Indian Institute of Technology Palakkad&nbsp;(IIT Palakkad or IIT PKD) is a public autonomous&nbsp;engineering&nbsp;and&nbsp;research&nbsp;institute located in&nbsp;Palakkad,&nbsp;Kerala. It was&nbsp;one of the five new&nbsp;IITs&nbsp;proposed in the&nbsp;2014 Union budget of India. The campus was inaugurated on 3 August 2015. The institute has 94 faculty, 978 students, and 63 non-teaching staffs.

IT Palakkad currently offers four-year Bachelor of Technology (B.Tech) and two years MS programmes in 8 different engineering disciplines including&nbsp;Computer Science, Electrical, Mechanical, Civil among others.

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IIT Palakkad

Membrane curvature of a biological cell is actively involved in various fundamental cell biological functions. It has been discovered that membrane curvature and binding of peripheral membrane proteins follow a symbiotic relationship. The exact mechanism behind this interplay of protein binding and membrane curvature has not yet been properly understood. To improve understanding of the mechanism, we study curvature sorting of proteins in a model system consisting of a tether pulled from a giant unilamellar vesicle using mechanical-thermodynamic models. The concentration of proteins bound to the membrane changes significantly due to curvature. This has also been observed in experiments by other researchers. We also find that there is a phase transition based on protein concentration and we discuss the coexistence of phases and stability of solutions. Furthermore, when sorting is favorable, the increase in protein concentration stabilizes the tether in the sense that less pulling force is required to maintain the tether. A similar mechanism may be in place, when motor proteins pull tethers from donor membranes. © 2012 American Physical Society.

World University root node

Department of Mechanical Engineering

Fulltext

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Curvature sorting of proteins on a cylindrical lipid membrane tether connected to a reservoir

The curvature of biological membranes is controlled by membrane-bound proteins. For example, during endocytosis, the sorting of membrane components, vesicle budding, and fission from the plasma membrane are mediated by adaptor and accessory proteins. Endophilin is a peripherally binding membrane protein that functions as an endocytic accessory protein. Endophilin's membrane tubulation capacity is well known. However, to understand the thermodynamic and mechanical aspects of endophilin function, experimental measurements need to be compared to quantitative theoretical models. We present measurements of curvature sorting and curvature generation of the endophilin A1 N-BAR domain on tubular membranes pulled from giant unilamellar vesicles. At low concentration, endophilin functions primarily as a membrane curvature sensor; at high concentrations, it also generates curvature. We determine the spontaneous curvature induced by endophilin and observe sigmoidal curvature/composition coupling isotherms that saturate at high membrane tensions and protein solution concentrations. The observation of saturation is supported by a strong dependence of lateral diffusion coefficients on protein density on the tether membrane. We develop a nonlinear curvature/composition coupling model that captures our experimental observations. Our model predicts a curvature-induced phase transition among two states with varying protein density and membrane curvature. This transition could act as a switch during endocytosis. © 2012 Biophysical Society.

Biophysical Journal

Nonlinear sorting, curvature generation, and crowding of endophilin N-BAR on tubular membranes

Research investigating lipid membrane curvature generation and sensing is a rapidly developing frontier in membrane physical chemistry and biophysics. The fast recent progress is based on the discovery of a plethora of proteins involved in coupling membrane shape to cellular membrane function, the design of new quantitative experimental techniques to study aspects of membrane curvature, and the development of analytical theories and simulation techniques that allow a mechanistic interpretation of quantitative measurements. The present review first provides an overview of important classes of membrane proteins for which function is coupled to membrane curvature. We then survey several mechanisms that are assumed to underlie membrane curvature sensing and generation. Finally, we discuss relatively simple thermodynamic/mechanical models that allow quantitative interpretation of experimental observations. © 2011 by Annual Reviews. All rights reserved.

Annual Review of Physical Chemistry

Thermodynamics and mechanics of membrane curvature generation and sensing by proteins and lipids

Micropipette aspiration technique can be very useful for describing the shape transitions of lipid bilayer vesicles with fluid phase coexistence modulated by the line tension and the bending rigidity. For example, composition dependence of the line tension at the liquid-ordered and liquid-disordered phase interface has been investigated using this technique. Recently, using a very simple mechanical model, the instabilities that occur during suction and release experiments of aspirated vesicles have been discussed. Due to its simplicity the model could not predict the influence of the bending rigidity. In this work, we incorporate the contributions from Helfrich bending energy and the line energy in the vesicle free energy and investigate the shape transitions in micropipette aspirated vesicles. We discuss how the critical aspiration pressure depends on the bending moduli of the phases, the line tension at the interface, and the reduced volume of the vesicle. The ratio of the bending moduli that we predict using the critical aspiration pressure data from recent experiments agrees with the literature. © 2010 The American Physical Society.

Influence of the bending rigidity and the line tension on the mechanical stability of micropipette aspirated vesicles

Lipid bilayer vesicles with fluid/fluid phase coexistence are promising model systems for biological cell membranes. They permit the investigation of the mechanical properties of lipid membranes that are important for understanding mechanistic aspects of biological membrane function. Comparison of experimentally obtained vesicle shapes to mechanical membrane theories has enabled us to determine the values of line tension and mean-curvature bending stiffness of liquid-ordered and -disordered membranes. An additional important parameter that controls membrane geometry is the spontaneous curvature, driven, for example, by peripheral protein coats or asymmetric lipid composition. We examine to what extent effects of differing spontaneous curvature and Gauss curvature stiffness between coexisting fluid phases can be distinguished by membrane shape analysis. We find that the equilibrium neck geometries of dumbbell-shaped vesicles and the shapes of vesicles close to budding are very similar for vesicles that differ in spontaneous curvature or Gauss curvature stiffness differences. However, the two parameters have qualitatively different influence on discontinuous budding transitions. © EPLA, 2009.

Neck geometry and shape transitions in vesicles with co-existing fluid phases: Role of Gaussian curvature stiffness vs. spontaneous curvature

We obtain approximate solutions to the equations that govern the shape of giant unilamellar vesicles (GUVs) with two fluid phases. The equations involve a dimensionless small parameter related to the resistance to changes in its local mean curvature. Asymptotic solutions for the shape are obtained up to and including terms of first order in the small parameter. At this order, we determine a relationship between the tangent angle at the interface and the difference in the Gaussian curvature stiffnesses of the co-existing phases. This relationship demonstrates that a difference in the Gaussian curvature stiffnesses moves the phase boundary away from the neck, as determined in previous numerical studies. The analytical expression for the tangent angle obtained here can be used to determine elastic parameters for the membranes from experimental data. Use of the analytical expression will eliminate the need for the repeated generation of numerical solutions in the estimation of the material parameters. Our analytical solution also reduces the number of measurements needed as inputs for an existing boundary layer analysis. © 2008 Cambridge University Press.

Journal of Fluid Mechanics

A higher-order boundary layer analysis for lipid vesicles with two fluid domains

Biophysical journal

An analysis of micropipette aspiration of one-phase and two-phase vesicles

The 2006 Spring National Meeting

Experimental Investigation and Kinetic Theory Based Model of an Annular Granular Shear Flow

Biological membranes are known to contain compositional heterogeneities, often termed rafts, with distinguishable composition and function, and these heterogeneities participate in vigorous transport processes. Membrane lipid phase coexistence is expected to modulate these processes through the differing mechanical properties of the bulk domains and line tension at phase boundaries. In this contribution, we compare the predictions from a shape theory derived for vesicles with fluid phase coexistence to the geometry of giant unilamellar vesicles with coexisting liquid-disordered (Ld) and liquid-ordered (Lo) phases. We find a bending modulus for the Lo phase higher than that of the Ld phase and a saddle-splay (Gauss) modulus difference with the Gauss modulus of the Lo phase being more negative than the Ld phase. The Gauss modulus critically influences membrane processes that change topology, such as vesicle fission or fusion, and could therefore be of significant biological relevance in heterogeneous membranes. Our observations of experimental vesicle geometries being modulated by Gaussian curvature moduli differences confirm the prediction by the theory of Juelicher and Lipowsky. © 2005 by the Biophysical Society.

Membrane elasticity in giant vesicles with fluid phase coexistence

We use the method of multiple scales (MMS) to study small perturbations governed by a parameter ε of a harmonic oscillator by a small term with a large delay. These systems differ significantly from others where small terms have script O sign(1) delays; or an script O sign(1) term has script O sign(1) delay in a system near a Hopf bifurcation. Here the slow flow in time ε t depends strongly on ε even at lowest order and itself has an script O sign(1) delay. The MMS has already been applied elsewhere for such systems but only to first order and with attention restricted to periodic and quasiperiodic solutions. Here we address transients as well as proceed to second order. The second order analysis holds unless a special resonance occurs (we assume it does not). Several numerical examples are presented. In each case the slow flows are infinite-dimensional show strong ε-dependence require significantly less computation time than the full solutions yet agree well with the same. © 2005 Springer Science + Business Media Inc.

Nonlinear Dynamics

Second order multiple scales for oscillators with large delay

The method of multiple scales and the related method of averaging are commonly used to study slowly modulated oscillations. If the system of interest is a slightly perturbed harmonic oscillator, then these techniques can be applied easily. If the unperturbed system is strongly nonlinear (though possibly conservative), then these methods can run into difficulties due to the impossibility of carrying out required analytical operations in closed form. In this paper, we abandon the requirement of closed form analytical treatment at all stages. Instead, Galerkin projections are used to obtain approximate realizations of the method of multiple scales. This paper adapts recent work using similar ideas for approximate realizations of the method of averaging. A key contribution of the present work is in the systematic identification and removal of secular terms in the general nonlinear case, a procedure that is more difficult than for the perturbed harmonic oscillator case, and that is unnecessary for averaging. A strength of the present work is that the heuristics (Galerkin) and asymptotics (multiple scales) are kept distinct, leaving room for systematic refinement of the former without compromising the asymptotic features of the latter.

Multiple scales via Galerkin projections: Approximate asymptotics for strongly nonlinear oscillations

We study small perturbations of three linear Delay Differential Equations (DDEs) close to Hopf bifurcation points. In analytical treatments of such equations, many authors recommend a center manifold reduction as a first step. We demonstrate that the method of multiple scales, on simply discarding the infinitely many exponentially decaying components of the complementary solutions obtained at each stage of the approximation, can bypass the explicit center manifold calculation. Analytical approximations obtained for the DDEs studied closely match numerical solutions.

Multiple scales without center manifold reductions for delay differential equations near Hopf bifurcations

We revisit the simplest walker studied earlier by Garcia and co-workers. We extend the small-slope stability analysis to second order, substantially improving accuracy, and also provide some details left out of the earlier work. We develop an alternative (reverse) approach for the stability analysis, which involves shorter calculations: for stability analysis upto any given order, the new procedure requires calculations to one order less than the previous (forward) procedure. The stability results obtained by the two methods are, nevertheless, equivalent.