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，以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）通过细胞自组装的细胞聚集体融合;（B）生物膜生长中的细菌模式形成。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影响，其中包括用于制造组织和器官的生物打印技术，细胞运动研究，药物设计和最终再生医学。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。这里开发的计算框架将广泛适用于建立类似的混合模型（生物）材料科学和（生物）流体动力学。教育计划的更广泛影响是增加在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。除了培养博士研究生外，本科生也将融入到拟开展的研究项目中。对于推力（a），PI建议通过整合分子信号传导途径的混合模型与机械运动的混合模型来研究粘附分子如何影响融合过程。特别是，信号传导途径，肌动球蛋白动力学和细胞水平的机械极化建模的连续变量，其演变和运输的反应和反应扩散（RD）方程的系统。而细胞系统的机械运动是由基于动力学蒙特卡罗（KMC）算法的非格模型描述的。晶格模型和连续体尺度RD之间的通信通过一套多尺度协议进行。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，每个细菌的特征在于一个单独的非格子颗粒或细长的杆形状，其位置，方向，其状态的应力施加的局部环境，而在环境中的胞外聚合物（EPS）的动力学描述的连续变化的字段。混合模型由一个常微分方程和偏微分方程组成。

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.