Bayesian inference for biophysical neuron models enables stimulus optimization for retinal neuroprosthetics

Abstract

Multicompartment models have long been used to study the biophysical mechanisms underlying neural information processing. However, it has been challenging to infer the parameters of such models from data. Here, we build on recent advances in Bayesian simulation-based inference to estimate the parameters of detailed models of retinal neurons whose anatomical structure was based on electron microscopy data. We demonstrate how parameters of a cone, an OFF-and an ON-cone bipolar cell model can be inferred from standard two-photon glutamate imaging with simple light stimuli. The inference method starts with a prior distribution informed by literature knowledge and yields a posterior distribution over parameters highlighting parameters consistent with the data. This posterior allows determining how well parameters are constrained by the data and to what extent changes in one parameter can be compensated for by changes in another. To demonstrate the potential of such data-driven mechanistic neuron models, we created a simulation environment for external electrical stimulation of the retina as used in retinal neuroprosthetic devices. We used the framework to optimize the stimulus waveform to selectively target OFFand ON-cone bipolar cells, a current major problem of retinal neuroprothetics. Taken together, this study demonstrates how a data-driven Bayesian simulation-based inference approach can be used to estimate parameters of complex mechanistic models with high-throughput imaging data.Constraining many of these model parameters such as channel densities requires highly specialized and technically challenging experiments, and, hence, it is usually not viable to measure every single parameter for a neuron model of a specific neuron type. Rather, parameters for mechanistic simulations are often aggregated over different neuron types and even across species. Even though this may be justified in specific cases it likely limits our ability to identify mechanistic models of individual cell types. Alternatively, parameter search methods have been proposed to identify the parameters of mechanistic neuron models from standardized patch-clamp protocols based on exhaustive grid-searches 9-11 or evolutionary algorithms [12][13][14][15] . Such methods are often inefficient, typically not applicable for models with many parameters and identify only a single point estimate consistent with the data instead of the entire distribution.Here, we built on recent advances in Bayesian simulation-based inference to fit multicompartment models of neurons with realistic anatomy in the mouse retina. We used a framework called Sequential Neural Posterior Estimation (SNPE) 16,17 to identify model parameters based on high-throughput two-photon measurements of these neurons' responses to light stimuli. SNPE is a Bayesian simulation-based inference algorithm that allows parameter estimation for simulator models for which the likelihood cannot be evaluated easily. The algorithm estimates the distribution of model parameters consistent with specified ...

System Identification with Biophysical Constraints: A Circuit Model of the Inner Retina

“…On a technical level, it would be highly desirable to perform inference for BCN parameters using recent advances in Approximate Bayesian Computation [29,30]. However, these approaches are typically limited to models with dozens of parameters [22,24]. When the technical challenges involved have been solved, this will allow for the identification of degenerate solutions and dependencies in the parameter space.…”

“…Mechanistic models for retinal neurons are typically biophysically realistic models based on Hodgkin-Huxley equations. For example, such models have been used to model the activity of BCs and RGCs, and can do very well in accounting for adaptive processes, as they incorporate the underlying biophysical mechanisms [21,22]. Such models are based on large amounts of biological detail and knowledge, thus enabling a mechanistic investigation into a specific computation, but are time-consuming to simulate and notoriously hard to fit to data.…”

“…Using this network to model temporal processing in the IPL, we obtain accurate predictions of BC activity across a wide range of stimuli while maintaining a high degree of biological interpretability. In contrast to the often involved inference necessary for biophysically realistic models [22], our model is completely differentiable and can be efficiently learned end-to-end with modern deep learning frameworks.…”

“…1C). The chirp stimulus was slightly intensity and time corrected (as in [22]) to account for slight deviations in frame rate of the projector (not exactly at 60 Hz) and an offset between digital synchronization signal ("trigger") and stimulus presentation (∼34 ms), as well as for the gamma distortion of the projector.…”

Near-optimal rotation of colour space by zebrafish cones in vivo

“…Fitting procedure. We used the Sequential Neural Posterior Estimation method (also called SNPE-B) described in Ref 34 (code available at https://github.com/mackelab/delfi, version: 0.5.1) with small modifications which were already applied in 47 to fit our model.…”