Li J, Dao M, Lim C T, Suresh S
Department of Materials Science and Engineering, Ohio State University, Columbus, Ohio, USA.
Biophys J. 2005 May;88(5):3707-19. doi: 10.1529/biophysj.104.047332. Epub 2005 Mar 4.
We present a three-dimensional computational study of whole-cell equilibrium shape and deformation of human red blood cell (RBC) using spectrin-level energetics. Random network models consisting of degree-2, 3, ..., 9 junction complexes and spectrin links are used to populate spherical and biconcave surfaces and intermediate shapes, and coarse-grained molecular dynamics simulations are then performed with spectrin connectivities fixed. A sphere is first filled with cytosol and gradually deflated while preserving its total surface area, until cytosol volume consistent with the real RBC is reached. The equilibrium shape is determined through energy minimization by assuming that the spectrin tetramer links satisfy the worm-like chain free-energy model. Subsequently, direct stretching by optical tweezers of the initial equilibrium shape is simulated to extract the variation of axial and transverse diameters with the stretch force. At persistence length p = 7.5 nm for the spectrin tetramer molecule and corresponding in-plane shear modulus mu(0) approximately 8.3 microN/m, our models show reasonable agreement with recent experimental measurements on the large deformation of RBC with optical tweezers. We find that the choice of the reference state used for the in-plane elastic energy is critical for determining the equilibrium shape. If a position-independent material reference state such as a full sphere is used in defining the in-plane energy, then the bending modulus kappa needs to be at least a decade larger than the widely accepted value of 2 x 10(-19) J to stabilize the biconcave shape against the cup shape. We demonstrate through detailed computations that this paradox can be avoided by invoking the physical hypothesis that the spectrin network undergoes constant remodeling to always relax the in-plane shear elastic energy to zero at any macroscopic shape, at some slow characteristic timescale. We have devised and implemented a liquefied network structure evolution algorithm that relaxes shear stress everywhere in the network and generates cytoskeleton structures that mimic experimental observations.
我们使用血影蛋白水平的能量学方法，对人类红细胞（RBC）的全细胞平衡形状和变形进行了三维计算研究。由2、3、……、9度连接复合体和血影蛋白链组成的随机网络模型用于填充球形和双凹形表面以及中间形状，然后在血影蛋白连接性固定的情况下进行粗粒度分子动力学模拟。首先用细胞溶质填充一个球体，并在保持其总表面积的同时逐渐放气，直到达到与真实红细胞一致的细胞溶质体积。通过假设血影蛋白四聚体链满足类蠕虫链自由能模型，通过能量最小化来确定平衡形状。随后，模拟用光学镊子对初始平衡形状进行直接拉伸，以提取轴向和横向直径随拉伸力的变化。对于血影蛋白四聚体分子，在持久长度p = 7.5 nm且相应的面内剪切模量μ(0)约为8.3 μN/m时，我们的模型与最近关于用光学镊子对红细胞进行大变形的实验测量结果显示出合理的一致性。我们发现，用于面内弹性能量的参考状态的选择对于确定平衡形状至关重要。如果在定义面内能量时使用与位置无关的材料参考状态，如完整球体，则弯曲模量κ需要比广泛接受的2×10⁻¹⁹ J的值至少大一个数量级，以稳定双凹形形状以对抗杯形。我们通过详细计算证明，通过引入物理假设，即血影蛋白网络在某个缓慢的特征时间尺度上不断重塑，以在任何宏观形状下始终将面内剪切弹性能量松弛到零，可以避免这个悖论。我们设计并实现了一种液化网络结构演化算法，该算法可松弛网络中各处的剪应力，并生成模仿实验观察结果的细胞骨架结构。
