CAREER: Theory of Membrane Shape Sensing at the Micron Scale

这个职业奖支持理论和计算研究，以及相关的教育，以研究蛋白质分子如何分辨细胞膜的形状。为了使细胞分裂或产生突起，蛋白质必须最终到达细胞中的正确位置——例如，定位于具有特定弯曲形状的膜部分。令人惊讶的是，即使膜弯曲的尺度比蛋白质大几千倍，这种情况也会发生。因为膜是柔软的，可以很容易地改变它们的形状，它们也可以非常粗糙，这使得蛋白质“感知”细胞形状的问题变得更加困难。这个项目是关于理解形状感知是如何发生的。蛋白质如何在这些点上结束有两种广泛的可能性：1)每个单独的蛋白质可以对局部膜进行令人难以置信的精确测量，从而找到正确的形状，或者2)许多蛋白质可以协同工作，在许多蛋白质大小的长度范围内测量细胞的形状。单个蛋白质必须多精确地测量膜的形状才能定位它们的去向？蛋白质是否可以根据与形状相关但更容易测量的东西来定位自己？如果蛋白质一起工作来感知膜的形状，那么它们找到膜的位置会有多好呢？PI将使用计算机模型、数学计算和合作者共享的实验数据来解决这些问题。这项研究还将提供一种在更广泛的背景下更好地理解图案如何与表面形状耦合的方法；类似的问题也出现在生物学和其他粗糙表面的图案形成中。该项目包括将计算研究与一项教育计划联系起来，其中包括开发一门以细胞物理学为重点的新课程，以及指导和培训从高中到研究生院的学生。受资助的人将与巴尔的摩市公立高中学生、小组内的巴尔的摩市学生以及与公立高中一起工作的小组成员合作。特别是，PI和研究生将与当地高中教师合作，开发计算“实验室”，向高中学生讲授随机性在物理和生物学中的作用，并协助展示这些实验室。该职业奖支持理论和计算研究，以及相关的教育，以研究纳米级蛋白质如何感知细胞膜的微米级曲率。曲率传感是一个关键的软物质物理问题，但它如何在微米尺度上工作的指导原则仍然不清楚。PI旨在开发有用的预测边界，显示形状传感中的限制因素。如果成功，这项研究将通过使用最小的现象学模型和详细的反应扩散方法，导致对生化极性和细胞几何如何耦合的广泛理解。在膜动力学、统计传感极限（如Berg-Purcell极限）和生化模型的界面上建立有趣的联系，旨在获得对细胞膜和相关生物系统的组织和动力学的新见解。这种见解将用于构建预测模型。本研究将沿着两个主要方向进行：1。确定单个蛋白质感知膜曲率的准确性。即使一种蛋白质可以完美地测量局部膜的形状，它也不能精确地确定微米尺度的膜曲率，因为热波动会产生局部曲率。在曲率半径较大的情况下，将弯曲膜区域与平坦膜区域区分开来更加困难——信噪比降低。感知微米级曲率的蛋白质接近这个基本的物理极限吗？为了确定这一点，研究小组将把估计理论应用于约束内外波动膜的连续体模型。蛋白质结合可能取决于膜曲率的代用物，例如脂质包装中的局部缺陷。这些影响，以及脂质倾斜和膜波动的非热起源也将被研究。综上所述，这些模型预测了曲率依赖性结合如何取决于膜张力、弯曲模量、固体支撑的存在以及小叶之间的脂质不对称性。2. 波动膜上图案形成的紧急形状感知。最初的模拟表明，膜表面的简单双稳态反应可以重现秀丽隐杆线虫胚胎中观察到的形状感知，其中蛋白质定位于细胞的狭窄末端。然而，细胞膜是高度动态的-波动和脂质流动。这些形状的变化和流动是阻碍细胞感知自身形状还是帮助细胞感知自身形状？PI将首先开发和测试形状感知的能量景观模型，以描述蛋白质定位如何依赖于膜形状。为了确定形状波动何时有助于或阻碍形状传感，将对波动膜上的反应扩散动力学进行模拟。这些模型将预测细胞的模式在多大程度上取决于膜-皮质附着、细胞质黏度和其他已知的调节活性膜波动的因素。该项目包括将计算研究与一项教育计划联系起来，其中包括开发一门以细胞物理学为重点的新课程，以及指导和培训从高中到研究生院的学生。受资助的人将与巴尔的摩市公立高中学生、小组内的巴尔的摩市学生以及与公立高中一起工作的小组成员合作。特别是，PI和研究生将与当地高中教师合作，开发计算“实验室”，向高中学生讲授随机性在物理和生物学中的作用，并协助展示这些实验室。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYThis CAREER award supports theoretical and computational research, and associated education to investigate how protein molecules can tell the shape of a cell membrane. For cells to divide or make protrusions, proteins must end up in the right position in the cell – for instance, being localized to parts of the membrane that have particular curved shapes. Surprisingly, this can happen even when the scale over which the membranes curve is far larger, some thousand times larger, than the size of a protein. Because membranes are soft, and can change their shape easily, they also can be very rough, making the problem of the proteins "sensing" the cell’s shape even harder. This project is about understanding how shape sensing can happen. Two broad possibilities for how proteins end up in these spots are either: 1) each single protein can make incredibly precise measurements of the local membrane, allowing it to find the right shape, or 2) many proteins can work together cooperatively to measure the cell’s shape over a length scale of many protein sizes. How precisely must single proteins measure the membrane’s shape in order to locate where they go? Could proteins instead position themselves based on something correlated with shape but easier to measure? If proteins work together to sense the membrane’s shape, how much better will they be at finding their locations? The PI will use computer models, mathematical calculations, and experimental data shared from collaborators to address these questions. This research will also provide a way to better understand how patterning is coupled to surface shape in a broader context; similar problems show up both in biology and in the formation of patterns on other rough surfaces.This project includes linking computational research to an education plan including development of a new class focused on the physics of cells, as well as mentoring and training students from high school to graduate school. People supported by this grant will work in collaboration with Baltimore City public high school students, with Baltimore City students within the group as well as group members working with the public high school. In particular, the PI and graduate student will work with local high school teachers to develop computational “labs” to teach high school students about the role of randomness in physics and biology and assist in presenting these labs. TECHNICAL SUMMARYThis CAREER award supports theoretical and computational research, and associated education to investigate how nanometer-scale proteins sense micron-scale curvature of the cell membrane. Curvature sensing is a critical soft matter physics problem, but the guiding principles of how it operates at the micron scale are still unclear. The PI aims to develop useful predictive bounds showing the limiting factors in shape sensing. If successful, this research will lead to a broad understanding of how biochemical polarity and cell geometry are coupled by using both minimal phenomenological models and detailed reaction-diffusion approaches. Interesting connections at the interfaces of membrane dynamics, statistical sensing limits like the Berg-Purcell limit, and biochemical models, will be developed with the aim to gain new insight into of the organization and dynamics of cell membranes and related biological systems. This insight will be used in building predictive models. This research will be pursued along two primary directions:1. Determining the accuracy with which single proteins can sense membrane curvature. Even if a protein could perfectly measure the local membrane shape, it could not precisely determine the micron-scale membrane curvature, because thermal fluctuations create local curvature. Distinguishing curved membrane regions from flat is harder at larger radii of curvature – the signal-to-noise ratio decreases. Are proteins that sense micron-scale curvature near this basic physical limit? To determine this, the research group will apply estimation theory to continuum models of fluctuating membranes in and out of confinement. Protein binding may depend on proxies for membrane curvature, for example local defects in lipid packing. These effects, as well as lipid tilt and non-thermal origins of membrane fluctuations will also be studied. In combination, these models predict how curvature-dependent binding depends on membrane tension, bending modulus, the presence of a solid support, and lipid asymmetries between leaflets. 2. Emergent shape sensing by pattern formation on a fluctuating membrane. Initial simulations suggest simple bistable reactions on a membrane surface can reproduce the shape sensing observed in C. elegans embryos, where proteins localize to narrow ends of a cell. However, cell membranes are highly dynamic – fluctuating and undergoing lipid flow. Will these shape changes and flows prevent cells from sensing their own shape or help them? The PI will begin by developing and testing an energy landscape model of shape sensing, to describe how protein localization depends on membrane shape. Simulations of reaction-diffusion dynamics on fluctuating membranes will be carried out in order to determine when shape fluctuations can help or hinder shape sensing. These models will predict the extent to which the cell's patterning depends on membrane-cortex attachment, cytosol viscosity, and other factors known to modulate active membrane fluctuations. This project includes linking computational research to an education plan including development of a new class focused on the physics of cells, as well as mentoring and training students from high school to graduate school. People supported by this grant will work in collaboration with Baltimore City public high school students, with Baltimore City students within the group as well as group members working with the public high school. In particular, the PI and graduate student will work with local high school teachers to develop computational “labs” to teach high school students about the role of randomness in physics and biology and assist in presenting these labs.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.