Search for: All records

Observations of power laws in neural activity data have raised the intriguing notion that brains may operate in a critical state. One example of this critical state is "avalanche criticality," which has been observed in a range of systems, including cultured neurons, zebrafish, and human EEG. More recently, power laws have also been observed in neural populations in the mouse under a coarse-graining procedure, and they were explained as a consequence of the neural activity being coupled to multiple latent dynamical variables. An intriguing possibility is that avalanche criticality emerges due to a similar mechanism. Here, we determine the conditions under which dynamical latent variables give rise to avalanche criticality. We find that a single, quasi-static latent variable can generate critical avalanches, but that multiple latent variables lead to critical behavior in a broader parameter range. We identify two regimes of avalanches, both of which are critical, but differ in the amount of information carried about the latent variable. Our results suggest that avalanche criticality arises in neural systems in which there is an emergent dynamical variable or shared inputs creating an effective latent dynamical variable, and when this variable can be inferred from the population activity. 

A fundamental problem in analysis of complex systems is getting a reliable estimate of entropy of their probability distributions over the state space. This is difficult because unsampled states can contribute substantially to the entropy, while they do not contribute to the Maximum Likelihood estimator of entropy, which replaces probabilities by the observed frequencies. Bayesian estimators overcome this obstacle by introducing a model of the low-probability tail of the probability distribution. Which statistical features of the observed data determine the model of the tail, and hence the output of such estimators, remains unclear. Here we show that well-known entropy estimators for probability distributions on discrete state spaces model the structure of the low probability tail based largely on few statistics of the data: the sample size, the Maximum Likelihood estimate, the number of coincidences among the samples, the dispersion of the coincidences. We derive approximate analytical entropy estimators for undersampled distributions based on these statistics, and we use the results to propose an intuitive understanding of how the Bayesian entropy estimators work. 

Quantitative models of associative learning that explain the behavior of real animals with high precision have turned out very difficult to construct. We do this in the context of the dynamics of the thermal preference of C. elegans. For this, we quantify C. elegans thermotaxis in response to various conditioning parameters, genetic perturbations, and operant behavior using a fast, high-throughput microfluidic droplet assay. We then model this data comprehensively, within a new, biologically interpretable, multi-modal framework. We discover that the dynamics of thermal preference are described by two independent contributions and require a model with at least four dynamical variables. One pathway positively associates the experienced temperature independently of food and the other negatively associates to the temperature when food is absent. 

The problem of deciphering how low-level patterns (action potentials in the brain, amino acids in a protein, etc.) drive high-level biological features (sensorimotor behavior, enzymatic function) represents the central challenge of quantitative biology. The lack of general methods for doing so from the size of datasets that can be collected experimentally severely limits our understanding of the biological world. For example, in neuroscience, some sensory and motor codes have been shown to consist of precisely timed multi-spike patterns. However, the combinatorial complexity of such pattern codes have precluded development of methods for their comprehensive analysis. Thus, just as it is hard to predict a protein’s function based on its sequence, we still do not understand how to accurately predict an organism’s behavior based on neural activity. Here, we introduce the unsupervised Bayesian Ising Approximation (uBIA) for solving this class of problems. We demonstrate its utility in an application to neural data, detecting precisely timed spike patterns that code for specific motor behaviors in a songbird vocal system. In data recorded during singing from neurons in a vocal control region, our method detects such codewords with an arbitrary number of spikes, does so from small data sets, and accounts for dependencies in occurrences of codewords. Detecting such comprehensive motor control dictionaries can improve our understanding of skilled motor control and the neural bases of sensorimotor learning in animals. To further illustrate the utility of uBIA, we used it to identify the distinct sets of activity patterns that encode vocal motor exploration versus typical song production. Crucially, our method can be used not only for analysis of neural systems, but also for understanding the structure of correlations in other biological and nonbiological datasets. 

The number of neurons in mammalian cortex varies by multiple orders of magnitude across different species. In contrast, the ratio of excitatory to inhibitory neurons (E:I ratio) varies in a much smaller range, from 3:1 to 9:1 and remains roughly constant for different sensory areas within a species. Despite this structure being important for understanding the function of neural circuits, the reason for this consistency is not yet understood. While recent models of vision based on the efficient coding hypothesis show that increasing the number of both excitatory and inhibitory cells improves stimulus representation, the two cannot increase simultaneously due to constraints on brain volume. In this work, we implement an efficient coding model of vision under a constraint on the volume (using number of neurons as a surrogate) while varying the E:I ratio. We show that the performance of the model is optimal at biologically observed E:I ratios under several metrics. We argue that this happens due to trade-offs between the computational accuracy and the representation capacity for natural stimuli. Further, we make experimentally testable predictions that 1) the optimal E:I ratio should be higher for species with a higher sparsity in the neural activity and 2) the character of inhibitory synaptic distributions and firing rates should change depending on E:I ratio. Our findings, which are supported by our new preliminary analyses of publicly available data, provide the first quantitative and testable hypothesis based on optimal coding models for the distribution of excitatory and inhibitory neural types in the mammalian sensory cortices. 

Biochemical processes in cells are governed by complex networks of many chemical species interacting stochastically in diverse ways and on different time scales. Constructing microscopically accurate models of such networks is often infeasible. Instead, here we propose a systematic framework for building phenomenological models of such networks from experimental data, focusing on accurately approximating the time it takes to complete the process, the First Passage (FP) time. Our phenomenological models are mixtures of Gamma distributions, which have a natural biophysical interpretation. The complexity of the models is adapted automatically to account for the amount of available data and its temporal resolution. The framework can be used for predicting behavior of FP systems under varying external conditions. To demonstrate the utility of the approach, we build models for the distribution of inter-spike intervals of a morphologically complex neuron, a Purkinje cell, from experimental and simulated data. We demonstrate that the developed models can not only fit the data, but also make nontrivial predictions. We demonstrate that our coarse-grained models provide constraints on more mechanistically accurate models of the involved phenomena.