Hybrid Computational Methods and Algorithms for Complex Biological Systems

在这个项目中，PI将开发新的混合计算方法和算法来研究复杂的生物系统和生物材料和组织工程中出现的问题：(A)通过细胞自组装实现细胞聚集体融合；(B)在生物膜生长过程中形成细菌模式。这项研究将对生物材料、生物技术和生物医学科学的应用产生积极的影响，包括组织器官制造的生物打印技术、细胞运动研究、药物设计以及最终的再生医学。在这个项目中开发的混合计算工具和算法将帮助我们更好地理解细胞系统和细菌系统中的复杂机制。本文开发的计算框架将广泛适用于在(生物)材料科学和(生物)流体力学中建立类似的混合模型。教育计划的更广泛影响是增加计算数学和数学生物学中代表性不足的少数群体的代表性。除了博士研究生的培养，本科生也将被纳入建议的研究项目。对于推力(A)，PI建议通过整合分子信号通路和机械运动的混合模型来研究黏附分子如何影响融合过程。特别是，信号通路、肌动蛋白动力学和细胞水平的机械极化由连续变量模拟，其演化和传输由反应系统和反应-扩散(RD)方程控制。而细胞系统的机械运动用基于动力学蒙特卡罗(KMC)算法的格子模型来描述。格子模型和连续尺度RDS之间的通信是通过一套多尺度协议实现的。对于推力(B)，PI建议研究影响生物膜中细菌模式形成的几个主要因素：细菌的趋化性、运动性和相互作用。在所提出的混合模型中，每个细菌都被描述为一个单独的非晶格颗粒或细长的杆状，其位置、取向及其在局部环境中的受力状态，而胞外聚合物(EPS)在环境中的动态则通过连续变化的场来描述。混合模型由常微分方程组和偏微分方程组描述。

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.