Padmini Rangamani

Cell shape and mechanics are intricately connected and tightly regulated by mechanochemical events including biochemical signaling, cytoskeletal remodeling, and plasma membrane mechanics. While experimental advances in microscopy have shed light on the intricate coordination involved in cell shape change in response to different cues, the ability to conduct three-dimensional simulations in realistic geometries remains an open computational challenge. In this work, we develop a finite-element framework that incorporates advection-diffusion-reaction equations coupled with equations governing the kinematics of a deformable interface representing the cell membrane. We applied this framework to three distinct coupled mechanochemical systems, each governed by geometric partial differential equations, resulting in large deformations of the interface. In all three examples, our simulations revealed the emergence of feedback between cellular signaling, cytoskeletal organization, and cell shape. In our first two sets of simulations, we observed that cell migration and neutrophil protrusion were regulated by membrane tension-mediated feedback. In our final application, we predicted shape changes of a dendritic spine starting from a realistic geometry, and found that the complex shape of the spine gives rise to localized regimes of actin cytoskeleton remodeling not previously observed with idealized geometries. Thus, our finite-element framework allows us to generate new mechanistic insights for biophysical problems.

Abstract Exercise stimulates skeletal muscle signalling and mitochondrial metabolism. Emerging evidence shows that mitochondrial dynamics (i.e. fission and fusion) could be regulated by exercise. Yet, key gaps remain in identifying (i) the signals that drive fission vs . fusion; (ii) how energy status and reactive oxygen species (ROS) shift control between dynamin‐related protein 1 (DRP1) and mitofusin (MFN)/optic atrophy 1 (OPA1); and (iii) which intensity–duration combinations yield similar cytosolic signals but different mitochondrial remodelling. Therefore, we developed an integrative computational framework connecting exercise regimens to mitochondria fission–fusion machinery by linking blood–myofibre energetics in cytosol and mitochondria to signalling pathways. The influence of sprint, resistance and endurance exercise regimens on mitochondrial fission and fusion has been simulated. Classified qualitative validation of the signalling network model achieved 80% accuracy. The model predicts regimen‐specific dynamics starting with an acute DRP1‐driven fission during exercise followed by MFN1/2–OPA1‐mediated re‐fusion as energy stress declines, consistent with a cyclical triage‐then‐rebuild paradigm. Changes are most pronounced and sustained with endurance, sharp but brief with sprint, and minimal with resistance. Global sensitivity analysis identified AMP‐activated protein kinase (AMPK)/peroxisome proliferator‐activated receptor gamma coactivator‐1α→MFN1/2 as dominant fusion drivers, ROS and AMPK→mitochondrial fission factor/DRP1 as primary fission switches, and Ca 2 + –calmodulin, extracellular‐signal‐regulated kinase and liver kinase B1/AMPK as shared regulators. The model predicts that an endurance base, augmented with one or two weekly high intensity interval training/sprint interval training sessions could maximize AMPK–ROS pulses and mitochondrial fission–fusion. This framework unifies muscle's signalling logic with energetic state to explain how intensity–volume combinations, bout spacing and kinase modulation tune mitochondrial remodelling, yielding testable predictions for optimizing training and adjuvant therapies to enhance mitochondrial quality and performance. image Key points Different exercise regimes such as sprint, resistance, and endurance can trigger different signalling pathways. Exercise also triggers mitochondrial remodelling in skeletal muscle. Using a systems biology model, we developed a systems biology model for skeletal muscle signalling and mitochondrial metabolism for exercise. Our model predicts the dynamics of mitochondrial fusion and fission in different exercise regimes and identifies which signalling pathways dominassste these remodelling mechanisms.

Cellular morphodynamics requires solving systems of coupled partial differential equations on moving bulk and surface domains, where advection-dominant transport, structure preservation, and severe mesh distortions make robust simulation difficult. We present a holistic finite element framework that jointly addresses these obstacles for biophysical applications by combining model-agnostic structure-preserving postprocessing, ALE-based mesh redistribution strategies driven by surface-tangential velocities, and stabilized discretization for advection-diffusion-reaction problems tailored to evolving domains. The methodology is modular and applies to advection-diffusion-reaction systems, Cahn-Hilliard phase separation, Helfrich-type geometric flows, as well as their staggered and potentially mixed-dimensional couplings. We provide a concise notation for evolving bulk and surface geometries, extend positivity-, bound-, and mass-preserving projections to moving meshes, and develop a two-step redistribution procedure that maintains element quality without remeshing. Convergence studies, manufactured solutions, and biologically motivated test cases -- including tumor-growth surrogates and phase segregation on deformable membranes -- demonstrate accuracy, stability, and versatility across the problem classes considered.

Human induced pluripotent stem cell-derived cardiomyocytes are valuable for studying cell-cell communication and synchronization, but remain immature and often lack robust electrical and mechanical coupling. To address this, we investigated gap junction-mediated communication and developed plasma membrane vesicles enriched in functional connexin hemichannels, termed Connectosomes, to enhance intercellular coupling. Connectosomes display properly oriented connexins and enrich the Cx43 expression at cell-cell borders between cardiomyocytes. Through mathematical modeling and experimental validation, we demonstrate that Connectosome incorporation reinforces endogenous gap junctions, promotes synchronous calcium transients, and improves spatial coordination of beating across networks. Mechanistic studies using engineered cell lines with tagged connexin-43 confirm that channel orientation and functionality are critical, supporting a model in which Connectosomes contribute to gap junction coupling. These results show that Connectosomes can synchronize the beating of immature cardiomyocytes by boosting electrochemical communication, laying the groundwork for future therapeutic advances.

1 Abstract Neuronal function requires precise spatial organization of mitochondria to meet localized energetic demand. However, the physical constraints governing mitochondrial transport in axons remain poorly defined. Bidirectional motor-driven trafficking inherently introduces the potential for collisions, but the implications of these interactions for transport failure and structural damage are not understood. Here, we develop an agent-based model that couples mitochondrial motility, morphology, and lifecycle dynamics to a deformable axonal boundary. We show that mitochondrial traffic jams emerge from a force balance between active propulsion and steric interactions, and that their severity is governed by organelle shape and mechanical properties. Elongated, mechanically rigid mitochondria remain aligned and are transported rapidly, whereas flexible, low-aspect-ratio mitochondria are prone to jamming and accumulation. Incorporating fission and fusion dynamics reveals that fission amplifies transport disruption by generating collision-prone populations, while fusion restores transport by producing anisotropic structures that navigate crowded environments more efficiently. Importantly, we find that sustained jamming generates mechanical stress on the axonal membrane, leading to deformation and swelling. Together, these results establish a physical framework linking mitochondrial dynamics to axonal integrity and provide testable predictions for how dysregulated fission-fusion balance can drive transport failure and structural pathology in neurons. 2 Significance Axonal deformation is implicated in myriad neurodegenerative conditions. Mitochondrial transport disruption is inextricably linked to axonal deformation and disease progression. Mechanistic understanding of the interplay between mitochondrial transport and axon stability remains opaque. Here, we developed an agent-based model of mitochondrial transport through axons. We found that mitochondria, driven to-ward presynapses for energy supply and toward the soma for repositioning or recycling, can collide, jam, and accumulate within axonal segments. The severity of jamming is sensitive to mitochondrial density as well as mechanical and morphological properties. Further, we found a balance between lifecycle dynamics including fission and fusion is paramount to maintaining homeostatic transport. Lastly, we predict that accumulated mitochondria can deform the axonal membrane, thereby elucidating a direct mechanical link between mitochondrial transport disruption and axonal deformation.

1 Abstract Nuclear envelope stretch and rupture are common to cell spreading and migration in a variety of microenvironments, leading to marked changes in nucleocytoplasmic transport. Predicting cell response to different mechanochemical cues that are transmitted to the nucleus remains an open problem in the field of mechanomedicine. We developed a predictive modeling framework to examine how nuclear deformation on substrates with different nanotopographies influences nucleocytoplasmic transport and rearrangement of the nuclear lamina. Using the finite element method, we simulated nuclear compression by the perinuclear actin cap on substrates with arrays of nanopillars, modeling the nuclear envelope as a nonlinear elastic structure and coupling deformations to a biochemical model of lamin remodeling and nucleocytoplasmic transport. These simulations predicted regions of high nuclear envelope stretch adjacent to cell-nanopillar contacts, leading to maximized nuclear envelope tension on small nanopillars spaced by 4-5 microns. We then considered the effects on nuclear transport of YAP and TAZ and found that increased nuclear compression led to YAP/TAZ nuclear localization in agreement with previous experiments. Furthermore, the simulated force load per lamin was maximized on nanopillar substrates with high nuclear stretch. The magnitude of this load was modulated by the rate of actin cap assembly and the overall expression level of lamin A/C – decreasing lamin content in the nuclear envelope led to a higher likelihood of rupture. We validated this prediction in subsequent experiments with lamin-depleted U2OS cells, establishing the central importance of lamin transport and microenvironment nanotopography to nuclear mechanotransduction. 2 Significance Cell nuclei commonly experience large strains, but existing computational models do not explain the coupling between such deformations and molecular transport. Here, we present a modeling framework that includes the mechanics of nuclear deformations and the reaction-transport of molecules within the cytoplasm, nuclear envelope, and nuclear interior. As a well-controlled setup for comparing experiments and simulations, we consider nuclear indentations exhibited by cells on nanopillar substrates. Our simulations recapitulate measurements of nuclear YAP/TAZ localization from the literature and predict that low-lamin cells experience higher force loads at the nuclear envelope. We validate this prediction experimentally, showing that lamin-depleted cells are more likely to exhibit nuclear rupture. Overall, our framework presents opportunities to predict nuclear mechanoadaptation to different microenvironments.

Caveolins are monotopic membrane proteins essential for caveolae formation and play a key role in signaling and lipid regulation. Recent structural studies show that caveolins assemble into amphipathic disc-shaped oligomers with a central β-barrel, an architecture conserved across species and distinct from other membrane-remodeling proteins. These discs embed in the membrane by displacing lipids from a single leaflet, inducing membrane curvature. However, the mechanism of disc-driven bending remains unresolved. Using cryo-electron tomography, structure-guided mutagenesis, and mammalian cell studies, we show that evolutionarily distinct caveolins differ dramatically in their ability to induce membrane curvature despite sharing a conserved global architecture. Through computational and theoretical analyses, we further demonstrate that patterning of hydrophobic residues along the outer rim of the disc of human Caveolin-1 induces the deformation of the surrounding leaflet, which, in turn, dictates membrane bending. Finally, we determine a 4.1 A resolution structure of human Caveolin-1 within heterologous caveolae in situ, revealing that the disc adopts a funnel-like conformation, further shaping membrane architecture. Together, these findings reveal fundamental structural principles that empower caveolins to sculpt and remodel cellular membranes.

Forces applied to cellular membranes lead to transient membrane tension gradients. The way membrane tension propagates away from the stimulus site into the membrane reservoir is a key property in cellular adaptation. However, it remains unclear how tension propagation in membranes is regulated and how it depends on the cell type. Here we investigate plasma membrane tension propagation in cultured Caenorhabditis elegans mechanosensory neurons. We show that tension propagation travels quickly and is restricted to a particular distance in neurites—projections from the cell body of a neuron. A biophysical model of tension propagation suggests that periodic obstacle density and arrangement play key roles in controlling the propagation of mechanical information. Our experiments show that tension propagation is strongly dependent on the intact actin and microtubule cytoskeleton, whereas membrane lipid properties have a minimal impact. In particular, organization of the α/β-spectrin network and the MEC-2 stomatin condensates in a periodic scaffold acts as barriers to tension propagation, limiting the spread of tension. Our findings suggest that restricting membrane tension propagation in space and time enables precise localized signalling, allowing a single neuron to process mechanical signals in multiple distinct domains and, thus, expanding its computational capacity. Propagation of membrane tension mediates communication on the membrane surface. It is now shown that membrane-bound obstacles can obstruct tension propagation, which helps to localize signalling.

Abstract Exercise stimulates skeletal muscle signaling and mitochondrial metabolism. Emerging evidence shows that mitochondrial dynamics (i.e., fission and fusion) could be regulated by exercise. Yet, there are knowledge gaps on the following questions: (i) which upstream signals are necessary and sufficient to bias mitochondria toward fission versus fusion? (ii) How does cellular energy status and ROS partition control between DRP1 and MFN/OPA1? And (iii) which combinations of intensity and duration produce similar cytosolic signals but distinct mitochondrial remodeling? To address these gaps, we developed an integrative computational framework that connects exercise regimens to mitochondria fission-fusion machinery by linking blood-myofiber energetics in cytosol and mitochondria to skeletal muscle signaling network. The influence of three exercise regimen (i.e., sprint, resistance, and endurance) on mitochondrial fission and fusion was simulated. Classified qualitative validation of signaling network model against studies not used in developing the model achieved 80% accuracy. The model predicts regimen-specific dynamics starting with acute DRP1-driven fission during exercise followed by MFN1/2–OPA1-mediated re-fusion as energy stress declines, consistent with a cyclical triage-then-rebuild paradigm. Changes are most pronounced and sustained with endurance, sharp but brief with sprint, and minimal with resistance. Global sensitivity analysis identified AMPK/PGC-1α→MFN1/2 as dominant fusion drivers, ROS and AMPK→MFF/DRP1 as primary fission switches, and Ca²⁺-calmodulin, ERK, and LKB1/AMPK as shared regulators of fission and fusion. Our model also predicts that an endurance base, augmented with 1–2 weekly high intensity interval traning (HIIT)/ sprint interval training (SIT) sessions could maximize AMPK-ROS pulses and mitochondrial fission-fusion. This framework unifies muscle’s signaling logic with the energetic state to explain how intensity-volume combinations, bout spacing, and kinase modulation tune mitochondrial remodeling, yielding testable predictions for optimizing training and adjuvant therapies for enhanced human performance.

We consider moving boundary problems for biophysics and introduce a new computational framework to handle the complexity of the bulk-surface PDEs. In our framework, interpretability is maintained by adapting the fast, generalizable and accurate structure preservation scheme in [29]. We show that mesh distortion is mitigated by adopting the pioneering work of [36], which is tied to an Arbitrary Lagrangian Eulerian (ALE) framework. We test our algorithms accuracy on moving surfaces with boundary for the following PDEs: advection-diffusion-reaction equations, phase-field models of Cahn-Hilliard type, and Helfrich energy gradient flows. We performed convergence studies for all the schemes introduced to demonstrate accuracy. We use a staggered approach to achieve coupling and further verify the convergence of this coupling using numerical experiments. Finally, we demonstrate broad applicability of our work by simulating state-of-the-art tests of biophysical models that involve membrane deformation.

AMP-activated protein kinase (AMPK) plays a key role in restoring cellular metabolic homeostasis after energy stress. Importantly, AMPK acts as a hub of metabolic signaling, integrating multiple inputs and acting on numerous downstream targets to activate catabolic processes and inhibit anabolic ones. Despite the importance of AMPK signaling, unlike other well-studied pathways, such as MAPK/ERK or NF-κB, only a handful of mechanistic models of AMPK signaling have been developed. Epistemic uncertainty in the biochemical mechanism of AMPK activation, combined with the complexity of the AMPK pathway, makes model development particularly challenging. Here, we leveraged uncertainty quantification (UQ) methods and recently developed AMPK biosensors to construct a new, data-informed model of AMPK signaling. Specifically, we applied Bayesian parameter estimation and model selection to ensure that model predictions and assumptions are well-constrained to measurements of AMPK activity using recently developed AMPK biosensors. As an application of the new model, we predicted AMPK activity in response to exercise-like stimuli. We found that AMPK acts as a time- and exercise-dependent integrator of its input. Our results highlight how UQ can facilitate model development and address epistemic uncertainty in a complex signaling pathway, such as AMPK. This work shows the potential for future applications of UQ in systems biology to drive new biological insights by incorporating state-of-the-art experimental data at all stages of model development.

Spatiotemporal dynamics of calcium regulation in subcellular regions is critical for precise local control of cell signaling. Recent studies have shown that, in addition to biochemical control of localized calcium signaling through buffers and channels, the geometry of the small spaces in which calcium signaling occurs also matters. Geometric organization becomes particularly important when considering the role of organelles such as the mitochondria and endoplasmic reticulum in regulating calcium signaling. Here, we discuss recent advances in our understanding of calcium dynamics in small spaces such as dendritic spines and how computational modeling can reveal a complex interplay between geometry and receptor clustering. We close with other biological examples where such interactions may be important and suggest the possibility of generalizable biophysical principles of localized calcium control.

OBJECTIVE: Type 2 diabetes (T2D) and its associated complications develop heterogeneously over decades, but few studies span the progression from prediabetes to clinical events. We investigated whether long-term metabolic trajectories beginning in prediabetes delineate subgroups with differential complication risk. RESEARCH DESIGN AND METHODS: Clinical data from 1,732 Diabetes Prevention Program/Outcomes Study participants (follow-up 19 years) were analyzed across 12 phenotypes. Tensor decomposition was used to capture longitudinal patterns, and Gaussian mixture modeling was used to define longitudinal clusters. Cluster-specific complications were quantified with Cox and logistic regression. RESULTS: Four clusters emerged. Clusters 1 and 2 (73% of participants) maintained stable glycemia, blood pressure, and lipids. Although 49% and 71%, respectively, developed T2D, cumulative micro- and macrovascular events remained low. Cluster 3 (12%) showed the steepest rise in insulin resistance and hyperglycemia, with 92% of the subgroup progressing to T2D and a markedly higher rate of retinopathy (odds ratio [OR] 8.8, 95% CI 3.9-20.1) and neuropathy (OR 3.4, 95% CI 2.1-5.5). Cluster 4 (15%) presented with baseline microalbuminuria often prior to the development of T2D (73%). It was distinguished by progressive estimated glomerular filtration rate decline and a doubling of cardiovascular events (hazard ratio 2.0, 95% CI 1.4-3.0), despite serum lipids comparable with other groups. CONCLUSIONS: Two-thirds of individuals with prediabetes follow metabolically resilient trajectories, whereas distinct insulin-resistant or renal-dysfunction trajectories precede micro- or macrovascular complications, respectively. The optimal window for macrovascular complication prevention in individuals with prediabetes microalbuminuria may precede progression to T2D.

<p dir="ltr"><b>Objective</b>: Type 2 diabetes (T2D) and its associated complications develop heterogeneously over decades, but few studies span the progression from prediabetes to clinical events. We investigated whether long-term metabolic trajectories beginning in prediabetes delineate subgroups with differential complication risk.</p><p><br></p><p dir="ltr"><b>Research Design and Methods</b>: Clinical data from 1,732 Diabetes Prevention Program/Outcomes Study participants (follow-up 19 years) were analyzed across 12 phenotypes. Tensor decomposition was used to capture longitudinal patterns, and Gaussian Mixture Modeling to define longitudinal clusters. Cluster-specific complications were quantified with Cox and logistic regression.</p><p><br></p><p dir="ltr"><b>Results</b>: Four clusters emerged. Clusters 1 and 2 (73% of participants) maintained stable glycemia, blood pressure, and lipids. Although 49% and 71% developed T2D, cumulative micro and macrovascular events remained low. Cluster 3 (12%) showed the steepest rise in insulin resistance and hyperglycemia, with 92% of participants progressing to T2D and markedly higher rate of retinopathy (odds ratio (OR) 8.8, 95% CI 3.9-20.1) and neuropathy (OR 3.4, 95% CI 2.1-5.5). Cluster 4 (15%) presented with baseline microalbuminuria often prior to the development of T2D (73%). It was distinguished by progressive eGFR decline and a doubling of cardiovascular events (hazard ratio 2.0, 95% CI 1.4-3.0) despite comparable serum lipids to other groups.</p><p><br></p><p dir="ltr"><b>Conclusions</b>: Two-thirds of individuals with prediabetes follow metabolically resilient trajectories, whereas distinct insulin-resistant or renal-dysfunction trajectories precede micro or macrovascular complications respectively. The optimal window for macrovascular complication prevention in individuals with prediabetic microalbuminuria may precede progression to T2D.</p>

<p dir="ltr"><b>Objective</b>: Type 2 diabetes (T2D) and its associated complications develop heterogeneously over decades, but few studies span the progression from prediabetes to clinical events. We investigated whether long-term metabolic trajectories beginning in prediabetes delineate subgroups with differential complication risk.</p><p><br></p><p dir="ltr"><b>Research Design and Methods</b>: Clinical data from 1,732 Diabetes Prevention Program/Outcomes Study participants (follow-up 19 years) were analyzed across 12 phenotypes. Tensor decomposition was used to capture longitudinal patterns, and Gaussian Mixture Modeling to define longitudinal clusters. Cluster-specific complications were quantified with Cox and logistic regression.</p><p><br></p><p dir="ltr"><b>Results</b>: Four clusters emerged. Clusters 1 and 2 (73% of participants) maintained stable glycemia, blood pressure, and lipids. Although 49% and 71% developed T2D, cumulative micro and macrovascular events remained low. Cluster 3 (12%) showed the steepest rise in insulin resistance and hyperglycemia, with 92% of participants progressing to T2D and markedly higher rate of retinopathy (odds ratio (OR) 8.8, 95% CI 3.9-20.1) and neuropathy (OR 3.4, 95% CI 2.1-5.5). Cluster 4 (15%) presented with baseline microalbuminuria often prior to the development of T2D (73%). It was distinguished by progressive eGFR decline and a doubling of cardiovascular events (hazard ratio 2.0, 95% CI 1.4-3.0) despite comparable serum lipids to other groups.</p><p><br></p><p dir="ltr"><b>Conclusions</b>: Two-thirds of individuals with prediabetes follow metabolically resilient trajectories, whereas distinct insulin-resistant or renal-dysfunction trajectories precede micro or macrovascular complications respectively. The optimal window for macrovascular complication prevention in individuals with prediabetic microalbuminuria may precede progression to T2D.</p>

Abstract Dendritic spines are small protrusions on dendrites in neurons and serve as sites of postsynaptic activity. Some of these spines contain smooth endoplasmic reticulum (SER), and sometimes an even further specialized SER known as the spine apparatus (SA). In this work we developed a stochastic spatial model to investigate the role of the SER and the SA in modulating Ca 2+ dynamics. Using this model, we investigated how ryanodine receptor (RyR) localization, IP 3 R localization, spine membrane geometry and SER geometry can impact Ca 2+ transients in the spine and in the dendrite. Our simulations found that RyR opening is dependent on its location in the SER and on the SER geometry. To maximize Ca 2+ in the dendrites (for activating clusters of spines and spine‐to‐spine communication), a laminar SA was favourable with RyRs localized in the neck region, closer to the dendrite. Furthermore locating the IP 3 Rs in the dendrite, as measured experimentally, also increases Ca 2+ in the dendrite. We also found that the presence of the SER without the laminar structure, coupled with RyR localization at the head, leads to higher Ca 2+ presence in the spine. These predictions serve as design principles for understanding how spines with an ER can regulate Ca 2+ dynamics differently from spines without ER through a combination of geometry and receptor localization. image Key points Ca 2+ transients in the spine are characterized by the interplay among membrane receptors, RyRs, SERCA, and IP 3 Rs. Here we build a spatial, particle‐based stochastic model that integrates these components to study how the spine apparatus and receptor localization affect Ca 2+ signaling. Our results show that positioning RyRs near the neck of the spine apparatus enhances spine‐to‐dendrite communication. Additionally, our model highlights the importance of membrane curvature and spine apparatus shape for Ca 2+ signaling within dendritic spines.

Mathematical models are indispensable for studying the architecture and behavior of intracellular signaling networks. It is common to develop models using phenomenological approximations due to the difficulty of fully observing the intermediate steps in intracellular signaling pathways. Thus, multiple models can be built to represent the same pathway. This opens up challenges for model selection and decreases certainty in predictions. Here, we investigate Bayesian multimodel inference (MMI) as an approach to increase certainty in systems biology predictions, which becomes relevant when one wants to leverage a set of potentially incomplete models. Using existing models of the extracellular-regulated kinase (ERK) pathway, we show that MMI successfully combines models and yields predictors robust to model set changes and data uncertainties. We then use MMI to identify possible mechanisms of experimentally measured subcellular location-specific ERK activity. This work highlights MMI as a disciplined approach to increasing the certainty of intracellular signaling activity predictions.

Organelles such as mitochondria have characteristic shapes that are critical to their function. Recent efforts have revealed that the curvature contributions of individual lipid species can be a factor in the generation of membrane shape in these organelles. Inspired by lipidomics data from yeast mitochondrial membranes, we used Martini coarse-grained molecular dynamics simulations to investigate how lipid composition facilitates membrane shaping. We found that increasing lipid saturation increases bending rigidity while reducing the monolayer spontaneous curvature. We also found that systems containing cardiolipin exhibited decreased bending rigidity and increased spontaneous curvature when compared with bilayers containing its precursor, phosphatidylglycerol. This finding contradicts some prior experimental results that suggest that bilayers containing tetraoleoyl cardiolipin have greater rigidity than dioleoyl phosphatidylcholine bilayers. To investigate this discrepancy, we analyzed our simulations for correlations between lipid localization and local curvature. We found that there are transient correlations between curved lipids, such as cardiolipin and phosphatidylethanolamine, and curvature; these interactions enrich specific bilayer undulatory modes and cause bilayer softening. Furthermore, we show that curvature localization of some lipids such as cardiolipin can influence lipids in the opposing leaflet. These observations add to the emerging evidence that lipid geometric features give rise to local interactions, which can cause membrane compositional heterogeneities. The cross talk between composition-driven tuning of membrane properties and membrane shape has implications for membrane organization and its related functions.

Protein condensates use multivalent binding and surface tension to assemble actin filaments into diverse architectures, reminiscent of filopodia and stress fibers. During this process, nucleation of new filaments and elongation of existing filaments inherently compete for a shared pool of actin monomers. Here we show that a balance between these competing processes is required to deform condensates of VASP, an actin binding protein, into structures with high aspect ratios. Addition of magnesium, which promotes filament nucleation, helped actin to deform condensates into high aspect ratio structures. In contrast, addition of profilin, which inhibits filament nucleation, allowing existing filaments to elongate, caused actin to assemble into ring-like bundles that failed to substantially increase condensate aspect ratio. Computational modeling helped to explain these results by predicting that a group of short linear filaments, which can apply asymmetric pressure to the condensate boundary, is needed to increase condensate aspect ratio. In contrast, a small number of long filaments with the same total actin content should fail to overcome the droplet surface tension, forming a ring-like bundle. To test these predictions, we introduced gelsolin, which severed log filaments within rings, creating new barbed ends. The resulting set of shorter filaments regained the ability to deform condensates into high aspect ratio structures. Collectively, these results suggest that a balance of actin filament nucleation and elongation is required to deform protein condensates. More broadly, these findings illustrate how protein condensates can balance multiple kinetic processes to direct the assembly of diverse cytoskeletal architectures.

Several actin-binding proteins can form liquid-liquid phase-separated condensates that promote actin filament assembly and bundling, which is crucial for local actin network organization. Previous studies have established that phase-separated condensates composed of actin-binding proteins, such as vasodilator-stimulated phosphoprotein (VASP) and Lamellipodin (Lpd), restrict the organization of actin filaments to structures such as rings, shells, discs, and rods through kinetic trapping. However, the mechanism by which crosslinker multivalency, actin growth, and condensate properties tune actin organization and droplet shape is not well understood. Using a combination of agent-based simulations and experiments, we find that the deformability of the droplet interface allows for the emergence of not just tightly-bundled actin rings but also weakly-bundled actin discs. We find two major quantitative relationships between actin bundling and droplet deformation. The first relationship shows that the crosslinked bundle thickness and droplet diameter followed a power law, consistent with experiments. The second one is that the kinetics of droplet deformation follows a dynamic snapping behavior that depends on the droplet surface tension and the multivalent VASP-actin binding kinetics. We predicted that these two relationships were generalizable to dynamic multimers and to weak actin crosslinkers. Our predictions were experimentally tested using two additional condensate-forming proteins, lamellipodin and RGG. Taken together, we show that mechanochemical feedback between the droplet interface properties and crosslinker multivalency tune actin organization and control the dynamics of droplet deformation by actin networks.

Cell-secreted extracellular vesicles (EVs) play a pivotal role in local and distant cell-to-cell communication by delivering specific cargoes to other cells or to the extracellular space. In many cells, the glycocalyx, a thick sugar-rich layer at the cell surface, and the membrane-cortex attachment are crucially linked to the formation of EVs, yet it is unclear what determines the successful formation of EVs when multiple physical factors are involved. In this work, we developed a model for glycocalyx-membrane-cortex composite to investigate the effects of glycocalyx and membrane-cortex adhesion on the formation of EVs by combining polymer physics-based theory and Helfrich membrane theory. By performing linear stability analysis, we show that modulating the mechanical feedback among the glycocalyx, membrane-cortex attachment, and membrane curvature can give rise to two types of instabilities: a conserved Turing-type instability and a Cahn-Hilliard-type instability. Furthermore, using an equilibrium model, we identified two critical conditions for EV formation: an initial detachment of the membrane from the underlying cortex and then a sufficient driving force to induce membrane deformation for successful EV formation. We further demonstrated that there exists an optimal glycocalyx coating area at which the formation of EVs is most favorable. Finally, we use our model to predict that a heterogeneous size distribution of EVs can be generated through the regulation of glycocalyx properties, shedding insight into how EVs of different radii may be generated.

Abstract AMP-activated protein kinase (AMPK) plays a key role in restoring cellular metabolic homeostasis after energy stress. Importantly, AMPK acts as a hub of metabolic signaling, integrating multiple inputs and acting on numerous downstream targets to activate catabolic processes and inhibit anabolic ones. Despite the importance of AMPK signaling, unlike other well-studied pathways, such as MAPK/ERK or NF- κ B, only a handful of mechanistic models of AMPK signaling have been developed. Epistemic uncertainty in the biochemical mechanism of AMPK activity, combined with the complexity of the AMPK pathway, makes model development particularly challenging. Here, we leveraged uncertainty quantification methods and recently developed AMPK biosensors to construct a new, data-informed model of AMPK signaling. Specifically, we applied Bayesian parameter estimation and model selection to ensure that model predictions and assumptions are well-constrained to measurements of AMPK activity using recently developed AMPK biosensors. As an application of the new model, we predicted AMPK activity in response to exercise-like stimuli. We found that AMPK acts as a time- and exercise-dependent integrator of its input. Our results highlight how uncertainty quantification can facilitate model development and address epistemic uncertainty in a complex signaling pathway, such as AMPK. This work shows the potential for future applications of uncertainty quantification in systems biology to drive new biological insights by incorporating state-of-the-art experimental data at all stages of model development.

Nuclear translocation of the transcription regulatory proteins yes-associated protein (YAP) and transcriptional coactivator with PDZ-binding motif (TAZ) is a critical readout of cellular mechanotransduction. Recent experiments have demonstrated that cells on substrates with well-defined nanotopographies demonstrate mechanoadaptation through a multitude of effects - increased integrin endocytosis as a function of nanopillar curvature, increased local actin assembly on nanopillars but decreased global cytoskeletal stiffness, and enhanced nuclear deformation. How do cells respond to local nanotopographical cues and integrate their responses across multiple length scales? This question is addressed using a biophysical model that incorporates plasma membrane (PM) curvature-dependent endocytosis, PM curvature-sensitive actin assembly, and stretch-induced opening of nuclear pore complexes (NPCs) in the nuclear envelope (NE). This model recapitulates lower levels of global cytoskeletal assembly on nanopillar substrates, which can be partially compensated for by local actin assembly and NE indentation, leading to enhanced YAP/TAZ transport through stretched NPCs. Using cell shapes informed by electron micrographs and fluorescence images, the model predicts lamin A and F-actin localization around nanopillars, in agreement with experimental measurements. Finally, simulations predict nuclear accumulation of YAP/TAZ following rupture of the NE and this is validated by experiments. Overall, this study indicates that nanotopography tunes mechanoadaptation through both positive and negative feedback on mechanotransduction.

Abstract The dynamics of calcium ions (Ca 2+ ) in skeletal muscles link electrochemical activation and contractile force generation. An improved quantitative understanding of the mechanisms by which Ca 2+ dynamics modulate force production is crucial for optimizing muscle performance. Recent experimental data suggest that store-operated Ca 2+ entry (SOCE), the process of extracellular Ca 2+ influx upon depletion of Ca 2+ from the sarcoplasmic reticulum (SR), helps delay the onset of muscle fatigue. However, the mechanistic links between SOCE and sustained force generation in muscle remain unclear. We hypothesize that SOCE regulates force generation during sustained muscle activity by allowing for increased Ca 2+ release from the SR. We test this hypothesis with a quantitative biophysical model that simulates the biochemical events of muscle contraction, from initial depolarization at the sarcolemma and T-tubules to Ca 2+ release from the SR to Ca 2+ binding and force generation throughout the myoplasm. We also consider the balance between Ca 2+ removal from the myoplasm and SOCE through the T-tubule membrane. We estimate the free parameters in the model by fitting them to experiments that measured sarcolemma membrane voltage and myoplasmic Ca 2+ transients in single muscle fibers in vitro. We then test the effects of SOCE inhibition on Ca 2+ dynamics and force production and find that the magnitude of myoplasmic Ca 2+ and force are lower than in wild-type cells over repetitive stimuli. Finally, we predict the effects of varying the degree of SOCE inhibition during patterns of stimulus chosen to mimic those observed during resistance exercise or high-intensity interval training. These simulations predict a context-dependent relationship between force generation and SOCE, wherein increased SOCE is associated with greater force production during resistance exercise, but worsens the effects of fatigue in certain cases of high-intensity training.

-shaped clathrin assemblies function as the coat of endocytic vesicles, while flat clathrin assemblies, also known as flat clathrin lattices, serve as signaling hubs for various signaling pathways. Multiple flat clathrin lattices exist on the cell membrane, and these lattices grow after epidermal growth factor stimulation (EGF) and then return to baseline. In this work, we used a particle-based model to simulate the assembly and disassembly of flat clathrin lattices to capture these dynamics. We found that the formation of flat clathrin lattices is highly dynamic, that is, cluster number, size and dwelling time often change even in the absence of any stimulus. Moreover, these key features are affected by adaptor protein 2 (AP-2) number, clathrin-clathrin binding rate, and clathrin diffusion coefficient. Specifically, an increase in AP-2 number leads to the transition from no cluster, short-lasting multiple small clusters, to a long-lasting single giant cluster. An increased clathrin-clathrin binding rate or decreased clathrin diffusion coefficient both result in an increased cluster number, reduced cluster size, and shortened dwelling time. Furthermore, we also predicted that under EGF stimulation, simultaneous changes in the AP-2 number, the clathrin-clathrin binding rate, and the clathrin diffusion coefficient can reproduce the experimentally observed trend of FCLs: an increase in cluster number and size in the first 30 minutes, followed by a decrease after 30 minutes. These findings reveal kinetic mechanisms underlying the formation of multiple FCLs and how EGF regulates FCL dynamics.

There is a morphodynamic component to synaptic learning by which changes in dendritic (postsynaptic) spine head size are associated with the strengthening or weakening of the synaptic connection between two neurons. The membrane shape and size dynamics is sculpted by the growth dynamics of the enclosed actin cytoskeleton. We use Dynamical Graph Grammars (DGGs) governing dynamic labelled graphs embedded in two dimensions to model networks of actin filaments and the enclosing membrane in spine head morphology. We demonstrate the flexibility and extensibility of the framework by encoding detailed biophysical as well as biochemical models, obeying constraints of invariance and conservation, in DGG rule sets. From graph-local energy functions for cytoskeleton actin interacting and membrane, we specialize dissipative stochastic dynamics to an exhaustive collection of graph-local neighborhood types for the rule left hand sides. Extensively simulating the resulting model delineates effects of four actin-binding proteins, and their epistatic relationships, on morphology.

Tubular membrane structures are ubiquitous in cells and in the membranes of intracellular organelles such as the Golgi complex and the endoplasmic reticulum. Tubulation plays essential roles in numerous biological processes, including filopodia growth, trafficking, ion transport, and cellular motility. Understanding the fundamental mechanism of the formation of membrane tubes is thus an important problem in the fields of biology and biophysics. Although extensive studies have shown that tubes can be formed due to localized forces acting on the membrane or by the spontaneous curvature induced by membrane-bound proteins, little is known about how membrane tubes are induced by glycocalyx, a sugar-rich layer at the cell surface. In this work, we develop a biophysical model that combines polymer physics theory and the Canham-Helfrich membrane theory to investigate how the glycocalyx generates cylindrical tubular protrusions on the cell membrane. Our results show that the glycocalyx alone can induce the formation of tubular membrane structures. This tube formation involves a first-order shape transition without any externally applied force or other curvature-inducing mechanisms. We also find there exist critical values of glycocalyx grafting density and glycopolymer length needed to induce the formation of tubular structures. The presence of a vertical actin force, line tension, and spontaneous curvature reduce this critical grafting density and length of polymer that triggers the formation of membrane tube, which suggests that the glycocalyx makes tube formation energetically more favorable when combined with an actin force, line tension, and spontaneous curvature.

Long-term potentiation (LTP) is a biochemical process that underlies learning in excitatory glutamatergic synapses in the Central Nervous System (CNS). A critical early driver of LTP is autophosphorylation of the abundant postsynaptic enzyme, Ca 2+ /calmodulin-dependent protein kinase II (CaMKII). Autophosphorylation is initiated by Ca 2+ flowing through NMDA receptors activated by strong synaptic activity. Its lifetime is ultimately determined by the balance of the rates of autophosphorylation and of dephosphorylation by protein phosphatase 1 (PP1). Here we have modeled the autophosphorylation and dephosphorylation of CaMKII during synaptic activity in a spine synapse using MCell4, an open source computer program for creating particle-based stochastic, and spatially realistic models of cellular microchemistry. The model integrates four earlier detailed models of separate aspects of regulation of spine Ca 2+ and CaMKII activity, each of which incorporate experimentally measured biochemical parameters and have been validated against experimental data. We validate the composite model by showing that it accurately predicts previous experimental measurements of effects of NMDA receptor activation, including high sensitivity of induction of LTP to phosphatase activity in vivo, and persistence of autophosphorylation for a period of minutes after the end of synaptic stimulation. We then use the model to probe aspects of the mechanism of regulation of autophosphorylation of CaMKII that are difficult to measure in vivo . We examine the effects of “CaM-trapping,” a process in which the affinity for Ca 2+ /CaM increases several hundred-fold after autophosphorylation. We find that CaM-trapping does not increase the proportion of autophosphorylated subunits in holoenzymes after a complex stimulus, as previously hypothesized. Instead, CaM-trapping may dramatically prolong the lifetime of autophosphorylated CaMKII through steric hindrance of dephosphorylation by protein phosphatase 1. The results provide motivation for experimental measurement of the extent of suppression of dephosphorylation of CaMKII by bound Ca 2+ /CaM. The composite MCell4 model of biochemical effects of complex stimuli in synaptic spines is a powerful new tool for realistic, detailed dissection of mechanisms of synaptic plasticity.

Continuum modeling of lipid bilayer mechanics has played a critical role in our understanding of the physics underlying membrane curvature generation. Minimization of the bending energy of the lipid bilayer, usually taken to be the Helfrich energy, is the standard way to obtain the shape of the membrane. In this chapter, I will introduce some of the fundamentals of membrane mechanics and then focus on how these models can address critical questions in cellular processes. Using endocytosis and organelle geometries as two illustrative examples, I will elaborate on how mechanical models can generate predictions for biological phenomena. Finally, I will discuss how the dynamics of protein transport can be modelled using a thermodynamically complete model.

Understanding interaction mechanisms within cells, tissues, and organisms is crucial for driving developments across biology and medicine. Mathematical modeling is an essential tool for simulating such biological systems. Building on experiments, mechanistic models are widely used to describe small-scale intracellular networks. The development of sequencing techniques and computational tools has recently enabled multiscale models. Combining such larger scale network modeling with mechanistic modeling provides us with an opportunity to reveal previously unknown disease mechanisms and pharmacological interventions. Here, we review systems biology models from mechanistic models to multiscale models that integrate multiple layers of cellular networks and discuss how they can be used to shed light on disease states and even wellness-related states. Additionally, we introduce several methods that increase the certainty and accuracy of model predictions. Thus, combining mechanistic models with emerging mathematical and computational techniques can provide us with increasingly powerful tools to understand disease states and inspire drug discoveries.

Generation of membrane curvature is fundamental to cellular function. Recent studies have established that the glycocalyx, a sugar-rich polymer layer at the cell surface, can generate membrane curvature. While there have been some theoretical efforts to understand the interplay between the glycocalyx and membrane bending, there remain open questions about how the properties of the glycocalyx affect membrane bending. For example, the relationship between membrane curvature and the density of glycosylated proteins on its surface remains unclear. In this work, we use polymer brush theory to develop a detailed biophysical model of the energetic interactions of the glycocalyx with the membrane. Using this model, we identify the conditions under which the glycocalyx can both generate and sense curvature. Our model predicts that the extent of membrane curvature generated depends on the grafting density of the glycocalyx and the backbone length of the polymers constituting the glycocalyx. Furthermore, when coupled with the intrinsic membrane properties such as spontaneous curvature and a line tension along the membrane, the curvature generation properties of the glycocalyx are enhanced. These predictions were tested experimentally by examining the propensity of glycosylated transmembrane proteins to drive the assembly of highly curved filopodial protrusions at the plasma membrane of adherent mammalian cells. Our model also predicts that the glycocalyx has curvature-sensing capabilities, in agreement with the results of our experiments. Thus, our study develops a quantitative framework for mapping the properties of the glycocalyx to the curvature generation capability of the membrane.

1 Abstract The generation of an epithelial sheet transforms fruit fly embryos from a single syncytial cell directly into a tissue. For this to happen, the apical microvillus membrane is pulled between peripherally anchored nuclei in a process known as furrow invagination. Experimental measurements of furrow invagination velocities have shown that the rate of invagination undergoes slow-to-fast and fast-to-stalled velocity transitions during the formation of individual cells. The causes of such changes are due to multiple intersecting mechanisms and molecular components, including motor proteins, microtubules, and F-actin. In this work, we develop a continuum model to describe the dynamics of furrow invagination. Our model is constrained by previously published experimental data and considers the roles of cytoskeletal forces, cytoplasmic drag, motor protein forces, and membrane tension. We find that the viscous forces produced by the cytoskeleton sliding beneath the plasma membrane dictates furrow velocity. We propose that the slow phase is slow because there is a high density of microvilli, which increases the number of viscous contact points between the plasma membrane and the underlying cytoskeleton. This in turn, results in a higher resistance to furrow invagination. We predict that the fast phase may benefit from fewer cytoskeleton-to-plasma membrane contact points, thus reducing viscous forces and promoting the slow-to-fast switch. Then, we use perturbation and loss-of-function simulations to show that microvillus and sub-apical membrane reservoirs are vital to setting furrow invagination dynamics. This work demonstrates how coupling between the cytoskeleton, the plasma membrane, and distinct membrane reservoirs affects the plasticity and dynamics of cellularization.

Summary Biomolecular condensates perform diverse physiological functions. Previous work showed that VASP, a processive actin polymerase, forms condensates that assemble and bundle actin. Here we show that this behavior does not require proteins with specific polymerase activity. Specifically, condensates composed of Lamellipodin, a protein that binds actin but is not an actin polymerase, were also capable of assembling actin filaments. To probe the minimum requirements for condensate-mediated actin bundling, we developed an agent-based computational model. Guided by its predictions, we hypothesized that any condensate-forming protein that binds filamentous actin could bundle filaments through multivalent crosslinking. To test this, we added a filamentous-actin-binding motif to Eps15, a condensate-forming protein that does not normally bind actin. The resulting chimera formed condensates that facilitated efficient assembly and bundling of actin filaments. Collectively, these findings broaden the family of proteins that could organize cytoskeletal filaments to include any filamentous-actin-binding protein that participates in protein condensation.

Correction to: Nature Computational Science https://doi.org/10.1038/s43588-024-00745-x , published online 19 December 2024.