Publications

The mitoribosome translates mitochondrial mRNAs and regulates energy conversion that is a signature of aerobic life forms. We present a 2.2 Å resolution structure of human mitoribosome together with validated mitoribosomal RNA (rRNA) modifications, including aminoacylated CP-tRNAVal. The structure shows how mitoribosomal proteins stabilise binding of mRNA and tRNA helping to align it in the decoding center, whereas the GDP-bound mS29 stabilizes intersubunit communication. Comparison between different states, with respect to tRNA position, allowed us to characterize a non-canonical L1 stalk, and molecular dynamics simulations revealed how it facilitates tRNA transitions in a way that does not require interactions with rRNA. We also report functionally important polyamines that are depleted when cells are subjected to an antibiotic treatment. The structural, biochemical, and computational data illuminate the principal functional components of the translation mechanism in mitochondria and provide a description of the structure and function of the human mitoribosome.

Protein synthesis by the ribosome requires large-scale rearrangements of the ‘small’ subunit (SSU; ∼1 MDa), including inter- and intra-subunit rotational motions. However, with nearly 2000 structures of ribosomes and ribosomal subunits now publicly available, it is exceedingly difficult to design experiments based on analysis of all known rotation states. To overcome this, we developed an approach where the orientation of each SSU head and body is described in terms of three angular coordinates (rotation, tilt and tilt direction) and a single translation. By considering the entire RCSB PDB database, we describe 1208 fully-assembled ribosome complexes and 334 isolated small subunits, which span >50 species. This reveals aspects of subunit rearrangements that are universal, and others that are organism/domain-specific. For example, we show that tilt-like rearrangements of the SSU body (i.e. ‘rolling’) are pervasive in both prokaryotic and eukaryotic (cytosolic and mitochondrial) ribosomes. As another example, domain orientations associated with frameshifting in bacteria are similar to those found in eukaryotic ribosomes. Together, this study establishes a common foundation with which structural, simulation, single-molecule and biochemical efforts can more precisely interrogate the dynamics of this prototypical molecular machine.

Evaluation of immunogenic epitopes for universal vaccine development in the face of ongoing SARS-CoV-2 evolution remains a challenge. Herein, we investigate the genetic and structural conservation of an immunogenically relevant epitope (C662–C671) of spike (S) protein across SARS-CoV-2 variants to determine its potential utility as a broad spectrum vaccine candidate against coronavirus diseases. Comparative sequence analysis, structural assessment, and molecular dynamics simulations of C662–C671 epitope were performed. Mathematical tools were employed to determine its mutational cost. We found that the amino acid sequence of C662–C671 epitope is entirely conserved across the observed major variants of SARS-CoV-2 in addition to SARS-CoV. Its conformation and accessibility are predicted to be conserved, even in the highly mutated Omicron variant. Costly mutational rate in the context of energy expenditure in genome replication and translation can explain this strict conservation. These observations may herald an approach to developing vaccine candidates for universal protection against emergent variants of coronavirus.

Estrogen receptor α (ERα) is a regulatory protein that can access a set of distinct structural configurations. ERα undergoes extensive remodeling as it interacts with different agonists and antagonists, as well as transcription activation and repression factors. Moreover, breast cancer tumors resistant to hormone therapy have been associated with the imbalance between the active and inactive ERα states. Cancer-activating mutations in ERα play a crucial role in this imbalance and can promote the progression of cancer. However, the rate of this progression can also be increased by dysregulated pH in the tumor microenvironment. Many molecular aspects of the process of activation of ERα that can be affected by these pH changes and mutations are still unclear. Thus, we applied computational and experimental techniques to explore the activation process dynamics of ER for environments with different pHs and in the presence of one of the most recurrent cancer-activating mutations, D538G. Our results indicated that the effect of the pH increase associated with the D538G mutation promoted a robust stabilization of the active state of ER. We were also able to determine the main protein regions that have the most potential to influence the activation process under different pH conditions, which may provide targets of future therapeutics for the treatment of hormone-resistant breast cancer tumors. Finally, the approach used here can be applied for proteins associated with the proliferation of other cancer types, which can also have their function affected by small pH changes.

The ribosome is a complex biomolecular machine that utilizes large-scale conformational rearrangements to synthesize proteins. For example, during the elongation cycle, the "head" domain of the ribosomal small subunit (SSU) is known to undergo transient rotation events that allow for movement of tRNA molecules (i.e., translocation). While the head may exhibit rigid-body-like properties, the precise relationship between experimentally accessible probes and multidimensional rotations has yet to be established. To address this gap, we perform molecular dynamics simulations of the translocation step of the elongation cycle in the ribosome, where the SSU head spontaneously undergoes rotation and tilt-like motions. With this data set (1250 simulated events), we used statistical and information-theory-based measures to identify possible single-molecule probes that can isolate SSU head rotation and head tilting. This analysis provides a molecular interpretation for previous single-molecule measurements, while establishing a framework for the design of next-generation experiments that may precisely probe the mechanistic and kinetic aspects of the ribosome.

Proper ionic concentrations are required for the functional dynamics of RNA and ribonucleoprotein (RNP) assemblies. While experimental and computational techniques have provided many insights into the properties of chelated ions, less is known about the energetic contributions of diffuse ions to large-scale conformational rearrangements. To address this, we present a model that is designed to quantify the influence of diffuse monovalent and divalent ions on the dynamics of biomolecular assemblies. This model employs all-atom (non-H) resolution and explicit ions, where effective potentials account for hydration effects. We first show that the model accurately predicts the number of excess Mg2+ ions for prototypical RNA systems, at a level comparable to modern coarse-grained models. We then apply the model to a complete ribosome and show how the balance between diffuse Mg2+ and K+ ions can control the dynamics of tRNA molecules during translation. The model predicts differential effects of diffuse ions on the free-energy barrier associated with tRNA entry and the energy of tRNA binding to the ribosome. Together, this analysis reveals the direct impact of diffuse ions on the dynamics of an RNP assembly.

Applying simulations with structure-based 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.

Protein synthesis involves a complex series of large-scale conformational changes in the ribosome. While long-lived intermediate states of these processes can be characterized by experiments, computational methods can be used to identify the interactions that contribute to the rate-limiting free-energy barriers. To this end, we use a simplified energetic model to perform molecular dynamics (MD) simulations of aminoacyl-tRNA (aa-tRNA) accommodation on the ribosome. While numerous studies have probed the energetics of the early stages of accommodation, we focus on the final stage of accommodation, where the 3′-CCA tail of aa-tRNA enters the peptidyl transferase center (PTC). These simulations show how a distinct intermediate is induced by steric confinement of the tail, immediately before it completes accommodation. Multiple pathways for 3′-CCA tail accommodation can be quantitatively distinguished, where the tail enters the PTC by moving past a pocket enclosed by Helix 89, 90, and 92, or through an alternate route formed by Helix 93 and the P-site tRNA. C2573, located within Helix 90, is shown to provide the largest contribution to this late-accommodation steric barrier, such that sub-Å perturbations to this residue can alter the time scale of tail accommodation by nearly an order of magnitude. In terms of biological function, these calculations suggest how this late-stage sterically induced barrier may contribute to tRNA proofreading by the ribosome.

Conformational changes are an essential feature for the function of some dynamic proteins. Understanding the mechanism of such motions may allow us to identify important properties, which may be directly related to the regulatory function of a protein. Also, this knowledge may be employed for a rational design of drugs that can shift the balance between active and inactive conformations, as well as affect the kinetics of the activation process. Here, the conformational changes in carboxyl-terminal Src kinase, the major catalytic repressor to the Src family of kinases, was investigated, and it was proposed as a functionally related hypothesis. A Cα Structure-Based Model (Cα-SBM) was applied to provide a description of the overall conformational landscape and further analysis complemented by detailed molecular dynamics simulations. As a first approach to Cα-SBM simulations, reversible transitions between active (closed) and inactive (open) forms were modeled as fluctuations between these two energetic basins. It was found that, in addition to the interdomain Carboxyl-terminal SRC Kinase (Csk) correlated motions, a conformational change in the αC helix is required for a complete conformational transition. The result reveals this as an important region of transition control and domain coordination. Restrictions in the αC helix region of the Csk protein were performed, and the analyses showed a direct correlation with the global conformational changes, with this location being propitious for future studies of ligands. Also, the Src Homology 3 (SH3) and SH3 plus Src Homology 2 (SH2) domains were excluded for a direct comparison with experimental results previously published. Simulations where the SH3 was deleted presented a reduction of the transitions during the simulations, while the SH3–SH2 deletion vanishes the Csk transitions, corroborating the experimental results mentioned and linking the conformational changes with the catalytic functionality of Csk. The study was complemented by the introduction of a known kinase inhibitor close to the Csk αC helix region where its consequences for the kinetic behavior and domain displacement of Csk were verified through detailed molecular dynamics. The findings describe the mechanisms involving the Csk αC helix for the transitions and also support the dynamic correlation between SH3 and SH2 domains against the Csk lobes and how local energetic restrictions or interactions in the Csk αC helix can play an important role for long-range motions. The results also allow speculation if the Csk activity is restricted to one specific conformation or a consequence of a state transition, this point being a target for future studies. However, the αC helix is revealed as a potential region for rational drug design.

Protein synthesis by the ribosome is coordinated by an intricate series of large-scale conformational rearrangements. Structural studies can provide information about long-lived states, however biological kinetics are controlled by the intervening free-energy barriers. While there has been progress describing the energy landscapes of bacterial ribosomes, very little is known about the energetics of large-scale rearrangements in eukaryotic systems. To address this topic, we constructed an all-atom model with simplified energetics and performed simulations of subunit rotation in the yeast ribosome. In these simulations, the small subunit (SSU; ¿1 MDa) undergoes spontaneous and reversible rotation events (¿8¿). By enabling the simulation of this rearrangement under equilibrium conditions, these calculations provide initial insights into the molecular factors that control dynamics in eukaryotic ribosomes. Through this, we are able to identify specific inter-subunit interactions that have a pronounced influence on the rate-limiting free-energy barrier. We also show that, as a result of changes in molecular flexibility, the thermodynamic balance between the rotated and unrotated states is temperature-dependent. This effect may be interpreted in terms of differential molecular flexibility within the rotated and unrotated states. Together, these calculations provide a foundation, upon which the field may begin to dissect the energetics of these complex molecular machines.

Modifications in the tRNA anticodon loop, adjacent to the three-nucleotide anticodon, influence translation fidelity by stabilizing the tRNA to allow for accurate reading of the mRNA genetic code. One example is the N1-methylguanosine modification at guanine nucleotide 37 (m1G37) located in the anticodon loop andimmediately adjacent to the anticodon nucleotides 34, 35, 36. The absence of m1G37 in tRNAPro causes +1 frameshifting on polynucleotide, slippery codons. Here, we report structures of the bacterial ribosome containing tRNAPro bound to either cognate or slippery codons to determine how the m1G37 modification prevents mRNA frameshifting. The structures reveal that certain codon–anticodon contexts and the lack of m1G37 destabilize interactions of tRNAPro with the P site of the ribosome, causing large conformational changes typically only seen during EF-G-mediated translocation of the mRNA-tRNA pairs. These studies provide molecular insights into how m1G37 stabilizes the interactions of tRNAPro with the ribosome in the context of a slippery mRNA codon.

The ribosome is a biomolecular machine that undergoes multiple large-scale structural rearrangements during protein elongation. Here, we focus on a conformational rearrangement during translocation, known as P/E hybrid-state formation. Using a model that explicitly represents all non-hydrogen atoms, we simulated more than 120 spontaneous transitions, where the tRNA molecule is displaced between the P and E sites of the large subunit. In addition to predicting a free-energy landscape that is consistent with previous experimental observations, the simulations reveal how a six-residue gate-like region can limit P/E formation, where sub-angstrom structural perturbations lead to an order-of-magnitude change in kinetics. Thus, this precisely defined set of residues represents a novel target that may be used to control functional dynamics in bacterial ribosomes. This theoretical analysis establishes a direct relationship between ribosome structure and large-scale dynamics, and it suggests how next-generation experiments may precisely dissect the energetics of hybrid formation on the ribosome.

Molecular dynamics techniques provide numerous strategies for investigating biomolecular energetics, though quantitative analysis is often only accessible for relatively small (frequently monomeric) systems. To address this limit, we use simulations in combination with a simplified energetic model to study complex rearrangements in a large assembly. We use cryo-EM reconstructions to simulate the DNA packaging-associated 3 nm expansion of the protein shell of an initially assembled phage T7 capsid (called procapsid or capsid I). This is accompanied by a disorder–order transition and expansion-associated externalization displacement of the 420 N-terminal tails of the shell proteins. For the simulations, we use an all-atom structure-based model (1.07 million atoms), which is specifically designed to probe the influence of molecular sterics on dynamics. We find that the rate at which the N-terminal tails undergo translocation depends heavily on their position within hexons and pentons. Specifically, trans-shell displacements of the hexon E subunits are the most frequent and hexon A subunits are the least frequent. The simulations also implicate numerous tail translocation intermediates during tail translocation that involve topological traps, as well as sterically induced barriers. The presented study establishes a foundation for understanding the precise relationship between molecular structure and phage maturation.

Electrokinetic translocation of biomolecules through solid-state nanopores represents a label-free single-molecule technique that may be used to measure biomolecular structure and dynamics. Recent investigations have attempted to distinguish individual transfer RNA (tRNA) species based on the associated pore translocation times, ion-current noise, and blockage currents. By manufacturing sufficiently smaller pores, each tRNA is required to undergo a deformation to translocate. Accordingly, differences in nanopore translocation times and distributions may be used to infer the mechanical properties of individual tRNA molecules. To bridge our understanding of tRNA structural dynamics and nanopore measurements, we apply molecular dynamics simulations using a simplified “structure-based” energetic model. Calculating the free-energy landscape for distinct tRNA species implicates transient unfolding of the terminal RNA helix during nanopore translocation. This provides a structural and energetic framework for interpreting current experiments, which can aid the design of methods for identifying macromolecules using nanopores.

Understanding how enzymes achieve their tremendous catalytic power is a major question in biochemistry. Greater understanding is also needed for enzyme engineering applications. In many cases, enzyme efficiency and specificity depend on residues not in direct contact with the substrate, termed remote residues. This work focuses on Escherichia coli ornithine transcarbamoylase (OTC), which plays a central role in amino acid metabolism. OTC has been reported to undergo an induced-fit conformational change upon binding its first substrate, carbamoyl phosphate (CP), and several residues important for activity have been identified. Using computational methods based on the computed chemical properties from theoretical titration curves, sequence-based scores derived from evolutionary history, and protein surface topology, residues important for catalytic activity were predicted. The roles of these residues in OTC activity were tested by constructing mutations at predicted positions, followed by steady-state kinetics assays and substrate binding studies with the variants. First-layer mutations R57A and D231A, second-layer mutation H272L, and third-layer mutation E299Q, result in 57- to 450-fold reductions in kcat/KM with respect to CP and 44- to 580-fold reductions with respect to ornithine. Second-layer mutations D140N and Y160S also reduce activity with respect to ornithine. Most variants had decreased stability relative to wild-type OTC, with variants H272L, H272N, and E299Q having the greatest decreases. Variants H272L, E299Q, and R57A also show compromised CP binding. In addition to direct effects on catalytic activity, effects on overall protein stability and substrate binding were observed that reveal the intricacies of how these residues contribute to catalysis.

https://pubs.aip.org/aip/jcp/article-abstract/151/11/114106/198886/Drift-diffusion-DrDiff-framework-determines

The accurate expression of proteins requires the ribosome to efficiently undergo elaborate conformational rearrangements. The most dramatic of these motions is subunit rotation, which is necessary for tRNA molecules to transition between ribosomal binding sites. While rigid-body descriptions provide a qualitative picture of the process, obtaining quantitative mechanistic insights requires one to account for the relationship between molecular flexibility and collective dynamics. Using simulated rotation events, we assess the quality of experimentally accessible measures for describing the collective displacement of the ∼4000-residue small subunit. For this, we ask whether each coordinate is able to identify the underlying free-energy barrier and transition state ensemble (TSE). We find that intuitive structurally motivated coordinates (e.g., rotation angle, interprotein distances) can distinguish between the endpoints, though they are poor indicators of barrier-crossing events, and they underestimate the free-energy barrier. In contrast, coordinates based on intersubunit bridges can identify the TSE. We additionally verify that the committor probability for the putative TSE configurations is 0.5, a hallmark feature of any transition state. In terms of structural properties, these calculations implicate a transition state in which flexibility allows for asynchronous rearrangements of the bridges, as the ribosome adopts a partially rotated orientation. This provides a theoretical foundation, upon which experimental techniques may precisely quantify the energy landscape of the ribosome.

Protein folding occurs in a high dimensional phase space, and the representation of the associated energy landscape is nontrivial. A widely applied approach to studying folding landscapes is to describe the dynamics along a small number of reaction coordinates. However, other strategies involve more elaborate analysis of the complex phase space. There have been many attempts to obtain a more detailed representation of all available conformations for a given system. In this work, we address this problem using a metric based on internal distances between amino acids to describe the differences between any two conformations. Using an effective projection method, we are able to go beyond the typical one-dimensional representation and provide intuitive two dimensional visualizations of the landscape. We refer to this method as the energy landscape visualization method (ELViM). We have applied this methodology using a Cα structure-based model to study the folding of two well-known proteins: SH3 domain and protein-A. Our visualization method yields a detailed description of the folding process, making possible the identification of transition state regions, and establishing the paths that lead to the native state. For SH3, we have analyzed structural differences in the distribution of folding routes. The competition between the native and mirror structures in protein A is also discussed. Finally, the method is applied to study conformational changes in the protein elongation factor thermally unstable. Distinct features of ELViM are that it does not require or assume a reaction coordinate, and it does not require analysis of kinetic aspects of the system.

Elongation factor Tu (EF-Tu) is a three-domain protein that is responsible for delivering aminoacyl-tRNA (aa-tRNA) molecules to the ribosome. During the delivery process, EF-Tu undergoes a large-scale (~50Å) conformational transition that results in rearrangement of domain I, relative to the II/III superdomain. Despite the central role of EF-Tu during protein synthesis, little is known about the structural and energetic properties of this reordering process. To study the physical-chemical properties of domain motion, we constructed a multi-basin structure-based (i.e., Gō-like) model, with which we have simulated hundreds of spontaneous conformational rearrangements. By analyzing the statistical properties of these events, we show that EF-Tu is likely to adopt a disordered intermediate ensemble during this transition. We further show that this disordered intermediate will favor a specific sequence of conformational substeps when bound to the ribosome, and the disordered ensemble can influence the kinetics of the incoming aa-tRNA molecule. Overall, this study highlights the dynamic nature of EF-Tu by revealing a relationship between conformational disorder and biological function.

A major challenge in the study of biomolecular assemblies is to identify reaction coordinates that precisely monitor conformational rearrangements. This is central to the interpretation of single-molecule fluorescence resonance energy transfer measurements, where the observed dynamics depends on the labeling strategy. As an example, different probes of subunit rotation in the ribosome have provided qualitatively distinct descriptions. In one study, changes in fluorescence suggested that the 30S body undergoes a single rotation/back-rotation cycle during the process of mRNA-tRNA translocation. In contrast, an alternate assay implicated the presence of reversible rotation events before completing translocation. For future single-molecule experiments to unambiguously measure the relationship between subunit rotation and translocation, it is necessary to rationalize these conflicting descriptions. To this end, we have simulated hundreds of spontaneous subunit rotation events (≈8°) using a residue-level coarse-grained model of the ribosome. We analyzed nine different reaction coordinates and found that the apparently inconsistent measurements are likely a consequence of ribosomal flexibility. Further, we propose a metric for quantifying the degree of energetic coupling between experimentally measured degrees of freedom and subunit rotation. This analysis provides a physically grounded framework that can guide the development of more precise single-molecule techniques.

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 Å displacement). 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.

Proteins are structurally dynamic macromolecules, and it is challenging to quantify the conformational properties of their native state in solution. Nanopores can be efficient tools to study proteins in a solution environment. In this method, an electric field induces electrophoretic and/or electro-osmotic transport of protein molecules through a nanopore slightly larger than the protein molecule. High-bandwidth ion current measurement is used to detect the transit of each protein molecule. First, our measurements reveal a correlation between the mean current blockade amplitude and the radius of gyration for each protein. Next, we find a correlation between the shape of the current signal amplitude distributions and the protein fluctuation as obtained from molecular dynamics simulations. Further, the magnitude of the structural fluctuations, as probed by experiments and simulations, correlates with the ratio of α-helix to β-sheet content. We highlight the resolution of our measurements by resolving two states of calmodulin, a canonical protein that undergoes a conformational change in response to calcium binding.

Proteins are synthesized by the joint action of the ribosome and tRNA molecules, where the rate of synthesis can be affected by numerous factors, such as the concentration of tRNA, the binding affinity of tRNA for the ribosome, or post-transcriptional modifications. Here, we expand this range of contributors by demonstrating how differences in tRNA structure can give rise to tRNA species-specific dynamics in the ribosome. To show this, we perform simulations of A/P hybrid-state formation for two tRNA species (tRNAPhe and tRNALeu), which differ in the size of their variable loops (VLs). These calculations reveal that steric interactions between the VL and the ribosomal A-site finger (ASF, i.e., H38 of 23S rRNA) can directly modulate the free-energy landscape for each tRNA species. We also find that tRNA and ASF motions are highly correlated, where fluctuations of the ASF are predictive of tRNA transition events. Finally, by introducing perturbations to the model, we demonstrate that ASF flexibility is a determinant of the rate of A/P hybrid-state formation.

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.

In order to quantitatively describe the energetics of biomolecular rearrangements, it is necessary to identify reaction coordinates that accurately capture the relevant transition events. Here, we perform simulations of A-site tRNA movement (∼20 Å) during hybrid-state formation in the ribosome and quantify the ability of interatomic distances to capture the transition state ensemble. Numerous coordinates are found to be accurate indicators of the transition state, allowing tRNA rearrangements to be described as diffusion across a one-dimensional free-energy surface. In addition to providing insights into the physical-chemical relationship between biomolecular structure and dynamics, these results can help enable single-molecule techniques to probe the free-energy landscape of the ribosome.

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

Translocation of mRNA and tRNA through the ribosome is associated with large-scale rearrangements of the head domain in the 30S ribosomal subunit. To elucidate the relationship between 30S head dynamics and mRNA–tRNA displacement, we apply molecular dynamics simulations using an all-atom structure-based model. Here we provide a statistical analysis of 250 spontaneous transitions between the A/P–P/E and P/P–E/E ensembles. Consistent with structural studies, the ribosome samples a chimeric ap/P–pe/E intermediate, where the 30S head is rotated ∼18°. It then transiently populates a previously unreported intermediate ensemble, which is characterized by a ∼10° tilt of the head. To identify the origins of head tilting, we analyse 781 additional simulations in which specific steric features are perturbed. These calculations show that head tilting may be attributed to specific steric interactions between tRNA and the 30S subunit (PE loop and protein S13). Taken together, this study demonstrates how molecular structure can give rise to large-scale collective rearrangements.

As our understanding of biological dynamics continues to be refined, it is becoming clear that biomolecules can undergo transitions between ordered and disordered states as they execute functional processes. From a computational perspective, studying disorder events poses a challenge, as they typically occur on long timescales, and the associated molecules are often large (i.e., hundreds of residues). These size and time requirements make it advantageous to use computationally inexpensive models to characterize large-scale dynamics, where more highly detailed models can provide information about individual sub-steps associated with function. To reduce computational demand, one often uses a coarse-grained representation of the molecule or a simplified description of the energetics. In order to use simpler models to identify transient disorder in RNA and proteins, it is imperative that these models can accurately capture structural fluctuations about folded configurations, as well as the overall stability of each molecule. Here, we explore a class of simplified model for which all non-hydrogen atoms are explicitly represented. We find that this model can provide a consistent description of protein folding and native-basin dynamics for several representative biomolecules. We additionally show that the native-basin fluctuations of tRNA and the ribosome are robust to variations in the model. Finally, the extended variable loop in tRNAIle is predicted to be very dynamic, which may facilitate biologically-relevant rearrangements. Together, this study provides a foundation that will aid in the application of simplified models to study disorder during function in ribonucleoprotein (RNP) assemblies.

Influenza hemagglutinin (HA), a homotrimeric glycoprotein crucial for membrane fusion, undergoes a large-scale structural rearrangement during viral invasion. X-ray crystallography has shown that the pre- and postfusion configurations of HA2, the membrane-fusion subunit of HA, have disparate secondary, tertiary, and quaternary structures, where some regions are displaced by more than 100 Å. To explore structural dynamics during the conformational transition, we studied simulations of a minimally frustrated model based on energy landscape theory. The model combines structural information from both the pre- and postfusion crystallographic configurations of HA2. Rather than a downhill drive toward formation of the central coiled-coil, we discovered an order-disorder transition early in the conformational change as the mechanism for the release of the fusion peptides from their burial sites in the prefusion crystal structure. This disorder quickly leads to a metastable intermediate with a broken threefold symmetry. Finally, kinetic competition between the formation of the extended coiled-coil and C-terminal melting results in two routes from this intermediate to the postfusion structure. Our study reiterates the roles that cracking and disorder can play in functional molecular motions, in contrast to the downhill mechanical interpretations of the “spring-loaded” model proposed for the HA2 conformational transition.

The stability of RNA tertiary structures depends heavily on Mg2+. The Mg2+-RNA interaction free energy that stabilizes an RNA structure can be computed experimentally through fluorescence-based assays that measure Γ2+, the number of excess Mg2+ associated with an RNA molecule. Previous explicit-solvent simulations predict that the majority of excess Mg2+ ions interact closely and strongly with the RNA, unlike monovalent ions such as K+, suggesting that an explicit treatment of Mg2+ is important for capturing RNA dynamics. Here we present a reduced model that accurately reproduces the thermodynamics of Mg2+-RNA interactions. This model is able to characterize long-timescale RNA dynamics coupled to Mg2+ through the explicit representation of Mg2+ ions. KCl is described by Debye-Hückel screening and a Manning condensation parameter, which represents condensed K+ and models its competition with condensed Mg2+. The model contains one fitted parameter, the number of condensed K+ ions in the absence of Mg2+. Values of Γ2+ computed from molecular dynamics simulations using the model show excellent agreement with both experimental data on the adenine riboswitch and previous explicit-solvent simulations of the SAM-I riboswitch. This agreement confirms the thermodynamic accuracy of the model via the direct relation of Γ2+ to the Mg2+-RNA interaction free energy, and provides further support for the predictions from explicit-solvent calculations. This reduced model will be useful for future studies of the interplay between Mg2+ and RNA dynamics.

Biomolecular simulations provide a means for exploring the relationship between flexibility, energetics, structure, and function. With the availability of atomic models from X-ray crystallography and cryoelectron microscopy (cryo-EM), and rapid increases in computing capacity, it is now possible to apply molecular dynamics (MD) simulations to large biomolecular machines, and systematically partition the factors that contribute to function. A large biomolecular complex for which atomic models are available is the ribosome. In the cell, the ribosome reads messenger RNA (mRNA) in order to synthesize proteins. During this essential process, the ribosome undergoes a wide range of conformational rearrangements. One of the most poorly understood transitions is translocation: the process by which transfer RNA (tRNA) molecules move between binding sites inside of the ribosome. The first step of translocation is the adoption of a “hybrid” configuration by the tRNAs, which is accompanied by large-scale rotations in the ribosomal subunits. To illuminate the relationship between these rearrangements, we apply MD simulations using a multi-basin structure-based (SMOG) model, together with targeted molecular dynamics protocols. From 120 simulated transitions, we demonstrate the viability of a particular route during P/E hybrid-state formation, where there is asynchronous movement along rotation and tRNA coordinates. These simulations not only suggest an ordering of events, but they highlight atomic interactions that may influence the kinetics of hybrid-state formation. From these simulations, we also identify steric features (H74 and surrounding residues) encountered during the hybrid transition, and observe that flexibility of the single-stranded 3′-CCA tail is essential for it to reach the endpoint. Together, these simulations provide a set of structural and energetic signatures that suggest strategies for modulating the physical-chemical properties of protein synthesis by the ribosome.

Functional rearrangements in biomolecular assemblies result from diffusion across an underlying energy landscape. While bulk kinetic measurements rely on discrete state-like approximations to the energy landscape, single-molecule methods can project the free energy onto specific coordinates. With measures of the diffusion, one may establish a quantitative bridge between state-like kinetic measurements and the continuous energy landscape. We used an all-atom molecular dynamics simulation of the 70S ribosome (2.1 million atoms; 1.3 microseconds) to provide this bridge for specific conformational events associated with the process of tRNA translocation. Starting from a pre-translocation configuration, we identified sets of residues that collectively undergo rotary rearrangements implicated in ribosome function. Estimates of the diffusion coefficients along these collective coordinates for translocation were then used to interconvert between experimental rates and measures of the energy landscape. This analysis, in conjunction with previously reported experimental rates of translocation, provides an upper-bound estimate of the free-energy barriers associated with translocation. While this analysis was performed for a particular kinetic scheme of translocation, the quantitative framework is general and may be applied to energetic and kinetic descriptions that include any number of intermediates and transition states.

Protein kinases use ATP as a phosphoryl donor for the posttranslational modification of signaling targets. It is generally thought that the binding of this nucleotide induces conformational changes leading to closed, more compact forms of the kinase domain that ideally orient active-site residues for efficient catalysis. The kinase domain is oftentimes flanked by additional ligand binding domains that up- or down-regulate catalytic function. C-terminal Src kinase (Csk) is a multidomain tyrosine kinase that is up-regulated by N-terminal SH2 and SH3 domains. Although the X-ray structure of Csk suggests the enzyme is compact, X-ray scattering studies indicate that the enzyme possesses both compact and open conformational forms in solution. Here, we investigated whether interactions with the ATP analog AMP-PNP and ADP can shift the conformational ensemble of Csk in solution using a combination of small angle x-ray scattering and molecular dynamics simulations. We find that binding of AMP-PNP shifts the ensemble towards more extended rather than more compact conformations. Binding of ADP further shifts the ensemble towards extended conformations, including highly extended conformations not adopted by the apo protein, nor by the AMP-PNP bound protein. These ensembles indicate that any compaction of the kinase domain induced by nucleotide binding does not extend to the overall multi-domain architecture. Instead, assembly of an ATP-bound kinase domain generates further extended forms of Csk that may have relevance for kinase scaffolding and Src regulation in the cell.

Experiments demonstrate that Mg2+ is crucial for structure and function of RNA systems, yet the detailed molecular mechanism of Mg2+ action on RNA is not well understood. We investigate the interplay between RNA and Mg2+ at atomic resolution through ten 2-μs explicit solvent molecular dynamics simulations of the SAM-I riboswitch with varying ion concentrations. The structure, including three stemloops, is very stable on this time scale. Simulations reveal that outer-sphere coordinated Mg2+ ions fluctuate on the same time scale as the RNA, and that their dynamics couple. Locally, Mg2+ association affects RNA conformation through tertiary bridging interactions; globally, increasing Mg2+ concentration slows RNA fluctuations. Outer-sphere Mg2+ ions responsible for these effects account for 80% of Mg2+ in our simulations. These ions are transiently bound to the RNA, maintaining interactions, but shuttled from site to site. Outer-sphere Mg2+ are separated from the RNA by a single hydration shell, occupying a thin layer 3–5 Å from the RNA. Distribution functions reveal that outer-sphere Mg2+ are positioned by electronegative atoms, hydration layers, and a preference for the major groove. Diffusion analysis suggests transient outer-sphere Mg2+ dynamics are glassy. Since outer-sphere Mg2+ ions account for most of the Mg2+ in our simulations, these ions may change the paradigm of Mg2+–RNA interactions. Rather than a few inner-sphere ions anchoring the RNA structure surrounded by a continuum of diffuse ions, we observe a layer of outer-sphere coordinated Mg2+ that is transiently bound but strongly coupled to the RNA.

Cryo-elecron microscopy (cryo-EM) can provide important structural information of large macromolecular assemblies in different conformational states. Recent years have seen an increase in structures deposited in the Protein Data Bank (PDB) by fitting a high-resolution structure into its low-resolution cryo-EM map. A commonly used protocol for accommodating the conformational changes between the X-ray structure and the cryo-EM map is rigid body fitting of individual domains. With the emergence of different flexible fitting approaches, there is a need to compare and revise these different protocols for the fitting. We have applied three diverse automated flexible fitting approaches on a protein dataset for which rigid domain fitting (RDF) models have been deposited in the PDB. In general, a consensus is observed in the conformations, which indicates a convergence from these theoretically different approaches to the most probable solution corresponding to the cryo-EM map. However, the result shows that the convergence might not be observed for proteins with complex conformational changes or with missing densities in cryo-EM map. In contrast, RDF structures deposited in the PDB can represent conformations that not only differ from the consensus obtained by flexible fitting but also from X-ray crystallography. Thus, this study emphasizes that a “consensus” achieved by the use of several automated flexible fitting approaches can provide a higher level of confidence in the modeled configurations. Following this protocol not only increases the confidence level of fitting, but also highlights protein regions with uncertain fitting. Hence, this protocol can lead to better interpretation of cryo-EM data.

We employ all-atom structure-based models with a force field with multiple energetic basins for the C-terminal (residues 166–226) of the mammalian prion protein. One basin represents the known alpha-helical (αH) structure while the other represents the same residues in a left-handed beta-helical (LHBH) conformation. The LHBH structure has been proposed to help describe one class of in vitro grown fibrils, as well as possibly self-templating the conversion of normal cellular prion protein to the infectious form. Yet, it is unclear how the protein may make this global rearrangement. Our results demonstrate that the conformation changes are not strongly limited by large-scale geometry modification and that there may exist an overall preference for the LHBH conformation. Furthermore, our model presents novel intermediate trapping conformations with twisted LHBH structure.

Structure-based models (SBMs) are simplified models of the biomolecular dynamics that arise from funneled energy landscapes. We recently introduced an all-atom SBM that explicitly represents the atomic geometry of a biomolecule. While this initial study showed the robustness of the all-atom SBM Hamiltonian to changes in many of the energetic parameters, an important aspect, which has not been explored previously, is the definition of native interactions. In this study, we propose a general definition for generating atomically grained contact maps called “Shadow”. The Shadow algorithm initially considers all atoms within a cutoff distance and then, controlled by a screening parameter, discards the occluded contacts. We show that this choice of contact map is not only well behaved for protein folding, since it produces consistently cooperative folding behavior in SBMs but also desirable for exploring the dynamics of macromolecular assemblies since, it distributes energy similarly between RNAs and proteins despite their disparate internal packing. All-atom structure-based models employing Shadow contact maps provide a general framework for exploring the geometrical features of biomolecules, especially the connections between folding and function.

The dynamic nature of biomolecules leads to significant challenges when characterizing the structural properties associated with function. While X-ray crystallography and imaging techniques (such as cryo-electron microscopy) can reveal the structural details of stable molecular complexes, strategies must be developed to characterize configurations that exhibit only marginal stability (such as intermediates) or configurations that do not correspond to minima on the energy landscape (such as transition-state ensembles). Here, we present a methodology (MDfit) that utilizes molecular dynamics simulations to generate configurations of excited states that are consistent with available biophysical and biochemical measurements. To demonstrate the approach, we present a sequence of configurations that are suggested to be associated with transfer RNA (tRNA) movement through the ribosome (translocation). The models were constructed by combining information from X-ray crystallography, cryo-electron microscopy, and biochemical data. These models provide a structural framework for translocation that may be further investigated experimentally and theoretically to determine the precise energetic character of each configuration and the transition dynamics between them.

Regulation of protein function via cracking, or local unfolding and refolding of substructures, is becoming a widely recognized mechanism of functional control. Oftentimes, cracking events are localized to secondary and tertiary structure interactions between domains that control the optimal position for catalysis and/or the formation of protein complexes. Small changes in free energy associated with ligand binding, phosphorylation, etc., can tip the balance and provide a regulatory functional switch. However, understanding the factors controlling function in single-domain proteins is still a significant challenge to structural biologists. We investigated the functional landscape of a single-domain plant-type ferredoxin protein and the effect of a distal loop on the electron-transfer center. We find the global stability and structure are minimally perturbed with mutation, whereas the functional properties are altered. Specifically, truncating the L1,2 loop does not lead to large-scale changes in the structure, determined via X-ray crystallography. Further, the overall thermal stability of the protein is only marginally perturbed by the mutation. However, even though the mutation is distal to the iron–sulfur cluster (∼20 Å), it leads to a significant change in the redox potential of the iron–sulfur cluster (57 mV). Structure-based all-atom simulations indicate correlated dynamical changes between the surface-exposed loop and the iron–sulfur cluster-binding region. Our results suggest intrinsic communication channels within the ferredoxin fold, composed of many short-range interactions, lead to the propagation of long-range signals. Accordingly, protein interface interactions that involve L1,2 could potentially signal functional changes in distal regions, similar to what is observed in other allosteric systems.

The elongation cycle of protein synthesis involves the delivery of aminoacyl-transfer RNAs to the aminoacyl-tRNA-binding site (A site) of the ribosome, followed by peptide-bond formation and translocation of the tRNAs through the ribosome to reopen the A site1,2. The translocation reaction is catalysed by elongation factor G (EF-G) in a GTP-dependent manner3. Despite the availability of structures of various EF-G–ribosome complexes, the precise mechanism by which tRNAs move through the ribosome still remains unclear. Here we use multiparticle cryoelectron microscopy analysis to resolve two previously unseen subpopulations within Thermus thermophilus EF-G–ribosome complexes at subnanometre resolution, one of them with a partly translocated tRNA. Comparison of these substates reveals that translocation of tRNA on the 30S subunit parallels the swivelling of the 30S head and is coupled to unratcheting of the 30S body. Because the tRNA maintains contact with the peptidyl-tRNA-binding site (P site) on the 30S head and simultaneously establishes interaction with the exit site (E site) on the 30S platform, a novel intra-subunit ‘pe/E’ hybrid state is formed. This state is stabilized by domain IV of EF-G, which interacts with the swivelled 30S-head conformation. These findings provide direct structural and mechanistic insight into the ‘missing link’ in terms of tRNA intermediates involved in the universally conserved translocation process.

C-terminal Src kinase (Csk) phosphorylates and down-regulates the Src family tyrosine kinases (SFKs). Crystallographic studies of Csk found an unusual arrangement of the SH2 and SH3 regulatory domains about the kinase core, forming a compact structure. However, recent structural studies of mutant Csk in the presence of an inhibitor indicate that the enzyme accesses an expanded structure. To investigate whether wt-Csk may also access open conformations we applied small angle x-ray scattering (SAXS). We find wt-Csk frequently occupies an extended conformation where the regulatory domains are removed from the kinase core. In addition, all-atom structure-based simulations indicate Csk occupies two free energy basins. These basins correspond to ensembles of distinct global conformations of Csk: a compact structure and an extended structure. The transitions between these structures are entropically driven and accessible via thermal fluctuations that break local interactions. We further characterized the ensemble by generating theoretical scattering curves for mixed populations of conformations from both basins and compared the predicted scattering curves to the experimental profile. This population-combination analysis is more consistent with the experimental data than any rigid model. It suggests that Csk adopts a broad ensemble of conformations in solution, populating extended conformations not observed in the crystal structure that may play an important role in the regulation of Csk. The methodology developed here is broadly applicable to biological macromolecules and will provide useful information about what ensembles of conformations are consistent with the experimental data as well as the ubiquitous dynamic reversible assembly processes inherent in biology.

Using explicit-solvent simulations of the 70S ribosome, the barrier-crossing attempt frequency was calculated for aminoacyl-tRNA elbow-accommodation. In seven individual trajectories (200−300 ns, each, for an aggregate time of 2.1 μs), the relaxation time of tRNA structural fluctuations was determined to be ∼10 ns, and the barrier-crossing attempt frequency of tRNA accommodation is ∼1−10 μs−1. These calculations provide a quantitative relationship between the free-energy barrier and experimentally measured rates of accommodation, which demonstrate that the free-energy barrier of elbow-accommodation is less than 15 kBT, in vitro and in vivo.

We present a method for calculating the configurational-dependent diffusion coefficient of a globular protein as a function of the global folding process. Using a coarse-grained structure-based model, we determined the diffusion coefficient, in reaction coordinate space, as a function of the fraction of native contacts formed Q for the cold shock protein (TmCSP). We find nonmonotonic behavior for the diffusion coefficient, with high values for the folded and unfolded ensembles and a lower range of values in the transition state ensemble. We also characterized the folding landscape associated with an energetically frustrated variant of the model. We find that a low-level of frustration can actually stabilize the native ensemble and increase the associated diffusion coefficient. These findings can be understood from a mechanistic standpoint, in that the transition state ensemble has a more homogeneous structural content when frustration is present. Additionally, these findings are consistent with earlier calculations based on lattice models of protein folding and more recent single-molecule fluorescence measurements.

Molecular dynamics simulations with coarse-grained and/or simplified Hamiltonians are an effective means of capturing the functionally important long-time and large-length scale motions of proteins and RNAs. Structure-based Hamiltonians, simplified models developed from the energy landscape theory of protein folding, have become a standard tool for investigating biomolecular dynamics. SMOG@ctbp is an effort to simplify the use of structure-based models. The purpose of the web server is two fold. First, the web tool simplifies the process of implementing a well-characterized structure-based model on a state-of-the-art, open source, molecular dynamics package, GROMACS. Second, the tutorial-like format helps speed the learning curve of those unfamiliar with molecular dynamics. A web tool user is able to upload any multi-chain biomolecular system consisting of standard RNA, DNA and amino acids in PDB format and receive as output all files necessary to implement the model in GROMACS. Both C(alpha) and all-atom versions of the model are available. SMOG@ctbp resides at http://smog.ucsd.edu.

The ribosome is a massive ribonucleoprotein complex ( approximately 2.4 MDa) that utilizes large-scale structural fluctuations to produce unidirectional protein synthesis. Accommodation is a key conformational change during transfer RNA (tRNA) selection that allows movement of tRNA into the ribosome. Here, we address the structure-function relationship that governs accommodation using all-atom molecular simulations and single-molecule fluorescence resonance energy transfer (smFRET). Simulations that employ an all-atom, structure-based (G{\=o}-like) model illuminate the interplay between configurational entropy and effective enthalpy during the accommodation process. This delicate balance leads to spontaneous reversible accommodation attempts, which are corroborated by smFRET measurements. The dynamics about the endpoints of accommodation (the A/T and A/A conformations) obtained from structure-based simulations are validated by multiple 100-200 ns explicit-solvent simulations (3.2 million atoms for a cumulative 1.4 mus), and previous crystallographic analysis. We find that the configurational entropy of the 3'-CCA end of aminoacyl-tRNA resists accommodation, leading to a multistep accommodation process that encompasses a distribution of parallel pathways. The calculated mechanism is robust across simulation methods and protocols, suggesting that the structure of the accommodation corridor imposes stringent limitations on the accessible pathways. The identified mechanism and observed parallel pathways establish an atomistic framework for interpreting a large body of biochemical data and demonstrate that conformational changes during translation occur through a stochastic trial-and-error process, rather than in concerted lock-step motions.

Protein dynamics take place on many time and length scales. Coarse-grained structure-based equation image models utilize the funneled energy landscape theory of protein folding to provide an understanding of both long time and long length scale dynamics. All-atom empirical forcefields with explicit solvent can elucidate our understanding of short time dynamics with high energetic and structural resolution. Thus, structure-based models with atomic details included can be used to bridge our understanding between these two approaches. We report on the robustness of folding mechanisms in one such all-atom model. Results for the B domain of Protein A, the SH3 domain of C-Src Kinase, and Chymotrypsin Inhibitor 2 are reported. The interplay between side chain packing and backbone folding is explored. We also compare this model to a Cα structure-based model and an all-atom empirical forcefield. Key findings include: (1) backbone collapse is accompanied by partial side chain packing in a cooperative transition and residual side chain packing occurs gradually with decreasing temperature, (2) folding mechanisms are robust to variations of the energetic parameters, (3) protein folding free-energy barriers can be manipulated through parametric modifications, (4) the global folding mechanisms in a Cα model and the all-atom model agree, although differences can be attributed to energetic heterogeneity in the all-atom model, and (5) proline residues have significant effects on folding mechanisms, independent of isomerization effects. Because this structure-based model has atomic resolution, this work lays the foundation for future studies to probe the contributions of specific energetic factors on protein folding and function.

Riboswitches are noncoding RNAs that regulate gene expression in response to changing concentrations of specific metabolites. Switching activity is affected by the interplay between the aptamer domain and expression platform of the riboswitch. The aptamer domain binds the metabolite, locking the riboswitch in a ligand-bound conformation. In absence of the metabolite, the expression platform forms an alternative secondary structure by sequestering the 3' end of a nonlocal helix called P1. We use all-atom structure-based simulations to characterize the folding, unfolding, and metabolite binding of the aptamer domain of the S-adenosylmethionine-1 (SAM-1) riboswitch. Our results suggest that folding of the nonlocal helix (P1) is rate-limiting in aptamer domain formation. Interestingly, SAM assists folding of the P1 helix by reducing the associated free energy barrier. Because the 3' end of the P1 helix is sequestered by an alternative helix in the absence of metabolites, this observed ligand-control of P1 formation provides a mechanistic explanation of expression platform regulation.

Despite having remarkably similar three-dimensional structures and stabilities, IL-1β promotes signaling, whereas IL-1Ra inhibits it. Their energy landscapes are similar and have coevolved to facilitate competitive binding to the IL-1 receptor. Nevertheless, we find that IL-1Ra folds faster than IL-1β. A structural alignment of the proteins shows differences mainly in two loops, a β-bulge of IL-1β and a loop in IL-1Ra that interacts with residue K145 and connects β-strands 11 and 12. Bioassays indicate that inserting the β-bulge from IL-1β confers partial signaling capability onto a K145D mutant of IL-1Ra. Based on the alignment, mutational assays and our computational folding results, we hypothesize that functional regions are not central to the β-trefoil motif and cause slow folding. The IL-1β β-bulge facilitates activity and replacing it by the IL-1Ra β-turn results in a hybrid protein that folds faster than IL-1β. Inserting the β11–β12 connecting-loop, which aids inhibition, into either IL-1β or the hybrid protein slows folding. Thus, regions that aid function (either through activity or inhibition) can be inferred from folding traps via structural differences. Mapping functional properties onto the numerous folds determined in structural genomics efforts is an area of intense interest. Our studies provide a systematic approach to mapping the functional genomics of a fold family.

Large conformational changes in the LID and NMP domains of adenylate kinase (AKE) are known to be key to ligand binding and catalysis, yet the order of binding events and domain motion is not well understood. Combining the multiple available structures for AKE with the energy landscape theory for protein folding, a theoretical model was developed for allostery, order of binding events, and efficient catalysis. Coarse-grained models and nonlinear normal mode analysis were used to infer that intrinsic structural fluctuations dominate LID motion, whereas ligand-protein interactions and cracking ( local unfolding) are more important during NMP motion. In addition, LID-NMP domain interactions are indispensable for efficient catalysis. LID domain motion precedes NMP domain motion, during both opening and closing. These findings provide a mechanistic explanation for the observed 1: 1: 1 correspondence between LID domain closure, NMP domain closure, and substrate turnover. This catalytic cycle has likely evolved to reduce misligation, and thus inhibition, of AKE. The separation of allosteric motion into intrinsic structural fluctuations and ligand-induced contributions can be generalized to further our understanding of allosteric transitions in other proteins.

The SH2 domain of the C-terminal Src kinase [Csk] contains a unique disulfide bond that is not present in other known SH2 domains. To investigate whether this unusual disulfide bond serves a novel function, the effects of disulfide bond formation on catalytic activity of the full-length protein and on the structure of the SH2 domain were investigated. The kinase activity of full-length Csk decreases by an order of magnitude upon formation of the disulfide bond in the distal SH2 domain. NMR spectra of the fully oxidized and fully reduced SH2 domains exhibit similar chemical shift patterns and are indicative of similar, well-defined tertiary structures. The solvent-accessible disulfide bond in the isolated SH2 domain is highly stable and far from the small lobe of the kinase domain. However, reduction of this bond results in chemical shift changes of resonances that map to a cluster of residues that extend from the disulfide bond across the molecule to a surface that is in direct contact with the small lobe of the kinase domain in the intact molecule. Normal mode analyses and molecular dynamics calculations suggest that disulfide bond formation has large effects on residues within the kinase domain, most notably within the active-site cleft. Overall, the data indicate that reversible cross-linking of two cysteine residues in the SH2 domain greatly impacts catalytic function and interdomain communication in Csk.

Conformational heterogeneity in proteins is known to often be the key to their function. We present a coarse grained model to explore the interplay between protein structure, folding and function which is applicable to allosteric or non-allosteric proteins. We employ the model to study the detailed mechanism of the reversible conformational transition of Adenylate Kinase (AKE) between the open to the closed conformation, a reaction that is crucial to the protein's catalytic function. We directly observe high strain energy which appears to be correlated with localized unfolding during the functional transition. This work also demonstrates that competing native interactions from the open and closed form can account for the large conformational transitions in AKE. We further characterize the conformational transitions with a new measure ΦFunc, and demonstrate that local unfolding may be due, in part, to competing intra-protein interactions.

Conformational transitions play a central role in regulating protein function. Structure-based models with multiple basins have been used to understand the mechanisms governing these transitions. A model able to accommodate multiple folding basins is proposed to explore the mutational effects in the folding of the Rop-dimer (Rop). In experiments, Rop mutants show unusually strong increases in folding rates with marginal effects on stability. We investigate the possibility of two competing conformations representing a parallel (P) and the wild-type antiparallel (AP) arrangement of the monomers as possible native conformations. We observe occupation of both distinct states and characterize the transition pathways. An interesting observation from the simulations is that, for equivalent energetic bias, the transition to the P basin (non-wild-type basin) shows a lower free-energy barrier. Thus, the rapid kinetics observed in experiments appear to be the result of two competing states with different kinetic behavior, triggered upon mutation by the opening of a trapdoor arising from Rop's symmetric structure. The general concept of having competing conformations for the native state goes beyond explaining Rop's mutational behaviors and can be applied to other systems. A switch between competing native structures might be triggered by external factors to allow, for example, allosteric control or signaling.

We report molecular-dynamics simulations on a three-dimensional, two-component Lennard-Jones fluid. We used 125 000 particles (equal numbers of A and B) at density N/V=1.29 and 34 temperatures T covering 5 x 10(4) > or =T > or =0.56. The pair potential was 4epsilon[(sigma(ij)/r)(12)-(sigma(ij)/r)(6)] with sigma(AA)=1, sigma(AB)=11/12, and sigma(BB)=5/6. We computed specific and generic radial distribution functions g(ij)(r), and several density-momentum dynamic correlation functions whose static (t=0) parts vanish by symmetry. Evidence is presented that our systems were adequately annealed to eliminate remnant initial order and were adequately equilibrated at each temperature. Static spatial correlations in cold Lennard-Jones liquids have longer ranges than are often reported: g(r)-1 unequal to 0 is found out to r > or =7 at T=2 and out to r > or =10 at T=0.56. |g(r)-1| has an envelope function that simultaneously fits both crests and troughs of g(r). The envelope function implies a temperature-dependent static length scale l(1); over (0.56 < or =T< or =100), l(1) approximately T(-0.3), contrary to suggestions that g(r) is temperature independent as the glass is approached. The highest-melting-point crystal that we identified melts at T(m) approximately 1.08. In the fluid phase, we observe short-range noncrystalline local structure formation in g(r) as the glass is approached. Local structure is only found below a local structure melting temperature T(mc)=2.0. Local structure vanishes above T=2. Local structure becomes more pronounced as temperature is reduced. However, at all temperatures at which there is local structure in g(r), the local structure is confined to r < or =4. Within the region r < or =4, the amplitude of the local structure diminishes with distance r from the central atom approximately as exp(-r/l(2)), thereby defining a second distance scale in the fluid. l(2), while more difficult to measure, appears to scale with temperature as l(2) approximately T(-0.6); l(2) is not the same as l(1). The static and dynamic properties of the local structure match properties assigned by Kivelson's glass model [S. A. Kivelson et al., J. Chem. Phys. 101, 2391 (1994)] to that model's frustration-limited local clusters.

A systematic analysis of the mode structure of diffusive relaxations in 1 MDa hydroxypropylcellulose(HPC):water is presented. New methods and data include (1) use of integral spectral moments to characterize nonexponential decays, (2) spectra of small probes in concentrated HPC solutions, (3) temperature dependence of the mode structure, and (4) comparison of optical probe spectra and spectra of probe-free polymer solutions. We find that (1) probe and polymer relaxations are in general not the same; (2) the apparent viscometric crossover near c(t)approximate to6 g/l is echoed by probe behavior; (3) our HPC solutions have a characteristic dynamic length, namely the 50 nm length that matches the polymer's hydrodynamic radius; (4) characterization of spectral modes with their mean relaxation time affords simplifications relative to other characterizations; and (5) contrary to some expectations, Stokes-Einsteinian behavior (diffusion rate determined by the macroscopic viscosity) is not observed, even for large probes in relatively concentrated solutions. We propose that the viscometric and light scattering effects found in HPC solutions at elevated concentrations reflect the incipient formation of a generalized Kivelson [S. A. Kivelson , J. Chem. Phys. 101, 2391 (1994)] glass. (C) 2003 American Institute of Physics.

The ribosome is a prototypical assembly that can be used to establish general principles and techniques for the study of biological molecular machines. Motivated by the fact that the dynamics of every biomolecule is governed by an underlying energy landscape, there has been great interest to understand and quantify ribosome energetics. In the present review, we will focus on theoretical and computational strategies for probing the interactions that shape the energy landscape of the ribosome, with an emphasis on more recent studies of the elongation cycle. These efforts include the application of quantum mechanical methods for describing chemical kinetics, as well as classical descriptions to characterize slower (microsecond to millisecond) large-scale (10-100 Å) rearrangements, where motion is described in terms of diffusion across an energy landscape. Together, these studies provide broad insights into the factors that control a diverse range of dynamical processes in this assembly.

Protein synthesis in the cell is controlled by an elaborate sequence of conformational rearrangements in the ribosome. The composition of a ribosome varies by species, though they typically contain ~ 50-100 RNA and protein molecules. While advances in structural techniques have revolutionized our understanding of long-lived conformational states, a vast range of transiently visited configurations can not be directly observed. In these cases, computational/simulation methods can be used to understand the mechanical properties of the ribosome. Insights from these approaches can then help guide next-generation experimental measurements. In this short review, we discuss theoretical strategies that have been deployed to quantitatively describe the energetics of collective rearrangements in the ribosome. We focus on efforts to probe large-scale subunit rotation events, which involve the coordinated displacement of large numbers of atoms (tens of thousands). These investigations are revealing how the molecular structure of the ribosome encodes the mechanical properties that control large-scale dynamics.

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.

Protein folding was the first area of molecular biology for which a systematic statistical–mechanical analysis of dynamics was developed. As a result, folding is described as a process by which a disordered protein chain diffuses across a high-dimensional energy landscape and finally reaches the folded ensemble. Folding studies have produced countless theoretical concepts that are generalizable to other biomolecular processes, such as the functional dynamics of molecular assemblies. Common themes in folding and function include the dominant role of excluded volume, that a balance between energetic roughness and geometrical effects guides dynamics, and that folding/functional landscapes are relatively smooth. Here, we discuss how insights into protein folding have been applied to investigate the functional dynamics of biomolecular assemblies.

Over the last 40 years, the area of computational molecular biophysics has grown and developed to the point where simulations can now provide detailed mechanistic insights, suggest theoretical principles that underpin function, and provide frameworks for understanding and interpreting experimental measurements. The success of molecular simulations has been the result of the unrelenting development of novel theoretical models, exponential growth in computational resources, and advances in structural biology techniques. Through the continued refinement and application of diverse classes of models, general themes in biomolecular dynamics are beginning to surface. In particular, molecular simulations are highlighting the pervasive role that order-disorder events play in molecular biology. These dynamic modes of function are transforming our perspective on the role that entropy has in many large-scale biological processes.

We developed both analytical and simulation methods to explore the diffusion dynamics in protein folding. We found the diffusion as a quantitative measure of escape from local traps along the protein folding funnel with chosen reaction coordinates has two remarkable effects on kinetics. At a fixed coordinate, local escape time depends on the distribution of barriers around it, therefore the diffusion is often time distributed. On the other hand, the environments (local escape barriers) change along the coordinates, therefore diffusion is coordinate dependent. The effects of time-dependent diffusion on folding can lead to non-exponential kinetics and non-Poisson statistics of folding time distribution. The effects of coordinate dependent diffusion on folding can lead to the change of the kinetic barrier height as well as the position of the corresponding transition state and therefore modify the folding kinetic rates as well as the kinetic routes. Our analytical models for folding are based on a generalized Fokker-Planck diffusion equation with diffusion coefficient both dependent on coordinate and time. Our simulation for folding are based on structure-based folding models with a specific fast folding protein CspTm studied experimentally on diffusion and folding with single molecules. The coordinate and time-dependent diffusion are especially important to be considered in fast folding and single molecule studies, when there is a small or no free energy barrier and kinetics is controlled by diffusion while underlying statistics of kinetics become important. Including the coordinate dependence of diffusion will challenge the transition state theory of protein folding. The classical transition state theory will have to be modified to be consistent. The more detailed folding mechanistic studies involving phi value analysis based on the classical transition state theory will also have to be quantitatively modified. Complex kinetics with multiple time scales may allow us not only to explore the folding kinetics but also probe the local landscape and barrier height distribution with single-molecule experiments.

The dynamics of biological polymers, including proteins, RNA, and DNA, occur in very high-dimensional spaces. Many naturally-occurring polymers can navigate a vast phase space and rapidly find their lowest free energy (folded) state. Thus, although the search process is stochastic, it is not completely random. Instead, it is best described in terms of diffusion along a downhill free energy landscape. In this context, there have been many efforts to use simplified representations of the energetics, for which the potential energy is chosen to be a relatively smooth function with a global minima that corresponds to the folded state. That is, instead of including every type of physical interaction, the broad characteristics of the landscape are encoded in approximate energy functions. We describe a particular class of models, called structure-based models, that can be used to explore the diffusive properties of biomolecular folding and conformational rearrangements. These energy functions may be regarded as the "spherical cow" for modeling molecular biophysics. We discuss the physical principles underlying these models and provide an entry-level tutorial, which may be adapted for use in curricula for physics and non-physics majors.

This chapter focuses on the development and application of energy landscape principles to study biomolecular dynamics. Over the last several decades, our understanding of biomolecular folding has transitioned from traditional biochemical ideas to a statistical-mechanical approach to studying dynamics. These fundamental concepts, which were developed for protein folding, are now ready to be extended and applied to investigate emergent phenomena related to the functional dynamics of biomolecules.

This chapter addresses the structural and energetic properties of macromolecular assemblies. We first describe the chemical composition of biomolecules and then elaborate on the dynamics of two classes of well-studied complexes: ribosomes and viruses. The biological context of each system is first presented, which is followed by a discussion of physical considerations and questions that have been posed, as well as an overview of experimental and theoretical approaches available for their study.

Over the last 20 years, the application of structure-based (G{\={o}}-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.

Structural biology techniques such as crystallography and cryo-EM produce high resolution snap shots of the ribosome at various stages of protein synthesis. Single molecule studies yield time-resolved measurements with low spatial resolution. Currently, there is no experimental technique capable of producing time-resolved trajectories of the ribosome with atomistic resolution. Computer simulations are critical for furthering our understanding of the ribosome because they fill this gap. We review computational studies of the ribosome, including structural modeling, normal mode calculations, coarse grain simulations, and molecular dynamics simulations. Several success stories have occurred, where predictions based on computer simulations were verified experimentally.

Single-molecule fluorescence resonance energy transfer (smFRET) (reviewed in Munro et al., 2009) and cryo-electron microscopy (cryo-EM) investigations (Frank and Spahn, 2006; Spahn and Penczek, 2009; Fischer et al., 2010) of the translation apparatus reveal the ribosome's propensity to undergo large-scale fluctuations in conformation during function. Progress in these areas, building upon achievements in high-resolution structure determination of ribosomal subunits and functional complexes of the ribosome (Yusupov et al., 2001; Wekselman et al., 2009: Zhang et al., 2009; Gao et al., 2009; Demeshkina et al., 2010; Stanley et al., 2010), combined with an ever increasing breadth of computational modeling, simulation (Sanbonmatsu and Tung, 2007; Whitford et al., 2010a), and bioinformatics approaches (Roberts et al., 2008; Alexander et al., 2010), offers the potential to further broaden our understanding of the dynamic nature of the ribosome and translation components during protein synthesis. The large fluctuations observed by single-molecule studies, and the multitude of conformations reported by cryo-EM, make it clear that each ``state'' of the ribosome is in fact an ensemble of structurally similar configurations that are localized to a particular minimum on the free-energy landscape.

In this session, experts in molecular biophysics described the dynamics of biopolymers across a wide range of length and time scales. This discussion highlighted numerous techniques that span from highly detailed simulations, to coarse-grained theoretical models, as well as high-resolution structural analysis. The topics were equally diverse, where there was discussion of biological processes at small (individual atoms), intermediate (assemblies) and very large scales (phase separation).

Are the most dynamically flexible regions around the equilibrium structure of an enzyme the same regions involved in the transition state for rate limiting processes involved in the enzymatic reaction? Kern and-coworkers, Wolf-Watz et al., 2004; Henzler-Wildman et al., 2007a, 2007b) have shown that insights about functionally relevant motions that determine the overall enzyme turnover rate can be obtained by investigating conformational dynamics around the equilibrium basin of the enzyme adenylate kinase. An allosteric change in protein structure turns out to be the controlling process. In this commentary we compare results of this study with earlier predictions of the route by which the enzyme undergoes its conformational change. These predictions are based on the idea that the energy surface for the protein is determined by the end structures of the conformational change. A key issue is whether the protein moves by specific hinges or whether it "cracks" and accesses partially unfolded states during its structural change.

For decades, protein folding and functional dynamics have been described in terms of diffusive motion across an underlying energy landscape. With continued advances in structural biology and high-performance computing, the field is positioned to extend these approaches to large biomolecular assemblies. Through the application of energy landscape techniques to the ribosome, one may work towards establishing a comprehensive description of the dynamics, which will bridge theoretical concepts and experimental observations. In this perspective, we discuss a few of the challenges that will need to be addressed as we extend the application of landscape principles to the ribosome.