Fatal dysfunction and disintegration of thrombin-stimulated platelets

Platelets play a key role in the formation of hemostatic clots and obstructive thrombi as well as in other biological processes. In response to physiological stimulants, including thrombin, platelets change shape, express adhesive molecules, aggregate, and secrete bioactive substances, but their subsequent fate is largely unknown. Here we examined late-stage structural, metabolic, and functional consequences of thrombin-induced platelet activation. Using a combination of confocal microscopy, scanning and transmission electron microscopy, flow cytometry, biochemical and biomechanical measurements, we showed that thrombin-induced activation is followed by time-dependent platelet dysfunction and disintegration. After ~30 minutes of incubation with thrombin, unlike with collagen or ADP, human platelets disintegrated into cellular fragments containing organelles, such as mitochondria, glycogen granules, and vacuoles. This platelet fragmentation was preceded by Ca²⁺ influx, integrin α_IIbβ₃ activation and phosphatidylserine exposure (activation phase), followed by mitochondrial depolarization, generation of reactive oxygen species, metabolic ATP depletion and impairment of platelet contractility along with dramatic cytoskeletal rearrangements, concomitant with platelet disintegration (death phase). Coincidentally with the platelet fragmentation, thrombin caused calpain activation but not activation of caspases 3 and 7. Our findings indicate that the late functional and structural damage of thrombin-activated platelets comprise a calpain-dependent platelet death pathway that shares some similarities with the programmed death of nucleated cells, but is unique to platelets, therefore representing a special form of cellular destruction. Fragmentation of activated platelets suggests that there is an underappreciated pathway of enhanced elimination of platelets from the circulation in (pro)thrombotic conditions once these cells have performed their functions.

Quantitative structural mechanobiology of platelet-driven blood clot contraction

Blood clot contraction plays an important role in prevention of bleeding and in thrombotic disorders. Here, we unveil and quantify the structural mechanisms of clot contraction at the level of single platelets. A key elementary step of contraction is sequential extension-retraction of platelet filopodia attached to fibrin fibers. In contrast to other cell-matrix systems in which cells migrate along fibers, the "hand-over-hand" longitudinal pulling causes shortening and bending of platelet-attached fibers, resulting in formation of fiber kinks. When attached to multiple fibers, platelets densify the fibrin network by pulling on fibers transversely to their longitudinal axes. Single platelets and aggregates use actomyosin contractile machinery and integrin-mediated adhesion to remodel the extracellular matrix, inducing compaction of fibrin into bundled agglomerates tightly associated with activated platelets. The revealed platelet-driven mechanisms of blood clot contraction demonstrate an important new biological application of cell motility principles.

Strong Binding of Platelet Integrin αIIbβ3 to Fibrin Clots: Potential Target to Destabilize Thrombi

The formation of platelet thrombi is determined by the integrin αIIbβ3-mediated interactions of platelets with fibrinogen and fibrin. Blood clotting in vivo is catalyzed by thrombin, which simultaneously induces fibrinogen binding to αIIbβ3 and converts fibrinogen to fibrin. Thus, after a short time, thrombus formation is governed by αIIbβ3 binding to fibrin fibers. Surprisingly, there is little understanding of αIIbβ3 interaction with fibrin polymers. Here we used an optical trap-based system to measure the binding of single αIIbβ3 molecules to polymeric fibrin and compare it to αIIbβ3 binding to monomeric fibrin and fibrinogen. Like αIIbβ3 binding to fibrinogen and monomeric fibrin, we found that αIIbβ3 binding to polymeric fibrin can be segregated into two binding regimes, one with weaker rupture forces of 30-60 pN and a second with stronger rupture forces >60 pN that peaked at 70-80 pN. However, we found that the mechanical stability of the bimolecular αIIbβ3-ligand complexes had the following order: fibrin polymer > fibrin monomer > fibrinogen. These quantitative differences reflect the distinct specificity and underlying molecular mechanisms of αIIbβ3-mediated reactions, implying that targeting platelet interactions with fibrin could increase the therapeutic indices of antithrombotic agents by focusing on the destabilization of thrombi rather than the prevention of platelet aggregation.

Whole blood clot optical clearing for nondestructive 3D imaging and quantitative analysis

A technological revolution in both light and electron microscopy imaging now allows unprecedented views of clotting, especially in animal models of hemostasis and thrombosis. However, our understanding of three-dimensional high-resolution clot structure remains incomplete since most of our recent knowledge has come from studies of relatively small clots or thrombi, due to the optical impenetrability of clots beyond a few cell layers in depth. Here, we developed an optimized optical clearing method termed cCLOT that renders large whole blood clots transparent and allows confocal imaging as deep as one millimeter inside the clot. We have tested this method by investigating the 3D structure of clots made from reconstituted pre-labeled blood components yielding new information about the effects of clot contraction on erythrocytes. Although it has been shown recently that erythrocytes are compressed to form polyhedrocytes during clot contraction, observations of this phenomenon have been impeded by the inability to easily image inside clots. As an efficient and non-destructive method, cCLOT represents a powerful research tool in studying blood clot structure and mechanisms controlling clot morphology. Additionally, cCLOT optical clearing has the potential to facilitate imaging of ex vivo clots and thrombi derived from healthy or pathological conditions.

Compression-induced structural and mechanical changes of fibrin-collagen composites

Fibrin and collagen as well as their combinations play an important biological role in tissue regeneration and are widely employed in surgery as fleeces or sealants and in bioengineering as tissue scaffolds. Earlier studies demonstrated that fibrin-collagen composite networks displayed improved tensile mechanical properties compared to the isolated protein matrices. Unlike previous studies, here unconfined compression was applied to a fibrin-collagen filamentous polymer composite matrix to study its structural and mechanical responses to compressive deformation. Combining collagen with fibrin resulted in formation of a composite hydrogel exhibiting synergistic mechanical properties compared to the isolated fibrin and collagen matrices. Specifically, the composite matrix revealed a one order of magnitude increase in the shear storage modulus at compressive strains>0.8 in response to compression compared to the mechanical features of individual components. These material enhancements were attributed to the observed structural alterations, such as network density changes, an increase in connectivity along with criss-crossing, and bundling of fibers. In addition, the compressed composite collagen/fibrin networks revealed a non-linear transformation of their viscoelastic properties with softening and stiffening regimes. These transitions were shown to depend on protein concentrations. Namely, a decrease in protein content drastically affected the mechanical response of the networks to compression by shifting the onset of stiffening to higher degrees of compression. Since both natural and artificially composed extracellular matrices experience compression in various (patho)physiological conditions, our results provide new insights into the structural biomechanics of the polymeric composite matrix that can help to create fibrin-collagen sealants, sponges, and tissue scaffolds with tunable and predictable mechanical properties.

Interactions between Tau and Different Conformations of Tubulin: Implications for Tau Function and Mechanism

Tau is a multifaceted neuronal protein that stabilizes microtubules (MTs), but the mechanism of this activity remains poorly understood. Questions include whether Tau binds MTs laterally or longitudinally and whether Tau's binding affinity depends on the nucleotide state of tubulin. We observed that Tau binds tightly to Dolastatin-10 tubulin rings and promotes the formation of Dolastatin-10 ring stacks, implying that Tau can crosslink MT protofilaments laterally. In addition, we found that Tau prefers GDP-like tubulin conformations, which implies that Tau binding to the MT surface is biased away from the dynamic GTP-rich MT tip. To investigate the potential impact of these Tau activities on MT stabilization, we incorporated them into our previously developed dimer-scale computational model of MT dynamics. We found that lateral crosslinking activities have a much greater effect on MT stability than do longitudinal crosslinking activities, and that introducing a bias toward GDP tubulin has little impact on the observed MT stabilization. To address the question of why Tau is GDP-tubulin-biased, we tested whether Tau might affect MT binding of the +TIP EB1. We confirmed recent reports that Tau binds directly to EB1 and that Tau competes with EB1 for MT binding. Our results lead to a conceptual model where Tau stabilizes the MT lattice by strengthening lateral interactions between protofilaments. We propose that Tau's GDP preference allows the cell to independently regulate the dynamics of the MT tip and the stability of the lattice.

A Hybrid Approach for Segmentation and Tracking of Myxococcus Xanthus Swarms

Cell segmentation and motion tracking in time-lapse images are fundamental problems in computer vision, and are also crucial for various biomedical studies. Myxococcus xanthus is a type of rod-like cells with highly coordinated motion. The segmentation and tracking of M. xanthus are challenging, because cells may touch tightly and form dense swarms that are difficult to identify individually in an accurate manner. The known cell tracking approaches mainly fall into two frameworks, detection association and model evolution, each having its own advantages and disadvantages. In this paper, we propose a new hybrid framework combining these two frameworks into one and leveraging their complementary advantages. Also, we propose an active contour model based on the Ribbon Snake, which is seamlessly integrated with our hybrid framework. Evaluated by 10 different datasets, our approach achieves considerable improvement over the state-of-the-art cell tracking algorithms on identifying complete cell trajectories, and higher segmentation accuracy than performing segmentation in individual 2D images.

Multicomponent model of deformation and detachment of a biofilm under fluid flow

A novel biofilm model is described which systemically couples bacteria, extracellular polymeric substances (EPS) and solvent phases in biofilm. This enables the study of contributions of rheology of individual phases to deformation of biofilm in response to fluid flow as well as interactions between different phases. The model, which is based on first and second laws of thermodynamics, is derived using an energetic variational approach and phase-field method. Phase-field coupling is used to model structural changes of a biofilm. A newly developed unconditionally energy-stable numerical splitting scheme is implemented for computing the numerical solution of the model efficiently. Model simulations predict biofilm cohesive failure for the flow velocity between [Formula: see text] and [Formula: see text] m s(-1) which is consistent with experiments. Simulations predict biofilm deformation resulting in the formation of streamers for EPS exhibiting a viscous-dominated mechanical response and the viscosity of EPS being less than [Formula: see text]. Higher EPS viscosity provides biofilm with greater resistance to deformation and to removal by the flow. Moreover, simulations show that higher EPS elasticity yields the formation of streamers with complex geometries that are more prone to detachment. These model predictions are shown to be in qualitative agreement with experimental observations.

Foam-like compression behavior of fibrin networks

The rheological properties of fibrin networks have been of long-standing interest. As such there is a wealth of studies of their shear and tensile responses, but their compressive behavior remains unexplored. Here, by characterization of the network structure with synchronous measurement of the fibrin storage and loss moduli at increasing degrees of compression, we show that the compressive behavior of fibrin networks is similar to that of cellular solids. A nonlinear stress-strain response of fibrin consists of three regimes: (1) an initial linear regime, in which most fibers are straight, (2) a plateau regime, in which more and more fibers buckle and collapse, and (3) a markedly nonlinear regime, in which network densification occurs by bending of buckled fibers and inter-fiber contacts. Importantly, the spatially non-uniform network deformation included formation of a moving "compression front" along the axis of strain, which segregated the fibrin network into compartments with different fiber densities and structure. The Young's modulus of the linear phase depends quadratically on the fibrin volume fraction while that in the densified phase depends cubically on it. The viscoelastic plateau regime corresponds to a mixture of these two phases in which the fractions of the two phases change during compression. We model this regime using a continuum theory of phase transitions and analytically predict the storage and loss moduli which are in good agreement with the experimental data. Our work shows that fibrin networks are a member of a broad class of natural cellular materials which includes cancellous bone, wood and cork.

Type IV pili interactions promote intercellular association and moderate swarming of Pseudomonas aeruginosa

Pseudomonas aeruginosa is a ubiquitous bacterium that survives in many environments, including as an acute and chronic pathogen in humans. Substantial evidence shows that P. aeruginosa behavior is affected by its motility, and appendages known as flagella and type IV pili (TFP) are known to confer such motility. The role these appendages play when not facilitating motility or attachment, however, is unclear. Here we discern a passive intercellular role of TFP during flagellar-mediated swarming of P. aeruginosa that does not require TFP extension or retraction. We studied swarming at the cellular level using a combination of laboratory experiments and computational simulations to explain the resultant patterns of cells imaged from in vitro swarms. Namely, we used a computational model to simulate swarming and to probe for individual cell behavior that cannot currently be otherwise measured. Our simulations showed that TFP of swarming P. aeruginosa should be distributed all over the cell and that TFP-TFP interactions between cells should be a dominant mechanism that promotes cell-cell interaction, limits lone cell movement, and slows swarm expansion. This predicted physical mechanism involving TFP was confirmed in vitro using pairwise mixtures of strains with and without TFP where cells without TFP separate from cells with TFP. While TFP slow swarm expansion, we show in vitro that TFP help alter collective motion to avoid toxic compounds such as the antibiotic carbenicillin. Thus, TFP physically affect P. aeruginosa swarming by actively promoting cell-cell association and directional collective motion within motile groups to aid their survival.

Structural basis for the nonlinear mechanics of fibrin networks under compression

Fibrin is a protein polymer that forms a 3D filamentous network, a major structural component of protective physiological blood clots as well as life threatening pathological thrombi. It plays an important role in wound healing, tissue regeneration and is widely employed in surgery as a sealant and in tissue engineering as a scaffold. The goal of this study was to establish correlations between structural changes and mechanical responses of fibrin networks exposed to compressive loads. Rheological measurements revealed nonlinear changes of fibrin network viscoelastic properties under dynamic compression, resulting in network softening followed by its dramatic hardening. Repeated compression/decompression enhanced fibrin clot stiffening. Combining fibrin network rheology with simultaneous confocal microscopy provided direct evidence of structural modulations underlying nonlinear viscoelasticity of compressed fibrin networks. Fibrin clot softening in response to compression strongly correlated with fiber buckling and bending, while hardening was associated with fibrin network densification. Our results suggest a complex interplay of entropic and enthalpic mechanisms accompanying structural changes and accounting for the nonlinear mechanical response in fibrin networks undergoing compressive deformations. These findings provide new insight into the fibrin clot structural mechanics and can be useful for designing fibrin-based biomaterials with modulated viscoelastic properties.

Microtubule dynamic instability: the role of cracks between protofilaments

Microtubules (MTs) are cytoplasmic protein polymers that are essential for fundamental cellular processes including the maintenance of cell shape, organelle transport and formation of the mitotic spindle. Microtubule dynamic instability is critical for these processes, but it remains poorly understood, in part because the relationship between the structure of the MT tip and the growth/depolymerization transitions is enigmatic. In previous work, we used computational models of dynamic instability to provide evidence that cracks (laterally unbonded regions) between protofilaments play a key role in the regulation of dynamic instability. Here we use computational models to investigate the connection between cracks and dynamic instability in more detail. Our work indicates that while cracks contribute to dynamic instability in a fundamental way, it is not the depth of the cracks per se that governs MT dynamic instability. Instead, what matters more is whether the cracks terminate in GTP-rich or GDP-rich regions of the MT. Based on these observations, we suggest that a functional "GTP cap" (i.e., one capable of promoting MT growth) is one where the cracks terminate in pairs of GTP-bound subunits, and that the likelihood of catastrophe rises significantly with the fraction of crack-terminating subunits that contain GDP. In addition to helping clarify the mechanism of dynamic instability, this idea could also explain how MT stabilizers work: proteins that introduce lateral cross-links between protofilaments would produce islands of GDP-bound tubulin that mimic GTP-rich regions in having strong lateral bonds, thus reducing crack propagation, suppressing catastrophe and promoting rescue.

A matching model based on earth mover's distance for tracking Myxococcus xanthus

Tracking the motion of Myxococcus xanthus is a crucial step for fundamental bacteria studies. Large number of bacterial cells involved, limited image resolution, and various cell behaviors (e.g., division) make tracking a highly challenging problem. A common strategy is to segment the cells first and associate detected cells into moving trajectories. However, known detection association algorithms that run in polynomial time are either ineffective to deal with particular cell behaviors or sensitive to segmentation errors. In this paper, we propose a polynomial time hierarchical approach for associating segmented cells, using a new Earth Mover's Distance (EMD) based matching model. Our method is able to track cell motion when cells may divide, leave/enter the image window, and the segmentation results may incur false alarm, detection lost, and falsely merged/split detections. We demonstrate it on tracking M. xanthus. Applied to error-prone segmented cells, our algorithm exhibits higher track purity and produces more complete trajectories, comparing to several state-of-the-art detection association algorithms.

Fibrin networks regulate protein transport during thrombus development

Thromboembolic disease is a leading cause of morbidity and mortality worldwide. In the last several years there have been a number of studies attempting to identify mechanisms that stop thrombus growth. This paper identifies a novel mechanism related to formation of a fibrin cap. In particular, protein transport through a fibrin network, an important component of a thrombus, was studied by integrating experiments with model simulations. The network permeability and the protein diffusivity were shown to be important factors determining the transport of proteins through the fibrin network. Our previous in vivo studies in mice have shown that stabilized non-occluding thrombi are covered by a fibrin network (‘fibrin cap’). Model simulations, calibrated using experiments in microfluidic devices and accounting for the permeable structure of the fibrin cap, demonstrated that thrombin generated inside the thrombus was washed downstream through the fibrin network, thus limiting exposure of platelets on the thrombus surface to thrombin. Moreover, by restricting the approach of resting platelets in the flowing blood to the thrombus core, the fibrin cap impaired platelets from reaching regions of high thrombin concentration necessary for platelet activation and limited thrombus growth. The formation of a fibrin cap prevents small thrombi that frequently develop in the absence of major injury in the 60000 km of vessels in the body from developing into life threatening events.

To restrict the loss of blood following rupture of blood vessels, the human body rapidly forms a clot consisting mainly of platelets and fibrin. However, to prevent formation of a pathological clot within vessels (thrombus) as a result of vessel damage or dysfunction, the response must be regulated, and clot formation must be limited. Our previous studies demonstrated that as a laser-induced thrombus stabilized in mice, the ratio of fibrin to platelets at the thrombus surface increased significantly. Stabilized non-occluding thrombi were observed to be covered by a fibrin network (‘fibrin cap’). In the present work the role of the fibrin network in protein transport is examined by integrating experiments in microfluidic devices with the hemodynamic thrombus model. The study reveals permeability of the fibrin network and protein diffusivity to be important factors determining the transport of blood proteins inside the thrombus. It is shown that the fibrin network does not dramatically limit the diffusion of thrombin but impairs flowing platelets in blood from reaching regions of high thrombin concentration thus, reducing the probability they are activated and stably integrated into the thrombus. This novel, counter-intuitive mechanism suggests that a fibrin network formed at early stages of thrombus initiation can prevent normally asymptomatic thrombi from developing into pathological clots.

Mathematical modeling of vertebrate limb development

In this paper, we review the major mathematical and computational models of vertebrate limb development and their roles in accounting for different aspects of this process. The main aspects of limb development that have been modeled include outgrowth and shaping of the limb bud, establishment of molecular gradients within the bud, and formation of the skeleton. These processes occur interdependently during development, although (as described in this review), there are various interpretations of the biological relationships among them. A wide range of mathematical and computational methods have been used to study these processes, including ordinary and partial differential equation systems, cellular automata and discrete, stochastic models, finite difference methods, finite element methods, the immersed boundary method, and various combinations of the above. Multiscale mathematical modeling and associated computational simulation have become integrated into the study of limb morphogenesis and pattern formation to an extent with few parallels in the field of developmental biology. These methods have contributed to the design and analysis of experiments employing microsurgical and genetic manipulations, evaluation of hypotheses for limb bud outgrowth, interpretation of the effects of natural mutations, and the formulation of scenarios for the origination and evolution of the limb skeleton.

Detecting and tracking motion of Myxococcus xanthus bacteria in swarms

Automatically detecting and tracking the motion of Myxococcus xanthus bacteria provide essential information for studying bacterial cell motility mechanisms and collective behaviors. However, this problem is difficult due to the low contrast of microscopy images, cell clustering and colliding behaviors, etc. To overcome these difficulties, our approach starts with a level set based pre-segmentation of cell clusters, followed by an enhancement of the rod-like cell features and detection of individual bacterium within each cluster. A novel method based on "spikes" of the outer medial axis is applied to divide touching (colliding) cells. The tracking of cell motion is accomplished by a non-crossing bipartite graph matching scheme that matches not only individual cells but also the neighboring structures around each cell. Our approach was evaluated on image sequences of moving M. xanthus bacteria close to the edge of their swarms, achieving high accuracy on the test data sets.

The mechanisms of microtubule catastrophe and rescue: implications from analysis of a dimer-scale computational model

ETOC: The behavior of a dimer-scale computational model predicts that short interprotofilament “cracks” (laterally unbonded regions between protofilaments) exist even at the tips of growing MTs and that rapid fluctuations in the depths of these cracks govern both catastrophe and rescue.

Microtubule (MT) dynamic instability is fundamental to many cell functions, but its mechanism remains poorly understood, in part because it is difficult to gain information about the dimer-scale events at the MT tip. To address this issue, we used a dimer-scale computational model of MT assembly that is consistent with tubulin structure and biochemistry, displays dynamic instability, and covers experimentally relevant spans of time. It allows us to correlate macroscopic behaviors (dynamic instability parameters) with microscopic structures (tip conformations) and examine protofilament structure as the tip spontaneously progresses through both catastrophe and rescue. The model's behavior suggests that several commonly held assumptions about MT dynamics should be reconsidered. Moreover, it predicts that short, interprotofilament “cracks” (laterally unbonded regions between protofilaments) exist even at the tips of growing MTs and that rapid fluctuations in the depths of these cracks influence both catastrophe and rescue. We conclude that experimentally observed microtubule behavior can best be explained by a “stochastic cap” model in which tubulin subunits hydrolyze GTP according to a first-order reaction after they are incorporated into the lattice; catastrophe and rescue result from stochastic fluctuations in the size, shape, and extent of lateral bonding of the cap.

Mean-field study of the role of lateral cracks in microtubule dynamics

A link between dimer-scale processes and microtubule (MT) dynamics at macroscale is studied by comparing simulations obtained using computational dimer-scale model with its mean-field approximation. The novelty of the mean-field model (MFM) is in its explicit representation of inter-protofilament cracks, as well as in the direct incorporation of the dimer-level kinetics. Due to inclusion of both longitudinal and lateral dimer interactions, the MFM is two dimensional, in contrast to previous theoretical models of MTs. It is the first analytical model that predicts and quantifies crucial features of MT dynamics such as (i) existence of a minimal soluble tubulin concentration needed for the polymerization (with concentration represented as a function of model parameters), (ii) existence of steady-state growth and shortening phases (given with their respective velocities), and (iii) existence of an unstable pause state near zero velocity. In addition, the size of the GTP cap of a growing MT is estimated. Theoretical predictions are shown to be in good agreement with the numerical simulations.

Bare bones pattern formation: a core regulatory network in varying geometries reproduces major features of vertebrate limb development and evolution

BACKGROUND

Major unresolved questions regarding vertebrate limb development concern how the numbers of skeletal elements along the proximodistal (P-D) and anteroposterior (A-P) axes are determined and how the shape of a growing limb affects skeletal element formation. There is currently no generally accepted model for these patterning processes, but recent work on cartilage development (chondrogenesis) indicates that precartilage tissue self-organizes into nodular patterns by cell-molecular circuitry with local auto-activating and lateral inhibitory (LALI) properties. This process is played out in the developing limb in the context of a gradient of fibroblast growth factor (FGF) emanating from the apical ectodermal ridge (AER).

RESULTS

We have simulated the behavior of the core chondrogenic mechanism of the developing limb in the presence of an FGF gradient using a novel computational environment that permits simulation of LALI systems in domains of varying shape and size. The model predicts the normal proximodistal pattern of skeletogenesis as well as distal truncations resulting from AER removal. Modifications of the model's parameters corresponding to plausible effects of Hox proteins and formins, and of the reshaping of the model limb, bud yielded simulated phenotypes resembling mutational and experimental variants of the limb. Hypothetical developmental scenarios reproduce skeletal morphologies with features of fossil limbs.

CONCLUSIONS

The limb chondrogenic regulatory system operating in the presence of a gradient has an inherent, robust propensity to form limb-like skeletal structures. The bare bones framework can accommodate ancillary gene regulatory networks controlling limb bud shaping and establishment of Hox expression domains. This mechanism accounts for major features of the normal limb pattern and, under variant geometries and different parameter values, those of experimentally manipulated, genetically aberrant and evolutionary early forms, with no requirement for an independent system of positional information.

Two-photon intravital imaging of thrombus development

Thrombus development in mouse mesenteric vessels following laser-induced injury was monitored by high-resolution, near-real-time, two-photon, intravital microscopy. In addition to the use of fluorescently tagged fibrin(ogen) and platelets, plasma was labeled with fluorescently tagged dextran. Because blood cells exclude the dextran in the single plane, blood cells appear as black silhouettes. Thus, in addition to monitoring the accumulation of platelets and fibrin in the thrombus, the protocol detects the movement and incorporation of unlabeled cells in and around it. The developing thrombus perturbs the blood flow near the thrombus surface, which affects the incorporation of platelets and blood cells into the structure. The hemodynamic effects and incorporation of blood cells lead to the development of thrombi with heterogeneous domain structures. Additionally, image processing algorithms and simulations were used to quantify structural features of developing thrombi. This analysis suggests a novel mechanism to stop the growth of developing thrombus.

From Genes to Organisms Via the Cell A Problem-Solving Environment for Multicellular Development

To gain performance, developers often build scientific applications in procedural languages, such as C or Fortran, which unfortunately reduces flexibility. To address this imbalance, the authors present CompuCell3D, a multitiered, flexible, and scalable problem-solving environment for morphogenesis simulations that's written in C++ using object-oriented design patterns.

A parallel implementation of the Cellular Potts Model for simulation of cell-based morphogenesis

The Cellular Potts Model (CPM) has been used in a wide variety of biological simulations. However, most current CPM implementations use a sequential modified Metropolis algorithm which restricts the size of simulations. In this paper we present a parallel CPM algorithm for simulations of morphogenesis, which includes cell-cell adhesion, a cell volume constraint, and cell haptotaxis. The algorithm uses appropriate data structures and checkerboard subgrids for parallelization. Communication and updating algorithms synchronize properties of cells simulated on different processor nodes. Tests show that the parallel algorithm has good scalability, permitting large-scale simulations of cell morphogenesis (10(7) or more cells) and broadening the scope of CPM applications. The new algorithm satisfies the balance condition, which is sufficient for convergence of the underlying Markov chain.

Patterns of mesenchymal condensation in a multiscale, discrete stochastic model

Cells of the embryonic vertebrate limb in high-density culture undergo chondrogenic pattern formation, which results in the production of regularly spaced “islands” of cartilage similar to the cartilage primordia of the developing limb skeleton. The first step in this process, in vitro and in vivo, is the generation of “cell condensations,” in which the precartilage cells become more tightly packed at the sites at which cartilage will form. In this paper we describe a discrete, stochastic model for the behavior of limb bud precartilage mesenchymal cells in vitro. The model uses a biologically motivated reaction–diffusion process and cell-matrix adhesion (haptotaxis) as the bases of chondrogenic pattern formation, whereby the biochemically distinct condensing cells, as well as the size, number, and arrangement of the multicellular condensations, are generated in a self-organizing fashion. Improving on an earlier lattice-gas representation of the same process, it is multiscale (i.e., cell and molecular dynamics occur on distinct scales), and the cells are represented as spatially extended objects that can change their shape. The authors calibrate the model using experimental data and study sensitivity to changes in key parameters. The simulations have disclosed two distinct dynamic regimes for pattern self-organization involving transient or stationary inductive patterns of morphogens. The authors discuss these modes of pattern formation in relation to available experimental evidence for the in vitro system, as well as their implications for understanding limb skeletal patterning during embryonic development.

The development of an organism from embryo to adult includes processes of pattern formation that involve the interactions over space and time of independent cells to form multicellular structures. Computational models permit exploration of possible alternative mechanisms that reproduce biological patterns and thereby provide hypotheses for empirical testing. In this article, we describe a biologically motivated discrete stochastic model that shows that the patterns of spots and stripes of tightly packed cells observed in cultures derived from the embryonic vertebrate limb can occur by a mechanism that uses only cell–cell signaling via diffusible molecules (morphogens) and cell substratum adhesion (haptotaxis). Moreover, similar-looking patterns can arise both from stable stationary dynamics and unstable transient dynamics of the same underlying core molecular–genetic mechanism. Simulations also show that spot and stripe patterns (which also correspond to the nodules and bars of the developing limb skeleton in vivo) are close in parameter space and can be generated in multiple ways with single-parameter variations. An important implication is that some developmental processes do not require a strict progression from one stable dynamic regime to another, but can occur by a succession of transient dynamic regimes tuned (e.g., by natural selection) to achieve a particular morphological outcome.

Insights into cytoskeletal behavior from computational modeling of dynamic microtubules in a cell-like environment

Microtubule dynamic instability plays a fundamental role in cell biology, enabling microtubules to find and interact with randomly distributed cargo and spatially localized signals. In vitro, microtubules transition between growth and shrinkage symmetrically, consistent with the theoretical understanding of the mechanism of dynamic instability. In vivo, however, microtubules commonly exhibit asymmetric dynamic instability, growing persistently in the cell interior and experiencing catastrophe near the cell edge. What is the origin of this behavior difference? One answer is that the cell edge causes the asymmetry by inducing catastrophe in persistently growing microtubules. However, the origin of the persistent growth itself is unclear. Using a simplified coarse-grained stochastic simulation of a system of dynamic microtubules, we provide evidence that persistent growth is a predictable property of a system of nucleated, dynamic, microtubules containing sufficient tubulin in a confined space--MAP activity is not required. Persistent growth occurs because cell-edge-induced catastrophe increases the concentration of free tubulin at steady-state. Our simulations indicate that other aspects of MT dynamics thought to require temporal or spatial changes in MAP activity are also predictable, perhaps unavoidable, outcomes of the "systems nature" of the cellular microtubule cytoskeleton. These include the mitotic increase in microtubule dynamics and the observation that defects in nucleation cause changes in the behavior of microtubule plus ends. These predictions are directly relevant to understanding of the microtubule cytoskeleton, but they are also attractive from an evolutionary standpoint because they provide evidence that apparently complex cellular behaviors can originate from simple interactions without a requirement for intricate regulatory machinery.

Analysis of a mesoscopic stochastic model of microtubule dynamic instability

A theoretical model of dynamic instability of a system of linear one-dimensional microtubules (MTs) in a bounded domain is introduced for studying the role of a cell edge in vivo and analyzing the effect of competition for a limited amount of tubulin. The model differs from earlier models in that the evolution of MTs is based on the rates of single-mesoscopic-unit (e.g., a heterodimer per protofilament) transformations, in contrast to postulating effective rates and frequencies of larger-scale macroscopic changes, extracted, e.g., from the length history plots of MTs. Spontaneous GTP hydrolysis with finite rate after polymerization is assumed, and theoretical estimates of an effective catastrophe frequency as well as other parameters characterizing MT length distributions and cap size are derived. We implement a simple cap model which does not include vectorial hydrolysis. We demonstrate that our theoretical predictions, such as steady-state concentration of free tubulin and parameters of MT length distributions, are in agreement with the numerical simulations. The present model establishes a quantitative link between mesoscopic parameters governing the dynamics of MTs and macroscopic characteristics of MTs in a closed system. Last, we provide an explanation for nonexponential MT length distributions observed in experiments. In particular, we show that the appearance of such nonexponential distributions in the experiments can occur because a true steady state has not been reached and/or due to the presence of a cell edge.

Agent-based modeling of the context dependency in T cell recognition

Antigen recognition by T cells is a key event in the adaptive immune response. T cells scan the surface of antigen-presenting cells (APCs) or target cells for specific peptides bound to MHC molecules. In the physiological setting, a typical APC presents tens of thousands of diverse endogenous self-derived peptides complexed to MHC (pMHC complexes). When 'foreign' peptides are presented, they constitute a small fraction of the total surface peptide repertoire. As T cells seem to be capable of discerning minute amounts of 'foreign' peptides among a complex background of self-peptides, endogenous peptides are generally assumed to play no role in recognition. However, recent results suggest that these background peptides may alter the sensitivity of T cells to foreign peptides. Current experimental limitations preclude analysis of peptide mixtures approaching physiological complexity, making it difficult to further address the role of complex background peptides. In this paper, we present a computational model to test how complex, varied peptide populations on an APC could potentially modulate a T cell's ability to detect the presence of small numbers of agonist peptides among a diverse population. We use the model to investigate the notion that under physiological conditions, T cell recognition of foreign peptides is context dependent, that is, T cells process signals gathered from all pMHC interactions, not just from a few agonist peptides while ignoring all others.

A framework for three-dimensional simulation of morphogenesis

We present COMPUCELL3D, a software framework for three-dimensional simulation of morphogenesis in different organisms. COMPUCELL3D employs biologically relevant models for cell clustering, growth, and interaction with chemical fields. COMPUCELL3D uses design patterns for speed, efficient memory management, extensibility, and flexibility to allow an almost unlimited variety of simulations. We have verified COMPUCELL3D by building a model of growth and skeletal pattern formation in the avian (chicken) limb bud. Binaries and source code are available, along with documentation and input files for sample simulations, at http:// compucell.sourceforge.net.

Role of streams in myxobacteria aggregate formation

Cell contact, movement and directionality are important factors in biological development (morphogenesis), and myxobacteria are a model system for studying cell-cell interaction and cell organization preceding differentiation. When starved, thousands of myxobacteria cells align, stream and form aggregates which later develop into round, non-motile spores. Canonically, cell aggregation has been attributed to attractive chemotaxis, a long range interaction, but there is growing evidence that myxobacteria organization depends on contact-mediated cell-cell communication. We present a discrete stochastic model based on contact-mediated signaling that suggests an explanation for the initialization of early aggregates, aggregation dynamics and final aggregate distribution. Our model qualitatively reproduces the unique structures of myxobacteria aggregates and detailed stages which occur during myxobacteria aggregation: first, aggregates initialize in random positions and cells join aggregates by random walk; second, cells redistribute by moving within transient streams connecting aggregates. Streams play a critical role in final aggregate size distribution by redistributing cells among fewer, larger aggregates. The mechanism by which streams redistribute cells depends on aggregate sizes and is enhanced by noise. Our model predicts that with increased internal noise, more streams would form and streams would last longer. Simulation results suggest a series of new experiments.

Interplay between activator-inhibitor coupling and cell-matrix adhesion in a cellular automaton model for chondrogenic patterning

We present a stochastic cellular automaton model for the behavior of limb bud precartilage mesenchymal cells undergoing chondrogenic patterning. This "agent-oriented" model represents cells by points on a lattice that obey rules motivated by experimental findings. The "cells" follow these rules as autonomous agents, interacting with other cells and with the microenvironments cell activities produce. The rules include random cell motion, production and lateral deposition of a substrate adhesion molecule (SAM, corresponding to fibronectin), production and release of a diffusible growth factor ("activator," corresponding to TGF-beta) that stimulates production of the SAM, and another diffusible factor ("inhibitor") that suppresses the activity of the activator. We implemented the cellular automaton on a two-dimensional (2D) square lattice to emulate the quasi-2D micromass culture extensively used to study patterning in avian limb bud precartilage cells. We identified parameters that produce nodular patterns that resemble, in size and distribution, cell condensations in leg-cell cultures, thus establishing a correspondence between in vitro and in silico results. We then studied the in vitro and in silico micromass cultures experimentally. We altered the standard in vitro micromass culture by diluting the initial cell density, transiently exposing it to exogenous activator, suppressing the inhibitor, and constitutively activating fibronectin production. We altered the standard in silico micromass culture in each case by changing the corresponding parameter. In vitro and in silico experiments agreed well. We also used the model to test hypotheses for differences in the in vitro patterns of cells derived from chick embryo forelimb and hindlimb. We discuss the applicability of this model to limb development in vivo and to other organ development.

Two-stage aggregate formation via streams in myxobacteria

In response to adverse conditions, myxobacteria form aggregates that develop into fruiting bodies. We model myxobacteria aggregation with a lattice cell model based entirely on short-range (nonchemotactic) cell-cell interactions. Local rules result in a two-stage process of aggregation mediated by transient streams. Aggregates resemble those observed in experiment and are stable against even very large perturbations. Noise in individual cell behavior increases the effects of streams and results in larger, more stable aggregates.