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.

Continuum mechanical parameterisation of cytoplasmic dynein from atomistic simulation.

Cytoplasmic dynein is responsible for intra-cellular transport in eukaryotic cells. Using Fluctuating Finite Element Analysis (FFEA), a novel algorithm that represents proteins as continuum viscoelastic solids subject to thermal noise, we are building computational tools to study the mechanics of these molecular machines. Here we present a methodology for obtaining the material parameters required to represent the flexibility of cytoplasmic dynein within FFEA from atomistic molecular dynamics (MD) simulations, and show that this continuum representation is sufficient to capture the principal dynamic properties of the motor.

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.

PolySTRAND Model of Flow-Induced Nucleation in Polymers.

We develop a thermodynamic continuum-level model, polySTRAND, for flow-induced nucleation in polymers suitable for use in computational process modeling. The model's molecular origins ensure that it accounts properly for flow and nucleation dynamics of polydisperse systems and can be extended to include effects of exhaustion of highly deformed chains and nucleus roughness. It captures variations with the key processing parameters, flow rate, temperature, and molecular weight distribution. Under strong flow, long chains are over-represented within the nucleus, leading to superexponential nucleation rate growth with shear rate as seen in experiments.

KOBRA: a fluctuating elastic rod model for slender biological macromolecules.

KOBRA (KirchOff Biological Rod Algorithm) is an algorithm and software package designed to perform dynamical simulations of elongated biomolecules such as those containing alpha-helices and coiled-coils. It represents these as coarsely-discretised Kirchoff rods, with linear elements that can stretch, bend and twist independently. These rods can have anisotropic and inhomogeneous parameters and bent or twisted equilibrium structures, allowing for a coarse-grained parameterisation of complex biological structures. Each element is non-inertial and subject to thermal fluctuations. The speed and simplicity of the algorithm allows KOBRA rods to easily access timescales from nanoseconds to seconds. To demonstrate this functionality, a KOBRA rod was parameterised using data from all-atom simulations of the Ndc80 protein complex, and compared against these simulations and negative-stain EM images. The distribution of bend angles and principal components were highly correlated between KOBRA, all-atom molecular dynamics, and experimental data. The properties of a hinge region, thought to be found at an unstructured loop, were studied. A C++ implementation of KOBRA is available under the GNU GPLv3 free software licence.

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.

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.

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

Advances in structural biology, such as cryo-electron microscopy (cryo-EM) have allowed for a number of sophisticated protein complexes to be characterized. However, often only a static snapshot of a protein complex is visualized despite the fact that conformational change is frequently inherent to biological function, as is the case for molecular motors. Computer simulations provide valuable insights into the different conformations available to a particular system that are not accessible using conventional structural techniques. For larger proteins and protein complexes, where a fully atomistic description would be computationally prohibitive, coarse-grained simulation techniques such as Elastic Network Modeling (ENM) are often employed, whereby each atom or group of atoms is linked by a set of springs whose properties can be customized according to the system of interest. Here we compare ENM with a recently proposed continuum model known as Fluctuating Finite Element Analysis (FFEA), which represents the biomolecule as a viscoelastic solid subject to thermal fluctuations. These two complementary computational techniques are used to answer a critical question in the rotary ATPase family; implicit within these motors is the need for a rotor axle and proton pump to rotate freely of the motor domain and stator structures. However, current single particle cryo-EM reconstructions have shown an apparent connection between the stators and rotor axle or pump region, hindering rotation. Both modeling approaches show a possible role for this connection and how it would significantly constrain the mobility of the rotary ATPase family.