An all-atom structure-based potential for proteins: bridging minimal models with all-atom empirical forcefields

Behavior of Proteins under Pressure from Experimental Pressure-Dependent Structures

Structure-based models are coarse-grained representations of the interactions responsible for the protein folding process. In their simplest form, they use only the native contact map of a given protein to predict the main features of its folding process by computer simulation. Given their limitations, these models are frequently complemented with sequence-dependent contributions or additional information. Specifically, to analyze the effect of pressure on the folding/unfolding transition, special forms of these interaction potentials are employed, which may a priori determine the outcome of the simulations. In this work, we have tried to keep the original simplicity of structure-based models. Therefore, we have used folded structures that have been experimentally determined at different pressures to define native contact maps and thus interactions dependent on pressure. Despite the apparently tiny structural differences induced by pressure, our simulation results provide different thermodynamic and kinetic behaviors, which roughly correspond to experimental observations (when there is a possible comparison) of two proteins used as benchmarks, hen egg-white lysozyme and dihydrofolate reductase. Therefore, this work shows the feasibility of using experimental native structures at different pressures to analyze the global effects of this physical property on the protein folding process.

From System Modeling to System Analysis: The Impact of Resolution Level and Resolution Distribution in the Computer-Aided Investigation of Biomolecules

The ever increasing computer power, together with the improved accuracy of atomistic force fields, enables researchers to investigate biological systems at the molecular level with remarkable detail. However, the relevant length and time scales of many processes of interest are still hardly within reach even for state-of-the-art hardware, thus leaving important questions often unanswered. The computer-aided investigation of many biological physics problems thus largely benefits from the usage of coarse-grained models, that is, simplified representations of a molecule at a level of resolution that is lower than atomistic. A plethora of coarse-grained models have been developed, which differ most notably in their granularity; this latter aspect determines one of the crucial open issues in the field, i.e. the identification of an optimal degree of coarsening, which enables the greatest simplification at the expenses of the smallest information loss. In this review, we present the problem of coarse-grained modeling in biophysics from the viewpoint of system representation and information content. In particular, we discuss two distinct yet complementary aspects of protein modeling: on the one hand, the relationship between the resolution of a model and its capacity of accurately reproducing the properties of interest; on the other hand, the possibility of employing a lower resolution description of a detailed model to extract simple, useful, and intelligible information from the latter.

The dynamics of subunit rotation in a eukaryotic ribosome

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; ~1MDa) undergoes spontaneous and reversible rotations (~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.

Shedding Light on the Inhibitory Mechanisms of SARS-CoV-1/CoV-2 Spike Proteins by ACE2-Designed Peptides

Angiotensin-converting enzyme 2 (ACE2) is the host cellular receptor that locks onto the surface spike protein of the 2002 SARS coronavirus (SARS-CoV-1) and of the novel, highly transmissible and deadly 2019 SARS-CoV-2, responsible for the COVID-19 pandemic. One strategy to avoid the virus infection is to design peptides by extracting the human ACE2 peptidase domain α1-helix, which would bind to the coronavirus surface protein, preventing the virus entry into the host cells. The natural α1-helix peptide has a stronger affinity to SARS-CoV-2 than to SARS-CoV-1. Another peptide was designed by joining α1 with the second portion of ACE2 that is far in the peptidase sequence yet grafted in the spike protein interface with ACE2. Previous studies have shown that, among several α1-based peptides, the hybrid peptidic scaffold is the one with the highest/strongest affinity for SARS-CoV-1, which is comparable to the full-length ACE2 affinity. In this work, binding and folding dynamics of the natural and designed ACE2-based peptides were simulated by the well-known coarse-grained structure-based model, with the computed thermodynamic quantities correlating with the experimental binding affinity data. Furthermore, theoretical kinetic analysis of native contact formation revealed the distinction between these processes in the presence of the different binding partners SARS-CoV-1 and SARS-CoV-2 spike domains. Additionally, our results indicate the existence of a two-state folding mechanism for the designed peptide en route to bind to the spike proteins, in contrast to a downhill mechanism for the natural α1-helix peptides. The presented low-cost simulation protocol demonstrated its efficiency in evaluating binding affinities and identifying the mechanisms involved in the neutralization of spike-ACE2 interaction by designed peptides. Finally, the protocol can be used as a computer-based screening of more potent designed peptides by experimentalists searching for new therapeutics against COVID-19.

Stability and folding pathways of tetra-nucleosome from six-dimensional free energy surface

The three-dimensional organization of chromatin is expected to play critical roles in regulating genome functions. High-resolution characterization of its structure and dynamics could improve our understanding of gene regulation mechanisms but has remained challenging. Using a near-atomistic model that preserves the chemical specificity of protein-DNA interactions at residue and base-pair resolution, we studied the stability and folding pathways of a tetra-nucleosome. Dynamical simulations performed with an advanced sampling technique uncovered multiple pathways that connect open chromatin configurations with the zigzag crystal structure. Intermediate states along the simulated folding pathways resemble chromatin configurations reported from in situ experiments. We further determined a six-dimensional free energy surface as a function of the inter-nucleosome distances via a deep learning approach. The zigzag structure can indeed be seen as the global minimum of the surface. However, it is not favored by a significant amount relative to the partially unfolded, in situ configurations. Chemical perturbations such as histone H4 tail acetylation and thermal fluctuations can further tilt the energetic balance to stabilize intermediate states. Our study provides insight into the connection between various reported chromatin configurations and has implications on the in situ relevance of the 30 nm fiber.

The three-dimensional organization of chromatin plays critical roles in regulating genome function. Here the authors apply a near atomistic model to study the structure and dynamics of the chromatin folding unit - the tetra-nucleosome - to provide insight into how chromatin folds.

RNA Pore Translocation with Static and Periodic Forces: Effect of Secondary and Tertiary Elements on Process Activation and Duration

We use MD simulations to study the pore translocation properties of a pseudoknotted viral RNA. We consider the 71-nucleotide-long xrRNA from the Zika virus and establish how it responds when driven through a narrow pore by static or periodic forces applied to either of the two termini. Unlike the case of fluctuating homopolymers, the onset of translocation is significantly delayed with respect to the application of static driving forces. Because of the peculiar xrRNA architecture, activation times can differ by orders of magnitude at the two ends. Instead, translocation duration is much smaller than activation times and occurs on time scales comparable at the two ends. Periodic forces amplify significantly the differences at the two ends, for both activation times and translocation duration. Finally, we use a waiting-times analysis to examine the systematic slowing downs in xrRNA translocations and associate them to the hindrance of specific secondary and tertiary elements of xrRNA. The findings provide a useful reference to interpret and design future theoretical and experimental studies of RNA translocation.

The Molecular Mechanism of Domain Swapping of the C-Terminal Domain of the SARS-Coronavirus Main Protease

In three-dimensional domain swapping, two protein monomers exchange a part of their structures to form an intertwined homodimer, whose subunits resemble the monomer. Several viral proteins domain swap to increase their structural complexity or functional avidity. The main protease (M^pro) of the severe acute respiratory syndrome (SARS) coronavirus proteolyzes viral polyproteins and has been a target for anti-SARS drug design. Domain swapping in the α-helical C-terminal domain of M^pro (M^proC) locks M^pro into a hyperactive octameric form that is hypothesized to promote the early stages of viral replication. However, in the absence of a complete molecular understanding of the mechanism of domain swapping, investigations into the biological relevance of this octameric M^pro have stalled. Isolated M^proC can exist as a monomer or a domain-swapped dimer. Here, we investigate the mechanism of domain swapping of M^proC using coarse-grained structure-based models and molecular dynamics simulations. Our simulations recapitulate several experimental features of M^proC folding. Further, we find that a contact between a tryptophan in the M^proC domain-swapping hinge and an arginine elsewhere forms early during folding, modulates the folding route, and promotes domain swapping to the native structure. An examination of the sequence and the structure of the tryptophan containing hinge loop shows that it has a propensity to form multiple secondary structures and contacts, indicating that it could be stabilized into either the monomer- or dimer-promoting conformations by mutations or ligand binding. Finally, because all residues in the tryptophan loop are identical in SARS-CoV and SARS-CoV-2, mutations that modulate domain swapping may provide insights into the role of octameric M^pro in the early-stage viral replication of both viruses.

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.

The ribosome undergoes multiple large-scale structural rearrangements during protein elongation. Here the authors present an all-atom model of the ribosome to study the energetics of P/E hybrid-state formation, an early conformational rearrangement occurring during translocation.

Simulations of Phage T7 Capsid Expansion Reveal the Role of Molecular Sterics on Dynamics

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.

Quantitative comparison between sub-millisecond time resolution single-molecule FRET measurements and 10-second molecular simulations of a biosensor protein

Molecular Dynamics (MD) simulations seek to provide atomic-level insights into conformationally dynamic biological systems at experimentally relevant time resolutions, such as those afforded by single-molecule fluorescence measurements. However, limitations in the time scales of MD simulations and the time resolution of single-molecule measurements have challenged efforts to obtain overlapping temporal regimes required for close quantitative comparisons. Achieving such overlap has the potential to provide novel theories, hypotheses, and interpretations that can inform idealized experimental designs that maximize the detection of the desired reaction coordinate. Here, we report MD simulations at time scales overlapping with in vitro single-molecule Förster (fluorescence) resonance energy transfer (smFRET) measurements of the amino acid binding protein LIV-BP^SS at sub-millisecond resolution. Computationally efficient all-atom structure-based simulations, calibrated against explicit solvent simulations, were employed for sampling multiple cycles of LIV-BP^SS clamshell-like conformational changes on the time scale of seconds, examining the relationship between these events and those observed by smFRET. The MD simulations agree with the smFRET measurements and provide valuable information on local dynamics of fluorophores at their sites of attachment on LIV-BP^SS and the correlations between fluorophore motions and large-scale conformational changes between LIV-BP^SS domains. We further utilize the MD simulations to inform the interpretation of smFRET data, including Förster radius (R₀) and fluorophore orientation factor (κ²) determinations. The approach we describe can be readily extended to distinct biochemical systems, allowing for the interpretation of any FRET system conjugated to protein or ribonucleoprotein complexes, including those with more conformational processes, as well as those implementing multi-color smFRET.

Förster (fluorescence) resonance energy transfer (FRET) has been used extensively by biophysicists as a molecular-scale ruler that yields fundamental structural and kinetic insights into transient processes including complex formation and conformational rearrangements required for biological function. FRET techniques require the identification of informative fluorophore labeling sites, spaced at defined distances to inform on a reaction coordinate of interest and consideration of noise sources that have the potential to obscure quantitative interpretations. Here, we describe an approach to leverage advancements in computationally efficient all-atom structure-based molecular dynamics simulations in which structural dynamics observed via FRET can be interpreted in full atomistic detail on commensurate time scales. We demonstrate the potential of this approach using a model FRET system, the amino acid binding protein LIV-BP^SS conjugated to self-healing organic fluorophores. LIV-BP^SS exhibits large scale, sub-millisecond clamshell-like conformational changes between open and closed conformations associated with ligand unbinding and binding, respectively. Our findings inform on the molecular basis of the dynamics observed by smFRET and on strategies to optimize fluorophore labeling sites, the manner of fluorophore attachment, and fluorophore composition.

Molecular mechanisms underlying the extreme mechanical anisotropy of the flaviviral exoribonuclease-resistant RNAs (xrRNAs)

Mechanical anisotropy is an essential property for many biomolecules to assume their structures, functions and applications, however, the mechanisms for their direction-dependent mechanical responses remain elusive. Herein, by using a single-molecule nanopore sensing technique, we explore the mechanisms of directional mechanical stability of the xrRNA1 RNA from ZIKA virus (ZIKV), which forms a complex ring-like architecture. We reveal extreme mechanical anisotropy in ZIKV xrRNA1 which highly depends on Mg²⁺ and the key tertiary interactions. The absence of Mg²⁺ and disruption of the key tertiary interactions strongly affect the structural integrity and attenuate mechanical anisotropy. The significance of ring structures in RNA mechanical anisotropy is further supported by steered molecular dynamics simulations in combination with force distribution analysis. We anticipate the ring structures can be used as key elements to build RNA-based nanostructures with controllable mechanical anisotropy for biomaterial and biomedical applications.

Intrinsically Disordered Regions of the DNA-Binding Domain of Human FoxP1 Facilitate Domain Swapping

Forkhead box P (FoxP) proteins are unique transcription factors that spatiotemporally regulate gene expression by tethering two chromosome loci together via functional domain-swapped dimers formed through their DNA-binding domains. Further, the differential kinetics on this dimerization mechanism underlie an intricate gene regulation network at physiological conditions. Nonetheless, poor understanding of the structural dynamics and steps of the association process impedes to link the functional domain swapping to human-associated diseases. Here, we have characterized the DNA-binding domain of human FoxP1 by integrating single-molecule Förster resonance energy transfer and hydrogen-deuterium exchange mass spectrometry data with molecular dynamics simulations. Our results confirm the formation of a previously postulated domain-swapped (DS) FoxP1 dimer in solution and reveal the presence of highly populated, heterogeneous, and locally disordered dimeric intermediates along the dimer dissociation pathway. The unique features of FoxP1 provide a glimpse of how intrinsically disordered regions can facilitate domain swapping oligomerization and other tightly regulated association mechanisms relevant in biological processes.

Structure dictates the mechanism of ligand recognition in the histidine and maltose binding proteins

Two mechanisms, induced fit (IF) and conformational selection (CS), have been proposed to explain ligand recognition coupled conformational changes. The histidine binding protein (HisJ) adopts the CS mechanism, in which a pre-equilibrium is established between the open and the closed states with the ligand binding to the closed state. Despite being structurally similar to HisJ, the maltose binding protein (MBP) adopts the IF mechanism, in which the ligand binds the open state and induces a transition to the closed state. To understand the molecular determinants of this difference, we performed molecular dynamics (MD) simulations of coarse-grained dual structure based models. We find that intra-protein contacts unique to the closed state are sufficient to promote the conformational transition in HisJ, indicating a CS-like mechanism. In contrast, additional ligand-mimicking contacts are required to “induce” the conformational transition in MBP suggesting an IF-like mechanism. In agreement with experiments, destabilizing modifications to two structural features, the spine helix (SH) and the balancing interface (BI), present in MBP but absent in HisJ, reduce the need for ligand-mimicking contacts indicating that SH and BI act as structural restraints that keep MBP in the open state. We introduce an SH like element into HisJ and observe that this can impede the conformational transition increasing the importance of ligand-mimicking contacts. Similarly, simultaneous mutations to BI and SH in MBP reduce the barrier to conformational transitions significantly and promote a CS-like mechanism. Together, our results show that structural restraints present in the protein structure can determine the mechanism of conformational transitions and even simple models that correctly capture such structural features can predict their positions. MD simulations of such models can thus be used, in conjunction with mutational experiments, to regulate protein ligand interactions, and modulate ligand binding affinities.

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MBP operates by induced fit, HisJ by the conformational selection mechanism.

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Dual structure based models (dSBMs) encode two structures of a protein.

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MD simulations of dSBMs can identify the mechanism of conformational transitions.

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Locks, absent in HisJ, hold MBP open with ligand contacts required for closing.

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Binding mechanisms can be modified by altering such structural locks.

Directional translocation resistance of Zika xrRNA

xrRNAs from flaviviruses survive in host cells because of their exceptional dichotomic response to the unfolding action of different enzymes. They can be unwound, and hence copied, by replicases, and yet can resist degradation by exonucleases. How the same stretch of xrRNA can encode such diverse responses is an open question. Here, by using atomistic models and translocation simulations, we uncover an elaborate and directional mechanism for how stress propagates when the two xrRNA ends, [Formula: see text] and [Formula: see text], are driven through a pore. Pulling the [Formula: see text] end, as done by replicases, elicits a progressive unfolding; pulling the [Formula: see text] end, as done by exonucleases, triggers a counterintuitive molecular tightening. Thus, in what appears to be a remarkable instance of intra-molecular tensegrity, the very pulling of the [Formula: see text] end is what boosts resistance to translocation and consequently to degradation. The uncovered mechanistic principle might be co-opted to design molecular meta-materials.

The accuracy of force fields on the simulation of intrinsically disordered proteins: A benchmark test on the human p53 tumor suppressor

Intrinsically disordered proteins (IDPs) are a class of proteins without stable three-dimensional structures under physiological conditions. IDPs exhibit high dynamic nature and could be described by structural ensembles. As one of the most widely used tools, molecular dynamics (MD) simulation could provide the atomic descriptions of the structural ensemble of IDPs. However, the accuracy of the MD simulation largely depends on the accuracy of the force field. In this paper, we compared the structural ensembles of the activation domain 1 (AD1) in p53 tumor suppressor obtained from the widely used force fields, AMBER99SB-ILDN, CHARMM27, CHARMM36m with different water models. The results show that CHARMM36m generates more extended conformations than other force fields, while CHARMM27 prefers to sample the [Formula: see text]-helical structure. Moreover, the chemical shifts obtained by CHARMM36m are the closest to the experimental measurements. These results indicate that the CHARMM36m force field performs best in characterizing the structure properties of p53 AD1. Water models are also critical to describe the structural ensemble of IDPs. TIP4P water model can obtain more extended conformations and produce more local helical conformations than the TIP3P model in our simulation. In addition, we also compare the chemical shifts predicted by different chemical shift predicting programs with experimental measurements, the results show that SHIFTX2 obtains the best performance in the chemical shifts prediction.

Elongation Factor Tu Switch I Element is a Gate for Aminoacyl-tRNA Selection

Selection of correct aminoacyl (aa)-tRNA at the ribosomal A site is fundamental to maintaining translational fidelity. Aa-tRNA selection is a multistep process facilitated by the guanosine triphosphatase elongation factor (EF)-Tu. EF-Tu delivers aa-tRNA to the ribosomal A site and participates in tRNA selection. The structural mechanism of how EF-Tu is involved in proofreading remains to be fully resolved. Here, we provide evidence that switch I of EF-Tu facilitates EF-Tu's involvement during aa-tRNA selection. Using structure-based and explicit solvent molecular dynamics simulations based on recent cryo-electron microscopy reconstructions, we studied the conformational change of EF-Tu from the guanosine triphosphate to guanine diphosphate conformation during aa-tRNA accommodation. Switch I of EF-Tu rapidly converts from an α-helix into a β-hairpin and moves to interact with the acceptor stem of the aa-tRNA. In doing so, switch I gates the movement of the aa-tRNA during accommodation through steric interactions with the acceptor stem. Pharmacological inhibition of the aa-tRNA accommodation pathway prevents the proper positioning of switch I with the aa-tRNA acceptor stem, suggesting that the observed interactions are specific for cognate aa-tRNA substrates, and thus capable of contributing to the fidelity mechanism.

Probing remote residues important for catalysis in Escherichia coli ornithine transcarbamoylase

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 k_cat/K_M 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.

How Nanopore Translocation Experiments Can Measure RNA Unfolding

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.

Evolutionary Switches Structural Transitions via Coarse-Grained Models

Transitions between different conformational states are ubiquitous in proteins. A vast class of conformation-changing proteins includes evolutionary switches, which vary their conformation as an effect of few mutations or weak environmental variations. However, modeling those processes is extremely difficult due to the need of efficiently exploring a vast conformational space to look for the actual transition path. In this study, we report a strategy that simplifies this task attacking the complexity on several sides. We first apply a minimalist coarse-grained model to the protein, based on an empirical force field with a partial structural bias toward one or both the reference structures. We then explore the transition paths by means of stochastic molecular dynamics and select representative structures by means of a principal path-based clustering algorithm. We finally compare this trajectory with that produced by independent methods adopting a morphing-oriented approach. Our analysis indicates that the minimalist model returns trajectories capable of exploring intermediate states with physical meaning, retaining a very low computational cost, which can allow systematic and extensive exploration of the multistable proteins transition pathways.

The Role of Electrostatics and Folding Kinetics on the Thermostability of Homologous Cold Shock Proteins

Understanding which aspects contribute to the thermostability of proteins is a challenge that has persisted for decades, and it is of great relevance for protein engineering. Several types of interactions can influence the thermostability of a protein. Among them, the electrostatic interactions have been a target of particular attention. Aiming to explore how this type of interaction can affect protein thermostability, this paper investigated four homologous cold shock proteins from psychrophilic, mesophilic, thermophilic, and hyperthermophilic organisms using a set of theoretical methodologies. It is well-known that electrostatics as well as hydrophobicity are key-elements for the stabilization of these proteins. Therefore, both interactions were initially analyzed in the native structure of each protein. Electrostatic interactions present in the native structures were calculated with the Tanford-Kirkwood model with solvent accessibility, and the amount of hydrophobic surface area buried upon folding was estimated by measuring both folded and extended structures. On the basis of Energy Landscape Theory, the local frustration and the simplified alpha-carbon structure-based model were modeled with a Debye-Hückel potential to take into account the electrostatics and the effects of an implicit solvent. Thermodynamic data for the structure-based model simulations were collected and analyzed using the Weighted Histogram Analysis and Stochastic Diffusion methods. Kinetic quantities including folding times, transition path times, folding routes, and Φ values were also obtained. As a result, we found that the methods are able to qualitatively infer that electrostatic interactions play an important role on the stabilization of the most stable thermophilic cold shock proteins, showing agreement with the experimental data.

Gō model revisited

This review discusses Gō models broadly used in biomolecular simulations. I start with a brief description of the original lattice model study by Nobuhiro Gō. Then, the theory of protein folding behind Gō model, free energy approaches, and off-lattice Gō models are reviewed. I also mention a stringent test for the assumption in Gō models given from all-atom molecular dynamics simulations. Subsequently, I move to application of Gō models to protein dynamical functions. Various extension of Gō models is also reviewed. Finally, some publicly available tools to use Gō models are listed.

Computational methods in the study of self-entangled proteins: a critical appraisal

The existence of self-entangled proteins, the native structure of which features a complex topology, unveils puzzling, and thus fascinating, aspects of protein biology and evolution. The discovery that a polypeptide chain can encode the capability to self-entangle in an efficient and reproducible way during folding, has raised many questions, regarding the possible function of these knots, their conservation along evolution, and their role in the folding paradigm. Understanding the function and origin of these entanglements would lead to deep implications in protein science, and this has stimulated the scientific community to investigate self-entangled proteins for decades by now. In this endeavour, advanced experimental techniques are more and more supported by computational approaches, that can provide theoretical guidelines for the interpretation of experimental results, and for the effective design of new experiments. In this review we provide an introduction to the computational study of self-entangled proteins, focusing in particular on the methodological developments related to this research field. A comprehensive collection of techniques is gathered, ranging from knot theory algorithms, that allow detection and classification of protein topology, to Monte Carlo or molecular dynamics strategies, that constitute crucial instruments for investigating thermodynamics and kinetics of this class of proteins.

Diffusion of tRNA inside the ribosome is position-dependent

In recent years, there has been a growing interest to quantify the energy landscape that governs ribosome dynamics. However, in order to quantitatively integrate theoretical predictions and experimental measurements, it is essential that one has a detailed understanding of the associated diffusive properties. Here, all-atom explicit-solvent simulations (50 μs of aggregate sampling) predict that the diffusion coefficient of a tRNA molecule will depend on its position within the ribosome. Specifically, during aa-tRNA accommodation (i.e., the process by which tRNA enters the ribosome), the apparent diffusion coefficient decreases by approximately an order of magnitude. By comparing these to values obtained with an energetically "smooth" model, we show that the observed nonuniform behavior likely arises from electrostatic and solvation interactions between the tRNA and ribosome. These calculations also reveal the hierarchical character of ribosomal energetics, where steric interactions induce a large-scale free-energy barrier, and short-scale roughness determines the rate of diffusive movement across the landscape.

Supercoiling in a Protein Increases its Stability

The supercoiling motif is the most complex type of nontrivial topology found in proteins with at least one disulfide bond and, to the best of our knowledge, it has not been studied before. We show that a protein from extremophilic species with such a motif can fold; however, the supercoiling changes a smooth landscape observed in reduced conditions into a two-state folding process in the oxidative conditions, with a deep intermediate state. The protein takes advantage of the hairpinlike motif to overcome the topological barrier and thus to supercoil. We find that the depth of the supercoiling motif, i.e., the length of the threaded terminus, has a crucial impact on the folding rates of the studied protein. We show that fluctuations of the minimal surface area can be used to measure local stability, and we find that supercoiling introduces stability into the protein. We suggest that the supercoiling motif enables the studied protein to live in physically extreme conditions, which are detrimental to most life on Earth.

Folding and Dynamics Are Strongly pH-Dependent in a Psychrophile Frataxin

Protein dynamics, folding, and thermodynamics represent a central aspect of biophysical chemistry. pH, temperature, and denaturant perturbations inform our understanding of diverse contributors to stability and rates. In this work, we performed a thermodynamic analysis using a combined experimental and computational approach to gain insights into the role of electrostatics in the folding reaction of a psychrophile frataxin variant from Psychromonas ingrahamii. This folding reaction is strongly modulated by pH with a single, narrow, and well-defined transition state with ∼80% compactness, ∼70% electrostatic interactions, and ∼60% hydration shell compared to the native state (αD = 0.82, αH = 0.67, and αΔCp = 0.59). Our results are best explained by a two-proton/two-state model with very different pKa values of the native and denatured states (∼5.5 and ∼8.0, respectively). As a consequence, the stability strongly increases from pH 8.0 to 6.0 (|ΔΔG°| = 5.2 kcal mol-1), mainly because of a decrease in the TΔS°. Variation of ΔH° and ΔS° at pH below 7.0 is dominated by a change in ΔHf⧧ and ΔSf⧧, while at pH above 7.0, it is governed by ΔHu⧧ and ΔSu⧧. Molecular dynamics simulations showed that these pH modulations could be explained by the fluctuations of two regions, rich in electrostatic contacts, whose dynamics are pH-dependent and motions are strongly correlated. Results presented herein contribute to the understanding of the stability and dynamics of this frataxin variant, pointing to an intrinsic feature of the family topology to support different folding mechanisms.

Recent Progress towards Chemically-Specific Coarse-Grained Simulation Models with Consistent Dynamical Properties

Coarse-grained (CG) models can provide computationally efficient and conceptually simple characterizations of soft matter systems. While generic models probe the underlying physics governing an entire family of free-energy landscapes, bottom-up CG models are systematically constructed from a higher-resolution model to retain a high level of chemical specificity. The removal of degrees of freedom from the system modifies the relationship between the relative time scales of distinct dynamical processes through both a loss of friction and a “smoothing” of the free-energy landscape. While these effects typically result in faster dynamics, decreasing the computational expense of the model, they also obscure the connection to the true dynamics of the system. The lack of consistent dynamics is a serious limitation for CG models, which not only prevents quantitatively accurate predictions of dynamical observables but can also lead to qualitatively incorrect descriptions of the characteristic dynamical processes. With many methods available for optimizing the structural and thermodynamic properties of chemically-specific CG models, recent years have seen a stark increase in investigations addressing the accurate description of dynamical properties generated from CG simulations. In this review, we present an overview of these efforts, ranging from bottom-up parameterizations of generalized Langevin equations to refinements of the CG force field based on a Markov state modeling framework. We aim to make connections between seemingly disparate approaches, while laying out some of the major challenges as well as potential directions for future efforts.

Searching the Optimal Folding Routes of a Complex Lasso Protein

Understanding how polypeptides can efficiently and reproducibly attain a self-entangled conformation is a compelling biophysical challenge that might shed new light on our general knowledge of protein folding. Complex lassos, namely self-entangled protein structures characterized by a covalent loop sealed by a cysteine bridge, represent an ideal test system in the framework of entangled folding. Indeed, because cysteine bridges form in oxidizing conditions, they can be used as on/off switches of the structure topology to investigate the role played by the backbone entanglement in the process. In this work, we have used molecular dynamics to simulate the folding of a complex lasso glycoprotein, granulocyte-macrophage colony-stimulating factor, modeling both reducing and oxidizing conditions. Together with a well-established Gō-like description, we have employed the elastic folder model, a coarse-grained, minimalistic representation of the polypeptide chain driven by a structure-based angular potential. The purpose of this study is to assess the kinetically optimal pathways in relation to the formation of the native topology. To this end, we have implemented an evolutionary strategy that tunes the elastic folder model potentials to maximize the folding probability within the early stages of the dynamics. The resulting protein model is capable of folding with high success rate, avoiding the kinetic traps that hamper the efficient folding in the other tested models. Employing specifically designed topological descriptors, we could observe that the selected folding routes avoid the topological bottleneck by locking the cysteine bridge after the topology is formed. These results provide valuable insights on the selection of mechanisms in self-entangled protein folding while, at the same time, the proposed methodology can complement the usage of established minimalistic models and draw useful guidelines for more detailed simulations.

A two-dimensional replica-exchange molecular dynamics method for simulating RNA folding using sparse experimental restraints

We present a 2D replica exchange protocol incorporating secondary structure information to dramatically improve 3D RNA folding using molecular dynamics simulations. We show that incorporating base-pairing restraints into all-atom, explicit solvent simulations enables the accurate recapitulation of the global tertiary fold for 4 representative RNAs ranging in length from 24 to 68 nt. This method can potentially utilize base-pairing information from a wide variety of experimental inputs to predict complex RNA tertiary folds including pseudoknots, multi-loop junctions, and non-canonical interactions.

Go-Kit: A Tool To Enable Energy Landscape Exploration of Proteins

Coarse-grained Go̅-like models, based on the principle of minimal frustration, provide valuable insight into fundamental questions in the field of protein folding and dynamics. In conjunction with commonly used molecular dynamics (MD) simulations, energy landscape exploration methods like discrete path sampling (DPS) with Go̅-like models can provide quantitative details of the thermodynamics and kinetics of proteins. Here we present Go-kit, a software that facilitates the setup of MD and DPS simulations of several flavors of Go̅-like models. Go-kit is designed for use with MD (GROMACS) and DPS (PATHSAMPLE) simulation engines that are open source. The Go-kit code is written in python2.7 and is also open source. A case study for the ribosomal protein S6 is discussed to illustrate the utility of the software, which is available at https://github.com/gokit1/gokit .

Rapid interpretation of small-angle X-ray scattering data

The fundamental aim of structural analyses in biophysics is to reveal a mutual relation between a molecule’s dynamic structure and its physiological function. Small-angle X-ray scattering (SAXS) is an experimental technique for structural characterization of macromolecules in solution and enables time-resolved analysis of conformational changes under physiological conditions. As such experiments measure spatially averaged low-resolution scattering intensities only, the sparse information obtained is not sufficient to uniquely reconstruct a three-dimensional atomistic model. Here, we integrate the information from SAXS into molecular dynamics simulations using computationally efficient native structure-based models. Dynamically fitting an initial structure towards a scattering intensity, such simulations produce atomistic models in agreement with the target data. In this way, SAXS data can be rapidly interpreted while retaining physico-chemical knowledge and sampling power of the underlying force field. We demonstrate our method’s performance using the example of three protein systems. Simulations are faster than full molecular dynamics approaches by more than two orders of magnitude and consistently achieve comparable accuracy. Computational demands are reduced sufficiently to run the simulations on commodity desktop computers instead of high-performance computing systems. These results underline that scattering-guided structure-based simulations provide a suitable framework for rapid early-stage refinement of structures towards SAXS data with particular focus on minimal computational resources and time.

Proteins are the molecular nanomachines in biological cells and thus vital to any known form of life. From the evolutionary perspective, viable protein structure emerges on the basis of a ‘form-follows-function’ principle. A protein’s designated function is inextricably linked to dynamic conformational changes, which can be observed by small-angle X-ray scattering. Intensities from SAXS contain low-resolution information on the protein’s shape at different steps of its functional cycle. We are interested in directly getting an atomistic model of this encoded structure. One powerful approach is to include the experimental data into computational simulations of the protein’s function-related physical motions. We combine scattering intensities with coarse-grained native structure-based models. These models are computationally highly efficient yet describe the system’s dynamics realistically. Here, we present our method for rapid interpretation of scattering intensities from SAXS to derive structural models, using minimal computational resources and time.

Structure-Based Model of RNA Pseudoknot Captures Magnesium-Dependent Folding Thermodynamics

We develop a simple, coarse-grained approach for simulating the folding of the Beet Western Yellow Virus (BWYV) pseudoknot toward the goal of creating a transferable model that can be used to study other small RNA molecules. This approach combines a structure-based model (SBM) of RNA with an electrostatic scheme that has previously been shown to correctly reproduce ionic condensation in the native basin. Mg²⁺ ions are represented explicitly, directly incorporating ion-ion correlations into the system, and K⁺ is represented implicitly, through the mean-field generalized Manning counterion condensation theory. Combining the electrostatic scheme with a SBM enables the electrostatic scheme to be tested beyond the native basin. We calibrate the SBM to reproduce experimental BWYV unfolding data by eliminating overstabilizing backbone interactions from the molecular contact map and by strengthening base pairing and stacking contacts relative to other native contacts, consistent with the experimental observation that relative helical stabilities are central determinants of the RNA unfolding sequence. We find that this approach quantitatively captures the Mg²⁺ dependence of the folding temperature and generates intermediate states that better approximate those revealed by experiment. Finally, we examine how our model captures Mg²⁺ condensation about the BWYV pseudoknot and a U-tail variant, for which the nine 3' end nucleotides are replaced with uracils, and find our results to be consistent with experimental condensation measurements. This approach can be easily transferred to other RNA molecules by eliminating and strengthening the same classes of contacts in the SBM and including generalized Manning counterion condensation.

The key role of electrostatic interactions in the induced folding in RNA recognition by DCL1-A

The intrinsically disordered protein domain DCL1-A is the first report of a complete double stranded RNA binding domain folding upon binding. DCL1-A recognizes the dsRNA by acquiring a well-folded structure after engagement with its interaction partner. Despite the structural characterization of the interaction complex underlying the recognition of dsRNA has been established, the dynamics of disorder-to-order transitions in the binding process remains elusive. Here we have developed a coarse-grained structure-based model with consideration of electrostatic interactions to explore the mechanism of the coupled folding and binding. Our approach led to remarkable agreements with both experimental and theoretical results. We quantified the global binding-folding landscape, which indicates a synergistic binding induced folding mechanism. We further investigated the effect of electrostatic interactions in this coupled folding and binding process. It reveals that non-native electrostatic interactions dominate the initial stage of the recognition. Our results help improve our understanding of the induced folding of the IDP DCL1-A upon binding to dsRNA. Such methods developed here can be applied for further explorations of the dynamics of coupled folding and binding systems.

A Dynamic Hydrophobic Core and Surface Salt Bridges Thermostabilize a Designed Three-Helix Bundle

Thermostable proteins are advantageous in industrial applications, as pharmaceuticals or biosensors, and as templates for directed evolution. As protein-design methodologies improve, bioengineers are able to design proteins to perform a desired function. Although many rationally designed proteins end up being thermostable, how to intentionally design de novo, thermostable proteins is less clear. UVF is a de novo-designed protein based on the backbone structure of the Engrailed homeodomain (EnHD) and is highly thermostable (T_m > 99°C vs. 52°C for EnHD). Although most proteins generally have polar amino acids on their surfaces and hydrophobic amino acids buried in their cores, protein engineers followed this rule exactly when designing UVF. To investigate the contributions of the fully hydrophobic core versus the fully polar surface to UVF’s thermostability, we built two hybrid, chimeric proteins combining the sets of buried and surface residues from UVF and EnHD. Here, we determined a structural, dynamic, and thermodynamic explanation for UVF’s thermostability by performing 4 μs of all-atom, explicit-solvent molecular dynamics simulations at 25 and 100°C, Tanford-Kirkwood solvent accessibility Monte Carlo electrostatic calculations, and a thermodynamic analysis of 40 temperature runs by the weighted-histogram analysis method of heavy-atom, structure-based models of UVF, EnHD, and both chimeric proteins. Our models showed that UVF was highly dynamic because of its fully hydrophobic core, leading to a smaller loss of entropy upon folding. The charged residues on its surface made favorable electrostatic interactions that contributed enthalpically to its thermostability. In the chimeric proteins, both the hydrophobic core and charged surface independently imparted thermostability.

Nonnative contact effects in protein folding

The folding simulations of three ββα-motifs and β-barrel structured proteins (NTL9, NuG2b, and CspA) were performed to determine the important roles of native and nonnative contacts in protein folding.

Using SMOG 2 to Simulate Complex Biomolecular Assemblies

Over the last 20 years, the application of structure-based (Gō-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.

Deciphering the structure of the condensin protein complex

Protein assemblies consisting of structural maintenance of chromosomes (SMC) and kleisin subunits are essential for the process of chromosome segregation across all domains of life. Prokaryotic condensin belonging to this class of protein complexes is composed of a homodimer of SMC that associates with a kleisin protein subunit called ScpA. While limited structural data exist for the proteins that comprise the (SMC)-kleisin complex, the complete structure of the entire complex remains unknown. Using an integrative approach combining both crystallographic data and coevolutionary information, we predict an atomic-scale structure of the whole condensin complex, which our results indicate being composed of a single ring. Coupling coevolutionary information with molecular-dynamics simulations, we study the interaction surfaces between the subunits and examine the plausibility of alternative stoichiometries of the complex. Our analysis also reveals several additional configurational states of the condensin hinge domain and the SMC-kleisin interaction domains, which are likely involved with the functional opening and closing of the condensin ring. This study provides the foundation for future investigations of the structure-function relationship of the various SMC-kleisin protein complexes at atomic resolution.

Role of Computational Methods in Going beyond X-ray Crystallography to Explore Protein Structure and Dynamics

Protein structural biology came a long way since the determination of the first three-dimensional structure of myoglobin about six decades ago. Across this period, X-ray crystallography was the most important experimental method for gaining atomic-resolution insight into protein structures. However, as the role of dynamics gained importance in the function of proteins, the limitations of X-ray crystallography in not being able to capture dynamics came to the forefront. Computational methods proved to be immensely successful in understanding protein dynamics in solution, and they continue to improve in terms of both the scale and the types of systems that can be studied. In this review, we briefly discuss the limitations of X-ray crystallography in studying protein dynamics, and then provide an overview of different computational methods that are instrumental in understanding the dynamics of proteins and biomacromolecular complexes.

Structural consequences of hereditary spastic paraplegia disease-related mutations in kinesin

A wide range of mutations in the kinesin motor Kif5A have been linked to a neuronal disorder called hereditary spastic paraplegia (HSP). The position of these mutations can vary, and a range of different motile behaviors have been observed, indicating that the HSP mutants can alter distinct aspects of kinesin mechanochemistry. While focusing on four key HSP-associated mutants, this study examined the structural and dynamic perturbations that arise from these mutations using a series of different computational methods, ranging from bioinformatics analyses to all-atom simulations, that account for solvent effects explicitly. We show that two catalytic domain mutations (R280S and K253N) reduce the microtubule (MT) binding affinity of the kinesin head domains appreciably, while N256S has a much smaller impact. Bioinformatics analysis suggests that the stalk mutation A361V perturbs motor dimerization. Subsequent integration of these effects into a coarse-grained structure-based model of dimeric kinesin revealed that the order-disorder transition of the neck linker is substantially affected, indicating a hampered directionality and processivity of kinesin. The present analyses therefore suggest that, in addition to kinesin-MT binding and coiled-coil dimerization, HSP mutations affecting motor stepping transitions and processivity can lead to disease.

The Sensitivity of Computational Protein Folding to Contact Map Perturbations: The Case of Ubiquitin Folding and Function

Ubiquitin is a small model protein, commonly used in protein folding experiments and simulations. We simulated ubiquitin using a well-tested structure-based model coarse-grained to a C_α level (C_α-SBM) and found that the simulated folding route did not agree with the experimentally observed one. Simulating the C_α-SBM with a cutoff contact map, instead of a screened contact map, switched the folding route with the new route matching the experimental route. Thus, the simulated folding of ubiquitin is sensitive to contact map definition. The screened contact map, which is used in folding simulations because it captures protein folding cooperativity, removes contacts in which the atoms in contact are occluded by a third atom and is less sensitive to the value of the cutoff distance in well-packed regions of the protein. In sparsely packed regions, the larger cutoff distance creates bridging contacts between atoms which are separated by voids. Such contacts do not seem to affect the folding of most proteins, including those of the ubiquitin fold. However, the surface of ubiquitin has several protruding functional side chains which naturally create bridging contacts. Together, our results show that subtle structural features of a protein that may not be apparent by mere observation can be identified by comparing folding simulations of SBMs in which these features are differently encoded. When such structural features are preserved for functional reasons, differences in computational folding can be leveraged to identify functional features. Notably, such features are accessible to a gradation of SBMs even in commonly studied proteins such as ubiquitin.

Acceleration of cryo-EM Flexible Fitting for Large Biomolecular Systems by Efficient Space Partitioning

Flexible fitting is a powerful technique to build the 3D structures of biomolecules from cryoelectron microscopy (cryo-EM) density maps. One popular method is a cross-correlation coefficient-based approach, where the molecular dynamics (MD) simulation is carried out with the biasing potential that includes the cross-correlation coefficient between the experimental and simulated density maps. Here, we propose efficient parallelization schemes for the calculation of the cross-correlation coefficient to accelerate flexible fitting. Our schemes are tested for small, medium, and large biomolecules using CPU and hybrid CPU + GPU architectures. The scheme for the atomic decomposition MD is suitable for small proteins such as Ca²⁺-ATPase with the all-atom Go model, while that for the domain decomposition MD is better for larger systems such as ribosome with the all-atom Go or the all-atom explicit solvent models. Our methods allow flexible fitting for various biomolecules with reasonable computational cost. This approach also connects high-resolution structure refinements with investigation of protein structure-function relationship.

Simulations Reveal Multiple Intermediates in the Unzipping Mechanism of Neuronal SNARE Complex

The assembling of the soluble N-ethylmaleimide-sensitive factor attachment protein receptor protein complex is a fundamental step in neuronal exocytosis, and it has been extensively studied in the last two decades. Yet, many details of this process remain inaccessible with the current experimental space and time resolution. Here, we study the zipping mechanism of the soluble N-ethylmaleimide-sensitive factor attachment protein receptor complex computationally by using a coarse-grained model. We explore the different pathways available and analyze their dependence on the computational model employed. We reveal and characterize multiple intermediate states, in agreement with previous experimental findings. We use our model to analyze the influence of single-residue mutations on the thermodynamics of the folding process.