On the role of chemical synapses in coupled neurons with noise

We examine the behavior in the presence of noise of an array of Morris-Lecar neurons coupled via chemical synapses. Special attention is devoted to comparing this behavior with the better known case of electrical coupling arising via gap junctions. In particular, our numerical simulations show that chemical synapses are more efficient than gap junctions in enhancing coherence at an optimal noise (what is known as array-enhanced coherence resonance): in the case of (nonlinear) chemical coupling, we observe a substantial increase in the stochastic coherence of the system, in comparison with (linear) electrical coupling. We interpret this qualitative difference between both types of coupling as arising from the fact that chemical synapses only act while the presynaptic neuron is spiking, whereas gap junctions connect the voltage of the two neurons at all times. This leads in the electrical coupling case to larger correlations during interspike time intervals which are detrimental to the array-enhanced coherence effect. Finally, we report on the existence of a system-size coherence resonance in this locally coupled system, exhibited by the average membrane potential of the array.Comment: 7 pages, 7 figure

A neural mechanism for binaural pitch perception via ghost stochastic resonance

We present a physiologically plausible binaural mechanism for the perception of the pitch of complex sounds via ghost stochastic resonance. In this scheme, two neurons are driven by noise and different periodic signal each (with frequencies f1=kf0 and f2=(k+1)f0, where k>1), and their outputs (plus noise) are applied synaptically to a third neuron. Our numerical results, using the Morris-Lecar neuron model with chemical synapses explicity considered, show that intermediate noise levels enhance the response of the third neuron at frequencies close to f0, as in the cases previously described of ghost resonance. For the case of inharmonic combinations of inputs (both frequencies shifted by the same amount Df) noise is also seen to enhance the response of the third neuron at a frequency fr with also shift linearly with Df. In addition, we show that similar resonances can be observed as a function of the synaptic time constant. The suggested ghost-resonance-based stochastic mechanism can thus arise either at the peripheral level or at a higher level of neural processing in the perception of the pitchComment: 7 pages, 5 figure

Mutual regulation causes co-entrainment between a synthetic oscillator and the bacterial cell cycle

The correct functioning of cells requires the orchestration of multiple cellular processes, many of which are inherently dynamical. The conditions under which these dynamical processes entrain each other remain unclear. Here we use synthetic biology to address this question in the case of concurrent cellular oscillations. Specifically, we study at the single-cell level the interaction between the cell division cycle and a robust synthetic gene oscillator in Escherichia coli. Our results suggest that cell division is able to partially entrain the synthetic oscillations under normal growth conditions, by driving the periodic replication of the genes involved in the oscillator. Coupling the synthetic oscillations back into the cell cycle via the expression of a key regulator of chromosome replication increases the synchronization between the two periodic processes. A simple computational model allows us to confirm this effect.Peer ReviewedPostprint (published version

Bistable phase control via rocking in a nonlinear electronic oscillator

We experimentally demonstrate the effective rocking of a nonlinear electronic circuit operating in a periodic regime. Namely, we show that driving a Chua circuit with a periodic signal, whose phase alternates (also periodically) in time, we lock the oscillation frequency of the circuit to that of the driving signal, and its phase to one of two possible values shifted by pi, and lying between the alternating phases of the input signal. In this way, we show that a rocked nonlinear oscillator displays phase bistability. We interpret the experimental results via a theoretical analysis of rocking on a simple oscillator model, based on a normal form description (complex Landau equation) of the rocked Hopf bifurcationComment: 7 pages, 10 figure

Synchronization by dynamical relaying in electronic circuit arrays

We experimentally study the synchronization of two chaotic electronic circuits whose dynamics is relayed by a third parameter-matched circuit, to which they are coupled bidirectionally in a linear chain configuration. In a wide range of operating parameters, this setup leads to synchronization between the outer circuits, while the relaying element remains unsynchronized. The specifics of the synchronization differ with the coupling level: for low couplings a state of intermittent synchronization between the outer circuits coexists with one of antiphase synchronization. Synchronization becomes in phase for moderate couplings, and for strong coupling identical synchronization is observed between the outer elements, which are themselves synchronized in a generalized way with the relaying element. In the latter situation, the middle element displays a triple scroll attractor that is not possible to obtain when the chaotic oscillator is isolated.Comment: 7 pages, 12 figure

Episodic synchronization in dynamically driven neurons

We examine the response of type II excitable neurons to trains of synaptic pulses, as a function of the pulse frequency and amplitude. We show that the resonant behavior characteristic of type II excitability, already described for harmonic inputs, is also present for pulsed inputs. With this in mind, we study the response of neurons to pulsed input trains whose frequency varies continuously in time, and observe that the receiving neuron synchronizes episodically to the input pulses, whenever the pulse frequency lies within the neuron's locking range. We propose this behavior as a mechanism of rate-code detection in neuronal populations. The results are obtained both in numerical simulations of the Morris-Lecar model and in an electronic implementation of the FitzHugh-Nagumo system, evidencing the robustness of the phenomenon.Comment: 7 pages, 8 figure

Noise-induced scenario for inverted phase diagrams

We introduce a class of exactly solvable models exhibiting an ordering noise-induced phase transition in which order arises as a result of a balance between the relaxing deterministic dynamics and the randomizing character of the fluctuations. A finite-size scaling analysis of the phase transition reveals that it belongs to the universality class of the equilibrium Ising model. All these results are analyzed in the light of the nonequilibrium probability distribution of the system, which can be obtained analytically. Our results could constitute a possible scenario of inverted phase diagrams in the so-called lower critical solution temperature transitions

Complex spatiotemporal oscillations emerge from transverse instabilities in large-scale brain networks

Spatiotemporal oscillations underlie all cognitive brain functions. Large-scale brain models, constrained by neuroimaging data, aim to trace the principles underlying such macroscopic neural activity from the intricate and multi-scale structure of the brain. Despite substantial progress in the field, many aspects about the mechanisms behind the onset of spatiotemporal neural dynamics are still unknown. In this work we establish a simple framework for the emergence of complex brain dynamics, including high-dimensional chaos and travelling waves. The model consists of a complex network of 90 brain regions, whose structural connectivity is obtained from tractography data. The activity of each brain area is governed by a Jansen neural mass model and we normalize the total input received by each node so it amounts the same across all brain areas. This assumption allows for the existence of an homogeneous invariant manifold, i.e., a set of different stationary and oscillatory states in which all nodes behave identically. Stability analysis of these homogeneous solutions unveils a transverse instability of the synchronized state, which gives rise to different types of spatiotemporal dynamics, such as chaotic alpha activity. Additionally, we illustrate the ubiquity of this route towards complex spatiotemporal activity in a network of next generation neural mass models. Altogehter, our results unveil the bifurcation landscape that underlies the emergence of function from structure in the brain.PC, GD, GR, and JGO have received funding from the Future and Emerging Technologies Programme (FET) of the European Union’s Horizon 2020 research and innovation programme (project NEUROTWIN, grant agreement No 101017716). JGO also acknowledges financial support from the Spanish Ministry of Science and Innovation and FEDER (grant PID2021-127311NB-I00), by the “Maria de Maeztu” Programme for Units of Excellence in R&D (grant CEX2018-000792-M), and by the Generalitat de Catalunya (ICREA Academia programme). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Peer ReviewedPostprint (published version

PERIOD–TIMELESS Interval Timer May Require an Additional Feedback Loop

In this study we present a detailed, mechanism-based mathematical framework of Drosophila circadian rhythms. This framework facilitates a more systematic approach to understanding circadian rhythms using a comprehensive representation of the network underlying this phenomenon. The possible mechanisms underlying the cytoplasmic “interval timer” created by PERIOD–TIMELESS association are investigated, suggesting a novel positive feedback regulatory structure. Incorporation of this additional feedback into a full circadian model produced results that are consistent with previous experimental observations of wild-type protein profiles and numerous mutant phenotypes

Zero-lag long-range synchronization via dynamical relaying

We show that simultaneous synchronization between two delay-coupled oscillators can be achieved by relaying the dynamics via a third mediating element, which surprisingly lags behind the synchronized outer elements. The zero-lag synchronization thus obtained is robust over a considerable parameter range. We substantiate our claims with experimental and numerical evidence of these synchronization solutions in a chain of three coupled semiconductor lasers with long inter-element coupling delays. The generality of the mechanism is validated in a neuronal model with the same coupling architecture. Thus, our results show that synchronized dynamical states can occur over long distances through relaying, without restriction by the amount of delay.Comment: 10 pages, 4 figure