Understanding the apparent stator-rotor connections in the rotary ATPase family using coarse-grained computer modeling

From System Modeling to System Analysis: The Impact of Resolution Level and Resolution Distribution in the Computer-Aided Investigation of Biomolecules

The ever increasing computer power, together with the improved accuracy of atomistic force fields, enables researchers to investigate biological systems at the molecular level with remarkable detail. However, the relevant length and time scales of many processes of interest are still hardly within reach even for state-of-the-art hardware, thus leaving important questions often unanswered. The computer-aided investigation of many biological physics problems thus largely benefits from the usage of coarse-grained models, that is, simplified representations of a molecule at a level of resolution that is lower than atomistic. A plethora of coarse-grained models have been developed, which differ most notably in their granularity; this latter aspect determines one of the crucial open issues in the field, i.e. the identification of an optimal degree of coarsening, which enables the greatest simplification at the expenses of the smallest information loss. In this review, we present the problem of coarse-grained modeling in biophysics from the viewpoint of system representation and information content. In particular, we discuss two distinct yet complementary aspects of protein modeling: on the one hand, the relationship between the resolution of a model and its capacity of accurately reproducing the properties of interest; on the other hand, the possibility of employing a lower resolution description of a detailed model to extract simple, useful, and intelligible information from the latter.

Combined Force-Torque Spectroscopy of Proteins by Means of Multiscale Molecular Simulation

Assessing the structural properties of large proteins is important to gain an understanding of their function in, e.g., biological systems or biomedical applications. We propose a method to examine the mechanical properties of proteins subject to applied forces by means of multiscale simulation. Both stretching and torsional forces are considered, and these may be applied independently of each other. As a proof of principle, we apply torsional forces to a coarse-grained continuum model of the antibody protein immunoglobulin G using fluctuating finite element analysis and use it to identify the area of strongest deformation. This region is essential to the torsional properties of the molecule as a whole because it represents the softest, most deformable domain. Zooming in, this part of the molecule is subjected to torques and stretching forces using molecular dynamics simulations on an atomistically resolved level to investigate its torsional properties. We calculate the torsional resistance as a function of the rotation of the domain while subjecting it to various stretching forces. From this, we assess how the measured twist-torque profiles develop with increasing stretching force and show that they exhibit torsion stiffening, in qualitative agreement with experimental findings. We argue that combining the twist-torque profiles for various stretching forces effectively results in a combined force-torque spectroscopy analysis, which may serve as a mechanical signature for a biological macromolecule.

Exploring the dynamics of flagellar dynein within the axoneme with Fluctuating Finite Element Analysis

Flagellar dyneins are the molecular motors responsible for producing the propagating bending motions of cilia and flagella. They are located within a densely packed and highly organised super-macromolecular cytoskeletal structure known as the axoneme. Using the mesoscale simulation technique Fluctuating Finite Element Analysis (FFEA), which represents proteins as viscoelastic continuum objects subject to explicit thermal noise, we have quantified the constraints on the range of molecular conformations that can be explored by dynein-c within the crowded architecture of the axoneme. We subsequently assess the influence of crowding on the 3D exploration of microtubule-binding sites, and specifically on the axial step length. Our calculations combine experimental information on the shape, flexibility and environment of dynein-c from three distinct sources; negative stain electron microscopy, cryo-electron microscopy (cryo-EM) and cryo-electron tomography (cryo-ET). Our FFEA simulations show that the super-macromolecular organisation of multiple protein complexes into higher-order structures can have a significant influence on the effective flexibility of the individual molecular components, and may, therefore, play an important role in the physical mechanisms underlying their biological function.

Nano-encapsulated Escherichia coli Divisome Anchor ZipA, and in Complex with FtsZ

The E. coli membrane protein ZipA, binds to the tubulin homologue FtsZ, in the early stage of cell division. We isolated ZipA in a Styrene Maleic Acid lipid particle (SMALP) preserving its position and integrity with native E. coli membrane lipids. Direct binding of ZipA to FtsZ is demonstrated, including FtsZ fibre bundles decorated with ZipA. Using Cryo-Electron Microscopy, small-angle X-ray and neutron scattering, we determine the encapsulated-ZipA structure in isolation, and in complex with FtsZ to a resolution of 1.6 nm. Three regions can be identified from the structure which correspond to, SMALP encapsulated membrane and ZipA transmembrane helix, a separate short compact tether, and ZipA globular head which binds FtsZ. The complex extends 12 nm from the membrane in a compact structure, supported by mesoscale modelling techniques, measuring the movement and stiffness of the regions within ZipA provides molecular scale analysis and visualisation of the early divisome.

Fluctuating Finite Element Analysis (FFEA): A continuum mechanics software tool for mesoscale simulation of biomolecules

Fluctuating Finite Element Analysis (FFEA) is a software package designed to perform continuum mechanics simulations of proteins and other globular macromolecules. It combines conventional finite element methods with stochastic thermal noise, and is appropriate for simulations of large proteins and protein complexes at the mesoscale (length-scales in the range of 5 nm to 1 μm), where there is currently a paucity of modelling tools. It requires 3D volumetric information as input, which can be low resolution structural information such as cryo-electron tomography (cryo-ET) maps or much higher resolution atomistic co-ordinates from which volumetric information can be extracted. In this article we introduce our open source software package for performing FFEA simulations which we have released under a GPLv3 license. The software package includes a C ++ implementation of FFEA, together with tools to assist the user to set up the system from Electron Microscopy Data Bank (EMDB) or Protein Data Bank (PDB) data files. We also provide a PyMOL plugin to perform basic visualisation and additional Python tools for the analysis of FFEA simulation trajectories. This manuscript provides a basic background to the FFEA method, describing the implementation of the core mechanical model and how intermolecular interactions and the solvent environment are included within this framework. We provide prospective FFEA users with a practical overview of how to set up an FFEA simulation with reference to our publicly available online tutorials and manuals that accompany this first release of the package.

Rotating with the brakes on and other unresolved features of the vacuolar ATPase

The rotary ATPase family comprises the ATP synthase (F-ATPase), vacuolar ATPase (V-ATPase) and archaeal ATPase (A-ATPase). These either predominantly utilize a proton gradient for ATP synthesis or use ATP to produce a proton gradient, driving secondary transport and acidifying organelles. With advances in EM has come a significant increase in our understanding of the rotary ATPase family. Following the sub nm resolution reconstructions of both the F- and V-ATPases, the secondary structure organization of the elusive subunit a has now been resolved, revealing a novel helical arrangement. Despite these significant developments in our understanding of the rotary ATPases, there are still a number of unresolved questions about the mechanism, regulation and overall architecture, which this mini-review aims to highlight and discuss.

Methods to account for movement and flexibility in cryo-EM data processing

Recent advances in direct electron detectors and improved CMOS cameras have been accompanied by the development of a range of software to take advantage of the data they produce. In particular they allow for the correction of two types of motion in cryo electron microscopy samples: motion correction for movements of the sample particles in the ice, and differential masking to account for heterogeneity caused by flexibility within protein complexes. Here we provide several scripts that allow users to move between RELION and standalone motion correction and centring programs. We then compare the computational cost and improvements in data quality with each program. We also describe our masking procedures to account for conformational flexibility. For the different elements of this study we have used three samples; a high symmetry virus, flexible protein complex (∼1 MDa) and a relatively small protein complex (∼550 kDa), to benchmark four widely available motion correction packages. Using these as test cases we demonstrate how motion correction and differential masking, as well as an additional particle re-centring protocol can improve final reconstructions when used within the RELION image-processing package.

Structure of the vacuolar H+-ATPase rotary motor reveals new mechanistic insights

Vacuolar H(+)-ATPases are multisubunit complexes that operate with rotary mechanics and are essential for membrane proton transport throughout eukaryotes. Here we report a ∼ 1 nm resolution reconstruction of a V-ATPase in a different conformational state from that previously reported for a lower-resolution yeast model. The stator network of the V-ATPase (and by implication that of other rotary ATPases) does not change conformation in different catalytic states, and hence must be relatively rigid. We also demonstrate that a conserved bearing in the catalytic domain is electrostatic, contributing to the extraordinarily high efficiency of rotary ATPases. Analysis of the rotor axle/membrane pump interface suggests how rotary ATPases accommodate different c ring stoichiometries while maintaining high efficiency. The model provides evidence for a half channel in the proton pump, supporting theoretical models of ion translocation. Our refined model therefore provides new insights into the structure and mechanics of the V-ATPases.

In pursuit of an accurate spatial and temporal model of biomolecules at the atomistic level: a perspective on computer simulation

Despite huge advances in the computational techniques available for simulating biomolecules at the quantum-mechanical, atomistic and coarse-grained levels, there is still a widespread perception amongst the experimental community that these calculations are highly specialist and are not generally applicable by researchers outside the theoretical community. In this article, the successes and limitations of biomolecular simulation and the further developments that are likely in the near future are discussed. A brief overview is also provided of the experimental biophysical methods that are commonly used to probe biomolecular structure and dynamics, and the accuracy of the information that can be obtained from each is compared with that from modelling. It is concluded that progress towards an accurate spatial and temporal model of biomacromolecules requires a combination of all of these biophysical techniques, both experimental and computational.