Topological Reaction Coordinate Captures the Folding Transition State Ensemble in a Pierced Lasso Protein.

Proteins with a pierced lasso topology (PLT) have a covalent loop created by a disulfide bond, and the backbone circles back to thread the loop. This threaded topology has unique features compared to knotted topologies; notably, the topology is controlled by the chemical environment and the covalent loop remains intact even when denatured. In this work, we use the hormone leptin as our model PLT system and study its folding using molecular dynamics simulations that employ a structure-based (Go̅-like) model. We find that the reduced protein has a two-state folding mechanism with a transition state ensemble (TSE) that can be characterized by the reaction coordinate Q, the fraction of native contacts formed. In contrast, the oxidized protein, which must thread part of the polypeptide chain through a covalent loop, has a folding process that is poorly characterized by Q. Instead, we find that a topological coordinate that monitors the residue crossing the loop can identify the TSE of oxidized leptin. By precisely identifying the predicted TSE, one may now reliably calculate theoretical phi-values for the PLT protein, thereby enabling a comparison with experimental measurements. We find the loop-threading constraint leads to noncanonical phi-values that are uniformly small because this PLT protein has a flat energy landscape through the TSE.

Cryo-electron tomography reveals structural insights into the membrane remodeling mode of dynamin-like EHD filaments.

Eps15-homology domain containing proteins (EHDs) are eukaryotic, dynamin-related ATPases involved in cellular membrane trafficking. They oligomerize on membranes into filaments that induce membrane tubulation. While EHD crystal structures in open and closed conformations were previously reported, little structural information is available for the membrane-bound oligomeric form. Consequently, mechanistic insights into the membrane remodeling mechanism have remained sparse. Here, by using cryo-electron tomography and subtomogram averaging, we determined structures of nucleotide-bound EHD4 filaments on membrane tubes of various diameters at an average resolution of 7.6 Å. Assembly of EHD4 is mediated via interfaces in the G-domain and the helical domain. The oligomerized EHD4 structure resembles the closed conformation, where the tips of the helical domains protrude into the membrane. The variation in filament geometry and tube radius suggests a spontaneous filament curvature of approximately 1/70 nm-1. Combining the available structural and functional data, we suggest a model for EHD-mediated membrane remodeling.

Structural insights into crista junction formation by the Mic60-Mic19 complex.

Mitochondrial cristae membranes are the oxidative phosphorylation sites in cells. Crista junctions (CJs) form the highly curved neck regions of cristae and are thought to function as selective entry gates into the cristae space. Little is known about how CJs are generated and maintained. We show that the central coiled-coil (CC) domain of the mitochondrial contact site and cristae organizing system subunit Mic60 forms an elongated, bow tie-shaped tetrameric assembly. Mic19 promotes Mic60 tetramerization via a conserved interface between the Mic60 mitofilin and Mic19 CHCH (CC-helix-CC-helix) domains. Dimerization of mitofilin domains exposes a crescent-shaped membrane-binding site with convex curvature tailored to interact with the curved CJ neck. Our study suggests that the Mic60-Mic19 subcomplex traverses CJs as a molecular strut, thereby controlling CJ architecture and function.

SMOG 2 and OpenSMOG: Extending the limits of structure-based models.

Applying simulations with structure-based Go¯-like models has proven to be an effective strategy for investigating the factors that control biomolecular dynamics. The common element of these models is that some (or all) of the intra/inter-molecular interactions are explicitly defined to stabilize an experimentally determined structure. To facilitate the development and application of this broad class of models, we previously released the SMOG 2 software package. This suite allows one to easily customize and distribute structure-based (i.e., SMOG) models for any type of polymer-ligand system. The force fields generated by SMOG 2 may then be used to perform simulations in highly optimized MD packages, such as Gromacs, NAMD, LAMMPS, and OpenMM. Here, we describe extensions to the software and demonstrate the capabilities of the most recent version (SMOG v2.4.2). Changes include new tools that aid user-defined customization of force fields, as well as an interface with the OpenMM simulation libraries (OpenSMOG v1.1.0). The OpenSMOG module allows for arbitrary user-defined contact potentials and non-bonded potentials to be employed in SMOG models, without source-code modifications. To illustrate the utility of these advances, we present applications to systems with millions of atoms, long polymers and explicit ions, as well as models that include non-structure-based (e.g., AMBER-based) energetic terms. Examples include large-scale rearrangements of the SARS-CoV-2 Spike protein, the HIV-1 capsid with explicit ions, and crystallographic lattices of ribosomes and proteins. In summary, SMOG 2 and OpenSMOG provide robust support for researchers who seek to develop and apply structure-based models to large and/or intricate biomolecular systems.

CryoEM structure of the super-constricted two-start dynamin 1 filament.

Dynamin belongs to the large GTPase superfamily, and mediates the fission of vesicles during endocytosis. Dynamin molecules are recruited to the neck of budding vesicles to assemble into a helical collar and to constrict the underlying membrane. Two helical forms were observed: the one-start helix in the constricted state and the two-start helix in the super-constricted state. Here we report the cryoEM structure of a super-constricted two-start dynamin 1 filament at 3.74 Å resolution. The two strands are joined by the conserved GTPase dimeric interface. In comparison with the one-start structure, a rotation around Hinge 1 is observed, essential for communicating the chemical power of the GTPase domain and the mechanical force of the Stalk and PH domain onto the underlying membrane. The Stalk interfaces are well conserved and serve as fulcrums for adapting to changing curvatures. Relative to one-start, small rotations per interface accumulate to bring a drastic change in the helical pitch. Elasticity theory rationalizes the diversity of dynamin helical symmetries and suggests corresponding functional significance.

Quantification and demonstration of the collective constriction-by-ratchet mechanism in the dynamin molecular motor.

Dynamin oligomerizes into helical filaments on tubular membrane templates and, through constriction, cleaves them in a GTPase-driven way. Structural observations of GTP-dependent cross-bridges between neighboring filament turns have led to the suggestion that dynamin operates as a molecular ratchet motor. However, the proof of such mechanism remains absent. Particularly, it is not known whether a powerful enough stroke is produced and how the motor modules would cooperate in the constriction process. Here, we characterized the dynamin motor modules by single-molecule Förster resonance energy transfer (smFRET) and found strong nucleotide-dependent conformational preferences. Integrating smFRET with molecular dynamics simulations allowed us to estimate the forces generated in a power stroke. Subsequently, the quantitative force data and the measured kinetics of the GTPase cycle were incorporated into a model including both a dynamin filament, with explicit motor cross-bridges, and a realistic deformable membrane template. In our simulations, collective constriction of the membrane by dynamin motor modules, based on the ratchet mechanism, is directly reproduced and analyzed. Functional parallels between the dynamin system and actomyosin in the muscle are seen. Through concerted action of the motors, tight membrane constriction to the hemifission radius can be reached. Our experimental and computational study provides an example of how collective motor action in megadalton molecular assemblies can be approached and explicitly resolved.

Bacterial Vipp1 and PspA are members of the ancient ESCRT-III membrane-remodeling superfamily.

Membrane remodeling and repair are essential for all cells. Proteins that perform these functions include Vipp1/IM30 in photosynthetic plastids, PspA in bacteria, and ESCRT-III in eukaryotes. Here, using a combination of evolutionary and structural analyses, we show that these protein families are homologous and share a common ancient evolutionary origin that likely predates the last universal common ancestor. This homology is evident in cryo-electron microscopy structures of Vipp1 rings from the cyanobacterium Nostoc punctiforme presented over a range of symmetries. Each ring is assembled from rungs that stack and progressively tilt to form dome-shaped curvature. Assembly is facilitated by hinges in the Vipp1 monomer, similar to those in ESCRT-III proteins, which allow the formation of flexible polymers. Rings have an inner lumen that is able to bind and deform membranes. Collectively, these data suggest conserved mechanistic principles that underlie Vipp1, PspA, and ESCRT-III-dependent membrane remodeling across all domains of life.

Polymer-like Model to Study the Dynamics of Dynamin Filaments on Deformable Membrane Tubes.

Peripheral membrane proteins with intrinsic curvature can act both as sensors of membrane curvature and shape modulators of the underlying membranes. A well-studied example of such proteins is the mechanochemical GTPase dynamin, which assembles into helical filaments around membrane tubes and catalyzes their scission in a GTPase-dependent manner. It is known that the dynamin coat alone, without GTP, can constrict membrane tubes to radii of ∼10 nm, indicating that the intrinsic shape and elasticity of dynamin filaments should play an important role in membrane remodeling. However, molecular and dynamic understanding of the process is lacking. Here, we develop a dynamical polymer-chain model for a helical elastic filament bound on a deformable membrane tube of conserved mass, accounting for thermal fluctuations in the filament and lipid flows in the membrane. The model is based on the locally cylindrical helix approximation for dynamin. We obtain the elastic parameters of the dynamin filament by molecular dynamics simulations of its tetrameric building block and also from coarse-grained structure-based simulations of a 17-dimer filament. The results show that the stiffness of dynamin is comparable to that of the membrane. We determine equilibrium shapes of the filament and the membrane and find that mostly the pitch of the filament, not its radius, is sensitive to variations in membrane tension and stiffness. The close correspondence between experimental estimates of the inner tube radius and those predicted by the model suggests that dynamin's "stalk" region is responsible for its GTP-independent membrane-shaping ability. The model paves the way for future mesoscopic modeling of dynamin with explicit motor function.

Using SMOG 2 to Simulate Complex Biomolecular Assemblies.

Over the last 20 years, the application of structure-based (Go-like) models has ranged from protein folding with coarse-grained models to all-atom representations of large-scale molecular assemblies. While there are many variants that may be employed, the common feature of these models is that some (or all) of the stabilizing energetic interactions are defined based on the knowledge of a particular experimentally obtained conformation. With the generality of this approach, there was a need for a versatile computational platform for designing and implementing this class of models. To this end, the SMOG 2 software package provides an easy-to-use interface, where the user has full control of the model parameters. This software allows the user to edit XML-formatted files in order to provide definitions of new structure-based models. SMOG 2 reads these "template" files and maps the interactions onto specific structures, which are provided in PDB format. The force field files produced by SMOG 2 may then be used to perform simulations with a variety of popular molecular dynamics suites. In this chapter, we describe some of the key features of the SMOG 2 package, while providing examples and strategies for applying these techniques to complex (often large-scale) molecular assemblies, such as the ribosome.

Structure and assembly of the mitochondrial membrane remodelling GTPase Mgm1.

Balanced fusion and fission are key for the proper function and physiology of mitochondria1,2. Remodelling of the mitochondrial inner membrane is mediated by the dynamin-like protein mitochondrial genome maintenance 1 (Mgm1) in fungi or the related protein optic atrophy 1 (OPA1) in animals3-5. Mgm1 is required for the preservation of mitochondrial DNA in yeast6, whereas mutations in the OPA1 gene in humans are a common cause of autosomal dominant optic atrophy-a genetic disorder that affects the optic nerve7,8. Mgm1 and OPA1 are present in mitochondria as a membrane-integral long form and a short form that is soluble in the intermembrane space. Yeast strains that express temperature-sensitive mutants of Mgm19,10 or mammalian cells that lack OPA1 display fragmented mitochondria11,12, which suggests that Mgm1 and OPA1 have an important role in inner-membrane fusion. Consistently, only the mitochondrial outer membrane-not the inner membrane-fuses in the absence of functional Mgm113. Mgm1 and OPA1 have also been shown to maintain proper cristae architecture10,14; for example, OPA1 prevents the release of pro-apoptotic factors by tightening crista junctions15. Finally, the short form of OPA1 localizes to mitochondrial constriction sites, where it presumably promotes mitochondrial fission16. How Mgm1 and OPA1 perform their diverse functions in membrane fusion, scission and cristae organization is at present unknown. Here we present crystal and electron cryo-tomography structures of Mgm1 from Chaetomium thermophilum. Mgm1 consists of a GTPase (G) domain, a bundle signalling element domain, a stalk, and a paddle domain that contains a membrane-binding site. Biochemical and cell-based experiments demonstrate that the Mgm1 stalk mediates the assembly of bent tetramers into helical filaments. Electron cryo-tomography studies of Mgm1-decorated lipid tubes and fluorescence microscopy experiments on reconstituted membrane tubes indicate how the tetramers assemble on positively or negatively curved membranes. Our findings convey how Mgm1 and OPA1 filaments dynamically remodel the mitochondrial inner membrane.

Studying ribosome dynamics with simplified models.

With the broad accessibility of high-performance computing resources, the significance of a molecular dynamics simulation is now rarely limited by hardware and/or software availability. Rather, the scientific value of each calculation is determined by the principles that underlie the theoretical model. The current review addresses this topic in the context of simplified models applied to large-scale (∼20-100 Å) dynamics in the ribosome. Specifically, we focus on applications of the "SMOG" class of structure-based models, which can be used to simulate spontaneous (i.e. non-targeted) conformational rearrangements in complex molecular assemblies. Here, we aim to provide an entry-level assessment of the methods, which can help bridge conceptual and communication gaps between the experimental and computational communities. In addition, inspecting the strategies that have been deployed previously can provide guidelines for future computational investigations into the relationship between structure, energetics and dynamics in other assemblies.

Structural basis for membrane tethering by a bacterial dynamin-like pair.

Dynamin-like proteins (DLPs) are large GTPases that restructure membrane. DLPs such as the mitofusins form heterotypic oligomers between isoform pairs that bridge and fuse opposing membranes. In bacteria, heterotypic oligomerisation may also be important for membrane remodelling as most DLP genes are paired within operons. How DLPs tether opposing membranes is unknown. Here we show the crystal structure of a DLP heterotypic pair from the pathogen Campylobacter jejuni. A 2:2 stoichiometric tetramer is observed where heterodimers, conjoined by a random coil linker, assemble back-to-back to form a tripartite DLP chain with extreme flexibility. In vitro, tetramerisation triggers GTPase activity and induces lipid binding. Liposomes are readily tethered and form tubes at high tetramer concentration. Our results provide a direct mechanism for the long-range binding and bridging of opposing membranes by a bacterial DLP pair. They also provide broad mechanistic and structural insights that are relevant to other heterotypic DLP complexes.

Atomistic simulations indicate the functional loop-to-coiled-coil transition in influenza hemagglutinin is not downhill.

Influenza hemagglutinin (HA) mediates viral entry into host cells through a large-scale conformational rearrangement at low pH that leads to fusion of the viral and endosomal membranes. Crystallographic and biochemical data suggest that a loop-to-coiled-coil transition of the B-loop region of HA is important for driving this structural rearrangement. However, the microscopic picture for this proposed "spring-loaded" movement is missing. In this study, we focus on understanding the transition of the B loop and perform a set of all-atom molecular dynamics simulations of the full B-loop trimeric structure with the CHARMM36 force field. The free-energy profile constructed from our simulations describes a B loop that stably folds half of the postfusion coiled coil in tens of microseconds, but the full coiled coil is unfavorable. A buried hydrophilic residue, Thr59, is implicated in destabilizing the coiled coil. Interestingly, this conserved threonine is the only residue in the B loop that strictly differentiates between the group 1 and 2 HA molecules. Microsecond-scale constant temperature simulations revealed that kinetic traps in the structural switch of the B loop can be caused by nonnative, intramonomer, or intermonomer ß-sheets. The addition of the A helix stabilized the postfusion state of the B loop, but introduced the possibility for further ß-sheet structures. Overall, our results do not support a description of the B loop in group 2 HAs as a stiff spring, but, rather, it allows for more structural heterogeneity in the placement of the fusion peptides during the fusion process.

Molecular Simulations Suggest a Force-Dependent Mechanism of Vinculin Activation.

Focal adhesions are dynamic constructs at the leading edge of migrating cells, linking them to the extracellular matrix and enabling force sensing and transmission. The lifecycle of a focal adhesion is a highly coordinated process involving spatial and temporal variations of protein composition, interaction, and cellular tension. The assembly of focal adhesions requires the recruitment and activation of vinculin. Vinculin is present in the cytoplasm in an autoinhibited conformation in which its tail is held pincerlike by its head domains, further stabilized by two high-affinity head-tail interfaces. Vinculin has binding sites for talin and F-actin, but effective binding requires vinculin activation to release its head-tail associations. In migrating cells, it has been shown that the locations of vinculin activation coincide with areas of high cellular tension, and that the highest recorded tensions across vinculin are associated with adhesion assembly. Here, we use a structure-based model to investigate vinculin activation by talin modulated by tensile force generated by transient associations with F-actin. We show that vinculin activation may proceed from an intermediate state stabilized by partial talin-vinculin association. There is a low-force regime and a high-force regime where vinculin activation is dominated by two different pathways with distinct responses to force. Specifically, at zero or low forces, vinculin activation requires substantial destabilization of the main head-tail interface, which is rigid and undergoes very limited fluctuations, despite the other being relatively flexible. This pathway is not significantly affected by force; instead, higher forces favor an alternative pathway, which seeks to release the vinculin tail from its pincerlike head domains before destabilizing the head-tail interfaces. This pathway has a force-sensitive activation barrier and is significantly accelerated by force. Experimental data of vinculin during various stages of the focal adhesion lifecycle are consistent with the proposed force-regulated activation pathway.

Anisotropic Fluctuations in the Ribosome Determine tRNA Kinetics.

The ribosome is a large ribonucleoprotein complex that is responsible for the production of proteins in all organisms. Accommodation is the process by which an incoming aminoacyl-tRNA (aa-tRNA) molecule binds the ribosomal A site, and its kinetics has been implicated in the accuracy of tRNA selection. In addition to rearrangements in the aa-tRNA molecule, the L11 stalk can undergo large-scale anisotropic motions during translation. To explore the potential impact of this protruding region on the rate of aa-tRNA accommodation, we used molecular dynamics simulations with a simplified model to evaluate the free energy as a function of aa-tRNA position. Specifically, these calculations describe the transition between A/T and elbow-accommodated (EA) configurations (∼20 Šdisplacement). We find that the free-energy barrier associated with elbow accommodation is proportional to the degree of mobility exhibited by the L11 stalk. That is, when L11 is more rigid, the free-energy barrier height is decreased. This effect arises from the ability of L11 to confine, and thereby destabilize, the A/T ensemble. In addition, when elongation factor Tu (EF-Tu) is present, the A/T ensemble is further destabilized in an L11-dependent manner. These results provide a framework that suggests how next-generation experiments may precisely control the dynamics of the ribosome.

How EF-Tu can contribute to efficient proofreading of aa-tRNA by the ribosome.

It has long been recognized that the thermodynamics of mRNA-tRNA base pairing is insufficient to explain the high fidelity and efficiency of aminoacyl-tRNA (aa-tRNA) selection by the ribosome. To rationalize this apparent inconsistency, Hopfield proposed that the ribosome may improve accuracy by utilizing a multi-step kinetic proofreading mechanism. While biochemical, structural and single-molecule studies have provided a detailed characterization of aa-tRNA selection, there is a limited understanding of how the physical-chemical properties of the ribosome enable proofreading. To this end, we probe the role of EF-Tu during aa-tRNA accommodation (the proofreading step) through the use of energy landscape principles, molecular dynamics simulations and kinetic models. We find that the steric composition of EF-Tu can reduce the free-energy barrier associated with the first step of accommodation: elbow accommodation. We interpret this effect within an extended kinetic model of accommodation and show how EF-Tu can contribute to efficient and accurate proofreading.

Lowered pH Leads to Fusion Peptide Release and a Highly Dynamic Intermediate of Influenza Hemagglutinin.

Hemagglutinin (HA), the membrane-bound fusion protein of the influenza virus, enables the entry of virus into host cells via a structural rearrangement. There is strong evidence that the primary trigger for this rearrangement is the low pH environment of a late endosome. To understand the structural basis and the dynamic consequences of the pH trigger, we employed explicit-solvent molecular dynamics simulations to investigate the initial stages of the HA transition. Our results indicate that lowered pH destabilizes HA and speeds up the dissociation of the fusion peptides (FPs). A buried salt bridge between the N-terminus and Asp1122 of HA stem domain locks the FPs and may act as one of the pH sensors. In line with recent observations from simplified protein models, we find that, after the dissociation of FPs, a structural order-disorder transition in a loop connecting the central coiled-coil to the C-terminal domains produces a highly mobile HA. This motion suggests the existence of a long-lived asymmetric or "symmetry-broken" intermediate during the HA conformational change. This intermediate conformation is consistent with models of hemifusion, and its early formation during the conformational change has implications for the aggregation seen in HA activity.

SMOG 2: A Versatile Software Package for Generating Structure-Based Models.

Molecular dynamics simulations with coarse-grained or simplified Hamiltonians have proven to be an effective means of capturing the functionally important long-time and large-length scale motions of proteins and RNAs. Originally developed in the context of protein folding, structure-based models (SBMs) have since been extended to probe a diverse range of biomolecular processes, spanning from protein and RNA folding to functional transitions in molecular machines. The hallmark feature of a structure-based model is that part, or all, of the potential energy function is defined by a known structure. Within this general class of models, there exist many possible variations in resolution and energetic composition. SMOG 2 is a downloadable software package that reads user-designated structural information and user-defined energy definitions, in order to produce the files necessary to use SBMs with high performance molecular dynamics packages: GROMACS and NAMD. SMOG 2 is bundled with XML-formatted template files that define commonly used SBMs, and it can process template files that are altered according to the needs of each user. This computational infrastructure also allows for experimental or bioinformatics-derived restraints or novel structural features to be included, e.g. novel ligands, prosthetic groups and post-translational/transcriptional modifications. The code and user guide can be downloaded at http://smog-server.org/smog2.

Sequence co-evolutionary information is a natural partner to minimally-frustrated models of biomolecular dynamics.

Experimentally derived structural constraints have been crucial to the implementation of computational models of biomolecular dynamics. For example, not only does crystallography provide essential starting points for molecular simulations but also high-resolution structures permit for parameterization of simplified models. Since the energy landscapes for proteins and other biomolecules have been shown to be minimally frustrated and therefore funneled, these structure-based models have played a major role in understanding the mechanisms governing folding and many functions of these systems. Structural information, however, may be limited in many interesting cases. Recently, the statistical analysis of residue co-evolution in families of protein sequences has provided a complementary method of discovering residue-residue contact interactions involved in functional configurations. These functional configurations are often transient and difficult to capture experimentally. Thus, co-evolutionary information can be merged with that available for experimentally characterized low free-energy structures, in order to more fully capture the true underlying biomolecular energy landscape.

Constructing sequence-dependent protein models using coevolutionary information.

Recent developments in global statistical methodologies have advanced the analysis of large collections of protein sequences for coevolutionary information. Coevolution between amino acids in a protein arises from compensatory mutations that are needed to maintain the stability or function of a protein over the course of evolution. This gives rise to quantifiable correlations between amino acid sites within the multiple sequence alignment of a protein family. Here, we use the maximum entropy-based approach called mean field Direct Coupling Analysis (mfDCA) to infer a Potts model Hamiltonian governing the correlated mutations in a protein family. We use the inferred pairwise statistical couplings to generate the sequence-dependent heterogeneous interaction energies of a structure-based model (SBM) where only native contacts are considered. Considering the ribosomal S6 protein and its circular permutants as well as the SH3 protein, we demonstrate that these models quantitatively agree with experimental data on folding mechanisms. This work serves as a new framework for generating coevolutionary data-enriched models that can potentially be used to engineer key functional motions and novel interactions in protein systems.