Interpretation of neuronal response properties with simplified neuron models

Computational neuroscience is a branch of the neurosciences that attempts to elucidate the principles underlying the operation of neurons with the help of mathematical modeling. In contrast with a number of fields pursuing a tightly related goal, such as machine learning or statistical learning, computational neuroscience emphasizes the realistic description of neuronal function and organization, and therefore requires a collaboration with experimental research in order to design new models and test their predictions. With the growing computational power available in modern computers, the simulation of neuronal networks with realistic numbers of neurons and functional organization is becoming routinely accessible. For the accurate design of such network models, the experimental characterization of neuronal response properties is required to probe the structural layout of biological networks at the single cell level. We develop here a novel method, the dynamic I-V method, that allows for the extraction of cellular response properties, and requires only a small amount of experimental data. Using this technique a simplified model of the neuronal response is obtained that is shown to accurately fit the experimental data. We demonstrate the use of the dynamic I-V method on both cortical pyramidal cells and inhibitory interneurons, and give the distributions of cellular parameters for the studied sample of cells. We also give theoretical results on the spike-triggered average, a quantity that is easily measured experimentally, which relate the neuronal response properties to identifiable features of the spike-triggered average, and can potentially be helpful to extend the dynamic I-V method in order to derive more accurate models. Potential applications and extensions of our results are discussed.

HippoUnit: A software tool for the automated testing and systematic comparison of detailed models of hippocampal neurons based on electrophysiological data

Shailesh Appukuttan, Luca Leonardo Bologna, Szabolcs Kali, Carmen Alina Lupascu, Rosanna Migliore, Eilif Benjamin Muller, Armando Romani, Sàra Sàray, Werner Alfons Hilda Van Geit

Anatomically and biophysically detailed data-driven neuronal models have become widely used tools for understanding and predicting the behavior and function of neurons. Due to the increasing availability of experimental data from anatomical and electrophysiological measurements as well as the growing number of computational and software tools that enable accurate neuronal modeling, there are now a large number of different models of many cell types available in the literature. These models were usually built to capture a few important or interesting properties of the given neuron type, and it is often unknown how they would behave outside their original context. In addition, there is currently no simple way of quantitatively comparing different models regarding how closely they match specific experimental observations. This limits the evaluation, re-use and further development of the existing models. Further, the development of new models could also be significantly facilitated by the ability to rapidly test the behavior of model candidates against the relevant collection of experimental data. We address these problems for the representative case of the CA1 pyramidal cell of the rat hippocampus by developing an open-source Python test suite, which makes it possible to automatically and systematically test multiple properties of models by making quantitative comparisons between the models and electrophysiological data. The tests cover various aspects of somatic behavior, and signal propagation and integration in apical dendrites. To demonstrate the utility of our approach, we applied our tests to compare the behavior of several different rat hippocampal CA1 pyramidal cell models from the ModelDB database against electrophysiological data available in the literature, and evaluated how well these models match experimental observations in different domains. We also show how we employed the test suite to aid the development of models within the European Human Brain Project (HBP), and describe the integration of the tests into the validation framework developed in the HBP, with the aim of facilitating more reproducible and transparent model building in the neuroscience community. Author summary Anatomically and biophysically detailed neuronal models are useful tools in neuroscience because they allow the prediction of the behavior and the function of the studied cell type under circumstances that are hard to investigate experimentally. However, most detailed biophysical models have been built to capture a few selected properties of the real neuron, and it is often unknown how they would behave under different circumstances, or whether they can be used to successfully answer different scientific questions. To help the modeling community develop better neural models, and to make the process of model building more reproducible and transparent, we developed a test suite that enables the comparison of the behavior of models of neurons in the rat hippocampus and their evaluation against experimental data. Applying our tests to several models available in the literature enabled us to assess and compare how precisely each of these models is able to match various electrophysiological properties of the real neurons. We also use the test suite in the model development workflow of the European Human Brain Project to aid the construction of better models of hippocampal neurons and networks.

PUBLIC LIBRARY SCIENCE2021

On the stability and dynamics of stochastic spiking neuron models: Nonlinear Hawkes process and point process GLMs

Moritz Deger, Joao Emanuel Felipe Gerhard

Point process generalized linear models (PP-GLMs) provide an important statistical framework for modeling spiking activity in single-neurons and neuronal networks. Stochastic stability is essential when sampling from these models, as done in computational neuroscience to analyze statistical properties of neuronal dynamics and in neuro-engineering to implement closed-loop applications. Here we show, however, that despite passing common goodness-of-fit tests, PP-GLMs estimated from data are often unstable, leading to divergent firing rates. The inclusion of absolute refractory periods is not a satisfactory solution since the activity then typically settles into unphysiological rates. To address these issues, we derive a framework for determining the existence and stability of fixed points of the expected conditional intensity function (CIF) for general PP-GLMs. Specifically, in nonlinear Hawkes PP-GLMs, the CIF is expressed as a function of the previous spike history and exogenous inputs. We use a mean-field quasi-renewal (QR) approximation that decomposes spike history effects into the contribution of the last spike and an average of the CIF over all spike histories prior to the last spike. Fixed points for stationary rates are derived as self-consistent solutions of integral equations. Bifurcation analysis and the number of fixed points predict that the original models can show stable, divergent, and metastable (fragile) dynamics. For fragile models, fluctuations of the single-neuron dynamics predict expected divergence times after which rates approach unphysiologically high values. This metric can be used to estimate the probability of rates to remain physiological for given time periods, e.g., for simulation purposes. We demonstrate the use of the stability framework using simulated single-neuron examples and neurophysiological recordings. Finally, we show how to adapt PPGLM estimation procedures to guarantee model stability. Overall, our results provide a stability framework for data-driven PP-GLMs and shed new light on the stochastic dynamics of state-of-the-art statistical models of neuronal spiking activity.

Public Library of Science2017

Functional shape of the spike-triggered adaptation

Christian Antonio Pozzorini

In computational neuroscience, it is of crucial importance to dispose of a model that is able to accurately describe the single-neuron activity. This model should be at the same time biologically relevant and computationally fast. Many different phenomenological models have been proposed. In particular, the adaptive exponential integrate-and-fire model (AdEX) introduced by R. Brette and W. Gerstner accounts for adaptation via spike-triggered currents and the dynamical threshold introduced by Badel et al. Includes refractoriness via a dynamical threshold. In real neurons, adaptation occurs on multiple timescales. Furthermore, it has also been shown that the dynamics of the adaptation depends on the timescale on which the input statistics varies. Here, a new model is proposed that combines both adaptation and refractoriness. In practice, a slightly modified version of the AdEX model was extended using different dynamics of the voltage threshold. To account for multiple-timescale adaptation, power law dynamics was considered. It was also investigated whether the ability to predict spike timing could be improved by driving the modified AdEX model with the fractional derivative of the injected current. All the proposed models were fitted on experimental data from rat cortical pyramidal neurons. The models proposed here can reproduce the activity of the real neuron with high accuracy and about 60% of the observed spikes were correctly predicted with a precision of ±3ms. The introduction of a moving threshold did not not improve in a drastic way the ability to predict spikes, but in the case of cumulative power law dynamics the model was able to capture scale-invariant adaptation. It turns out that the fractional derivative of the injected current can partially account for adaptation. However, the best model takes as input signal the injected current and has both cumulative power law threshold and spike-triggered current

2009