A Tractable Method for Describing Complex Couplings between Neurons and Population Rate

Evoked resonant neural activity long-term dynamics can be reproduced by a computational model with vesicle depletion

Subthalamic deep brain stimulation (DBS) robustly generates high-frequency oscillations known as evoked resonant neural activity (ERNA). Recently the importance of ERNA has been demonstrated through its ability to predict the optimal DBS contact in the subthalamic nucleus in patients with Parkinson's disease. However, the underlying mechanisms of ERNA are not well understood, and previous modelling efforts have not managed to reproduce the wealth of published data describing the dynamics of ERNA. Here, we aim to present a minimal model capable of reproducing the characteristics of the slow ERNA dynamics published to date. We make biophysically-motivated modifications to the Kuramoto model and fit its parameters to the slow dynamics of ERNA obtained from data. Our results demonstrate that it is possible to reproduce the slow dynamics of ERNA (over hundreds of seconds) with a single neuronal population, and, crucially, with vesicle depletion as one of the key mechanisms behind the ERNA frequency decay in our model. We further validate the proposed model against experimental data from Parkinson's disease patients, where it captures the variations in ERNA frequency and amplitude in response to variable stimulation frequency, amplitude, and to stimulation pulse bursting. We provide a series of predictions from the model that could be the subject of future studies for further validation.

Parametric Copula-GP model for analyzing multidimensional neuronal and behavioral relationships

One of the main goals of current systems neuroscience is to understand how neuronal populations integrate sensory information to inform behavior. However, estimating stimulus or behavioral information that is encoded in high-dimensional neuronal populations is challenging. We propose a method based on parametric copulas which allows modeling joint distributions of neuronal and behavioral variables characterized by different statistics and timescales. To account for temporal or spatial changes in dependencies between variables, we model varying copula parameters by means of Gaussian Processes (GP). We validate the resulting Copula-GP framework on synthetic data and on neuronal and behavioral recordings obtained in awake mice. We show that the use of a parametric description of the high-dimensional dependence structure in our method provides better accuracy in mutual information estimation in higher dimensions compared to other non-parametric methods. Moreover, by quantifying the redundancy between neuronal and behavioral variables, our model exposed the location of the reward zone in an unsupervised manner (i.e., without using any explicit cues about the task structure). These results demonstrate that the Copula-GP framework is particularly useful for the analysis of complex multidimensional relationships between neuronal, sensory and behavioral variables.

Understanding the relationship between a set of variables is a common problem in many fields, such as weather forecast or stock market data. In neuroscience, one of the main challenges is to characterize the dependencies between neuronal activity, sensory stimuli and behavioral outputs. A method of choice for modeling such statistical dependencies is based on copulas, which disentangle dependencies from single variable statistics. To account for changes in dependencies, we model changes in copula parameters by means of Gaussian Processes, conditioned on a task-related variable. The novelty of our approach includes 1) explicit modeling of the dependencies; and 2) combining different copulas to describe experimentally observed variability. We validate the goodness-of-fit as well as information estimates on synthetic data and on recordings from the visual cortex of mice performing a behavioral task. Our parametric model demonstrates significantly better performance in describing high dimensional dependencies compared to other commonly used techniques. We demonstrate that our model can estimate information and predict behaviorally-relevant parameters of the task without providing any explicit cues to the model. Our results indicate that our model is interpretable in the context of neuroscience applications, scalable to large datasets and suitable for accurate statistical modeling and information estimation.

Collapse of complexity of brain and body activity due to excessive inhibition and MeCP2 disruption

Complex body movements require complex dynamics and coordination among neurons in motor cortex. Conversely, a long-standing theoretical notion supposes that if many neurons in motor cortex become excessively synchronized, they may lack the necessary complexity for healthy motor coding. However, direct experimental support for this idea is rare and underlying mechanisms are unclear. Here we recorded three-dimensional body movements and spiking activity of many single neurons in motor cortex of rats with enhanced synaptic inhibition and a transgenic rat model of Rett syndrome (RTT). For both cases, we found a collapse of complexity in the motor system. Reduced complexity was apparent in lower-dimensional, stereotyped brain-body interactions, neural synchrony, and simpler behavior. Our results demonstrate how imbalanced inhibition can cause excessive synchrony among movement-related neurons and, consequently, a stereotyped motor code. Excessive inhibition and synchrony may underlie abnormal motor function in RTT.

Building population models for large-scale neural recordings: Opportunities and pitfalls

Modern recording technologies now enable simultaneous recording from large numbers of neurons. This has driven the development of new statistical models for analyzing and interpreting neural population activity. Here, we provide a broad overview of recent developments in this area. We compare and contrast different approaches, highlight strengths and limitations, and discuss biological and mechanistic insights that these methods provide.

Macroscopic Quantities of Collective Brain Activity during Wakefulness and Anesthesia

The study of states of arousal is key to understand the principles of consciousness. Yet, how different brain states emerge from the collective activity of brain regions remains unknown. Here, we studied the fMRI brain activity of monkeys during wakefulness and anesthesia-induced loss of consciousness. We showed that the coupling between each brain region and the rest of the cortex provides an efficient statistic to classify the two brain states. Based on this and other statistics, we estimated maximum entropy models to derive collective, macroscopic properties that quantify the system's capabilities to produce work, to contain information, and to transmit it, which were all maximized in the awake state. The differences in these properties were consistent with a phase transition from critical dynamics in the awake state to supercritical dynamics in the anesthetized state. Moreover, information-theoretic measures identified those parameters that impacted the most the network dynamics. We found that changes in the state of consciousness primarily depended on changes in network couplings of insular, cingulate, and parietal cortices. Our findings suggest that the brain state transition underlying the loss of consciousness is predominantly driven by the uncoupling of specific brain regions from the rest of the network.

Ensemble inhibition and excitation in the human cortex: An Ising-model analysis with uncertainties

The pairwise maximum entropy model, also known as the Ising model, has been widely used to analyze the collective activity of neurons. However, controversy persists in the literature about seemingly inconsistent findings, whose significance is unclear due to lack of reliable error estimates. We therefore develop a method for accurately estimating parameter uncertainty based on random walks in parameter space using adaptive Markov-chain Monte Carlo after the convergence of the main optimization algorithm. We apply our method to the activity patterns of excitatory and inhibitory neurons recorded with multielectrode arrays in the human temporal cortex during the wake-sleep cycle. Our analysis shows that the Ising model captures neuronal collective behavior much better than the independent model during wakefulness, light sleep, and deep sleep when both excitatory (E) and inhibitory (I) neurons are modeled; ignoring the inhibitory effects of I neurons dramatically overestimates synchrony among E neurons. Furthermore, information-theoretic measures reveal that the Ising model explains about 80-95% of the correlations, depending on sleep state and neuron type. Thermodynamic measures show signatures of criticality, although we take this with a grain of salt as it may be merely a reflection of long-range neural correlations.

Strong neuron-to-body coupling implies weak neuron-to-neuron coupling in motor cortex

Cortical neurons can be strongly or weakly coupled to the network in which they are embedded, firing in sync with the majority or firing independently. Both these scenarios have potential computational advantages in motor cortex. Commands to the body might be more robustly conveyed by a strongly coupled population, whereas a motor code with greater information capacity could be implemented by neurons that fire more independently. Which of these scenarios prevails? Here we measure neuron-to-body coupling and neuron-to-population coupling for neurons in motor cortex of freely moving rats. We find that neurons with high and low population coupling coexist, and that population coupling was tunable by manipulating inhibitory signaling. Importantly, neurons with different population coupling tend to serve different functional roles. Those with strong population coupling are not involved with body movement. In contrast, neurons with high neuron-to-body coupling are weakly coupled to other neurons in the cortical population.

Some cortical neurons fire together like a synchronized chorus, while others fire independently like soloists. Here, the authors show that soloist neurons in motor cortex tend to control body movements, while the choristers do not, and that soloists can become choristers by increasing inhibition.

Modeling the Correlated Activity of Neural Populations: A Review

The principles of neural encoding and computations are inherently collective and usually involve large populations of interacting neurons with highly correlated activities. While theories of neural function have long recognized the importance of collective effects in populations of neurons, only in the past two decades has it become possible to record from many cells simultaneously using advanced experimental techniques with single-spike resolution and to relate these correlations to function and behavior. This review focuses on the modeling and inference approaches that have been recently developed to describe the correlated spiking activity of populations of neurons. We cover a variety of models describing correlations between pairs of neurons, as well as between larger groups, synchronous or delayed in time, with or without the explicit influence of the stimulus, and including or not latent variables. We discuss the advantages and drawbacks or each method, as well as the computational challenges related to their application to recordings of ever larger populations.

Maximum-entropy models reveal the excitatory and inhibitory correlation structures in cortical neuronal activity

Maximum entropy models can be inferred from large datasets to uncover how collective dynamics emerge from local interactions. Here, such models are employed to investigate neurons recorded by multi-electrode arrays in the human and monkey cortex. Taking advantage of the separation of excitatory and inhibitory neuron types, we construct a model including this distinction. This approach allows us to shed light on differences between excitatory and inhibitory activity across different brain states such as wakefulness and deep sleep, in agreement with previous findings. Additionally, maximum entropy models can also unveil novel features of neuronal interactions, which are found to be dominated by pairwise interactions during wakefulness, but are population-wide during deep sleep. Overall, we demonstrate that maximum entropy models can be useful to analyze datasets with classified neuron types and to reveal the respective roles of excitatory and inhibitory neurons in organizing coherent dynamics in the cerebral cortex.

Blindfold learning of an accurate neural metric

The brain has no direct access to physical stimuli but only to the spiking activity evoked in sensory organs. It is unclear how the brain can learn representations of the stimuli based on those noisy, correlated responses alone. Here we show how to build an accurate distance map of responses solely from the structure of the population activity of retinal ganglion cells. We introduce the Temporal Restricted Boltzmann Machine to learn the spatiotemporal structure of the population activity and use this model to define a distance between spike trains. We show that this metric outperforms existing neural distances at discriminating pairs of stimuli that are barely distinguishable. The proposed method provides a generic and biologically plausible way to learn to associate similar stimuli based on their spiking responses, without any other knowledge of these stimuli.

Probabilistic models for neural populations that naturally capture global coupling and criticality

Advances in multi-unit recordings pave the way for statistical modeling of activity patterns in large neural populations. Recent studies have shown that the summed activity of all neurons strongly shapes the population response. A separate recent finding has been that neural populations also exhibit criticality, an anomalously large dynamic range for the probabilities of different population activity patterns. Motivated by these two observations, we introduce a class of probabilistic models which takes into account the prior knowledge that the neural population could be globally coupled and close to critical. These models consist of an energy function which parametrizes interactions between small groups of neurons, and an arbitrary positive, strictly increasing, and twice differentiable function which maps the energy of a population pattern to its probability. We show that: 1) augmenting a pairwise Ising model with a nonlinearity yields an accurate description of the activity of retinal ganglion cells which outperforms previous models based on the summed activity of neurons; 2) prior knowledge that the population is critical translates to prior expectations about the shape of the nonlinearity; 3) the nonlinearity admits an interpretation in terms of a continuous latent variable globally coupling the system whose distribution we can infer from data. Our method is independent of the underlying system’s state space; hence, it can be applied to other systems such as natural scenes or amino acid sequences of proteins which are also known to exhibit criticality.

Populations of sensory neurons represent information about the outside environment in a collective fashion. A salient property of this distributed neural code is criticality. Yet most models used to date to analyze recordings from large neural populations do not take this observation explicitly into account. Here we aim to bridge this gap by designing probabilistic models whose structure reflects the expectation that the population is close to critical. We show that such principled approach improves previously considered models, and we demonstrate a connection between our models and the presence of continuous latent variables which is a recently proposed mechanism underlying criticality in many natural systems.

The Population Tracking Model: A Simple, Scalable Statistical Model for Neural Population Data

Our understanding of neural population coding has been limited by a lack of analysis methods to characterize spiking data from large populations. The biggest challenge comes from the fact that the number of possible network activity patterns scales exponentially with the number of neurons recorded ([Formula: see text]). Here we introduce a new statistical method for characterizing neural population activity that requires semi-independent fitting of only as many parameters as the square of the number of neurons, requiring drastically smaller data sets and minimal computation time. The model works by matching the population rate (the number of neurons synchronously active) and the probability that each individual neuron fires given the population rate. We found that this model can accurately fit synthetic data from up to 1000 neurons. We also found that the model could rapidly decode visual stimuli from neural population data from macaque primary visual cortex about 65 ms after stimulus onset. Finally, we used the model to estimate the entropy of neural population activity in developing mouse somatosensory cortex and, surprisingly, found that it first increases, and then decreases during development. This statistical model opens new options for interrogating neural population data and can bolster the use of modern large-scale in vivo Ca[Formula: see text] and voltage imaging tools.