Bayesian parameter estimation for biochemical reaction networks using region-based adaptive parallel tempering.

Motivation: Mathematical models have become standard tools for the investigation of cellular processes and the unraveling of signal processing mechanisms. The parameters of these models are usually derived from the available data using optimization and sampling methods. However, the efficiency of these methods is limited by the properties of the mathematical model, e.g. nonidentifiabilities, and the resulting posterior distribution. In particular, multi-modal distributions with long valleys or pronounced tails are difficult to optimize and sample. Thus, the developement or improvement of optimization and sampling methods is subject to ongoing research. Results: We suggest a region-based adaptive parallel tempering algorithm which adapts to the problem-specific posterior distributions, i.e. modes and valleys. The algorithm combines several established algorithms to overcome their individual shortcomings and to improve sampling efficiency. We assessed its properties for established benchmark problems and two ordinary differential equation models of biochemical reaction networks. The proposed algorithm outperformed state-of-the-art methods in terms of calculation efficiency and mixing. Since the algorithm does not rely on a specific problem structure, but adapts to the posterior distribution, it is suitable for a variety of model classes

Multiscale Modeling of Neurobiological Systems

The central nervous system (CNS) is one of the most complicated living structures in the universe. A single gene expression, the expression level of a single protein or the concentration of a neurotransmitter could regulate the entire functionality of the CNS. The CNS needs to be investigated as a multiscale system with connections among different levels. The existing technology significantly limits experimental studies, and computational modeling is a useful tool for understanding how parts are connected, regulated, and function together. Ideally, the goal is to develop unified computational methodologies for exploring biological systems at multiple scales ranging from molecular to cellular to tissue level. While rigorous models have been developed at the molecular scale, higher level approaches usually suffer from lack of physical realism and lack of knowledge on model parameters. Molecular level studies can help to define reaction schemes and parameters which could be used in cellular microphysiology models, and image data provide a structural basis for reconstructing the surroundings of the cellular system of interest. This dissertation develops and tests a new multiscale model of dopaminergic signaling and a detailed model of the activation-triggered subunit exchange mechanism of calcium/calmodulin-dependent kinase type II (CaMKII). The goal is to develop and use computational models to understand the molecular mechanisms of neurotransmission, and how disruptions may cause complex disorders and conditions such as drug abuse. The simulations of the dopamine (DA) signaling model show that the addition of the geometry of the environment and localization of individual molecules significantly affect the DA reuptake. Consequently, the formation of DAT clusters reduces the DA clearance rate and increases DA receptor activity. In addition, the effects of the psychostimulants such as cocaine and amphetamine are also investigated. Constructed model and method can potentially serve as an in silico microscope to understand the molecular basis of signaling and regulation events in the CNS. Calibration of CaMKII model shows the limitations of the current parameter estimation methods for large biological models with long simulation times such as hours. The high dimensional parameter space and the limited and noisy data makes the parameter estimation task a challenge