Physical Explanation of Coupled Cell-Cell Rotational Behavior and Interfacial Morphology: A Particle Dynamics Model

Previous studies have reported persistent rotational behavior between adherent cell-cell pairs cultured on micropatterned substrates, and this rotation is often accompanied by a sigmoidal deflection of the cell-cell interface. Interestingly, the cell-cell rotation runs in the opposite reference frame from what could be expected of single cell locomotion. Specifically, the rotation of the cell pair consists of each individual cell protruding from the inwardly regressive arm of the cell-cell interface, and retracting from the other outwardly protrusive arm. To this author’s knowledge, the cause of this elusive behavior has not yet been clarified. Here, we propose a physical model based on particle dynamics, accounting for actomyosin forcing, viscous dissipation, and cortical tension. The results show that a correlation in actomyosin force vectors leads to both persistent rotational behavior and interfacial deflection in a simulated cell cluster. Significantly, the model, without any artificial cues, spontaneously and consistently reproduces the same rotational reference frame as experimentally observed. Further analyses show that the interfacial deflection depends predominantly on cortical tension, whereas the cluster rotation depends predominantly on actomyosin forcing. Together, these results corroborate the hypothesis that both rotational and morphological phenomena are, in fact, physically coupled by an intracellular torque of a common origin.     

Polarized interfacial tension induces collective migration of cells,as a cluster,in a 3D tissue

In embryogenesis and cancer invasion, cells collectively migrate as a cluster in 3D tissues. Many studies have elucidated mechanisms of either individual or collective cell migration on 2D substrates; however, it remains unclear how cells collectively migrate as a cluster through 3D tissues. To address this issue, we considered the interfacial tension at cell-cell boundaries expressing cortical actomyosin contractions and cell-cell adhesive interactions. The strength of this tension is polarized; i.e., spatially biased within each cell according to a chemoattractant gradient. Using a 3D vertex model, we performed numerical simulations of multicellular dynamics in 3D space. The simulations revealed that the polarized interfacial tension enables cells to migrate collectively as a cluster through a 3D tissue. In this mechanism, interfacial tension induces unidirectional flow of each cell surface from the front to the rear along the cluster surface. Importantly, this mechanism does not necessarily require convection of cells, i.e., cell rearrangement, within the cluster. Moreover, several migratory modes were induced, depending on the strengths of polarity, adhesion, and noise; i.e., cells migrate either as single cells, as a cluster, or aligned like beads on a string, as occurs in embryogenesis and cancer invasion. These results indicate that the simple expansion and contraction of cell-cell boundaries enables cells to move directionally forward and to produce the variety of collective migratory movements observed in living systems.     

EPH/EPHRIN regulates cellular organization by actomyosin contractility effects on cell contacts

EPH/EPHRIN signaling is essential to many aspects of tissue self-organization and morphogenesis, but little is known about how EPH/EPHRIN signaling regulates cell mechanics during these processes. Here, we use a series of approaches to examine how EPH/EPHRIN signaling drives cellular self-organization. Contact angle measurements reveal that EPH/EPHRIN signaling decreases the stability of heterotypic cell:cell contacts through increased cortical actomyosin contractility. We find that EPH/EPHRIN-driven cell segregation depends on actomyosin contractility but occurs independently of directed cell migration and without changes in cell adhesion. Atomic force microscopy and live cell imaging of myosin localization support that EPH/EPHRIN signaling results in increased cortical tension. Interestingly, actomyosin contractility also nonautonomously drives increased EPHB2:EPHB2 homotypic contacts. Finally, we demonstrate that changes in tissue organization are driven by minimization of heterotypic contacts through actomyosin contractility in cell aggregates and by mouse genetics experiments. These data elucidate the biomechanical mechanisms driving EPH/EPHRIN-based cell segregation wherein differences in interfacial tension, regulated by actomyosin contractility, govern cellular self-organization.     

Cortical tension initiates the positive feedback loop between cadherin and F-actin

Adherens junctions physically link two cells at their contact interface via extracellular binding between cadherin molecules and intracellular interactions between cadherins and the actin cytoskeleton. Cadherin and actomyosin cytoskeletal dynamics are regulated reciprocally by mechanical and chemical signals, which subsequently determine the strength of cell-cell adhesions and the emergent organization and stiffness of the tissues they form. However, an understanding of the integrated system is lacking. We present a new mechanistic computational model of intercellular junction maturation in a cell doublet to investigate the mechanochemical cross talk that regulates adherens junction formation and homeostasis. The model couples a two-dimensional lattice-based simulation of cadherin dynamics with a reaction-diffusion representation of the reorganising actomyosin network through its regulation by Rho signalling at the intracellular junction. We demonstrate that local immobilization of cadherin induces cluster formation in a cis-less-dependent manner. We then recapitulate the process of cell-cell contact formation. Our model suggests that cortical tension applied on the contact rim can explain the ring distribution of cadherin and actin filaments (F-actin) on the cell-cell contact of the cell doublet. Furthermore, we propose and test the hypothesis that cadherin and F-actin interact like a positive feedback loop, which is necessary for formation of the ring structure. Different patterns of cadherin distribution were observed as an emergent property of disturbances of this positive feedback loop. We discuss these findings in light of available experimental observations on underlying mechanisms related to cadherin/F-actin binding and the mechanical environment.     

Collective cell migration requires suppression of actomyosin at cell-cell contacts mediated by DDR1 and the cell polarity regulators Par3 and Par6

Collective cell migration occurs in a range of contexts: cancer cells frequently invade in cohorts while retaining cell-cell junctions. Here we show that collective invasion by cancer cells depends on decreasing actomyosin contractility at sites of cell-cell contact. When actomyosin is not downregulated at cell-cell contacts, migrating cells lose cohesion. We provide a molecular mechanism for this downregulation. Depletion of discoidin domain receptor 1 (DDR1) blocks collective cancer-cell invasion in a range of two-dimensional, three-dimensional and 'organotypic' models. DDR1 coordinates the Par3/Par6 cell-polarity complex through its carboxy terminus, binding PDZ domains in Par3 and Par6. The DDR1-Par3/Par6 complex controls the localization of RhoE to cell-cell contacts, where it antagonizes ROCK-driven actomyosin contractility. Depletion of DDR1, Par3, Par6 or RhoE leads to increased actomyosin contactility at cell-cell contacts, a loss of cell-cell cohesion and defective collective cell invasion.     

Dynamic modes of the cortical actomyosin gel during cell locomotion and division

Tight regulation of the contractility of the actomyosin cortex is essential for proper cell locomotion and division. Enhanced contractility leads, for example, to aberrations in the positioning of the mitotic spindle or to anomalous migration modes that allow tumor cells to escape anti-dissemination treatments. Spherical membrane protrusions called blebs occasionally appear during cell migration, cell division or apoptosis. We have shown that the cortex ruptures at sites where actomyosin cortical contractility is increased, leading to the formation of blebs. Here, we propose that bleb formation, which releases cortical tension, can be used as a reporter of cortical contractility. We go on to analyze the implications of spontaneous cortical contractile behaviors on cell locomotion and division and we particularly emphasize that variations in actomyosin contractility can account for a variety of migration modes.     

EPHecting cell contact by increasing cortical tension

EPH/EPHRIN signaling is crucial to the segregation of cell populations during the morphogenesis of many tissues. In this issue, Kindberg et al. (2021. J. Cell Biol. https://doi.org/10.1083/jcb.202005216) show that EPH activation can drive both heterotypic cell repulsion and homotypic aggregation by triggering increased cortical tension.

Heightened awareness of the ability of cells to sense and generate mechanical force has enhanced our appreciation of the sophisticated ways that cells self-organize to create architecturally patterned tissues (1). It is now clear that well-known patterns of cell fate gene expression are coordinated with biophysical patterns to segregate and organize cell populations. Central to understanding the design principles underlying tissue self-organization are studies of EPH receptors and their membrane-associated EPHRIN ligands, which are important drivers of morphogenesis across many tissues (2, 3). Both ligand and receptor are membrane bound, and signaling, which can be bidirectional, requires cell–cell contact, enabling the study of proximal influences of EPH/EPHRIN signaling on individual cells.The major consequence of EPH/EPHRIN signaling is to impair cell contact between ligand and receptor-expressing cells, thereby contributing to cell segregation and boundary formation in developing tissues (2, 3). Critical roles for EPH/EPHRIN signaling in neuronal pathfinding have uncovered a key role in repulsive migration, but this mechanism may not explain how EPH/EPHRIN signaling drives cell segregation in dense developing tissues where cells continuously contact other cells (4). Differential adhesion is also thought to contribute to EPH/EPHRIN-driven cell segregation, for example via EPH-stimulated E-cadherin cleavage (5). However, forces from adhesion tension are fundamentally integrated with those imparted by cortical tension, which govern many aspects of cell behavior and tissue morphogenesis (6). Indeed, the differential interfacial tension hypothesis holds that increased cortical tension can reduce the ability of cells to make stable cell contacts (7). Actomyosin accumulation occurs at EPH/EPHRIN interfaces, suggesting that interfacial tension driven by increased cortical actomyosin contractility may be an important driver of EPH/EPHRIN-mediated cell segregation (2, 3). In this issue, Kindberg et al. set out to test this directly by systematically stripping away the complexity of other inputs (8).First, the authors eliminated cell-matrix adhesion and therefore the contribution of cell migration by examining cell doublets cultured in engineered agarose-coated wells. In contrast to homotypic pairs of EPHB2 or EPHRIN-B1–expressing cells that formed an extended contact face with large contact angles, heterotypic EPHB2- and EPHRIN-B1–expressing cell pairs exhibited a signaling-dependent reduction in contact face and angle of contact, consistent with an increase in interfacial tension. Importantly, when EPHB2- and EPHRIN-B1–expressing cells were plated in 3D aggregates in the absence of extracellular matrix attachment, they segregated completely, suggesting that increased interfacial tension may be the key driver of cell segregation.Given the established interdependence of cortical tension and cadherin-based cell contact, Kindberg et al. investigated if the EPHB2/EPHRIN-B1–driven increase in interfacial tension required cadherin-mediated adhesion (6, 7). Surprisingly, the authors found that elimination of cadherin function in low calcium medium did not affect cell segregation, suggesting that EPH/EPHRIN may drive a more general increase in cortical tension. To test this, they pharmacologically interfered with actomyosin contractility, which restored large cell contact areas and angles to heterotypic EPHB2- and EPHRIN-B1–expressing cell pairs and reversibly impaired their ability to segregate in 3D aggregates. Direct measurement of cortical stiffness by atomic force microscopy confirmed an increase in cellular stiffness in both EPHB2- and EPHRIN-B1–expressing cells at early times after mixing and before the onset of segregation, consistent with a general increase in cortical tension.The authors noticed that EPHB2-expressing cells themselves tended to aggregate at a particularly high density in EPHB2/EPHRIN-B1 segregation assays. Importantly, when mixed with both wild-type and EPHRIN-B1–expressing cells, EPHB2-expressing cells segregated into clusters that excluded both cell types. Examination of doublets revealed close contact between EPHB2 homotypic cell pairs that was not influenced by calcium depletion, but was eliminated by inhibition of actomyosin contractility. These data strongly suggest that, in addition to increasing interfacial tension at heterotypic contacts, increased actomyosin contractility in EPHB2 cells elevates cortical tension at the cell–medium interface. This in turn favors the establishment of homotypic EPHB2 cell interactions to minimize tension with the medium. The authors then explored the physiological relevance of these findings and showed that EPHB2- and EPHRIN-B1–expressing cells segregate into more complex structures in free-form hanging drop culture in an actomyosin-dependent manner. Likewise, they demonstrated through elegant genetic experiments that myosin II is required for EPH/EPHRIN-driven cell segregation in a mouse model of X-linked craniofrontonasal syndrome.It seems clear that repulsive migration, differential adhesion, and increased interfacial tension can all contribute to EPH/EPHRIN-driven segregation, depending on the context. While cortical tension may play a more minor role in other contexts (9), the study by Kindberg et al. clearly shows that increased cortical tension can govern boundary formation, highlighting cortical tension modulation as a key driver of tissue self-organization. Exciting follow-up studies will identify the mechanisms by which EPH-driven changes in cortical tension are achieved and determine whether the cortex is organized differently at heterotypic and cell–medium interfaces. Possibilities include direct modulation of myosin II activity, which is thought to dominate cortical tension, alteration of the composition or configuration of the cortical actin network, plasma membrane-to-cortex attachment, and/or the organization of the plasma membrane itself (10). Clues may come from live imaging, which revealed strikingly dynamic cell–cell contacts among EPHB2/EPHRIN-B1 cell doublets, which could reflect pulsed cortical contractions that are now thought to be an inherent property of the cortical cytoskeleton that is stabilized in a regulated manner (10).Beyond aspects of morphogenesis, an appreciation that EPH-triggered changes in cortical tension can promote both heterotypic and homotypic cellular interactions could provide important insight into the heavily studied but poorly understood role of EPH receptors in cancer development and progression, particularly given the growing recognition of spatially important aspects of tumor heterogeneity. More broadly, these studies should prompt us to consider whether altering cortical tension is an important component of the signaling output of other membrane receptors. Many receptor tyrosine kinases are known to elicit changes in cell contact, surface topology, and cytoskeletal organization, but most studies focus on downstream signaling, leaving a largely unexplored chasm between receptor activation and cellular and tissue architecture.     

Collective Signal Processing in Cluster Chemotaxis: Roles of Adaptation,Amplification, and Co-attraction in Collective Guidance

Single eukaryotic cells commonly sense and follow chemical gradients, performing chemotaxis. Recent experiments and theories, however, show that even when single cells do not chemotax, clusters of cells may, if their interactions are regulated by the chemoattractant. We study this general mechanism of “collective guidance” computationally with models that integrate stochastic dynamics for individual cells with biochemical reactions within the cells, and diffusion of chemical signals between the cells. We show that if clusters of cells use the well-known local excitation, global inhibition (LEGI) mechanism to sense chemoattractant gradients, the speed of the cell cluster becomes non-monotonic in the cluster’s size—clusters either larger or smaller than an optimal size will have lower speed. We argue that the cell cluster speed is a crucial readout of how the cluster processes chemotactic signals; both amplification and adaptation will alter the behavior of cluster speed as a function of size. We also show that, contrary to the assumptions of earlier theories, collective guidance does not require persistent cell-cell contacts and strong short range adhesion. If cell-cell adhesion is absent, and the cluster cohesion is instead provided by a co-attraction mechanism, e.g. chemotaxis toward a secreted molecule, collective guidance may still function. However, new behaviors, such as cluster rotation, may also appear in this case. Co-attraction and adaptation allow for collective guidance that is robust to varying chemoattractant concentrations while not requiring strong cell-cell adhesion.     

Contribution of interfacial tension changes during cellular interaction to the energy balance

The energetics of cell-cell and cell-substrate interactions has been analyzed in terms of the lyophobic colloid stability theory adapted to biological conditions. Some important differences that exist between lyophobic particles and living cells are recognized and taken into account. The protein-aceous coat exterior to the lipid cell membrane (glycocalyx) is treated as a very thick Stern layer which has a constant electric capacitance. The cell itself is viewed as a fluid droplet due to the semi-fluid state of the cell membrane, and its outer boundary is assumed to have a constant electric charge density. When particles with constant surface charge density interact, their surface potential increases. Then the potential at the lipid-protein interface will also increase, hence the interfacial tension should decrease. The magnitude of the interfacial tension change at the lipid-protein interface occurring during the interaction of cells has been calculated for various thicknesses of the glycocalyx. This term, obtained for cells with a relatively thin proteinaceous coat, was found to dominate the energy balance, making the total energy of interaction negative.     

Septins and a formin have distinct functions in anaphase chiral cortical rotation in the Caenorhabditis elegans zygote

Many cells and tissues exhibit chirality that stems from the chirality of proteins and polymers. In the Caenorhabditis elegans zygote, actomyosin contractility drives chiral rotation of the entire cortex circumferentially around the division plane during anaphase. How contractility is translated to cell-scale chirality, and what dictates handedness, are unknown. Septins are candidate contributors to cell-scale chirality because they anchor and cross-link the actomyosin cytoskeleton. We report that septins are required for anaphase cortical rotation. In contrast, the formin CYK-1, which we found to be enriched in the posterior in early anaphase, is not required for cortical rotation but contributes to its chirality. Simultaneous loss of septin and CYK-1 function led to abnormal and often reversed cortical rotation. Our results suggest that anaphase contractility leads to chiral rotation by releasing torsional stress generated during formin-based polymerization, which is polarized along the cell anterior–posterior axis and which accumulates due to actomyosin network connectivity. Our findings shed light on the molecular and physical bases for cellular chirality in the C. elegans zygote. We also identify conditions in which chiral rotation fails but animals are developmentally viable, opening avenues for future work on the relationship between early embryonic cellular chirality and animal body plan.     

IQGAP-related Rng2p organizes cortical nodes and ensures position of cell division in fission yeast

Correct positioning of the cell division machinery is crucial for genomic stability and cell fate determination. The fission yeast Schizosaccharomyces pombe, like animal cells, divides using an actomyosin ring and is an attractive model to study eukaryotic cytokinesis. In S. pombe, positioning of the actomyosin ring depends on the anillin-related protein Mid1p. Mid1p arrives first at the medial cortex and recruits actomyosin ring components to node-like structures, although how this is achieved is unknown. Here we show that the IQGAP-related protein Rng2p, an essential component of the actomyosin ring, is a key element downstream of Mid1p. Rng2p physically interacts with Mid1p and is required for the organization of other actomyosin ring components into cortical nodes. Failure of localization of Rng2p to the nodes prevents medial retention of Mid1p and leads to actomyosin ring assembly in a node-independent manner at nonmedial locations. We conclude that Mid1p recruits Rng2p to cortical nodes at the division site and that Rng2p, in turn, recruits other components of the actomyosin ring to cortical nodes, thereby ensuring correct placement of the division site.     

Integrin-dependent actomyosin contraction regulates epithelial cell scattering

The scattering of Madin-Darby canine kidney cells in vitro mimics key aspects of epithelial-mesenchymal transitions during development, carcinoma cell invasion, and metastasis. Scattering is induced by hepatocyte growth factor (HGF) and is thought to involve disruption of cadherin-dependent cell-cell junctions. Scattering is enhanced on collagen and fibronectin, as compared with laminin1, suggesting possible cross talk between integrins and cell-cell junctions. We show that HGF does not trigger any detectable decrease in E-cadherin function, but increases integrin-mediated adhesion. Time-lapse imaging suggests that tension on cell-cell junctions may disrupt cell-cell adhesion. Varying the density and type of extracellular matrix proteins shows that scattering correlates with stronger integrin adhesion and increased phosphorylation of the myosin regulatory light chain. To directly test the role of integrin-dependent traction forces, substrate compliance was varied. Rigid substrates that produce high traction forces promoted scattering, in comparison to more compliant substrates. We conclude that integrin-dependent actomyosin traction force mediates the disruption of cell-cell adhesion during epithelial cell scattering.     

Cell chirality regulates coherent angular motion on small circular substrates

Collective cell migration occurs in a wide range of physiological and pathological processes, such as wound healing and tumor metastasis. Experiments showed that many types of cells confined in circular islands can perform coherent angular rotation, yet the underlying mechanisms remain unclear. Here we propose a biomechanical model, including the membrane, microtubules, and nucleus, to study the spatiotemporal evolutions of small cell clusters in confined space. We show that cells can spontaneously transfer from “radial pattern” to “chiral pattern” due to fluctuations. For a pair of cells with identical chiral orientation, the cluster rotates in the opposite direction of the chiral orientation, and the fluctuations can reverse the cluster’s rotational direction. Interestingly, during the persistent rotation, each cell rotates around its own centroid while it is revolving around the island center and shows a constant side to the island center, as tidal locking in astronomy. Furthermore, for a few more cells, coherent angular rotation also appears, and the emergence of a central cell can accelerate the cluster rotation. These findings shed light on collective cell migration in life processes and help to understand the spatiotemporal dynamics of active matter.     

Microtubules mediate changes in membrane cortical elasticity during contractile activation

The mechanical properties of living cells are highly regulated by remodeling dynamics of the cytoarchitecture, and are linked to a wide variety of physiological and pathological processes. Microtubules (MT) and actomyosin contractility are both involved in regulating focal adhesion (FA) size and cortical elasticity in living cells. Although several studies have examined the effects of MT depolymerization or actomyosin activation on biological processes, very few have investigated the influence of both on the mechanical properties, FA assembly, and spreading of fibroblast cells. Here, we examine how activation of both processes modulates cortical elasticity as a function of time. Enhancement of contractility (calyculin A treatment) or the depolymerization of MTs (nocodazole treatment) individually caused a time-dependent increase in FA size, decrease in cell height and an increase in cortical elasticity. Surprisingly, sequentially stimulating both processes led to a decrease in cortical elasticity, loss of intact FAs and a concomitant increase in cell height. Our results demonstrate that loss of MTs disables the ability of fibroblast cells to maintain increased contractility and cortical elasticity upon activation of myosin-II. We speculate that in the absence of an intact MT network, a large amount of contractile tension is transmitted directly to FA sites resulting in their disassembly. This implies that tension-mediated FA growth may have an upper bound, beyond which disassembly takes place. The interplay between cytoskeletal remodeling and actomyosin contractility modulates FA size and cell height, leading to dynamic time-dependent changes in the cortical elasticity of fibroblast cells.     

Molecular mechanisms of cell segregation and boundary formation in development and tumorigenesis

The establishment and maintenance of precisely organized tissues requires the formation of sharp borders between distinct cell populations. The maintenance of segregated cell populations is also required for tissue homeostasis in the adult, and deficiencies in segregation underlie the metastatic spreading of tumor cells. Three classes of mechanisms that underlie cell segregation and border formation have been uncovered. The first involves differences in cadherin-mediated cell-cell adhesion that establishes interfacial tension at the border between distinct cell populations. A second mechanism involves the induction of actomyosin-mediated contraction by intercellular signaling, such that cortical tension is generated at the border. Third, activation of Eph receptors and ephrins can lead to both decreased adhesion by triggering cleavage of E-cadherin, and to repulsion of cells by regulation of the actin cytoskeleton, thus preventing intermingling between cell populations. These mechanisms play crucial roles at distinct boundaries during development, and alterations in cadherin or Eph/ephrin expression have been implicated in tumor metastasis.     

CaATP as a substrate to investigate the myosin lever arm hypothesis of force generation

In an effort to test the lever arm model of force generation, the effects of replacing magnesium with calcium as the ATP-chelated divalent cation were determined for several myosin and actomyosin reactions. The isometric force produced by glycerinated muscle fibers when CaATP is the substrate is 20% of the value obtained with MgATP. For myosin subfragment 1 (S1), the degree of lever arm rotation, determined using transient electric birefringence to measure rates of rotational Brownian motion in solution, is not significantly changed when calcium replaces magnesium in an S1-ADP-vanadate complex. Actin activates S1 CaATPase activity, although less than it does MgATPase activity. The increase in actin affinity when S1. CaADP. P(i) is converted to S1. CaADP is somewhat greater than it is for the magnesium case. The ionic strength dependence of actin binding indicates that the change in apparent electrostatic charge at the acto-S1 interface for the S1. CaADP. P(i) to S1. CaADP step is similar to the change when magnesium is bound. In general, CaATP is an inferior substrate compared to MgATP, but all the data are consistent with force production by a lever arm mechanism for both substrates. Possible reasons for the reduced magnitude of force when CaATP is the substrate are discussed.     

Dynamic myosin activation promotes collective morphology and migration by locally balancing oppositional forces from surrounding tissue

Migrating cells need to overcome physical constraints from the local microenvironment to navigate their way through tissues. Cells that move collectively have the additional challenge of negotiating complex environments in vivo while maintaining cohesion of the group as a whole. The mechanisms by which collectives maintain a migratory morphology while resisting physical constraints from the surrounding tissue are poorly understood. Drosophila border cells represent a genetic model of collective migration within a cell-dense tissue. Border cells move as a cohesive group of 6−10 cells, traversing a network of large germ line–derived nurse cells within the ovary. Here we show that the border cell cluster is compact and round throughout their entire migration, a shape that is maintained despite the mechanical pressure imposed by the surrounding nurse cells. Nonmuscle myosin II (Myo-II) activity at the cluster periphery becomes elevated in response to increased constriction by nurse cells. Furthermore, the distinctive border cell collective morphology requires highly dynamic and localized enrichment of Myo-II. Thus, activated Myo-II promotes cortical tension at the outer edge of the migrating border cell cluster to resist compressive forces from nurse cells. We propose that dynamic actomyosin tension at the periphery of collectives facilitates their movement through restrictive tissues.     

Simulation of the effects of microtubules in the cortical rotation of amphibian embryos in normal and zero gravity

This paper reports the results of computer modeling of microtubules that end up in the cortical region of a one-cell amphibian embryo, prior to the first cell division. Microtubules are modeled as initially randomly oriented semi-flexible rods, represented by several lines of point-masses interacting with one another like masses on springs with longitudinal and transverse stiffness. They are also considered to be space-filling rods floating in a viscous fluid (cytoplasm) experiencing drag forces and buoyancy from the fluid under a variable gravity field to test gravitational effects. Their randomly distributed interactions with the surrounding spherical container (the cell membrane) have a statistical nonzero average that creates a torque causing a rotational displacement between the cytoplasm and the rigid cortex. The simulation has been done for zero and normal gravity and it validates the observation that cortical rotation occurs in microgravity as well as on Earth. The speed of rotation depends on gravity, but is still substantial in microgravity.