Experimentally Verified Parameter Sets for Modelling Heterogeneous Neocortical Pyramidal-Cell Populations

Abstract

Models of neocortical networks are increasingly including the diversity of excitatory and inhibitory neuronal classes. Significant variability in cellular properties are also seen within a nominal neuronal class and this heterogeneity can be expected to influence the population response and information processing in networks. Recent studies have examined the population and network effects of variability in a particular neuronal parameter with some plausibly chosen distribution. However, the empirical variability and covariance seen across multiple parameters are rarely included, partly due to the lack of data on parameter correlations in forms convenient for model construction. To addess this we quantify the heterogeneity within and between the neocortical pyramidal-cell classes in layers 2/3, 4, and the slender-tufted and thick-tufted pyramidal cells of layer 5 using a combination of intracellular recordings, single-neuron modelling and statistical analyses. From the response to both square-pulse and naturalistic fluctuating stimuli, we examined the class-dependent variance and covariance of electrophysiological parameters and identify the role of the h current in generating parameter correlations. A byproduct of the dynamic I-V method we employed is the straightforward extraction of reduced neuron models from experiment. Empirically these models took the refractory exponential integrate-and-fire form and provide an accurate fit to the perisomatic voltage responses of the diverse pyramidal-cell populations when the class-dependent statistics of the model parameters were respected. By quantifying the parameter statistics we obtained an algorithm which generates populations of model neurons, for each of the four pyramidal-cell classes, that adhere to experimentally observed marginal distributions and parameter correlations. As well as providing this tool, which we hope will be of use for exploring the effects of heterogeneity in neocortical networks, we also provide the code for the dynamic I-V method and make the full electrophysiological data set available.

Inferring and validating mechanistic models of neural microcircuits based on spike-train data

“…Both components are determined from the Fokker-Planck system and can be conveniently calculated without having to solve Eqs. (17)- (19) forward in time: the linear temporal filter is obtained from the first order spike rate response to small amplitude modulations of the mean input and the nonlinearity is obtained from the steady-state solution [57,58]. The filter is approximated by an exponential function and adapted to the input in order to allow for large deviations of µ.…”

“…Comparisons between models of this type and recorded spike trains have revealed that multiple combinations of biophysical parameters give rise to the same firing patterns [8,9]. This observation motivates the use of models at an intermediate level of complexity, and in particular integrate-and-fire (I&F) neurons, which implement in a simplified manner the key biophysical constraints with a reduced number of effective parameters and can be equipped with various mechanisms such as spike initiation [10][11][12], adaptive excitability [13,14] or distinct compartments [15,16] to generate diverse spiking behaviors [17,18] and model multiple neuron types [19,20]. I&F models can reproduce and predict neuronal activity with a remarkable degree of accuracy [11,21,22], essentially matching the performance of biophysically detailed models with many parameters [17,23]; thus, they have become state-of-the-art models for describing neural activity in in-vivo-like conditions [11,19,20,24].…”

“…This observation motivates the use of models at an intermediate level of complexity, and in particular integrate-and-fire (I&F) neurons, which implement in a simplified manner the key biophysical constraints with a reduced number of effective parameters and can be equipped with various mechanisms such as spike initiation [10][11][12], adaptive excitability [13,14] or distinct compartments [15,16] to generate diverse spiking behaviors [17,18] and model multiple neuron types [19,20]. I&F models can reproduce and predict neuronal activity with a remarkable degree of accuracy [11,21,22], essentially matching the performance of biophysically detailed models with many parameters [17,23]; thus, they have become state-of-the-art models for describing neural activity in in-vivo-like conditions [11,19,20,24]. In particular, they have been applied in a multitude of studies on local circuits [25][26][27][28][29][30][31], network dynamics [32][33][34][35][36], learning/computing in networks [37][38][39][40], as well as in neuromorphic hardware systems [37,[41][42][43].…”

“…I&F neurons can be fit in straightforward ways to membrane voltage recordings with knowledge of the neuronal input, typically from in-vitro preparations [11,17,19,20,24,44,45]. Having only access to the spike times as in a typical in-vivo setting however poses a substantial challenge for the estimation of parameters.…”

Inferring the collective dynamics of neuronal populations from single-trial spike trains using mechanistic models

“…An alternative, prominent class of models with reduced complexity are spiking neuron models of the integrate-and-fire (I&F) type, which implement in a simplified manner essential biophysical constraints. These models have been advanced in recent years to accurately predict neuronal activity [20][21][22] and classify multiple neuron types [17,23,24]. They have become state-of-the-art models for describing neural activity in in-vivo-like conditions and have been applied in a multitude of studies on neural network dynamics.…”