Collective dynamics in the presence of finite-width pulses.

The idealization of neuronal pulses as δ-spikes is a convenient approach in neuroscience but can sometimes lead to erroneous conclusions. We investigate the effect of a finite pulse width on the dynamics of balanced neuronal networks. In particular, we study two populations of identical excitatory and inhibitory neurons in a random network of phase oscillators coupled through exponential pulses with different widths. We consider three coupling functions inspired by leaky integrate-and-fire neurons with delay and type I phase-response curves. By exploring the role of the pulse widths for different coupling strengths, we find a robust collective irregular dynamics, which collapses onto a fully synchronous regime if the inhibitory pulses are sufficiently wider than the excitatory ones. The transition to synchrony is accompanied by hysteretic phenomena (i.e., the co-existence of collective irregular and synchronous dynamics). Our numerical results are supported by a detailed scaling and stability analysis of the fully synchronous solution. A conjectured first-order phase transition emerging for δ-spikes is smoothed out for finite-width pulses.

The Human Body as a Super Network: Digital Methods to Analyze the Propagation of Aging.

Biological aging is a complex process involving multiple biological processes. These can be understood theoretically though considering them as individual networks-e.g., epigenetic networks, cell-cell networks (such as astroglial networks), and population genetics. Mathematical modeling allows the combination of such networks so that they may be studied in unison, to better understand how the so-called "seven pillars of aging" combine and to generate hypothesis for treating aging as a condition at relatively early biological ages. In this review, we consider how recent progression in mathematical modeling can be utilized to investigate aging, particularly in, but not exclusive to, the context of degenerative neuronal disease. We also consider how the latest techniques for generating biomarker models for disease prediction, such as longitudinal analysis and parenclitic analysis can be applied to as both biomarker platforms for aging, as well as to better understand the inescapable condition. This review is written by a highly diverse and multi-disciplinary team of scientists from across the globe and calls for greater collaboration between diverse fields of research.

Ubiquity of collective irregular dynamics in balanced networks of spiking neurons.

We revisit the dynamics of a prototypical model of balanced activity in networks of spiking neurons. A detailed investigation of the thermodynamic limit for fixed density of connections (massive coupling) shows that, when inhibition prevails, the asymptotic regime is not asynchronous but rather characterized by a self-sustained irregular, macroscopic (collective) dynamics. So long as the connectivity is massive, this regime is found in many different setups: leaky as well as quadratic integrate-and-fire neurons; large and small coupling strength; and weak and strong external currents.

Cortical Spike Synchrony as a Measure of Input Familiarity.

Spike synchrony, which occurs in various cortical areas in response to specific perception, action, and memory tasks, has sparked a long-standing debate on the nature of temporal organization in cortex. One prominent view is that this type of synchrony facilitates the binding or grouping of separate stimulus components. We argue instead for a more general function: a measure of the prior probability of incoming stimuli, implemented by long-range, horizontal, intracortical connections. We show that networks of this kind-pulse-coupled excitatory spiking networks in a noisy environment-can provide a sufficient substrate for stimulus-dependent spike synchrony. This allows for a quick (few spikes) estimate of the match between inputs and the input history as encoded in the network structure. Given the ubiquity of small, strongly excitatory subnetworks in cortex, we thus propose that many experimental observations of spike synchrony can be viewed as signs of input patterns that resemble long-term experience-that is, of patterns with high prior probability.

Modelling Robust Feedback Control Mechanisms That Ensure Reliable Coordination of Histone Gene Expression with DNA Replication.

Histone proteins are key elements in the packing of eukaryotic DNA into chromosomes. A little understood control system ensures that histone gene expression is balanced with DNA replication so that histone proteins are produced in appropriate amounts. Disturbing or disrupting this system affects genome stability and gene expression, and has detrimental consequences for human development and health. It has been proposed that feedback control involving histone proteins contributes to this regulation and there is evidence implicating cell cycle checkpoint molecules activated when DNA synthesis is impaired in this control. We have developed mathematical models that incorporate these control modes in the form of inhibitory feedback of histone gene expression from free histone proteins, and alternatively a direct link that couples histone RNA synthesis to DNA synthesis. Using our experimental evidence and related published data we provide a simplified description of histone protein synthesis during S phase. Both models reproduce the coordination of histone gene expression with DNA replication during S phase and the down-regulation of histone RNA when DNA synthesis is interrupted, but only the model incorporating histone protein feedback control was able to effectively simulate the coordinate expression of a simplified histone gene family. Our combined theoretical and experimental approach supports the hypothesis that the regulation of histone gene expression involves feedback control.

Exponential signaling gain at the receptor level enhances signal-to-noise ratio in bacterial chemotaxis.

Cellular signaling systems show astonishing precision in their response to external stimuli despite strong fluctuations in the molecular components that determine pathway activity. To control the effects of noise on signaling most efficiently, living cells employ compensatory mechanisms that reach from simple negative feedback loops to robustly designed signaling architectures. Here, we report on a novel control mechanism that allows living cells to keep precision in their signaling characteristics - stationary pathway output, response amplitude, and relaxation time - in the presence of strong intracellular perturbations. The concept relies on the surprising fact that for systems showing perfect adaptation an exponential signal amplification at the receptor level suffices to eliminate slowly varying multiplicative noise. To show this mechanism at work in living systems, we quantified the response dynamics of the E. coli chemotaxis network after genetically perturbing the information flux between upstream and downstream signaling components. We give strong evidence that this signaling system results in dynamic invariance of the activated response regulator against multiplicative intracellular noise. We further demonstrate that for environmental conditions, for which precision in chemosensing is crucial, the invariant response behavior results in highest chemotactic efficiency. Our results resolve several puzzling features of the chemotaxis pathway that are widely conserved across prokaryotes but so far could not be attributed any functional role.

Parameter estimation methods for chaotic intercellular networks.

We have investigated simulation-based techniques for parameter estimation in chaotic intercellular networks. The proposed methodology combines a synchronization-based framework for parameter estimation in coupled chaotic systems with some state-of-the-art computational inference methods borrowed from the field of computational statistics. The first method is a stochastic optimization algorithm, known as accelerated random search method, and the other two techniques are based on approximate Bayesian computation. The latter is a general methodology for non-parametric inference that can be applied to practically any system of interest. The first method based on approximate Bayesian computation is a Markov Chain Monte Carlo scheme that generates a series of random parameter realizations for which a low synchronization error is guaranteed. We show that accurate parameter estimates can be obtained by averaging over these realizations. The second ABC-based technique is a Sequential Monte Carlo scheme. The algorithm generates a sequence of "populations", i.e., sets of randomly generated parameter values, where the members of a certain population attain a synchronization error that is lesser than the error attained by members of the previous population. Again, we show that accurate estimates can be obtained by averaging over the parameter values in the last population of the sequence. We have analysed how effective these methods are from a computational perspective. For the numerical simulations we have considered a network that consists of two modified repressilators with identical parameters, coupled by the fast diffusion of the autoinducer across the cell membranes.

Theoretical basis of the community effect in development.

BACKGROUND: Genetically identical cells often show significant variation in gene expression profile and behaviour even in the same physiological condition. Notably, embryonic cells destined to the same tissue maintain a uniform transcriptional regulatory state and form a homogeneous cell group. One mechanism to keep the homogeneity within embryonic tissues is the so-called community effect in animal development. The community effect is an interaction among a group of many nearby precursor cells, and is necessary for them to maintain tissue-specific gene expression and differentiate in a coordinated manner. Although it has been shown that the cell-cell communication by a diffusible factor plays a crucial role, it is not immediately obvious why a community effect needs many cells. RESULTS: In this work, we propose a model of the community effect in development, which consists in a linear gene cascade and cell-cell communication. We examined the properties of the model theoretically using a combination of stochastic and deterministic modelling methods. We have derived the analytical formula for the threshold size of a cell population that is necessary for a community effect, which is in good agreement with stochastic simulation results. CONCLUSIONS: Our theoretical analysis indicates that a simple model with a linear gene cascade and cell-cell communication is sufficient to reproduce the community effect in development. The model explains why a community needs many cells. It suggests that the community's long-term behaviour is independent of the initial induction level, although the initiation of a community effect requires a sufficient amount of inducing signal. The mechanism of the community effect revealed by our theoretical analysis is analogous to that of quorum sensing in bacteria. The community effect may underlie the size control in animal development and also the genesis of autosomal dominant diseases including tumorigenesis.

Abundance of stable periodic behavior in a Red Grouse population model with delay: a consequence of homoclinicity.

Shrimp-shaped periodic regions embedded in chaotic regions in two-dimensional parameter spaces are of specific interest for physical and biological systems. We provide the first observation of these shrimp-shaped stability regions in a parameter space of a continuous time-delayed population model, obtained by taking the delays as bifurcation parameters. The parameter space organization is governed by the presence of infinitely many periodicity hubs, which trigger the spiraling organization of these shrimp-shaped periodic regions around them. We provide evidence that this spiraling organization in the parameter space is a consequence of the existence of homoclinic orbits in the phase space.

Noise-induced coherence in multicellular circadian clocks.

In higher organisms, circadian rhythms are generated by a multicellular genetic clock that is entrained very efficiently to the 24-h light-dark cycle. Most studies done so far of these circadian oscillators have considered a perfectly periodic driving by light, in the form of either a square wave or a sinusoidal modulation. However, in natural conditions, organisms are subject to nonnegligible fluctuations in the light level all through the daily cycle. In this article, we investigate how the interplay between light fluctuations and intercellular coupling affects the dynamics of the collective rhythm in a large ensemble of nonidentical, globally coupled cellular clocks modeled as Goodwin oscillators. On the basis of experimental considerations, we assume an inverse dependence of the cell-cell coupling strength on the light intensity, in such a way that the larger the light intensity, the weaker the coupling. Our results show a noise-induced rhythm generation for constant light intensities at which the clock is arrhythmic in the noise-free case. Importantly, the rhythm shows a resonancelike phenomenon as a function of the noise intensity. Such improved coherence can be only observed at the level of the overt rhythm and not at the level of the individual oscillators, thus suggesting a cooperative effect of noise, coupling, and the emerging synchronization between the oscillators.

Multistability of synthetic genetic networks with repressive cell-to-cell communication.

We investigate an experimentally feasible synthetic genetic network consisting of two phase repulsively coupled repressilators, which evokes multiple coexisting stable attractors with different features. We perform a bifurcation analysis to determine and classify the dynamical structure of the system. Moreover, some of the dynamical regimes found, such as inhomogeneous steady states and inhomogeneous limit cycles can further be associated with artificial cell differentiation. We also report and characterize the emergence of chaotic dynamics resulting from the intercell coupling.

Multistability and clustering in a population of synthetic genetic oscillators via phase-repulsive cell-to-cell communication.

We show that phase-repulsive coupling eliminates oscillations in a population of synthetic genetic clocks. For this, we propose an experimentally feasible synthetic genetic network that contains phase repulsively coupled repressilators with broken temporal symmetry. As the coupling strength increases, silencing of oscillations is found to occur via the appearance of an inhomogeneous limit cycle, followed by oscillation death. Two types of oscillation death are observed: For lower couplings, the cells cluster in one of two stationary states of protein expression; for larger couplings, all cells end up in a single (stationary) cellular state. Several multistable regimes are observed along this route to oscillation death.