Morphogenesis of the T4 tail and tail fibers

Remarkable progress has been made during the past ten years in elucidating the structure of the bacteriophage T4 tail by a combination of three-dimensional image reconstruction from electron micrographs and X-ray crystallography of the components. Partial and complete structures of nine out of twenty tail structural proteins have been determined by X-ray crystallography and have been fitted into the 3D-reconstituted structure of the "extended" tail. The 3D structure of the "contracted" tail was also determined and interpreted in terms of component proteins. Given the pseudo-atomic tail structures both before and after contraction, it is now possible to understand the gross conformational change of the baseplate in terms of the change in the relative positions of the subunit proteins. These studies have explained how the conformational change of the baseplate and contraction of the tail are related to the tail's host cell recognition and membrane penetration function. On the other hand, the baseplate assembly process has been recently reexamined in detail in a precise system involving recombinant proteins (unlike the earlier studies with phage mutants). These experiments showed that the sequential association of the subunits of the baseplate wedge is based on the induced-fit upon association of each subunit. It was also found that, upon association of gp53 (gene product 53), the penultimate subunit of the wedge, six of the wedge intermediates spontaneously associate to form a baseplate-like structure in the absence of the central hub. Structure determination of the rest of the subunits and intermediate complexes and the assembly of the hub still require further study.

Molecular Modeling of Bacterial Nanomachineries

Matteo Thomas Degiacomi

Proteins have the ability to assemble in multimeric states to perform their specific biological function. Unfortunately, characterizing experimentally these structures at atomistic resolution is usually difficult. For this reason, in silico methodologies aiming at predicting how multiple protein copies arrange to forma multimeric complex would be desirable. We present Parallel OptimizationWorkbench (POW), a swarm intelligence based optimization framework able to deal, in principle, with any optimization problem. We show that POW can be applied to biologically relevant problems such as prediction of protein assemblies and the parameterization of a Coarse-Grained force field for proteins. By combining POW optimizations, Molecular Dynamics simulations, Poisson-Boltzmann calculations and a variety of experiments, we subsequently study two bacterial nanomachieries: Aeromonas hydrophila's pore-forming toxin aerolysin, and Yersinia enterocolitica injectisome. These structures are challenging both for their size, and for the timescales involved in their functioning. Aerolysin is a pore-forming toxin secreted as an hydrophilic monomer. By means of large conformational changes, the protein heptamerizes on the target cell's surface, and finally inserts β-barrel into its lipid bilayer, causing cell death. The main hurdle in the study of this structure is the complexity of the mode of action, which spans timescales currently unreachable by classical molecular dynamics. We show that aerolysin C-terminal region has the dual role of preventing premature oligomerization and helping the folding of tertiary structure, qualifying therefore as an intramolecular chaperone. We study the transmembrane β-barrel properties and compare them with those of the homologous protein α-hemolysin. We show that aerolysin's barrel is more rigid than α-hemolysin's, and should be anion selective. We present models for aerolysin heptamer both in prepore and, for the first time, in membrane-inserted conformation. Our results are validated experimentally, and are consistent with known biochemical and structural data. The injectisome is an example of a type III secretion system. Its most striking feature is probably its size: hundreds of proteins assemble in a unique structure spanning the Gram-negative bacterial double membrane, and protruding outside the cell as a needle for tenth of nanometers. Obtaining an atomistic representation of this massive structure, and therefore some insights about its mode of action, is one of the greatest challenges. We show that the final length of injectisome's needle is determined by the secondary structure content of a ruler protein located inside its cavity during assembly. Using POW, we also produce the first model for Yersinia injectisome's basal body, highlighting the flexibility of this region in adapting between the inner and outer membranes. As a whole, this work demonstrates that a synergy of dry and wet experiments can provide precious insights into macromolecular structure and function.

EPFL2012

Differential geometry applied to crystallography

Philippe Kocian

The mathematical facet of modern crystallography is essentially based on analytical geometry, linear algebra as well as group theory. This study endeavours to approach the geometry and symmetry of crystals using the tools furnished by differential geometry and the theory of Lie groups. These two branches of mathematics being little known to crystallographers, the pertinent definitions such as differentiable manifold, tangent space or metric tensor or even isometries on a manifold together with some important results are given first. The example of euclidean space, taken as riemannian manifold, is treated, in order to show that the affine aspect of this space is not at all an axiom but the consequence of the euclidean nature of the manifold. Attention is then directed to a particular subgroup of the group of euclidean isometries, namely that of translations. This has the property of a Lie group and it turns out that the action of its elements, as well as those of its Lie algebra, plays an important role in generating a lattice on a manifold and in its tangent space, too. In particular, it is pointed out that one and only one finite and free module of the Lie algebra of the group of translations can generate both, modulated and non-modulated lattices. This last classification therefore appears continuous rather than black and white and is entirely determined by the parametrisation considered. Since a lattice in a tangent space has the properties of a vector space, it always possesses the structure of a finite, free module, which shows that the assignment of aperiodicity to modulated structures is quite subjective, even unmotivated. Thanks to the concept of representation of a lattice or a crystal in a tangent space, novel definitions of the notions of symmetry operation of a space group and point symmetry operation, as well as symmetry element and intrinsic translation arise; they altogether naturally blend into the framework of differential geometry. In order to conveniently pass from one representation of a crystal in one tangent space to another or to the structure on a manifold, an equivalence relation on the tangent bundle of the manifold is introduced. This relation furthermore allows to extend the concept of symmetry operation to the tangent bundle; this extension furnishes, particularly in the euclidean case, a very practical way of representing symmetry operations of space groups completely devoid of any dependence on an origin, or, in other words, in which each and every point may be considered the origin. The investigation of the group of translations having being completed, the study of the linear parts of the isometries comes naturally. Based on the fact that the set of linear parts possesses the structure of a Lie group, several results are proven in a rigorous manner, such as the fact that a rotation angle of π/3 is incompatible with a three-dimensional cubic lattice. Procedures for determining different crystal systems in function of the type of rotation are laid out by way of the study of orthogonal matrices and their relation to the matrix associated with the type of system. Finally, the description of a crystal by its diffraction patterns is taken on. It is shown that the general aspect of such a pattern is directly linked to the action of that free and finite module of the Lie algebra of translations which generates a lattice on a manifold. In the case of modulated crystals, it is demonstrated that the appearance of supplementary spots is caused by the geometry, i.e. by the parametrisation of the manifold in which the crystal exists and not by the action of the module in the Lie algebra. Thus, there exists a neat separation: the geometrical aspect on the one hand, and the action of the group on the other. As the last topic, other ways of interpreting the diffraction pattern of a modulated structure are laid out in order to argue that mere experimental data do not warrant the uniqueness of a model. The goal of this study is by no means an attempt at overthrowing existing structural models such as the superspace-formalism or at revolutionising the methods for determining structures, but is rather aimed at sustaining that the definition of certain notions becomes thoroughly natural within the appropriate mathematical framework, and, that the term aperiodicity assigned to modulated structures no longer has a true meaning.

EPFL2009

The Baseplate Wedges of Bacteriophage T4 Spontaneously Assemble into Hubless Baseplate-Like Structure In Vitro

Petr Leiman

The baseplate of phage T4 is an important model system in viral supramolecular assembly. The baseplate consists of six wedges surrounding the central hub. We report the first successful attempt at complete wedge assembly using an in vitro approach based on recombinant proteins. The cells expressing the individual wedge proteins were mixed in a combinatorial manner and then lysed. Using this approach, we could both reliably isolate the complete wedge along with a series of intermediate complexes as well as determine the exact sequence of assembly. The individual proteins and intermediate complexes at each step of the wedge assembly were successfully purified and characterized by sedimentation velocity and electron microscopy. Although our results mostly confirmed the hypothesized sequential wedge assembly pathway as established using phage mutants, interestingly, we also detected some protein interactions not following the specified order. It was found that association of gene product 53 to the immediate precursor complex induces spontaneous association of the wedges to form a six-fold star-shaped baseplate-like structure in the absence of the hub. The formation of the baseplate-like structure was facilitated by the addition of gene product 25. The complete wedge in the star-shaped supramolecular complex has a structure similar to the baseplate in the expanded "star" conformation found after infection. Based on the results of the present and previous studies, we assume that the strict order of wedge assembly is due to the induced conformational change caused by every new binding event. The significance of a 40-S star-shaped baseplate structure, which was previously reported and was also found in this study, is discussed in the light of a new paradigm for T4 baseplate assembly involving the star-shaped wedge ring and the central hub. Importantly, the methods described in this article suggest a novel methodology for future structural characterization of supramolecular protein assemblies. (C) 2009 Elsevier Ltd. All rights reserved.

2010