Probabilistic and maximum entropy modeling of chemical reaction systems: Characteristics and comparisons to mass action kinetic models.

We demonstrate and characterize a first-principles approach to modeling the mass action dynamics of metabolism. Starting from a basic definition of entropy expressed as a multinomial probability density using Boltzmann probabilities with standard chemical potentials, we derive and compare the free energy dissipation and the entropy production rates. We express the relation between entropy production and the chemical master equation for modeling metabolism, which unifies chemical kinetics and chemical thermodynamics. Because prediction uncertainty with respect to parameter variability is frequently a concern with mass action models utilizing rate constants, we compare and contrast the maximum entropy model, which has its own set of rate parameters, to a population of standard mass action models in which the rate constants are randomly chosen. We show that a maximum entropy model is characterized by a high probability of free energy dissipation rate and likewise entropy production rate, relative to other models. We then characterize the variability of the maximum entropy model predictions with respect to uncertainties in parameters (standard free energies of formation) and with respect to ionic strengths typically found in a cell.

Combined computational modeling and experimental analysis integrating chemical and mechanical signals suggests possible mechanism of shoot meristem maintenance.

Stem cell maintenance in multilayered shoot apical meristems (SAMs) of plants requires strict regulation of cell growth and division. Exactly how the complex milieu of chemical and mechanical signals interact in the central region of the SAM to regulate cell division plane orientation is not well understood. In this paper, simulations using a newly developed multiscale computational model are combined with experimental studies to suggest and test three hypothesized mechanisms for the regulation of cell division plane orientation and the direction of anisotropic cell expansion in the corpus. Simulations predict that in the Apical corpus, WUSCHEL and cytokinin regulate the direction of anisotropic cell expansion, and cells divide according to tensile stress on the cell wall. In the Basal corpus, model simulations suggest dual roles for WUSCHEL and cytokinin in regulating both the direction of anisotropic cell expansion and cell division plane orientation. Simulation results are followed by a detailed analysis of changes in cell characteristics upon manipulation of WUSCHEL and cytokinin in experiments that support model predictions. Moreover, simulations predict that this layer-specific mechanism maintains both the experimentally observed shape and structure of the SAM as well as the distribution of WUSCHEL in the tissue. This provides an additional link between the roles of WUSCHEL, cytokinin, and mechanical stress in regulating SAM growth and proper stem cell maintenance in the SAM.

Computational modeling of blood component transport related to coronary artery thrombosis in Kawasaki disease.

Coronary artery thrombosis is the major risk associated with Kawasaki disease (KD). Long-term management of KD patients with persistent aneurysms requires a thrombotic risk assessment and clinical decisions regarding the administration of anticoagulation therapy. Computational fluid dynamics has demonstrated that abnormal KD coronary artery hemodynamics can be associated with thrombosis. However, the underlying mechanisms of clot formation are not yet fully understood. Here we present a new model incorporating data from patient-specific simulated velocity fields to track platelet activation and accumulation. We use a system of Reaction-Advection-Diffusion equations solved with a stabilized finite element method to describe the evolution of non-activated platelets and activated platelet concentrations [AP], local concentrations of adenosine diphosphate (ADP) and poly-phosphate (PolyP). The activation of platelets is modeled as a function of shear-rate exposure and local concentration of agonists. We compared the distribution of activated platelets in a healthy coronary case and six cases with coronary artery aneurysms caused by KD, including three with confirmed thrombosis. Results show spatial correlation between regions of higher concentration of activated platelets and the reported location of the clot, suggesting predictive capabilities of this model towards identifying regions at high risk for thrombosis. Also, the concentration levels of ADP and PolyP in cases with confirmed thrombosis are higher than the reported critical values associated with platelet aggregation (ADP) and activation of the intrinsic coagulation pathway (PolyP). These findings suggest the potential initiation of a coagulation pathway even in the absence of an extrinsic factor. Finally, computational simulations show that in regions of flow stagnation, biochemical activation, as a result of local agonist concentration, is dominant. Identifying the leading factors to a pro-coagulant environment in each case-mechanical or biochemical-could help define improved strategies for thrombosis prevention tailored for each patient.

Epithelial organ shape is generated by patterned actomyosin contractility and maintained by the extracellular matrix.

Epithelial sheets define organ architecture during development. Here, we employed an iterative multiscale computational modeling and quantitative experimental approach to decouple direct and indirect effects of actomyosin-generated forces, nuclear positioning, extracellular matrix, and cell-cell adhesion in shaping Drosophila wing imaginal discs. Basally generated actomyosin forces generate epithelial bending of the wing disc pouch. Surprisingly, acute pharmacological inhibition of ROCK-driven actomyosin contractility does not impact the maintenance of tissue height or curved shape. Computational simulations show that ECM tautness provides only a minor contribution to modulating tissue shape. Instead, passive ECM pre-strain serves to maintain the shape independent from actomyosin contractility. These results provide general insight into how the subcellular forces are generated and maintained within individual cells to induce tissue curvature. Thus, the results suggest an important design principle of separable contributions from ECM prestrain and actomyosin tension during epithelial organogenesis and homeostasis.

Role of combined cell membrane and wall mechanical properties regulated by polarity signals in cell budding.

Budding yeast, Saccharomyces cerevisiae, serves as a prime biological model to study mechanisms underlying asymmetric growth. Previous studies have shown that prior to bud emergence, polarization of a conserved small GTPase Cdc42 must be established on the cell membrane of a budding yeast. Additionally, such polarization contributes to the delivery of cell wall remodeling enzymes and hydrolase from cytosol through the membrane, to change the mechanical properties of the cell wall. This leads to the hypothesis that Cdc42 and its associated proteins at least indirectly regulate cell surface mechanical properties. However, how the surface mechanical properties in the emerging bud are changed and whether such change is important are not well understood. To test several hypothesised mechanisms, a novel three-dimensional coarse-grained particle-based model has been developed which describes inhomogeneous mechanical properties of the cell surface. Model simulations predict alternation of the levels of stretching and bending stiffness of the cell surface in the bud region by the polarized Cdc42 signals is essential for initiating bud formation. Model simulations also suggest that bud shape depends strongly on the distribution of the polarized signaling molecules while the neck width of the emerging bud is strongly impacted by the mechanical properties of the chitin and septin rings. Moreover, the temporal change of the bud mechanical properties is shown to affect the symmetry of the bud shape. The 3D model of asymmetric cell growth can also be used for studying viral budding and other vegetative reproduction processes performed via budding, as well as detailed studies of cell growth.

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 αIIbß3 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.

Cell-Based Model of the Generation and Maintenance of the Shape and Structure of the Multilayered Shoot Apical Meristem of Arabidopsis thaliana.

One of the central problems in animal and plant developmental biology is deciphering how chemical and mechanical signals interact within a tissue to produce organs of defined size, shape, and function. Cell walls in plants impose a unique constraint on cell expansion since cells are under turgor pressure and do not move relative to one another. Cell wall extensibility and constantly changing distribution of stress on the wall are mechanical properties that vary between individual cells and contribute to rates of expansion and orientation of cell division. How exactly cell wall mechanical properties influence cell behavior is still largely unknown. To address this problem, a novel, subcellular element computational model of growth of stem cells within the multilayered shoot apical meristem (SAM) of Arabidopsis thaliana is developed and calibrated using experimental data. Novel features of the model include separate, detailed descriptions of cell wall extensibility and mechanical stiffness, deformation of the middle lamella, and increase in cytoplasmic pressure generating internal turgor pressure. The model is used to test novel hypothesized mechanisms of formation of the shape and structure of the growing, multilayered SAM based on WUS concentration of individual cells controlling cell growth rates and layer-dependent anisotropic mechanical properties of subcellular components of individual cells determining anisotropic cell expansion directions. Model simulations also provide a detailed prediction of distribution of stresses in the growing tissue which can be tested in future experiments.

Multi-scale computational study of the mechanical regulation of cell mitotic rounding in epithelia.

Mitotic rounding during cell division is critical for preventing daughter cells from inheriting an abnormal number of chromosomes, a condition that occurs frequently in cancer cells. Cells must significantly expand their apical area and transition from a polygonal to circular apical shape to achieve robust mitotic rounding in epithelial tissues, which is where most cancers initiate. However, how cells mechanically regulate robust mitotic rounding within packed tissues is unknown. Here, we analyze mitotic rounding using a newly developed multi-scale subcellular element computational model that is calibrated using experimental data. Novel biologically relevant features of the model include separate representations of the sub-cellular components including the apical membrane and cytoplasm of the cell at the tissue scale level as well as detailed description of cell properties during mitotic rounding. Regression analysis of predictive model simulation results reveals the relative contributions of osmotic pressure, cell-cell adhesion and cortical stiffness to mitotic rounding. Mitotic area expansion is largely driven by regulation of cytoplasmic pressure. Surprisingly, mitotic shape roundness within physiological ranges is most sensitive to variation in cell-cell adhesivity and stiffness. An understanding of how perturbed mechanical properties impact mitotic rounding has important potential implications on, amongst others, how tumors progressively become more genetically unstable due to increased chromosomal aneuploidy and more aggressive.

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.

Sizing it up: the mechanical feedback hypothesis of organ growth regulation.

The question of how the physical dimensions of animal organs are specified has long fascinated both experimentalists and computational scientists working in the field of developmental biology. Research over the last few decades has identified many of the genes and signaling pathways involved in organizing the emergent multi-scale features of growth and homeostasis. However, an integrated model of organ growth regulation is still unrealized due to the numerous feedback control loops found within and between intercellular signaling pathways as well as a lack of understanding of the exact role of mechanotransduction. Here, we review several computational and experimental studies that have investigated the mechanical feedback hypothesis of organ growth control, which postulates that mechanical forces are important for regulating the termination of growth and hence the final physical dimensions of organs. In particular, we highlight selected computational studies that have focused on the regulation of growth of the Drosophila wing imaginal disc. In many ways, these computational and theoretical approaches continue to guide experimental inquiry. We demonstrate using several examples how future progress in dissecting the crosstalk between the genetic and biophysical mechanisms controlling organ growth might depend on the close coupling between computational and experimental approaches, as well as comparison of growth control mechanisms in other systems.

Mechanism for the catastrophe-promoting activity of the microtubule destabilizer Op18/stathmin.

Regulation of microtubule dynamic instability is crucial for cellular processes, ranging from mitosis to membrane transport. Stathmin (also known as oncoprotein 18/Op18) is a prominent microtubule destabilizer that acts preferentially on microtubule minus ends. Stathmin has been studied intensively because of its association with multiple types of cancer, but its mechanism of action remains controversial. Two models have been proposed. One model is that stathmin promotes microtubule catastrophe indirectly, and does so by sequestering tubulin; the other holds that stathmin alters microtubule dynamics by directly destabilizing growing microtubules. Stathmin's sequestration activity is well established, but the mechanism of any direct action is mysterious because stathmin binds to microtubules very weakly. To address these issues, we have studied interactions between stathmin and varied tubulin polymers. We show that stathmin binds tightly to Dolastatin-10 tubulin rings, which mimic curved tubulin protofilaments, and that stathmin depolymerizes stabilized protofilament-rich polymers. These observations lead us to propose that stathmin promotes catastrophe by binding to and acting upon protofilaments exposed at the tips of growing microtubules. Moreover, we suggest that stathmin's minus-end preference results from interactions between stathmin's N terminus and the surface of α-tubulin that is exposed only at the minus end. Using computational modeling of microtubule dynamics, we show that these mechanisms could account for stathmin's observed activities in vitro, but that both the direct and sequestering activities are likely to be relevant in a cellular context. Taken together, our results suggest that stathmin can promote catastrophe by direct action on protofilament structure and interactions.

Cell division resets polarity and motility for the bacterium Myxococcus xanthus.

Links between cell division and other cellular processes are poorly understood. It is difficult to simultaneously examine division and function in most cell types. Most of the research probing aspects of cell division has experimented with stationary or immobilized cells or distinctly asymmetrical cells. Here we took an alternative approach by examining cell division events within motile groups of cells growing on solid medium by time-lapse microscopy. A total of 558 cell divisions were identified among approximately 12,000 cells. We found an interconnection of division, motility, and polarity in the bacterium Myxococcus xanthus. For every division event, motile cells stop moving to divide. Progeny cells of binary fission subsequently move in opposing directions. This behavior involves M. xanthus Frz proteins that regulate M. xanthus motility reversals but is independent of type IV pilus "S motility." The inheritance of opposing polarity is correlated with the distribution of the G protein RomR within these dividing cells. The constriction at the point of division limits the intracellular distribution of RomR. Thus, the asymmetric distribution of RomR at the parent cell poles becomes mirrored at new poles initiated at the site of division.

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.

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.

Systems biology of platelet-vessel wall interactions.

Platelets are small, anucleated cells that participate in primary hemostasis by forming a hemostatic plug at the site of a blood vessel's breach, preventing blood loss. However, hemostatic events can lead to excessive thrombosis, resulting in life-threatening strokes, emboli, or infarction. Development of multi-scale models coupling processes at several scales and running predictive model simulations on powerful computer clusters can help interdisciplinary groups of researchers to suggest and test new patient-specific treatment strategies.

Balancing competing effects of tissue growth and cytoskeletal regulation during Drosophila wing disc development.

How a developing organ robustly coordinates the cellular mechanics and growth to reach a final size and shape remains poorly understood. Through iterations between experiments and model simulations that include a mechanistic description of interkinetic nuclear migration, we show that the local curvature, height, and nuclear positioning of cells in the Drosophila wing imaginal disc are defined by the concurrent patterning of actomyosin contractility, cell-ECM adhesion, ECM stiffness, and interfacial membrane tension. We show that increasing cell proliferation via different growth-promoting pathways results in two distinct phenotypes. Triggering proliferation through insulin signaling increases basal curvature, but an increase in growth through Dpp signaling and Myc causes tissue flattening. These distinct phenotypic outcomes arise from differences in how each growth pathway regulates the cellular cytoskeleton, including contractility and cell-ECM adhesion. The coupled regulation of proliferation and cytoskeletal regulators is a general strategy to meet the multiple context-dependent criteria defining tissue morphogenesis.

Study of Impacts of Two Types of Cellular Aging on the Yeast Bud Morphogenesis.

Understanding the mechanisms of cellular aging processes is crucial for attempting to extend organismal lifespan and for studying age-related degenerative diseases. Yeast cells divide through budding, providing a classical biological model for studying cellular aging. With their powerful genetics, relatively short lifespan and well-established signaling pathways also found in animals, yeast cells offer valuable insights into the aging process. Recent experiments suggested the existence of two aging modes in yeast characterized by nucleolar and mitochondrial declines, respectively. In this study, by analyzing experimental data it was shown that cells evolving into those two aging modes behave differently when they are young. While buds grow linearly in both modes, cells that consistently generate spherical buds throughout their lifespan demonstrate greater efficacy in controlling bud size and growth rate at young ages. A three-dimensional chemical-mechanical model was developed and used to suggest and test hypothesized mechanisms of bud morphogenesis during aging. Experimentally calibrated simulations showed that tubular bud shape in one aging mode could be generated by locally inserting new materials at the bud tip guided by the polarized Cdc42 signal during the early stage of budding. Furthermore, the aspect ratio of the tubular bud could be stabilized during the late stage, as observed in experiments, through a reduction on the new cell surface material insertion or an expansion of the polarization site. Thus model simulations suggest the maintenance of new cell surface material insertion or chemical signal polarization could be weakened due to cellular aging in yeast and other cell types.

Interconnected cavernous structure of bacterial fruiting bodies.

The formation of spore-filled fruiting bodies by myxobacteria is a fascinating case of multicellular self-organization by bacteria. The organization of Myxococcus xanthus into fruiting bodies has long been studied not only as an important example of collective motion of bacteria, but also as a simplified model for developmental morphogenesis. Sporulation within the nascent fruiting body requires signaling between moving cells in order that the rod-shaped self-propelled cells differentiate into spores at the appropriate time. Probing the three-dimensional structure of myxobacteria fruiting bodies has previously presented a challenge due to limitations of different imaging methods. A new technique using Infrared Optical Coherence Tomography (OCT) revealed previously unknown details of the internal structure of M. xanthus fruiting bodies consisting of interconnected pockets of relative high and low spore density regions. To make sense of the experimentally observed structure, modeling and computer simulations were used to test a hypothesized mechanism that could produce high-density pockets of spores. The mechanism consists of self-propelled cells aligning with each other and signaling by end-to-end contact to coordinate the process of differentiation resulting in a pattern of clusters observed in the experiment. The integration of novel OCT experimental techniques with computational simulations can provide new insight into the mechanisms that can give rise to the pattern formation seen in other biological systems such as dictyostelids, social amoeba known to form multicellular aggregates observed as slugs under starvation conditions.

Continuum modeling of clustering of myxobacteria.

In this paper we develop a continuum theory of clustering in ensembles of self-propelled inelastically colliding rods with applications to collective dynamics of common gliding bacteria Myxococcus Xanthus. A multiphase hydrodynamic model that couples densities of oriented and isotropic phases is described. This model is used for the analysis of an instability that leads to spontaneous formation of directionally moving dense clusters within initially dilute isotropic "gas" of myxobacteria. Numerical simulations of this model confirm the existence of stationary dense moving clusters and also elucidate the properties of their collisions. The results are shown to be in a qualitative agreement with experiments.