Identifying Bayesian Optimal Experiments for Uncertain Biochemical Pathway Models

Pharmacodynamic (PD) models are mathematical models of cellular reaction networks that include drug mechanisms of action. These models are useful for studying predictive therapeutic outcomes of novel drug therapies in silico. However, PD models are known to possess significant uncertainty with respect to constituent parameter data, leading to uncertainty in the model predictions. Furthermore, experimental data to calibrate these models is often limited or unavailable for novel pathways. In this study, we present a Bayesian optimal experimental design approach for improving PD model prediction accuracy. We then apply our method using simulated experimental data to account for uncertainty in hypothetical laboratory measurements. This leads to a probabilistic prediction of drug performance and a quantitative measure of which prospective laboratory experiment will optimally reduce prediction uncertainty in the PD model. The methods proposed here provide a way forward for uncertainty quantification and guided experimental design for models of novel biological pathways

Current state and challenges for dynamic metabolic modeling

While the stoichiometry of metabolism is probably the best studied cellular level, the dynamics in metabolism can still not be well described, predicted and, thus, engineered. Unknowns in the metabolic flux behavior arise from kinetic interactions, especially allosteric control mechanisms. While the stoichiometry of enzymes is preserved in vitro, their activity and kinetic behavior differs from the in vivo situation. Next to this challenge, it is infeasible to test the interaction of each enzyme with each intracellular metabolite in vitro exhaustively. As a consequence, the whole interacting metabolome has to be studied in vivo to identify the relevant enzymes properties. In this review we discuss current approaches for in vivo perturbation experiments, that is, stimulus response experiments using different setups and quantitative analytical approaches, including dynamic carbon tracing. Next to reliable and informative data, advanced modeling approaches and computational tools are required to identify kinetic mechanisms and their parameters.The authors EV, AT, KN, IR, MO, DM and AW are part of the ERA-IB funded consortium DYNAMICS (ERA-IB-14-081, NWO 053.80.724)

Modelling heterogeneous intracellular networks at the cellular scale

Cell function relies on the coordinated action of heterogeneous interconnected networks of biomolecules. Mathematical models help us explore the dynamics and behaviour of these intracellular networks in greater detail. Models of increasing scale and complexity are being developed to probe cellular processes, often necessitating the use of several types of mathematical representation in hybrid models. Here we review recent efforts to incorporate the influences of stochasticity and spatial heterogeneity into cellular level models, ranging from abstract coarse-grained representations to large-scale hybrid models comprising thousands of biological components. We discuss the key challenges involved in, and recent mathematical advances enabling the development and analysis of mathematical models of complex intracellular processes

Bayesian inference for protein signalling networks

Cellular response to a changing chemical environment is mediated by a complex system of interactions involving molecules such as genes, proteins and metabolites. In particular, genetic and epigenetic variation ensure that cellular response is often highly specific to individual cell types, or to different patients in the clinical setting. Conceptually, cellular systems may be characterised as networks of interacting components together with biochemical parameters specifying rates of reaction. Taken together, the network and parameters form a predictive model of cellular dynamics which may be used to simulate the effect of hypothetical drug regimens. In practice, however, both network topology and reaction rates remain partially or entirely unknown, depending on individual genetic variation and environmental conditions. Prediction under parameter uncertainty is a classical statistical problem. Yet, doubly uncertain prediction, where both parameters and the underlying network topology are unknown, leads to highly non-trivial probability distributions which currently require gross simplifying assumptions to analyse. Recent advances in molecular assay technology now permit high-throughput data-driven studies of cellular dynamics. This thesis sought to develop novel statistical methods in this context, focussing primarily on the problems of (i) elucidating biochemical network topology from assay data and (ii) prediction of dynamical response to therapy when both network and parameters are uncertain

Modeling and Optimization of Dynamical Systems in Epidemiology using Sparse Grid Interpolation

Infectious diseases pose a perpetual threat across the globe, devastating communities, and straining public health resources to their limit. The ease and speed of modern communications and transportation networks means policy makers are often playing catch-up to nascent epidemics, formulating critical, yet hasty, responses with insufficient, possibly inaccurate, information. In light of these difficulties, it is crucial to first understand the causes of a disease, then to predict its course, and finally to develop ways of controlling it. Mathematical modeling provides a methodical, in silico solution to all of these challenges, as we explore in this work. We accomplish these tasks with the aid of a surrogate modeling technique known as sparse grid interpolation, which approximates dynamical systems using a compact polynomial representation. Our contributions to the disease modeling community are encapsulated in the following endeavors. We first explore transmission and recovery mechanisms for disease eradication, identifying a relationship between the reproductive potential of a disease and the maximum allowable disease burden. We then conduct a comparative computational study to improve simulation fits to existing case data by exploiting the approximation properties of sparse grid interpolants both on the global and local levels. Finally, we solve a joint optimization problem of periodically selecting field sensors and deploying public health interventions to progressively enhance the understanding of a metapopulation-based infectious disease system using a robust model predictive control scheme

The effect of noise on dynamics and the influence of biochemical systems

Understanding a complex system requires integration and collective analysis of data from many levels of organisation. Predictive modelling of biochemical systems is particularly challenging because of the nature of data being plagued by noise operating at each and every level. Inevitably we have to decide whether we can reliably infer the structure and dynamics of biochemical systems from present data. Here we approach this problem from many fronts by analysing the interplay between deterministic and stochastic dynamics in a broad collection of biochemical models. In a classical mathematical model we first illustrate how this interplay can be described in surprisingly simple terms; we furthermore demonstrate the advantages of a statistical point of view also for more complex systems. We then investigate strategies for the integrated analysis of models characterised by different organisational levels, and trace the propagation of noise through such systems. We use this approach to uncover, for the first time, the dynamics of metabolic adaptation of a plant pathogen throughout its life cycle and discuss the ecological implications. Finally, we investigate how reliably we can infer model parameters of biochemical models. We develop a novel sensitivity/inferability analysis framework that is generally applicable to a large fraction of current mathematical models of biochemical systems. By using this framework to quantify the effect of parametric variation on system dynamics, we provide practical guidelines as to when and why certain parameters are easily estimated while others are much harder to infer. We highlight the limitations on parameter inference due to model structure and qualitative dynamical behaviour, and identify candidate elements of control in biochemical pathways most likely of being subjected to regulation