The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell

Canham, Peter B.

doi:10.1016/s0022-5193(70)80032-7

Cited by 1,439 publications

(1,204 citation statements)

References 10 publications

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“…Note that there exists a term involving explicitly the background curvature in Eq. (13). Now, in the next lines we will take particular cases of the Lagrangian given in equation (2) using the previous results we will confirm the results given in [3]; for this, we take as first example the [DNG] p-branes action.…”

Section: Symplectic Potentials For P-branes In a Curved Backgroundsupporting

confidence: 57%

Simplectic Geometry and the Canonical Variables for Dirac–Nambu–Goto and Gauss–Bonnet System in String Theory

Escalante

2006

Int J Theor Phys

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Section: Symplectic Potentials For P-branes In a Curved Backgroundsupporting

confidence: 57%

Simplectic Geometry and the Canonical Variables for Dirac–Nambu–Goto and Gauss–Bonnet System in String Theory

Escalante

2006

Int J Theor Phys

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“…In the context of membranes, elastic continuum theories have been very successful as evidenced by a very rich literature starting with the seminal works of Canham, 59 Evans 60 and in particular Helfrich. 61 Here, membranes are described as twodimensional fluid surfaces with an energy density that can be expanded in local geometric invariants-the curvature terms being of particular significance.…”

Section: Beyond Moleculesmentioning

confidence: 99%

Multiscale modeling of emergent materials: biological and soft matter

Murtola

Bunker

Vattulainen

et al. 2009

Phys. Chem. Chem. Phys.

257

234

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On using a too large integration time step in molecular dynamics simulations of coarse-grained molecular models Moritz Winger, Daniel Trzesniak, Riccardo Baron and Wilfred F. In this review, we focus on four current related issues in multiscale modeling of soft and biological matter. First, we discuss how to use structural information from detailed models (or experiments) to construct coarse-grained ones in a hierarchical and systematic way. This is discussed in the context of the so-called Henderson theorem and the inverse Monte Carlo method of Lyubartsev and Laaksonen. In the second part, we take a different look at coarse graining by analyzing conformations of molecules. This is done by the application of self-organizing maps, i.e., a neural network type approach. Such an approach can be used to guide the selection of the relevant degrees of freedom. Then, we discuss technical issues related to the popular dissipative particle dynamics (DPD) method. Importantly, the potentials derived using the inverse Monte Carlo method can be used together with the DPD thermostat. In the final part we focus on solvent-free modeling which offers a different route to coarse graining by integrating out the degrees of freedom associated with solvent.

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“…The free elastic energy of a symmetric, nearly flat, biomembrane sheet is described by the Canham-Helfrich Hamiltonian [22,23] …”

Section: Energetics Of the Biomembrane In Presence Of Surface Tensionmentioning

confidence: 99%

Numerical simulation of the stochastic dynamics of inclusions in biomembranes in the presence of surface tension

Rafii-Tabar¹,

Sepangi²

2005

Physica A: Statistical Mechanics and its Applications

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The stochastic dynamics of inclusions in a randomly fluctuating biomembrane is simulated. These inclusions can represent the embedded proteins and the external particles arriving at a cell membrane. The energetics of the biomembrane is modelled via the Canham-Helfrich Hamiltonian. The contributions of both the bending elastic-curvature energy and the surface tension of the biomembrane are taken into account. The biomembrane is treated as a two-dimensional sheet whose height variations from a reference frame is treated as a stochastic Wiener process. The lateral diffusion parameter associated with this Wiener process coupled with the longitudinal diffusion parameter obtained from the standard Einsteinian diffusion theory completely determine the stochastic motion of the inclusions. It is shown that the presence of surface tension significantly affects the overall dynamics of the inclusions, particularly the rate of capture of the external inclusions, such as drug particles, at the site of the embedded inclusions, such as the embedded proteins.

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The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell

Cited by 1,439 publications

References 10 publications

Simplectic Geometry and the Canonical Variables for Dirac–Nambu–Goto and Gauss–Bonnet System in String Theory

Simplectic Geometry and the Canonical Variables for Dirac–Nambu–Goto and Gauss–Bonnet System in String Theory

Multiscale modeling of emergent materials: biological and soft matter

Numerical simulation of the stochastic dynamics of inclusions in biomembranes in the presence of surface tension

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