Mathematical Biology

Minxin Chen; Ling Yang; Shenggao Zhou                                

Molecular Boiology: Aqueous solvent plays a significant role in dynamical processes of biological molecules, such as conformational changes, molecular recognition, and molecular assembly. Implicit-solvent models are efficient descriptions of such dynamics of biomolecular interactions. Central in such models is the solute-solvent interface that separates solute atoms from the solvent that is coarse-grained. We develop a series of models to describe the dynamics of the solute-solvent interface, probe the effect of solvent as continuum fluids, and study biomolecular interactions in an aqueous environment. We also analyze the mathematical properties of the models and developnumerical software packages for the community.

Another topic of our research is developing multiscale mathematical models, numerical algorithms, and simulation software for modelingand simulating specific large bio-molecular systems, such as ion-channel, DNA chains and other interesting and important biomolecular systems. With these models, algorithms and software, many experimental results could be reproduced, understood better and predicted in computers.

Mathematical modeling of biological signal transduction networks: This field is to apply dynamical theories to biological signal transduction networks at the systems level and to collaborate with biologist to achieve the Inter-Disciplinary researches. The specific research areas are:

1. Dynamics of circadian clock. Circadian clocks, which mean the oscillators with a period of about 24 hours, have been found in many organisms, including cyanobacteria, fungi, plants, invertebrate and vertebrate animals. The circadian clocks are all composed of a negative feedback loop (the gene product inactivates its own production) with a delay. Circadian clock systems have some novel dynamical properties, such as robust period length, entrainment dynamics, periodic memory effects and nocturnal/diurnal switch pattern (bi-stable phases). We use mathematical models to understand the underlying mechanisms and make predictions. Wet lab experiments are also applied to verify the theoretical perditions.

2. Cell cycle control and other biological signal transductions. Biological processes are regulated by complex networks of genes, proteins, and metabolites. Although understanding the functions of individual genes or proteins provides critical detailed information, this reductionist approach normally favored by biologists has limitations and it is far from understanding the whole system, since the interactions between the building blocks are complex and nonlinear. Due to the complexity, intuition has limited capability for synthesizing all of the information gathered from the biological experiments into a cohesive holistic understanding of the system behavior. Computer modeling and complex system theory become more and more important for understanding the behaviors of signal transduction networks