Quantification of neuronal correlations in neuron populations helps us to understand neural coding rules. Such quantification could also reveal how neurons encode information in normal and disease conditions like Alzheimer's and Parkinson's. While neurons communicate with each other by transmitting spikes, there would be a change in calcium concentration within the neurons inherently. Accordingly, there would be correlations in calcium spike trains and they could have heterogeneous memory structures. In this context, estimation of mutual information rate in calcium spike trains assumes primary significance. However, such estimation is difficult with available methods which would consider longer blocks for convergence without noticing that neuronal information changes in short time windows. Against this backdrop, we propose a faster method that exploits the memory structures in pair of calcium spike trains to quantify mutual information shared between them. Our method has shown superior performance with example Markov processes as well as experimental spike trains. Such mutual information rate analysis could be used to identify signatures of neuronal behavior in large populations in normal and abnormal conditions.
Statistical similarities between neuronal spike trains could reveal significant information on complex underlying processing. In general, the similarity between synchronous spike trains is somewhat easy to identify. However, the similar patterns also potentially appear in an asynchronous manner. However, existing methods for their identification tend to converge slowly, and cannot be applied to short sequences. In response, we propose Hellinger distance measure based on empirical probabilities, which we show to be as accurate as existing techniques, yet faster to converge for synthetic as well…
With the increasing popularity of calcium imaging data in neuroscience research, methods for analyzing calcium trace data are critical to address various questions. The observed calcium traces are either analyzed directly or deconvolved to spike trains to infer neuronal activities. When both approaches are applicable, it is unclear whether deconvolving calcium traces is a necessary step. In this article, we compare the performance of using calcium traces or their deconvolved spike trains for three common analyses: clustering, principal component analysis (PCA), and population decoding. Our sim…
NMDA receptors (NMDA-R) typically contribute to excitatory synaptic transmission in the central nervous system. While calcium influx through NMDA-R plays a critical role in synaptic plasticity, experimental evidence indicates that NMDAR-mediated calcium influx also modifies neuronal excitability through the activation of calcium-activated potassium channels. This mechanism has not yet been studied theoretically. Our theoretical model provides a simple description of neuronal electrical activity that takes into account the tonic activity of extrasynaptic NMDA receptors and a cytosolic calcium c…
Understanding the role of astrocytes in brain computation is a nascent challenge, promising immense rewards, in terms of new neurobiological knowledge that can be translated into artificial intelligence. In our ongoing effort to identify principles endow-ing the astrocyte with unique functions in brain computation, and translate them into neural-astrocytic networks (NANs), we propose a biophysically realistic model of an astrocyte that preserves the experimentally observed spatial allocation of its distinct subcellular compartments. We show how our model may encode, and modu-late, the extent o…
Calcium imaging has become a powerful and popular technique to monitor the activity of large populations of neurons in vivo. However, for ethical considerations and despite recent technical developments, recordings are still constrained to a limited number of trials and animals. This limits the amount of data available from individual experiments and hinders the development of analysis techniques and models for more realistic sizes of neuronal populations. The ability to artificially synthesize realistic neuronal calcium signals could greatly alleviate this problem by scaling up the number of …
Neuronal assemblies, loosely defined as subsets of neurons with reoccurring spatio-temporally coordinated activation patterns, or "motifs", are thought to be building blocks of neural representations and information processing. We here propose LeMoNADe, a new exploratory data analysis method that facilitates hunting for motifs in calcium imaging videos, the dominant microscopic functional imaging modality in neurophysiology. Our nonparametric method extracts motifs directly from videos, bypassing the difficult intermediate step of spike extraction. Our technique augments variational autoencode…
Connected networks are a fundamental structure of neurobiology. Understanding these networks will help us elucidate the neural mechanisms of computation. Mathematically speaking these networks are `graphs' - structures containing objects that are connected. In neuroscience, the objects could be regions of the brain, e.g. fMRI data, or be individual neurons, e.g. calcium imaging with fluorescence microscopy. The formal study of graphs, graph theory, can provide neuroscientists with a large bank of algorithms for exploring networks. Graph theory has already been applied in a variety of ways to f…
Neuronal spiking exhibits an exquisite combination of modulation and robustness properties, rarely matched in artificial systems. We exploit the particular interconnection structure of conductance based models to investigate this remarkable property. We find that much of neuronal modulation and robustness can be explained by separating the total transmembrane current into three different components corresponding to the three time scales of neuronal bursting. Each equivalent current aggregates many ionic contributions into an equivalent voltage-dependent conductance, which defines a key modulat…
We establish a general linear response relation for spiking neuronal networks, based on chains with unbounded memory. This relation allows us to predict the influence of a weak amplitude time-dependent external stimuli on spatio-temporal spike correlations, from the spontaneous statistics (without stimulus) in a general context where the memory in spike dynamics can extend arbitrarily far in the past. Using this approach, we show how linear response is explicitly related to neuronal dynamics with an example, the gIF model, introduced by M. Rudolph and A. Destexhe. This example illustrates the …
Application of an attention-based CNN-BiLSTM framework for in vivo two-photon calcium imaging of neuronal ensembles: decoding complex bilateral forelimb movements from unilateral M1
West Virginia University（西弗吉尼亚大学）；University of Miami（迈阿密大学）；Leonard M. Miller School of Medicine（伦纳德·M·米勒医学院）；Rockefeller Neuroscience Institute（洛克菲勒神经科学研究所）
Neuronal dynamics are fundamentally constrained by the underlying structural network architecture, yet much of the details of this synaptic connectivity are still unknown even in neuronal cultures in vitro. Here we extend a previous approach based on information theory, the Generalized Transfer Entropy, to the reconstruction of connectivity of simulated neuronal networks of both excitatory and inhibitory neurons. We show that, due to the model-free nature of the developed measure, both kinds of connections can be reliably inferred if the average firing rate between synchronous burst events exc…
At functional scales, cortical behavior results from the complex interplay of a large number of excitable cells operating in noisy environments. Such systems resist to mathematical analysis, and computational neurosciences have largely relied on heuristic partial (and partially justified) macroscopic models, which successfully reproduced a number of relevant phenomena. The relationship between these macroscopic models and the spiking noisy dynamics of the underlying cells has since then been a great endeavor. Based on recent mean-field reductions for such spiking neurons, we present here {a pr…
A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically unfeasible even in dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct approximations to network structural connectivities from network activity monitored through calcium fluorescence imaging. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time-series of ca…
Investigating the spectral properties of the neural covariates that underlie spiking activity is an important problem in systems neuroscience, as it allows to study the role of brain rhythms in cognitive functions. While the spectral estimation of continuous time-series is a well-established domain, computing the spectral representation of these neural covariates from spiking data sets forth various challenges due to the intrinsic non-linearities involved. In this paper, we address this problem by proposing a variant of the multitaper method specifically tailored for point process data. To thi…
We examine whether a single biophysical cortical circuit model can explain both spiking and perceptual variability. We consider perceptual rivalry, which provides a window into intrinsic neural processing since neural activity in some brain areas is correlated to the alternating perception rather than the constant ambiguous stimulus. The prevalent theory for spiking variability is a chaotic attractor called the balanced state; whereas, the source of perceptual variability is an open question. We present a dynamical model with a chaotic attractor that explains both spiking and perceptual variab…
The influence of temperature on neuronal excitability is studied by numerical simulations on the spiking threshold characteristics of bushy cells in cochlear nucleus periodically stimulated by synaptic currents. The results reveal that there is a cut-off frequency for the spiking of bushy cell in a specific temperature environment, corresponding to the existence of a critical temperature for the neuron to respond with real spikes to the synaptic stimulus of a given frequency, due to the finiteness of spike width. An optimal temperature range for neuronal spiking is also found for a specific st…
Harmonic fractal transformation for modeling complex neuronal effects: from bursting and noise shaping to waveform sensitivity and noise-induced subthreshold spiking
Rapid action potential generation --- spiking --- and alternating intervals of spiking and quiescence --- bursting --- are two dynamic patterns observed in neuronal activity. In computational models of neuronal systems, the transition from spiking to bursting often exhibits complex bifurcation structure. One type of transition involves the torus canard, which was originally observed in a simple biophysical model of a Purkinje cell. In this article, we expand on that original result by showing that torus canards arise in a broad array of well-known computational neuronal models with three diffe…
Persistent activity is postulated to drive neural network plasticity and learning. To investigate its underlying cellular mechanisms, we developed a biophysically tractable model that explains the emergence, sustenance, and eventual termination of short-term persistent activity. Using the model, we reproduced the features of reverberating activity that were observed in small (50-100 cells) networks of cultured hippocampal neurons, such as the appearance of polysynaptic current clusters, the typical inter-cluster intervals, the typical duration of reverberation, and the response to changes in e…
Integration of Calcium Imaging Traces via Deep Generative Modeling
Dept. of Biomedical Sciences \& Institute of Neurosciences, Universitat de Barcelona, Barcelona, Spain Dept. of Condensed Matter Physics, Universitat de Barcelona, Barcelona, Spain
Computational modeling is becoming a widely used methodology in modern neuroscience. However, as the complexity of the phenomena under study increases, the analysis of the results emerging from the simulations concomitantly becomes more challenging. In particular, the configuration and validation of brain circuits involving learning often require the processing of large amounts of action potentials and their comparison to the stimulation being presented to the input of the system. In this study we present a systematic work-flow for the configuration of spiking-neuronal-network-based learning s…
The recent development of genetically encoded calcium indicators enables monitoring in vivo the activity of neuronal populations. Most analysis of these calcium transients relies on linear regression analysis based on the sensory stimulus applied or the behavior observed. To estimate the basic properties of the functional neural circuitry, we propose a network-based approach based on calcium imaging recorded at single cell resolution. Differently from previous analysis based on cross-correlation, we used Granger-causality estimates to infer activity propagation between the activities of differ…
Although there is increasing evidence of criticality in the brain, the processes that guide neuronal networks to reach or maintain criticality remain unclear. The present research examines the role of neuronal gain plasticity in time-series of simulated neuronal networks composed of integrate-and-fire stochastic spiking neurons, and the utility of fractal methods in assessing network criticality. Simulated time-series were derived from a network model of fully connected discrete-time stochastic excitable neurons. Monofractal and multifractal analyses were applied to neuronal gain time-series. …
Deducing the structure of neural circuits is one of the central problems of modern neuroscience. Recently-introduced calcium fluorescent imaging methods permit experimentalists to observe network activity in large populations of neurons, but these techniques provide only indirect observations of neural spike trains, with limited time resolution and signal quality. In this work we present a Bayesian approach for inferring neural circuitry given this type of imaging data. We model the network activity in terms of a collection of coupled hidden Markov chains, with each chain corresponding to a si…
A common approach to interpreting spiking activity is based on identifying the firing fields---regions in physical or configuration spaces that elicit responses of neurons. Common examples include hippocampal place cells that fire at preferred locations in the navigated environment, head direction cells that fire at preferred orientations of the animal's head, view cells that respond to preferred spots in the visual field, etc. In all these cases, firing fields were discovered empirically, by trial and error. We argue that the existence and a number of properties of the firing fields can be es…
We consider here a single-compartment model of these neurons which is capable of describing many of the known features of spike generation, particularly the slow rhythmic pacemaking activity often observed in these cells in a variety of species. Included in the model are ten kinds of voltage dependent ion channels as well as calcium-dependent potassium current. Calcium dynamics includes buffering and pumping. In sections 3-9, each component is considered in detail and parameters estimated from voltage clamp data where possible. In the next two sections simplified versions of some components ar…
We study the effect of intrinsic heterogeneity on the activity of a population of leaky integrate-and-fire neurons. By rescaling the dynamical equation, we derive mathematical relations between multiple neuronal parameters and a fluctuating input noise. To this end, common input to heterogeneous neurons is conceived as an identical noise with neuron-specific mean and variance. As a consequence, the neuronal output rates can differ considerably, and their relative spike timing becomes desynchronized. This theory can quantitatively explain some recent experimental findings.
When neural circuits learn to perform a task, it is often the case that there are many sets of synaptic connections that are consistent with the task. However, only a small number of possible solutions are robust to noise in the input and are capable of generalizing their performance of the task to new inputs. Finding such good solutions is an important goal of learning systems in general and neuronal circuits in particular. For systems operating with static inputs and outputs, a well known approach to the problem is the large margin methods such as Support Vector Machines (SVM). By maximizing…
Calcium imaging is an essential tool to study the activity of neuronal populations. However, the high level of background fluorescence in images hinders the accurate identification of neurons and the extraction of neuronal activities. While robust principal component analysis (RPCA) is a promising method that can decompose the foreground and background in such images, its computational complexity and memory requirement are prohibitively high to process large-scale calcium imaging data. Here, we propose BEAR, a simple bilinear neural network for the efficient approximation of RPCA which achieve…
Neuro-inspired models and systems have great potential for applications in unconventional computing. Often, the mechanisms of biological neurons are modeled or mimicked in simulated or physical systems in an attempt to harness some of the computational power of the brain. However, the biological mechanisms at play in neural systems are complicated and challenging to capture and engineer; thus, it can be simpler to turn to a data-driven approach to transfer features of neural behavior to artificial substrates. In the present study, we used an evolutionary algorithm (EA) to produce spiking neura…
Many types of neurons exhibit spike rate adaptation, mediated by intrinsic slow $\mathrm{K}^+$-currents, which effectively inhibit neuronal responses. How these adaptation currents change the relationship between in-vivo like fluctuating synaptic input, spike rate output and the spike train statistics, however, is not well understood. In this computational study we show that an adaptation current which primarily depends on the subthreshold membrane voltage changes the neuronal input-output relationship (I-O curve) subtractively, thereby increasing the response threshold. A spike-dependent adap…
We numerically investigate the influence of intrinsic channel noise on the dynamical response of delay-coupling in neuronal systems. The stochastic dynamics of the spiking is modeled within a stochastic modification of the standard Hodgkin-Huxley model wherein the delay-coupling accounts for the finite propagation time of an action potential along the neuronal axon. We quantify this delay-coupling of the Pyragas-type in terms of the difference between corresponding presynaptic and postsynaptic membrane potentials. For an elementary neuronal network consisting of two coupled neurons we detect c…
Cortical neural circuits display highly irregular spiking in individual neurons but variably sized collective firing, oscillations and critical avalanches at the population level, all of which have functional importance for information processing. Theoretically, the balance of excitation and inhibition inputs is thought to account for spiking irregularity and critical avalanches may originate from an underlying phase transition. However, the theoretical reconciliation of these multilevel dynamic aspects in neural circuits remains an open question. Herein, we study excitation-inhibition (E-I) b…
We present a modified library-based method for simulating the Hodgkin-Huxley (HH) neuronal networks. By pre-computing a high resolution data library during the interval of an action potential (spike), we can avoid evolving the HH equations during the spike and can use a large time step to raise efficiency. The library method can stably achieve at most 10 times of speedup compared with the regular Runge-Kutta method while capturing most statistical properties of HH neurons like the distribution of spikes which data is widely used in the statistical analysis like transfer entropy and Granger cau…
An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad principles underlying collective spiking activity in neural circuits. The first is that local features of network connectivity can be surprisingly effective in predicting global statistics of activity across a network. The second is that, for the important case of large networks with excitatory-inhibitory balance, correlated spiking persists or vanishes depending …
Macroscopic EEG fields can be an explicit top-down neocortical mechanism that directly drives bottom-up processes that describe memory, attention, and other neuronal processes. The top-down mechanism considered are macrocolumnar EEG firings in neocortex, as described by a statistical mechanics of neocortical interactions (SMNI), developed as a magnetic vector potential $\mathbf{A}$. The bottom-up process considered are $\mathrm{Ca}^{2+}$ waves prominent in synaptic and extracellular processes that are considered to greatly influence neuronal firings. Here, the complimentary effects are conside…
We present a structured matrix factorization approach to analyzing calcium imaging recordings of large neuronal ensembles. Our goal is to simultaneously identify the locations of the neurons, demix spatially overlapping components, and denoise and deconvolve the spiking activity of each neuron from the slow dynamics of the calcium indicator. The matrix factorization approach relies on the observation that the spatiotemporal fluorescence activity can be expressed as a product of two matrices: a spatial matrix that encodes the location of each neuron in the optical field and a temporal matrix th…
Neurons in cortical circuits exhibit coordinated spiking activity, and can produce correlated synchronous spikes during behavior and cognition. We recently developed a method for estimating the dynamics of correlated ensemble activity by combining a model of simultaneous neuronal interactions (e.g., a spin-glass model) with a state-space method (Shimazaki et al. 2012 PLoS Comput Biol 8 e1002385). This method allows us to estimate stimulus-evoked dynamics of neuronal interactions which is reproducible in repeated trials under identical experimental conditions. However, the method may not be sui…
Recent remarkable advances in the experimental techniques have provided a background for inferring neuronal couplings from point process data that includes a great number of neurons. Here, we propose a systematic procedure for pre- and post-processing generic point process data in an objective manner, to handle data in the framework of a binary simple statistical model, the Ising or generalized McCulloch--Pitts model. The procedure involves two steps: (1) determining time-bin size for transforming the point-process data into discrete-time binary data and (2) screening relevant couplings from t…
We study an abstracted model of neuronal activity via numerical simulation, and report spatiotemporal pattern formation and critical like dynamics. A population of pulse coupled, discretised, relaxation oscillators is simulated over networks with varying edge density and spatial embedded ness. For intermediate edge density and sufficiently strong spatial embeddedness, we observe a novel spatiotemporal pattern in the field of oscillator phases, visually resembling the surface of a frothing liquid. Increasing the edge density results in critical dynamics, with the distribution of neuronal avalan…
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,…
Determining how synaptic coupling within and between regions is modulated during sensory processing is an important topic in neuroscience. Electrophysiological recordings provide detailed information about neural spiking but have traditionally been confined to a particular region or layer of cortex. Here we develop new theoretical methods to study interactions between and within two brain regions, based on experimental measurements of spiking activity simultaneously recorded from the two regions. By systematically comparing experimentally-obtained spiking statistics to (efficiently computed) m…
Many neurons display bistability - coexistence of two firing modes such as bursting and tonic spiking or tonic spiking and silence. Bistability has been proposed to endow neurons with richer forms of information processing in general and to be involved in short-term memory in particular by allowing a brief signal to elicit long-lasting changes in firing. In this paper, we focus on bistability that allows for a choice between tonic spiking and depolarization block in a wide range of the depolarization levels. We consider the spike-producing currents in two neurons, models of which differ by the…
Chemical and electrical synapses shape the dynamics of neuronal networks. Numerous theoretical studies have investigated how each of these types of synapses contributes to the generation of neuronal oscillations, but their combined effect is less understood. This limitation is further magnified by the impossibility of traditional neuronal mean-field models ---also known as firing rate models, or firing rate equations--- to account for electrical synapses. Here we introduce a novel firing rate model that exactly describes the mean field dynamics of heterogeneous populations of quadratic integra…
