The evolution of archaeal flagellar filaments.

Flagellar motility has independently arisen three times during evolution: in bacteria, archaea, and eukaryotes. In prokaryotes, the supercoiled flagellar filaments are composed largely of a single protein, bacterial or archaeal flagellin, although these two proteins are not homologous, while in eukaryotes, the flagellum contains hundreds of proteins. Archaeal flagellin and archaeal type IV pilin are homologous, but how archaeal flagellar filaments (AFFs) and archaeal type IV pili (AT4Ps) diverged is not understood, in part, due to the paucity of structures for AFFs and AT4Ps.

Convergent evolution in the supercoiling of prokaryotic flagellar filaments.

The supercoiling of bacterial and archaeal flagellar filaments is required for motility. Archaeal flagellar filaments have no homology to their bacterial counterparts and are instead homologs of bacterial type IV pili. How these prokaryotic flagellar filaments, each composed of thousands of copies of identical subunits, can form stable supercoils under torsional stress is a fascinating puzzle for which structural insights have been elusive.

An amateur's contribution to the design of Telford's Menai Suspension Bridge: a commentary on Gilbert (1826) 'On the mathematical theory of suspension bridges'.

Davies Gilbert's work on the catenary is notable on two counts. First, it influenced Thomas Telford in formulating his final design for the Menai Strait suspension bridge (1826); and second, it established for the first time the form of the 'catenary of equal strength'. The classical catenary is a uniform flexible chain or cable hanging freely under gravity between supports.

Geometric principles in the assembly of α-helical bundles.

α-Helical coiled coils are usually stabilized by hydrophobic interfaces between the two constituent α-helices, in the form of 'knobs-into-holes' packing of non-polar residues arranged in repeating heptad patterns. Here we examine the corresponding 'hydrophobic cores' that stabilize bundles of four α-helices. In particular, we study three different kinds of bundle, involving four α-helices of identical sequence: two pack in a parallel and one in an anti-parallel orientation.

A "mechanistic" explanation of the multiple helical forms adopted by bacterial flagellar filaments.

The corkscrew-like flagellar filaments emerging from the surface of bacteria such as Salmonella typhimurium propel the cells toward nutrient and away from repellents. This kind of motility depends upon the ability of the flagellar filaments to adopt a range of distinct helical forms. A filament is typically constructed from ~30,000 identical flagellin molecules, which self-assemble into a tubular structure containing 11 near-longitudinal protofilaments.

A potential molecular switch in an alpha-helical coiled coil.

The yeast DNA-binding protein GCN4 forms a homo-dimer through a self-complementary coiled-coil interface. In this article, we describe how such coiled-coils might be bistable and, through Molecular Dynamics computations on the GCN4 coiled coil, we show that the coiled coil can indeed switch between the two states by a pathway in which there is a progressive "flipping" of consecutive steps along the interface. We discuss the general implications of potentially bistable coiled-coil interfaces for allosteric signal-transmission mechanisms along homo-dimeric coiled coils and for the packing of helices in globular proteins.

The buckling of spherical liposomes.

In the classical "first approximation" theory of thin-shell structures, the constitutive relations for a generic shell element--i.e. the elastic relations between the bending moments and membrane stresses and the corresponding changes in curvature and strain, respectively-are written as if an element of the shell is flat, although in reality it is curved.

Mechanics of tether formation in liposomes.

It is well-known that a "tether" may be drawn out from a pressurized liposome by means of a suitably applied radial-outward force applied locally to the lipid bilayer. The tether is a narrow, uniform cylindrical tube, which joins the main vesicle in a short "transition region." A first-order energy analysis establishes the broad relationship between the force F needed to draw the tether, the radius R0 of the tether, the bending-stiffness constant B for the lipid bilayer and the membrane tension T in the pressurized liposome.

The role of the TolC family in protein transport and multidrug efflux. From stereochemical certainty to mechanistic hypothesis.

Gram-negative bacteria are enveloped by a system of two membranes, and they use specialized multicomponent, energy-driven pumps to transport molecules directly across this double-layered partition from the cell interior to the extra-cellular environment. One component of these pumps is embedded in the outer-membrane, and the paradigm for its structure and function is the TolC protein from Escherichia coli. A common component of a wide variety of efflux pumps, TolC and its homologues are involved in the export of chemically diverse molecules ranging from large protein toxins, such as alpha-hemolysin, to small toxic compounds, such as antibiotics.

How to untwist an alpha-helix: structural principles of an alpha-helical barrel.

Recent crystallographic studies have revealed that 12 alpha-helices can pack in an anti-parallel fashion to form a hollow cylinder of nearly uniform radius. In this architecture, which we refer to as an alpha-barrel, the helices are inclined with respect to the cylindrical axis, and thus they curve and twist. As with conventional coiled-coils, the helices of the barrel associate via "knobs-into-holes" interactions; however, their packing is distinct in several important ways.

Two distinct modes of protein-induced bending in DNA.

Crystallised "naked" DNA oligomers in the B form show significant conformational mobility, particularly at CA/TG and TA/TA steps: there is a range in Roll angle of some 15 degrees between consecutive base-pairs, and Slide and Twist are directly coupled to Roll. We call such motions "mode I". They are sufficient to enable DNA to curve gently around proteins such as histone octamers in the nucleosome particle.

Aspects of the mechanics of lobed liposomes.

Hotani has studied, by means of dark-field light microscopy, morphological transformations which unilamellar liposomes undergo when their interior volume decreases steadily with time as a consequence of osmosis. In a previous paper, we made a theoretical study of the initial buckling of an originally spherical vesicle into the observed oblate spheroidal shape; and we argued that some in-plane shear elastic stiffness is required-in addition to the well-known flexural stiffness of the lipid bilayer-in order to explain the observed phenomena. In the present paper, we consider a later stage in the chain of morphological transitions observed by Hotani, when a series of cudgel-shaped lobes have sprung out of a previously axisymmetric, biconcave-shaped vesicle.

Topological measurement of protein-induced DNA bend angles.

A new method measures independently the changes in the DNA bend and winding angles that occur when a protein binds to its specific site in DNA. The procedure requires an investigation of the change in DNA topology induced when the protein binds to tandemly repeated sites of varying repeat length in circular DNA. This new method is superior to currently used methods because topology permits the measurements to be derived absolutely from first principles, and no comparison standards are required.

Propeller-twisting of base-pairs and the conformational mobility of dinucleotide steps in DNA.

When DNA is bent around a protein, it must distort. The distortion occurs by changes in the conformation of successive dinucleotide steps. Bending does not necessarily occur uniformly: some steps might remain particularly rigid, i.

A useful role for "static" models in elucidating the behaviour of DNA in solution.

Double-helical DNA is a long and flexible molecule that is in constant motion under thermal perturbations, more so in solution that in the crystal. Some workers, for example Olsen et al., have argued that the behaviour of this molecule in assays such as circularization or gel electrophoresis can only be understood properly by means of theories that take full account of its dynamical nature due to thermal motions.

Structural mechanics of bent DNA.

The DNA molecule is a familiar object. It is often depicted in magazines and advertisements as a double helix, with the letters of the genetic code strung along the two spiral backbones and joined together in pairs. In such pictures the molecule is usually shown as straight; yet in the chromosomes of living organisms, DNA is curved and wound up into condensed packages.

The assessment of the geometry of dinucleotide steps in double-helical DNA; a new local calculation scheme.

In this paper, we develop a new local Euler-angle-based scheme for assessing the internal kinematics or geometry of a general dinucleotide step in double-helical DNA. The geometry of a dinucleotide step is completely defined by: (1) the base-pair parameters that describe the relative position and orientation of one base with respect to the other in a standard Watson-Crick base-pair, and (2) the step parameters that describe the relative position and orientation of the two base-pairs. The key feature of our scheme is that it makes use of the concept of a mid-step reference frame.

The mechanics of axially symmetric liposomes.

Hotani has filmed morphological transformations in unilamellar liposomes, starting from a spherical shape, when the interior volume decreases steadily. Hotani's liposomes showed no evidence of general thermal fluctuations. We use a finite-deformation theory of axisymmetric, quasi-static thin shells to analyze theoretically bifurcations and changes of shape in liposomes under decreasing volume.

A study of electrophoretic mobility of DNA in agarose and polyacrylamide gels.

The aim of this paper is to clarify the mechanism of gel electrophoresis of DNA under constant-field conditions. We have conducted a large number of experiments on double-stranded DNA varying in length between approximately 10 and approximately 50,000 base-pairs, in both agarose and polyacrylamide gels ranging from 0.5% to 12% concentration, and with electric field strengths ranging from 0.

The intrinsic curvature of DNA in solution.

We propose a detailed quantitative scheme for explaining the anomalous electrophoretic mobility in polyacrylamide gels of repeating sequence DNA. We assume that such DNA adopts a superhelical configuration in these circumstances, and migrates less quickly than straight DNA of the same length because it can only pass through larger holes. The retardation is maximal when the length of the DNA reaches one superhelical turn, but is less for shorter pieces.

Sequence-specific positioning of core histones on an 860 base-pair DNA. Experiment and theory.

Previous experiments have shown that the locations of the histone octamer on DNA molecules of 140 to 240 base-pairs (bp) are influenced strongly by the nucleotide sequence. Here we have studied the locations of the histone octamer on a relatively long DNA molecule of 860 bp, using two different nucleases, micrococcal and DNAase I. Data were obtained from both the protein--DNA complexes and from the naked DNA at single-bond resolution, and then were analyzed by densitometry to yield plots of differential cleavage, which show clearly the changes in cutting due to the addition of protein.