Phase resetting and phase locking in hybrid circuits of one model and one biological neuron (original) (raw)
Related papers
Journal of Neurophysiology, 2009
Sieling FH, Canavier CC, Prinz AA. Predictions of phaselocking in excitatory hybrid networks: excitation does not promote phase-locking in pattern-generating networks as reliably as inhibition. locked activity is thought to underlie many high-level functions of the nervous system, the simplest of which are produced by central pattern generators (CPGs). It is not known whether we can define a theoretical framework that is sufficiently general to predict phase-locking in actual biological CPGs, nor is it known why the CPGs that have been characterized are dominated by inhibition. Previously, we applied a method based on phase response curves measured using inputs of biologically realistic amplitude and duration to predict the existence and stability of 1:1 phase-locked modes in hybrid networks of one biological and one model bursting neuron reciprocally connected with artificial inhibitory synapses. Here we extend this analysis to excitatory coupling. Using the pyloric dilator neuron from the stomatogastric ganglion of the American lobster as our biological cell, we experimentally prepared 86 networks using five biological neurons, four model neurons, and heterogeneous synapse strengths between 1 and 10,000 nS. In 77% of networks, our method was robust to biological noise and accurately predicted the phasic relationships. In 3%, our method was inaccurate. The remaining 20% were not amenable to analysis because our theoretical assumptions were violated. The high failure rate for excitation compared with inhibition was due to differential effects of noise and feedback on excitatory versus inhibitory coupling and suggests that CPGs dominated by excitatory synapses would require precise tuning to function, which may explain why CPGs rely primarily on inhibitory synapses.
Predicting phase-locking in excitatory hybrid circuits
Welcome to CNS*2008! The international Computational Neuroscience meeting (CNS) has been a premier forum for presenting experimental and theoretical results exploring the biology of computation in the nervous system for the last 17 years. The meeting is organized by the Organization for Computational Neurosciences (OCNS), a non-profit organization governed by an international executive committee and board of directors. A separate program committee is responsible for the scientific program of the meeting. Participants at the meeting are from academia and industry. The meeting not only provides a venue for research presentation and discussion by senior scientists but actively offers a forum for promoting and supporting young scientists and students from around the world.
Journal of Computational Neuroscience, 2008
Our goal is to understand how nearly synchronous modes arise in heterogenous networks of neurons. In heterogenous networks, instead of exact synchrony, nearly synchronous modes arise, which include both 1:1 and 2:2 phase-locked modes. Existence and stability criteria for 2:2 phase-locked modes in reciprocally coupled two neuron circuits were derived based on the open loop phase resetting curve (PRC) without the assumption of weak coupling. The PRC for each component neuron was generated using the change in synaptic conductance produced by a presynaptic action potential as the perturbation. Separate derivations were required for modes in which the firing order is preserved and for those in which it alternates. Networks composed of two model neurons coupled by reciprocal inhibition were examined to test the predictions. The parameter regimes in which both types of nearly synchronous modes are exhibited were accurately predicted both qualitatively and quantitatively provided that the synaptic time constant is short with respect to the period and that the effect of second order resetting is considered. In contrast, PRC methods based on weak coupling could not predict 2:2 modes and did not predict the 1:1 modes with the level of accuracy achieved by the strong coupling methods. The strong coupling prediction methods provide insight into what manipulations promote near-synchrony in a two neuron network and may also have predictive value for larger networks, which can also manifest changes in firing order. We also identify a novel route by which synchrony is lost in mildly heterogenous networks.
Dynamic control of irregular bursting in an identified neuron of an oscillatory circuit
Journal of neurophysiology, 1999
In the oscillatory circuits known as central pattern generators (CPGs), most synaptic connections are inhibitory. We have assessed the effects of inhibitory synaptic input on the dynamic behavior of a component neuron of the pyloric CPG in the lobster stomatogastric ganglion. Experimental perturbations were applied to the single, lateral pyloric neuron (LP), and the resulting voltage time series were analyzed using an entropy measure obtained from power spectra. When isolated from phasic inhibitory input, LP generates irregular spiking-bursting activity. Each burst begins in a relatively stereotyped manner but then evolves with exponentially increasing variability. Periodic, depolarizing current pulses are poor regulators of this activity, whereas hyperpolarizing pulses exert a strong, frequency-dependent regularizing action. Rhythmic inhibitory inputs from presynaptic pacemaker neurons also regularize the bursting. These inputs 1) reset LP to a similar state at each cycle, 2) exten...
PLoS computational biology, 2014
In order to study the ability of coupled neural oscillators to synchronize in the presence of intrinsic as opposed to synaptic noise, we constructed hybrid circuits consisting of one biological and one computational model neuron with reciprocal synaptic inhibition using the dynamic clamp. Uncoupled, both neurons fired periodic trains of action potentials. Most coupled circuits exhibited qualitative changes between one-to-one phase-locking with fairly constant phasic relationships and phase slipping with a constant progression in the phasic relationships across cycles. The phase resetting curve (PRC) and intrinsic periods were measured for both neurons, and used to construct a map of the firing intervals for both the coupled and externally forced (PRC measurement) conditions. For the coupled network, a stable fixed point of the map predicted phase locking, and its absence produced phase slipping. Repetitive application of the map was used to calibrate different noise models to simult...
International Journal of Bifurcation and Chaos, 2014
In this paper, we study the combined effect of dynamic chemical and electrical synapses in time-delay-induced phase-transition to synchrony in coupled bursting neurons. Time-delay in coupled nonlinear oscillators or in a network of coupled nonlinear oscillators has been found to be responsible for striking dynamical behaviors such as phase-flip-transitions. These phenomena lead to synchrony or out of synchrony in different oscillators of the system. Here, we show that synaptic parameters, more precisely the neurotransmitters binding time constant influences the phase-flip-transitions of the system. We discuss how the system goes to the phase-flip-transitions when both electrical and dynamic chemical synapses are taken into account. The fourth-order Hindmarsh-Rose neuronal oscillator is considered here for the study of these transitions. A discussion on the importance of these results in brain researches is given, particularly to understand the collective dynamics of bursting neurons.
Phase Response Curves in Neuroscience, 2011
We use phase resetting curve (PRC) theory to analyze phase-locked patterns in pulse-coupled all to all network of N neurons that receive multiple inputs per cycle. The basic principles are that the phase must be updated each time an input is received, and simultaneous inputs do not sum linearly for strong coupling, but the conductances do. Therefore, the dependence of the resetting on conductance must be known. We analyze a splay mode in which no neurons fire simultaneously, global synchrony in which all neurons fire together, and clustering modes in which the firing breaks up into a small number of clusters. The key idea is to identify the appropriate perturbation in order to determine the stability of a given mode. For the splay mode, jitter is introduced into all firing times. For synchrony, a single neuron is perturbed from the rest, and for the two cluster mode, a single neuron is perturbed from one cluster. Global synchrony can be destabilized by increasing the network size or the strength of the individual synapses. At most, a small number of M clusters form because the M 1 locking points are more likely to sample destabilizing regions of the PRC as M increases. Between cluster interactions can enforce synchrony on subclusters that are incapable of synchronizing themselves. For the two cluster case, general results were obtained for clusters of any size. These results can be used to gain insights into the activity of networks of biological neurons whose PRCs can be measured.
Journal of Neuroscience, 2009
Networks of model neurons were constructed and their activity was predicted using an iterated map based solely on the phase-resetting curves (PRCs). The predictions were quite accurate provided that the resetting to simultaneous inputs was calculated using the sum of the simultaneously active conductances, obviating the need for weak coupling assumptions. Fully synchronous activity was observed only when the slope of the PRC at a phase of zero, corresponding to spike initiation, was positive. A novel stability criterion was developed and tested for all-to-all networks of identical, identically connected neurons. When the PRC generated using N Ϫ 1 simultaneously active inputs becomes too steep, the fully synchronous mode loses stability in a network of N model neurons. Therefore, the stability of synchrony can be lost by increasing the slope of this PRC either by increasing the network size or the strength of the individual synapses. Existence and stability criteria were also developed and tested for the splay mode in which neurons fire sequentially. Finally, N/M synchronous subclusters of M neurons were predicted using the intersection of parameters that supported both between-cluster splay and within-cluster synchrony. Surprisingly, the splay mode between clusters could enforce synchrony on subclusters that were incapable of synchronizing themselves. These results can be used to gain insights into the activity of networks of biological neurons whose PRCs can be measured.
Order parameter for bursting polyrhythms in multifunctional central pattern generators
2011
We examine multistability of several coexisting bursting patterns in a central pattern generator network composed of three Hodgkin-Huxley type cells coupled reciprocally by inhibitory synapses. We establish that the control of switching between bursting polyrhythms and their bifurcations are determined by the temporal characteristics, such as the duty cycle, of networked interneurons and the coupling strength asymmetry. A computationally effective approach to the reduction of dynamics of the nine-dimensional network to twodimensional Poincaré return mappings for phase lags between the interneurons is presented.
Inhibitory synchronization of bursting in biological neurons: dependence on synaptic time constant
Journal of neurophysiology, 2002
Using the dynamic clamp technique, we investigated the effects of varying the time constant of mutual synaptic inhibition on the synchronization of bursting biological neurons. For this purpose, we constructed artificial half-center circuits by inserting simulated reciprocal inhibitory synapses between identified neurons of the pyloric circuit in the lobster stomatogastric ganglion. With natural synaptic interactions blocked (but modulatory inputs retained), these neurons generated independent, repetitive bursts of spikes with cycle period durations of approximately 1 s. After coupling the neurons with simulated reciprocal inhibition, we selectively varied the time constant governing the rate of synaptic activation and deactivation. At time constants <or=100 ms, bursting was coordinated in an alternating (anti-phase) rhythm. At longer time constants (>400 ms), bursts became phase-locked in a fully overlapping pattern with little or no phase lag and a shorter period. During the...