Hybrid Computational Methods and Algorithms for Complex Biological Systems

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In this project the PI will develop new hybrid computational methods and algorithms to study complex biological systems and problems arising in biomaterials and tissue engineering: (a) cellular aggregate fusion via cell self-assembly; (b) bacterial patterns formation in biofilm growth. This research will positively impact the applications in biomaterials, biotechnology, and biomedical sciences, which include bio-printing technology for fabricating tissues and organs, study of cell motions, drug design and ultimately regenerative medicine. The hybrid computational tools and algorithms developed in this project will help us to better understand complex mechanisms in the cellular system and the bacterial system. The computational framework developed here will be broadly applicable to build up similar hybrid models in (bio)material sciences and (bio)fluid dynamics. Broader impacts of the education plan is to increase the representation of underrepresented minority groups in computational mathematics and mathematical biology. In addition to the training of doctoral graduate students, undergraduate students will also be integrated into the proposed research projects. For the thrust (a), the PI proposes to investigate how the adhesion molecules effect the fusion processes by integrating hybrid models for molecular signaling pathways with those for mechanical motion. In particular, signaling pathways, actomyosin dynamics and the cellular level mechanical polarization are modeled by continuum variables, whose evolution and transport are governed by systems of reaction and reaction-diffusion (RD) equations. Whereas, mechanical motion of the cellular system is described by an on-lattice model based on the kinetic Monte Carlo (KMC) algorithm. Communication between the lattice model and the continuum scale RDs is carried out via a suite of multiscale protocols. For the thrust (b), the PI proposes to study several major factors that affect the formation of bacterial patterns in biofilms: bacterial chemotaxis, motility, and interactions. In the proposed hybrid model, each of bacteria is characterized by an individual off-lattice particle or an elongated rod shape with its location, orientation, and its state of stress exerted by local environment, while the dynamics of extracellular polymeric substances (EPS) in the environment is described by continuously changing fields. The hybrid model is described by a system of ordinary and partial differential equations.