Theoretical and computational investigations of single biomolecule and multicellular morphogenetic processes

在这个建议中，我们从物理学的角度，使用分析和计算工具来研究生物学中的基本现象。我们主要对3个研究领域感兴趣。一个是生物启发的最优化问题。通常，进化寻求通过改变形状、运动或分子来优化有机体的适应性。在某些情况下，这种优化可以在数学上理解，在其他情况下，可以通过计算机算法来理解。我们特别关注一个对理解蛋白质如何折叠到其生物功能结构的重要问题，这涉及到将通常在点之间的距离的概念推广到更高维度的对象。另一个优化问题与生命树--系统发育树有关，涉及构建最小长度的高维网络，表明现有物种的亲缘关系有多近，以及它们的共同祖先可能是什么样子。我们对构建这样的网络并了解它们的普遍属性很感兴趣。他说，第二个研究领域与生物分子如何通过穿孔细胞隔膜的小孔或小孔移动有关。有趣的是，通过分析电流信号和移位时间，一组穿过单个纳米孔的DNA线可能是一种潜在的DNA测序工具。为了研究这些现象，DNA的计算机模型必须得到简化，这样模拟才能在合理的时间内运行。这将涉及到将DNA建模为一系列椭球体，其动态最好地通过称为四元数的超复数来描述。这一框架避免了传统方法中出现的能量病理性差异的问题。他说，第三个研究领域解决了为什么几乎每个人的心脏都在左手，肝脏在右手。这个深层次且悬而未决的问题源于这样一个事实，即生命只使用左旋氨基酸来制造蛋白质。我们计划研究在脊椎动物发育的第8天左右发生的最初的对称破坏事件，以及它们随后放大到宏观的左右不对称。

In this proposal, we investigate fundamental phenomena in biology from the viewpoint of physics, using analytical and computational tools. We are interested primarily in 3 research areas. One is in biologically inspired optimization problems. Often evolution seeks to optimize the fitness of an organism by modifying shape, motion, or molecules. In some cases such optimization may be understood mathematically, in others, through computer algorithms. We focus specifically on a problem important to understanding how a protein folds to its biologically functional structure, which involves generalizing the notion of distance, normally taken between points, to objects of higher dimension. Another optimization problem is related to phylogenetic trees, the tree of life, and involves the construction of high-dimensional networks of minimal length indicating how closely related living species are, as well as what their common ancestors may have looked like. We are interested in constructing such networks and understanding their universal properties.     The second research area is related to how biomolecules move around through small holes or pores which perforate membranes compartmentalizing the cell. Interestingly, a controlled study where a single stand of DNA threads through a single nanopore may be a potential tool allowing DNA to be sequenced, by analyzing current signals and translocation times. Computer models of DNA must be simplified to study these phenomena so simulations can run in reasonable time. This will involve modeling DNA as a sequence of ellipsoids, the dynamics of which are best described through hyper-complex numbers called quaternions. This framework avoids the problem of pathological divergences in energy that arise in traditional approaches.     The third research area addresses why almost everyone has their heart on their left hand side, and liver on their right. This deep and unresolved problem stems back to the fact that life uses only left-handed amino acids to make proteins. We plan to investigate the initial symmetry-breaking events that occur around day 8 in vertebrate development, and their subsequent amplification into macroscopic left-right asymmetry.