Proposed Spring Network Cell Model Based on a Minimum Energy Concept

Chemo-mechanical model of cell polarization initiated by structural polarity

Cell polarization is crucial in most physiological functions. Living cells at the extracellular matrix (ECM) actively coordinate a polarized morphology to target the preferred signals. In particular, the initial heterogeneity of subcellular components, termed as structural polarity, has been discovered to mediate the early attachment and transmigration of cells in tumour metastasis. However, how heterogeneous cells initiate the early polarization remains incompletely discovered. Here, we establish a multiscale model of a cell to explore the chemo-mechanical mechanisms of cell polarization initiated by structural polarity. The two-dimensional vertex model of the cell is built with the main mechanical components of eukaryotic cells. The initial structural polarity of the modeled cell is introduced by seeding heterogeneous actin filaments at the cell cortex and quantified by the ratio of the filamentous forces at the vertices. Then, the structural polarity is integrated in the reaction-diffusion system of Rho GTPase (Cdc42) at the cell cortex to obtain the traction forces at the leading vertices. Finally, the modeled cell is actuated to spread under the traction forces and discovered to develop into a characteristic polarized morphology. The results indicate that the cell polarization is initiated and dynamically developed by structural polarity through the reaction-diffusion system of Cdc42. In addition, the bistability of Cdc42 activation at the cell cortex is defined and discovered to dominate the polarization status of the cell. Furthermore, biphasic (i.e., positive and negative) durotaxis of the cell is successfully modeled at an ECM with a stiffness gradient, and concluded to be codetermined by the chemo-mechanical coupling of the initial structural polarity and ECM stiffness gradient. The proposed multiscale model provides a quantitative way to probe cell polarization coupled with mechanical stimuli, biochemical reaction and cytoskeletal reorganization, and holds the potential to guide studies of cell polarization under multiple stimuli.

Electromechanical interactions between cell membrane and nuclear envelope: Beyond the standard Schwan's model of biological cells

We investigate little-appreciated features of the hierarchical core-shell (CS) models of the electrical, mechanical, and electromechanical interactions between the cell membrane (CM) and nuclear envelope (NE). We first consider a simple model of an individual cell based on a coupled resistor-capacitor (Schwan model (SM)) network and show that the CM, when exposed to ac electric fields, acts as a low pass filter while the NE acts as a wide and asymmetric bandpass filter. We provide a simplified calculation for characteristic time associated with the capacitive charging of the NE and parameterize its range of behavior. We furthermore observe several new features dealing with mechanical analogs of the SM based on elementary spring-damper combinations. The chief merit of these models is that they can predict creep compliance responses of an individual cell under static stress and their effective retardation time constants. Next, we use an alternative and a more accurate CS physical model solved by finite element simulations for which geometrical cell reshaping under electromechanical stress (electrodeformation (ED)) is included in a continuum approach with spatial resolution. We show that under an electric field excitation, the elongated nucleus scales differently compared to the electrodeformed cell.

Subcellular elements responsive to the biomechanical activity of triple-negative breast cancer-derived small extracellular vesicles

Triple-negative breast cancer (TNBC) stands out for its aggressive, fast spread, and highly metastatic behavior and for being unresponsive to the classical hormonal therapy. It is considered a disease with a poor prognosis and limited treatment options. Among the mechanisms that contribute to TNBC spreading, attention has been recently paid to small extracellular vesicles (sEVs), nano-sized vesicles that by transferring bioactive molecules to recipient cells play a crucial role in the intercellular communication among cancer, healthy cells, and tumor microenvironment. In particular, TNBC-derived sEVs have been shown to alter proliferation, metastasis, drug resistance, and biomechanical properties of target cells. To shed light on the molecular mechanisms involved in sEVs mediation of cell biomechanics, we investigated the effects of sEVs on the main subcellular players, i.e., cell membrane, cytoskeleton, and nuclear chromatin organization. Our results unveiled that TNBC-derived sEVs are able to promote the formation and elongation of cellular protrusions, soften the cell body, and induce chromatin decondensation in recipient cells. In particular, our data suggest that chromatin decondensation is the main cause of the global cell softening. The present study added new details and unveiled a novel mechanism of activity of the TNBC-derived sEVs, providing information for the efficient translation of sEVs to cancer theranostics.

Biomechanical model of cells probing the myosin-II-independent mechanosensing mechanism

Mechanosensing of cells to extracellular matrix (ECM) is highly active and plays a crucial role in various physiological processes. Growing numbers of studies provide evidence that cell sensitivity to ECM stiffness is a complex stress-strain feedback process. However, the mechanisms that rule this process are still not fully known. Here, an alternative mechanosensing scheme of cells, which is different from the previous myosin-II-based mechanisms, is proposed by employing the tension in cortical cytoskeletons (CSKs) as a force module to probe the substrate. The molecular mechanotransduction from cortical CSKs, through actin filaments and focal adhesions, and finally to the substrate, is mechanically modeled to scale the dynamic traction forces of cells. The developed model captures the characteristic spread of cells with respect to ECM stiffness whereby the spread is fully developed on a stiff substrate but not on a soft one. Furthermore, durotactic migration of cells on an elastic-gradient substrate is successfully modeled by the current method. The cells are concluded to migrate, actuated by the polarized traction forces from the stiffness gradient of the substrate and the stiffness matching between cells and substrate. Finally, the cells are proposed to actively target the preferred substrate by following a rule of mechanical matching between cells and substrate. This study provides a theoretical tool to advance our knowledge regarding the passive mechanical properties and the active sensing of cells, and further promotes the discovery of mechanosensing mechanisms as well as the material design for embryonic development and tissue homeostasis.

B16 Melanoma Cancer Cells with Higher Metastatic Potential are More Deformable at a Whole-Cell Level

INTRODUCTION

Metastasis is a process in which cancer cells spread from the primary focus site to various other organ sites. Many studies have suggested that reduced stiffness would facilitate passing through extracellular matrix when cancer cells instigate a metastatic process. Here we investigated the compressive properties of melanoma cancer cells with different metastatic potentials at the whole-cell level. Differences in their compressive properties were analyzed by examining actin filament structure and actin-related gene expression.

METHODS

Compressive tests were carried out for two metastatic B16 melanoma variants (B16-F1 and B16-F10) to characterize global compressive properties of cancer cells. RNA-seq analysis and fluorescence microscopic imaging were performed to clarify contribution of actin filaments to the global compressive properties.

RESULTS

RNA-seq analysis and fluorescence microscopic imaging revealed the undeveloped structure of actin filaments in B16-F10 cells. The Young's modulus of B16-F10 cells was significantly lower than that of B16-F1 cells. Disruption of the actin filaments in B16-F1 cells reduced the Young's modulus to the same level as that of B16-F10 cells, while the Young's modulus in B16-F10 cells remained the same regardless of the disruption.

CONCLUSIONS

In B16 melanoma cancer cell lines, cells with higher metastatic potential were more deformable at the whole-cell level with undeveloped actin filament structure, even when highly deformed. These results imply that invasive cancer cells may gain the ability to inhibit actin filament development.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at (10.1007/s12195-021-00677-w).

A data-driven approach to modeling cancer cell mechanics during microcirculatory transport

In order to understand the effect of cellular level features on the transport of circulating cancer cells in the microcirculation, there has been an increasing reliance on high-resolution in silico models. Accurate simulation of cancer cells flowing with blood cells requires resolving cellular-scale interactions in 3D, which is a significant computational undertaking warranting a cancer cell model that is both computationally efficient yet sufficiently complex to capture relevant behavior. Given that the characteristics of metastatic spread are known to depend on cancer type, it is crucial to account for mechanistic behavior representative of a specific cancer's cells. To address this gap, in the present work we develop and validate a means by which an efficient and popular membrane model-based approach can be used to simulate deformable cancer cells and reproduce experimental data from specific cell lines. Here, cells are modeled using the immersed boundary method (IBM) within a lattice Boltzmann method (LBM) fluid solver, and the finite element method (FEM) is used to model cell membrane resistance to deformation. Through detailed comparisons with experiments, we (i) validate this model to represent cancer cells undergoing large deformation, (ii) outline a systematic approach to parameterize different cell lines to optimally fit experimental data over a range of deformations, and (iii) provide new insight into nucleated vs. non-nucleated cell models and their ability to match experiments. While many works have used the membrane-model based method employed here to model generic cancer cells, no quantitative comparisons with experiments exist in the literature for specific cell lines undergoing large deformation. Here, we describe a phenomenological, data-driven approach that can not only yield good agreement for large deformations, but explicitly detail how it can be used to represent different cancer cell lines. This model is readily incorporated into cell-resolved hemodynamic transport simulations, and thus offers significant potential to complement experiments towards providing new insights into various aspects of cancer progression.

Computational models of cancer cell transport through the microcirculation

The transport of cancerous cells through the microcirculation during metastatic spread encompasses several interdependent steps that are not fully understood. Computational models which resolve the cellular-scale dynamics of complex microcirculatory flows offer considerable potential to yield needed insights into the spread of cancer as a result of the level of detail that can be captured. In recent years, in silico methods have been developed that can accurately and efficiently model the circulatory flows of cancer and other biological cells. These computational methods are capable of resolving detailed fluid flow fields which transport cells through tortuous physiological geometries, as well as the deformation and interactions between cells, cell-to-endothelium interactions, and tumor cell aggregates, all of which play important roles in metastatic spread. Such models can provide a powerful complement to experimental works, and a promising approach to recapitulating the endogenous setting while maintaining control over parameters such as shear rate, cell deformability, and the strength of adhesive binding to better understand tumor cell transport. In this review, we present an overview of computational models that have been developed for modeling cancer cells in the microcirculation, including insights they have provided into cell transport phenomena.

Finite Element Simulations of Mechanical Behaviour of Endothelial Cells

Biomechanical models based on the finite element method have already shown their potential in the simulation of the mechanical behaviour of cells. For instance, development of atherosclerosis is accelerated by damage of the endothelium, a monolayer of endothelial cells on the inner surface of arteries. Finite element models enable us to investigate mechanical factors not only at the level of the arterial wall but also at the level of individual cells. To achieve this, several finite element models of endothelial cells with different shapes are presented in this paper. Implementing the recently proposed bendotensegrity concept, these models consider the flexural behaviour of microtubules and incorporate also waviness of intermediate filaments. The suspended and adherent cell models are validated by comparison of their simulated force-deformation curves with experiments from the literature. The flat and dome cell models, mimicking natural cell shapes inside the endothelial layer, are then used to simulate their response in compression and shear which represent typical loads in a vascular wall. The models enable us to analyse the role of individual cytoskeletal components in the mechanical responses, as well as to quantify the nucleus deformation which is hypothesized to be the quantity decisive for mechanotransduction.

Tools for computational analysis of moving boundary problems in cellular mechanobiology

A cell's ability to change shape is one of the most fundamental biological processes and is essential for maintaining healthy organisms. When the ability to control shape goes awry, it often results in a diseased system. As such, it is important to understand the mechanisms that allow a cell to sense and respond to its environment so as to maintain cellular shape homeostasis. Because of the inherent complexity of the system, computational models that are based on sound theoretical understanding of the biochemistry and biomechanics and that use experimentally measured parameters are an essential tool. These models involve an inherent feedback, whereby shape is determined by the action of regulatory signals whose spatial distribution depends on the shape. To carry out computational simulations of these moving boundary problems requires special computational techniques. A variety of alternative approaches, depending on the type and scale of question being asked, have been used to simulate various biological processes, including cell motility, division, mechanosensation, and cell engulfment. In general, these models consider the forces that act on the system (both internally generated, or externally imposed) and the mechanical properties of the cell that resist these forces. Moving forward, making these techniques more accessible to the non-expert will help improve interdisciplinary research thereby providing new insight into important biological processes that affect human health. This article is categorized under: Cancer > Cancer>Computational Models Cancer > Cancer>Molecular and Cellular Physiology.

Nonlinear Elastic and Inelastic Properties of Cells

Mechanical forces play an important role in various physiological processes, such as morphogenesis, cytokinesis, and migration. Thus, in order to illuminate mechanisms underlying these physiological processes, it is crucial to understand how cells deform and respond to external mechanical stimuli. During recent decades, the mechanical properties of cells have been studied extensively using diverse measurement techniques. A number of experimental studies have shown that cells are far from linear elastic materials. Cells exhibit a wide variety of nonlinear elastic and inelastic properties. Such complicated properties of cells are known to emerge from unique mechanical characteristics of cellular components. In this review, we introduce major cellular components that largely govern cell mechanical properties and provide brief explanations of several experimental techniques used for rheological measurements of cell mechanics. Then, we discuss the representative nonlinear elastic and inelastic properties of cells. Finally, continuum and discrete computational models of cell mechanics, which model both nonlinear elastic and inelastic properties of cells, will be described.

An Active Biomechanical Model of Cell Adhesion Actuated by Intracellular Tensioning-Taxis

Cell adhesion to the extracellular matrix (ECM) is highly active and plays a crucial role in various physiological functions. The active response of cells to physicochemical cues has been universally discovered in multiple microenvironments. However, the mechanisms to rule these active behaviors of cells are still poorly understood. Here, we establish an active model to probe the biomechanical mechanisms governing cell adhesion. The framework of cells is modeled as a tensional integrity that is maintained by cytoskeletons and extracellular matrices. Active movement of the cell model is self-driven by its intrinsic tendency to intracellular tensioning, defined as tensioning-taxis in this study. Tensioning-taxis is quantified as driving potential to actuate cell adhesion, and the traction forces are solved by our proposed numerical method of local free energy adaptation. The modeling results account for the active adhesion of cells with dynamic protruding of leading edge and power-law development of mechanical properties. Furthermore, the morphogenesis of cells evolves actively depending on actin filaments alignments by a predicted mechanism of scaling and directing traction forces. The proposed model provides a quantitative way to investigate the active mechanisms of cell adhesion and holds the potential to guide studies of more complex adhesion and motion of cells coupled with multiple external cues.

A Finite Element Bendo-Tensegrity Model of Eukaryotic Cell

Mechanical interaction of cell with extracellular environment affects its function. The mechanisms by which mechanical stimuli are sensed and transduced into biochemical responses are still not well understood. Considering this, two finite element (FE) bendo-tensegrity models of a cell in different states are proposed with the aim to characterize cell deformation under different mechanical loading conditions: a suspended cell model elucidating the global response of cell in tensile test simulation and an adherent cell model explicating its local response in atomic force microscopy (AFM) indentation simulation. The force-elongation curve obtained from tensile test simulation lies within the range of experimentally obtained characteristics of smooth muscle cells (SMCs) and illustrates a nonlinear increase in reaction force with cell stretching. The force-indentation curves obtained from indentation simulations lie within the range of experimentally obtained curves of embryonic stem cells (ESCs) and exhibit the influence of indentation site on the overall reaction force of cell. Simulation results have demonstrated that actin filaments (AFs) and microtubules (MTs) play a crucial role in the cell stiffness during stretching, whereas actin cortex (AC) along with actin bundles (ABs) and MTs are essential for the cell rigidity during indentation. The proposed models quantify the mechanical contribution of individual cytoskeletal components to cell mechanics and the deformation of nucleus under different mechanical loading conditions. These results can aid in better understanding of structure-function relationships in living cells.

Heterogeneous structure and surface tension effects on mechanical response in pulmonary acinus: A finite element analysis

BACKGROUND

The pulmonary acinus is a dead-end microstructure that consists of ducts and alveoli. High-resolution micro-CT imaging has recently provided detailed anatomical information of a complete in vivo acinus, but relating its mechanical response with its detailed acinar structure remains challenging. This study aimed to investigate the mechanical response of acinar tissue in a whole acinus for static inflation using computational approaches.

METHODS

We performed finite element analysis of a whole acinus for static inflation. The acinar structure model was generated based on micro-CT images of an intact acinus. A continuum mechanics model of the lung parenchyma was used for acinar tissue material model, and surface tension effects were explicitly included. An anisotropic mechanical field analysis based on a stretch tensor was combined with a curvature-based local structure analysis.

FINDINGS

The airspace of the acinus exhibited nonspherical deformation as a result of the anisotropic deformation of acinar tissue. A strain hotspot occurred at the ridge-shaped region caused by a rod-like deformation of acinar tissue on the ridge. The local structure becomes bowl-shaped for inflation and, without surface tension effects, the surface of the bowl-shaped region primarily experiences isotropic deformation. Surface tension effects suppressed the increase in airspace volume and inner surface area, while facilitating anisotropic deformation on the alveolar surface.

INTERPRETATION

In the lungs, the heterogeneous acinar structure and surface tension induce anisotropic deformation at the acinar and alveolar scales. Further research is needed on structural variation of acini, inter-acini connectivity, or dynamic behavior to understand multiscale lung mechanics.

Modeling thermal inkjet and cell printing process using modified pseudopotential and thermal lattice Boltzmann methods

Pseudopotential lattice Boltzmann methods (LBMs) can simulate a phase transition in high-density ratio multiphase flow systems. If coupled with thermal LBMs through equation of state, they can be used to study instantaneous phase transition phenomena with a high-temperature gradient where only one set of formulations in an LBM system can handle liquid, vapor, phase transition, and heat transport. However, at lower temperatures an unrealistic spurious current at the interface introduces instability and limits its application in real flow system. In this study, we proposed new modifications to the LBM system to minimize a spurious current which enables us to study nucleation dynamic at room temperature. To demonstrate the capabilities of this approach, the thermal ejection process is modeled as one example of a complex flow system. In an inkjet printer, a thermal pulse instantly heats up the liquid in a microfluidic chamber and nucleates bubble vapor providing the pressure pulse necessary to eject droplets at high speed. Our modified method can present a more realistic model of the explosive vaporization process since it can also capture a high-temperature/density gradient at nucleation region. Thermal inkjet technology has been successfully applied for printing cells, but cells are susceptible to mechanical damage or death as they squeeze out of the nozzle head. To study cell deformation, a spring network model, representing cells, is connected to the LBM through the immersed boundary method. Looking into strain and stress distribution of a cell membrane at its most deformed state, it is found that a high stretching rate effectively increases the rupture tension. In other words, membrane deformation energy is released through creation of multiple smaller nanopores rather than big pores. Overall, concurrently simulating multiphase flow, phase transition, heat transfer, and cell deformation in one unified LB platform, we are able to provide a better insight into the bubble dynamic and cell mechanical damage during the printing process.

Mechanical Regulation of Three-Dimensional Epithelial Fold Pattern Formation in the Mouse Oviduct

Epithelia exhibit various three-dimensional morphologies linked to organ function in animals. However, the mechanisms of three-dimensional morphogenesis remain elusive. The luminal epithelium of the mouse oviduct forms well-aligned straight folds along the longitudinal direction of the tubes. Disruption of the Celsr1 gene, a planar cell polarity-related gene, causes ectopically branched folds. Here, we evaluated the mechanical contributions of the epithelium to the fold pattern formation. In the mutant oviduct, the epithelium was more intricate along the longitudinal direction than in the wild-type, suggesting a higher ratio of the longitudinal length of the epithelial layer to that of the surrounding smooth muscle (SM) layer (L-Epi/SM ratio). Our mathematical modeling and computational simulations suggested that the L-Epi/SM ratio could explain the differences in fold branching between the two genotypes. Longitudinal epithelial tensions were increased in well-aligned folds compared with those in disorganized folds both in the simulations and in experimental estimations. Artificially increasing the epithelial tensions suppressed the branching in simulations, suggesting that the epithelial tensions can regulate fold patterning. The epithelial tensions could be explained by the combination of line tensions along the epithelial cell-cell boundaries with the polarized cell arrays observed in vivo. These results suggest that the fold pattern is associated with the polarized cell array through the longitudinal epithelial tension. Further simulations indicated that the L-Epi/SM ratio could contribute to fold pattern diversity, suggesting that the L-Epi/SM ratio is a critical parameter in the fold patterning in tubular organs.

Characterization of biomechanical properties of cells through dielectrophoresis-based cell stretching and actin cytoskeleton modeling

Background

Cytoskeleton is a highly dynamic network that helps to maintain the rigidity of a cell, and the mechanical properties of a cell are closely related to many cellular functions. This paper presents a new method to probe and characterize cell mechanical properties through dielectrophoresis (DEP)-based cell stretching manipulation and actin cytoskeleton modeling.

Methods

Leukemia NB4 cells were used as cell line, and changes in their biological properties were examined after chemotherapy treatment with doxorubicin (DOX). DEP-integrated microfluidic chip was utilized as a low-cost and efficient tool to study the deformability of cells. DEP forces used in cell stretching were first evaluated through computer simulation, and the results were compared with modeling equations and with the results of optical stretching (OT) experiments. Structural parameters were then extracted by fitting the experimental data into the actin cytoskeleton model, and the underlying mechanical properties of the cells were subsequently characterized.

Results

The DEP forces generated under different voltage inputs were calculated and the results from different approaches demonstrate good approximations to the force estimation. Both DEP and OT stretching experiments confirmed that DOX-treated NB4 cells were stiffer than the untreated cells. The structural parameters extracted from the model and the confocal images indicated significant change in actin network after DOX treatment.

Conclusion

The proposed DEP method combined with actin cytoskeleton modeling is a simple engineering tool to characterize the mechanical properties of cells.

Stem cell mechanical behaviour modelling: substrate's curvature influence during adhesion

Recent experiments hint that adherent cells are sensitive to their substrate curvature. It is already well known that cells behaviour can be regulated by the mechanical properties of their environment. However, no mechanisms have been established regarding the influence of cell-scale curvature of the substrate. Using a numerical cell model, based on tensegrity structures theory and the non-smooth contact dynamics method, we propose to investigate the mechanical state of adherent cells on concave and convex hemispheres. Our mechanical cell model features a geometrical description of intracellular components, including the cell membrane, the focal adhesions, the cytoskeleton filament networks, the stress fibres, the microtubules, the nucleus membrane and the nucleoskeleton. The cell model has enabled us to analyse the evolution of the mechanical behaviour of intracellular components with varying curvature radii and with the removal of part of these components. We have observed the influence of the convexity of the substrate on the cell shape, the cytoskeletal force networks as well as on the nucleus strains. The more convex the substrate, the more tensed the stress fibres and the cell membrane, the more compressed the cytosol and the microtubules, leading to a stiffer cell. Furthermore, the more concave the substrate, the more stable and rounder the nucleus. These findings achieved using a verified virtual testing methodology, in particular regarding the nucleus stability, might be of significant importance with respect to the division and differentiation of mesenchymal stem cells. These results can also bring some hindsights on cell migration on curved substrates.

Non-uniform force allocation for area preservation in spring network models

In modeling of elastic objects in a flow such as red blood cells, white blood cells, or tumor cells, several elastic moduli are involved. One of them is the area conservation modulus. In this paper, we focus on spring network models, and we introduce a new way of modeling the area preservation modulus. We take into account the current shape of the individual triangles and find the proportional allocation of area conservation forces, which would for individual triangles preserve their shapes. The analysis shows that this approach tends to regularize the triangulation. We demonstrate this effect on individual triangles as well as on the complete triangulations. Copyright © 2015 John Wiley & Sons, Ltd.

Modeling the mechanics of cells in the cell-spreading process driven by traction forces

Mechanical properties of cells and their mechanical interaction with the extracellular environments are main factors influencing cellular function, thus indicating the progression of cells in different disease states. By considering the mechanical interactions between cell adhesion molecules and the extracellular environment, we developed a cell mechanical model that can characterize the mechanical changes in cells during cell spreading. A cell model was established that consisted of various main subcellular components, including cortical cytoskeleton, nuclear envelope, actin filaments, intermediate filaments, and microtubules. We demonstrated the structural changes in subcellular components and the changes in spreading areas during cell spreading driven by traction forces. The simulation of nanoindentation tests was conducted by integrating the indenting force to the cell model. The force-indentation curve of the cells at different spreading states was simulated, and the results showed that cell stiffness increased with increasing traction forces, which were consistent with the experimental results. The proposed cell mechanical model provides a strategy to investigate the mechanical interactions of cells with the extracellular environments through the adhesion molecules and to reveal the cell mechanical properties at the subcellular level as cells shift from the suspended state to the adherent state.

A phenomenological particle-based platelet model for simulating filopodia formation during early activation

We developed a phenomenological three-dimensional platelet model to characterize the filopodia formation observed during early stage platelet activation. Departing from continuum mechanics based approaches, this coarse-grained molecular dynamics (CGMD) particle-based model can deform to emulate the complex shape change and filopodia formation that platelets undergo during activation. The platelet peripheral zone is modeled with a two-layer homogeneous elastic structure represented by spring-connected particles. The structural zone is represented by a cytoskeletal assembly comprising of a filamentous core and filament bundles supporting the platelet's discoid shape, also modeled by spring-connected particles. The interior organelle zone is modeled by homogeneous cytoplasm particles that facilitate the platelet deformation. Nonbonded interactions among the discrete particles of the membrane, the cytoskeletal assembly, and the cytoplasm are described using the Lennard-Jones potential with empirical constants. By exploring the parameter space of this CGMD model, we have successfully simulated the dynamics of varied filopodia formations. Comparative analyses of length and thickness of filopodia show that our numerical simulations are in agreement with experimental measurements of flow-induced activated platelets. Copyright © 2015 John Wiley & Sons, Ltd.

A multi-structural single cell model of force-induced interactions of cytoskeletal components

Several computational models based on experimental techniques and theories have been proposed to describe cytoskeleton (CSK) mechanics. Tensegrity is a prominent model for force generation, but it cannot predict mechanics of individual CSK components, nor explain the discrepancies from the different single cell stimulating techniques studies combined with cytoskeleton-disruptors. A new numerical concept that defines a multi-structural 3D finite element (FE) model of a single-adherent cell is proposed to investigate the biophysical and biochemical differences of the mechanical role of each cytoskeleton component under loading. The model includes prestressed actin bundles and microtubule within cytoplasm and nucleus surrounded by the actin cortex. We performed numerical simulations of atomic force microscopy (AFM) experiments by subjecting the cell model to compressive loads. The numerical role of the CSK components was corroborated with AFM force measurements on U2OS-osteosarcoma cells and NIH-3T3 fibroblasts exposed to different cytoskeleton-disrupting drugs. Computational simulation showed that actin cortex and microtubules are the major components targeted in resisting compression. This is a new numerical tool that explains the specific role of the cortex and overcomes the difficulty of isolating this component from other networks in vitro. This illustrates that a combination of cytoskeletal structures with their own properties is necessary for a complete description of cellular mechanics.

Modeling cell proliferation for simulating three-dimensional tissue morphogenesis based on a reversible network reconnection framework

Tissue morphogenesis in multicellular organisms is accompanied by proliferative cell behaviors: cell division (increase in cell number after each cell cycle) and cell growth (increase in cell volume during each cell cycle). These proliferative cell behaviors can be regulated by multicellular dynamics to achieve proper tissue sizes and shapes in three-dimensional (3D) space. To analyze multicellular dynamics, a reversible network reconnection (RNR) model has been suggested, in which each cell shape is expressed by a single polyhedron. In this study, to apply the RNR model to simulate tissue morphogenesis involving proliferative cell behaviors, we model cell proliferation based on a RNR model framework. In this model, cell division was expressed by dividing a polyhedron at a planar surface for which cell division behaviors were characterized by three quantities: timing, intracellular position, and normal direction of the dividing plane. In addition, cell growth was expressed by volume growth as a function of individual cell times within their respective cell cycles. Numerical simulations using the proposed model showed that tissues grew during successive cell divisions with several cell cycle times. During these processes, the cell number in tissues increased while maintaining individual cell size and shape. Furthermore, tissue morphology dramatically changed based on different regulations of cell division directions. Thus, the proposed model successfully provided a basis for expressing proliferative cell behaviors during morphogenesis based on a RNR model framework.

Influence of semiflexible structural features of actin cytoskeleton on cell stiffness based on actin microstructural modeling

A new actin cytoskeleton microstructural model based on the semiflexible polymer nature of the actin filament is proposed. The relationship between the stretching force and the mechanical properties of cells was examined. Experiments on deforming hematopoietic cells with distinct primitiveness from normal and leukemic sources were conducted via optical tweezer manipulation at single-cell level. The modeling results were demonstrated to be in good agreement with the experimental data. We characterized how the structural properties of the actin cytoskeleton, such as prestress, density of cross-links, and actin concentration, affect the mechanical behavior of cells based on the proposed model. Increasing prestress, actin concentration, and density of cross-links reduced cell deformation, and the cell also exhibited strain stiffening behavior with an increase in the stretching force. Compared with existing models, the proposed model exhibits a distinct feature in probing the influence of semiflexible polymer nature of the actin filament on cell mechanical behavior.

Contribution of actin filaments to the global compressive properties of fibroblasts

Actin filaments are often regarded as tension-bearing components. Here, we examined the effects of actin filaments on global compressive properties of cells experimentally and numerically. Fibroblasts were harvested from the patellar tendon of a mature Japanese white rabbit and treated with cytochalasin D to depolymerize the actin filaments. Intact cells and cells with disrupted actin filaments were subjected to the compressive tests. Each floating cell was held between the cantilever and compressive plates and compressed by moving the compressive plate with a linear actuator to obtain a load-deformation curve under quasi-static conditions. The experimental results demonstrated that the initial stiffness of a cell with disrupted actin filaments decreased by 51%. After the experiments, we simulated the compressive test of cells with/without bundles of actin filaments. A bundle of actin filaments was modeled as a tension-bearing component that generates a force based on Hooke's law only when it was elongated. By contrast, if it was shortened, it was assumed to exert no force. The computational results revealed that the alignment of bundles of actin filaments significantly affected the cell stiffness. In addition, the passive reorientation of bundles of actin filaments perpendicular to the compression induced an increase in the resistance to the vertical elongation of a cell and thereby increased the cell stiffness. These results clearly indicated that bundles of actin filaments contribute to the compressive properties of a cell, even if they are tension-bearing components.

A multiphysical model of cell migration integrating reaction-diffusion, membrane and cytoskeleton

Cellular motility is a complicated phenomenon that involves multiphysics, including the cytoskeleton, the plasma membrane and intracellular signal transduction. In this study, a hybrid computational model was developed for the simulation of whole-cell migration behaviors. The model integrates sub-models of reaction-diffusion, actin filaments (F-actin) and the plasma membrane. Reaction-diffusion was calculated as if enclosed by a moving membrane. Individual F-actins were reorganized on the basis of stochastic kinetic events, such as polymerization, capping, branching and severing. Membrane dynamics were modeled using an optimization of energy function that depends on cell volume, surface area, smoothness and the elasticity of F-actin against the membrane. Simulations of this model demonstrated self-organization of F-actin networks, as in lamellipodia, and chemotactic migration. Furthermore, this method was extended to address external obstacles to simulate the dynamic cellular morphological changes seen during invasive migration.