Biophysical Modulation and Robustness of Itinerant Complexity in Neuronal Networks
Siva Venkadesh, Asmir Shaikh, Heman Shakeri, Ernest Barreto, and John Van Horn
Abstract
Transient synchronization of bursting activity in neuronal networks, which occurs in patterns of metastable itinerant phase relationships between neurons, is a notable feature of network dynamics observed in vivo. However, the mechanisms that contribute to this dynamical complexity in neuronal circuits are not well understood. Local circuits in cortical regions consist of populations of neurons with diverse intrinsic oscillatory features. In this study, we numerically show that the phenomenon of transient synchronization, also referred to as metastability, can emerge in an inhibitory neuronal population when the neurons' intrinsic fast-spiking dynamics are appropriately modulated by slower inputs from an excitatory neuronal population. Using a compact model of a mesoscopic-scale network consisting of excitatory pyramidal and inhibitory fast-spiking neurons, our work demonstrates a relationship between the frequency of pyramidal population oscillations and the features of emergent metastability. In addition, we introduce a method to characterize collective transitions in metastable networks. Finally, we discuss potential applications of this study in mechanistically understanding cortical network dynamics.
Frontiers in Network Physiology 4:1302499 (2024). Journal link.—This article is included in the Frontiers Research Topic Synchronization and Multistability in Neural Networks.
Itinerant Complexity in Networks of Intrinsically Bursting Neurons
Siva Venkadesh, Ernest Barreto, and Giorgio Ascoli
Abstract
Active neurons can be broadly classified by their intrinsic oscillation patterns into two classes characterized by spiking or bursting. Here we show that networks of identical bursting neurons with inhibitory pulsatory coupling exhibit itinerant dynamics. Using the relative phases of bursts between neurons, we numerically demonstrate that the network exhibits endogenous transitions between multiple modes of transient synchrony. This is true even for bursts consisting of two spikes. In contrast, our simulations reveal that networks of identical singlet-spiking neurons do not exhibit such complexity. These results suggest a role for bursting dynamics in realizing itinerant complexity in neural circuits.
Chaos 30, 061106 (2020). Journal link.
Synaptic Diversity Suppresses Complex Collective Behavior in Networks of Theta Neurons
Lucas Lin, Ernest Barreto, and Paul So
Abstract
Comprehending how the brain functions requires an understanding of the dynamics of neuronal assemblies. Previous work used a mean-field reduction method to determine the collective dynamics of a large heterogeneous network of uniformly and globally coupled theta neurons, which are a canonical formulation of Type I neurons. However, in modeling neuronal networks, it is unreasonable to assume that the coupling strength between every pair of neurons is identical. The goal in the present work is to analytically examine the collective macroscopic behavior of a network of theta neurons that is more realistic in that it includes heterogeneity in the coupling strength as well as in neuronal excitability. We consider the occurrence of dynamical structures that give rise to complicated dynamics via bifurcations of macroscopic collective quantities, concentrating on two biophysically relevant cases: (1) predominantly excitable neurons with mostly excitatory connections, and (2) predominantly spiking neurons with inhibitory connections. We find that increasing the synaptic diversity moves these dynamical structures to distant extremes of parameter space, leaving simple collective equilibrium states in the physiologically relevant region. We also study the node versus focus nature of stable macroscopic equilibrium solutions and discuss our results in the context of recent literature.
Frontiers in Computational Neuroscience 14:44 (2020). Journal link (open access).
Synchronization-Induced Spike Termination in Networks of Bistable Neurons
Muhammet Uzuntarla, Joaquin J. Torres, Ali Çalım, and Ernest Barreto
Abstract
We observe and study a self-organized phenomenon whereby the activity in a network of spiking neurons spontaneously terminates. We consider different types of populations, consisting of bistable model neurons connected electrically by gap junctions, or by either excitatory or inhibitory synapses, in a scale-free connection topology. We find that strongly synchronized population spiking events lead to complete cessation of activity in excitatory networks, but not in gap-junction or inhibitory networks. We identify the underlying mechanism responsible for this phenomenon by examining the particular shape of the excitatory post-synaptic currents that arise in the neurons. We also examine the effects of the synaptic time constant, coupling strength, and channel noise on the occurrence of the phenomenon.
Neural Networks 110, 131-140 (2019). Journal link.
Inverse Stochastic Resonance in Networks of Spiking
Neurons
Muhammet Uzuntarla, Ernest Barreto, and Joaquin J. Torres
Abstract
Inverse Stochastic Resonance (ISR) is a phenomenon in which the average spiking rate of a neuron exhibits a minimum with respect to noise. ISR has been studied in individual neurons, but here, we investigate ISR in scale-free networks, where the average spiking rate is calculated over the neuronal population. We use Hodgkin-Huxley model neurons with channel noise (i.e., stochastic gating variable dynamics), and the network connectivity is implemented via electrical or chemical connections (i.e., gap junctions or excitatory/inhibitory synapses). We find that the emergence of ISR depends on the interplay between each neuron's intrinsic dynamical structure, channel noise, and network inputs, where the latter in turn depend on network structure parameters. We observe that with weak gap junction or excitatory synaptic coupling, network heterogeneity and sparseness tend to favor the emergence of ISR. With inhibitory coupling, ISR is quite robust. We also identify dynamical mechanisms that underlie various features of this ISR behavior. Our results suggest possible ways of experimentally observing ISR in actual neuronal systems.
PLoS Computational Biology 13(7): e1005646 (2017). Journal link (open access).—This article was among the top 10% most cited PLOS Computational Biology papers published in 2017.
Double Inverse Stochastic Resonance with Dynamic Synapses
Muhammet Uzuntarla, Joaquin J. Torres, Paul So, Mahmut Ozer, and Ernest Barreto
Abstract
We investigate the behavior of a model neuron that receives a biophysically-realistic noisy post-synaptic current based on uncorrelated spiking activity from a large number of afferents. We show that, with static synapses, such noise can give rise to inverse stochastic resonance (ISR) as a function of the presynaptic firing rate. We compare this to the case with dynamic synapses that feature short-term synaptic plasticity, and show that the interval of presynaptic firing rate over which ISR exists can be extended or diminished. We consider both short-term depression and facilitation. Interestingly, we find that a double inverse stochastic resonance (DISR), with two distinct wells centered at different presynaptic firing rates, can appear.
Physical Review E 95, 012404 (2017). Journal link
Effects of Polarization Induced by Non-Weak Electric Fields
on the Excitability of Elongated Neurons With Active
Dendrites
Robert I. Reznik, Ernest Barreto, Evelyn Sander, and Paul So
Abstract
An externally-applied electric field can polarize a neuron, especially a neuron with elongated dendrites, and thus modify its excitability. Here we use a computational model to examine, predict, and explain these effects. We use a two-compartment Pinsky-Rinzel model neuron polarized by an electric potential difference imposed between its compartments, and we apply an injected ramp current. We vary three model parameters: the magnitude of the applied potential difference, the extracellular potassium concentration, and the rate of current injection. A study of the Time-To-First-Spike (TTFS) as a function of polarization leads to the identification of three regions of polarization strength that have di erent effects. In the weak region, the TTFS increases linearly with polarization. In the intermediate region, the TTFS increases either sub- or super-linearly, depending on the current injection rate and the extracellular potassium concentration. In the strong region, the TTFS decreases. Our results in the weak and strong region are consistent with experimental observations, and in the intermediate region, we predict novel e ects that depend on experimentally-accessible parameters. We find that active channels in the dendrite play a key role in these effects. Our qualitative results were found to be robust over a wide range of inter-compartment conductances and the ratio of somatic to dendritic membrane areas. In addition, we discuss preliminary results where synaptic inputs replace the ramp injection protocol. The insights and conclusions were found to extend from our polarized PR model to a polarized PR model with Ih dendritic currents. Finally, we discuss the degree to which our results may be generalized.
Journal of Computational Neuroscience 40, 27-50 (2016). Journal link
Macroscopic Complexity from an Autonomous Network of Networks of Theta Neurons
Tanushree B Luke, Ernest Barreto, and Paul So
Abstract
We examine the emergence of collective dynamical structures and complexity in a network of interacting populations of neuronal oscillators. Each population consists of a heterogeneous collection of globally-coupled theta neurons, which are a canonical representation of Type-1 neurons. For simplicity, the populations are arranged in a fully autonomous driver-response configuration, and we obtain a full description of the asymptotic macroscopic dynamics of this network. We find that the collective macroscopic behavior of the response population can exhibit equilibrium and limit cycle states, multistability, quasiperiodicity, and chaos, and we obtain detailed bifurcation diagrams that clarify the transitions between these macrostates. Furthermore, we show that despite the complexity that emerges, it is possible to understand the complicated dynamical structure of this system by building on the understanding of the collective behavior of a single population of theta neurons. This work is a first step in the construction of a mathematically-tractable network-of-networks representation of neuronal network dynamics.
Frontiers in Computational Neuroscience 8, 145 (2014). Journal link (open access)—This paper was included in Mattei, T. A., ed. (2016). Nonlinear Analysis in Neuroscience and Behavioral Research. Lausanne: Frontiers Media. doi: 10.3389/978-2-88919-996-9
Control of Collective Network Chaos
Alexandre Wagemakers, Ernest Barreto, Miguel A.F. Sanjuan, and Paul So
Abstract
Under certain conditions, the collective behavior of a large globally-coupled heterogeneous network of coupled oscillators, as quantified by the macroscopic mean field or order parameter, can exhibit low-dimensional chaotic behavior. Recent advances describe how a small set of reduced ordinary differential equations can be derived that captures this mean field behavior. Here, we show that chaos control algorithms designed using the reduced equations can be successfully applied to imperfect realizations of the full network. To systematically study the effectiveness of this technique, we measure the quality of control as we relax conditions that are required for the strict accuracy of the reduced equations, and hence, the controller. Although the effects are network-dependent, we show that the method is effective for surprisingly small networks, for modest departures from global coupling, and even with mild inaccuracy in the estimate of network heterogeneity.
Chaos 24, 023127 (2014). Journal link PDF.
Networks of Theta Neurons with Time-Varying Excitability: Macroscopic Chaos, Multistability, and
Final-State Uncertainty
Paul So, Tanushree B. Luke, and Ernest Barreto
Abstract
Using recently developed analytical techniques, we study the macroscopic dynamics of a large heterogeneous network of theta neurons in which the neurons' excitability parameter varies in time. We demonstrate that such periodic variation can lead to the emergence of macroscopic chaos, multistability, and final-state uncertainty in the collective behavior of the network. Finite-size network effects and rudimentary control via an accessible macroscopic network parameter is also investigated.
Physica D 267, 16-26 (2014). Journal link.
Dynamical Structure Underlying Inverse Stochastic Resonance
and its Implications
Muhammet Uzuntarla, John R. Cressman, Mahmut Ozer, and Ernest Barreto
Abstract
We investigate Inverse Stochastic Resonance (ISR), a recently-reported phenomenon in which the spiking activity of a Hodgkin-Huxley model neuron subject to external noise exhibits a pronounced minimum as the noise intensity increases. We clarify the mechanism that underlies ISR and show that its most surprising features are a consequence of the dynamical structure of the model. Furthermore, we show that the ISR effect depends strongly on the procedures used to measure it. Our results are important for the experimentalist who seeks to observe the ISR phenomenon.
Physical Review E 88, 042712 (2013). A PDF is available. Journal link (open access).
Complete Classification of the Macroscopic Behavior of a Heterogeneous Network of Theta Neurons
Tanushree B. Luke, Ernest Barreto, and Paul So
Abstract
We design and analyze the dynamics of a large network of theta neurons, which are idealized Type-I neurons. The network is heterogeneous in that it includes both inherently spiking and excitable neurons. The coupling is global, via pulse-like synapses of adjustable sharpness. Using recently-developed analytical methods, we identify all possible asymptotic states that can be exhibited by a mean-field variable that captures the network's macroscopic state. These consist of two equilibrium states that reflect partial synchronization in the network, and a limit cycle state in which the degree of network synchronization oscillates in time. Our approach also permits a complete bifurcation analysis, which we carry out with respect to parameters that capture the degree of excitability of the neurons, the heterogeneity in the population, and the coupling strength (which can be excitatory or inhibitory). We find that the network typically tends towards the two macroscopic equilibrium states when the neuron's intrinsic dynamics and the network interactions reinforce one another. In contrast, the limit cycle state, bifurcations, and multistability tend to occur when there is competition between these network features. Finally, we show that our results are exhibited by finite network realizations of reasonable size.
Neural Computation 25, 3207-3234 (2013). Journal link Author-generated PDF Animations
Controlling Seizure-Like Events by Perturbing Ion Concentration Dynamics with Periodic Stimulation
Jeremy A. Owen, Ernest Barreto, and John R. Cressman
Abstract
We investigate the effects of adding periodic stimulation to a generic, conductance-based neuron model that includes ion concentration dynamics of sodium and potassium. Under conditions of high extracellular potassium, the model exhibits repeating, spontaneous, seizure-like bursting events associated with slow modulation of the ion concentrations local to the neuron. We show that for a range of parameter values, depolarizing and hyperpolarizing periodic stimulation pulses (including frequencies lower than 4 Hz) can stop the spontaneous bursting by interacting with the ion concentration dynamics. Stimulation can also control the magnitude of evoked responses to modeled physiological inputs. We develop an understanding of the nonlinear dynamics of this system by a dimension reduction procedure that identifies effective nullclines in the ion concentration parameter space. Our results suggest that the manipulation of ion concentration dynamics via external or endogenous stimulation may play an important role in neuronal excitability, seizure dynamics, and control.
PLoS ONE 8(9): e73820 (2013). Journal link (open access).
The Role of Inhibition in Oscillatory Wave Dynamics in Cortex
Ying Xiao, Xiao-ying Huang, Stephen Van Wert, Ernest Barreto, Jian-young Wu, Bruce J. Gluckman, and Steven J. Schiff
Abstract
Cortical oscillations arise during behavioral and mental tasks, and all temporal oscillations have particular spatial patterns. Studying the mechanisms that generate and modulate the spatiotemporal characteristics of oscillations is important for understanding neural information processing and the signs and symptoms of dynamical diseases of the brain. Nevertheless, it remains unclear how GABAergic inhibition modulates these oscillation dynamics. Using voltage sensitive dye imaging, pharmacological methods, and tangentially cut occipital neocortical brain slices (including layers 3-5) of Sprague-Dawley rat, we found that GABAa disinhibition with bicuculline can progressively simplify oscillation dynamics in the presence of carbachol in a concentration-dependent way. Additionally, GABAb disinhibition can further simplify oscillation dynamics after GABAa receptors are blocked. Both GABAa and GABAb disinhibition increase the synchronization of the neural network. By using a combination of GABAa and GABAb antagonists alone, theta frequency (5-15Hz) oscillations are reliably generated. These theta oscillations have basic spatiotemporal patterns similar to those generated by carbachol/bicuculline. These results are illustrative of how GABAergic inhibition increases the complexity of patterns of activity and contributes to the regulation of cortex.
European Journal of Neuroscience 36, 2201-2212 (2012). A PDF is available. Journal link
Generating Macroscopic Chaos in a Network of Globally Coupled Phase Oscillators
Paul So and Ernest Barreto
Abstract
We consider an infinite network of globally-coupled phase oscillators in which the natural frequencies of the oscillators are drawn from a symmetric bimodal distribution. We demonstrate that macroscopic chaos can occur in this system when the coupling strength varies periodically in time. We identify period-doubling cascades to chaos, attractor crises, and horseshoe dynamics for the macroscopic mean field. Based on recent work that clarified the bifurcation structure of the static bimodal Kuramoto system, we qualitatively describe the mechanism for the generation of such complicated behavior in the time varying case.
This paper appears in Chaos 21, 21, 033127 (2011). A PDF is available. Journal link
Ion Concentration Dynamics as a Mechanism for Neuronal Bursting
Ernest Barreto and John R. Cressman
Abstract
We describe a simple conductance-based model neuron that includes intra- and extra-cellular ion concentration dynamics and show that this model exhibits periodic bursting. The bursting arises as the fast spiking behavior of the neuron is modulated by the slow oscillatory behavior in the ion concentration variables, and vice versa. By separating these time scales and studying the bifurcation structure of the neuron, we catalog several qualitatively different bursting profiles that are strikingly similar to those seen in experimental preparations. Our work suggests that ion concentration dynamics may play an important role in modulating neuronal excitability in real biological systems.
This paper appears in the Journal of Biological Physics 37, 361-373 (2011). An author-generated version is available, and the published version is here: Journal link
Synchronized
Changes to Relative Neuron Populations in Postnatal Human Neocortical
Development
David L. Cooper, James E.
Gentle, Ernest
Barreto, and James L. Olds
Abstract
Mammalian prenatal neocortical development is dominated by the synchronized formation of the laminae and migration of neurons. Postnatal development likewise contains "sensitive periods" during which functions such as ocular dominance emerge. Here we introduce a novel neuroinformatics approach to identify and study these periods of active development. Although many aspects of the approach can be used in other studies, some specific techniques were chosen because of a legacy dataset of human histological data (Conel in "The postnatal development of the human cerebral cortex", vol 1-8. Harvard University Press, Cambridge, 1939-1967). Our method calculates normalized change vectors from the raw histological data, and then employs k-means cluster analysis of the change vectors to explore the population dynamics of neurons from 37 neocortical areas across eight postnatal developmental stages from birth to 72 months in 54 subjects. We show that the cortical "address" (Brodmann area/ sub-area and layer) provides the necessary resolution to segregate neuron population changes into seven correlated "k-clusters" in k-means cluster analysis. The members in each k-cluster share a single change interval where the relative share of the cortex by the members undergoes its maximum change. The maximum change occurs in a different change interval for each k-cluster. Each k-cluster has at least one totally connected maximal "clique" which appears to correspond to cortical function.
This paper appears in Cognitive Neurodynamics 4, 151-163 (2010). Journal link
Exact
Results for the Kuramoto Model with a
Bimodal
Frequency Distribution
Erik A. Martens, Ernest
Barreto, Steven H. Strogatz, Edward
Ott, Paul So, and Thomas M. Antonsen
Abstract
We analyze a large system of globally coupled phase oscillators whose natural frequencies are bimodally distributed. The dynamics of this system has been the subject of long-standing interest. In 1984 Kuramoto proposed several conjectures about its behavior; ten years later, Crawford obtained the first analytical results by means of a local center manifold calculation. Nevertheless, many questions have remained open, especially about the possibility of global bifurcations. Here we derive the system's complete stability diagram for the special case where the bimodal distribution consists of two equally weighted Lorentzians. Using an ansatz recently discovered by Ott and Antonsen, we show that in this case the infinite-dimensional problem reduces exactly to a flow in four dimensions. Depending on the parameters and initial conditions, the long-term dynamics evolves to one of three states: incoherence, where all the oscillators are desynchronized; partial synchrony, where a macroscopic group of phase-locked oscillators coexists with a sea of desynchronized ones; and a standing wave state, where two counter-rotating groups of phase-locked oscillators emerge. Analytical results are presented for the bifurcation boundaries between these states. Similar results are also obtained for the case in which the bimodal distribution is given by the sum of two Gaussians.
This paper appears in Physical Review E, Vol. 79, 026204 (2009).A PDF file of this paper is available.
