Biomedical Engineering Reference
In-Depth Information
contribute to the strength of the hydrophobic coupling of the membrane proteins
with the host phospholipid bilayer. Several novel analytical and numerical techniques
will be introduced to correctly address this important problem. Although we have
developed a theoretical model published earlier, which aims to explain the related
experimental phenomena, we have also presented the results here to describe the
problem in a comprehensive fashion.
The experimental study focused on a few ion channel phenomena which will be
used as tools to address the problem. We also discuss some of the lipid- membrane
protein interactions using molecular dynamics (MD) simulations. The powerful MD
methodology mimics the cell membrane with most of the constituents within the
membrane simulated by computer modeling. This helps understand the dynamics and
energetics of various compartments, especially considering them to be independent
of other compartments in membranes in real time which is experimentally almost
impossible to investigate due to the complex organization of biological systems. It
is also necessary to emphasize that MD can never provide absolute values of the
physical parameters which should fit the biological environment but it can often
provide enough information to help understand the phenomena involved.
5.1 Lipid Membrane-Membrane Protein Coupling
Due to Membrane Elasticity
5.1.1 Definition of Elasticity
According to the fluid mosaic model [ 82 ], lipids freely move on the membrane
surface like a fluid. This is well-known, as a liquid crystalline structure. Liquid
crystalline membranes exist in different thermotropic phases. This was discussed in
Chap. 3 . Within any specific phase, the structure requires specific organization of the
lipid molecules, and such organization raises the possibility of the membrane having
certain distinguishable biophysical properties. Elasticity is claimed to be one of the
few most important ones. However, the question arises whether this type of elasticity
resembles the elasticity of a solid state material, which follows Hooke's law. If any
object quickly regains its original shape and dimensions following the withdrawal of
the force creating the deformation in the first place, with the molecules or atoms of
the object returning to their initial state of stable equilibrium, the object is considered
to be elastic and it obeys Hooke's law. Specifically, in mechanics, Hooke's law of
elasticity is an approximation that states that the amount of deformation (represented
by strain) is linearly related to the force causing the deformation (represented by
stress). This hypothesis best fits with the extension of a spring due to the suspension
of a load at the bottom (see Fig. 5.1 ). If the load is removed, the extended spring
returns to its original structure and length.
The mathematical form of the spring's distortion follows the equation
 
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