Bayesian Inference for Biophysical Neuron Models

We can describe the functioning of neurons with mathematical models. Using these models, we can emulate the behavior of neurons with computer simulations. The parameters of the mathematical model describe specific biophysical properties of the neurons (e.g., passive membrane conductance, axial resistance, etc...). The main goal is to estimate these parameters from experimental data.

Conventionally, researchers record the voltage response of the neuron (e.g., with the patch-clamp method) given a stimulus (specific current injection) and tune the model parameters so that its output matches the data with some optimization technique (e.g., least squares method). The problem is that fitting a multi-parameter model to data is ambiguous, as multiple parameter combinations can result in a good fit (i.e. the model has large degree of freedom). Therefore, a good fit might not necessarily imply a reliable estimate of the actual biophysical parameter. Moreover, electrophysiological recordings contain inherent noise, further obscuring the estimation of the model parameters. This is an inverse problem where we want to indirectly recover the system's hidden parameters from the observed noisy data – assuming that our physical model of the neuron is accurate.

The abovementioned issues motivated us to apply the methodology of Bayesian Inference to this problem where instead of a point estimate, we get a probability distribution of the model parameters (posterior distribution). This method can also incorporate the noise characteristics of the experimental data. We discovered that electrophysiological recordings have a complex, correlated noise pattern, not just a simple white noise (the assumption for least squares fit), which could be built into our inference method. Thus, the inferred probability distributions tell us how well the parameters are confined given the data. Moreover, we can inspect the interdependence of the parameters with the joint distributions.

Finally, we can construct synthetic experimental data with the noise model and run computer simulations for different experimental stimulating protocols (e.g., sinus current injection, step functions, combinations). Therefore, we can recommend experimental stimulating protocol designs in advance to maximize the recording's information content for inferring the model parameters as precisely as possible.

This work formed the basis of my BSc thesis and continued for several years after my graduation. The GitHub repository of the project can be found here: https://github.com/terbed/parameter-inference.