Myelin: A One-Dimensional Biological “Crystal” for X-Ray and Neutron Scattering - Molecules: Nucleation, Aggregation and Crystallization - page 79

on model systems consisting of zwitterionic phosphatidylcholine (PC), neg-
atively charged phosphatidylserine (PS), and the cytoplasmic domains of
positively charged human and zebrafish P0's show that the apposition is
likely stabilized by the hydrogen-bonding between β -sheets of apposed P0

molecules (Luo et al ., 2007a, 2007b).
To calculate the number of charges on the membrane surfaces and the
electrostatic repulsion force between the apposed membranes as a func-
tion of pH and ionic strength requires having a plausible chemical model
(Inouye, Kirschner, 1988; Luo et al ., 2008). Such a model should be con-
sistent with the observed electron and neutron scattering length density
distributions. In this brief review, we first show how one may apply ele-
mentary diffraction theory to derive an absolute density distribution for
the 1D myelin lattice of the internode (Fig. 2), and then interpret this den-
sity distribution in terms of the available chemical composition data.

Electron Density Profile on an Absolute Scale

The electron density distribution for the myelin sheath on an absolute
scale — i.e. electrons per Å 3 — is not readily calculated from the observed
intensity because of the missing intensity at the origin of the pattern and
the unknown scale factor that relates the observed intensity to the structure
amplitude. Sucrose and glycerol, for which electron densities can be calcu-
lated, have been used to derive an absolute scale between the myelin mem-
brane and the medium (Blaurock, 1971; Blaurock, Caspar, 1971; McIntosh,
Worthington, 1974; Inouye et al ., 1999). To illustrate, we consider the case
where the fluid layer is at the extracellular space. Here, r is in the radial direc-
tion of the cylindrically symmetric multilamellar structure of period d . The
exclusion thickness of the membrane r 0 is defined as that part of the structure
where the extracellular medium is not accessible. The “minus” fluid electron
density of the unit structure ∆ρ ( r ) is written as ∆ρ ( r ) = ρ ( r ) − f at − r 0 /2 ≤ r ≤

r 0 /2, where f is the elec-
tron density of the fluid. For example, the fluid electron densities (in elec-
trons/Å 3 ) are 0.334 for distilled water, 0.336 for 154 mM NaCl, 0.335 for
60 mM NaCl, 0.343 for 0.24 M sucrose, and 0.347 for 10% glycerol.

r 0 /2, and ∆ρ ( r ) = 0 at d /2 > r > r 0 /2 and − r 0 /2 < r <