulation of the reciprocal coefficient of variance of interspike intervals of calcium spikes by the method of second-order algorithm, the results indicate that: (i) The stochastic or reverse synchronization is induced by a certain value of time delay or correlation time; (ii) A phenomenon of reverse resonance can be obtained in the function of reciprocal coefficient of variance vs. time delay or vs. strength of noises as time delay increases; (iii) Both stochastic and reverse resonance are observed in the function of reciprocal coefficient of variance vs. correlation time with varying strength of noises.

Synchronization of Nonidentical Coupled Phase Oscillators in the Presence of Time Delay and Noise

We have studied in this paper the dynamics of globally coupled phase oscillators having the Lorentzian frequency distribution with zero mean in the presence of both time delay and noise. Noise may be Gaussian or non-Gaussian in characteristics. In the limit of zero noise strength, we find that the critical coupling strength (CCS) increases linearly as a function of time delay. Thus the role of time delay in the dynamics for the deterministic system is qualitatively equivalent to the effect of frequency fluctuations of the phase oscillators by additive white noise in absence of time delay. But for the stochastic model, the critical coupling strength grows nonlinearly with the increase of the time delay. The linear dependence of the critical coupling strength on the noise intensity also changes to become nonlinear due to creation of additional phase difference among the oscillators by the time delay. We find that the creation of phase difference plays an important role in the dynamics of the system when the intrinsic correlation induced by the finite correlation time of the noise is small. We also find that the critical coupling is higher for the non-Gaussian noise compared to the Gaussian one due to higher effective noise strength.

Effects of time delay and coupling strength on synchronization transitions in excitable homogeneous random network

In this paper we numerically investigate the effects of time delay and coupling strength on synchronization transitions in excitable homogeneous random network. Different roles of time delay and coupling strength have been discovered by synchronization parameter and space–time plots. Specifically, we have found three distinct parameter regions, i.e., asynchronous region (domain I for small time delay), transition region (domain II for moderate time delay) and synchronous region (domain III for large time delay) as time delay is increased. The phenomenon of multi-stability is observed in the transition region. While coupling strength can enhance synchronization in the transition region and can reduce synchronization time in the synchronous region. All these results are independence on the system size.

The Compatibility Between Sociological and Cognitive Neuroscientific Ideas on Consciousness: Is a Neurosociology of Consciousness Possible?

This article considers the possibility of integrating sociological and cognitive neuroscience ideas on consciousness and developing a new research area: neurosociology of consciousnesses. Research was conducted taking into account the limited knowledge on consciousness produced in these disciplines and the necessity of finding ways to study the social roles concerning the neural correlates of consciousness. Applying several ideas on consciousness from these disciplines (intersubjectivity, close connection with collective forms representations, deriving awareness from the brain's processes, and so on), I show that it is difficult to reconcile the differences in the treatment of consciousness through the simple combination of the different ideas. The integration should be pursued in light of the neuroscientific findings concerning consciousness in different social contexts (role behavior, social interactions, and so on). In integrating the concepts, I predicted the role of time delay in conscious awareness in decision making, synchronization of neural oscillations under conscious perception, and the activations of certain brain zones in correspondence to different conscious cognitive processes for understanding in face-to-face situations. The study reveals that the optimal path for neurosociological research on consciousness is in its primary development without a rigid binding to either sociology or neuroscience.

Mathematical modelling of immune reaction against gliomas: Sensitivity analysis and influence of delays

In the paper we considered a model of immune reaction against malignant glioma. The model proposed by Kronik et al. (Cancer Immunol. Immunother., 2008) describes simplified interactions between tumour cells and five components of the immune system. We studied the effects of uncertainties of the parameters values to the system behaviour. We showed that the tumour growth rate is one of the most important parameters only in case of fast growing tumours, that is for GBM in our case.On the basis of the performed sensitivity analysis we proposed a reduced model in which the role of time delays in loops appearing in the described interactions is considered. The proposed model includes only two main components of the reaction, that is tumour cells and cytotoxic T-lymphocytes. It occurs that although the reduced system is described by several non-linear terms with three time delays, its dynamics is simple and time delays have hardly any influence on it.Both considered models confirmed that the non-linearities present in interactions between tumour cells and CTLs play a major role in the system dynamics, while other components or delays can be taken into account as supplementary elements only.

Delay-induced diversity of firing behavior and ordered chaotic firing in adaptive neuronal networks

In this paper, we study the effect of time delay on the firing behavior and temporal coherence and synchronization in Newman–Watts thermosensitive neuron networks with adaptive coupling. At beginning, the firing exhibit disordered spiking in absence of time delay. As time delay is increased, the neurons exhibit diversity of firing behaviors including bursting with multiple spikes in a burst, spiking, bursting with four, three and two spikes, firing death, and bursting with increasing amplitude. The spiking is the most ordered, exhibiting coherence resonance (CR)-like behavior, and the firing synchronization becomes enhanced with the increase of time delay. As growth rate of coupling strength or network randomness increases, CR-like behavior shifts to smaller time delay and the synchronization of firing increases. These results show that time delay can induce diversity of firing behaviors in adaptive neuronal networks, and can order the chaotic firing by enhancing and optimizing the temporal coherence and enhancing the synchronization of firing. However, the phenomenon of firing death shows that time delay may inhibit the firing of adaptive neuronal networks. These findings provide new insight into the role of time delay in the firing activity of adaptive neuronal networks, and can help to better understand the complex firing phenomena in neural networks.

Time delay induced transition of gene switch and stochastic resonance in a genetic transcriptional regulatory model

BackgroundNoise, nonlinear interactions, positive and negative feedbacks within signaling pathways, time delays, protein oligomerization, and crosstalk between different pathways are main characters in the regulatory of gene expression. However, only a single noise source or only delay time in the deterministic model is considered in the gene transcriptional regulatory system in previous researches. The combined effects of correlated noise and time delays on the gene regulatory model still remain not to be fully understood.ResultsThe roles of time delay on gene switch and stochastic resonance are systematically explored based on a famous gene transcriptional regulatory model subject to correlated noise. Two cases, including linear time delay appearing in the degradation process (case I) and nonlinear time delay appearing in the synthesis process (case II) are considered, respectively. For case I: Our theoretical results show that time delay can induce gene switch, i.e., the TF-A monomer concentration shifts from the high concentration state to the low concentration state ("on"→"off"). With increasing the time delay, the transition from "on" to "off" state can be further accelerated. Moreover, it is found that the stochastic resonance can be enhanced by both the time delay and correlated noise intensity. However, the additive noise original from the synthesis rate restrains the stochastic resonance. It is also very interesting that a resonance bi-peaks structure appears under large additive noise intensity. The theoretical results by using small-delay time-approximation approach are consistent well with our numerical simulation. For case II: Our numerical simulation results show that time delay can also induce the gene switch, however different with case I, the TF-A monomer concentration shifts from the low concentration state to the high concentration state ("off"→"on"). With increasing time delay, the transition from "on" to "off" state can be further enhanced. Moreover, it is found that the stochastic resonance can be weaken by the time delay.ConclusionsThe stochastic delay dynamic approach can identify key physiological control parameters to which the behavior of special genetic regulatory systems is particularly sensitive. Such parameters might provide targets for pharmacological intervention. Thus, it would be highly interesting to investigate if similar experimental techniques could be used to bring out the delay-induced switch and stochastic resonance in the stochastic gene transcriptional regulatory process.

Role of Time Delay and Noise Color in Bistable System with Dichotomous Noise

The effect of time delay and noise color in a time-delayed bistable system subject to asymmetric dichotomous noise and colored noise as well as to square-wave signal is studied. Applying small delay-time approximation, under the adiabatic limit condition, we obtain the expression of the signal-to-noise ratio (SNR) of the system. By virtue of the SNR expression, we find that, the SNR varies non-monotonously with the delayed-time and the correlation of the colored noise. Moreover, the SNR exhibits SR behavior as a function of the strength of the colored noise

Synchrony of Two Brain Regions Predicts the Blood Oxygen Level Dependent Activity of a Third

Spontaneously emerging coherent fluctuations have been long observed in electrophysiological and functional magnetic resonance imaging studies. These dynamics have been identified in multiple brain areas in the 1-100 and < 0.1 Hz frequency ranges spanning neurophysiological oscillations and blood oxygen level dependent (BOLD) signals, respectively. In this article, we demonstrate that transient neural synchronization between two sites may lead to the emergence of ultra-slow frequency fluctuations in the BOLD signal at another (third) site. Starting with a network model comprised of three neural oscillators, we illustrate the critical role of time delay and coupling strength in generating these slow coherent fluctuations as a function of intermittently occurring neural coherence. When extending the network toward biologically realistic primate connectivity, we find that the BOLD activation patterns arise from neurophysiological coherence, especially among medial cortical areas. This finding demonstrates a network-level mechanism whereby the BOLD activity at a given region is critically influenced by the neuroelectric synchronization patterns of other regions in the network.

Sensitivity to social contingency or stability of interaction? Modelling the dynamics of perceptual crossing

We introduce a series of evolutionary robotics simulations that address the behaviour of individuals in socially contingent interactions. The models are based on a recent study by Auvray, Lenay and Stewart [(2006). The attribution of intentionality in a simulated environment: The case of minimalist devices. In Tenth meeting of the association for the scientific study of consciousness, Oxford, UK, 23–26 June, 2006] on tactile perceptual crossing in a minimal virtual environment. In accordance, both the empirical experiments and our simulations point out the essential character of global embodied interaction dynamics for the sensitivity to contingency to arise. Rather than being individually perceived by any of the interactors, sensitivity to contingency arises from processes of circular causality that characterise the collective dynamics. Such global dynamical aspects are frequently neglected when studying social cognition. Furthermore, our synthetic studies point out interesting aspects of the task that are not immediately obvious in the empirical data. They, in addition, generate new hypotheses for further experiments. We conclude by promoting a minimal but tractable, dynamic and embodied account to social interaction, combining synthetic and empirical findings as well as concrete predictions regarding sensorimotor strategies, the role of time-delays and robustness to perturbations in interactive dynamics.

The role of time delays in a non-autonomous host–parasitoid model of slug biocontrol with nematodes

Motivated by the difficulty in designing efficacious biocontrol strategies for dominant, agriculturally damaging slug species using naturally occurring parasitic nematodes, we investigate theory for the significant impact of stage structured delays on a non-autonomous host–parasitoid system. Initially, we mathematically strengthen existing stability results for a general class of autonomous system with delays at different trophic levels using analytical and numerical continuation methods. These results are employed to guide theoretical analyses of the effect of delays in a particular, seasonally forced, host–parasitoid system that can model aspects of slug–nematode biocontrol dynamics. Significantly, the model reveals a log-dose response consistent with experiments, and suggests that the optimal timing and frequency of applications is highly dependent on the form of the control required. We find that short-term high-level as well as less dramatic but sustained control are both possible by varying the timing of application. Moreover, we establish that resonance can occur between application and slug life-cycle frequencies inducing potentially undesirable large amplitude fluctuations in slug numbers. Finally, we assess the practicality of planning a crop protection response in the field.

The Role Of Time Delays, Slow Processes And Chaos In Modulating The Cell-Cycle Clock

The regulation of the cell cycle clock is examined using a theoretical model for the embryonic cell cycle, where the clock is described as a single-limit cycle [1]. By taking the coefficient of the autocatalytic reaction as proportional to the deviation of the system from its equilibrium state, we show how such clocks can be adjusted to function on several time scales. This feedback control, causing a periodic change in the sign of the autocatalytic reaction, may be interpreted as a periodic change in the ratio of cdc25/wee1 activity. Its introduction results in the appearance of a double limit cycle, signifying the acquisition of the G1 phase and the G2 phase, during embryonic development. Following the loss of stability of the double cycle, through a period-doubling bifurcation, another limit set|a strange attractor|is born. The complicated geometry of this strange attractor can be viewed as an unlimited reservoir of periods in the phase space. We hypothesize that the existence of such a reservoir is advantageous in morphogenetic tissues, such as the bone marrow, as it enables time- and site-specific selection of the optimal cell-cycle period for any specific microenvironment. This can be obtained by the addition of a time delay in the autocatalytic reaction, reflecting, for example, the influence of external molecular signals on cell-cycle progression.

Logarithmic integrals, interpolation bounds, and performance limitations in MIMO feedback systems

We study performance limitation issues found in linear multivariable feedback systems. Our main contributions include Bode and Poisson type integral inequalities and performance limits for the sensitivity and complementary sensitivity functions. These results characterize and quantify explicitly how open-loop unstable poles and nonminimum phase zeros may impose inherent limitations on feedback design and fundamental limits on the best achievable performance. The role of time delay is also studied in this context. Most notably, we show that the performance and design limitations in multivariable systems intrinsically depend on the locations as well as directions of unstable poles and nonminimum phase zeros, and in particular, on how pole and zero directions are aligned. The latter is characterized by angles measuring the mutual orientation between zero and pole directions, and it is shown to play a crucial role in multivariable system design.

Role of Time Delay in Chemical Reaction Rates

Using the concept of resonant states, the expressions for the rate of association and dissociation are derived. A density matrix formalism is developed, which enables us to discuss the conditions for which conventional expressions of the reaction rates are valid. It is shown that an Arrhenius type expression is only valid if the widths of the resonant states are larger than π kT, which implies that the decay of resonant states is independent of the way they are formed. As long as this condition and the steady state assumption holds for the concentration of molecules in resonant states, the interference effects of overlapping resonances are found to vanish. The connection with transition state theory is derived. General new expressions valid for all pressures are presented. The role of time delay in them is discussed.