I have been reading on the spontaneous curvature of bilayer membranes but am unable to find the significance of describing the membrane curvature by its spontaneous curvature rather than its mean curvature. What exactly is the difference between these two and why is earlier preferred over latter?
The spontaneous curvature tells you the curvature that the membrane would have if it was unconstrained. If the actual (mean) curvature is not equal to the spontaneous curvature, then the system is frustrated, because it is prevented from reaching the configuration of minimum curvature energy. The difference between the actual and spontaneous curvature is key information to understand how, or if, the system will evolve.
The spontaneous curvature tells you the curvature that the membrane would have if it was unconstrained. If the actual (mean) curvature is not equal to the spontaneous curvature, then the system is frustrated, because it is prevented from reaching the configuration of minimum curvature energy. The difference between the actual and spontaneous curvature is key information to understand how, or if, the system will evolve.
It is, in my opinion, and based on molecular point of view, as if how a folded biomolecule differed from the unfolded one, embarking on many corresponding unfolded states of it: this is really as if it would be an as-yet unsoved problem of the ground state of a (bio)molecule, perhaps in vaccum at zeroth approximation: am I right?
Adam, I'm afraid that you are not right here. The curvature that we are discussing is that of the membrane, made up of sheets, or bilayers, of molecules, not the molecular curvature of individual molecules.
Thank you, Dr. Parker, for such a simplified yet elegant response. Also, thanks to Prof. Gadomski for bringing out the molecular perspective but I think I was referring to the curvature of bilayers rather than the molecular curvature of individual molecules.
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