arXiv subjects

Padmini Rangamani

Publications and source records attributed to Padmini Rangamani.

At least 19 recordsLinked to original sources

arXiv2026

Mitochondrial mechanics nucleates axonal jamming and swelling

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.

physics.bio-ph↗

arXiv2025

A finite element framework for solving coupled multiphysics problem with moving boundaries in cell biophysics

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.

math.NA↗

arXiv2025

Synaptic spine head morphodynamics from graph grammar rules for actin 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.

q-bio.QM↗

arXiv2024

The evolution of systems biology and systems medicine: From mechanistic models to uncertainty quantification

Understanding the mechanisms of interactions within cells, tissues, and organisms is crucial to driving developments across biology and medicine. Mathematical modeling is an essential tool for simulating biological systems and revealing biochemical regulatory mechanisms. Building on experiments, mechanistic models are widely used to describe small-scale intracellular networks and uncover biochemical mechanisms in healthy and diseased states. The rapid development of high-throughput sequencing techniques and computational tools has recently enabled models that span multiple scales, often integrating signaling, gene regulatory, and metabolic networks. These multiscale models enable comprehensive investigations of cellular networks and thus reveal previously unknown disease mechanisms and pharmacological interventions. Here, we review systems biology models from classical mechanistic models to larger, multiscale models that integrate multiple layers of cellular networks. We introduce several examples of models of hypertrophic cardiomyopathy, exercise, and cancer cell proliferation. Additionally, we discuss methods that increase the certainty and accuracy of model predictions. Integrating multiscale models has become a powerful tool for understanding disease and inspiring drug discoveries by incorporating omics data within the cell and across tissues and organisms.

q-bio.MN↗

arXiv2024

Increasing certainty in systems biology models using Bayesian multimodel inference

Mathematical models are indispensable to the system biology toolkit for studying the structure and behavior of intracellular signaling networks. A common approach to modeling is to develop a system of equations that encode the known biology using approximations and simplifying assumptions. As a result, the same signaling pathway can be represented by multiple models, each with its set of underlying assumptions, which opens up challenges for model selection and decreases certainty in model predictions. Here, we use Bayesian multimodel inference to develop a framework to increase certainty in systems biology models. Using models of the extracellular regulated kinase (ERK) pathway, we first show that multimodel inference increases predictive certainty and yields predictors that are robust to changes in the set of available models. We then show that predictions made with multimodel inference are robust to data uncertainties introduced by decreasing the measurement duration and reducing the sample size. Finally, we use multimodel inference to identify a new model to explain experimentally measured sub-cellular location-specific ERK activity dynamics. In summary, our framework highlights multimodel inference as a disciplined approach to increasing the certainty of intracellular signaling activity predictions.

q-bio.QM↗

arXiv2024

Spatial modeling algorithms for reactions and transport (SMART) in biological cells

Biological cells rely on precise spatiotemporal coordination of biochemical reactions to control their many functions. Such cell signaling networks have been a common focus for mathematical models, but they remain challenging to simulate, particularly in realistic cell geometries. Herein, we present our software, Spatial Modeling Algorithms for Reactions and Transport (SMART), a package that takes in high-level user specifications about cell signaling networks and molecular transport, and then assembles and solves the associated mathematical and computational systems. SMART uses state-of-the-art finite element analysis, via the FEniCS Project software, to efficiently and accurately resolve cell signaling events over discretized cellular and subcellular geometries. We demonstrate its application to several different biological systems, including YAP/TAZ mechanotransduction, calcium signaling in neurons and cardiomyocytes, and ATP generation in mitochondria. Throughout, we utilize experimentally-derived realistic cellular geometries represented by well-conditioned tetrahedral meshes. These scenarios demonstrate the applicability, flexibility, accuracy and efficiency of SMART across a range of temporal and spatial scales.

q-bio.QM↗

arXiv2024

Interplay between cortical adhesion and membrane bending regulates microparticle formation

The formation of microparticles requires the bending of the plasma membrane away from the cytosol. The capcity of the cell membrane to form a microparticle, and the rate of membrane deformation, are controlled by multiple factors, including loss of lipid asymmetry (primarily the exposure of phosphatidylserine on the outer leaflet), detachment of the membrane from the cortical cytoskeleton, and bleb expansion due to pressure. In this work, we develop a biophysical model that accounts for the interaction between these different factors. Our findings reveal that the linkage between the membrane and cortex is a key determinant of outward budding. Ultimately, the rates and mechanical parameters regulating cortical linkage interact with the kinetics of phosphatidylserine flipping, laying out a mechanical phase space for regulating the outward budding of the plasma membrane.

cond-mat.soft↗

arXiv2023

SMART: Spatial Modeling Algorithms for Reaction and Transport

Recent advances in microscopy and 3D reconstruction methods have allowed for characterization of cellular morphology in unprecedented detail, including the irregular geometries of intracellular subcompartments such as membrane-bound organelles. These geometries are now compatible with predictive modeling of cellular function. Biological cells respond to stimuli through sequences of chemical reactions generally referred to as cell signaling pathways. The propagation and reaction of chemical substances in cell signaling pathways can be represented by coupled nonlinear systems of reaction-transport equations. These reaction pathways include numerous chemical species that react across boundaries or interfaces (e.g., the cell membrane and membranes of organelles within the cell) and domains (e.g., the bulk cell volume and the interior of organelles). Such systems of multi-dimensional partial differential equations (PDEs) are notoriously difficult to solve because of their high dimensionality, non-linearities, strong coupling, stiffness, and potential instabilities. In this work, we describe Spatial Modeling Algorithms for Reactions and Transport (SMART), a high-performance finite-element-based simulation package for model specification and numerical simulation of spatially-varying reaction-transport processes. SMART is based on the FEniCS finite element library, provides a symbolic representation framework for specifying reaction pathways, and supports geometries in 2D and 3D including large and irregular cell geometries obtained from modern ultrastructural characterization methods.

q-bio.QM↗

arXiv2023

Cell motility modes are selected by the interplay of mechanosensitive adhesion and membrane tension

The initiation of directional cell motion requires symmetry breaking that can happen both with or without external stimuli. During cell crawling, forces generated by the cytoskeleton and their transmission through mechanosensitive adhesions to the extracellular substrate play a crucial role. In a recently proposed 1D model (Sens, PNAS 2020), a mechanical feedback loop between force-sensitive adhesions and cell tension was shown to be sufficient to explain spontaneous symmetry breaking and multiple motility patterns through stick-slip dynamics, without the need to account for signaling networks or active polar gels. We extended this model to 2D to study the interplay between cell shape and mechanics during crawling. Through a local force balance along a deformable boundary, we show that the membrane tension coupled with shape change can regulate the spatiotemporal evolution of the stochastic binding of mechanosensitive adhesions. Linear stability analysis identified the unstable parameter regimes where spontaneous symmetry breaking can take place. sing simulations to solve the fully coupled nonlinear system of equations, we show that starting from a randomly perturbed circular shape, this instability can lead to keratocyte-like shapes. Simulations predict that different adhesion kinetics and membrane tension can result in different cell motility modes including gliding, zigzag, rotating, and sometimes chaotic movements. Thus, using a minimal model of cell motility, we identify that the interplay between adhesions and tension can select emergent motility modes.

q-bio.CB↗

arXiv2023

Bayesian Parameter Estimation for Dynamical Models in Systems Biology

Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent advances in experimental measurements, including sensor development and '-omics' studies that have helped populate protein-protein interaction networks in great detail, modeling in systems biology lacks systematic methods to estimate kinetic parameters and quantify associated uncertainties. This is because of multiple reasons, including sparse and noisy experimental measurements, lack of detailed molecular mechanisms underlying the reactions, and missing biochemical interactions. Additionally, the inherent nonlinearities with respect to the states and parameters associated with the system of differential equations further compound the challenges of parameter estimation. In this study, we propose a comprehensive framework for Bayesian parameter estimation and complete quantification of the effects of uncertainties in the data and models. We apply these methods to a series of signaling models of increasing mathematical complexity. Systematic analysis of these dynamical systems showed that parameter estimation depends on data sparsity, noise level, and model structure, including the existence of multiple steady states. These results highlight how focused uncertainty quantification can enrich systems biology modeling and enable additional quantitative analyses for parameter estimation.

q-bio.QM↗

arXiv2022

Modeling membrane curvature generation using mechanics and machine learning

The deformation of cellular membranes regulates trafficking processes, such as exocytosis and endocytosis. Classically, the Helfrich continuum model is used to characterize the forces and mechanical parameters that cells tune to accomplish membrane shape changes. While this classical model effectively captures curvature generation, one of the core challenges in using it to approximate a biological process is selecting a set of mechanical parameters (including bending modulus and membrane tension) from a large set of reasonable values. We used the Helfrich model to generate a large synthetic dataset from a random sampling of realistic mechanical parameters and used this dataset to train machine learning models. These models produced promising results, accurately classifying model behavior and predicting membrane shape from mechanical parameters. We also note emerging methods in machine learning that can leverage the physical insight of the Helfrich model to improve performance and draw greater insight into how cells control membrane shape change.

q-bio.QM↗

arXiv2022

Formation of protein-mediated tubes is governed by a snapthrough transition

Plasma membrane tubes are ubiquitous in cellular membranes and in the membranes of intracellular organelles. They play crucial roles in trafficking, ion transport, and cellular motility. The formation of plasma membrane tubes can be due to localized forces acting on the membrane or by curvature-induced by membrane-bound proteins. Here, we present a mathematical framework to model cylindrical tubular protrusions formed by proteins that induce anisotropic spontaneous curvature. Our analysis revealed that the tube radius depends on an effective tension that includes contributions from the bare membrane tension and the protein-induced curvature. We also found that the length of the tube undergoes an abrupt transition from a short, dome-shaped membrane to a long cylinder and this transition is characteristic of a snapthrough instability. Finally, we show that the snapthrough instability depends on the different parameters including coat area, bending modulus, and extent of protein-induced curvature. Our findings have implications for tube formation due to BAR-domain proteins in processes such as endocytosis, t-tubule formation in myocytes, and cristae formation in mitochondria.

cond-mat.soft↗

arXiv2022

Can biophysical models give insight into the synaptic changes associated with addiction?

Effective treatments that prevent or reduce drug relapse vulnerability should be developed to relieve the high burden of drug addiction to society. This will only be possible by enhancing the understanding of the molecular mechanisms underlying the neurobiology of addiction. Recent experimental data have shown that dendritic spines, small protrusions from the dendrites that receive input from excitatory neurons, from spiny neurons in the nucleus accumbens exhibit morphological changes during drug exposure and withdrawal. Moreover, these changes relate to the characteristic drug-seeking behavior of addiction. However, due to the complexity of the dendritic spines, we do not yet fully understand the processes underlying their structural changes in response to different inputs. We propose that biophysical models can enhance the current understanding of these processes by incorporating different, and sometimes, discrepant experimental data to identify the shared underlying mechanisms and generate experimentally testable hypotheses. This review aims to give an up-to-date report on biophysical models of dendritic spines, focusing on those models that describe their shape changes, which are well-known to relate to learning and memory. Moreover, it examines how these models can enhance our understanding of the effect of the drugs and the synaptic changes during disease progression.

physics.bio-ph↗

arXiv2021

Mem3DG: Modeling Membrane Mechanochemical Dynamics in 3D using Discrete Differential Geometry

Biomembranes adopt varying morphologies that are vital to cellular functions. Many studies use computational modeling to understand how various mechanochemical factors contribute to membrane shape transformations. Compared to approximation-based methods (e.g., finite element method), the class of discrete mesh models offers greater flexibility to simulate complex physics and shapes in three dimensions; its formulation produces an efficient algorithm while maintaining coordinate-free geometric descriptions. However, ambiguities in geometric definitions in the discrete context have led to a lack of consensus on which discrete mesh model is theoretically and numerically optimal; a bijective relationship between the terms contributing to both the energy and forces from the discrete and smooth geometric theories remains to be established. We address this and present an extensible framework, $\texttt{Mem3DG}$, for modeling 3D mechanochemical dynamics of membranes based on Discrete Differential Geometry (DDG) on triangulated meshes. The formalism of DDG resolves the inconsistency and provides a unifying perspective on how to relate the smooth and discrete energy and forces. To demonstrate, $\texttt{Mem3DG}$ is used to model a sequence of examples with increasing mechanochemical complexity: recovering classical shape transformations such as 1) biconcave disk, dumbbell, and unduloid and 2) spherical bud on spherical, flat-patch membrane; investigating how the coupling of membrane mechanics with protein mobility jointly affects phase and shape transformation. As high-resolution 3D imaging of membrane ultrastructure becomes more readily available, we envision Mem3DG to be applied as an end-to-end tool to simulate realistic cell geometry under user-specified mechanochemical conditions.

cs.CE↗

arXiv2021

Curvature-driven feedback on aggregation-diffusion of proteins in lipid bilayers

Membrane bending is an extensively studied problem from both modeling and experimental perspectives because of the wide implications of curvature generation in cell biology. Many of the curvature generating aspects in membranes can be attributed to interactions between proteins and membranes. These interactions include protein diffusion and formation of aggregates due to protein-protein interactions in the plane of the membrane. Recently, we developed a model that couples the in-plane flow of lipids and diffusion of proteins with the out-of-plane bending of the membrane. Building on this work, here, we focus on the role of explicit aggregation of proteins on the surface of the membrane in the presence of membrane bending and diffusion. We develop a comprehensive framework that includes lipid flow, membrane bending, the entropy of protein distribution, along with an explicit aggregation potential and derive the governing equations for the coupled system. We compare this framework to the Cahn-Hillard formalism to predict the regimes in which the proteins form patterns on the membrane. We demonstrate the utility of this model using numerical simulations to predict how aggregation and diffusion, when coupled with curvature generation, can alter the landscape of membrane-protein interactions.

cond-mat.soft↗

arXiv2021

Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff-Love kinematics and revealed by a three dimensional computational framework

Biomembranes play a central role in various phenomena like locomotion of cells, cell-cell interactions, packaging of nutrients, and in maintaining organelle morphology and functionality. During these processes, the membranes undergo significant morphological changes through deformation, scission, and fusion. Modeling the underlying mechanics of such morphological changes has traditionally relied on reduced order axisymmetric representations of membrane geometry and deformation. Axisymmetric representations, while robust and extensively deployed, suffer from their inability to model symmetry breaking deformations and structural bifurcations. To address this limitation, a 3D computational mechanics framework for high fidelity modeling of biomembrane deformation is presented. The proposed framework brings together Kirchhoff-Love thin-shell kinematics, Helfrich-energy based mechanics, and state-of-the-art numerical techniques for modeling deformation of surface geometries. Lipid bilayers are represented as spline-based surfaces immersed in a 3D space; this enables modeling of a wide spectrum of membrane geometries, boundary conditions, and deformations that are physically admissible in a 3D space. The mathematical basis of the framework and its numerical machinery are presented, and their utility is demonstrated by modeling 3 classical, yet non-trivial, membrane problems: formation of tubular shapes and their lateral constriction, Piezo1-induced membrane footprint generation and gating response, and the budding of membranes by protein coats during endocytosis. For each problem, the full 3D membrane deformation is captured, potential symmetry-breaking deformation paths identified, and various case studies of boundary and load conditions are presented. Using the endocytic vesicle budding as a case study, we also present a "phase diagram" for its symmetric and broken-symmetry states.

q-bio.QM↗

arXiv2020

The mechanics and thermodynamics of tubule formation in biological membranes

Membrane tubulation is a ubiquitous process that occurs both at the plasma membrane and on the membranes of intracellular organelles. These tubulation events are known to be mediated by forces applied on the membrane either due to motor proteins, by polymerization of the cytoskeleton, or due to the interactions between membrane proteins binding onto the membrane. The numerous experimental observations of tube formation have been amply supported by mathematical modeling of the associated membrane mechanics and have provided insights into the force-displacement relationships of membrane tubes. Recent advances in quantitative biophysical measurements of membrane-protein interactions and tubule formation have necessitated the need for advances in modeling that will account for the interplay of multiple aspects of physics that occur simultaneously. Here, we present a comprehensive review of experimental observations of tubule formation and provide context from the framework of continuum modeling. Finally, we explore the scope for future research in this area with an emphasis on iterative modeling and experimental measurements that will enable us to expand our mechanistic understanding of tubulation processes in cells.

cond-mat.soft↗

arXiv2020

Stability analysis of a signaling circuit with dual species of GTPase switches

GTPases are molecular switches that regulate a wide range of cellular processes, such as organelle biogenesis, position, shape, and signal transduction. These enzymes operate by toggling between an active ("ON") guanosine triphosphate (GTP)-bound state and an inactive ("OFF") guanosine diphosphate (GDP)-bound state; such a toggle is regulated by GEFs (guanine nucleotide exchange factors) and GAPs (GTPase activating proteins). Here we dissect a network motif between monomeric (m) and trimeric (t) GTPases assembled exclusively in eukaryotic cells of multicellular organisms. To this end, we develop a system of ordinary differential equations in which these two classes of GTPases are interlinked conditional to their ON/OFF states within a motif through feedforward and feedback loops. We provide formulas for the steady states of the system and perform local stability analysis to investigate the role of the different connections between the GTPase switches. A feedforward from the active mGTPase to the GEF of the tGTPase was sufficient to provide two locally stable states: one where both active/inactive forms of the mGTPase can be interpreted as having low concentrations and the other where both m- and tGTPase have high concentrations. When a feedback loop from the GEF of the tGTPase to the GAP of the mGTPase was added to the feedforward system, two other locally stable states emerged, both having the tGTPase inactivated and being interpreted as having low active tGTPase concentrations. Finally, the addition of a second feedback loop, from the active tGTPase to the GAP of the mGTPase, gives rise to a family of steady states parametrized by the inactive tGTPase concentrations. Our findings reveal that the coupling of these two different GTPase motifs can dramatically change their steady state behaviors and shed light on how such coupling may impact information processing in eukaryotic cells.

q-bio.SC↗