Accuracy of Determination of Position and Width of Molecular Groups in Biological and Lipid Membranes via Neutron Diffraction

Neutron diffraction combined with the deuterium-labelled molecular groups of biological and model membrane components allows one to detect with high accuracy the structure of these objects. Experiments of this kind are only possible at unique high-flux neutron sources, and the planning of neutron-diffraction experiments must take into account some special requirements primarily related to the duration of the experiment and the accuracy of estimation of membrane structure parameters as a result of finite time of the measurements. This paper deals with the question of statistical accuracy of the position x₀ and width v of the distribution of deuterium labels in membranes along the normal of their plane, which are determined in a neutron diffraction experiment. It is shown that the accuracy of x₀ and v estimation does not depend on membrane constitution. It is dependent only on the scattering amplitude of the deuterium label, the label position x₀ and the distribution width v. Analytic calculations show that the statistical errors Δx₀ and Δv are inversely proportional to the scattering amplitude of the label and, as usual, to the square root of measurement time. The question of Δx0 and Δv dependence on the number of structure factors used in the calculations of x₀ and v is also studied. It is shown that, the accuracy of x₀ estimation is approximately constant with down to four structure factors used, and, with the number of the factors below four, it deteriorates drastically. Analogous is the behaviour of Δv(h_max) relation with one exception: abrupt deterioration of the accuracy occurs beginning with five structure factors used. One does not have to measure the highest diffraction reflections which takes a much longer time compared with the first ones. It is an important result. All the problems mentioned above have also been considered for the case of two different deuterium labels in membranes.