Modeling the Mechanics of Cell Division: Influence of Spontaneous Membrane Curvature, Surface Tension, and Osmotic Pressure
Many cell division processes have been conserved throughout evolution and are being revealed by studies on model organisms such as bacteria, yeasts, and protozoa. Cellular membrane constriction is one of these processes, observed almost universally during cell division. It happens similarly in all o...
Main Authors: | , , , |
---|---|
Format: | Article |
Language: | English |
Published: |
Frontiers Media S.A.
2017-05-01
|
Series: | Frontiers in Physiology |
Subjects: | |
Online Access: | http://journal.frontiersin.org/article/10.3389/fphys.2017.00312/full |
id |
doaj-c464ae984e304fe389ec8ce48484b508 |
---|---|
record_format |
Article |
spelling |
doaj-c464ae984e304fe389ec8ce48484b5082020-11-25T00:20:57ZengFrontiers Media S.A.Frontiers in Physiology1664-042X2017-05-01810.3389/fphys.2017.00312252567Modeling the Mechanics of Cell Division: Influence of Spontaneous Membrane Curvature, Surface Tension, and Osmotic PressureElena Beltrán-Heredia0Elena Beltrán-Heredia1Víctor G. Almendro-Vedia2Víctor G. Almendro-Vedia3Francisco Monroy4Francisco Monroy5Francisco J. Cao6Departamento de Física Atómica, Molecular y Nuclear, Universidad Complutense de MadridMadrid, SpainDepartamento de Química Física I, Universidad Complutense de MadridMadrid, SpainDepartamento de Física Atómica, Molecular y Nuclear, Universidad Complutense de MadridMadrid, SpainDepartamento de Química Física I, Universidad Complutense de MadridMadrid, SpainDepartamento de Química Física I, Universidad Complutense de MadridMadrid, SpainTranslational Biophysics, Instituto de Investigación Sanitaria Hospital 12 de Octubre (imas12)Madrid, SpainDepartamento de Física Atómica, Molecular y Nuclear, Universidad Complutense de MadridMadrid, SpainMany cell division processes have been conserved throughout evolution and are being revealed by studies on model organisms such as bacteria, yeasts, and protozoa. Cellular membrane constriction is one of these processes, observed almost universally during cell division. It happens similarly in all organisms through a mechanical pathway synchronized with the sequence of cytokinetic events in the cell interior. Arguably, such a mechanical process is mastered by the coordinated action of a constriction machinery fueled by biochemical energy in conjunction with the passive mechanics of the cellular membrane. Independently of the details of the constriction engine, the membrane component responds against deformation by minimizing the elastic energy at every constriction state following a pathway still unknown. In this paper, we address a theoretical study of the mechanics of membrane constriction in a simplified model that describes a homogeneous membrane vesicle in the regime where mechanical work due to osmotic pressure, surface tension, and bending energy are comparable. We develop a general method to find approximate analytical expressions for the main descriptors of a symmetrically constricted vesicle. Analytical solutions are obtained by combining a perturbative expansion for small deformations with a variational approach that was previously demonstrated valid at the reference state of an initially spherical vesicle at isotonic conditions. The analytic approximate results are compared with the exact solution obtained from numerical computations, getting a good agreement for all the computed quantities (energy, area, volume, constriction force). We analyze the effects of the spontaneous curvature, the surface tension and the osmotic pressure in these quantities, focusing especially on the constriction force. The more favorable conditions for vesicle constriction are determined, obtaining that smaller constriction forces are required for positive spontaneous curvatures, low or negative membrane tension and hypertonic media. Conditions for spontaneous constriction at a given constriction force are also determined. The implications of these results for biological cell division are discussed. This work contributes to a better quantitative understanding of the mechanical pathway of cellular division, and could assist the design of artificial divisomes in vesicle-based self-actuated microsystems obtained from synthetic biology approaches.http://journal.frontiersin.org/article/10.3389/fphys.2017.00312/fullcell divisionmembrane constrictionbending energyspontaneous curvaturesurface tensionosmotic pressure |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Elena Beltrán-Heredia Elena Beltrán-Heredia Víctor G. Almendro-Vedia Víctor G. Almendro-Vedia Francisco Monroy Francisco Monroy Francisco J. Cao |
spellingShingle |
Elena Beltrán-Heredia Elena Beltrán-Heredia Víctor G. Almendro-Vedia Víctor G. Almendro-Vedia Francisco Monroy Francisco Monroy Francisco J. Cao Modeling the Mechanics of Cell Division: Influence of Spontaneous Membrane Curvature, Surface Tension, and Osmotic Pressure Frontiers in Physiology cell division membrane constriction bending energy spontaneous curvature surface tension osmotic pressure |
author_facet |
Elena Beltrán-Heredia Elena Beltrán-Heredia Víctor G. Almendro-Vedia Víctor G. Almendro-Vedia Francisco Monroy Francisco Monroy Francisco J. Cao |
author_sort |
Elena Beltrán-Heredia |
title |
Modeling the Mechanics of Cell Division: Influence of Spontaneous Membrane Curvature, Surface Tension, and Osmotic Pressure |
title_short |
Modeling the Mechanics of Cell Division: Influence of Spontaneous Membrane Curvature, Surface Tension, and Osmotic Pressure |
title_full |
Modeling the Mechanics of Cell Division: Influence of Spontaneous Membrane Curvature, Surface Tension, and Osmotic Pressure |
title_fullStr |
Modeling the Mechanics of Cell Division: Influence of Spontaneous Membrane Curvature, Surface Tension, and Osmotic Pressure |
title_full_unstemmed |
Modeling the Mechanics of Cell Division: Influence of Spontaneous Membrane Curvature, Surface Tension, and Osmotic Pressure |
title_sort |
modeling the mechanics of cell division: influence of spontaneous membrane curvature, surface tension, and osmotic pressure |
publisher |
Frontiers Media S.A. |
series |
Frontiers in Physiology |
issn |
1664-042X |
publishDate |
2017-05-01 |
description |
Many cell division processes have been conserved throughout evolution and are being revealed by studies on model organisms such as bacteria, yeasts, and protozoa. Cellular membrane constriction is one of these processes, observed almost universally during cell division. It happens similarly in all organisms through a mechanical pathway synchronized with the sequence of cytokinetic events in the cell interior. Arguably, such a mechanical process is mastered by the coordinated action of a constriction machinery fueled by biochemical energy in conjunction with the passive mechanics of the cellular membrane. Independently of the details of the constriction engine, the membrane component responds against deformation by minimizing the elastic energy at every constriction state following a pathway still unknown. In this paper, we address a theoretical study of the mechanics of membrane constriction in a simplified model that describes a homogeneous membrane vesicle in the regime where mechanical work due to osmotic pressure, surface tension, and bending energy are comparable. We develop a general method to find approximate analytical expressions for the main descriptors of a symmetrically constricted vesicle. Analytical solutions are obtained by combining a perturbative expansion for small deformations with a variational approach that was previously demonstrated valid at the reference state of an initially spherical vesicle at isotonic conditions. The analytic approximate results are compared with the exact solution obtained from numerical computations, getting a good agreement for all the computed quantities (energy, area, volume, constriction force). We analyze the effects of the spontaneous curvature, the surface tension and the osmotic pressure in these quantities, focusing especially on the constriction force. The more favorable conditions for vesicle constriction are determined, obtaining that smaller constriction forces are required for positive spontaneous curvatures, low or negative membrane tension and hypertonic media. Conditions for spontaneous constriction at a given constriction force are also determined. The implications of these results for biological cell division are discussed. This work contributes to a better quantitative understanding of the mechanical pathway of cellular division, and could assist the design of artificial divisomes in vesicle-based self-actuated microsystems obtained from synthetic biology approaches. |
topic |
cell division membrane constriction bending energy spontaneous curvature surface tension osmotic pressure |
url |
http://journal.frontiersin.org/article/10.3389/fphys.2017.00312/full |
work_keys_str_mv |
AT elenabeltranheredia modelingthemechanicsofcelldivisioninfluenceofspontaneousmembranecurvaturesurfacetensionandosmoticpressure AT elenabeltranheredia modelingthemechanicsofcelldivisioninfluenceofspontaneousmembranecurvaturesurfacetensionandosmoticpressure AT victorgalmendrovedia modelingthemechanicsofcelldivisioninfluenceofspontaneousmembranecurvaturesurfacetensionandosmoticpressure AT victorgalmendrovedia modelingthemechanicsofcelldivisioninfluenceofspontaneousmembranecurvaturesurfacetensionandosmoticpressure AT franciscomonroy modelingthemechanicsofcelldivisioninfluenceofspontaneousmembranecurvaturesurfacetensionandosmoticpressure AT franciscomonroy modelingthemechanicsofcelldivisioninfluenceofspontaneousmembranecurvaturesurfacetensionandosmoticpressure AT franciscojcao modelingthemechanicsofcelldivisioninfluenceofspontaneousmembranecurvaturesurfacetensionandosmoticpressure |
_version_ |
1725364727739056128 |