The complexity of biochemical networks derives from the fact that they are governed by nonlinear kinetics far-from-equilibrium. In recent years, systems biology has emerged as a discipline to examine biological complexity from the point-of-view of integrated systems rather than separate components (the reductionists? point-of-view). A systems approach may help to resolve many fundamental issues in the life sciences that relate to systems-level interactions rather than individual biomolecular species. To achieve a full systems-level description, many new analytical techniques and theories need to be developed, in addition to new experimental advances. One major challenge concerns computational modeling of biological dynamics by differential equations. Due to the complexity of any particular biochemical control system, a large number of variables and parameters are needed to describe its dynamics. To have the desired predictive power, the values of these parameters need to be determined with sufficient precision, but for most systems the requisite experimental data are not available. This is a general problem in many areas of science, including physics and chemistry, where the powerful Mori-Zwanzig projection method is widely used for studying Hamiltonian dynamics. In this method, the complex dynamical system is first separated into primary and secondary subsystems. Through systematic information contraction, one can focus on the primary system, which contains the variables of primary interest (in particular, experimentally resolvable variables). The secondary subsystem is not treated explicitly, but its effect on the primary system is properly accounted for mathematically. In this proposal, the researchers will develop a general formalism and numerical algorithms for non-Hamiltonian systems without detailed balance, with a focus on cellular regulatory networks. The method will be especially useful in three cases: 1) where a coarse-grained model is desirable, or available data prevents a more detailed model; 2) where the network under study is embedded in a larger network; and 3) where one wants to perform multi-scale modeling.
The proposed methods will provide a powerful tool for systems biologists to approach the ultimate goals of understanding complex biological processes and of improving human health. One encounters similar situations, of dealing with a complex system with incomplete information, in many other research areas, for example: financial transactions, the power supply network, and the spread and evolution of viruses during an epidemic or a bioterrorist attack.
