Predictive coding networks for temporal prediction.

One of the key problems the brain faces is inferring the state of the world from a sequence of dynamically changing stimuli, and it is not yet clear how the sensory system achieves this task. A well-established computational framework for describing perceptual processes in the brain is provided by the theory of predictive coding. Although the original proposals of predictive coding have discussed temporal prediction, later work developing this theory mostly focused on static stimuli, and key questions on neural implementation and computational properties of temporal predictive coding networks remain open. Here, we address these questions and present a formulation of the temporal predictive coding model that can be naturally implemented in recurrent networks, in which activity dynamics rely only on local inputs to the neurons, and learning only utilises local Hebbian plasticity. Additionally, we show that temporal predictive coding networks can approximate the performance of the Kalman filter in predicting behaviour of linear systems, and behave as a variant of a Kalman filter which does not track its own subjective posterior variance. Importantly, temporal predictive coding networks can achieve similar accuracy as the Kalman filter without performing complex mathematical operations, but just employing simple computations that can be implemented by biological networks. Moreover, when trained with natural dynamic inputs, we found that temporal predictive coding can produce Gabor-like, motion-sensitive receptive fields resembling those observed in real neurons in visual areas. In addition, we demonstrate how the model can be effectively generalized to nonlinear systems. Overall, models presented in this paper show how biologically plausible circuits can predict future stimuli and may guide research on understanding specific neural circuits in brain areas involved in temporal prediction.

A robust balancing mechanism for spiking neural networks.

Dynamical balance of excitation and inhibition is usually invoked to explain the irregular low firing activity observed in the cortex. We propose a robust nonlinear balancing mechanism for a random network of spiking neurons, which works also in the absence of strong external currents. Biologically, the mechanism exploits the plasticity of excitatory-excitatory synapses induced by short-term depression. Mathematically, the nonlinear response of the synaptic activity is the key ingredient responsible for the emergence of a stable balanced regime. Our claim is supported by a simple self-consistent analysis accompanied by extensive simulations performed for increasing network sizes. The observed regime is essentially fluctuation driven and characterized by highly irregular spiking dynamics of all neurons.

How neuronal morphology impacts the synchronisation state of neuronal networks.

The biophysical properties of neurons not only affect how information is processed within cells, they can also impact the dynamical states of the network. Specifically, the cellular dynamics of action-potential generation have shown relevance for setting the (de)synchronisation state of the network. The dynamics of tonically spiking neurons typically fall into one of three qualitatively distinct types that arise from distinct mathematical bifurcations of voltage dynamics at the onset of spiking. Accordingly, changes in ion channel composition or even external factors, like temperature, have been demonstrated to switch network behaviour via changes in the spike onset bifurcation and hence its associated dynamical type. A thus far less addressed modulator of neuronal dynamics is cellular morphology. Based on simplified and anatomically realistic mathematical neuron models, we show here that the extent of dendritic arborisation has an influence on the neuronal dynamical spiking type and therefore on the (de)synchronisation state of the network. Specifically, larger dendritic trees prime neuronal dynamics for in-phase-synchronised or splayed-out activity in weakly coupled networks, in contrast to cells with otherwise identical properties yet smaller dendrites. Our biophysical insights hold for generic multicompartmental classes of spiking neuron models (from ball-and-stick-type to anatomically reconstructed models) and establish a connection between neuronal morphology and the susceptibility of neural tissue to synchronisation in health and disease.

Unsupervised learning of perceptual feature combinations.

In many situations it is behaviorally relevant for an animal to respond to co-occurrences of perceptual, possibly polymodal features, while these features alone may have no importance. Thus, it is crucial for animals to learn such feature combinations in spite of the fact that they may occur with variable intensity and occurrence frequency. Here, we present a novel unsupervised learning mechanism that is largely independent of these contingencies and allows neurons in a network to achieve specificity for different feature combinations. This is achieved by a novel correlation-based (Hebbian) learning rule, which allows for linear weight growth and which is combined with a mechanism for gradually reducing the learning rate as soon as the neuron's response becomes feature combination specific. In a set of control experiments, we show that other existing advanced learning rules cannot satisfactorily form ordered multi-feature representations. In addition, we show that networks, which use this type of learning always stabilize and converge to subsets of neurons with different feature-combination specificity. Neurons with this property may, thus, serve as an initial stage for the processing of ecologically relevant real world situations for an animal.

Mean-field method for generic conductance-based integrate-and-fire neurons with finite timescales.

The construction of transfer functions in theoretical neuroscience plays an important role in determining the spiking rate behavior of neurons in networks. These functions can be obtained through various fitting methods, but the biological relevance of the parameters is not always clear. However, for stationary inputs, such functions can be obtained without the adjustment of free parameters by using mean-field methods. In this work, we expand current Fokker-Planck approaches to account for the concurrent influence of colored and multiplicative noise terms on generic conductance-based integrate-and-fire neurons. We reduce the resulting stochastic system through the application of the diffusion approximation to a one-dimensional Langevin equation. An effective Fokker-Planck is then constructed using Fox Theory, which is solved numerically using a newly developed double integration procedure to obtain the transfer function and the membrane potential distribution. The solution is capable of reproducing the transfer function and the stationary voltage distribution of simulated neurons across a wide range of parameters. The method can also be easily extended to account for different sources of noise with various multiplicative terms, and it can be used in other types of problems in principle.

Linear and nonlinear integrate-and-fire neurons driven by synaptic shot noise with reversal potentials.

The steady-state firing rate and firing-rate response of the leaky and exponential integrate-and-fire models receiving synaptic shot noise with excitatory and inhibitory reversal potentials is examined. For the particular case where the underlying synaptic conductances are exponentially distributed, it is shown that the master equation for a population of such model neurons can be reduced from an integrodifferential form to a more tractable set of three differential equations. The system is nevertheless more challenging analytically than for current-based synapses: where possible, analytical results are provided with an efficient numerical scheme and code provided for other quantities. The increased tractability of the framework developed supports an ongoing critical comparison between models in which synapses are treated with and without reversal potentials, such as recently in the context of networks with balanced excitatory and inhibitory conductances.

Applications of information geometry to spiking neural network activity.

The space of possible behaviors that complex biological systems may exhibit is unimaginably vast, and these systems often appear to be stochastic, whether due to variable noisy environmental inputs or intrinsically generated chaos. The brain is a prominent example of a biological system with complex behaviors. The number of possible patterns of spikes emitted by a local brain circuit is combinatorially large, although the brain may not make use of all of them. Understanding which of these possible patterns are actually used by the brain, and how those sets of patterns change as properties of neural circuitry change is a major goal in neuroscience. Recently, tools from information geometry have been used to study embeddings of probabilistic models onto a hierarchy of model manifolds that encode how model outputs change as a function of their parameters, giving a quantitative notion of "distances" between outputs. We apply this method to a network model of excitatory and inhibitory neural populations to understand how the competition between membrane and synaptic response timescales shapes the network's information geometry. The hyperbolic embedding allows us to identify the statistical parameters to which the model behavior is most sensitive, and demonstrate how the ranking of these coordinates changes with the balance of excitation and inhibition in the network.

Synchrony in Networks of Type 2 Interneurons Is More Robust to Noise with Hyperpolarizing Inhibition Compared to Shunting Inhibition in Both the Stochastic Population Oscillator and the Coupled Oscillator Regimes.

Synchronization in the gamma band (25-150 Hz) is mediated by PV+ inhibitory interneurons, and evidence is accumulating for the essential role of gamma oscillations in cognition. Oscillations can arise in inhibitory networks via synaptic interactions between individual oscillatory neurons (mean-driven) or via strong recurrent inhibition that destabilizes the stationary background firing rate in the fluctuation-driven balanced state, causing an oscillation in the population firing rate. Previous theoretical work focused on model neurons with Hodgkin's Type 1 excitability (integrators) connected by current-based synapses. Here we show that networks comprised of simple Type 2 oscillators (resonators) exhibit a supercritical Hopf bifurcation between synchrony and asynchrony and a gradual transition via cycle skipping from coupled oscillators to stochastic population oscillator (SPO), as previously shown for Type 1. We extended our analysis to homogeneous networks with conductance rather than current based synapses and found that networks with hyperpolarizing inhibitory synapses were more robust to noise than those with shunting synapses, both in the coupled oscillator and SPO regime. Assuming that reversal potentials are uniformly distributed between shunting and hyperpolarized values, as observed in one experimental study, converting synapses to purely hyperpolarizing favored synchrony in all cases, whereas conversion to purely shunting synapses made synchrony less robust except at very high conductance strengths. In mature neurons the synaptic reversal potential is controlled by chloride cotransporters that control the intracellular concentrations of chloride and bicarbonate ions, suggesting these transporters as a potential therapeutic target to enhance gamma synchrony and cognition.

Cortical cell assemblies and their underlying connectivity: An in silico study.

Recent developments in experimental techniques have enabled simultaneous recordings from thousands of neurons, enabling the study of functional cell assemblies. However, determining the patterns of synaptic connectivity giving rise to these assemblies remains challenging. To address this, we developed a complementary, simulation-based approach, using a detailed, large-scale cortical network model. Using a combination of established methods we detected functional cell assemblies from the stimulus-evoked spiking activity of 186,665 neurons. We studied how the structure of synaptic connectivity underlies assembly composition, quantifying the effects of thalamic innervation, recurrent connectivity, and the spatial arrangement of synapses on dendrites. We determined that these features reduce up to 30%, 22%, and 10% of the uncertainty of a neuron belonging to an assembly. The detected assemblies were activated in a stimulus-specific sequence and were grouped based on their position in the sequence. We found that the different groups were affected to different degrees by the structural features we considered. Additionally, connectivity was more predictive of assembly membership if its direction aligned with the temporal order of assembly activation, if it originated from strongly interconnected populations, and if synapses clustered on dendritic branches. In summary, reversing Hebb's postulate, we showed how cells that are wired together, fire together, quantifying how connectivity patterns interact to shape the emergence of assemblies. This includes a qualitative aspect of connectivity: not just the amount, but also the local structure matters; from the subcellular level in the form of dendritic clustering to the presence of specific network motifs.

Ensemble dynamics and information flow deduction from whole-brain imaging data.

The recent advancements in large-scale activity imaging of neuronal ensembles offer valuable opportunities to comprehend the process involved in generating brain activity patterns and understanding how information is transmitted between neurons or neuronal ensembles. However, existing methodologies for extracting the underlying properties that generate overall dynamics are still limited. In this study, we applied previously unexplored methodologies to analyze time-lapse 3D imaging (4D imaging) data of head neurons of the nematode Caenorhabditis elegans. By combining time-delay embedding with the independent component analysis, we successfully decomposed whole-brain activities into a small number of component dynamics. Through the integration of results from multiple samples, we extracted common dynamics from neuronal activities that exhibit apparent divergence across different animals. Notably, while several components show common cooperativity across samples, some component pairs exhibited distinct relationships between individual samples. We further developed time series prediction models of synaptic communications. By combining dimension reduction using the general framework, gradient kernel dimension reduction, and probabilistic modeling, the overall relationships of neural activities were incorporated. By this approach, the stochastic but coordinated dynamics were reproduced in the simulated whole-brain neural network. We found that noise in the nervous system is crucial for generating realistic whole-brain dynamics. Furthermore, by evaluating synaptic interaction properties in the models, strong interactions within the core neural circuit, variable sensory transmission and importance of gap junctions were inferred. Virtual optogenetics can be also performed using the model. These analyses provide a solid foundation for understanding information flow in real neural networks.

The generative neural microdynamics of cognitive processing.

The entorhinal cortex and hippocampus form a recurrent network that informs many cognitive processes, including memory, planning, navigation, and imagination. Neural recordings from these regions reveal spatially organized population codes corresponding to external environments and abstract spaces. Aligning the former cognitive functionalities with the latter neural phenomena is a central challenge in understanding the entorhinal-hippocampal circuit (EHC). Disparate experiments demonstrate a surprising level of complexity and apparent disorder in the intricate spatiotemporal dynamics of sequential non-local hippocampal reactivations, which occur particularly, though not exclusively, during immobile pauses and rest. We review these phenomena with a particular focus on their apparent lack of physical simulative realism. These observations are then integrated within a theoretical framework and proposed neural circuit mechanisms that normatively characterize this neural complexity by conceiving different regimes of hippocampal microdynamics as neuromarkers of diverse cognitive computations.

Task-anchored grid cell firing is selectively associated with successful path integration-dependent behaviour.

Grid firing fields have been proposed as a neural substrate for spatial localisation in general or for path integration in particular. To distinguish these possibilities, we investigate firing of grid and non-grid cells in the mouse medial entorhinal cortex during a location memory task. We find that grid firing can either be anchored to the task environment, or can encode distance travelled independently of the task reference frame. Anchoring varied between and within sessions, while spatial firing of non-grid cells was either coherent with the grid population, or was stably anchored to the task environment. We took advantage of the variability in task-anchoring to evaluate whether and when encoding of location by grid cells might contribute to behaviour. We find that when reward location is indicated by a visual cue, performance is similar regardless of whether grid cells are task-anchored or not, arguing against a role for grid representations when location cues are available. By contrast, in the absence of the visual cue, performance was enhanced when grid cells were anchored to the task environment. Our results suggest that anchoring of grid cells to task reference frames selectively enhances performance when path integration is required.

Neural waves and computation in a neural net model I: Convolutional hierarchies.

The computational resources of a neuromorphic network model introduced earlier are investigated in the context of such hierarchical systems as the mammalian visual cortex. It is argued that a form of ubiquitous spontaneous local convolution, driven by spontaneously arising wave-like activity-which itself promotes local Hebbian modulation-enables logical gate-like neural motifs to form into hierarchical feed-forward structures of the Hubel-Wiesel type. Extra-synaptic effects are shown to play a significant rôle in these processes. The type of logic that emerges is not Boolean, confirming and extending earlier findings on the logic of schizophrenia.

Spontaneous Dynamics of Hippocampal Place Fields in a Model of Combinatorial Competition among Stable Inputs.

We present computer simulations illustrating how the plastic integration of spatially stable inputs could contribute to the dynamic character of hippocampal spatial representations. In novel environments of slightly larger size than typical apparatus, the emergence of well-defined place fields in real place cells seems to rely on inputs from normally functioning grid cells. Theoretically, the grid-to-place transformation is possible if a place cell is able to respond selectively to a combination of suitably aligned grids. We previously identified the functional characteristics that allow a synaptic plasticity rule to accomplish this selection by synaptic competition during rat foraging behavior. Here, we show that the synaptic competition can outlast the formation of place fields, contributing to their spatial reorganization over time, when the model is run in larger environments and the topographical/modular organization of grid inputs is taken into account. Co-simulated cells that differ only by their randomly assigned grid inputs display different degrees and kinds of spatial reorganization-ranging from place-field remapping to more subtle in-field changes or lapses in firing. The model predicts a greater number of place fields and propensity for remapping in place cells recorded from more septal regions of the hippocampus and/or in larger environments, motivating future experimental standardization across studies and animal models. In sum, spontaneous remapping could arise from rapid synaptic learning involving inputs that are functionally homogeneous, spatially stable, and minimally stochastic.

Synaptic wiring motifs in posterior parietal cortex support decision-making.

The posterior parietal cortex exhibits choice-selective activity during perceptual decision-making tasks1-10. However, it is not known how this selective activity arises from the underlying synaptic connectivity. Here we combined virtual-reality behaviour, two-photon calcium imaging, high-throughput electron microscopy and circuit modelling to analyse how synaptic connectivity between neurons in the posterior parietal cortex relates to their selective activity. We found that excitatory pyramidal neurons preferentially target inhibitory interneurons with the same selectivity. In turn, inhibitory interneurons preferentially target pyramidal neurons with opposite selectivity, forming an opponent inhibition motif. This motif was present even between neurons with activity peaks in different task epochs. We developed neural-circuit models of the computations performed by these motifs, and found that opponent inhibition between neural populations with opposite selectivity amplifies selective inputs, thereby improving the encoding of trial-type information. The models also predict that opponent inhibition between neurons with activity peaks in different task epochs contributes to creating choice-specific sequential activity. These results provide evidence for how synaptic connectivity in cortical circuits supports a learned decision-making task.

Inference of network connectivity from temporally binned spike trains.

BACKGROUND: Processing neural activity to reconstruct network connectivity is a central focus of neuroscience, yet the spatiotemporal requisites of biological nervous systems are challenging for current neuronal sensing modalities. Consequently, methods that leverage limited data to successfully infer synaptic connections, predict activity at single unit resolution, and decipher their effect on whole systems, can uncover critical information about neural processing. Despite the emergence of powerful methods for inferring connectivity, network reconstruction based on temporally subsampled data remains insufficiently unexplored. NEW METHOD: We infer synaptic weights by processing firing rates within variable time bins for a heterogeneous feed-forward network of excitatory, inhibitory, and unconnected units. We assess classification and optimize model parameters for postsynaptic spike train reconstruction. We test our method on a physiological network of leaky integrate-and-fire neurons displaying bursting patterns and assess prediction of postsynaptic activity from microelectrode array data. RESULTS: Results reveal parameters for improved prediction and performance and suggest that lower resolution data and limited access to neurons can be preferred. COMPARISON WITH EXISTING METHOD(S): Recent computational methods demonstrate highly improved reconstruction of connectivity from networks of parallel spike trains by considering spike lag, time-varying firing rates, and other underlying dynamics. However, these methods insufficiently explore temporal subsampling representative of novel data types. CONCLUSIONS: We provide a framework for reverse engineering neural networks from data with limited temporal quality, describing optimal parameters for each bin size, which can be further improved using non-linear methods and applied to more complicated readouts and connectivity distributions in multiple brain circuits.

Shared input and recurrency in neural networks for metabolically efficient information transmission.

Shared input to a population of neurons induces noise correlations, which can decrease the information carried by a population activity. Inhibitory feedback in recurrent neural networks can reduce the noise correlations and thus increase the information carried by the population activity. However, the activity of inhibitory neurons is costly. This inhibitory feedback decreases the gain of the population. Thus, depolarization of its neurons requires stronger excitatory synaptic input, which is associated with higher ATP consumption. Given that the goal of neural populations is to transmit as much information as possible at minimal metabolic costs, it is unclear whether the increased information transmission reliability provided by inhibitory feedback compensates for the additional costs. We analyze this problem in a network of leaky integrate-and-fire neurons receiving correlated input. By maximizing mutual information with metabolic cost constraints, we show that there is an optimal strength of recurrent connections in the network, which maximizes the value of mutual information-per-cost. For higher values of input correlation, the mutual information-per-cost is higher for recurrent networks with inhibitory feedback compared to feedforward networks without any inhibitory neurons. Our results, therefore, show that the optimal synaptic strength of a recurrent network can be inferred from metabolically efficient coding arguments and that decorrelation of the input by inhibitory feedback compensates for the associated increased metabolic costs.

Data-driven multiscale computational models of cortical and subcortical regions.

Data-driven computational models of neurons, synapses, microcircuits, and mesocircuits have become essential tools in modern brain research. The goal of these multiscale models is to integrate and synthesize information from different levels of brain organization, from cellular properties, dendritic excitability, and synaptic dynamics to microcircuits, mesocircuits, and ultimately behavior. This article surveys recent advances in the genesis of data-driven computational models of mammalian neural networks in cortical and subcortical areas. I discuss the challenges and opportunities in developing data-driven multiscale models, including the need for interdisciplinary collaborations, the importance of model validation and comparison, and the potential impact on basic and translational neuroscience research. Finally, I highlight future directions and emerging technologies that will enable more comprehensive and predictive data-driven models of brain function and dysfunction.

Ion-concentration gradients induced by synaptic input increase the voltage depolarization in dendritic spines.

The vast majority of excitatory synaptic connections occur on dendritic spines. Due to their extremely small volume and spatial segregation from the dendrite, even moderate synaptic currents can significantly alter ionic concentrations. This results in chemical potential gradients between the dendrite and the spine head, leading to measurable electrical currents. In modeling electric signals in spines, different formalisms were previously used. While the cable equation is fundamental for understanding the electrical potential along dendrites, it only considers electrical currents as a result of gradients in electrical potential. The Poisson-Nernst-Planck (PNP) equations offer a more accurate description for spines by incorporating both electrical and chemical potential. However, solving PNP equations is computationally complex. In this work, diffusion currents are incorporated into the cable equation, leveraging an analogy between chemical and electrical potential. For simulating electric signals based on this extension of the cable equation, a straightforward numerical solver is introduced. The study demonstrates that this set of equations can be accurately solved using an explicit finite difference scheme. Through numerical simulations, this study unveils a previously unrecognized mechanism involving diffusion currents that amplify electric signals in spines. This discovery holds crucial implications for both numerical simulations and experimental studies focused on spine neck resistance and calcium signaling in dendritic spines.