An intensity expression of optical diffraction from striated muscle fibres

From a simple statistical argument, an intensity expression was formulated for optical diffraction from striated muscle fibres. In terms of the reciprocal space coordinate (Ξ, Φ,u) which corresponds to the real space coordinate (r, φ,x) (thex-axis being parallel to the fibre axis), the intensityI(u, Ξ, Φ) is given by $$\begin{gathered} I(u,{\text{ }}\Xi ,{\text{ }}\Phi {\text{) = }}\Psi (u,{\text{ }}\Xi ,{\text{ }}\Phi {\text{)(}}\pi R^2 )^2 [2J_1 (\Xi R)/\Xi R]^2 L(u){\text{ | }}F(u){\text{ |}}^{\text{2}} \hfill \\ {\text{ }}\Psi {\text{(}}u,{\text{ }}\Xi ,{\text{ }}\Phi {\text{) = }}P\{ 1{\text{ + exp(}} - u^2 {\text{ }}\Delta ^{\text{2}} {\text{ }}P_{e{\text{ff}}} \exp [ - (\Xi R_{e{\text{ff}}} /2)^2 ]\} \hfill \\ \end{gathered}$$ whereR is the radius of a fibril,J ₁(z) is the first-order Bessel function,L(u) is the Laue function for sarcomere repeat along thex-axis,F(u) is the unit cell (or sarcomere) structure factor, Ψ(u, Ξ, Φ) is the structure factor for fibril arrangement in the fibre, 2Δ² is the variance of out-of-register of fibrils in thex-axis,P is the total number of fibrils in the fibre andP _eff is the number of fibrils in an effective rangeR _eff of short range order in a cross-section of the fibre. The quantity Ψ(u, Ξ, Φ) expresses the volume effect emphasized from formulation based on the Bragg plane concept. Simulation of the intensity distribution of diffraction lines will be given and an application of the model will be discussed. A reciprocal space representation will also be given of diffraction for a ‘tilt’ Bragg plane model.