Linear Elastic Model for Generating Wavy Structure Wavy in Lipid - PowerPoint PPT Presentation

Linear Elastic Model for Generating Linear Elastic Model for Generating Wavy Structure Wavy in Lipid Membrane by Peripheral Proteins Structure in Lipid Membrane by by Paritosh Mahata Paritosh Mahata PRAVARTANA - 2016 Indian Institute of Technology Kanpur Kanpur 208016, India

Outline Linear Elastic Introduction Model for - Lipid Molecule and Cell Membrane Generating - Mechanisms of Membrane Curvature Generation Wavy - Qualitative Essence of Wavy Structure Structure in Lipid Membrane as Linear Elastic Material Lipid - Assumptions Membrane by Computational Model Paritosh - Model Parameters Mahata Computations Results - For Single Monolayer - For Lipid Bilayer Conclusions

Introduction Linear Elastic Model for Generating Wavy Structure in Lipid Membrane Lipid Molecule 1 Cell Membrane 2 by Binding of proteins, cholesterol, and other cellular components make the Paritosh Mahata membrane non-homogeneous in structure Peripheral proteins can sense and generate membrane curvature to maintain biological processes like Endocytosis and Exocytosis Malfunctioning of binding interplay between protein and membrane produces several diseases like cancer, Parkinsons, etc 1 http://commons.wikimedia.org/wiki/File: 0312 Animal Cell and Components.jpg 2 www.wcc.hawaii.edu/facstaff/.../005%20Biological%20Molecules.ppt

Introduction Linear Elastic Mechanisms of Membrane Curvature Generation Model for Ref: http://www.endocytosis.org/research/structur/structure.html Generating Wavy Structure in Lipid Membrane by Paritosh Mahata Ref: T. Baumgart et al. Annu. Rev. Phys. Chem, 62,483 (2011)

Introduction Qualitative Essence of Wavy Structure Linear Elastic Model for Generating Wavy Structure in Lipid Membrane by Paritosh Mahata Ref: Kabaso et al. Annu. Rev. Phys. Chem 62, 483 (2011) Ref: Arkhipov et al. Biophys. J. 95, 2806 (2008)

Lipid Membrane as Linear Elastic Material Linear Elastic Hooke’s Law 3 : Model for σ ij = C ijkl ǫ kl Generating � ∂u k Wavy ǫ kl = 1 + ∂u l � Structure in 2 ∂x l ∂x k Lipid Equilibrium Equations: Membrane σ ij,j + f i = 0 by Elastic moduli tensor C has total 21 independent constants Paritosh Mahata Assumptions 4 : - Membrane is isotropic in lateral direction and solid in transverse direction - Plane strain deformation of the membrane in the plane of cross-section - Two volume stretching-compression moduli are equal 3 W. S. Slaughter (2002). The linearized theory of elasticity, First Edition 4 Campelo et al. Biophys. J. 95, 2325 (2008)

Lipid Membrane as Linear Elastic Material Linear Elastic Model for Generating Independent elastic moduli constants of the membrane material reduce Wavy into three - C xxxx , C xxyy , and C xyxy Structure in Displacement Equations: Lipid ∂ 2 u x ∂ 2 u x ∂y 2 + ( C xxyy + C xyxy ) ∂ 2 u y Membrane C xxxx ∂x 2 + C xyxy ∂x∂y = 0 by Paritosh ∂ 2 u y ∂ 2 u y ∂y 2 + ( C xxyy + C xyxy ) ∂ 2 u x Mahata C xyxy ∂x 2 + C yyyy ∂x∂y = 0 Displacement equations are solved using Finite Element Method in ABAQUS

Computational Model Linear Elastic y Model for p ( x ) Rigid Inclusion Generating f = qE Wavy r H d p Head 3 y c Structure in H Tail Lipid (0,0) x L Membrane Boundary Conditions: by σ yy ( x, 0) = σ xy ( x, 0) = 0 ( Lower surface ) Paritosh Mahata σ yy ( x, H ) = p ( x ) , σ xy ( x, H ) = 0 ( Upper surface ) u x ( L, y ) = 0 , and σ xy ( L, y ) = 0 ( Right surface ) u x ( L, y ) = 0 , for y < y c − r � r 2 − ( y − y c ) 2 = y ≥ y c − r ( Left surface ) for and σ xy = 0 To restrict rigid motion: u y (0 , y c − r ) = 0

Model Parameters Linear Elastic H = 2 nm, r = 0.5 nm, and d p = 0 . 8 nm Model for Generating L is obtained from the binding data of peripheral proteins Wavy Elastic Constants 5 : Structure in - For Head Lipid xxxx = 4 × 10 9 N/m 2 , C h xxyy = 3 . 93 × 10 9 N/m 2 , C h Membrane by xyxy = 1 . 5 × 10 7 N/m 2 C h and Paritosh Mahata - For Tail xxxx = 1 × 10 9 N/m 2 , C t xxyy = 0 . 98 × 10 9 N/m 2 , C t xyxy = 1 . 5 × 10 7 N/m 2 C t and 5 Campelo et al. Biophys. J. 95, 2325(2008)

Model Parameters Linear Elastic Electrostatic Force: Model for p ( x ) = f x L ( Linear ) Generating � x Wavy p ( x ) = f L ( Convex Parabolic ) Structure in and p ( x ) = f x 2 L 2 ( Concave Parabolic ) Lipid Membrane where f = electrostatic force = qE by Paritosh Mahata Ref: Kabaso et al. Annu. Rev. Phys. Chem 62,483(2011).

Computations Linear Elastic Model for Deformed Upper Surface of Membrane Generating L a C Wavy d c A L Structure in B D Lipid Membrane Φ R by Paritosh Mahata O For different variations of p ( x ) , charge intensity q is computed to get d c for corresponding R Binding data of peripheral proteins are used to get L and R

Results For Monolayer (Binding of Amphiphysin N-BAR): Linear Elastic Model for (a) 0.12 Hydrophobic and Electrostatic Generating 0.09 Only Electrostatic Interaction q (C/m 2 ) 0.06 Wavy p ( x ) = f x 0.03 L Structure in 0 5 10 15 20 25 30 35 R (nm) Lipid (b) (c) 0.08 0.12 p ( x ) = f � x p ( x ) = f x 2 Membrane 0.06 0.09 L L 2 q (C/m 2 ) q (C/m 2 ) 0.04 0.06 by 0.02 0.03 Paritosh 0 0 Mahata 5 10 15 20 25 30 35 5 10 15 20 25 30 35 R (nm) R (nm)

Results For Lipid Bilayer (Binding of Amphiphysin N-BAR): Linear Elastic Model for Generating Wavy Structure in Lipid Membrane by 0.07 Monolayer Paritosh Bilayer Mahata 0.06 0.05 q (C/m 2 ) p ( x ) = f x 2 0.04 L 2 0.03 0.02 0.01 10 15 20 25 30 35 R (nm)

Results Linear Elastic For Lipid Bilayer (Different depth of penetration of inclusion): Model for Generating Linear Convex Parabolic Concave Parabolic 0.08 0.04 Wavy Structure in 0.06 0.03 q (C/m 2 ) q (C/m 2 ) Lipid 0.04 0.02 Membrane R = 20 nm R = 15 nm by 0.02 0.01 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 Paritosh d p (nm) d p (nm) Mahata 0.025 0.02 0.02 0.015 q (C/m 2 ) q (C/m 2 ) 0.015 0.01 R = 30 nm R = 25 nm 0.01 0.005 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 d p (nm) d p (nm)

Results Linear Elastic For Lipid Bilayer (Only Hydrophobic Interaction): Model for Generating Wavy −0.2 −0.2 L = 7 . 84 nm −0.25 L = 8 . 02 nm Structure in L = 8 . 11 nm L = 8 . 15 nm −0.3 Lipid −0.35 Membrane −0.4 d c (nm) by −0.45 Only Hydrophobic Interaction Paritosh −0.5 Mahata −0.55 −0.6 −0.65 −0.7 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 d p (nm)

Conclusions Linear Elastic Model for Generating Electrostatic interaction between protein and membrane plays an important Wavy role in membrane curvature generation Structure in Lipid Insertion of amphipathic helices of the BAR protein reduces the positive Membrane deformations of the membrane towards binding proteins by In comparison to the single monolayer, higher charge intensities are Paritosh required to bend lipid bilayer membrane Mahata Shallow insertion of amphipathic helices produces negative curvature to the membrane

Acknowledgment Linear Elastic Model for Generating Wavy Structure in Dr. Sovan Lal Das Lipid Associate Professor, Membrane Department of Mechanical Engineering, by IIT Kanpur Paritosh Mahata

Linear Elastic Model for Generating Wavy Structure in Lipid THANK YOU Membrane by Paritosh Mahata