CompuCell3D Simulations Reproduce Mesenchymal Cell Migration on Flat Substrates.

Mesenchymal cell crawling is a critical process in normal development, in tissue function, and in many diseases. Quantitatively predictive numerical simulations of cell crawling thus have multiple scientific, medical, and technological applications. However, we still lack a low-computational-cost approach to simulate mesenchymal three-dimensional (3D) cell crawling. Here, we develop a computationally tractable 3D model (implemented as a simulation in the CompuCell3D simulation environment) of mesenchymal cells crawling on a two-dimensional substrate. The Fürth equation, the usual characterization of mean-squared displacement (MSD) curves for migrating cells, describes a motion in which, for increasing time intervals, cell movement transitions from a ballistic to a diffusive regime. Recent experiments have shown that for very short time intervals, cells exhibit an additional fast diffusive regime. Our simulations' MSD curves reproduce the three experimentally observed temporal regimes, with fast diffusion for short time intervals, slow diffusion for long time intervals, and intermediate time -interval-ballistic motion. The resulting parameterization of the trajectories for both experiments and simulations allows the definition of time- and length scales that translate between computational and laboratory units. Rescaling by these scales allows direct quantitative comparisons among MSD curves and between velocity autocorrelation functions from experiments and simulations. Although our simulations replicate experimentally observed spontaneous symmetry breaking, short-timescale diffusive motion, and spontaneous cell-motion reorientation, their computational cost is low, allowing their use in multiscale virtual-tissue simulations. Comparisons between experimental and simulated cell motion support the hypothesis that short-time actomyosin dynamics affects longer-time cell motility. The success of the base cell-migration simulation model suggests its future application in more complex situations, including chemotaxis, migration through complex 3D matrices, and collective cell motion.

Polarity sorting drives remodeling of actin-myosin networks.

Cytoskeletal networks of actin filaments and myosin motors drive many dynamic cell processes. A key characteristic of these networks is their contractility. Despite intense experimental and theoretical efforts, it is not clear what mechanism favors network contraction over expansion. Recent work points to a dominant role for the nonlinear mechanical response of actin filaments, which can withstand stretching but buckle upon compression. Here, we present an alternative mechanism. We study how interactions between actin and myosin-2 at the single-filament level translate into contraction at the network scale by performing time-lapse imaging on reconstituted quasi-2D networks mimicking the cell cortex. We observe myosin end-dwelling after it runs processively along actin filaments. This leads to transport and clustering of actin filament ends and the formation of transiently stable bipolar structures. Further, we show that myosin-driven polarity sorting produces polar actin asters, which act as contractile nodes that drive contraction in crosslinked networks. Computer simulations comparing the roles of the end-dwelling mechanism and a buckling-dependent mechanism show that the relative contribution of end-dwelling contraction increases as the network mesh-size decreases.

Fibroblast state switching orchestrates dermal maturation and wound healing.

Murine dermis contains functionally and spatially distinct fibroblast lineages that cease to proliferate in early postnatal life. Here, we propose a model in which a negative feedback loop between extracellular matrix (ECM) deposition and fibroblast proliferation determines dermal architecture. Virtual-tissue simulations of our model faithfully recapitulate dermal maturation, predicting a loss of spatial segregation of fibroblast lineages and dictating that fibroblast migration is only required for wound healing. To test this, we performed in vivo live imaging of dermal fibroblasts, which revealed that homeostatic tissue architecture is achieved without active cell migration. In contrast, both fibroblast proliferation and migration are key determinants of tissue repair following wounding. The results show that tissue-scale coordination is driven by the interdependence of cell proliferation and ECM deposition, paving the way for identifying new therapeutic strategies to enhance skin regeneration.

A theory that predicts behaviors of disordered cytoskeletal networks.

Morphogenesis in animal tissues is largely driven by actomyosin networks, through tensions generated by an active contractile process. Although the network components and their properties are known, and networks can be reconstituted in vitro, the requirements for contractility are still poorly understood. Here, we describe a theory that predicts whether an isotropic network will contract, expand, or conserve its dimensions. This analytical theory correctly predicts the behavior of simulated networks, consisting of filaments with varying combinations of connectors, and reveals conditions under which networks of rigid filaments are either contractile or expansile. Our results suggest that pulsatility is an intrinsic behavior of contractile networks if the filaments are not stable but turn over. The theory offers a unifying framework to think about mechanisms of contractions or expansion. It provides the foundation for studying a broad range of processes involving cytoskeletal networks and a basis for designing synthetic networks.

A Notch positive feedback in the intestinal stem cell niche is essential for stem cell self-renewal.

The intestinal epithelium is the fastest regenerative tissue in the body, fueled by fast-cycling stem cells. The number and identity of these dividing and migrating stem cells are maintained by a mosaic pattern at the base of the crypt. How the underlying regulatory scheme manages this dynamic stem cell niche is not entirely clear. We stimulated intestinal organoids with Notch ligands and inhibitors and discovered that intestinal stem cells employ a positive feedback mechanism via direct Notch binding to the second intron of the Notch1 gene. Inactivation of the positive feedback by CRISPR/Cas9 mutation of the binding sequence alters the mosaic stem cell niche pattern and hinders regeneration in organoids. Dynamical system analysis and agent-based multiscale stochastic modeling suggest that the positive feedback enhances the robustness of Notch-mediated niche patterning. This study highlights the importance of feedback mechanisms in spatiotemporal control of the stem cell niche.

Filopodial-Tension Model of Convergent-Extension of Tissues.

In convergent-extension (CE), a planar-polarized epithelial tissue elongates (extends) in-plane in one direction while shortening (converging) in the perpendicular in-plane direction, with the cells both elongating and intercalating along the converging axis. CE occurs during the development of most multicellular organisms. Current CE models assume cell or tissue asymmetry, but neglect the preferential filopodial activity along the convergent axis observed in many tissues. We propose a cell-based CE model based on asymmetric filopodial tension forces between cells and investigate how cell-level filopodial interactions drive tissue-level CE. The final tissue geometry depends on the balance between external rounding forces and cell-intercalation traction. Filopodial-tension CE is robust to relatively high levels of planar cell polarity misalignment and to the presence of non-active cells. Addition of a simple mechanical feedback between cells fully rescues and even improves CE of tissues with high levels of polarity misalignments. Our model extends easily to three dimensions, with either one converging and two extending axes, or two converging and one extending axes, producing distinct tissue morphologies, as observed in vivo.

3D simulations of wet foam coarsening evidence a self similar growth regime.

In wet liquid foams, slow diffusion of gas through bubble walls changes bubble pressure, volume and wall curvature. Large bubbles grow at the expenses of smaller ones. The smaller the bubble, the faster it shrinks. As the number of bubbles in a given volume decreases in time, the average bubble size increases: i.e. the foam coarsens. During coarsening, bubbles also move relative to each other, changing bubble topology and shape, while liquid moves within the regions separating the bubbles. Analyzing the combined effects of these mechanisms requires examining a volume with enough bubbles to provide appropriate statistics throughout coarsening. Using a Cellular Potts model, we simulate these mechanisms during the evolution of three-dimensional foams with wetnesses of ϕ = 0.00, 0.05 and 0.20. We represent the liquid phase as an ensemble of many small fluid particles, which allows us to monitor liquid flow in the region between bubbles. The simulations begin with 2 × 105 bubbles for ϕ = 0.00 and 1.25 × 105 bubbles for ϕ = 0.05 and 0.20, allowing us to track the distribution functions for bubble size, topology and growth rate over two and a half decades of volume change. All simulations eventually reach a self-similar growth regime, with the distribution functions time independent and the number of bubbles decreasing with time as a power law whose exponent depends on the wetness.

Microtubule competition and cell growth recenter the nucleus after anaphase in fission yeast.

Cells actively position their nuclei based on their activity. In fission yeast, microtubule-dependent nuclear centering is critical for symmetrical cell division. After spindle disassembly at the end of anaphase, the nucleus recenters over an ∼90-min period, approximately half of the duration of the cell cycle. Live-cell and simulation experiments support the cooperation of two distinct microtubule competition mechanisms in the slow recentering of the nucleus. First, a push-push mechanism acts from spindle disassembly to septation and involves the opposing actions of the mitotic spindle pole body microtubules that push the nucleus away from the ends of the cell, while a postanaphase array of microtubules baskets the nucleus and limits its migration toward the division plane. Second, a slow-and-grow mechanism slowly centers the nucleus in the newborn cell by a combination of microtubule competition and asymmetric cell growth. Our work underlines how intrinsic properties of microtubules differently impact nuclear positioning according to microtubule network organization and cell size.

A multi-cell, multi-scale model of vertebrate segmentation and somite formation.

Somitogenesis, the formation of the body's primary segmental structure common to all vertebrate development, requires coordination between biological mechanisms at several scales. Explaining how these mechanisms interact across scales and how events are coordinated in space and time is necessary for a complete understanding of somitogenesis and its evolutionary flexibility. So far, mechanisms of somitogenesis have been studied independently. To test the consistency, integrability and combined explanatory power of current prevailing hypotheses, we built an integrated clock-and-wavefront model including submodels of the intracellular segmentation clock, intercellular segmentation-clock coupling via Delta/Notch signaling, an FGF8 determination front, delayed differentiation, clock-wavefront readout, and differential-cell-cell-adhesion-driven cell sorting. We identify inconsistencies between existing submodels and gaps in the current understanding of somitogenesis mechanisms, and propose novel submodels and extensions of existing submodels where necessary. For reasonable initial conditions, 2D simulations of our model robustly generate spatially and temporally regular somites, realistic dynamic morphologies and spontaneous emergence of anterior-traveling stripes of Lfng. We show that these traveling stripes are pseudo-waves rather than true propagating waves. Our model is flexible enough to generate interspecies-like variation in somite size in response to changes in the PSM growth rate and segmentation-clock period, and in the number and width of Lfng stripes in response to changes in the PSM growth rate, segmentation-clock period and PSM length.

Mechanical competition alters the cellular interpretation of an endogenous genetic program.

The intrinsic genetic program of a cell is not sufficient to explain all of the cell's activities. External mechanical stimuli are increasingly recognized as determinants of cell behavior. In the epithelial folding event that constitutes the beginning of gastrulation in Drosophila, the genetic program of the future mesoderm leads to the establishment of a contractile actomyosin network that triggers apical constriction of cells and thereby tissue folding. However, some cells do not constrict but instead stretch, even though they share the same genetic program as their constricting neighbors. We show here that tissue-wide interactions force these cells to expand even when an otherwise sufficient amount of apical, active actomyosin is present. Models based on contractile forces and linear stress-strain responses do not reproduce experimental observations, but simulations in which cells behave as ductile materials with nonlinear mechanical properties do. Our models show that this behavior is a general emergent property of actomyosin networks in a supracellular context, in accordance with our experimental observations of actin reorganization within stretching cells.

A mechanical model of early somite segmentation.

Somitogenesis is often described using the clock-and-wavefront (CW) model, which does not explain how molecular signaling rearranges the pre-somitic mesoderm (PSM) cells into somites. Our scanning electron microscopy analysis of chicken embryos reveals a caudally-progressing epithelialization front in the dorsal PSM that precedes somite formation. Signs of apical constriction and tissue segmentation appear in this layer 3-4 somite lengths caudal to the last-formed somite. We propose a mechanical instability model in which a steady increase of apical contractility leads to periodic failure of adhesion junctions within the dorsal PSM and positions the future inter-somite boundaries. This model produces spatially periodic segments whose size depends on the speed of the activation front of contraction (F), and the buildup rate of contractility (Λ). The Λ/F ratio determines whether this mechanism produces spatially and temporally regular or irregular segments, and whether segment size increases with the front speed.

A disassembly-driven mechanism explains F-actin-mediated chromosome transport in starfish oocytes.

While contraction of sarcomeric actomyosin assemblies is well understood, this is not the case for disordered networks of actin filaments (F-actin) driving diverse essential processes in animal cells. For example, at the onset of meiosis in starfish oocytes a contractile F-actin network forms in the nuclear region transporting embedded chromosomes to the assembling microtubule spindle. Here, we addressed the mechanism driving contraction of this 3D disordered F-actin network by comparing quantitative observations to computational models. We analyzed 3D chromosome trajectories and imaged filament dynamics to monitor network behavior under various physical and chemical perturbations. We found no evidence of myosin activity driving network contractility. Instead, our observations are well explained by models based on a disassembly-driven contractile mechanism. We reconstitute this disassembly-based contractile system in silico revealing a simple architecture that robustly drives chromosome transport to prevent aneuploidy in the large oocyte, a prerequisite for normal embryonic development.

Large-scale microtubule networks contract quite well.

The quantitative investigation of how networks of microtubules contract can boost our understanding of actin biology.

A Liver-Centric Multiscale Modeling Framework for Xenobiotics.

We describe a multi-scale, liver-centric in silico modeling framework for acetaminophen pharmacology and metabolism. We focus on a computational model to characterize whole body uptake and clearance, liver transport and phase I and phase II metabolism. We do this by incorporating sub-models that span three scales; Physiologically Based Pharmacokinetic (PBPK) modeling of acetaminophen uptake and distribution at the whole body level, cell and blood flow modeling at the tissue/organ level and metabolism at the sub-cellular level. We have used standard modeling modalities at each of the three scales. In particular, we have used the Systems Biology Markup Language (SBML) to create both the whole-body and sub-cellular scales. Our modeling approach allows us to run the individual sub-models separately and allows us to easily exchange models at a particular scale without the need to extensively rework the sub-models at other scales. In addition, the use of SBML greatly facilitates the inclusion of biological annotations directly in the model code. The model was calibrated using human in vivo data for acetaminophen and its sulfate and glucuronate metabolites. We then carried out extensive parameter sensitivity studies including the pairwise interaction of parameters. We also simulated population variation of exposure and sensitivity to acetaminophen. Our modeling framework can be extended to the prediction of liver toxicity following acetaminophen overdose, or used as a general purpose pharmacokinetic model for xenobiotics.

Virtual-tissue computer simulations define the roles of cell adhesion and proliferation in the onset of kidney cystic disease.

In autosomal dominant polycystic kidney disease (ADPKD), cysts accumulate and progressively impair renal function. Mutations in PKD1 and PKD2 genes are causally linked to ADPKD, but how these mutations drive cell behaviors that underlie ADPKD pathogenesis is unknown. Human ADPKD cysts frequently express cadherin-8 (cad8), and expression of cad8 ectopically in vitro suffices to initiate cystogenesis. To explore cell behavioral mechanisms of cad8-driven cyst initiation, we developed a virtual-tissue computer model. Our simulations predicted that either reduced cell-cell adhesion or reduced contact inhibition of proliferation triggers cyst induction. To reproduce the full range of cyst morphologies observed in vivo, changes in both cell adhesion and proliferation are required. However, only loss-of-adhesion simulations produced morphologies matching in vitro cad8-induced cysts. Conversely, the saccular cysts described by others arise predominantly by decreased contact inhibition, that is, increased proliferation. In vitro experiments confirmed that cell-cell adhesion was reduced and proliferation was increased by ectopic cad8 expression. We conclude that adhesion loss due to cadherin type switching in ADPKD suffices to drive cystogenesis. Thus, control of cadherin type switching provides a new target for therapeutic intervention.

Somites without a clock.

The formation of body segments (somites) in vertebrate embryos is accompanied by molecular oscillations (segmentation clock). Interaction of this oscillator with a wave traveling along the body axis (the clock-and-wavefront model) is generally believed to control somite number, size, and axial identity. Here we show that a clock-and-wavefront mechanism is unnecessary for somite formation. Non-somite mesoderm treated with Noggin generates many somites that form simultaneously, without cyclic expression of Notch-pathway genes, yet have normal size, shape, and fate. These somites have axial identity: The Hox code is fixed independently of somite fate. However, these somites are not subdivided into rostral and caudal halves, which is necessary for neural segmentation. We propose that somites are self-organizing structures whose size and shape is controlled by local cell-cell interactions.

Multi-scale modeling of tissues using CompuCell3D.

The study of how cells interact to produce tissue development, homeostasis, or diseases was, until recently, almost purely experimental. Now, multi-cell computer simulation methods, ranging from relatively simple cellular automata to complex immersed-boundary and finite-element mechanistic models, allow in silico study of multi-cell phenomena at the tissue scale based on biologically observed cell behaviors and interactions such as movement, adhesion, growth, death, mitosis, secretion of chemicals, chemotaxis, etc. This tutorial introduces the lattice-based Glazier-Graner-Hogeweg (GGH) Monte Carlo multi-cell modeling and the open-source GGH-based CompuCell3D simulation environment that allows rapid and intuitive modeling and simulation of cellular and multi-cellular behaviors in the context of tissue formation and subsequent dynamics. We also present a walkthrough of four biological models and their associated simulations that demonstrate the capabilities of the GGH and CompuCell3D.

Self-propelled particle model for cell-sorting phenomena.

A self-propelled particle model is introduced to study cell sorting occurring in some living organisms. This allows us to evaluate the influence of intrinsic cell motility separately from differential adhesion with fluctuations, a mechanism previously shown to be sufficient to explain a variety of cell rearrangement processes. We find that the tendency of cells to actively follow their neighbors greatly reduces segregation time scales. A finite-size analysis of the sorting process reveals clear algebraic growth laws as in physical phase-ordering processes, albeit with unusual scaling exponents.