SGER: Mathematical Modeling of Living Cell Membranes: Application to AFM-Based Recognition Microscopy

【摘要】SGER奖支持的研究是用原子力显微镜（AFM）对体内细胞膜的反应进行定量研究。长期目标是了解细胞膜在多大程度上反映了细胞内的某些生化过程，以及细胞膜的生物物理特性如何提供对细胞健康的洞察。这种研究的核心是一个能够模拟AFM探针和软细胞膜之间复杂相互作用的理论。这样的理论使得原子力显微镜成为表征细胞膜生物力学特性的有力工具。本文提出的研究是基于由具有局部弯曲阻力的流体膜的第一性原理导出的一般连续统理论。根据问题的物理性质，假设膜包裹着流体介质，流体介质向膜传递静水压力，并在膜的极点施加点载荷以模拟AFM探针的效果。这两种载荷都与电位有关，然后将问题置于变分设置中，该变分设置用于获得描述细胞膜轴对称平衡状态的方程。进一步的改进与封闭体积的全局约束和与刚性衬底的接触有关，并提出了一种求解策略，该策略依赖于计算相关拉格朗日乘子的迭代方案。然后，主要目标是使用该模型的数值实现，通过与AFM数据的相关性和模型的进一步细化来识别与细胞膜力学行为相关的材料常数。该种子资助项目的预期结果将是第一个实验验证的模型，该模型表征了AFM探针与细胞膜之间的非线性相互作用。拟议研究的更广泛影响是生物研究新技术的发展，包括原子力显微镜在细胞研究中使用的工具之一。所提出的理论/计算方法与实验程序具有深远的潜在应用价值。利用这种方法，可以研究病原体对健康细胞膜的影响，从而产生识别和检测这些病原体的物理方法（例如制定针对生物和化学剂的防御措施）。一个有前景的研究领域将是研究肿瘤细胞膜的变化，使细胞能够分裂和转移。这可能导致早期发现和确认恶性肿瘤。然而，另一个富有成效的研究途径将是使用这种方法来深入了解细胞运动的潜在机制。最后，这种方法可以促进对膜特性和疾病之间关系的更深层次的理解，即膜特性和膜结合蛋白的变化如何导致（或指示）疾病，从而可能导致替代治疗策略。

ABSTRACTThe research supported by this SGER award addresses the quantification of the response of the in vivo cell membranes probed with Atomic Force Microscope (AFM). The long-term objective is to understand the extent to which the membrane of a cell mirrors certain biochemical processes within the cell and how the biophysical properties of the membrane provide insight into the health of a cell. At the heart of such an investigation is a theory capable of modeling the complex interaction between an AFM probe and the soft cell membrane. Such a theory then renders the AFM a powerful tool for characterizing the biomechanical properties of cell membranes. The investigation proposed here is based on a general continuum theory derived from first principles of fluid membranes endowed with local bending resistance. In accordance with the physics of the problem the membrane is assumed to enclose a fluid medium, which transmits hydrostatic pressure to the membrane, and a point load is applied at the pole of the membrane to simulate the effect of an AFM probe. Both types of loading are associated with a potential and the problem is then cast in a variational setting, which is used to obtain the equations that describe axisymmetric equilibrium states of the cell membrane. Further refinements associated with global constraints on the enclosed volume and contact with a rigid substrate are proposed together with a solution strategy that relies on an iterative scheme for calculating the associated Lagrange multipliers. The main goal then is to use the numerical implementation of the model to identify the material constants associated with the mechanical behavior of the cell membrane through correlation with AFM data and further refinement of the model. The expected outcome of this seed grant project would be the first experimentally validated model that characterizes the nonlinear interaction between an AFM probe and a cell membrane.The broader impact of the proposed research is the development of new technology for biological research, by including Atomic Force Microscope among the tools used in cell investigation. The proposed theoretical/computational approach together with the experimental program has far reaching potential applications. Using this method, the effect of pathogens on healthy cell membranes can be studied resulting in physical methods for identification and detection of these pathogens (for e.g. in developing defensive measures against biological and chemical agents). A promising area of investigation would be to investigate changes in the membrane of tumor cells that enable cells to divide and metastasize. This could potentially lead to earlier detection and confirmation of malignancy. Yet another fruitful avenue of research would be to use this method to gain a deep understanding of the underlying mechanics of cell motility. Finally this method could facilitate a deeper understanding of the relationship between membrane properties and disease, i.e. how changes in membrane properties and membrane-bound proteins leads to (or are indicative of) disease, which in turn could lead to alternative treatment strategies.