Computational inference of biopathway dynamics and structures

The mathematical modelling of regulatory interactions and signalling processes in living cells is a growing research area, aiming to elucidate the molecular mechanisms that give rise to complex biological phenomena. Examples include circadian clock models describing how plants predict the length of night and adjust their metabolism to prevent carbon starvation before dawn, or carcinogenesis models aiming to explain how aberrant cellular signalling pathways lead to tumour growth and metastasis. Ambitious current approaches in systems biology aim to develop mechanistic models of the relevant cellular networks, using methods from chemical kinetics and control theory. However, due to the large number of chemical kinetic parameters, inference remains an extremely challenging problem, restricting current applications to small a priori identified model pathways. The objective of the proposed research project is to advance the current state of the art of computational/statistical inference in mechanistic models, with a particular focus on applications in systems biology. To this end, we aim to explore and hone a portfolio of methods combining ideas based on (i) gradient matching, (ii) modularization, (iii) parallel tempering, and (iv) focus statistics. The idea of gradient matching (i) is to avoid a computationally expensive explicit solution of the differential equations and instead infer kinetic parameters that give the best agreement between the gradients predicted from the differential equations and those obtained from the tangent to the interpolant of the data. The aim of modularization (ii) is to decompose a complex system into a collection of simpler weakly coupled subsystems for which inference is less challenging, and then reduce inconsistencies between the subsystems in an iterative manner. Parallel tempering (iii) proceeds by carrying out inference on a set of several increasingly smoothed (tempered) versions of the mismatch function in parallel, as a way to avoid suboptimal local optima. As an alternative to smoothing, we aim to adopt ideas from approximate Bayesian computation (iv) and replace the data in parallel chains by sets of focus statistics to extract relevant patterns from the data. This mimics heuristic procedures that are currently carried out by biological modellers, who aim to find chemical kinetic parameters that match certain signatures in the data, like phase shifts, frequency variations, amplitude alterations, etc. All approaches, in isolation and in combination, aim to reduce the computational complexity at a high level of accuracy, thereby enabling an application of inference in mechanistic models to larger and more complex systems. For regulatory networks whose structure is a priori unknown, we precede the above procedures with novel structure learning algorithms from machine learning, aiming for fast search through network topology space based on abstract models of molecular interactions. For both structure learning with machine learning methods and kinetic parameter inference for mechanistic models we will exploit modern PC clusters for parallel processing. The results of our research will be implemented in a user-friendly software toolbox that will be integrated into GLAMA, a widely used systems biology and polyomic data analysis software package (http://www.brc.dcs.gla.ac.uk/systems/glama/), for maximal impact in the biological end-user community.

THE IMMEDIATE TARGET GROUP who will benefit from the proposed research are quantitative biologists working in a variety of disciplines, including (1) pathway medicine, (2) human biomonitoring, (3) molecular plant biology, and (4) ecology.
1) Researchers in PATHWAY MEDICINE will benefit from the deeper understanding of pathogenesis at the molecular level. In particular, the research carried out in the project will lead to a more thorough insight into the consequences of a dysregulation of the pro-inflammatory Interleukin-6 biopathway, which is a potential causal factor in the development of cardiovascular diseases and diabetes.
2) HUMAN BIOMONITORING provides an important source of information on routes of intake of drugs or potentially toxic chemicals in the human body over a wide range of exposure conditions. The mathematical modelling relies on physiologically-based pharmacokinetic or toxicokinetic differential equation models that describe the transfer and perfusion of chemicals between different organs or lumped tissues. The improvement of parameter inference achieved with our work will enable exposure pathways to be identified more accurately. Our work will therefore contribute to improved toxicokinetic screening and risk assessment, to the benefit of the patient community.
3) A challenging problem in MOLECULAR PLANT BIOLOGY is to understand the interplay between internal time keeping (circadian regulation) and metabolism in plants. In the last few years, substantial progress has been made to mathematically model the central processes of circadian regulation at the molecular level. By enabling faster parameter inference and model selection of larger systems, the proposed project will provide the tools for elucidating the detailed structure of the molecular regulatory networks and signalling pathways that enable the interplay between circadian and metabolic processes, to the immediate benefit of the molecular plant biology community. The long-term impact will be a better understanding and control of biomass production in plants, with the ultimate objective to improve food security and biofuel production.
4) ECOLOGICAL SYSTEMS consist of complex interactions among species and their environment, the understanding of which has implications for predicting environmental response to perturbations such as invading species and climate change. However, the revelation of these interactions is not straightforward, nor are the interactions necessarily stable across space and time. By improving the methodology to scale up reliable parameter inference in mechanistic models of diverse species interactions to larger and more complex systems, the proposed project will help ecologists to predict critical regime shifts, i.e. the rapid transition from one stable community structure to another, often ecologically inferior, state. Understanding such regime shifts is particularly critical to assess the impact of climate change on biodiversity, and our work will therefore contribute to the development of more reliable decision support systems on which policy makers can base their risk assessment and adoption of mitigating measures.
A SECOND TARGET GROUP are statisticians, informaticians and quantitative scientists, as our project contributes to the development of improved inference tools for computational statistics and machine learning. This includes nonparametric Bayesian modelling, the modularisation of complex systems, parallel tempering and annealing, emulation versus calibration, mixing of Markov chains, and approximate computation of Bayes factors.
While the primary focus of our project is systems biology, we note that mathematical modelling with differential equations is highly relevant to several other research areas, including chemical engineering, seismology, and epidemiology. The proposed project will therefore make an important methodological contribution that a variety of other scientific disciplines will profit from.