Sorting, topology, and structural control in cells

高尔基体是真核细胞中处理和运输分子的关键细胞器。修饰蛋白质/脂质，然后将它们分布，这对细胞的运作至关重要。因此，高尔基体的结构问题与神经退行性疾病、心血管疾病和癌症等疾病有关就不足为奇了。膜结合细胞器表现出强大的调节反应；尽管高尔基体的结构支持分子的不断流动，但它非常稳定，如果被破坏或在有丝分裂事件之后，它会迅速重组。然而，经过一个世纪的研究，人们对这种细胞器如何调节其形态和功能知之甚少。我们将用物理方法来解决这个问题。由高尔基复合体和反高尔基网络（TGN）组成的高尔基体可以被建模为具有非常不同拓扑特征的表面的集合。这个建筑群由许多囊状蓄水池组成，就像一叠煎饼。从高斯曲率的积分来看，它的曲率是正的。这与TGN的负曲率形成鲜明对比，TGN是一个由许多把手的杯状和小管组成的网络。我们的初步研究提供了物理方法如何解释这种结构的稳定性的理解。我们将使用膜能量的物理描述将其构建成一个健壮的模型。实现这一目标依赖于数学知识背景，但也受益于居里研究所合作伙伴提供的生物学见解，确保理论可以根据实验观察进行检验。这些包括，但不限于，高尔基体或ER上的囊泡交通上调。在我们的方法中，我们根据系统自由能的变化来描述一些事件，比如当一个小的膜球脱离高尔基体时的囊泡。自由能可以被描述为膜和囊泡的弯曲能，由称为赫尔弗里希哈密顿量的积分形式给出，加上由表面蛋白质优先招募引起的熵贡献。这些分子被其（高度正的）高斯曲率的偏好驱使到囊泡上，留下具有更高负曲率倾向的分子。通过调用近平衡近似，我们可以计算出使自由能最小的囊泡组成。然后，我们必须将其嵌入表示膜供应和去除的动力系统的体系结构中。我们寻求分析性见解，因此首先考虑一个确定性系统，这将有助于描述贩运的稳定状态。下一个任务是建立更深层次的复杂性模型，直到我们能够准确地描述真实世界的系统。

The Golgi Apparatus, a key organelle in eukaryotic cells, processes and traffics molecules. Modifying proteins/lipids and then distributing them, it is essential to the operation of the cell. It is not surprising then that structural issues in the Golgi are linked to neurodegenerative diseases, cardiovascular disease and cancer, to name but a few. Membrane bound organelles exhibit robust regulatory response; despite supporting a constant flux of molecules the structure of the Golgi is very stable and reforms rapidly if destroyed or after a mitotic event. Yet after a century of research, how this organelle regulates its morphology and function is poorly understood. We will tackle this problem using a physical approach. The Golgi, consisting of the Golgi complex and Trans Golgi Network (TGN), can be modelled as acollection of surfaces with very different topological characteristics. The complex is comprised of many sac-like cisternae- picture a stack of pancakes. It has positive curvature in the sense of the integral of its Gaussian curvature. This is in stark contrast to the very negative curvature of the TGN, a network of cups and tubules with many handles. Our preliminary research provided understanding of how a physical approach could explain the stability of this structure. We will build this into a robust model using a physical description of the membrane energy. Achieving this relies on a background of mathematical knowledge but also benefits from the biological insights that partners in Institut Curie provide, ensuring the theory can be tested against experimental observations. These include, but are not limited to, the up-regulation of vesicular traffic on the Golgi or ER. In our approach we characterise events such as vesiculation, when a small sphere of membrane buds off the Golgi, based on the resulting changes to the free energy of the system. The free energy can be described as the bending energy of the membrane and vesicle, given by an integral form known as the Helfrich Hamiltonian, plus entropy contribution arising from preferential recruitment of surface proteins. These are driven onto the vesicle by a preference for its (highly positive) Gaussian curvature, leaving behind molecules with a higher propensity for negative curvature. By invoking a near-equilibrium approximation we can calculate the vesicle composition that minimises the free energy. We must then embed this into the architecture of a dynamical system representing the supply and removal of membrane. We seek analytical insights and so consider a deterministic system first, which will facilitate the description of the trafficking steady state. The next task is to model deeper levels of complexity until we are accurately describing the real world system.