Ulisse Ferrari

Functional coupling networks inferred from prefrontal cortex activity show experience-related effective plasticity

Functional coupling networks are widely used to characterize collective patterns of activity in neural populations. Here, we ask whether functional couplings reflect the subtle changes, such as in physiological interactions, believed to take place during learning. We infer functional network models reproducing the spiking activity of simultaneously recorded neurons in prefrontal cortex (PFC) of rats, during the performance of a cross-modal rule shift task (task epoch), and during preceding and following sleep epochs. A large-scale study of the 96 recorded sessions allows us to detect, in about 20% of sessions, effective plasticity between the sleep epochs. These coupling modifications are correlated with the coupling values in the task epoch, and are supported by a small subset of the recorded neurons, which we identify by means of an automatized procedure. These potentiated groups increase their coativation frequency in the spiking data between the two sleep epochs, and, hence, participate to putative experience-related cell assemblies. Study of the reactivation dynamics of the potentiated groups suggests a possible connection with behavioral learning. Reactivation is largely driven by hippocampal ripple events when the rule is not yet learned, and may be much more autonomous, and presumably sustained by the potentiated PFC network, when learning is consolidated. Author Summary Cell assemblies coding for memories are widely believed to emerge through synaptic modification resulting from learning, yet their identification from activity is very arduous. We propose a functional-connectivity-based approach to identify experience-related cell assemblies from multielectrode recordings in vivo, and apply it to the prefrontal cortex activity of rats recorded during a task epoch and the preceding and following sleep epochs. We infer functional couplings between the recorded cells in each epoch. Comparisons of the functional coupling networks across the epochs allow us to identify effective potentiation between the two sleep epochs. The neurons supporting these potentiated interactions strongly coactivate during the task and subsequent sleep epochs, but not in the preceding sleep, and, hence, presumably belong to an experience-related cell assembly. Study of the reactivation of this assembly in response to hippocampal ripple inputs suggests possible relations between the stage of behavorial learning and memory consolidation mechanisms.

Learning maximum entropy models from finite-size data sets: A fast data-driven algorithm allows sampling from the posterior distribution

Inverse problems consist in inferring parameters of model distributions that are able to fit properly chosen features of experimental data-sets. The Inverse Ising problem specifically consists of searching for the maximal entropy distribution reproducing frequencies and correlations of a binary data-set. In order to solve this task, we propose an algorithm that takes advantage of the provided by the data knowledge of the log-likelihood function around the solution. We show that the present algorithm is faster than standard gradient ascent methods. Moreover, by looking at the algorithm convergence as a stochastic process, we properly define over-fitting and we show how the present algorithm avoids it by construction.

Finite-size corrections to disordered systems on Erdös-Rényi random graphs

We study the finite size corrections to the free energy density in disorder spin systems on sparse random graphs, using both replica theory and cavity method. We derive an analytical expressions for the

Random versus maximum entropy models of neural population activity

O(1/N)

Multiplexed computations in retinal ganglion cells of a single type

corrections in the replica symmetric phase as a linear combination of the free energies of open and closed chains. We perform a numerical check of the formulae on the Random Field Ising Model at zero temperature, by computing finite size corrections to the ground state energy density.

Inferred Model of the Prefrontal Cortex Activity Unveils Cell Assemblies and Memory Replay

The principle of maximum entropy provides a useful method for inferring statistical mechanics models from observations in correlated systems, and is widely used in a variety of fields where accurate data are available. While the assumptions underlying maximum entropy are intuitive and appealing, its adequacy for describing complex empirical data has been little studied in comparison to alternative approaches. Here, data from the collective spiking activity of retinal neurons is reanalyzed. The accuracy of the maximum entropy distribution constrained by mean firing rates and pairwise correlations is compared to a random ensemble of distributions constrained by the same observables. For most of the tested networks, maximum entropy approximates the true distribution better than the typical or mean distribution from that ensemble. This advantage improves with population size, with groups as small as eight being almost always better described by maximum entropy. Failure of maximum entropy to outperform random models is found to be associated with strong correlations in the population.

Inferred network from prefrontal cortex activity of rats unveils cell assemblies

In the early visual system, cells of the same type perform the same computation in different places of the visual field. How these cells code together a complex visual scene is unclear. A common assumption is that cells of a single-type extract a single-stimulus feature to form a feature map, but this has rarely been observed directly. Using large-scale recordings in the rat retina, we show that a homogeneous population of fast OFF ganglion cells simultaneously encodes two radically different features of a visual scene. Cells close to a moving object code quasilinearly for its position, while distant cells remain largely invariant to the object’s position and, instead, respond nonlinearly to changes in the object’s speed. We develop a quantitative model that accounts for this effect and identify a disinhibitory circuit that mediates it. Ganglion cells of a single type thus do not code for one, but two features simultaneously. This richer, flexible neural map might also be present in other sensory systems.Retinal ganglion cell subtypes are traditionally thought to encode a single visual feature across the visual field to form a feature map. Here the authors show that fast OFF ganglion cells in fact respond to two visual features, either object position or speed, depending on the stimulus location.

Closed-loop estimation of retinal network sensitivity reveals signature of efficient coding

Cell assemblies are thought to be the units of information representation in the brain, yet their detection from experimental data is arduous. Here, we propose to infer effective coupling networks and model distributions for the activity of simultaneously recorded neurons in prefrontal cortex, during the performance of a decision-making task, and during preceding and following sleep epochs. Our approach, inspired from statistical physics, allows us to define putative cell assemblies as the groups of co-activated neurons in the models of the three recorded epochs. It reveals the existence of task-related changes of the effective couplings between the sleep epochs. The assemblies which strongly coactivate during the task epoch are found to replay during subsequent sleep, in correspondence to the changes of the inferred network. Across sessions, a variety of different network scenarios is observed, providing insight in cell assembly formation and replay. Author Summary Memories are thought to be represented in the brain through groups of coactivating neurons, the so-called cell assemblies. We propose an approach to identify cell assemblies from multi-electrode recordings of neural activity in vivo, and apply it to the prefrontal cortex activity of a behaving rat. Our statistical physics inspired approach consists in inferring effective interactions between the recorded cells, which reproduce the correlations in their spiking activities. The analysis of the effective interaction networks and of the model distributions allows us to identify cell assemblies, which strongly co-activate when the rat is learning, and also during subsequent sleep. Our approach is thus capable of providing detailed insights in cell-assembly formation and replay, crucial for memory consolidation.

Maximum entropy models reveal the correlation structure in cortical neural activity during wakefulness and sleep

We analyzed recordings of prefrontal cortex activity of a rat in three different phases: while the animal faces a task in which a rule has to be learned and during the previous and subsequent sleep phases. We inferred an Ising model (characterized by binary variables and local fields and couplings as parameters) from the recorded spiking frequencies and pairwise correlations between neurons. We have shown how the inferred model can be used to deepen the analysis of the recordings, unveiling the presence of highly coordinated groups of neurons (cell assemblies), that is neurons that are activated together and synchronously inhibit the activity of other specific neurons. To identify the coactivated groups, we found the maxima of the log-likelihood of a configuration of neurons (stable states), defined as the sum of all the fields and couplings relative to the active neurons, performing an ascent dynamics on the energy landscape. When the model is inferred from the activity binned into 10 ms time bins, the only stable state is the one with all silent neurons. By adding an external input into the model and slowly increasing its value, stable states with more and more active neurons appear (see Figure ​Figure1A),1A), starting from the neurons with higher spiking frequency. Remarkably, the curves in Figure ​Figure1A1A show large jumps at specific values of the input strength, corresponding to the co-activation of strongly interconnected neurons, which not necessarily have high average activity. These highly synchronized neurons have been found from the models of both the awake and sleep epochs (see Figure ​Figure1B),1B), and are partially shared between different phases. Figure 1 Co-activation of neurons as a function of the input strength and of the time bin. A: Number of active neurons A(H) in the stable states vs external input H. Parameters (fields and couplings) of the Ising model were inferred from the activity of the Maze ... We investigated the meaning of the external input parameter, discovering that it carries information on the time scale at which we observe correlations between neurons, namely the time bin width. In fact, the two curves of Figure ​Figure1A,1A, which refer to the model inferred from the neuronal activity binned into two different time bins (10 ms and 30 ms), overlap by applying a translation of log(30 ms/10 ms) in the input strength. The fact that at Δt = 30 ms the first co-activated group appears for a small input strength H~1 means that the group is likely to be co-activated in a 30 ms time scale. Neurons found in activated and inhibited groups extracted from our model correspond to large entries in the two principal eigenvectors of the Pearson correlation matrix obtained from the recorded activity. In particular the 1st component has large and positive entries on both activated groups, and the 2nd component shows negative entries on the 1st group, and positive ones on the 2nd group which entails that the groups can activate together or not. Moreover the activation of a group causes the inhibition of another group, which has also large entries on the 1st and 2nd components but with opposite signs. The sign of the components therefore refects in an intricate manner the activation-inhibition relationships between different groups.

A Simple Model for Low Variability in Neural Spike Trains

According to the theory of efficient coding, sensory systems are adapted to represent natural scenes with high fidelity and at minimal metabolic cost. Testing this hypothesis for sensory structures performing non-linear computations on high dimensional stimuli is still an open challenge. Here we develop a method to characterize the sensitivity of the retinal network to perturbations of a stimulus. Using closed-loop experiments, we explore selectively the space of possible perturbations around a given stimulus. We then show that the response of the retinal population to these small perturbations can be described by a local linear model. Using this model, we computed the sensitivity of the neural response to arbitrary temporal perturbations of the stimulus, and found a peak in the sensitivity as a function of the frequency of the perturbations. Based on a minimal theory of sensory processing, we argue that this peak is set to maximize information transmission. Our approach is relevant to testing the efficient coding hypothesis locally in any context where no reliable encoding model is known.