Dynamics of spiking neurons: between homogeneity and synchrony

Randomly connected networks of neurons driven by Poisson inputs are often assumed to produce “homogeneous” dynamics, characterized by largely independent firing and approximable by diffusion processes. At the same time, it is well known that such networks can fire synchronously. Between these two much studied scenarios lies a vastly complex dynamical landscape that is relatively unexplored. In this paper, we discuss a phenomenon which commonly manifests in these intermediate regimes, namely brief spurts of spiking activity which we call multiple firing events (MFE). These events do not depend on structured network architecture nor on structured input; they are an emergent property of the system. We came upon them in an earlier modeling paper, in which we discovered, through a careful benchmarking process, that MFEs are the single most important dynamical mechanism behind many of the V1 phenomena we were able to replicate. In this paper we explain in a simpler setting how MFEs come about, as well as their potential dynamic consequences. Although the mechanism underlying MFEs cannot easily be captured by current population dynamics models, this phenomena should not be ignored during analysis; there is a growing body of evidence that such collaborative activity may be a key towards unlocking the possible functional properties of many neuronal networks.     

Distribution of correlated spiking events in a population-based approach for Integrate-and-Fire networks

Randomly connected populations of spiking neurons display a rich variety of dynamics. However, much of the current modeling and theoretical work has focused on two dynamical extremes: on one hand homogeneous dynamics characterized by weak correlations between neurons, and on the other hand total synchrony characterized by large populations firing in unison. In this paper we address the conceptual issue of how to mathematically characterize the partially synchronous “multiple firing events” (MFEs) which manifest in between these two dynamical extremes. We further develop a geometric method for obtaining the distribution of magnitudes of these MFEs by recasting the cascading firing event process as a first-passage time problem, and deriving an analytical approximation of the first passage time density valid for large neuron populations. Thus, we establish a direct link between the voltage distributions of excitatory and inhibitory neurons and the number of neurons firing in an MFE that can be easily integrated into population–based computational methods, thereby bridging the gap between homogeneous firing regimes and total synchrony.     

Establishing a Statistical Link between Network Oscillations and Neural Synchrony

Pairs of active neurons frequently fire action potentials or “spikes” nearly synchronously (i.e., within 5 ms of each other). This spike synchrony may occur by chance, based solely on the neurons’ fluctuating firing patterns, or it may occur too frequently to be explicable by chance alone. When spike synchrony above chances levels is present, it may subserve computation for a specific cognitive process, or it could be an irrelevant byproduct of such computation. Either way, spike synchrony is a feature of neural data that should be explained. A point process regression framework has been developed previously for this purpose, using generalized linear models (GLMs). In this framework, the observed number of synchronous spikes is compared to the number predicted by chance under varying assumptions about the factors that affect each of the individual neuron’s firing-rate functions. An important possible source of spike synchrony is network-wide oscillations, which may provide an essential mechanism of network information flow. To establish the statistical link between spike synchrony and network-wide oscillations, we have integrated oscillatory field potentials into our point process regression framework. We first extended a previously-published model of spike-field association and showed that we could recover phase relationships between oscillatory field potentials and firing rates. We then used this new framework to demonstrate the statistical relationship between oscillatory field potentials and spike synchrony in: 1) simulated neurons, 2) in vitro recordings of hippocampal CA1 pyramidal cells, and 3) in vivo recordings of neocortical V4 neurons. Our results provide a rigorous method for establishing a statistical link between network oscillations and neural synchrony.     

To Perceive or Not Perceive: The Role of Gamma-band Activity in Signaling Object Percepts

The relation of gamma-band synchrony to holistic perception in which concerns the effects of sensory processing, high level perceptual gestalt formation, motor planning and response is still controversial. To provide a more direct link to emergent perceptual states we have used holistic EEG/ERP paradigms where the moment of perceptual “discovery” of a global pattern was variable. Using a rapid visual presentation of short-lived Mooney objects we found an increase of gamma-band activity locked to perceptual events. Additional experiments using dynamic Mooney stimuli showed that gamma activity increases well before the report of an emergent holistic percept. To confirm these findings in a data driven manner we have further used a support vector machine classification approach to distinguish between perceptual vs. non perceptual states, based on time-frequency features. Sensitivity, specificity and accuracy were all above 95%. Modulations in the 30–75 Hz range were larger for perception states. Interestingly, phase synchrony was larger for perception states for high frequency bands. By focusing on global gestalt mechanisms instead of local processing we conclude that gamma-band activity and synchrony provide a signature of holistic perceptual states of variable onset, which are separable from sensory and motor processing.     

Spatial variability in prey phenology determines predator movement patterns and prey survival

Species have phenological variation among local habitats that are located at relatively small spatial scales. However, less studies have tested how this spatial variability in phenology can mediate intra-/inter-specific interactions. When predators track phenological variation of prey among local habitats, survival of prey within a local habitat strongly influenced by phenological synchrony with their conspecifics in adjacent habitats. Theory predicts that phenological synchrony among local habitats increases prey survival in local habitat within spatially structured environments because the predators have to make a habitat choice for foraging. Consequently, total survival of prey at regional scale should be higher. By using a spatially explicit field experiment, we tested above hypothesis using a prey–predator interaction between tadpole (Rhacophorus arboreus) and newt (Cynops pyrrhogaster). We established enclosures (≈regional scale) consisting of two tanks (≈local habitat scale) with different degree of prey phenological synchrony. We found that phenological synchrony of prey between tanks within each enclosure decreased the mean residence time of the predator in each tank, which resulted in higher survival of prey at a local habitat scale, supporting the theoretical prediction. Furthermore, individual-level variation in predator residence time explained the between-tank variation in prey survival in enclosures with phenological synchrony, implying that movement patterns of the predator can mediate variation in local population dynamics of their prey. However, total survival at each enclosure was not higher under phenological synchrony. These results suggest the importance of relative timing of prey phenology, not absolute timing, among local habitats in determining prey–predator interactions.     

Developmental synchrony in multivoltine insects: generation separation versus smearing

Many insect species undergo multiple generations each year. They are found across biomes that vary in their strength of seasonality and, depending on location and species, can display a wide range of population dynamics. Some species exhibit cycles with distinct generations (developmental synchrony/generation separation), some exhibit overlapping generations with multiple life stages present simultaneously (generation smearing), while others have intermediate dynamics with early season separation followed by late season smearing. There are two main hypotheses to explain these dynamics. The first is the ‘seasonal disturbance’ hypothesis where winter synchronizes the developmental clock among individuals, which causes transient generation separation early in the season that erodes through the summer. The second is the ‘temperature destabilization’ hypothesis where warm temperatures during the summer cause population dynamics to become unstable giving rise to single generation cycles. Both hypotheses are supported by detailed mathematical theory incorporating mechanisms that are likely to drive dynamics in nature. In this review, we synthesize the theory and propose a conceptual framework—where each mechanism may be seen as an independent axis shaping the developmental (a)synchrony—that allows us to predict dynamic patterns from insect life-history characteristics. High fecundity, short adult life-span and strong seasonality enhance synchrony, while developmental plasticity and environmental heterogeneity erode synchrony. We further review current mathematical and statistical tools to study multi-generational dynamics and illustrate using case studies of multivoltine tortrix moths. By integrating two disparate bodies of theory, we articulate a deep connection among temperature, stability, developmental synchrony and inter-generational dynamics of multivoltine insects that is missing in current literature.     

Periodic forcing of microbial cultures: a model for induction synchrony

Periodic environmental shifts have been used to induce synchrony in many different microbial populations. In this article, the induction synchrony phenomenon is analyzed using an age distribution model in which the age at which the cells divide is subjected to periodic forcing. It is found that synchrony will occur whenever the period of the forcing lies in the interval between the youngest and the oldest division age that occur in the population during the forcing. The analysis also predicts that under certain conditions it should be possible to obtain a multimodal synchrony in which cells in the population are distributed among a set of discrete, synchronized cell lines. The behavior of the age distribution when the conditions for synchrony are not satisfied is briefly explored. It is found that the age distribution model is able to exhibit a very rich spectrum of possible dynamic behavior. Many of the phenomena observed can be thought of in terms that are familiar from nonlinear analysis, such as stable and unstable limit cycles, period doubling, halving, and chaos. The richness of dynamic behavior opens the possibility that environmental shifts or periodic forcing could be used as a powerful tool in discriminating models of microbial kinetics and cell cycle control.     

The frustrated brain: from dynamics on motifs to communities and networks

Cognitive function depends on an adaptive balance between flexible dynamics and integrative processes in distributed cortical networks. Patterns of zero-lag synchrony likely underpin numerous perceptual and cognitive functions. Synchronization fulfils integration by reducing entropy, while adaptive function mandates that a broad variety of stable states be readily accessible. Here, we elucidate two complementary influences on patterns of zero-lag synchrony that derive from basic properties of brain networks. First, mutually coupled pairs of neuronal subsystems—resonance pairs—promote stable zero-lag synchrony among the small motifs in which they are embedded, and whose effects can propagate along connected chains. Second, frustrated closed-loop motifs disrupt synchronous dynamics, enabling metastable configurations of zero-lag synchrony to coexist. We document these two complementary influences in small motifs and illustrate how these effects underpin stable versus metastable phase-synchronization patterns in prototypical modular networks and in large-scale cortical networks of the macaque (CoCoMac). We find that the variability of synchronization patterns depends on the inter-node time delay, increases with the network size and is maximized for intermediate coupling strengths. We hypothesize that the dialectic influences of resonance versus frustration may form a dynamic substrate for flexible neuronal integration, an essential platform across diverse cognitive processes.     

On the parallelisation of bioinformatics applications

This paper surveys the computational strategies followed to parallelise the most used software in the bioinformatics arena. The studied algorithms are computationally expensive and their computational patterns range from regular, such as database-searching applications, to very irregularly structured patterns (phylogenetic trees). Fine- and coarse-grained parallel strategies are discussed for these very diverse sets of applications. This overview outlines computational issues related to parallelism, physical machine models, parallel programming approaches and scheduling strategies for a broad range of computer architectures. In particular, it deals with shared, distributed and shared/distributed memory architectures.     

Simulated Cytoskeletal Collapse via Tau Degradation

We present a coarse-grained two dimensional mechanical model for the microtubule-tau bundles in neuronal axons in which we remove taus, as can happen in various neurodegenerative conditions such as Alzheimers disease, tauopathies, and chronic traumatic encephalopathy. Our simplified model includes (i) taus modeled as entropic springs between microtubules, (ii) removal of taus from the bundles due to phosphorylation, and (iii) a possible depletion force between microtubules due to these dissociated phosphorylated taus. We equilibrate upon tau removal using steepest descent relaxation. In the absence of the depletion force, the transverse rigidity to radial compression of the bundles falls to zero at about 60% tau occupancy, in agreement with standard percolation theory results. However, with the attractive depletion force, spring removal leads to a first order collapse of the bundles over a wide range of tau occupancies for physiologically realizable conditions. While our simplest calculations assume a constant concentration of microtubule intercalants to mediate the depletion force, including a dependence that is linear in the detached taus yields the same collapse. Applying percolation theory to removal of taus at microtubule tips, which are likely to be the protective sites against dynamic instability, we argue that the microtubule instability can only obtain at low tau occupancy, from 0.06–0.30 depending upon the tau coordination at the microtubule tips. Hence, the collapse we discover is likely to be more robust over a wide range of tau occupancies than the dynamic instability. We suggest in vitro tests of our predicted collapse.     

Quantitative Assessment of the Importance of Phenotypic Plasticity in Adaptation to Climate Change in Wild Bird Populations

Predictions about the fate of species or populations under climate change scenarios typically neglect adaptive evolution and phenotypic plasticity, the two major mechanisms by which organisms can adapt to changing local conditions. As a consequence, we have little understanding of the scope for organisms to track changing environments by in situ adaptation. Here, we use a detailed individual-specific long-term population study of great tits (Parus major) breeding in Wytham Woods, Oxford, UK to parameterise a mechanistic model and thus directly estimate the rate of environmental change to which in situ adaptation is possible. Using the effect of changes in early spring temperature on temporal synchrony between birds and a critical food resource, we focus in particular on the contribution of phenotypic plasticity to population persistence. Despite using conservative estimates for evolutionary and reproductive potential, our results suggest little risk of population extinction under projected local temperature change; however, this conclusion relies heavily on the extent to which phenotypic plasticity tracks the changing environment. Extrapolating the model to a broad range of life histories in birds suggests that the importance of phenotypic plasticity for adjustment to projected rates of temperature change increases with slower life histories, owing to lower evolutionary potential. Understanding the determinants and constraints on phenotypic plasticity in natural populations is thus crucial for characterising the risks that rapidly changing environments pose for the persistence of such populations.     

Dose-Dependent Regulation of Alternative Splicing by MBNL Proteins Reveals Biomarkers for Myotonic Dystrophy

Alternative splicing is a regulated process that results in expression of specific mRNA and protein isoforms. Alternative splicing factors determine the relative abundance of each isoform. Here we focus on MBNL1, a splicing factor misregulated in the disease myotonic dystrophy. By altering the concentration of MBNL1 in cells across a broad dynamic range, we show that different splicing events require different amounts of MBNL1 for half-maximal response, and respond more or less steeply to MBNL1. Motifs around MBNL1 exon 5 were studied to assess how cis-elements mediate the MBNL1 dose-dependent splicing response. A framework was developed to estimate MBNL concentration using splicing responses alone, validated in the cell-based model, and applied to myotonic dystrophy patient muscle. Using this framework, we evaluated the ability of individual and combinations of splicing events to predict functional MBNL concentration in human biopsies, as well as their performance as biomarkers to assay mild, moderate, and severe cases of DM.     

OLA-1, an Obg-like ATPase,integrates hunger with temperature information in sensory neurons in C. elegans

Animals detect changes in both their environment and their internal state and modify their behavior accordingly. Yet, it remains largely to be clarified how information of environment and internal state is integrated and how such integrated information modifies behavior. Well-fed C. elegans migrates to past cultivation temperature on a thermal gradient, which is disrupted when animals are starved. We recently reported that the neuronal activities synchronize between a thermosensory neuron AFD and an interneuron AIY, which is directly downstream of AFD, in well-fed animals, while this synchrony is disrupted in starved animals. However, it remained to be determined whether the disruption of the synchrony is derived from modulation of the transmitter release from AFD or from the modification of reception or signal transduction in AIY. By performing forward genetics on a transition of thermotaxis behavior along starvation, we revealed that OLA-1, an Obg-like ATPase, functions in AFD to promote disruption of AFD-AIY synchrony and behavioral transition. Our results suggest that the information of hunger is delivered to the AFD thermosensory neuron and gates transmitter release from AFD to disrupt thermotaxis, thereby shedding light onto a mechanism for the integration of environmental and internal state to modulate behavior.     

Emergent dynamics in a model of visual cortex

This paper proposes that the network dynamics of the mammalian visual cortex are highly structured and strongly shaped by temporally localized barrages of excitatory and inhibitory firing we call ‘multiple-firing events’ (MFEs). Our proposal is based on careful study of a network of spiking neurons built to reflect the coarse physiology of a small patch of layer 2/3 of V1. When appropriately benchmarked this network is capable of reproducing the qualitative features of a range of phenomena observed in the real visual cortex, including spontaneous background patterns, orientation-specific responses, surround suppression and gamma-band oscillations. Detailed investigation into the relevant regimes reveals causal relationships among dynamical events driven by a strong competition between the excitatory and inhibitory populations. It suggests that along with firing rates, MFE characteristics can be a powerful signature of a regime. Testable predictions based on model observations and dynamical analysis are proposed.     

Heterogeneity versus homogeneity: A conceptual and mathematical theory in terms of scale-invariant and scale-covariant distributions

Ecologists often use the words heterogeneity and homogeneity when they are describing the distribution of a variable, yet there has been no formal exploration into the relation of these two states to one another. This work formalizes their relationship within statistical theory with a conceptual framework that includes five parameters: L, K, S, D, and R. These parameters provide an increasing degree of specificity about a distribution as they are enumerated and accord with measurements of system extent, richness, evenness, variance, and scale-covariance. Moreover, a mathematical and physical basis for understanding heterogeneity and homogeneity is outlined in terms of Brownian motion, where the Hurst exponent H and the notion of variance are utilized to delimit these two states. Spatial and temporal patterns are quantified and classified according to the mathematical and physical basis at multiple scales, as well as within the conceptual framework that can be applied to other metrics. Concepts of scale-invariance and scale-covariance are discussed in terms of hierarchy theory. It is argued that in hierarchical distributions, we should expect more than simple scale-covariance; we should expect division by a transitional state that divides heterogeneity from homogeneity at some scale. By revisiting the underlying statistical theory behind these concepts, a more efficient approach to quantifying ecological distributions can result.     

Hysteresis in Audiovisual Synchrony Perception

The effect of stimulation history on the perception of a current event can yield two opposite effects, namely: adaptation or hysteresis. The perception of the current event thus goes in the opposite or in the same direction as prior stimulation, respectively. In audiovisual (AV) synchrony perception, adaptation effects have primarily been reported. Here, we tested if perceptual hysteresis could also be observed over adaptation in AV timing perception by varying different experimental conditions. Participants were asked to judge the synchrony of the last (test) stimulus of an AV sequence with either constant or gradually changing AV intervals (constant and dynamic condition, respectively). The onset timing of the test stimulus could be cued or not (prospective vs. retrospective condition, respectively). We observed hysteretic effects for AV synchrony judgments in the retrospective condition that were independent of the constant or dynamic nature of the adapted stimuli; these effects disappeared in the prospective condition. The present findings suggest that knowing when to estimate a stimulus property has a crucial impact on perceptual simultaneity judgments. Our results extend beyond AV timing perception, and have strong implications regarding the comparative study of hysteresis and adaptation phenomena.     

The effects of large and small-scale random events on the synchrony of metapopulation dynamics: a theoretical analysis

We present an analysis of the conditions under which migration and global random factors may determine large scale synchrony in the dynamics of spatially structured populations. We derive an analytic approximation which describes how the desynchronizing influence of local environmental stochasticity combines with the synchronizing influences of larger scale environmental stochastic variation and migration to determine population cross correlation coefficients. Despite the simplifications made by this analysis, computer simulations show that the behaviour of more complicated models is well described by our approximation over considerable regions of parameter space. We conclude that population synchrony is largely determined by the coefficients of variation (CVs) of the local and larger scale stochastic processes, and that migration alone is only likely to maintain population synchrony when the CV of the local stochastic process is very small.