Question

A picture I would like to share with the biology group: Some of the ideas about our beloved membranes

Answer 1

WHAT the flip is this?

Answer 2

THIS is how we "should" describe a membrane :P

Answer 3

Wow

Answer 4

You make me wish I knew more about membranes. Can you describe your diagram a little more? :D

Answer 5

That I would like to learn.

Answer 6

Sure can TranceNova :D

******************************************
***************WARNING*****************
******************************************
*****Mathematics and Physics ahead*****
******************************************

First a minor history:

It is not unusual that the lipid bilayer of a membrane can be modeled as a two-dimensional surface embedded in three-dimensinal euclidean space. In this kind of modeling, proteins or other entities that can bind to the membrane as represented by solid particles that impose deformations/curvatures in the surface. Acording to physics/chemical-physics the behavior of the membrane under deformations can be predicted by knowing the change in energy. Wolfram Helfrich suggested in 1973 that the deformation energy of a thin fluid membrane as a sum of three energies: The bending energy, the frame energy and the energy as result of change in gaussian curvature.

The bending energy:
\[E _{bending}=\frac{ \kappa A }{ 2 }(H-H _{0})\]
The frame energy:
\[E _{frame }=\sigma(A-A _{flat})\]
The gaussian energy:
\[E _{graussian}=\kappa \prime K A\]

Many of the equations shown the diagram can be deduced from the three equations here.

But now to the main point: A description of the diagram.
The diagram show what kind of models that works within property of the change in time (change in time -> change in energy (perhaps)) and the lenght scale/zoom. Depending on what we research in, where a membrane is involved, we need to be aware on this concept becuase the model we use make a limit to fx only see the initial energy of the membrane insted of the change over time.

Answer 7

I do Computational Biophysics & Biochemistry, although I don't model cell membranes, this is more or less how I view DNA and Ligand interactions ;)

It's always fun to see the math behind the structures.

Answer 8

This is very interesting, thanks for sharing. :)

Answer 9

what those parameters refer to??

Answer 10

@rahulchatterjee
If you are thinking about the equations i set up the in aditional answer it is as follow:
Equation 1:
H = C1 + C2 where the following is:
C1 and C2 are the principal curvatures when the membrane is modeled as a surface embedded in 3-dimensional space and H0 is the spontaneous curvature of the membrane, κ is the bending rigidity, A is the surface area of a piece of the membrane which is denoted as a domain.

Equation 2:
σ is the frame tension and Aflat is the projected area of the membrane domain area A onto the flat plane.

Equation 3:
κ' is the splay modulus and K is the Gaussian curvature over the membrane domain with area A.

Answer 11

thats cool(:

Answer 12

Else if you want to know more about it read about the Helfrich Hamiltonian Membrane