Distribution of mechanical stress in the Escherichia coli cell envelope

Hwang, Hyea; Paracini, Nicolò; Parks, Jerry M.; Lakey, Jeremy H.; Gumbart, James C.

doi:10.1016/j.bbamem.2018.09.020

Title: Distribution of mechanical stress in the Escherichia coli cell envelope

Abstract

The cell envelope in Gram-negative bacteria comprises two distinct membranes with a cell wall between them. There has been a growing interest in understanding the mechanical adaptation of this cell envelope to the osmotic pressure (or turgor pressure), which is generated by the difference in the concentration of solutes between the cytoplasm and the external environment. However, it remains unexplored how the cell wall, the inner membrane (IM), and the outer membrane (OM) effectively protect the cell from this pressure by bearing the resulting surface tension, thus preventing the formation of inner membrane bulges, abnormal cell morphology, spheroplasts and cell lysis. In this study, we have used molecular dynamics (MD) simulations combined with experiments to resolve how and to what extent models of the IM, OM, and cell wall respond to changes in surface tension. We calculated the area compressibility modulus of all three components in simulations from tension-area isotherms. Experiments on monolayers mimicking individual leaflets of the IM and OM were also used to characterize their compressibility. While the membranes become softer as they expand, the cell wall exhibits significant strain stiffening at moderate to high tensions. We integrate these results into a model of the cell envelope inmore »« less

Authors:

Hwang, Hyea;

; Parks, Jerry M.;

;

Publication Date:: Sat Dec 01 00:00:00 EST 2018

Research Org.:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1576681

Alternate Identifier(s):: OSTI ID: 1504012

Grant/Contract Number:: SC0014664; AC05-00OR22725

Resource Type:: Published Article

Journal Name:: Biochimica et Biophysica Acta. Biomembranes

Additional Journal Information:: Journal Name: Biochimica et Biophysica Acta. Biomembranes Journal Volume: 1860 Journal Issue: 12; Journal ID: ISSN 0005-2736

Publisher:: Elsevier

Country of Publication:: Netherlands

Language:: English

Subject:: 59 BASIC BIOLOGICAL SCIENCES; Membrane mechanics; Area compressibility; Turgor pressure; Bacterial cell wall; Lipopolysaccharides

Citation Formats


                    Hwang, Hyea, Paracini, Nicolò, Parks, Jerry M., Lakey, Jeremy H., and Gumbart, James C. Distribution of mechanical stress in the Escherichia coli cell envelope.  Netherlands: N. p., 2018. 
Web.  doi:10.1016/j.bbamem.2018.09.020.

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                    Hwang, Hyea, Paracini, Nicolò, Parks, Jerry M., Lakey, Jeremy H., & Gumbart, James C. Distribution of mechanical stress in the Escherichia coli cell envelope.  Netherlands.  https://doi.org/10.1016/j.bbamem.2018.09.020

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                    Hwang, Hyea, Paracini, Nicolò, Parks, Jerry M., Lakey, Jeremy H., and Gumbart, James C. Sat .  
"Distribution of mechanical stress in the Escherichia coli cell envelope".  Netherlands.  https://doi.org/10.1016/j.bbamem.2018.09.020.

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@article{osti_1576681,

  title        = {Distribution of mechanical stress in the Escherichia coli cell envelope},

  author       = {Hwang, Hyea and Paracini, Nicolò and Parks, Jerry M. and Lakey, Jeremy H. and Gumbart, James C.},

  abstractNote = {The cell envelope in Gram-negative bacteria comprises two distinct membranes with a cell wall between them. There has been a growing interest in understanding the mechanical adaptation of this cell envelope to the osmotic pressure (or turgor pressure), which is generated by the difference in the concentration of solutes between the cytoplasm and the external environment. However, it remains unexplored how the cell wall, the inner membrane (IM), and the outer membrane (OM) effectively protect the cell from this pressure by bearing the resulting surface tension, thus preventing the formation of inner membrane bulges, abnormal cell morphology, spheroplasts and cell lysis. In this study, we have used molecular dynamics (MD) simulations combined with experiments to resolve how and to what extent models of the IM, OM, and cell wall respond to changes in surface tension. We calculated the area compressibility modulus of all three components in simulations from tension-area isotherms. Experiments on monolayers mimicking individual leaflets of the IM and OM were also used to characterize their compressibility. While the membranes become softer as they expand, the cell wall exhibits significant strain stiffening at moderate to high tensions. We integrate these results into a model of the cell envelope in which the OM and cell wall share the tension at low turgor pressure (0.3 atm) but the tension in the cell wall dominates at high values (>1 atm).},

  doi          = {10.1016/j.bbamem.2018.09.020},

  journal      = {Biochimica et Biophysica Acta. Biomembranes},

  number       = 12,

  volume       = 1860,

  place        = {Netherlands},

  year         = {Sat Dec 01 00:00:00 EST 2018},

  month        = {Sat Dec 01 00:00:00 EST 2018}

}

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Isolation of differentiated membrane domains from Escherichia coli and Salmonella typhimurium, including a fraction containing sites between the inner and outer membranes and Murein skeleton of the cell envelope

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Cell envelopes of Salmonella typhimurium and Escherichia coli were disrupted in a French pressure cell and fractionated by successive cycles of sedimentation and floatation density gradient centrifugation. This permitted the identification and isolation of several membrane fractions in addition to the major inner membrane and murein-outer membrane fractions. One of these fractions (fraction OM/sub L/) accounted for about 10% of the total cell envelope protein, and is likely to include the murein-membrane adhesion zones that are seen in electron micrographs of plasmolyzed cells. Fraction OM/sub L/ contained inner membrane, murein, and outer membrane in an apparently normal configuration, was capablemore »« less
Cryo-EM structure of OSCA1.2 from Oryza sativa elucidates the mechanical basis of potential membrane hyperosmolality gating

Journal Article Maity, Koustav ; Heumann, John M. ; McGrath, Aaron P. ; ... - Proceedings of the National Academy of Sciences of the United States of America

Sensing and responding to environmental water deficiency and osmotic stresses are essential for the growth, development, and survival of plants. Recently, an osmolality-sensing ion channel called OSCA1 was discovered that functions in sensing hyperosmolality inArabidopsis. In this paper, we report the cryo-electron microscopy (cryo-EM) structure and function of an OSCA1 homolog from rice (Oryza sativa; OsOSCA1.2), leading to a model of how it could mediate hyperosmolality sensing and transport pathway gating. The structure reveals a dimer; the molecular architecture of each subunit consists of 11 transmembrane (TM) helices and a cytosolic soluble domain that has homology to RNA recognition proteins.more »« less
Cited by 39
https://doi.org/10.1073/pnas.1900774116

Full Text Available
Structure and mutagenic analysis of the lipid II flippase MurJ from Escherichia coli

Journal Article Zheng, Sanduo ; Sham, Lok-To ; Rubino, Frederick A. ; ... - Proceedings of the National Academy of Sciences of the United States of America

The peptidoglycan cell wall provides an essential protective barrier in almost all bacteria, defining cellular morphology and conferring resistance to osmotic stress and other environmental hazards. The precursor to peptidoglycan, lipid II, is assembled on the inner leaflet of the plasma membrane. However, peptidoglycan polymerization occurs on the outer face of the plasma membrane, and lipid II must be flipped across the membrane by the MurJ protein before its use in peptidoglycan synthesis. Due to its central role in cell wall assembly, MurJ is of fundamental importance in microbial cell biology and is a prime target for novel antibiotic development.more »« less
Cited by 34
https://doi.org/10.1073/pnas.1802192115

Full Text Available
Localization of core lipopolysaccharide on the inner membrane of Salmonella typhimurium

Conference Marino, P A ; Osborn, M J - Fed. Proc., Fed. Am. Soc. Exp. Biol.; (United States)

The mechanism of lipopolysaccharide (LPS) translocation to the outer membrane (OM) is poorly defined. The authors have used affinity purified antiR/sub a/ LPS-IgG in immunoelectron microscopy and /sup 125/I protein A radio-labeling experiments to localize newly synthesized R/sub a/ LPS on the inner and outer faces of the inner membrane (IM)/sup a/. Cells were pulsed with galactose for 5 min to permit synthesis of R/sub a/ LPS and chased 0-20' by dilution into glucose medium. LPS translocation was halted by addition of DNP at 0/sup 0/. Samples +/-gal were spheroplasted or french pressed to expose outer and inner faces ofmore »« less
Molecular characterization of the outer membrane of Pseudomonas aeruginosa

Journal Article López, Cesar A. ; Zgurskaya, Helen ; Gnanakaran, S. - Biochimica et Biophysica Acta. Biomembranes

Discovery of new antibiotics effective against Gram-negative bacteria is hampered by the low permeability of the bacterial two-membrane cell envelopes. The outer membrane (OM) is an asymmetric bilayer of lipopolysaccharides (LPS) and phospholipids and is a significant permeability barrier to noxious compounds. Molecular characterization of the OM is essential for understanding how antibiotics penetrate this barrier, and for the development of new therapeutic strategies and rational drug design. We carry out all-atom (AA) and coarse-grained (CG) molecular dynamics (MD) simulations to characterize the fully assembled OM bilayer of Pseudomonas aeruginosa, a human pathogen resistant to most clinical antibiotics. These simulationsmore »« less
https://doi.org/10.1016/j.bbamem.2019.183151

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Title: Distribution of mechanical stress in the Escherichia coli cell envelope

Abstract

Citation Formats

Response of Escherichia coli growth rate to osmotic shock journal, May 2014

Nonlinear elasticity in biological gels journal, May 2005

Protein area occupancy at the center of the red blood cell membrane journal, February 2008

Constant surface tension simulations of lipid bilayers: The sensitivity of surface areas and compressibilities journal, July 1999

Reconstruction and modeling protein translocation and compartmentalization in Escherichia coli at the genome-scale journal, September 2014

Monolayer Film Behavior of Lipopolysaccharide from Pseudomonas aeruginosa at the Air−Water Interface journal, October 2008

Elasticity and Phase Behavior of DPPC Membrane Modulated by Cholesterol, Ergosterol, and Ethanol journal, October 2005

The Biophysics of the Gram-Negative Periplasmic Space journal, January 1998

Cryo-Transmission Electron Microscopy of Frozen-Hydrated Sections of Escherichia coli and Pseudomonas aeruginosa journal, October 2003

The Bacterial Cell Envelope journal, April 2010

Scalable molecular dynamics with NAMD journal, January 2005

Disruption of Asymmetric Lipid Bilayer Models Mimicking the Outer Membrane of Gram-Negative Bacteria by an Active Plasticin journal, October 2017

Electroporation of the E. coli and S. Aureus Membranes: Molecular Dynamics Simulations of Complex Bacterial Membranes journal, November 2011

MreB Actin-Mediated Segregation of a Specific Region of a Bacterial Chromosome journal, February 2005

Morphology, Growth, and Size Limit of Bacterial Cells journal, July 2010

Supramolecular assemblies underpin turnover of outer membrane proteins in bacteria journal, June 2015

Molecular Dynamics Simulations of Hydrophilic Pores in Lipid Bilayers journal, April 2004

Effect of Chain Length and Unsaturation on Elasticity of Lipid Bilayers journal, July 2000

Structure of lipid bilayers journal, November 2000

Covalent lipoprotein from the outer membrane of escherichia coli journal, October 1975

Lateral pressure in membranes journal, October 1996

Estimation of macromolecule concentrations and excluded volume effects for the cytoplasm of Escherichia coli journal, December 1991

Growth of the Stress-Bearing and Shape-Maintaining Murein Sacculus of Escherichia coli journal, January 1998

Thickness and Elasticity of Gram-Negative Murein Sacculi Measured by Atomic Force Microscopy journal, November 1999

Gram-negative trimeric porins have specific LPS binding sites that are essential for porin biogenesis journal, August 2016

Murein-lipoprotein of Escherichia coli: A protein involved in the stabilization of bacterial cell envelope journal, January 1978

Mechanical properties of lipid bilayers from molecular dynamics simulation journal, November 2015

Phosphatidylethanolamine-Phosphatidylglycerol Bilayer as a Model of the Inner Bacterial Membrane journal, February 2005

Lipopolysaccharide Endotoxins journal, June 2002

Molecular Basis of Bacterial Outer Membrane Permeability Revisited journal, December 2003

OmpA: A Flexible Clamp for Bacterial Cell Wall Attachment journal, December 2016

Mechanics of membrane bulging during cell-wall disruption in Gram-negative bacteria journal, April 2011

Molecular imaging of glycan chains couples cell-wall polysaccharide architecture to bacterial cell morphology journal, March 2018

Communication across the bacterial cell envelope depends on the size of the periplasm journal, December 2017

GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers journal, September 2015

CHARMM-GUI Membrane Builder toward realistic biological membrane simulations journal, August 2014

Inclusion of Many-Body Effects in the Additive CHARMM Protein CMAP Potential Results in Enhanced Cooperativity of α-Helix and β-Hairpin Formation journal, September 2012

Macromolecular crowding: obvious but underappreciated journal, October 2001

Peptidoglycan transformations during Bacillus subtilis sporulation : Peptidoglycan remodelling journal, March 2013

Constant pressure molecular dynamics simulation: The Langevin piston method journal, September 1995

Architecture and assembly of the Gram-positive cell wall: Gram-positive peptidoglycan structure journal, April 2013

Dynamics of Escherichia coli ’s passive response to a sudden decrease in external osmolarity journal, September 2016

Critical Temperature of 1-Palmitoyl-2-oleoyl- sn -glycero-3-phosphoethanolamine Monolayers and Its Possible Biological Relevance journal, July 2017

Structural Characterization of a Model Gram-Negative Bacterial Surface Using Lipopolysaccharides from Rough Strains of Escherichia coli journal, May 2013

Role of the Native Outer-Membrane Environment on the Transporter BtuB journal, October 2016

Update of the CHARMM All-Atom Additive Force Field for Lipids: Validation on Six Lipid Types journal, June 2010

Quantitative determination of ion distributions in bacterial lipopolysaccharide membranes by grazing-incidence X-ray fluorescence journal, May 2010

A unified formulation of the constant temperature molecular dynamics methods journal, July 1984

Membrane models of E. coli containing cyclic moieties in the aliphatic lipid chain journal, May 2012

Protein Diffusion in the Periplasm of E. coli under Osmotic Stress journal, January 2011

Molecular dynamics simulations of rupture in lipid bilayers journal, February 2010

Core structure of the outer membrane lipoprotein from Escherichia coli at 1.9 å resolution 1 1Edited by D. Rees journal, June 2000

Membrane stiffness is modified by integral membrane proteins journal, January 2016

Coarse-grained simulations of membranes under tension journal, March 2010

Entropic Tension in Crowded Membranes journal, March 2012

Simulation of Pore Formation in Lipid Bilayers by Mechanical Stress and Electric Fields journal, May 2003

Cryo-EM structure of the ribosome–SecYE complex in the membrane environment journal, April 2011

Particle mesh Ewald: An N ⋅log( N ) method for Ewald sums in large systems journal, June 1993

Pal Lipoprotein of Escherichia coli Plays a Major Role in Outer Membrane Integrity journal, February 2002

Direct Measurement of Cell Wall Stress Stiffening and Turgor Pressure in Live Bacterial Cells journal, October 2011

Strain Stiffening in Synthetic and Biopolymer Networks journal, May 2010

Mechanisms for maintaining cell shape in rod-shaped Gram-negative bacteria: Rod-shape maintenance in Gram-negative bacteria journal, April 2011

Cell envelope and shape of Escherichia coli: multiple mutants missing the outer membrane lipoprotein and other major outer membrane proteins. journal, January 1978

Microsecond Molecular Dynamics Simulations of Lipid Mixing journal, September 2014

The outer membrane is an essential load-bearing element in Gram-negative bacteria journal, July 2018

Water Permeability and Mechanical Strength of Polyunsaturated Lipid Bilayers journal, July 2000

Polymorphic transitions in single crystals: A new molecular dynamics method journal, December 1981

Peptidoglycan structure and architecture journal, March 2008

Measuring the stiffness of bacterial cells from growth rates in hydrogels of tunable elasticity: Measuring cellular mechanical properties with hydrogels journal, May 2012

Architecture of peptidoglycan: more data and more models journal, February 2010

Escherichia coli Peptidoglycan Structure and Mechanics as Predicted by Atomic-Scale Simulations journal, February 2014

Pressure−Area Isotherm of a Lipid Monolayer from Molecular Dynamics Simulations journal, December 2007

Canonical dynamics: Equilibrium phase-space distributions journal, March 1985

Molecular organization of Gram-negative peptidoglycan journal, November 2008

Atomic force microscopy and theoretical considerations of surface properties and turgor pressures of bacteria journal, February 2002

Fast, Multiphase Volume Adaptation to Hyperosmotic Shock by Escherichia coli journal, April 2012

Elastic deformation and failure of lipid bilayer membranes containing cholesterol journal, October 1990

Response of Escherichia coli growth rate to osmotic shock
journal, May 2014

Nonlinear elasticity in biological gels
journal, May 2005

Protein area occupancy at the center of the red blood cell membrane
journal, February 2008

Constant surface tension simulations of lipid bilayers: The sensitivity of surface areas and compressibilities
journal, July 1999

Reconstruction and modeling protein translocation and compartmentalization in Escherichia coli at the genome-scale
journal, September 2014

Monolayer Film Behavior of Lipopolysaccharide from Pseudomonas aeruginosa at the Air−Water Interface
journal, October 2008

Elasticity and Phase Behavior of DPPC Membrane Modulated by Cholesterol, Ergosterol, and Ethanol
journal, October 2005

The Biophysics of the Gram-Negative Periplasmic Space
journal, January 1998

Cryo-Transmission Electron Microscopy of Frozen-Hydrated Sections of Escherichia coli and Pseudomonas aeruginosa
journal, October 2003

The Bacterial Cell Envelope
journal, April 2010

Scalable molecular dynamics with NAMD
journal, January 2005

Disruption of Asymmetric Lipid Bilayer Models Mimicking the Outer Membrane of Gram-Negative Bacteria by an Active Plasticin
journal, October 2017

Electroporation of the E. coli and S. Aureus Membranes: Molecular Dynamics Simulations of Complex Bacterial Membranes
journal, November 2011

MreB Actin-Mediated Segregation of a Specific Region of a Bacterial Chromosome
journal, February 2005

Morphology, Growth, and Size Limit of Bacterial Cells
journal, July 2010

Supramolecular assemblies underpin turnover of outer membrane proteins in bacteria
journal, June 2015

Molecular Dynamics Simulations of Hydrophilic Pores in Lipid Bilayers
journal, April 2004

Effect of Chain Length and Unsaturation on Elasticity of Lipid Bilayers
journal, July 2000

Structure of lipid bilayers
journal, November 2000

Covalent lipoprotein from the outer membrane of escherichia coli
journal, October 1975

Lateral pressure in membranes
journal, October 1996

Estimation of macromolecule concentrations and excluded volume effects for the cytoplasm of Escherichia coli
journal, December 1991

Growth of the Stress-Bearing and Shape-Maintaining Murein Sacculus of Escherichia coli
journal, January 1998

Thickness and Elasticity of Gram-Negative Murein Sacculi Measured by Atomic Force Microscopy
journal, November 1999

Gram-negative trimeric porins have specific LPS binding sites that are essential for porin biogenesis
journal, August 2016

Murein-lipoprotein of Escherichia coli: A protein involved in the stabilization of bacterial cell envelope
journal, January 1978

Mechanical properties of lipid bilayers from molecular dynamics simulation
journal, November 2015

Phosphatidylethanolamine-Phosphatidylglycerol Bilayer as a Model of the Inner Bacterial Membrane
journal, February 2005

Lipopolysaccharide Endotoxins
journal, June 2002

Molecular Basis of Bacterial Outer Membrane Permeability Revisited
journal, December 2003

OmpA: A Flexible Clamp for Bacterial Cell Wall Attachment
journal, December 2016

Mechanics of membrane bulging during cell-wall disruption in Gram-negative bacteria
journal, April 2011

Molecular imaging of glycan chains couples cell-wall polysaccharide architecture to bacterial cell morphology
journal, March 2018

Communication across the bacterial cell envelope depends on the size of the periplasm
journal, December 2017

GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers
journal, September 2015

CHARMM-GUI Membrane Builder toward realistic biological membrane simulations
journal, August 2014

Inclusion of Many-Body Effects in the Additive CHARMM Protein CMAP Potential Results in Enhanced Cooperativity of α-Helix and β-Hairpin Formation
journal, September 2012

Macromolecular crowding: obvious but underappreciated
journal, October 2001

Peptidoglycan transformations during Bacillus subtilis sporulation : Peptidoglycan remodelling
journal, March 2013

Constant pressure molecular dynamics simulation: The Langevin piston method
journal, September 1995

Architecture and assembly of the Gram-positive cell wall: Gram-positive peptidoglycan structure
journal, April 2013

Dynamics of Escherichia coli ’s passive response to a sudden decrease in external osmolarity
journal, September 2016

Critical Temperature of 1-Palmitoyl-2-oleoyl- sn -glycero-3-phosphoethanolamine Monolayers and Its Possible Biological Relevance
journal, July 2017

Structural Characterization of a Model Gram-Negative Bacterial Surface Using Lipopolysaccharides from Rough Strains of Escherichia coli
journal, May 2013

Role of the Native Outer-Membrane Environment on the Transporter BtuB
journal, October 2016

Update of the CHARMM All-Atom Additive Force Field for Lipids: Validation on Six Lipid Types
journal, June 2010

Quantitative determination of ion distributions in bacterial lipopolysaccharide membranes by grazing-incidence X-ray fluorescence
journal, May 2010

A unified formulation of the constant temperature molecular dynamics methods
journal, July 1984

Membrane models of E. coli containing cyclic moieties in the aliphatic lipid chain
journal, May 2012

Protein Diffusion in the Periplasm of E. coli under Osmotic Stress
journal, January 2011

Molecular dynamics simulations of rupture in lipid bilayers
journal, February 2010

Core structure of the outer membrane lipoprotein from Escherichia coli at 1.9 å resolution 1 1Edited by D. Rees
journal, June 2000

Membrane stiffness is modified by integral membrane proteins
journal, January 2016

Coarse-grained simulations of membranes under tension
journal, March 2010

Entropic Tension in Crowded Membranes
journal, March 2012

Simulation of Pore Formation in Lipid Bilayers by Mechanical Stress and Electric Fields
journal, May 2003

Cryo-EM structure of the ribosome–SecYE complex in the membrane environment
journal, April 2011

Particle mesh Ewald: An N ⋅log( N ) method for Ewald sums in large systems
journal, June 1993

Pal Lipoprotein of Escherichia coli Plays a Major Role in Outer Membrane Integrity
journal, February 2002

Direct Measurement of Cell Wall Stress Stiffening and Turgor Pressure in Live Bacterial Cells
journal, October 2011

Strain Stiffening in Synthetic and Biopolymer Networks
journal, May 2010

Mechanisms for maintaining cell shape in rod-shaped Gram-negative bacteria: Rod-shape maintenance in Gram-negative bacteria
journal, April 2011

Cell envelope and shape of Escherichia coli: multiple mutants missing the outer membrane lipoprotein and other major outer membrane proteins.
journal, January 1978

Microsecond Molecular Dynamics Simulations of Lipid Mixing
journal, September 2014

The outer membrane is an essential load-bearing element in Gram-negative bacteria
journal, July 2018

Water Permeability and Mechanical Strength of Polyunsaturated Lipid Bilayers
journal, July 2000

Polymorphic transitions in single crystals: A new molecular dynamics method
journal, December 1981

Peptidoglycan structure and architecture
journal, March 2008

Measuring the stiffness of bacterial cells from growth rates in hydrogels of tunable elasticity: Measuring cellular mechanical properties with hydrogels
journal, May 2012

Architecture of peptidoglycan: more data and more models
journal, February 2010

Escherichia coli Peptidoglycan Structure and Mechanics as Predicted by Atomic-Scale Simulations
journal, February 2014

Pressure−Area Isotherm of a Lipid Monolayer from Molecular Dynamics Simulations
journal, December 2007

Canonical dynamics: Equilibrium phase-space distributions
journal, March 1985

Molecular organization of Gram-negative peptidoglycan
journal, November 2008

Atomic force microscopy and theoretical considerations of surface properties and turgor pressures of bacteria
journal, February 2002

Fast, Multiphase Volume Adaptation to Hyperosmotic Shock by Escherichia coli
journal, April 2012

Elastic deformation and failure of lipid bilayer membranes containing cholesterol
journal, October 1990

Effect of membrane tension on the physical properties of DOPC lipid bilayer membrane
journal, September 2012

Spatial and energetic-entropic decomposition of surface tension in lipid bilayers from molecular dynamics simulations
journal, September 2000

Elasticity of the sacculus of Escherichia coli.
journal, January 1992