arXiv subjects

N. Ramakrishnan

Publications and source records attributed to N. Ramakrishnan.

14 recordsLinked to original sources

arXiv2018

Tubulation pattern of membrane vesicles coated with bio filaments

Narrow membrane tubes are commonly pulled out from the surface of phospholipid vesicles using forces applied either through laser or magnetic tweezers or through the action of processive motor proteins. Recent examples have emerged where such tubes spontaneously grow from vesicles coated with bioactive cytoskeletal filaments (e.g. FtsZ, microtubule) in the presence GTP. We show how a soft vesicle deforms due to the interplay between its topology, local curvature and the forces due to the active filaments. We present results from Dynamically Triangulated Monte Carlo simulations of a spherical continuum membrane coated with a nematic field and show how the intrinsic curvature of the filaments and their ordering interactions drive membrane tubulation. We predict interesting patterns of nematic defects, on curved 2D membrane surfaces, which promote tube formation. Implication of our model for more dynamic cases where vesicles coated with an active mixture of microtubule and myosin show shape oscillation, are also discussed. All these cases point to a common theme that defect locations on 2D membrane surfaces are hot spots of membrane deformation activity.

physics.bio-ph↗

arXiv2018

Computational investigation of multivalent binding of a ligand coated particle: Role of shape, size and ligand heterogeneity from a free energy landscape perspective

We utilize a multiscale modeling framework to study the effect of shape, size and ligand composition on the efficacy of binding of a ligand-coated-particle to a substrate functionalized with the target receptors. First, we show how molecular dynamics (MD) along with Steered MD calculations can be used to accurately parameterize the molecular binding free energy and the effective spring constant for a receptor-ligand pair. We demonstrate this for two ligands that bind to the $α_5β_1$-domain of integrin. Next, we show how these effective potentials can be used to build computational models at the meso- and continuum- scales. These models incorporate the molecular nature of the receptor-ligand interactions and yet provide an inexpensive route to study the multivalent interaction of receptors and ligands through the construction of Bell potentials customized to the molecular identities. We quantify the binding efficacy of the ligand-coated-particle in terms of its multivalency, binding free energy landscape and the losses in the configurational entropies. We show that (i) the binding avidity for particle sizes less than $350$ nm is set by the competition between the enthalpic and entropic contributions while that for sizes above $350$ nm is dominated by the enthalpy of binding, (ii) anisotropic particles display higher multivalent binding compared to spherical particles and (iii) variations in ligand composition can alter binding avidity without altering the average multivalency. The methods and results presented here have wide applications in the rational design of functionalized carriers and also in understanding cell adhesion.

cond-mat.soft↗

arXiv2016

Motion of a nano-ellipsoid in a cylindrical vessel flow: Brownian and hydrodynamic interactions

We present comprehensive numerical studies of the motion of a buoyant or a nearly neutrally buoyant nano-sized ellipsoidal particle in a fluid filled cylindrical tube without or with the presence of imposed pressure gradient (weak Poiseuille flow). The Fluctuating hydrodynamics approach and the Deterministic method are both employed. We ensure that the fluctuation-dissipation relation and the principle of thermal equipartition of energy are both satisfied. The major focus is on the effect of the confining boundary. Results for the velocity and angular velocity autocorrelations (VACF and AVACF), diffusivities, and drag and lift forces as functions of shape, aspect ratio, inclination angle, and proximity to the wall are presented. For the parameters considered, the boundary modifies the VACF and AVACF such that three distinct regimes are discernible --- an initial exponential decay, followed by an algebraic decay culminating in a second exponential decay. The first is due to thermal noise, the algebraic regime is due to both thermal noise and hydrodynamic correlations, while the second exponential decay shows the effect of momentum reflection from the confining wall. Our predictions display excellent comparison with published results for the algebraic regime (the only regime for which earlier results exist). We also discuss the role of off-diagonal elements of the mobility and diffusivity tensor that enables the quantification of the degree of lift and margination of the NC in the vessel. Our study covers a range of parameters that are of wide applicability in nanotechnology and in targeted drug delivery related to the health sciences.

physics.comp-ph↗

arXiv2016

Excess area dependent scaling behavior of nano-sized membrane tethers

Thermal fluctuations in cell membranes manifest as an excess area (${\cal A}_{\rm ex}$) which governs a multitude of physical process at the sub-micron scale. We present a theoretical framework, based on an in silico tether pulling method, which may be used to reliably estimate ${\cal A}_{\rm ex}$ in live cells. The tether forces estimated from our simulations compare well with our experimental measurements for tethers extracted from ruptured GUVs and HeLa cells. We demonstrate the significance and validity of our method by showing that all our calculations along with experiments of tether extraction in 15 different cell types collapse onto two unified scaling relationships mapping tether force, tether radius, bending stiffness $κ$, and membrane tension $σ$. We show that $R_{\rm bead}$, the size of the wetting region, is an important determinant of the radius of the extracted tether, which is equal to $ξ=\sqrt{κ/2σ}$ (a characteristic length scale of the membrane) for $R_{\rm bead}<ξ$, and is equal to $R_{\rm bead}$ for $R_{\rm bead}>ξ$. We also find that the estimated excess area follows a linear scaling behavior that only depends on the true value of ${\cal A}_{\rm ex}$ for the membrane, based on which we propose a self-consistent technique to estimate the range of excess membrane areas in a cell.

physics.bio-ph↗

arXiv2015

Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins

Biological membranes constitute boundaries of cells and cell organelles. Physico-chemical mechanisms at the atomic scale are dictated by protein-lipid interaction strength, lipid composition, lipid distribution in the vicinity of the protein, shape and amino acid composition of the protein, and its amino acid contents. The specificity of molecular interactions together with the cooperativity of multiple proteins induce and stabilize complex membrane shapes at the mesoscale. These shapes span a wide spectrum ranging from the spherical plasma membrane to the complex cisternae of the Golgi apparatus. Mapping the relation between the protein-induced deformations at the molecular scale and the resulting mesoscale morphologies is key to bridging cellular experiments across the various length scales. In this review, we focus on the theoretical and computational methods used to understand the phenomenology underlying protein-driven membrane remodeling. The suite of methods discussed here can be tailored to applications in specific cellular settings such as endocytosis during cargo trafficking and tubulation of filopodial structures in migrating cells, which makes these methods a powerful complement to experimental studies.

physics.bio-ph↗

arXiv2015

Active remodeling of chromatin and implications for in-vivo folding

Recent high resolution experiments have provided a quantitative description of the statistical properties of interphase chromatin at large scales. These findings have stimulated a search for generic physical interactions that give rise to such specific statistical conformations. Here, we show that an active chromatin model of in-vivo folding, based on the interplay between polymer elasticity, confinement, topological constraints and active stresses arising from the (un)binding of ATP-dependent chromatin-remodeling proteins gives rise to steady state conformations consistent with these experiments. Our results lead us to conjecture that the chromatin conformation resulting from this active folding optimizes information storage by co-locating gene loci which share transcription resources.

physics.bio-ph↗

arXiv2015

Thermodynamic Free Energy Methods to Investigate Shape Transitions In Bilayer Membranes

The conformational free energy landscape of a system is a fundamental thermodynamic quantity of importance particularly in the study of soft matter and biological systems, in which the entropic contributions play a dominant role. While computational methods to delineate the free energy landscape are routinely used to analyze the relative stability of conformational states, to determine phase boundaries, and to compute ligand-receptor binding energies its use in problems involving the cell membrane is limited. Here, we present an overview of four different free energy methods to study morphological transitions in bilayer membranes, induced either by the action of curvature remodeling proteins or due to the application of external forces. Using a triangulated surface as a model for the cell membrane and using the framework of dynamical triangulation Monte Carlo, we have focused on the methods of Widom insertion, thermodynamic integration, Bennett acceptance scheme, and umbrella sampling and weighted histogram analysis. We have demonstrated how these methods can be employed in a variety of problems involving the cell membrane. Specifically, we have shown that the chemical potential, computed using Widom insertion, and the relative free energies, computed using thermodynamic integration and Bennett acceptance method, are excellent measures to study the transition from curvature sensing to curvature inducing behavior of membrane associated proteins. The umbrella sampling and WHAM analysis has been used to study the thermodynamics of tether formation in cell membranes and the quantitative predictions of the computational model are in excellent agreement with experimental measurements. Furthermore, we also present a method based on WHAM and thermodynamic integration to handle problems related to end-point-catastrophe that are common in most free energy methods

physics.bio-ph↗

arXiv2015

Application of a Free Energy Landscape Approach to Study Tension Dependent Bilayer Tubulation Mediated by Curvature Inducing Proteins

We investigate the phenomenon of protein induced tubulation of lipid bilayer membranes within a continuum framework using Monte Carlo simulations coupled with the Widom insertion technique to compute excess chemical potentials. Tubular morphologies are spontaneously formed when the density and the curvature-field strength of the membrane bound proteins exceed their respective thresholds and this transition is marked by a sharp drop in the excess chemical potential. We find that the planar to tubular transition can be described by a micellar model and that the corresponding free energy barrier increases with increase in the curvature-field strength, (i.e. of protein-membrane interactions), and also with increase in membrane tension.

physics.bio-ph↗

arXiv2015

Defining the Free-Energy Landscape of Curvature-Inducing Proteins on Membrane Bilayers

Curvature-sensing and curvature-remodeling proteins are known to reshape cell membranes, and this remodeling event is essential for key biophysical processes such as tubulation, exocytosis, and endocytosis. Curvature-inducing proteins can act as curvature sensors as well as induce curvature in cell membranes to stabilize emergent high curvature, non-spherical, structures such as tubules, discs, and caveolae. A definitive understanding of the interplay between protein recruitment and migration, the evolution of membrane curvature, and membrane morphological transitions is emerging but remains incomplete. Here, within a continuum framework and using the machinery of Monte Carlo simulations, we introduce and compare three free-energy methods to delineate the free-energy landscape of curvature-inducing proteins on bilayer membranes. We demonstrate the utility of the Widom test-particle/field insertion methodology in computing the excess chemical potentials associated with curvature-inducing proteins on the membrane-- in particular, we use this method to track the onset of morphological transitions in the membrane at elevated protein densities. We validate this approach by comparing the results from the Widom method with those of thermodynamic integration and Bennett acceptance ratio methods. Furthermore, the predictions from the Widom method have been tested against analytical calculations of the excess chemical potential at infinite dilution. Our results are useful in precisely quantifying the free-energy landscape, and also in determining the phase boundaries associated with curvature-induction, curvature-sensing, and morphological transitions. This approach can be extended to studies exploring the role of thermal fluctuations and other external (control) variables, such as membrane excess area, in shaping curvature-mediated interactions on bilayer membranes.

physics.bio-ph↗

arXiv2014

Organelle morphogenesis by active remodeling

Intracellular organelles are subject to a steady flux of lipids and proteins through active, energy consuming transport processes. Active fission and fusion are promoted by GTPases, e.g., Arf-Coatamer and the Rab-Snare complexes, which both sense and generate local membrane curvature. Here we investigate through Dynamical Triangulation Monte Carlo simulations, the role that these active processes play in determining the morphology and compositional segregation in closed membranes. Our results suggest that the ramified morphologies of organelles observed in-vivo are a consequence of driven nonequilibrium processes rather than equilibrium forces.

physics.bio-ph↗

arXiv2013

Membrane mediated aggregation of curvature inducing nematogens and membrane tubulation

The shapes of cell membranes are largely regulated by membrane associated, curvature active, proteins. We use a numerical model of the membrane with elongated membrane inclusions, recently developed by us, which posses spontaneous directional curvatures that could be different along and perpendicular to its long axis. We show that, due to membrane mediated interactions these curvature inducing membrane nematogens can oligomerize spontaneously, even at low concentrations, and change the local shape of the membrane. We demonstrate that for a large group of such inclusions, where the two spontaneous curvatures have equal sign, the tubular conformation and sometime the sheet conformation of the membrane are the common equilibrium shapes. We elucidate the factors necessary for the formation of these {\it protein lattices}. Furthermore, the elastic properties of the tubes, like their compressional stiffness and persistence length are calculated. Finally, we discuss the possible role of nematic disclination in capping and branching of the tubular membranes.

physics.bio-ph↗

arXiv2012

Role of disclinations in determining the morphology of deformable fluid interfaces

We study the equilibrium shapes of vesicles, with an in-plane nematic order, using a Monte-Carlo scheme and show that highly curved shapes, like tubes and discs, with a striking similarity to the structures engendered by certain curvature sensing peripheral membrane proteins, can be spontaneously generated by anisotropic directional curvature with nematic disclinations playing and important role. We show that the coupling between nematic order and local curvature could lead to like defects moving towards each other and unlike defects moving away, in turn leading to tube formation. Thermally induced defect pair production lead to branched tubular structures. It is also shown that helical arrangement of the membrane tubes, with nematic field spiraling around it, is a dominant soft mode of the system.

physics.bio-ph↗

arXiv2011

Modeling anisotropic elasticity of fluid membranes

The biological membrane, which compartmentalizes the cell and its organelles, exhibit wide variety of macroscopic shapes of varying morphology and topology. A systematic understanding of the relation of membrane shapes to composition, external field, environmental conditions etc. have important biological relevance. Here we review the triangulated surface model, used in the macroscopic simulation of membranes and the associated Monte Carlo (DTMC) methods. New techniques to calculate surface quantifiers, that will facilitate the study of additional in-plane orientational degrees of freedom, has been introduced. The mere presence of a polar and nematic fields in the ordered phase drives the ground state conformations of the membrane to a cylinder and tetrahedron respectively.

physics.bio-ph↗

arXiv2010

Monte Carlo simulations of fluid vesicles with in plane orientational ordering

We present a method for simulating fluid vesicles with in-plane orientational ordering. The method involves computation of local curvature tensor and parallel transport of the orientational field on a randomly triangulated surface. It is shown that the model reproduces the known equilibrium conformation of fluid membranes and work well for a large range of bending rigidities. Introduction of nematic ordering leads to stiffening of the membrane. Nematic ordering can also result in anisotropic rigidity on the surface leading to formation of membrane tubes.

physics.bio-ph↗