Diffuse Ions Coordinate Dynamics in a Ribonucleoprotein Assembly.

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.

Modeling of sustained spontaneous network oscillations of a sexually dimorphic brainstem nucleus: the role of potassium equilibrium potential.

Intrinsic oscillators in the central nervous system play a preeminent role in the neural control of rhythmic behaviors, yet little is known about how the ionic milieu regulates their output patterns. A powerful system to address this question is the pacemaker nucleus of the weakly electric fish Apteronotus leptorhynchus. A neural network comprised of an average of 87 pacemaker cells and 20 relay cells produces tonic oscillations, with higher frequencies in males compared to females. Previous empirical studies have suggested that this sexual dimorphism develops and is maintained through modulation of buffering of extracellular K+ by a massive meshwork of astrocytes enveloping the pacemaker and relay cells. Here, we constructed a model of this neural network that can generate sustained spontaneous oscillations. Sensitivity analysis revealed the potassium equilibrium potential, EK (as a proxy of extracellular K+ concentration), and corresponding somatic channel conductances as critical determinants of oscillation frequency and amplitude. In models of both the pacemaker nucleus network and isolated pacemaker and relay cells, the frequency increased almost linearly with EK, whereas the amplitude decreased nonlinearly with increasing EK. Our simulations predict that this frequency increase is largely caused by a shift in the minimum K+ conductance over one oscillation period. This minimum is close to zero at more negative EK, converging to the corresponding maximum at less negative EK. This brings the resting membrane potential closer to the threshold potential at which voltage-gated Na+ channels become active, increasing the excitability, and thus the frequency, of pacemaker and relay cells.

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.

Quantifying the Relationship between Single-Molecule Probes and Subunit Rotation in the Ribosome.

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.

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.

A steric gate controls P/E hybrid-state formation of tRNA on the ribosome.

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.

Dissecting the Energetics of Subunit Rotation in the Ribosome.

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.

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.