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

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.Author Summary: Neurons are the fundamental components of the nervous system and a quantitative description of their properties is a prerequisite to understanding the complex structures they comprise, from microcircuits to networks. Mathematical modelling provides an essential tool to this end and there has been intense effort directed at analysing networks constructed from different classes of neurons. However, even neurons from the same class show a broad variability in parameter values and the distributions and correlations between these parameters are likely to significantly affect network properties. To quantify this variability, we used a combination of intracellular recording, single-neuron modelling, and statistical analysis to measure the physiological variability in pyramidal-cell populations of the neocortex. We employ protocols that measure parameters from both square-pulse and naturalistic stimuli, characterising the perisomatic integration properties of these cells and allowing for the straightforward extraction of mathematically tractable reduced neuron models. We provide algorithms to generate populations of these neuron models that respect the parameter variability and co-variability observed in our experiments. These represent novel tools for exploring heterogeneity in neocortical networks that will be useful for subsequent theoretical and numerical studies. Finally, we make our full electrophysiological dataset available for other research groups to extend and improve on our analysis.