Coarse-grained molecular dynamics simulations of a rotating bacterial flagellum

Ensuring thermodynamic consistency with invertible coarse-graining

Coarse-grained models are a core computational tool in theoretical chemistry and biophysics. A judicious choice of a coarse-grained model can yield physical insights by isolating the essential degrees of freedom that dictate the thermodynamic properties of a complex, condensed-phase system. The reduced complexity of the model typically leads to lower computational costs and more efficient sampling compared with atomistic models. Designing "good" coarse-grained models is an art. Generally, the mapping from fine-grained configurations to coarse-grained configurations itself is not optimized in any way; instead, the energy function associated with the mapped configurations is. In this work, we explore the consequences of optimizing the coarse-grained representation alongside its potential energy function. We use a graph machine learning framework to embed atomic configurations into a low-dimensional space to produce efficient representations of the original molecular system. Because the representation we obtain is no longer directly interpretable as a real-space representation of the atomic coordinates, we also introduce an inversion process and an associated thermodynamic consistency relation that allows us to rigorously sample fine-grained configurations conditioned on the coarse-grained sampling. We show that this technique is robust, recovering the first two moments of the distribution of several observables in proteins such as chignolin and alanine dipeptide.

Accurate predictions of thermoset resin glass transition temperatures from all-atom molecular dynamics simulation

To enable the design and development of the next generation of high-performance composite materials, there is a need to establish improved computational simulation protocols for accurate and efficient prediction of physical, mechanical, and thermal properties of thermoset resins. This is especially true for the prediction of glass transition temperature (T_g), as there are many discrepancies in the literature regarding simulation protocols and the use of cooling rate correction factors for predicting values using molecular dynamics (MD) simulation. The objectives of this study are to demonstrate accurate prediction the T_g with MD without the use of cooling rate correction factors and to establish the influence of simulated conformational state and heating/cooling cycles on physical, mechanical, and thermal properties predicted with MD. The experimentally-validated MD results indicate that accurate predictions of T_g, elastic modulus, strength, and coefficient of thermal expansion are highly reliant upon establishing MD models with mass densities that match experiment within 2%. The results also indicate the cooling rate correction factors, model building within different conformational states, and the choice of heating/cooling simulation runs do not provide statistically significant differences in the accurate prediction of T_g values, given the typical scatter observed in MD predictions of amorphous polymer properties.

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.

Ligilactobacillus agilis BKN88 possesses thermo-/acid-stable heteropolymeric flagellar filaments

Many flagellated bacteria possess multiple flagellins, but the roles and the compositions of each flagellin are diverse and poorly understood. In Ligilactobacillus agilis BKN88, there are two active flagellin gene paralogues but their function and composition in its flagellar filaments have not been described. The aim of this study is to find the function and composition of the flagellins by employing mutant strains each of which expresses a single flagellin or a modified flagellin. Two single flagellin-expressing strains were both flagellated while the number of flagella per cell in the single flagellin-expressing derivatives was lower than that in the wild type. Nonetheless, these derivative strains were apparently equally motile as the wild type. This indicates that either flagellin is sufficient for cell motility. The immunological activity via Toll-like receptor 5 of the single flagellin-expressing strains or purified single flagellins was readily detectable but mostly variably weaker than that of the wild type. The flagellar filaments of wild type L. agilis BKN88 were more acid-/thermo-stable than those of single flagellin-expressing derivatives. Using a combination of immunoprecipitation and flagellin-specific staining, wild type BKN88 appeared to possess heteropolymeric flagellar filaments consisting of both flagellins and each flagellin appeared to be equally distributed throughout the filaments. The results of this study suggest that the two flagellins together form a more robust filament than either alone and are thus functionally complementary.

Energy landscape of domain motion in glutamate dehydrogenase deduced from cryo-electron microscopy

Analysis of the conformational changes of protein is important to elucidate the mechanisms of protein motions correlating with their function. Here, we studied the spontaneous domain motion of unliganded glutamate dehydrogenase from Thermococcus profundus using cryo-electron microscopy and proposed a novel method to construct free-energy landscape of protein conformations. Each subunit of the homo-hexameric enzyme comprises nucleotide-binding domain (NAD domain) and hexamer-forming core domain. A large active-site cleft is situated between the two domains and varies from open to close according to the motion of a NAD domain. A three-dimensional map reconstructed from all cryo-electron microscopy images displayed disordered volumes of NAD domains, suggesting that NAD domains in the collected images adopted various conformations in domain motion. Focused classifications on NAD domain of subunits provided several maps of possible conformations in domain motion. To deduce what kinds of conformations appeared in EM images, we developed a novel analysis method that describe the EM maps as a linear combination of representative conformations appearing in a 200-ns molecular dynamics simulation as reference. The analysis enabled us to estimate the appearance frequencies of the representative conformations, which illustrated a free-energy landscape in domain motion. In the open/close domain motion, two free-energy basins hindered the direct transformation from open to closed state. Structure models constructed for representative EM maps in classifications demonstrated the correlation between the energy landscape and conformations in domain motion. Based on the results, the domain motion in glutamate dehydrogenase and the analysis method to visualize conformational changes and free-energy landscape were discussed. DATABASE: The EM maps of the four conformations were deposited to Electron Microscopy Data Bank (EMDB) as accession codes EMD-9845 (open), EMD-9846 (half-open1), EMD-9847 (half-open2), and EMD-9848 (closed), respectively. In addition, the structural models built for the four conformations were deposited to the Protein Data Bank (PDB) as accession codes 6JN9 (open), 6JNA (half-open1), 6JNC (half-open2), and 6JND (closed), respectively.

Computational Nanoscopy of Tight Junctions at the Blood-Brain Barrier Interface

The selectivity of the blood-brain barrier (BBB) is primarily maintained by tight junctions (TJs), which act as gatekeepers of the paracellular space by blocking blood-borne toxins, drugs, and pathogens from entering the brain. The BBB presents a significant challenge in designing neurotherapeutics, so a comprehensive understanding of the TJ architecture can aid in the design of novel therapeutics. Unraveling the intricacies of TJs with conventional experimental techniques alone is challenging, but recently developed computational tools can provide a valuable molecular-level understanding of TJ architecture. We employed the computational methods toolkit to investigate claudin-5, a highly expressed TJ protein at the BBB interface. Our approach started with the prediction of claudin-5 structure, evaluation of stable dimer conformations and nanoscale assemblies, followed by the impact of lipid environments, and posttranslational modifications on these claudin-5 assemblies. These led to the study of TJ pores and barriers and finally understanding of ion and small molecule transport through the TJs. Some of these in silico, molecular-level findings, will need to be corroborated by future experiments. The resulting understanding can be advantageous towards the eventual goal of drug delivery across the BBB. This review provides key insights gleaned from a series of state-of-the-art nanoscale simulations (or computational nanoscopy studies) performed on the TJ architecture.

Coarse-Grained Molecular Dynamics Force-Field for Polyacrylamide in Infinite Dilution Derived from Iterative Boltzmann Inversion and MARTINI Force-Field

We present a mesoscale model of aqueous polyacrylamide in the infinitely dilute concentration regime, by combining an extant coarse-grained (CG) force-field, MARTINI, and the Iterative Boltzmann Inversion protocol (IBI). MARTINI force-field was used to retain the thermodynamics of solvation of the polymer in water, whereas the structural properties and intrapolymer interactions were optimized by IBI. Atomistic molecular dynamics simulations of polymer in water were performed to benchmark the mesoscale simulations. Our results from the CG model show excellent agreement in structure with the atomistic system. We also studied the dynamical behavior of our CG system by computing the shear viscosity and compared it with the standard IBI model. The viscosity trends of our model were similar to the atomistic system, whereas the standard IBI model was highly dissimilar as expected. In summary, our hybrid CG model sufficiently mimics an infinitely dilute system, and is superior to both MARTINI and IBI in representing the structure and thermodynamics of the atomistic system, respectively. Our hybrid coarse-graining strategy promises applicability in large-scale simulations of polymeric/biological systems where the structure needs to be replicated accurately while preserving the thermodynamics of a smoother surrounding.

Molecular dynamics simulation of bacterial flagella

The bacterial flagellum is a biological nanomachine for the locomotion of bacteria, and is seen in organisms like Salmonella and Escherichia coli. The flagellum consists of tens of thousands of protein molecules and more than 30 different kinds of proteins. The basal body of the flagellum contains a protein export apparatus and a rotary motor that is powered by ion motive force across the cytoplasmic membrane. The filament functions as a propeller whose helicity is controlled by the direction of the torque. The hook that connects the motor and filament acts as a universal joint, transmitting torque generated by the motor to different directions. This report describes the use of molecular dynamics to study the bacterial flagellum. Molecular dynamics simulation is a powerful method that permits the investigation, at atomic resolution, of the molecular mechanisms of biomolecular systems containing many proteins and solvent. When applied to the flagellum, these studies successfully unveiled the polymorphic supercoiling and transportation mechanism of the filament, the universal joint mechanism of the hook, the ion transfer mechanism of the motor stator, the flexible nature of the transport apparatus proteins, and activation of proteins involved in chemotaxis.

Transport of nanoparticles across pulmonary surfactant monolayer: a molecular dynamics study

Three types of nanoparticles, including hydrophobic nanoparticles, hydrophilic nanoparticles, and hydrophilic nanoparticles coated with lipids, were found by our molecular dynamics simulations to be transported across the pulmonary surfactant monolayer, but via different pathways, which affect their subsequent interactions with target cell membranes.

Characterization of the flexibility of the peripheral stalk of prokaryotic rotary A-ATPases by atomistic simulations

Rotary ATPases are involved in numerous physiological processes, with the three distinct types (F/A/V‐ATPases) sharing functional properties and structural features. The basic mechanism involves the counter rotation of two motors, a soluble ATP hydrolyzing/synthesizing domain and a membrane‐embedded ion pump connected through a central rotor axle and a stator complex. Within the A/V‐ATPase family conformational flexibility of the EG stators has been shown to accommodate catalytic cycling and is considered to be important to function. For the A‐ATPase three EG structures have been reported, thought to represent conformational states of the stator during different stages of rotary catalysis. Here we use long, detailed atomistic simulations to show that those structures are conformers explored through thermal fluctuations, but do not represent highly populated states of the EG stator in solution. We show that the coiled coil tail domain has a high persistence length (∼100 nm), but retains the ability to adapt to different conformational states through the presence of two hinge regions. Moreover, the stator network of the related V‐ATPase has been suggested to adapt to subunit interactions in the collar region in addition to the nucleotide occupancy of the catalytic domain. The MD simulations reported here, reinforce this observation showing that the EG stators have enough flexibility to adapt to significantly different structural re‐arrangements and accommodate structural changes in the catalytic domain whilst resisting the large torque generated by catalytic cycling. These results are important to understand the role the stators play in the rotary‐ATPase mechanism. Proteins 2016; 84:1203–1212. © 2016 The Authors. Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.

Residue Specific and Chirality Dependent Interactions between Carbon Nanotubes and Flagellin

Flagellum is a lash-like cellular appendage found in many single-celled living organisms. The flagellin protofilaments contain 11-helix dual turn structure in a single flagellum. Each flagellin consists of four sub-domains - two inner domains (D0, D1) and two outer domains (D2, D3). While inner domains predominantly consist of α-helices, the outer domains are primarily beta sheets with D3. In flagellum, the outermost sub-domain is the only one that is exposed to the native environment. This study focuses on the interactions of the residues of D3 of an R-type flagellin with 5nm long chiral (5,15) and arm-chair (12,12) single-walled carbon nanotubes (SWNT) using molecular dynamics simulation. It presents the interactive forces between the SWNT and the residues of D3 from the perspectives of size and chirality of the SWNT. It is found that the metallic (arm-chair) SWNT interacts the most with glycine and threonine residues through van der Waals and hydrophobic interactions, whereas the semiconducting (chiral) SWNT interacts largely with the area of protein devoid of glycine by van der Waals, hydrophobic interactions, and hydrogen bonding. This indicates a crucial role that glycine plays in distinguishing metallic from semiconducting SWNTs.

A Nonradial Coarse-Grained Potential for Proteins Produces Naturally Stable Secondary Structure Elements

We introduce a nonradial potential term for coarse-grained (CG) molecular simulations of proteins. This term mimics the backbone dipole-dipole interactions and accounts for the needed directionality to form stable folded secondary structure elements. We show that α-helical and β-sheet peptide chains are correctly described in dynamics without the need of introducing any a priori bias potentials or ad hoc parametrizations, which limit broader applicability of CG simulations for proteins. Moreover, our model is able to catch the formation of supersecondary structural motifs, like transitions from long single α-helices to helix-coil-helix or β-hairpin assemblies. This novel scheme requires the structural information of Cα beads only; it does not introduce any additional degrees of freedom to the system and has a general formulation, which allows it to be used in synergy with various CG protocols, leading to an improved description of the structural and dynamic properties of protein assemblies and networks.

A flagellum based study of semiconductor nanofabrication through magnetotaxis

Magnetospirillum magneticum (AMB-1), which belong to alpha-protobacterium are gram-negative, single-celled prokaryotic organisms consisting of a lash-like cellular appendage called flagella. These filamentous structures are made up of a protein called flagellin that in turn consist of four sub-domains, two inner domains (D0, D1) made up of alpha-helices and two outer domains (D2, D3) made up of beta sheets. It is wrapped in a helical fashion around the longitudinal filament with the outermost sub-domain (D3) exposed to the surrounding environment. This study focuses on the interaction of the D3 with semiconducting as well as metallic single-walled carbon nanotubes (m-SWNT) and in turn presents the interactive forces between the SWNT and D3 from the perspective of size and type of SWNT. It is found that the SWNT interacts the most with glycine and threonine residues of flagellin both electrostatically as well as through van der waals. Further, the viability of magnetotactic bacteria Magnetospirillum magneticum (AMB-1) in the presence of SWNT is experimentally investigated and it is found that magnetotaxis in AMB-1 is preserved without any toxic effects due to SWNT. It is proposed that AMB-1 can be used as an efficient carrier of carbon nanotubes through its flagellum for semiconductor nanofabrication tasks.

Recent advances in transferable coarse-grained modeling of proteins

Computer simulations are indispensable tools for studying the structure and dynamics of biological macromolecules. Biochemical processes occur on different scales of length and time. Atomistic simulations cannot cover the relevant spatiotemporal scales at which the cellular processes occur. To address this challenge, coarse-grained (CG) modeling of the biological systems is employed. Over the last few years, many CG models for proteins continue to be developed. However, many of them are not transferable with respect to different systems and different environments. In this review, we discuss those CG protein models that are transferable and that retain chemical specificity. We restrict ourselves to CG models of soluble proteins only. We also briefly review recent progress made in the multiscale hybrid all-atom/CG simulations of proteins.

Transferring the PRIMO Coarse-Grained Force Field to the Membrane Environment: Simulations of Membrane Proteins and Helix-Helix Association

An extension of the recently developed PRIMO coarse-grained force field to membrane environments, PRIMO-M, is described. The membrane environment is modeled with the heterogeneous dielectric generalized Born (HDGB) methodology that simply replaces the standard generalized Born model in PRIMO without further parametrization. The resulting model was validated by comparing amino acid insertion free energy profiles and application in molecular dynamics simulations of membrane proteins and membrane-interacting peptides. Membrane proteins with 148–661 amino acids show stable root-mean-squared-deviations (RMSD) between 2 and 4 Å for most systems. Transmembrane helical peptides maintain helical shape and exhibit tilt angles in good agreement with experimental or other simulation data. The association of two glycophorin A (GpA) helices was simulated using replica exchange molecular dynamics simulations yielding the correct dimer structure with a crossing angle in agreement with previous studies. Finally, conformational sampling of the influenza fusion peptide also generates structures in agreement with previous studies. Overall, these findings suggest that PRIMO-M can be used to study membrane bound peptides and proteins and validates the transferable nature of the PRIMO coarse-grained force field.

Correlation between supercoiling and conformational motions of the bacterial flagellar filament

The bacterial flagellar filament is a very large macromolecular assembly of a single protein, flagellin. Various supercoiled states of the filament exist, which are formed by two structurally different conformations of flagellin in different ratios. We investigated the correlation between supercoiling of the protofilaments and molecular dynamics in the flagellar filament using quasielastic and elastic incoherent neutron scattering on the picosecond and nanosecond timescales. Thermal fluctuations in the straight L- and R-type filaments were measured and compared to the resting state of the wild-type filament. Amplitudes of motion on the picosecond timescale were found to be similar in the different conformational states. Mean-square displacements and protein resilience on the 0.1 ns timescale demonstrate that the L-type state is more flexible and less resilient than the R-type, whereas the wild-type state lies in between. Our results provide strong support that supercoiling of the protofilaments in the flagellar filament is determined by the strength of molecular forces in and between the flagellin subunits.

Microcapsule mechanics: from stability to function

Microcapsules are reviewed with special emphasis on the relevance of controlled mechanical properties for functional aspects. At first, assembly strategies are presented that allow control over the decisive geometrical parameters, diameter and wall thickness, which both influence the capsule's mechanical performance. As one of the most powerful approaches the layer-by-layer technique is identified. Subsequently, ensemble and, in particular, single-capsule deformation techniques are discussed. The latter generally provide more in-depth information and cover the complete range of applicable forces from smaller than pN to N. In a theory chapter, we illustrate the physics of capsule deformation. The main focus is on thin shell theory, which provides a useful approximation for many deformation scenarios. Finally, we give an overview of applications and future perspectives where the specific design of mechanical properties turns microcapsules into (multi-)functional devices, enriching especially life sciences and material sciences.

A theoretical view of protein dynamics

Proteins are fascinating supramolecular structures, which are able to recognize ligands transforming binding information into chemical signals. They can transfer information across the cell, can catalyse complex chemical reactions, and are able to transform energy into work with much more efficiency than any human engine. The unique abilities of proteins are tightly coupled with their dynamic properties, which are coded in a complex way in the sequence and carefully refined by evolution. Despite its importance, our experimental knowledge of protein dynamics is still rather limited, and mostly derived from theoretical calculations. I will review here, in a systematic way, the current state-of-the-art theoretical approaches to the study of protein dynamics, emphasizing the most recent advances, examples of use and the expected lines of development in the near future.

Development of flagella bio-templated nanomaterials for electronics

Bacterial flagella with their unique structural properties have proven to be promising bio-templates and can be exploited for the creation of nanomaterial with very high aspect ratio and surface area. Their chemically modifiable surfaces allow the flagella be modified to possess electrical/electronic properties. Their extraordinary physical properties along with the many possibilities for manipulation make them ideal systems to study for the purpose of developing nanoelectronics. First, this article reviews the characteristics of bacterial flagella and their utilization as biologically inspired templates. Next, the use of bio-templates for electronic systems such as dye-sensitized solar cell and lithium ion battery is discussed. Finally, we show the future directions for the use of flagella biotemplatednanomaterials for applications in electrical engineering fields.

PRIMO: A Transferable Coarse-grained Force Field for Proteins

We describe here the PRIMO (PRotein Intermediate Model) force field, a physics-based fully transferable additive coarse-grained potential energy function that is compatible with an all-atom force field for multi-scale simulations. The energy function consists of standard molecular dynamics energy terms plus a hydrogen-bonding potential term and is mainly parameterized based on the CHARMM22/CMAP force field in a bottom-up fashion. The solvent is treated implicitly via the generalized Born model. The bonded interactions are either harmonic or distance-based spline interpolated potentials. These potentials are defined on the basis of all-atom molecular dynamics (MD) simulations of dipeptides with the CHARMM22/CMAP force field. The non-bonded parameters are tuned by matching conformational free energies of diverse set of conformations with that of CHARMM all-atom results. PRIMO is designed to provide a correct description of conformational distribution of the backbone (ϕ/ψ) and side chains (χ1) for all amino acids with a CMAP correction term. The CMAP potential in PRIMO is optimized based on the new CHARMM C36 CMAP. The resulting optimized force field has been applied in MD simulations of several proteins of 36-155 amino acids and shown that the root-mean-squared-deviation of the average structure from the corresponding crystallographic structure varies between 1.80 and 4.03 Å. PRIMO is shown to fold several small peptides to their native-like structures from extended conformations. These results suggest the applicability of the PRIMO force field in the study of protein structures in aqueous solution, structure predictions as well as ab initio folding of small peptides.

Validating a Coarse-Grained Potential Energy Function through Protein Loop Modelling

Coarse-grained (CG) methods for sampling protein conformational space have the potential to increase computational efficiency by reducing the degrees of freedom. The gain in computational efficiency of CG methods often comes at the expense of non-protein like local conformational features. This could cause problems when transitioning to full atom models in a hierarchical framework. Here, a CG potential energy function was validated by applying it to the problem of loop prediction. A novel method to sample the conformational space of backbone atoms was benchmarked using a standard test set consisting of 351 distinct loops. This method used a sequence-independent CG potential energy function representing the protein using -carbon positions only and sampling conformations with a Monte Carlo simulated annealing based protocol. Backbone atoms were added using a method previously described and then gradient minimised in the Rosetta force field. Despite the CG potential energy function being sequence-independent, the method performed similarly to methods that explicitly use either fragments of known protein backbones with similar sequences or residue-specific /-maps to restrict the search space. The method was also able to predict with sub-Angstrom accuracy two out of seven loops from recently solved crystal structures of proteins with low sequence and structure similarity to previously deposited structures in the PDB. The ability to sample realistic loop conformations directly from a potential energy function enables the incorporation of additional geometric restraints and the use of more advanced sampling methods in a way that is not possible to do easily with fragment replacement methods and also enable multi-scale simulations for protein design and protein structure prediction. These restraints could be derived from experimental data or could be design restraints in the case of computational protein design. C++ source code is available for download from http://www.sbg.bio.ic.ac.uk/phyre2/PD2/.

A generic force field for protein coarse-grained molecular dynamics simulation

Coarse-grained (CG) force fields have become promising tools for studies of protein behavior, but the balance of speed and accuracy is still a challenge in the research of protein coarse graining methodology. In this work, 20 CG beads have been designed based on the structures of amino acid residues, with which an amino acid can be represented by one or two beads, and a CG solvent model with five water molecules was adopted to ensure the consistence with the protein CG beads. The internal interactions in protein were classified according to the types of the interacting CG beads, and adequate potential functions were chosen and systematically parameterized to fit the energy distributions. The proposed CG force field has been tested on eight proteins, and each protein was simulated for 1000 ns. Even without any extra structure knowledge of the simulated proteins, the Cα root mean square deviations (RMSDs) with respect to their experimental structures are close to those of relatively short time all atom molecular dynamics simulations. However, our coarse grained force field will require further refinement to improve agreement with and persistence of native-like structures. In addition, the root mean square fluctuations (RMSFs) relative to the average structures derived from the simulations show that the conformational fluctuations of the proteins can be sampled.

Gauging the flexibility of the active site in soybean lipoxygenase-1 (SLO-1) through an atom-centered density matrix propagation (ADMP) treatment that facilitates the sampling of rare events

We present a computational methodology to sample rare events in large biological enzymes that may involve electronically polarizing, reactive processes. The approach includes simultaneous dynamical treatment of electronic and nuclear degrees of freedom, where contributions from the electronic portion are computed using hybrid density functional theory and the computational costs are reduced through a hybrid quantum mechanics/molecular mechanics (QM/MM) treatment. Thus, the paper involves a QM/MM dynamical treatment of rare events. The method is applied to probe the effect of the active site elements on the critical hydrogen transfer step in the soybean lipoxygenase-1 (SLO-1) catalyzed oxidation of linoleic acid. It is found that the dynamical fluctuations and associated flexibility of the active site are critical toward maintaining the electrostatics in the regime where the reactive process can occur smoothly. Physical constraints enforced to limit the active site flexibility are akin to mutations and, in the cases studied, have a detrimental effect on the electrostatic fluctuations, thus adversely affecting the hydrogen transfer process.

Multiscale modeling of cellular actin filaments: from atomistic molecular to coarse-grained dynamics

In this article, we present a computational multiscale model for the characterization of subcellular proteins. The model is encoded inside a simulation tool that builds coarse-grained (CG) force fields from atomistic simulations. Equilibrium molecular dynamics simulations on an all-atom model of the actin filament are performed. Then, using the statistical distribution of the distances between pairs of selected groups of atoms at the output of the MD simulations, the force field is parameterized using the Boltzmann inversion approach. This CG force field is further used to characterize the dynamics of the protein via Brownian dynamics simulations. This combination of methods into a single computational tool flow enables the simulation of actin filaments with length up to 400 nm, extending the time and length scales compared to state-of-the-art approaches. Moreover, the proposed multiscale modeling approach allows to investigate the relationship between atomistic structure and changes on the overall dynamics and mechanics of the filament and can be easily (i) extended to the characterization of other subcellular structures and (ii) used to investigate the cellular effects of molecular alterations due to pathological conditions.

Fluid-mechanical interaction of flexible bacterial flagella by the immersed boundary method

Flagellar bundling is an important aspect of locomotion in bacteria such as Escherichia coli. To study the hydrodynamic behavior of helical flagella, we present a computational model that is based on the geometry of the bacterial flagellar filament at the micrometer scale. We consider two model flagella, each of which has a rotary motor at its base with the rotation rate of the motor set at 100 Hz. Bundling occurs when both flagella are left-handed helices turning counterclockwise (when viewed from the nonmotor end of the flagellum looking back toward the motor) or when both flagella are right-handed helices turning clockwise. Helical flagella of the other combinations of handedness and rotation direction do not bundle.

Coarse-graining of multiprotein assemblies

Multiscale models are important tools to elucidate how small changes in local subunit conformations may propagate to affect the properties of macromolecular complexes. We review recent advances in coarse-graining methods for poly-protein assemblies, systems that are composed of many copies of relatively few components, with a particular focus on viral capsids and cytoskeletal filaments. These methods are grouped into two broad categories-mapping methods, which use information from one scale of representation to parameterize a lower resolution model, and bridging methods, which repeatedly connect different scales during simulation-and we provide examples of both classes at different levels of complexity. Collectively, these models illustrate the numerous approaches to information transfer between scales and demonstrate that the complexity required of the model depends in general on the nature of the information sought.

Mass spectrometry of intact V-type ATPases reveals bound lipids and the effects of nucleotide binding

The ability of electrospray to propel large viruses into a mass spectrometer is established and is rationalized by analogy to the atmospheric transmission of the common cold. Much less clear is the fate of membrane-embedded molecular machines in the gas phase. Here we show that rotary adenosine triphosphatases (ATPases)/synthases from Thermus thermophilus and Enterococcus hirae can be maintained intact with membrane and soluble subunit interactions preserved in vacuum. Mass spectra reveal subunit stoichiometries and the identity of tightly bound lipids within the membrane rotors. Moreover, subcomplexes formed in solution and gas phases reveal the regulatory effects of nucleotide binding on both ATP hydrolysis and proton translocation. Consequently, we can link specific lipid and nucleotide binding with distinct regulatory roles.

Virtual interface substructure synthesis method for normal mode analysis of super-large molecular complexes at atomic resolution

Normal mode analysis of large biomolecular complexes at atomic resolution remains challenging in computational structure biology due to the requirement of large amount of memory space and central processing unit time. In this paper, we present a method called virtual interface substructure synthesis method or VISSM to calculate approximate normal modes of large biomolecular complexes at atomic resolution. VISSM introduces the subunit interfaces as independent substructures that join contacting molecules so as to keep the integrity of the system. Compared with other approximate methods, VISSM delivers atomic modes with no need of a coarse-graining-then-projection procedure. The method was examined for 54 protein-complexes with the conventional all-atom normal mode analysis using CHARMM simulation program and the overlap of the first 100 low-frequency modes is greater than 0.7 for 49 complexes, indicating its accuracy and reliability. We then applied VISSM to the satellite panicum mosaic virus (SPMV, 78,300 atoms) and to F-actin filament structures of up to 39-mer, 228,813 atoms and found that VISSM calculations capture functionally important conformational changes accessible to these structures at atomic resolution. Our results support the idea that the dynamics of a large biomolecular complex might be understood based on the motions of its component subunits and the way in which subunits bind one another.

Theoretical and computational investigation of flagellin translocation and bacterial flagellum growth

The bacterial flagellum is a self-assembling filament, which bacteria use for swimming. It is built from tens of thousands of flagellin monomers in a self-assembly process that involves translocation of the monomers through the flagellar interior, a channel, to the growing tip. Flagellum monomers are pumped into the filament at the base, move unfolded along the channel and then bind to the tip of the filament, thereby extending the growing flagellum. The flagellin translocation process, due to the flagellum maximum length of 20 μm, is an extreme example of protein transport through channels. Here, we derive a model for flagellin transport through the long confining channel, testing the key assumptions of the model through molecular dynamics simulations that also furnish system parameters needed for quantitative description. Together, mathematical model and molecular dynamics simulations explain why the growth rate of flagellar filaments decays exponentially with filament length and why flagellum growth ceases at a certain maximum length.

Coarse-grained representation of protein flexibility. Foundations, successes, and shortcomings

Flexibility is the key magnitude to understand the variety of functions of proteins. Unfortunately, its experimental study is quite difficult, and in fact, most experimental procedures are designed to reduce flexibility and allow a better definition of the structure. Theoretical approaches have become then the alternative but face serious timescale problems, since many biologically relevant deformation movements happen in a timescale that is far beyond the possibility of current atomistic models. In this complex scenario, coarse-grained simulation methods have emerged as a powerful and inexpensive alternative. Along this chapter, we will review these coarse-grained methods, and explain their physical foundations and their range of applicability.

Internal Dynamics of a Coarse-Grained Protein Using Analytical Harmonic Representation

An analytical coarse-grained model (ACG) is introduced to represent individual macromolecules for simulation of dynamic processes in cells. In the ACG model, a macromolecular structure is treated as a fully coarse-grained entity with a uniform mass density without the explicit atomic details. The excluded volume and surface of the ACG macromolecular species are explicitly treated by a spherical harmonic representation in the present study (although ellipsoidal, solid, and radial augmented functions can be used), which can provide any desired accuracy and detail depending on the problem of interest. The present paper focuses on the description of the internal fluctuations of a single ACG macromolecule, modeled by the superposition of low frequency quasiharmonic modes from explicit molecular dynamics simulation. A procedure for estimating the amplitudes, time scales of the quasiharmonic motions and the corresponding phases is presented and used to synthesize the complex motion. The analytical description and numerical algorithm can provide an adequate representation of the internal protein fluctuations revealed from the corresponding atomistic simulations, although the internal motions of ACG macromolecules do not explore motions not exhibited in the dynamic simulations.

Force-extension curves of bacterial flagella

Bacterial flagella assume different helical shapes during the tumbling phase of a bacterium but also in response to varying environmental conditions. Force-extension measurements by Darnton and Berg explicitly demonstrate a transformation from the coiled to the normal helical state (N.C. Darnton, H.C. Berg, Biophys. J. 92, 2230 (2007)). We here develop an elastic model for the flagellum based on Kirchhoff's theory of an elastic rod that describes such a polymorphic transformation and use resistive force theory to couple the flagellum to the aqueous environment. We present Brownian-dynamics simulations that quantitatively reproduce the force-extension curves and study how the ratio Γ of torsional to bending rigidity and the extensional rate influence the response of the flagellum. An upper bound for Γ is given. Using clamped flagella, we show in an adiabatic approximation that the mean extension, where a local coiled-to-normal transition occurs first, depends on the logarithm of the extensional rate.

Coarse-grained molecular dynamics simulations of shear-induced instabilities of lipid bilayer membranes in water

We study shear-induced instabilities of lipid bilayers immersed in water using coarse-grained molecular dynamics simulations. The shear imposed by the flow of the water induces initially microscopic structural changes of the membrane, starting with tilting of the molecules in the direction of the shear. The tilting propagates in the spanwise direction when the shear rate exceeds a critical value and the membrane undergoes a bucklinglike deformation in the direction perpendicular to the shear. The bucklinglike undulation continues until a localized Kelvin-Helmholtz-like instability leads to membrane rupture. We study the different modes of membrane undulation using membranes of different geometries and quantify the relative importance of the bucklinglike bending and the Kelvin-Helmholtz-like instability of the membrane.

Mimicking coarse-grained simulations without coarse-graining: enhanced sampling by damping short-range interactions

The damped-short-range-interaction (DSRI) method is proposed to mimic coarse-grained simulations by propagating an atomistic scale system on a smoothed potential energy surface. The DSRI method has the benefit of enhanced sampling provided by a typical coarse-grained simulation without the need to perform coarse-graining. Our method was used to simulate liquid water, alanine dipeptide folding, and the self-assembly of dimyristoylphosphatidylcholine lipid. In each case, our method appreciably accelerated the dynamics without significantly changing the free energy surface. Additional insights from DSRI simulations and the promise of coupling our DSRI method with Hamiltonian replica-exchange molecular dynamics are discussed.

Coarse-Grained Representations of Large Biomolecular Complexes from Low-Resolution Structural Data

High-resolution atomistic structures of many large biomolecular complexes have not yet been solved by experiments, such as X-ray crystallography or NMR. Often however low-resolution information is obtained by alternative techniques, such as cryo-electron microscopy or small-angle X-ray scattering. Coarse-grained (CG) models are an appropriate choice to computationally study these complexes given the limited resolution experimental data. One of the important questions therefore is how to define CG representations from these low-resolution density maps. This work provides a space-based essential dynamics coarse-graining (ED-CG) method to define a CG representation from a density map without detailed knowledge of its underlying atomistic structure and primary sequence information. This method is demonstrated on G-actin (both the atomic structure and its density map). It is then applied to the density maps of the Escherichia coli 70S ribosome and the microtubule. The results indicate that the method can define highly CG models that still preserve functionally important dynamics of large biomolecular complexes.

Role of a Burkholderia pseudomallei polyphosphate kinase in an oxidative stress response, motilities, and biofilm formation

Burkholderia pseudomallei, a motile and rod Gram-negative bacterium, is the causative agent of melioidosis. The bacterium is an intracellular pathogen and that motility is generally crucial for their survival in a natural environment and for systemic infection inside a host. We report here a role of B. pseudomallei polyphosphate kinase in virulence, such as an oxidative stress response, motilities and biofilm formation. The polyphosphate kinase (ppk) mutant is susceptible to hydrogen peroxide in an oxidative stress condition, unable to perform swimming, swarming motilities, and has lower density biofilm forming capacity than the wild-type strain. We also demonstrated that both polyphosphate kinase and motile flagella are essential and independently involved in biofilm formation. The B. pseudomallei flagellin (fliC) mutant and B. mallei, a nonmotile species, are shown to produce higher density biofilm formation than the ppk mutant, but less than wild type B. pseudomallei.

Defining coarse-grained representations of large biomolecules and biomolecular complexes from elastic network models

Coarse-grained (CG) models of large biomolecular complexes enable simulations of these systems over long timescales that are not accessible for atomistic molecular dynamics (MD) simulations. A systematic methodology, called essential dynamics coarse-graining (ED-CG), has been developed for defining coarse-grained sites in a large biomolecule. The method variationally determines the CG sites so that key dynamic domains in the protein are preserved in the CG representation. The original ED-CG method relies on a principal component analysis (PCA) of a MD trajectory. However, for many large proteins and multi-protein complexes such an analysis may not converge or even be possible. This work develops a new ED-CG scheme using an elastic network model (ENM) of the protein structure. In this procedure, the low-frequency normal modes obtained by ENM are used to define dynamic domains and to define the CG representation accordingly. The method is then applied to several proteins, such as the HIV-1 CA protein dimer, ATP-bound G-actin, and the Arp2/3 complex. Numerical results show that ED-CG with ENM (ENM-ED-CG) is much faster than ED-CG with PCA because no MD is necessary. The ENM-ED-CG models also capture functional essential dynamics of the proteins almost as well as those using full MD with PCA. Therefore, the ENM-ED-CG method may be better suited to coarse-grain a very large biomolecule or biomolecular complex that is too computationally expensive to be simulated by conventional MD, or when a high resolution atomic structure is not even available.