A two phase field model for tracking vesicle–vesicle adhesion

Mechanical deformation and death of circulating tumor cells in the bloodstream

The circulation of tumor cells through the bloodstream is a significant step in tumor metastasis. To better understand the metastatic process, circulating tumor cell (CTC) survival in the circulation must be explored. While immune interactions with CTCs in recent decades have been examined, research has yet to sufficiently explain some CTC behaviors in blood flow. Studies related to CTC mechanical responses in the bloodstream have recently been conducted to further study conditions under which CTCs might die. While experimental methods can assess the mechanical properties and death of CTCs, increasingly sophisticated computational models are being built to simulate the blood flow and CTC mechanical deformation under fluid shear stresses (FSS) in the bloodstream.Several factors contribute to the mechanical deformation and death of CTCs as they circulate. While FSS can damage CTC structure, diverse interactions between CTCs and blood components may either promote or hinder the next metastatic step-extravasation at a remote site. Overall understanding of how these factors influence the deformation and death of CTCs could serve as a basis for future experiments and simulations, enabling researchers to predict CTC death more accurately. Ultimately, these efforts can lead to improved metastasis-specific therapeutics and diagnostics specific in the future.

Phase field modeling and computation of vesicle growth or shrinkage

We present a phase field model for vesicle growth or shrinkage induced by an osmotic pressure due to a chemical potential gradient. The model consists of an Allen-Cahn equation describing the evolution of the phase field parameter that describes the shape of the vesicle and a Cahn-Hilliard-type equation describing the evolution of the ionic fluid. We establish conditions for vesicle growth or shrinkage via a common tangent construction using free energy curves. During the membrane deformation, the model ensures total mass conservation of the ionic fluid, and we weakly enforce a surface area constraint of the vesicle. We develop a stable numerical scheme and an efficient nonlinear multigrid solver to evolve the phase and concentration fields, and we use this to evolve the fields to near equilibrium for 2D vesicles. Convergence tests confirm an [Formula: see text] accuracy for our scheme and near-optimal convergence for our multigrid solver. Numerical results reveal that the diffuse interface model captures the main features of cell shape dynamics: for a growing vesicle, there exist circle-like equilibrium shapes if the concentration difference across the membrane and the initial osmotic pressure are large enough; while for a shrinking vesicle, there exists a rich collection of finger-like equilibrium morphologies.

Activation energy and force fields during topological transitions of fluid lipid vesicles

Topological transitions of fluid lipid membranes are fundamental processes for cell life. For example, they are required for endo- and exocytosis or to enable neurotransmitters to cross the neural synapses. Here, inspired by the idea that fusion and fission proteins could have evolved in Nature in order to carry out a minimal work expenditure, we evaluate the minimal free energy pathway for the transition between two spherical large unilamellar vesicles and a dumbbell-shaped one. To address the problem, we propose and successfully use a Ginzburg-Landau type of free energy, which allows us to uniquely describe without interruption the whole, full-scale topological change. We also compute the force fields needed to overcome the involved energy barriers. The obtained forces are in excellent agreement, in terms of intensity, scale, and spatial localization with experimental data on typical fission protein systems, whereas they suggest the presence of additional features in fusion proteins.

Biomechanics in thrombus formation from direct cellular simulations

Numerically reproducing the process of thrombus formation is highly desired for understanding its mechanism but still remains challenging due to the polydisperse feature of blood components and their multiple biochemical or biomechanical behaviors involved. We numerically implemented a simplified version of the process from the perspective of biomechanics, using a mesoscale particle-based method, smoothed dissipative particle dynamics-immersed boundary method. This version covers the adhesion and aggregation of platelets (PLTs), the deformation and aggregation of red blood cells (RBCs), and the interaction between PLTs and RBCs, as well as the blockage of microvessels. Four critical factors that can affect thrombus formation were investigated: the velocity of blood flow, the adhesive ability of PLTs, the interaction strength between PLTs and RBCs, and the deformability of RBCs. Increasing the velocity of blood flow was found to be the most effective way to reduce the microvessel blockage, and reducing the adhesive ability of PLTs is also a direct and efficient way. However, decreasing the interaction strength between PLTs and RBCs sometimes does not alleviate thrombus formation, and similarly, increasing the deformability of RBCs does not have a significant improvement for the severely blocked microvessel. These results imply that maintaining high-rate blood flow plays a crucial role in the prevention and treatment of thrombosis, which is even more effective than antiplatelet or anticoagulant drugs. The drugs or treatments concentrating on reducing the PLT-RBC interaction or softening the RBCs may not have a significant effect on the thrombosis.

Diffusive Interface Model for Actomyosin Driven Cell Oscillations

In this paper, we build phase-field models for the actomyosin driven cell oscillations. In our modeling, an oscillation starts from an actin cortex breakage. After the breakage, due to the unbalanced distribution of actin and myosin, there is unbalanced contraction force in different membrane components, which then results in the lipids transferring to the bulged membrane compartment. As such we can observe a cell oscillation. During the whole process, the actin and myosin polymerization and depolymerization play important roles. We give detailed formulations under the framework of phase-field methodology, in which phase-field functions are used to describe different parts of the cell membrane, integrated with the distribution of the actin and myosin at different components. The whole system is described as a set of time-dependent partial differential equations in three-dimensional space. Forward Euler method is used to solve the system. The spectral method is used for spatial discretizations for efficiency and accuracy purpose. Given carefully selected parameters, three-dimensional simulations are performed and compared with biological images. The simulations prove that actomyosin dynamics are the major reasons for cell oscillations. Further, our method can be easily extended into the simulations of cell polarization. We also compared our numerical simulations with biological experiments. This modeling gives an example of applying diffusive interface methods toward complex biology experiments.

Morphologies of Vesicle Doublets: Competition among Bending Elasticity, Surface Tension, and Adhesion

To study the mechanical laws governing the form of multicellular organisms, we examine the morphology of adhering vesicle doublets as the simplest model system. We monitor the morphological transformations of doublets induced by changes of adhesion strength and volume/area ratio, which are controlled by intermembrane interactions and thermal area expansion, respectively. When we increase the temperature in the weak adhesion regime, a dumbbell flat-contact doublet is transformed to a parallel-prolate doublet, whereas in the strong adhesion regime, heating transforms the dumbbell flat-contact doublet into a spherical sigmoid-contact doublet. We reproduce the observed doublet morphologies by numerically minimizing the total energy, including the contact-potential adhesion term as well as the surface and bending terms, using the Surface Evolver package. From the reproduced morphologies, we extract the adhesion strength, the surface tension, and the volume/area ratio of the vesicles, which reveals the detailed mechanisms of the morphological transitions in doublets.

Effect of spectrin network elasticity on the shapes of erythrocyte doublets

Red blood cell (RBC) aggregates play an important role in determining blood rheology. RBCs in plasma or polymer solution interact attractively to form various shapes of RBC doublets, where the attractive interactions can be varied by changing the solution conditions. A systematic numerical study on RBC doublet formation is performed, which takes into account the shear elasticity of the RBC membrane due to the spectrin cytoskeleton, in addition to the membrane bending rigidity. RBC membranes are modeled by two-dimensional triangular networks of linked vertices, which represent three-dimensional cell shapes. The phase space of RBC doublet shapes in a wide range of adhesion strengths, reduced volumes, and shear elasticities is obtained. The shear elasticity of the RBC membrane changes the doublet phases significantly. Experimental images of RBC doublets in different solutions show similar configurations. Furthermore, we show that rouleau formation is affected by the doublet structure.