多细胞系统的计算机建模已经成为解释和指导与胚胎形态发生、肿瘤生长、血管生成以及最近将细胞聚集体打印为生物墨水颗粒后的结构形成相关的体外实验的有价值的工具。基于Metropolis Monte Carlo（MMC）算法的计算机模拟成功地解释和预测了所得的固定结构（对应于最低的粘附能态）。在这里，我们提出了两种替代MMC方法来模拟细胞运动和自组装：（1）动力学蒙特卡罗（KMC），（2）细胞粒子动力学（CPD）方法。与MMC不同，KMC和CPD方法都能够实时模拟细胞系统的动力学。在KMC方法中，转换速率与蜂窝系统的可能重排相关联，并且相应的时间演化用这些速率来表示。在CPD方法中，细胞被建模为相互作用的细胞粒子（CP）和多细胞系统的时间演化是通过整合所有CP的运动方程来确定的。KMC和CPD方法通过模拟两种实验上熟知的现象进行测试和比较：（1）在由具有不同粘附性的两种类型的细胞形成的聚集体内的细胞分选，以及（2）活细胞的两个球形聚集体的融合。
英文摘要：
Computer modeling of multicellular systems has been a valuable tool for interpreting and guiding in vitro experiments relevant to embryonic morphogenesis, tumor growth, angiogenesis and, lately, structure formation following the printing of cell aggregates as bioink particles. Computer simulations based on Metropolis Monte Carlo (MMC) algorithms were successful in explaining and predicting the resulting stationary structures (corresponding to the lowest adhesion energy state). Here we present two alternatives to the MMC approach for modeling cellular motion and self-assembly: (1) a kinetic Monte Carlo (KMC), and (2) a cellular particle dynamics (CPD) method. Unlike MMC, both KMC and CPD methods are capable of simulating the dynamics of the cellular system in real time. In the KMC approach a transition rate is associated with possible rearrangements of the cellular system, and the corresponding time evolution is expressed in terms of these rates. In the CPD approach cells are modeled as interacting cellular particles (CPs) and the time evolution of the multicellular system is determined by integrating the equations of motion of all CPs. The KMC and CPD methods are tested and compared by simulating two experimentally well known phenomena: (1) cell-sorting within an aggregate formed by two types of cells with different adhesivities, and (2) fusion of two spherical aggregates of living cells.
We formulate an active-gel theory for multicellular migration in the extra-cellular matrix (ECM). The cells are modeled as an active, polar solvent, and the ECM as a viscoelastic solid. Our theory enables to analyze the dynamic reciprocity between the migrating cells and their environment in terms of distinct relative forces and alignment mechanisms. We analyze the linear stability of polar cells migrating homogeneously in the ECM. Our theory predicts that, as a consequence of cell-matrix alignment, contractile cells migrate homogeneously for small wave vectors, while sufficiently extensile ce…
The prevalence of multicellular organisms is due in part to their ability to form complex structures. How cells pack in these structures is a fundamental biophysical issue, underlying their functional properties. However, much remains unknown about how cell packing geometries arise, and how they are affected by random noise during growth - especially absent developmental programs. Here, we quantify the statistics of cellular neighborhoods of two different multicellular eukaryotes: lab-evolved "snowflake" yeast and the green alga $Volvox~carteri$. We find that despite large differences in cellu…
Cells self-organize into functional, ordered structures during tissue morphogenesis, a process that is evocative of colloidal self-assembly into engineered soft materials. Understanding how inter-cellular mechanical interactions may drive the formation of ordered and functional multicellular structures is important in developmental biology and tissue engineering. Here, by combining an agent-based model for contractile cells on elastic substrates with endothelial cell culture experiments, we show that substrate deformation-mediated mechanical interactions between cells can cluster and align the…
Collections of cells exhibit coherent migration during morphogenesis, cancer metastasis, and wound healing. In many cases, bigger clusters split, smaller sub-clusters collide and reassemble, and gaps continually emerge. The connections between cell-level adhesion and cluster-level dynamics, as well as the resulting consequences for cluster properties such as migration velocity, remain poorly understood. Here we investigate collective migration of one- and two-dimensional cell clusters that collectively track chemical gradients using a mechanism based on contact inhibition of locomotion. We dev…
Flow, dynamics and active fracture in hydraulic multicellular systems
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；Max Planck Institute of Molecular Cell Biology and Genetics（马克斯·普朗克分子细胞生物学与遗传学研究所）
The phase field model can accurately simulate the evolution of microstructures with complex morphologies, and it has been widely used for cell modeling in the last two decades. However, compared to other cellular models such as the coarse-grained model and the vertex model, its high computational cost caused by three-dimensional spatial discretization hampered its application and scalability, especially for multicellular organisms. Recently, we built a phase field model coupled with in vivo imaging data to accurately reconstruct the embryonic morphogenesis of Caenorhabditis elegans from 1- to …
We describe a viscocapillary instability that can perturb the spherical symmetry of cellular aggregates in culture, also called multicellular spheroids. In the condition where the cells constituting the spheroid get their necessary metabolites from the immediate, outer microenvironment, a permanent cell flow exists within the spheroid from its outer rim where cells divide toward its core where they die. A perturbation of the spherical symmetry induces viscous shear stresses within the tissue that can destabilise the aggregate. The proposed instability is viscocapillary in nature and does not r…
The multicellular organization of diverse systems, such as embryos, intestines and tumours, relies on the coordinated migration of cells in 3D curved environments. In these settings, cells establish supracellular patterns of motion, including collective rotation and invasion. While such collective modes are increasingly well understood in 2D flat systems, the consequences of geometrical and topological constraints on collective cell migration in 3D curved tissues are largely unknown. Here, we study 3D collective migration in mammary cell spheroids, which represent a common and conceptually sim…
Multicellular collective migration is a ubiquitous strategy of cells to translocate spatially in diverse tissue environments to accomplish a wide variety of biological phenomena, viz. embryonic development, wound healing, and tumor progression. Diverse cellular functions and behaviors, for instance, cell protrusions, active contractions, cell-cell adhesion, biochemical signaling, remodeling of tissue micro-environment, etc., play their own role concomitantly to have a single concerted consequence of multicellular migration. Thus unveiling the driving principles, both biochemical and biophysica…
The internal and external mechanical environment plays an important role in tumorogenesis. As a proxy of an avascular early state tumor, we use multicellular spheroids, a composite material made of cells, extracellular matrix and permeating fluid. We characterize its effective rheology at the timescale of minutes to hours by compressing the aggregates with osmotic shocks and modeling the experimental results with an active poroelastic material that reproduces the stress and strain distributions in the aggregate. The model also predicts how the emergent bulk modulus of the aggregate as well as …
Multicellular organisms exhibit a high degree of structural organization with specific cell types always occurring in characteristic locations. The conventional framework for describing the emergence of such consistent spatial patterns is provided by Wolpert's "French flag" paradigm. According to this view, intra-cellular genetic regulatory mechanisms use positional information provided by morphogen concentration gradients to differentially express distinct fates, resulting in a characteristic pattern of differentiated cells. However, recent experiments have shown that suppression of inter-cel…
The bacterium Myxoccocus xanthus produces multicellular protective droplets called fruiting bodies when starved. These structures form initially through the active dewetting of cells into surface-bound droplets, where substantial flows of the material are needed as the fruiting bodies grow and become round. These dynamics are followed by a primitive developmental process in which the fluid-like droplets of motile cells mature into mechanically-resilient mounds of non-motile spores that can resist significant mechanical perturbation from the external environment. To date, the mechanical propert…
Fine-grain patterns produced by juxtacrine signalling, have been studied using static monolayers as cellular domains. Unfortunately, analytical results are restricted to a few cells due to the algebraic complexity of nonlinear dynamical systems. Motivated by concentric patterning of Notch expression observed in the mammary gland, we combine concepts from graph and control theory to represent cellular connectivity. The resulting theoretical framework allows us to exploit the symmetry of multicellular bilayer structures in 2D and 3D, thereby deriving analytical conditions that drive the dynamica…
Entropy-Driven Initiation and Cellular Uptake Mediated by Viscoelastic Cytoskeleton: A Kinetic Phase Diagram from Onsager Variational Principle
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Zhejiang Key Laboratory of Soft Matter Biomedical Materials, Wenzhou Institute, University of Chinese Academy of Sciences（温州研究院，中国科学院大学，浙江省软物质生物医用材料重点实验室）
The cytoskeleton -- a collection of polymeric filaments, molecular motors, and crosslinkers -- is a foundational example of active matter, and in the cell assembles into organelles that guide basic biological functions. Simulation of cytoskeletal assemblies is an important tool for modeling cellular processes and understanding their surprising material properties. Here we present aLENS, a novel computational framework to surmount the limits of conventional simulation methods. We model molecular motors with crosslinking kinetics that adhere to a thermodynamic energy landscape, and integrate the…
