Firing rate dynamics in recurrent spiking neural networks with intrinsic and network heterogeneity

Modeling realistic synaptic inputs of CA1 hippocampal pyramidal neurons and interneurons via Adaptive Generalized Leaky Integrate-and-Fire models

Computational models of brain regions are crucial for understanding neuronal network dynamics and the emergence of cognitive functions. However, current supercomputing limitations hinder the implementation of large networks with millions of morphological and biophysical accurate neurons. Consequently, research has focused on simplified spiking neuron models, ranging from the computationally fast Leaky Integrate and Fire (LIF) linear models to more sophisticated non-linear implementations like Adaptive Exponential (AdEX) and Izhikevic models, through Generalized Leaky Integrate and Fire (GLIF) approaches. However, in almost all cases, these models are tuned (and can be validated) only under constant current injections and they may not, in general, also reproduce experimental findings under variable currents. This study introduces an Adaptive GLIF (A-GLIF) approach that addresses this limitation by incorporating a new set of update rules. The extended A-GLIF model successfully reproduces both constant and variable current inputs, and it was validated against the results obtained using a biophysical accurate model neuron. This enhancement provides researchers with a tool to optimize spiking neuron models using classic experimental traces under constant current injections, reliably predicting responses to synaptic inputs, which can be confidently used for large-scale network implementations.

Mathematical generation of data-driven hippocampal CA1 pyramidal neurons and interneurons copies via A-GLIF models for large-scale networks covering the experimental variability range

Efficient and accurate large-scale networks are a fundamental tool in modeling brain areas, to advance our understanding of neuronal dynamics. However, their implementation faces two key issues: computational efficiency and heterogeneity. Computational efficiency is achieved using simplified neurons, whereas there are no practical solutions available to solve the problem of reproducing in a large-scale network the experimentally observed heterogeneity of the intrinsic properties of neurons. This is important, because the use of identical nodes in a network can generate artifacts which can hinder an adequate representation of the properties of a real network. To this aim, we introduce a mathematical procedure to generate an arbitrary large number of copies of simplified hippocampal CA1 pyramidal neurons and interneurons models, which exhibit the full range of firing dynamics observed in these cells - including adapting, non-adapting and bursting. For this purpose, we rely on a recently published adaptive generalized leaky integrate-and-fire (A-GLIF) modeling approach, leveraging on its ability to reproduce the rich set of electrophysiological behaviors of these types of neurons under a variety of different stimulation currents. The generation procedure is based on a perturbation of model's parameters related to the initial data, firing block, and internal dynamics, and suitably validated against experimental data to ensure that the firing dynamics of any given cell copy remains within the experimental range. A classification procedure confirmed that the firing behavior of most of the pyramidal/interneuron copies was consistent with the experimental data. This approach allows to obtain heterogeneous copies with mathematically controlled firing properties. A full set of heterogeneous neurons composing the CA1 region of a rat hippocampus (approximately 1.2 million neurons), are provided in a database freely available in the live paper section of the EBRAINS platform. By adapting the underlying A-GLIF framework, it will be possible to extend the numerical approach presented here to create, in a mathematically controlled manner, an arbitrarily large number of non-identical copies of cell populations with firing properties related to other brain areas.

Statistical Analysis of Decoding Performances of Diverse Populations of Neurons

A central theme in computational neuroscience is determining the neural correlates of efficient and accurate coding of sensory signals. Diversity, or heterogeneity, of intrinsic neural attributes is known to exist in many brain areas and is thought to significantly affect neural coding. Recent theoretical and experimental work has argued that in uncoupled networks, coding is most accurate at intermediate levels of heterogeneity. Here we consider this question with data from in vivo recordings of neurons in the electrosensory system of weakly electric fish subject to the same realization of noisy stimuli; we use a generalized linear model (GLM) to assess the accuracy of (Bayesian) decoding of stimulus given a population spiking response. The long recordings enable us to consider many uncoupled networks and a relatively wide range of heterogeneity, as well as many instances of the stimuli, thus enabling us to address this question with statistical power. The GLM decoding is performed on a single long time series of data to mimic realistic conditions rather than using trial-averaged data for better model fits. For a variety of fixed network sizes, we generally find that the optimal levels of heterogeneity are at intermediate values, and this holds in all core components of GLM. These results are robust to several measures of decoding performance, including the absolute value of the error, error weighted by the uncertainty of the estimated stimulus, and the correlation between the actual and estimated stimulus. Although a quadratic fit to decoding performance as a function of heterogeneity is statistically significant, the result is highly variable with low R2 values. Taken together, intermediate levels of neural heterogeneity are indeed a prominent attribute for efficient coding even within a single time series, but the performance is highly variable.

Investigating the Correlation-Firing Rate Relationship in Heterogeneous Recurrent Networks

The structure of spiking activity in cortical networks has important implications for how the brain ultimately codes sensory signals. However, our understanding of how network and intrinsic cellular mechanisms affect spiking is still incomplete. In particular, whether cell pairs in a neural network show a positive (or no) relationship between pairwise spike count correlation and average firing rate is generally unknown. This relationship is important because it has been observed experimentally in some sensory systems, and it can enhance information in a common population code. Here we extend our prior work in developing mathematical tools to succinctly characterize the correlation and firing rate relationship in heterogeneous coupled networks. We find that very modest changes in how heterogeneous networks occupy parameter space can dramatically alter the correlation-firing rate relationship.

Toward a multiscale modeling framework for understanding serotonergic function

Despite its importance in regulating emotion and mental wellbeing, the complex structure and function of the serotonergic system present formidable challenges toward understanding its mechanisms. In this paper, we review studies investigating the interactions between serotonergic and related brain systems and their behavior at multiple scales, with a focus on biologically-based computational modeling. We first discuss serotonergic intracellular signaling and neuronal excitability, followed by neuronal circuit and systems levels. At each level of organization, we will discuss the experimental work accompanied by related computational modeling work. We then suggest that a multiscale modeling approach that integrates the various levels of neurobiological organization could potentially transform the way we understand the complex functions associated with serotonin.

Sleep regulation of the distribution of cortical firing rates

Sleep is thought to mediate both mnemonic and homeostatic functions. However, the mechanism by which this brain state can simultaneously implement the 'selective' plasticity needed to consolidate novel memory traces and the 'general' plasticity necessary to maintain a well-functioning neuronal system is unclear. Recent findings show that both of these functions differentially affect neurons based on their intrinsic firing rate, a ubiquitous neuronal heterogeneity. Furthermore, they are both implemented by the NREM slow oscillation, which also distinguishes neurons based on firing rate during sequential activity at the DOWN→UP transition. These findings suggest a mechanism by which spiking activity during the slow oscillation acts to maintain network statistics that promote a skewed distribution of neuronal firing rates, and perturbation of that activity by hippocampal replay acts to integrate new memory traces into the existing cortical network.