Understanding melanopsin using bayesian generative models – an Introduction

Abstract

Understanding biological processes implies a quantitative description. In recent years a new tool set, Bayesian hierarchical modeling, has seen rapid development. We use these methods to model kinetics of a specific protein in a neuroscience context: melanopsin. Melanopsin is a photoactive protein in retinal ganglion cells. Due to its photoactivity, melanopsin is widely used in optogenetic experiments and an important component in the elucidation of neuronal interactions. Thus it is important to understand the relevant processes and develop mechanistic models. Here, with a focus on methodological aspects, we develop, implement, fit and discuss Bayesian generative models of melanopsin dynamics.We start with a sketch of a basic model and then translate it into formal probabilistic language. As melanopsin occurs in at least two states, a resting and a firing state, a basic model is defined by a non-stationary two state hidden Markov process. Subsequently we add complexities in the form of (1) a hierarchical extension to fit multiple cells; (2) a wavelength dependency, to investigate the response at different color of light stimulation; (3) an additional third state to investigate whether melanopsin is bi-or tri-stable; (4) differences between different sub-types of melanopsin as found in different species. This application of modeling melanopsin dynamics demonstrates several benefits of Bayesian methods. They directly model uncertainty of parameters, are flexible in the distributions and relations of parameters in the modeling, and allow including prior knowledge, for example parameter values based on biochemical data.. CC-BY 4.0 International license not peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was . http://dx.doi.org/10.1101/043273 doi: bioRxiv preprint first posted online Mar. 11, 2016; IntroductionTime-varying data can be analyzed with a multitude of statistical methods. Integrating ordinary or partial differential equations is one of the major tools in the natural sciences. For example in order to analyze the morphology of an action potential we could model the rise and fall by a system of two coupled differential equations. In a linear approximation this results in two exponential functions, where the time-constants of the exponential describe the rise and fall.Alternatively we could use the more complex Hodgkin-Huxley model (Hodgkin and Huxley, 1952). This system of equations does not only better describe the data, but allows a direct interpretation of model variables in terms of molecular and cellular properties. Furthermore, in many experiments, multiple factors influence the dependent variable concurrently and the process of interest is non-stationary. In that case, extracting single time constants can be biased and unable to explain the data. And consequently the mechanistic model should be preferred.The benefit of such generative models is the ability to generate 'fake-data' using previously fitted parameters. It allows t...