In the brain, fine-scale correlations combine to produce macroscopic patterns of activity. However, as experiments record from larger and larger populations, we approach a fundamental bottleneck: the number of correlations one would like to include in a model grows larger than the available data. In this undersampled regime, one must focus on a sparse subset of correlations; the optimal choice contains the maximum information about patterns of activity or, equivalently, minimizes the entropy of the inferred maximum entropy model. Applying this ``minimax entropy" principle is generally intractable, but here we present an exact and scalable solution for pairwise correlations that combine to form a tree (a network without loops). Applying our method to over one thousand neurons in the mouse hippocampus, we find that the optimal tree of correlations reduces our uncertainty about the population activity by 14% (over 50 times more than a random tree). Despite containing only 0.1% of all pairwise correlations, this minimax entropy model accurately predicts the observed large-scale synchrony in neural activity and becomes even more accurate as the population grows. The inferred Ising model is almost entirely ferromagnetic (with positive interactions) and exhibits signatures of thermodynamic criticality. These results suggest that a sparse backbone of excitatory interactions may play an important role in driving collective neuronal activity.
The repertoire of neural activity patterns that a cortical network can produce constrains the network's ability to transfer and process information. Here, we measured activity patterns obtained from multi-site local field potential (LFP) recordings in cortex cultures, urethane anesthetized rats, and awake macaque monkeys. First, we quantified the information capacity of the pattern repertoire of ongoing and stimulus-evoked activity using Shannon entropy. Next, we quantified the efficacy of information transmission between stimulus and response using mutual information. By systematically changi…
Neuronal avalanches are a novel mode of activity in neuronal networks, experimentally found in vitro and in vivo, and exhibit a robust critical behaviour: These avalanches are characterized by a power law distribution for the size and duration, features found in other problems in the context of the physics of complex systems. We present a recent model inspired in self-organized criticality, which consists of an electrical network with threshold firing, refractory period and activity-dependent synaptic plasticity. The model reproduces the critical behaviour of the distribution of avalanche size…
The mechanisms responsible for contention of activity in systems represented by networks are crucial in various phenomena, as in diseases such as epilepsy that affects the neuronal networks, and for information dissemination in social networks. The first models to account for contained activity included triggering and inhibition processes, but they cannot be applied to social networks where inhibition is clearly absent. A recent model showed that contained activity can be achieved with no need of inhibition processes provided that the network is subdivided in modules (communities). In this pap…
We study the role of scale-free structure and noise in collective dynamics of neuronal networks. For this purpose, we simulate and study analytically a cortical circuit model with stochastic neurons. We compare collective neuronal activity of networks with different topologies: classical random graphs and scale-free networks. We show that, in scale-free networks with divergent second moment of degree distribution, an influence of noise on neuronal activity is strongly enhanced in comparison with networks with a finite second moment. A very small noise level can stimulate spontaneous activity o…
Recent efforts in neuroscience research seek to obtain detailed anatomical neuronal wiring maps as well as information on how neurons in these networks engage in dynamic activities. Although the entire connectivity map of the nervous system of C. elegans has been known for more than 25 years, this knowledge has not been sufficient to predict all functional connections underlying behavior. To approach this goal, we developed a two-photon technique for brain-wide calcium imaging in C. elegans using wide-field temporal focusing (WF-TEFO). Pivotal to our results was the use of a nuclear-localized,…
We study the impact of the decrease in the neural population on the neuronal firing rate. We propose a cellular automaton model from cancerous growth in a brain tissue and the death of neurons due absence of cells that help support to neurons. We use this model to study how the firing rate changes when the neuronal networks is under different external stimuli and the cancerous cells have different proliferation rate. Our work shows that the cancer proliferation decreases the neuronal firing rate.
Thermodynamic criticality describes emergent phenomena in a wide variety of complex systems. In the mammalian brain, the complex dynamics that spontaneously emerge from neuronal interactions have been characterized as neuronal avalanches, a form of critical branching dynamics. Here, we show that neuronal avalanches also reflect that the brain dynamics are organized close to a thermodynamic critical point. We recorded spontaneous cortical activity in monkeys and humans at rest using high-density intracranial microelectrode arrays and magnetoencephalography, respectively. By numerically changing…
Optogenetics has emerged as an exciting tool for manipulating neural activity, which in turn, can modulate behavior in live organisms. However, detecting the response to the optical stimulation requires electrophysiology with physical contact or fluorescent imaging at target locations, which is often limited by photobleaching and phototoxicity. In this paper, we show that phase imaging can report the intracellular transport induced by optogenetic stimulation. We developed a multimodal instrument that can both stimulate cells with high spatial resolution and detect optical pathlength changes wi…
Cross-correlations in the activity in neural networks are commonly used to characterize their dynamical states and their anatomical and functional organizations. Yet, how these latter network features affect the spatiotemporal structure of the correlations in recurrent networks is not fully understood. Here, we develop a general theory for the emergence of correlated neuronal activity from the dynamics in strongly recurrent networks consisting of several populations of binary neurons. We apply this theory to the case in which the connectivity depends on the anatomical or functional distance be…
An important tool in the investigation of the early stages of neurodegenerative disease is the study of dissected living tissue from the brain of an animal model. Such investigations allow the physical structure of individual neurons and neural circuits to be probed alongside neuronal electrical activity, disruption of which can shed light on the mechanisms of emergence of disease. Existing techniques for recording activity rely on potentially damaging direct interaction with the sample, either mechanically as point electrical probes or via intense focused laser light combined with highly spec…
It has recently been discovered that single neuron stimulation can impact network dynamics in immature and adult neuronal circuits. Here we report a novel mechanism which can explain in neuronal circuits, at an early stage of development, the peculiar role played by a few specific neurons in promoting/arresting the population activity. For this purpose, we consider a standard neuronal network model, with short-term synaptic plasticity, whose population activity is characterized by bursting behavior. The addition of developmentally inspired constraints and correlations in the distribution of th…
We study numerically and analytically first- and second-order phase transitions in neuronal networks stimulated by shot noise (a flow of random spikes bombarding neurons). Using an exactly solvable cortical model of neuronal networks on classical random networks, we find critical phenomena accompanying the transitions and their dependence on the shot noise intensity. We show that a pattern of spontaneous neuronal activity near a critical point of a phase transition is a characteristic property that can be used to identify the bifurcation mechanism of the transition. We demonstrate that bursts …
The spontaneous activity pattern of cortical neurons in dissociated culture is characterized by burst firing that is highly synchronized among a wide population of cells. The degree of synchrony, however, is excessively higher than that in cortical tissues. Here, we employed polydimethylsiloxane (PDMS) elastomers to establish a novel system for culturing neurons on a scaffold with an elastic modulus resembling brain tissue, and investigated the effect of the scaffold's elasticity on network activity patterns in cultured rat cortical neurons. Using whole-cell patch clamp to assess the scaffold …
This paper deals with the EEG/MEG neuroimaging problem: given measurements of scalp electric potential differences (EEG: electroencephalogram) and extracranial magnetic fields (MEG: magnetoencephalogram), find the 3D distribution of the generating electric neuronal activity. This problem has no unique solution. Only particular solutions with "good" localization properties are of interest, since neuroimaging is concerned with the localization of brain function. In this paper, a general family of linear imaging methods with exact, zero error localization to point-test sources is presented. One p…
A model of the columnar functional organization of neocortical association areas is studied. The neuronal network is composed of many Hebbian autoassociators, or modules, each of which interacts with a relatively small number of the others. Every module encodes and stores a number of elementary percepts, or features. Memory items, or patterns, are peculiar combinations of features sparsely distributed over the multi-modular network. Any feature stored in any module can be involved in several of the stored patterns; feature-sharing is in fact source of local ambiguities and, consequently, a pot…
The mammalian brain is a densely interconnected network that consists of millions to billions of neurons. Decoding how information is represented and processed by this neural circuitry requires the ability to capture and manipulate the dynamics of large populations at high speed and resolution over a large area of the brain. While there has been a rapid increase in use of optical approaches in the neuroscience community over the last two decades, most microscopy approaches lack the ability to record the activity of all neurons comprising a functional network across the mammalian brain at relev…
Intracellular access with high spatiotemporal resolution can enhance our understanding of how neurons or cardiomyocytes regulate and orchestrate network activity, and how this activity can be affected with pharmacology or other interventional modalities. Nanoscale devices often employ electroporation to transiently permeate the cell membrane and record intracellular potentials, which tend to decrease rapidly to extracellular potential amplitudes with time. Here, we report innovative scalable, vertical, ultra-sharp nanowire arrays that are individually addressable to enable long-term, native re…
Many experiments have evidenced that electrical and chemical synapses -- hybrid synapses -- coexist in most organisms and brain structures. The role of electrical and chemical synapse connection in diversity of neural activity generation has been investigated separately in networks of varying complexities. Nevertheless, theoretical understanding of hybrid synapses in diverse dynamical states of neural networks for self-organization and robustness still has not been fully studied. Here, we present a model of neural network built with hybrid synapses to investigate the emergence of global and co…
Sequences of events in noise-driven excitable systems with slow variables often show serial correlations among their intervals of events. Here, we employ a master equation for general non-renewal processes to calculate the interval and count statistics of superimposed processes governed by a slow adaptation variable. For an ensemble of spike-frequency adapting neurons this results in the regularization of the population activity and an enhanced post-synaptic signal decoding. We confirm our theoretical results in a population of cortical neurons.
