Biology subjects

Rangamani, P.

Publications and source records attributed to Rangamani, P..

At least 73 records · Page 4Linked to original sources

bioRxiv2022

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, systems biology modeling 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.

systems biology↗

bioRxiv2021

Crosstalk between biochemical signaling and trafficking determines AMPAR dynamics in synaptic plasticity

Synaptic plasticity involves the modification of both biochemical and structural components of neurons. Many studies have revealed that the change in the number density of the glutamatergic receptor AMPAR at the synapse is proportional to synaptic weight update; increase in AMPAR corresponds to strengthening of synapses while decrease in AMPAR density weakens synaptic connections. The dynamics of AMPAR are thought to be regulated by upstream signaling, primarily the calcium-CaMKII pathway, trafficking to and from the synapse, and influx from extrasynaptic sources. Here, we have developed a set of models using compartmental ordinary differential equations to systematically investigate contributions of signaling and trafficking variations on AMPAR dynamics at the synaptic site. We find that the model properties including network architecture and parameters significantly affect the integration of fast upstream species by slower downstream species. Furthermore, we predict that the model outcome, as determined by bound AMPAR at the synaptic site, depends on (a) the choice of signaling model (bistable CaMKII or monostable CaMKII dynamics), (b) trafficking versus influx contributions, and (c) frequency of stimulus. Therefore, AMPAR dynamics can have unexpected dependencies when upstream signaling dynamics (such as CaMKII and PP1) are coupled with trafficking modalities.

neuroscience↗

bioRxiv2021

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, 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, Mem3DG is used to model a sequence of examples with increasing mechanochemical complexity: recovering classical shape transformations such as 1) biconcave disk, dumb-bell, 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. Why it mattersCellular membranes have shapes and shape changes which characterize cells/organelles, and support nutrient trafficking among other critical processes. Modeling membrane shape changes using mechanical principles can provide insight into how cells robustly bend membranes to support life. Mathematical and computational strategies to solve the equations describing membrane shape evolution can be complex and challenging without simplifying assumptions. Here, we present a new, general, numerical approach to model arbitrary 3D membrane shapes in response to interaction with curvature sensing and generating membrane proteins. The accompanying implementation, Mem3DG, is a software tool to make computational membrane mechanics accessible to the general researcher. HighlightsO_LIIntroduces a discrete theory for membrane mechanics which connects with smooth theory C_LIO_LIDiscrete energy/force are functions of basic geometric quantities C_LIO_LIRecipes for extending the discrete framework with additional physics are provided C_LIO_LIDescribes a user-friendly software implementation called Mem3DG C_LIO_LIMem3DG is designed to facilitate modeling in tandem with experimental studies C_LI Significance and noveltyHelfrich Hamiltonian is widely used to model biomembranes. Many numerical methods have been developed to solve the geometric PDE. Compared to approximation-based methods, discrete-mesh-based models have many advantages when incorporating multiphysics in 3D due to their flexibility, efficiency, and straightforward implementation. However, there is no consensus on which mesh-based model is optimal, and a connection between the discrete and smooth geometric theory remains obscure. In this work, we provide a unifying perspective by identifying fundamental geometric invariants of the discrete force derived from a discrete energy. As a demonstration of generality of the framework to various physics, we follow a formulaic procedure to derive additional physics such as interfacial line tension, surface-bulk adsorption, protein lateral diffusion, and curvature-dependent protein aggregation.

biophysics↗

bioRxiv2021

Nanoscale organization of ryanodine receptor distribution and phosphorylation pattern determines the dynamics of calcium sparks

Super-resolution imaging techniques have provided a better understanding of the relationship between the nanoscale organization of function of ryanodine receptors (RyRs) in cardiomy-ocytes. Interestingly recent data have indicated that this relationship is disrupted in heart failure (HF), as RyRs are dispersed into smaller and more numerous clusters. However, RyRs are also hyperphosphorylated in this condition, and this is reported to occur preferentially within the cluster centre. Thus, the combined impact of RyR relocalization and sensitization on Ca2+ spark generation in failing cardiomyocytes is likely complex and these observations suggest that both the nanoscale organization of RyRs and the pattern of phosphorylated RyRs within clusters could be critical determinants of Ca2+ spark dynamics. To test this hypothesis, we used computational modeling to quantify the relationships between RyR cluster geometry, phosphorylation patterns, and sarcoplasmic reticulum (SR) Ca2+ release. We found that RyR cluster disruption results in a decrease in spark fidelity and longer sparks with a lower amplitude. Phosphorylation of some RyRs within the cluster can play a compensatory role, recovering healthy spark dynamics. Interestingly, our model predicts that such compensation is critically dependent on the phosphorylation pattern, as phosphorylation localized within the cluster center resulted in longer Ca2+ sparks and higher spark fidelity compared to a uniformly distributed phosphorylation pattern. Our results strongly suggest that both the phosphorylation pattern and nanoscale RyR reorganization are critical determinants of Ca2+ dynamics in HF. Significance StatementRyRs are ion channels located on the membrane of the sarcoplasmic reticulum that are responsible for an increase in cytosolic Ca2+ during cell excitation. Here, we investigate how the geometry of RyR clusters combined with spatial phosphorylation patterns impacts on Ca2+ spark generation and kinetics. The findings from our study show that both phosphorylation pattern and RyR cluster shape and dispersion have implications on Ca2+ spark activity and provide insights into altered Ca2+ dynamics during HF.

biophysics↗

bioRxiv2021

Spatial regulation of AMPK signaling revealed by a sensitive kinase activity reporter

AMP-activated protein kinase (AMPK) is a master regulator of cellular energetics which coordinates metabolism by phosphorylating a plethora of substrates throughout the cell. But whether AMPK activity is regulated at different subcellular locations to provide precise spatial and temporal control over metabolism is unclear. Genetically encoded AMPK activity reporters (AMPKAR) have provided a window into spatial AMPK activity, but the limited dynamic range of current AMPKARs hinders detailed study. To monitor the dynamic activity of AMPK with high sensitivity, we developed a single-fluorophore AMPK activity reporter (ExRai AMPKAR) that exhibits an excitation ratiometric fluorescence change upon phosphorylation by AMPK, with over 3-fold greater response compared to previous AMPKARs. Using subcellularly localized ExRai AMPKAR, we found that the activity of AMPK at the lysosome and mitochondria are differentially regulated. While different activating conditions, irrespective of their effects on ATP, robustly yet gradually increase mitochondrial AMPK activity, lysosomal AMPK activity accumulates with much faster kinetics. Genetic deletion of the canonical upstream kinase liver kinase B1 (LKB1) resulted in slower AMPK activity at lysosomes but did not affect the response amplitude at either location, in sharp contrast to the necessity of LKB1 for maximal cytoplasmic AMPK activity. We further discovered AMPK activity in the nucleus, which resulted from LKB1-mediated cytoplasmic activation of AMPK followed by nuclear shuttling. Thus, a new, sensitive reporter for AMPK activity, ExRai AMPKAR, in complement with mathematical and biophysical methods, captured subcellular AMPK activity dynamics in living cells and unveiled complex regulation of AMPK signaling within subcellular compartments.

molecular biology↗

bioRxiv2021

Actin force generation in vesicle formation: mechanistic insights from cryo-electron tomography

Actin assembly provides force for a multitude of cellular processes. Compared to actin assembly- based force production during cell migration, relatively little is understood about how actin assembly generates pulling forces for vesicle formation. Here, cryo-electron tomography revealed actin filament number, organization, and orientation during clathrin-mediated endocytosis in human cells, showing that force generation is robust despite variance in network organization. Actin dynamics simulations incorporating a measured branch angle indicate that sufficient force to drive membrane internalization is generated through polymerization, and that assembly is triggered from [~]4 founding "mother" filaments, consistent with tomography data. Hip1R actin filament anchoring points are present along the entire endocytic invagination, where simulations show that it is key to pulling force generation, and along the neck, where it targets filament growth and makes internalization more robust. Actin cytoskeleton organization described here allowed direct translation of structure to mechanism with broad implications for other actin-driven processes. Highlights- Filament anchorage points are key to pulling force generation and efficiency. - Native state description of CME-associated actin force-producing networks. - Branched actin filament assembly is triggered from multiple mother filaments. - Actin force production is robust despite considerable network variability.

cell biology↗

bioRxiv2021

Stochastic simulations reveal that dendritic spine morphology regulates synaptic plasticity in a deterministic manner

Dendritic spines act as biochemical computational units and must adapt their responses according to their activation history. Calcium influx acts as the first signaling step during post-synaptic activation and is a determinant of synaptic weight change. Dendritic spines also come in a variety of sizes and shapes. To probe the relationship between calcium dynamics and spine morphology, we used a stochastic reaction-diffusion model of calcium dynamics in idealized and realistic geometries. We show that despite the stochastic nature of the various calcium channels, receptors, and pumps, spine size and shape can modulate calcium dynamics and subsequently synaptic weight updates in a deterministic manner. Through a series of exhaustive simulations, we find that the calcium dynamics and synaptic weight change depend on the volume-to-surface area of the spine. The relationships between calcium dynamics and spine morphology identified in idealized geometries also hold in realistic geometries suggesting that there are geometrically determined deterministic relationships that may modulate synaptic weight change.

neuroscience↗

bioRxiv2021

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

AO_SCPLOWBSTRACTC_SCPLOWMembrane 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 energy, the entropy of protein distribution, and an explicit aggregation potential and derive the governing equations. 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, coupled with curvature generation, can alter the landscape of membrane-protein interactions.

biophysics↗

bioRxiv2021

Closed-Loop Control between Two GTPase Switches makes the Secretory Functions of the Golgi Responsive to Growth Factors

Cancers represent complex autonomous systems, displaying self-sufficiency in growth signaling. Autonomous growth is fueled by a cancer cells ability to secrete-and-sense growth factors: a poorly understood phenomenon. Using an integrated systems and experimental approach, here we dissect the impact of a feedback-coupled GTPase circuit within the secretory pathway that imparts secretion-coupled autonomy. The circuit is assembled when the Ras-superfamily monomeric GTPase Arf1, and the heterotrimeric GTPase Gi{beta}{gamma} and their corresponding GAPs and GEFs are coupled by GIV/Girdin, a protein that is known to fuel aggressive traits in diverse cancers. One forward and two key negative feedback loops within the circuit create closed-loop control (CLC), allow the two GTPases to coregulate each other, and convert the expected switch-like behavior of Arf1-dependent secretion into an unexpected dose response alignment behavior of sensing and secretion. Such behavior translates into cell survival that is self-sustained by stimulus-proportionate secretion. Proteomic studies and protein-protein interaction network analyses pinpoint growth factors (e.g., the epidermal growth factor; EGF) as a key stimuli for such self-sustenance. Findings highlight how enhanced coupling of two biological switches in cancer cells is critical for multiscale feedback control to achieve secretion-coupled autonomy of growth factors. SYNOPSIS IMAGE O_FIG_DISPLAY_L [Figure 1] M_FIG_DISPLAY C_FIG_DISPLAY STANDFIRST TEXTThis work defines the inner workings of a Golgi-localized molecular circuitry comprised of coupled GTPases, which empowers cells to achieve self-sufficiency in growth factor signaling by creating a secrete-and-sense autocrine loop. HIGHLIGHTS/MAIN FINDINGSO_LIModeling and experimental approaches were used to dissect a coupled GTPase circuit. C_LIO_LICoupling enables closed loop feedback and mutual control of GTPases. C_LIO_LICoupling generates dose response alignment behavior of sensing and secretion of growth factors. C_LIO_LICoupling is critical for multiscale feedback control to achieve secretion-coupled autonomy. C_LI

systems biology↗

bioRxiv2021

Morphological principles of neuronal mitochondria

In the highly dynamic metabolic landscape of a neuron, mitochondrial membrane architectures can provide critical insight into the unique energy balance of the cell. Current theoretical calculations of functional outputs like ATP and heat often represent mitochondria as idealized geometries and therefore can miscalculate the metabolic fluxes. To analyze mitochondrial morphology in neurons of mouse cerebellum neuropil, 3D tracings of complete synaptic and axonal mitochondria were constructed using a database of serial TEM tomography images and converted to watertight meshes with minimal distortion of the original microscopy volumes with a granularity of 1.6 nanometer isotropic voxels. The resulting in silico representations were subsequently quantified by differential geometry methods in terms of the mean and Gaussian curvatures, surface areas, volumes, and membrane motifs, all of which can alter the metabolic output of the organelle. Finally, we identify structural motifs that are present across this population of mitochondria; observations which may contribute to future modeling studies of mitochondrial physiology and metabolism in neurons.

neuroscience↗

bioRxiv2021

Nanoscale organization of Actin Filaments in the Red Blood Cell Membrane Skeleton

Red blood cell (RBC) shape and deformability are supported by a planar network of short actin filament (F-actin) nodes interconnected by long spectrin molecules at the inner surface of the plasma membrane. Spectrin-F-actin network structure underlies quantitative modelling of forces controlling RBC shape, membrane curvature and deformation, yet the nanoscale organization of F-actin nodes in the network in situ is not understood. Here, we examined F-actin distribution in RBCs using fluorescent-phalloidin labeling of F-actin imaged by multiple microscopy modalities. Total internal reflection fluorescence (TIRF) and Zeiss Airyscan confocal microscopy demonstrate that F-actin is concentrated in multiple brightly stained F-actin foci [~]200-300 nm apart interspersed with dimmer F-actin staining regions. Live cell imaging reveals dynamic lateral movements, appearance and disappearance of F-actin foci. Single molecule STORM imaging and computational cluster analysis of experimental and synthetic data sets indicate that individual filaments are non-randomly distributed, with the majority as multiple filaments, and the remainder sparsely distributed as single filaments. These data indicate that F-actin nodes are non-uniformly distributed in the spectrin-F-actin network and necessitate reconsideration of current models of forces accounting for RBC shape and membrane deformability, predicated upon uniform distribution of F-actin nodes and associated proteins across the micron-scale RBC membrane.

biophysics↗

bioRxiv2021

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 and transport of nutrients, transmission of nerve impulses, 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 three-dimensional 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 surface discretizations immersed in a three-dimensional 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 three classical, yet non-trivial, membrane deformation 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 three dimensional 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.

biophysics↗

bioRxiv2020

Transfer function for YAP/TAZ nuclear translocation revealed through spatial systems modeling

YAP/TAZ is a master regulator of mechanotransduction whose functions rely on translocation from the cytoplasm to the nucleus in response to diverse physical cues. Substrate stiffness, substrate dimensionality, and cell shape are all input signals for YAP/TAZ, and through this pathway, regulate critical cellular functions and tissue homeostasis. Yet, the relative contributions of each biophysical signal and the mechanisms by which they synergistically regulate YAP/TAZ in realistic tissue microenvironments that provide multiplexed input signals remains unclear. For example, in simple 2D culture, YAP/TAZ nuclear localization correlates strongly with substrate stiffness, while in 3D environments, YAP/TAZ translocation can increase with stiffness, decrease with stiffness, or remain unchanged. Here, we develop a spatial model of YAP/TAZ translocation to enable quantitative analysis of the relationships between substrate stiffness, substrate dimensionality, and cell shape. Our model couples cytosolic stiffness to nuclear mechanics to replicate existing experimental trends, and extends beyond current data to predict that increasing substrate activation area through changes in culture dimensionality, while conserving cell volume, forces distinct shape changes that result in nonlinear effect on YAP/TAZ nuclear localization. Moreover, differences in substrate activation area versus total membrane area can account for counterintuitive trends in YAP/TAZ nuclear localization in 3D culture. Based on this multiscale investigation of the different system features of YAP/TAZ nuclear translocation, we predict that how a cell reads its environment is a complex information transfer function of multiple mechanical and biochemical factors. These predictions reveal design principles of cellular and tissue engineering for YAP/TAZ mechanotransduction. STATEMENT OF SIGNIFICANCEIn chemical engineering, a transfer function is a mathematical function that models the output of a reactor for all possible inputs, and enables the reliable design and operation of complex reaction systems. Here, we apply this principle to cells to derive the transfer function by which substrate stiffness is converted into YAP/TAZ nuclear localization. This function is defined by a spatial model of the YAP/TAZ mechano-chemical sensing network, wherein key spatial and physical inputs to the system, namely cell and nuclear shape, surface area to volume ratios of cytoplasmic and nuclear compartments, substrate dimensionality, substrate activation area, and substrate stiffness, are all integrated. The resulting model accounts for seemingly contradictory experimental trends and lends new insight into controlling YAP/TAZ signalling.

biophysics↗

bioRxiv2020

Deciphering the postsynaptic calcium-mediated energy homeostasis through mitochondria-endoplasmic reticulum contact sites using systems modeling

Spatiotemporal compartmentation of calcium dynamics is critical for neuronal function, particularly in post-synaptic spines. This exquisite level of Ca2+ compartmentalization is achieved through the storage and release of Ca2+ from various intracellular organelles particularly the endoplasmic reticulum (ER) and the mitochondria. Mitochondria and ER are established storage organelles controlling Ca2+ dynamics in neurons. Mitochondria also generate a majority of energy used within postsynaptic spines to support the downstream events associated with neuronal stimulus. Recently, high resolution microscopy has unveiled direct contact sites between the ER and the mitochondria, which directly channel Ca2+ release from the ER into the mitochondrial membrane. In this study, we develop a computational 3D reaction-diffusion model to investigate the role of MERCs in regulating Ca2+ and ATP dynamics. This spatiotemporal model accounts for Ca2+ oscillations initiated by glutamate stimulus of metabotropic and ionotropic glutamate receptors and Ca2+ changes in four different compartments: cytosol, ER, mitochondria, and the MERC microdomain. Our simulations predict that the organization of these organelles and differential distribution of key Ca2+ channels such as IP3 receptor and ryanodine receptor modulate Ca2+ dynamics in response to different stimuli. We further show that the crosstalk between geometry (mitochondria and MERC) and metabolic parameters (cytosolic ATP hydrolysis, ATP generation) influences the cellular energy state. Our findings shed light on the importance of organelle interactions in predicting Ca2+ dynamics in synaptic signaling. Overall, our model predicts that a combination of MERC linkage and mitochondria size is necessary for optimal ATP production in the cytosol.

systems biology↗

bioRxiv2020

Mechanical principles governing the shapes of dendritic spines

Dendritic spines are small, bulbous protrusions along the dendrites of neurons and are sites of excitatory postsynaptic activity. The morphology of spines has been implicated in their function in synaptic plasticity and their shapes have been well-characterized, but the potential mechanics underlying their shape development and maintenance have not yet been fully understood. In this work, we explore the mechanical principles that could underlie specific shapes using a minimal biophysical model of membrane-actin interactions. Using this model, we first identify the possible force regimes that give rise to the classic spine shapes - stubby, filopodia, thin, and mushroom-shaped spines. We also use this model to investigate how the spine neck might be stabilized using periodic rings of actin or associated proteins. Finally, we use this model to predict that the cooperation between force generation and ring structures can regulate the energy landscape of spine shapes across a wide range of tensions. Thus, our study provides insights into how mechanical aspects of actin-mediated force generation and tension can play critical roles in spine shape maintenance.

biophysics↗

bioRxiv2020

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

AO_SCPLOWBSTRACTC_SCPLOWGTPases are molecular switches that regulate a wide range of cellular processes, such as organelle biogenesis, position, shape, and function, vesicular transport between organelles, and signal transduction. These hydrolase 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 propose a model for a network motif between monomeric (m) and trimeric (t) GTPases assembled exclusively in eukaryotic cells of multicellular organisms. We develop a system of ordinary differential equations in which these two classes of GT-Pases are interlinked conditional to their ON/OFF states within a motif through coupling and feedback loops. We provide explicit formulae for the steady states of the system and perform classical local stability analysis to systematically investigate the role of the different connections between the GTPase switches. Interestingly, a coupling of 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. Moreover, when a feedback loop from the GEF of the tGTPase to the GAP of the mGTPase was added to the coupled 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 tGT-Pase to the GAP of the mGTPase, gives rise to a family of steady states that can be parametrized by a range of 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 signaling mechanisms in eukaryotic cells.

cell biology↗

bioRxiv2020

Local sensitivity analysis of the 'Membrane shape equation'derived from the Helfrich energy

The Helfrich energy is commonly used to model the elastic bending energy of lipid bilayers in membrane mechanics. The governing differential equations for certain geometric characteristics of the shape of the membrane can be obtained by applying variational methods (minimization principles) to the Helfrich energy functional and are well-studied in the axisymmetric framework. However, the Helfrich energy functional and the resulting differential equations involve a number of parameters, and there is little explanation of the choice of parameters in the literature, particularly with respect to the choice of the "spontaneous curvature" term that appears in the functional. In this paper, we present a careful analytical and numerical study of certain aspects of parametric sensitivity of Helfrichs model. Using simulations of specific model systems, we demonstrate the application of our scheme to the formation of spherical buds and pearled shapes in membrane vesicles.

biophysics↗

bioRxiv2020

Membrane bending by protein phase separation

Membrane bending is a ubiquitous cellular process that is required for membrane traffic, cell motility, organelle biogenesis, and cell division. Proteins that bind to membranes using specific structural features, such as wedge-like amphipathic helices and crescent-shaped scaffolds, are thought to be the primary drivers of membrane bending. However, many membrane-binding proteins have substantial regions of intrinsic disorder, which lack a stable three-dimensional structure. Interestingly, many of these disordered domains have recently been found to form networks stabilized by weak, multi-valent contacts, leading to assembly of protein liquid phases on membrane surfaces. Here we ask how membrane-associated protein liquids impact membrane curvature. We find that protein phase separation on the surfaces of synthetic and cell-derived membrane vesicles creates a substantial compressive stress in the plane of the membrane. This stress drives the membrane to bend inward, creating protein-lined membrane tubules. A simple mechanical model of this process accurately predicts the experimentally measured relationship between the rigidity of the membrane and the diameter of the membrane tubules. Discovery of this mechanism, which may be relevant to a broad range of cellular protrusions, illustrates that membrane remodeling is not exclusive to structured scaffolds, but can also be driven by the rapidly emerging class of liquid-like protein networks that assemble at membranes. Significance StatementCellular membranes take on an elaborate set of highly curved and bent shapes, which are essential to diverse cellular functions from endocytosis to cell division. The prevailing view has been that membrane bending is driven by proteins with curved shapes, which assemble at the membrane surface to form solid scaffolds. In contrast, here we show that proteins which form liquid-like assemblies on membranes are also potent drivers of bending. These "liquid scaffolds" apply compressive stress to the membrane surface, generating a diverse and dynamic family of membrane shapes. These data, which come at a time when liquid-like protein assemblies are being identified throughout the cell, suggest that liquid-like protein assemblies may play an important role in shaping cellular membranes.

biophysics↗