The structure of bacterial flagella: the packing of the polypeptide chains within a flagellum

Abstract

The X-ray diffraction patterns from specimens of bacterial flagella taken by Astbury, Weibull and others consist essentially of three sets of reflexions, two sets on the meridian and one set on the equator. The equatorial set gives information on the packing arrangement of the polypeptide chains within a single flagellum. This paper is concerned with the interpretation in terms of a physical model of the equatorial diffraction from flagella from Proteus vulgaris for which the published diffraction data are most detailed. The polypeptide chains are all assumed to be in the $\alpha$-helical form though the meridional diffraction gives some indication that a smaller `cross-$\beta$' component may also be present. The separation (121 $^\overset\circ{A}$) between the flagella in the X-ray specimens is inferred from the spacings of the equatorial reflexions and two alternative models (model I and model II) for the detailed structure of a flagellum are inferred from the intensity data. The structures proposed are similar in outline but differ in detail and postulate that a flagellum is composed of a number of identical interwoven filaments which themselves comprise a limited number of $\alpha$-helices in a centred hexagonal or pseudo-hexagonal array. In model I the flagella are assumed to be in contact in the X-ray specimens and the structure comprises three filaments of diameter 56 $^\overset\circ{A}$ each containing 19 single $\alpha$-helices. In model II the flagella are not in contact and each of the seven filaments of diameter 33 $^\overset\circ{A}$ contains seven $\alpha$-helices; the diameter of the flagellum on this model is about 100 $^\overset\circ{A}$. The equatorial X-ray patterns from the two models are calculated in detail including effects due to the packing of the flagella within an X-ray specimen, for comparison with the observed diffraction. Both calculated patterns give a satisfactory explanation of the spacings of the observed reflexions and show reasonable agreement with the experimental intensities. The relative merits of the two models are discussed from the diffraction point of view and in conjunction with available data from electron microscopy. The diffraction pattern from model II is in better agreement with the experimental results than the pattern from model I but the latter agreement may be improved if the hexagonal packing of the $\alpha$-helices within a filament is slightly modified; a cylindrical lattice is considered from this point of view. It is concluded that, at the present time, there is insufficient evidence to differentiate between the two models of a flagellum presented.