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.

Combined computational modeling and experimental study of the biomechanical mechanisms of platelet-driven contraction of fibrin clots.

While blood clot formation has been relatively well studied, little is known about the mechanisms underlying the subsequent structural and mechanical clot remodeling called contraction or retraction. Impairment of the clot contraction process is associated with both life-threatening bleeding and thrombotic conditions, such as ischemic stroke, venous thromboembolism, and others. Recently, blood clot contraction was observed to be hindered in patients with COVID-19. A three-dimensional multiscale computational model is developed and used to quantify biomechanical mechanisms of the kinetics of clot contraction driven by platelet-fibrin pulling interactions. These results provide important biological insights into contraction of platelet filopodia, the mechanically active thin protrusions of the plasma membrane, described previously as performing mostly a sensory function. The biomechanical mechanisms and modeling approach described can potentially apply to studying other systems in which cells are embedded in a filamentous network and exert forces on the extracellular matrix modulated by the substrate stiffness.

Role of turgor-pressure induced boundary tension in the maintenance of the shoot apical meristem of Arabidopsis thaliana.

In plants, the robust maintenance of tissue structure is crucial to supporting its functionality. The multi-layered shoot apical meristem (SAM) of Arabidopsis, containing stem cells, is an approximately radially symmetric tissue whose shape and structure is maintained throughout the life of the plant. In this paper, a new biologically calibrated pseudo-three-dimensional (P3D) computational model of a longitudinal section of the SAM is developed. It includes anisotropic expansion and division of cells out of the cross-section plane, as well as representation of tension experienced by the SAM epidermis. Results from the experimentally calibrated P3D model provide new insights into maintenance of the structure of the SAM epidermal cell monolayer under tension and quantify dependence of epidermal and subepidermal cell anisotropy on the amount of tension. Moreover, the model simulations revealed that out-of-plane cell growth is important in offsetting cell crowding and regulating mechanical stresses experienced by tunica cells. Predictive model simulations show that tension-determined cell division plane orientation in the apical corpus may be regulating cell and tissue shape distributions needed for maintaining structure of the wild-type SAM. This suggests that cells' responses to local mechanical cues may serve as a mechanism to regulate cell- and tissue-scale patterning.

A multiscale chemical-mechanical model predicts impact of morphogen spreading on tissue growth.

The exact mechanism controlling cell growth remains a grand challenge in developmental biology and regenerative medicine. The Drosophila wing disc tissue serves as an ideal biological model to study mechanisms involved in growth regulation. Most existing computational models for studying tissue growth focus specifically on either chemical signals or mechanical forces. Here we developed a multiscale chemical-mechanical model to investigate the growth regulation mechanism based on the dynamics of a morphogen gradient. By comparing the spatial distribution of dividing cells and the overall tissue shape obtained in model simulations with experimental data of the wing disc, it is shown that the size of the domain of the Dpp morphogen is critical in determining tissue size and shape. A larger tissue size with a faster growth rate and more symmetric shape can be achieved if the Dpp gradient spreads in a larger domain. Together with Dpp absorbance at the peripheral zone, the feedback regulation that downregulates Dpp receptors on the cell membrane allows for further spreading of the morphogen away from its source region, resulting in prolonged tissue growth at a more spatially homogeneous growth rate.

Concentration-dependent transcriptional switching through a collective action of cis-elements.

Gene expression specificity of homeobox transcription factors has remained paradoxical. WUSCHEL activates and represses CLAVATA3 transcription at lower and higher concentrations, respectively. We use computational modeling and experimental analysis to investigate the properties of the cis-regulatory module. We find that intrinsically each cis-element can only activate CLAVATA3 at a higher WUSCHEL concentration. However, together, they repress CLAVATA3 at higher WUSCHEL and activate only at lower WUSCHEL, showing that the concentration-dependent interactions among cis-elements regulate both activation and repression. Biochemical experiments show that two adjacent functional cis-elements bind WUSCHEL with higher affinity and dimerize at relatively lower levels. Moreover, increasing the distance between cis-elements prolongs WUSCHEL monomer binding window, resulting in higher CLAVATA3 activation. Our work showing a constellation of optimally spaced cis-elements of defined affinities determining activation and repression thresholds in regulating CLAVATA3 transcription provides a previously unknown mechanism of cofactor-independent regulation of transcription factor binding in mediating gene expression specificity.

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 Biomechanical Modeling of Fibrin Networks and Platelet-Fiber Network Interactions.

Fibrin deformation and interaction of fibrin with other blood components play critical roles in hemostasis and thrombosis. In this review, computational and mathematical biomechanical models of fibrin network deformation and contraction at different spatio-temporal scales as well as challenges in developing and calibrating multiscale models are discussed. There are long standing challenges. For instance, applicability of models to identify and test potential mechanisms of the biomechanical processes mediating interactions between platelets and fiber networks in blood clot stretching and contraction needs to be examined carefully. How the structural and mechanical properties of major blood clot components influences biomechanical responses of the entire clot subjected to external forces, such as blood flow or vessel wall deformations needs to be investigated thoroughly.

Quantification of microtubule stutters: dynamic instability behaviors that are strongly associated with catastrophe.

Microtubules (MTs) are cytoskeletal fibers that undergo dynamic instability (DI), a remarkable process involving phases of growth and shortening separated by stochastic transitions called catastrophe and rescue. Dissecting DI mechanism(s) requires first characterizing and quantifying these dynamics, a subjective process that often ignores complexity in MT behavior. We present a Statistical Tool for Automated Dynamic Instability Analysis (STADIA) that identifies and quantifies not only growth and shortening, but also a category of intermediate behaviors that we term "stutters." During stutters, the rate of MT length change tends to be smaller in magnitude than during typical growth or shortening phases. Quantifying stutters and other behaviors with STADIA demonstrates that stutters precede most catastrophes in our in vitro experiments and dimer-scale MT simulations, suggesting that stutters are mechanistically involved in catastrophes. Related to this idea, we show that the anticatastrophe factor CLASP2γ works by promoting the return of stuttering MTs to growth. STADIA enables more comprehensive and data-driven analysis of MT dynamics compared with previous methods. The treatment of stutters as distinct and quantifiable DI behaviors provides new opportunities for analyzing mechanisms of MT dynamics and their regulation by binding proteins.

CLAVATA3 mediated simultaneous control of transcriptional and post-translational processes provides robustness to the WUSCHEL gradient.

Regulation of the homeodomain transcription factor WUSCHEL concentration is critical for stem cell homeostasis in Arabidopsis shoot apical meristems. WUSCHEL regulates the transcription of CLAVATA3 through a concentration-dependent activation-repression switch. CLAVATA3, a secreted peptide, activates receptor kinase signaling to repress WUSCHEL transcription. Considering the revised regulation, CLAVATA3 mediated repression of WUSCHEL transcription alone will lead to an unstable system. Here we show that CLAVATA3 signaling regulates nuclear-cytoplasmic partitioning of WUSCHEL to control nuclear levels and its diffusion into adjacent cells. Our work also reveals that WUSCHEL directly interacts with EXPORTINS via EAR-like domain which is also required for destabilizing WUSCHEL in the cytoplasm. We develop a combined experimental and computational modeling approach that integrates CLAVATA3-mediated transcriptional repression of WUSCHEL and post-translational control of nuclear levels with the WUSCHEL concentration-dependent regulation of CLAVATA3. We show that the dual control by the same signal forms a seamless connection between de novo WUSCHEL synthesis and sub-cellular partitioning in providing robustness to the WUSCHEL gradient.

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.

Multiscale modeling meets machine learning: What can we learn?

Machine learning is increasingly recognized as a promising technology in the biological, biomedical, and behavioral sciences. There can be no argument that this technique is incredibly successful in image recognition with immediate applications in diagnostics including electrophysiology, radiology, or pathology, where we have access to massive amounts of annotated data. However, machine learning often performs poorly in prognosis, especially when dealing with sparse data. This is a field where classical physics-based simulation seems to remain irreplaceable. In this review, we identify areas in the biomedical sciences where machine learning and multiscale modeling can mutually benefit from one another: Machine learning can integrate physics-based knowledge in the form of governing equations, boundary conditions, or constraints to manage ill-posted problems and robustly handle sparse and noisy data; multiscale modeling can integrate machine learning to create surrogate models, identify system dynamics and parameters, analyze sensitivities, and quantify uncertainty to bridge the scales and understand the emergence of function. With a view towards applications in the life sciences, we discuss the state of the art of combining machine learning and multiscale modeling, identify applications and opportunities, raise open questions, and address potential challenges and limitations. We anticipate that it will stimulate discussion within the community of computational mechanics and reach out to other disciplines including mathematics, statistics, computer science, artificial intelligence, biomedicine, systems biology, and precision medicine to join forces towards creating robust and efficient models for biological systems.

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.

Enzyme activities predicted by metabolite concentrations and solvent capacity in the cell.

Experimental measurements or computational model predictions of the post-translational regulation of enzymes needed in a metabolic pathway is a difficult problem. Consequently, regulation is mostly known only for well-studied reactions of central metabolism in various model organisms. In this study, we use two approaches to predict enzyme regulation policies and investigate the hypothesis that regulation is driven by the need to maintain the solvent capacity in the cell. The first predictive method uses a statistical thermodynamics and metabolic control theory framework while the second method is performed using a hybrid optimization-reinforcement learning approach. Efficient regulation schemes were learned from experimental data that either agree with theoretical calculations or result in a higher cell fitness using maximum useful work as a metric. As previously hypothesized, regulation is herein shown to control the concentrations of both immediate and downstream product concentrations at physiological levels. Model predictions provide the following two novel general principles: (1) the regulation itself causes the reactions to be much further from equilibrium instead of the common assumption that highly non-equilibrium reactions are the targets for regulation; and (2) the minimal regulation needed to maintain metabolite levels at physiological concentrations maximizes the free energy dissipation rate instead of preserving a specific energy charge. The resulting energy dissipation rate is an emergent property of regulation which may be represented by a high value of the adenylate energy charge. In addition, the predictions demonstrate that the amount of regulation needed can be minimized if it is applied at the beginning or branch point of a pathway, in agreement with common notions. The approach is demonstrated for three pathways in the central metabolism of E. coli (gluconeogenesis, glycolysis-tricarboxylic acid (TCA) and pentose phosphate-TCA) that each require different regulation schemes. It is shown quantitatively that hexokinase, glucose 6-phosphate dehydrogenase and glyceraldehyde phosphate dehydrogenase, all branch points of pathways, play the largest roles in regulating central metabolism.

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.

Behaviors of individual microtubules and microtubule populations relative to critical concentrations: dynamic instability occurs when critical concentrations are driven apart by nucleotide hydrolysis.

The concept of critical concentration (CC) is central to understanding the behavior of microtubules (MTs) and other cytoskeletal polymers. Traditionally, these polymers are understood to have one CC, measured in multiple ways and assumed to be the subunit concentration necessary for polymer assembly. However, this framework does not incorporate dynamic instability (DI), and there is work indicating that MTs have two CCs. We use our previously established simulations to confirm that MTs have (at least) two experimentally relevant CCs and to clarify the behavior of individuals and populations relative to the CCs. At free subunit concentrations above the lower CC (CCElongation), growth phases of individual filaments can occur transiently; above the higher CC (CCNetAssembly), the population's polymer mass will increase persistently. Our results demonstrate that most experimental CC measurements correspond to CCNetAssembly, meaning that "typical" DI occurs below the concentration traditionally considered necessary for polymer assembly. We report that [free tubulin] at steady state does not equal CCNetAssembly, but instead approaches CCNetAssembly asymptotically as [total tubulin] increases, and depends on the number of stable MT nucleation sites. We show that the degree of separation between CCElongation and CCNetAssembly depends on the rate of nucleotide hydrolysis. This clarified framework helps explain and unify many experimental observations.

Integrating machine learning and multiscale modeling-perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences.

Fueled by breakthrough technology developments, the biological, biomedical, and behavioral sciences are now collecting more data than ever before. There is a critical need for time- and cost-efficient strategies to analyze and interpret these data to advance human health. The recent rise of machine learning as a powerful technique to integrate multimodality, multifidelity data, and reveal correlations between intertwined phenomena presents a special opportunity in this regard. However, machine learning alone ignores the fundamental laws of physics and can result in ill-posed problems or non-physical solutions. Multiscale modeling is a successful strategy to integrate multiscale, multiphysics data and uncover mechanisms that explain the emergence of function. However, multiscale modeling alone often fails to efficiently combine large datasets from different sources and different levels of resolution. Here we demonstrate that machine learning and multiscale modeling can naturally complement each other to create robust predictive models that integrate the underlying physics to manage ill-posed problems and explore massive design spaces. We review the current literature, highlight applications and opportunities, address open questions, and discuss potential challenges and limitations in four overarching topical areas: ordinary differential equations, partial differential equations, data-driven approaches, and theory-driven approaches. Towards these goals, we leverage expertise in applied mathematics, computer science, computational biology, biophysics, biomechanics, engineering mechanics, experimentation, and medicine. Our multidisciplinary perspective suggests that integrating machine learning and multiscale modeling can provide new insights into disease mechanisms, help identify new targets and treatment strategies, and inform decision making for the benefit of human health.

Contribution of nascent cohesive fiber-fiber interactions to the non-linear elasticity of fibrin networks under tensile load.

Fibrin is a viscoelastic proteinaceous polymer that determines the deformability and integrity of blood clots and fibrin-based biomaterials in response to biomechanical forces. Here, a previously unnoticed structural mechanism of fibrin clots' mechanical response to external tensile loads is tested using high-resolution confocal microscopy and recently developed three-dimensional computational model. This mechanism, underlying local strain-stiffening of individual fibers as well as global stiffening of the entire network, is based on previously neglected nascent cohesive pairwise interactions between individual fibers (crisscrossing) in fibrin networks formed under tensile load. Existence of fiber-fiber crisscrossings of reoriented fibers was confirmed using 3D imaging of experimentally obtained stretched fibrin clots. The computational model enabled us to study structural details and quantify mechanical effects of the fiber-fiber cohesive crisscrossing during stretching of fibrin gels at various spatial scales. The contribution of the fiber-fiber cohesive contacts to the elasticity of stretched fibrin networks was characterized by changes in individual fiber stiffness, the length, width, and alignment of fibers, as well as connectivity and density of the entire network. The results show that the nascent cohesive crisscrossing of fibers in stretched fibrin networks comprise an underappreciated important structural mechanism underlying the mechanical response of fibrin to (patho)physiological stresses that determine the course and outcomes of thrombotic and hemostatic disorders, such as heart attack and ischemic stroke. STATEMENT OF SIGNIFICANCE: Fibrin is a viscoelastic proteinaceous polymer that determines the deformability and integrity of blood clots and fibrin-based biomaterials in response to biomechanical forces. In this paper, a novel structural mechanism of fibrin clots' mechanical response to external tensile loads is tested using high-resolution confocal microscopy and newly developed computational model. This mechanism, underlying local strain-stiffening of individual fibers as well as global stiffening of the entire network, is based on previously neglected nascent cohesive pairwise interactions between individual fibers (crisscrossing) in fibrin networks formed under tensile load. Cohesive crisscrossing is an important structural mechanism that influences the mechanical response of blood clots and which can determine the outcomes of blood coagulation disorders, such as heart attacks and strokes.

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.