MTB Group Seminar Series: Statistical approach for model calibration by pattern data

Abstract
Pattern formation in biological tissues plays an important role in the development of living organisms. Since the classical paper of Alan Turing , a way of modelling biological patterns has been through reaction-diffusion mechanisms. It is postulated that there are two signalling molecules, an activator and an inhibitor, whose interaction and diffusion lead to the destabilization of a spatially homogeneous steady state and to the formation of a stable concentration pattern. While the validity of such models has been experimentally confirmed for some chemical reaction systems, questions remain open in biology. Several different competing approaches have been presented. For example, in mechano-chemical models curvature plays the role of the slowly diffusing inhibitor, setting diffusion coefficient of the slower component in a reaction-diffusion model is set to zero leads to a hysteresis effect. In order to distinguish between rival theories the respective models should be calibrated and verified against empirical data. However, in many experimental situations only the stationary regime of the pattern formation process is observable without any knowledge on the initial state or the transient behavior of the system. An observed pattern represents then one realization from a family of possible patterns, and standard calibration methods measuring the residual between a deterministic model output and data become meaningless. Here we present a solution for such problems. We consider several types of pattern formation models: classical Turing-type reaction-diffusion systems, one-dimensional mechano-chemical models of pattern formation, and reaction-diffusion-ODE systems. We modify a recently developed analogical statistical approach for parameter studies of chaotic systems to the non-chaotic pattern formation models. We demonstrate how the approach provides a cost function that enables a statistically sound identification of the model parameters by steady-state pattern data only, without known initial values or transient data. The accuracy of the approachis verified by adaptive MCMC methods

Link to the session: 
https://us06web.zoom.us/j/86190288386?pwd=RUlZZU9XY2U5aWxMUnVzRDlsRDFZdz09