Inferring neuronal ionic conductances from membrane potentials using CNNs

The neuron is the fundamental unit of computation in the nervous system, and different neuron types produce different temporal patterns of voltage fluctuations in response to input currents. Understanding the mechanism of single neuron firing patterns requires accurate knowledge of the spatial densities of diverse ion channels along the membrane. However, direct measurements of these microscopic variables are difficult to obtain experimentally. Alternatively, one can attempt to infer those microscopic variables from the membrane potential (a mesoscopic variable), or features thereof, which are more experimentally tractable. One approach in this direction is to infer the ionic densities as parameters of a neuronal model. Traditionally this is done using a Multi-Objective Optimization (MOO) method to minimize the differences between features extracted from a simulated neurons membrane potential and the same features extracted from target data. Here, we use Convolutional Neural Networks (CNNs) to directly regress generative parameters (e.g., ionic conductances, membrane resistance, etc.,) from simulated time-varying membrane potentials in response to an input stimulus. We simulated diverse neuron models of increasing complexity (Izikivich: 4 parameters; Hodgkin-Huxley: 7 parameters; Mainen-Sejnowski: 10 parameters) with a large range of variation in the underlying parameter values. We show that hyperparameter optimized CNNs can accurately infer the values of generative variables for these neuron models, and that these results far surpass the previous state-of-the-art method (MOO). We discuss the benefits of optimizing the CNN architecture, improvements in accuracy with additional training data, and some observed limitations. Based on these results, we propose that CNNs may be able to infer the spatial distribution of diverse ionic densities from spatially resolved measurements of neuronal membrane potentials (e.g. voltage imaging).