Noise, transient dynamics, and the generation of realistic interspike interval variation in square-wave burster neurons

First return maps of interspike intervals for biological neurons that generate repetitive bursts of impulses can display stereotyped structures (neuronal signatures). Such structures have been linked to the possibility of multicoding and multifunctionality in neural networks that produce and control rhythmical motor patterns. In some cases, isolating the neurons from their synaptic network revealsirregular, complex signatures that have been regarded as evidence of intrinsic, chaotic behavior. We show that incorporation of dynamical noise into minimal neuron models of square-wave bursting (either conductance-based or abstract) produces signatures akin to those observed in biological examples, without the need for fine-tuning of parameters or ad hoc constructions for inducing chaotic activity. The form of the stochastic term is not strongly constrained, and can approximate several possible sources of noise, e.g. random channel gating or synaptic bombardment. The cornerstone of this signature generation mechanism is the rich, transient, but deterministic dynamics inherent in the square-wave (saddle-node/homoclinic) mode of neuronal bursting. We show that noise causes the dynamics to populate a complex transient scaffolding or skeleton in state space, even for models that (without added noise) generate only periodic activity (whether in bursting or tonic spiking mode).Comment: REVTeX4-1, 18 pages, 9 figure

Efficiency characterization of a large neuronal network: a causal information approach

When inhibitory neurons constitute about 40% of neurons they could have an important antinociceptive role, as they would easily regulate the level of activity of other neurons. We consider a simple network of cortical spiking neurons with axonal conduction delays and spike timing dependent plasticity, representative of a cortical column or hypercolumn with large proportion of inhibitory neurons. Each neuron fires following a Hodgkin-Huxley like dynamics and it is interconnected randomly to other neurons. The network dynamics is investigated estimating Bandt and Pompe probability distribution function associated to the interspike intervals and taking different degrees of inter-connectivity across neurons. More specifically we take into account the fine temporal ``structures'' of the complex neuronal signals not just by using the probability distributions associated to the inter spike intervals, but instead considering much more subtle measures accounting for their causal information: the Shannon permutation entropy, Fisher permutation information and permutation statistical complexity. This allows us to investigate how the information of the system might saturate to a finite value as the degree of inter-connectivity across neurons grows, inferring the emergent dynamical properties of the system.Comment: 26 pages, 3 Figures; Physica A, in pres

Comparing the dynamics of periodically forced lasers and neurons

Neuromorphic photonics is a new paradigm for ultra-fast neuro-inspired optical computing that canrevolutionize information processing and artificial intelligence systems. To implement practicalphotonic neural networks is crucial to identify low-cost energy-efficient laser systems that can mimicneuronal activity. Here we study experimentally the spiking dynamics of a semiconductor laser withoptical feedback under periodic modulation of the pump current, and compare with the dynamics of aneuron that is simulated with the stochastic FitzHugh–Nagumo model, with an applied periodicsignal whose waveform is the same as that used to modulate the laser current. Sinusoidal and pulse-down waveforms are tested. Wefind that the laser response and the neuronal response to the periodicforcing, quantified in terms of the variation of the spike rate with the amplitude and with the frequencyof the forcing signal, is qualitatively similar. We also compare the laser and neuron dynamics usingsymbolic time series analysis. The characterization of the statistical properties of the relative timing ofthe spikes in terms of ordinal patterns unveils similarities, and also some differences. Our resultsindicate that semiconductor lasers with optical feedback can be used as low-cost, energy-efficientphotonic neurons, the building blocks of all-optical signal processing systems; however, the length ofthe external cavity prevents optical feedback on the chip.Peer ReviewedPostprint (published version

A propensity criterion for networking in an array of coupled chaotic systems

We examine the mutual synchronization of a one dimensional chain of chaotic identical objects in the presence of a stimulus applied to the first site. We first describe the characteristics of the local elements, and then the process whereby a global nontrivial behaviour emerges. A propensity criterion for networking is introduced, consisting in the coexistence within the attractor of a localized chaotic region, which displays high sensitivity to external stimuli,and an island of stability, which provides a reliable coupling signal to the neighbors in the chain. Based on this criterion we compare homoclinic chaos, recently explored in lasers and conjectured to be typical of a single neuron, with Lorenz chaos.Comment: 4 pages, 3 figure

Feature binding as neuron synchronization: quantum aspects

Feature binding denotes how a large collection of coupled neurons combines external signals with internal memories into new coherent patterns of meaning. An external stimulus spreads over an assembly of coupled neurons, building up a corresponding collective state. Thus, the synchronization of spike trains of many individual neurons is the basis of a coherent perception. Homoclinic chaos has been proposed as the most suitable way to code information in time by trains of equal spikes occurring at apparently erratic times; a new quantitative indicator, called propensity, is introduced to select the most appropriate neuron model. In order to classify the set of different perceptions, the percept space is given a metric structure. The distance in percept space is conjugate to the duration of the perception in the sense that an uncertainty relation in percept space is associated with time limited perceptions. Thus coding of different percepts by synchronized spike trains entails fundamental quantum features with a quantum constant related to the details of the perceptual chain and very different from Planck's action

Stochastic and deterministic dynamics of intrinsically irregular firing in cortical inhibitory interneurons

Most cortical neurons fire regularly when excited by a constant stimulus. In contrast, irregular-spiking (IS) interneurons are remarkable for the intrinsic variability of their spike timing, which can synchronize amongst IS cells via specific gap junctions. Here, we have studied the biophysical mechanisms of this irregular spiking in mice, and how IS cells fire in the context of synchronous network oscillations. Using patch-clamp recordings, artificial dynamic conductance injection, pharmacological analysis and computational modeling, we show that spike time irregularity is generated by a nonlinear dynamical interaction of voltage-dependent sodium and fast-inactivating potassium channels just below spike threshold, amplifying channel noise. This $\textit{active irregularity}$ may help IS cells synchronize with each other at gamma range frequencies, while resisting synchronization to lower input frequencies.Biotechnology and Biological Sciences Research Council, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Cambridge Overseas Trus

Limitations of perturbative techniques in the analysis of rhythms and oscillations

Perturbation theory is an important tool in the analysis of oscillators and their response to external stimuli. It is predicated on the assumption that the perturbations in question are “sufficiently weak”, an assumption that is not always valid when perturbative methods are applied. In this paper, we identify a number of concrete dynamical scenarios in which a standard perturbative technique, based on the infinitesimal phase response curve (PRC), is shown to give different predictions than the full model. Shear-induced chaos, i.e., chaotic behavior that results from the amplification of small perturbations by underlying shear, is missed entirely by the PRC. We show also that the presence of “sticky” phase–space structures tend to cause perturbative techniques to overestimate the frequencies and regularity of the oscillations. The phenomena we describe can all be observed in a simple 2D neuron model, which we choose for illustration as the PRC is widely used in mathematical neuroscience