Models of spatio-temporal reaction systems with applications to systems and synthetic biology

The applicant plans to combine mathematical tools with multi-resolution data to develop models and methods in a framework that considers both space and time. Due to the nonlinear nature of the real-world, understanding behaviors of the physical, biological and social fields require general and widely applicable mathematical frameworks. To do this, the applicant will focus on a particular biological problem of widespread interest: protein interactions and their ability to regulate cellular decision making. This is of paramount importance; for example, in cancer, a cell is unable to transmit a death signal through protein interactions, causing the cell to continue to proliferate when it should arrest. Often these signaling processes involve many agents, all interacting in nontrivial ways, in different locations and at different levels of organization.

The development and analysis of mathematical models describing protein interactions will, crucially, allow us to understand their dynamics, predict molecular mechanisms, reveal their function, and guide cell decisions. This is an ongoing biologically and medically relevant problem of fundamental importance and mathematical/statistical approaches may provide insights into the role and dynamics in spatial organization in cells, but more generally, to other systems. Dynamical approaches will be used for model development since these consider the temporal deterministic evolution of the system and may provide mechanistic information about the system.

Throughout the fellowship, analysis and methods will be developed with chemically resolved data of the protein interaction system. Multi-resolution data of these protein interactions will be collected from Supporting Partners at the Weizmann Institute, Princeton University and University of Tokyo to test our predictions and methods. A range of mathematical/statistical approaches will be used for analysis and method development. One particular problem we will focus on is how to determine which model could describe data generated from a system. This question of model selection, or model discrmination, has led the applicant to work and develop a range of methods to distinguish between models.

Understanding the mechanisms responsible for the behavior of protein signaling in a spatio-temporal framework would advance the fields of mathematics and biology. The Supporting Partners and applicant have already contributed to this arena of studying complex systems; moreover, they share a mutual interest to advance the field through the construction of spatio-temporal models of protein interactions and develop novel mathematical techniques that may be applicable to other inherently spatial systems.

More generally, the research has direct biological implications-the work may provide insights for dysfunction of protein signaling resulting in diseases such as cancer, and we can extend our framework to analyze other biological processes inside living organism. These types of investigations will benefit from the mathematical, statistical and computational protocols that are developed in this project. Furthermore, the nonparametric and statistical methods developed for different types of spatial models can be applied to other contexts.

Spatio-temporal systems are pervasive in the life and physical sciences, in particular, reaction systems are studied in biology and related engineering disciplines. The immediate and mid-term impact of this research is developing an integrative framework of spatio-temporal models and methods with this spatially resolved data. There is a large scope for applying such methods in other systems in computational biology.

Other application areas include:
- pharmacology and predicting behavior to a particular drug
- developmental and stem cell biology
- ecology and species interactions

To maximize short-term impact we will present results at conferences and post them on the preprint server arxiv. The results involving the Bayesian analysis for PDEs will be incorporated into the ABS-SysBio software framework which is freely available online.

In the medium term we will also discuss the application of the signaling findings as potential drug targets and the often-overlooked effects of space in the system.

In addition there is a lack of individuals conversant in both computational and laboratory techniques, the need for such individuals in academia and industry is likely to increase. The proposed program is an intradisciplinary project, at the wet/dry interface of systems biology. I believe the format of this science proposed in this research project will form an important milestone in my career progression.