Capturing the essence of folding and functions of biomolecules using coarse-grained models

Sequence-Dependent Unzipping Dynamics of DNA Hairpins in a Nanopore

By applying an electric field to an insulating membrane, movement of charged particles through a nanopore can be induced. The measured ionic current reports on biomolecules passing through the nanopore. In this paper, we explore the sequence-dependent dynamics of DNA unzipping using our recently developed coarse-grained model. We estimated three molecular profiles (the potential of mean force, position-dependent diffusion coefficient, and position-dependent effective charge) for the DNA unzipping of four hairpins with different sequences. We found that the molecular profiles are correlated with the ionic current and molecular events. We also explored the unzipping kinetics using Brownian dynamics. We found that the effect of hairpin structure on the unzipping/translocation times is not only energetic (weaker hairpins unzip more quickly) but also kinetic (different unzipping and translocation pathways play an important role).

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.

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.

Dynamics of Allosteric Transitions in Dynein

Cytoplasmic dynein, whose motor domain belongs to the AAA+ family, walks on microtubules toward the minus end. Using the available structures in different nucleotide states, we performed simulations of a coarse-grained model to elucidate the dynamics of allosteric transitions. Binding of ATP closes the cleft between the AAA1 and AAA2 domains, triggering conformational changes in the rest of the motor domain, thus forming the pre-power stroke state. Interactions with the microtubule, modeled implicitly, enhance ADP release rate, and the formation of the post-power stroke state. The dynamics of the linker (LN), which reversibly changes from a straight to a bent state, is heterogeneous. Persistent interactions between the LN and the insert loops in the AAA2 domain prevent the formation of pre-power stroke state when ATP is bound to AAA3, thus locking dynein in a repressed non-functional state. Application of mechanical force to the LN restores motility in the repressed state.

Modeling Structure, Stability, and Flexibility of Double-Stranded RNAs in Salt Solutions

Double-stranded (ds) RNAs play essential roles in many processes of cell metabolism. The knowledge of three-dimensional (3D) structure, stability, and flexibility of dsRNAs in salt solutions is important for understanding their biological functions. In this work, we further developed our previously proposed coarse-grained model to predict 3D structure, stability, and flexibility for dsRNAs in monovalent and divalent ion solutions through involving an implicit structure-based electrostatic potential. The model can make reliable predictions for 3D structures of extensive dsRNAs with/without bulge/internal loops from their sequences, and the involvement of the structure-based electrostatic potential and corresponding ion condition can improve the predictions for 3D structures of dsRNAs in ion solutions. Furthermore, the model can make good predictions for thermal stability for extensive dsRNAs over the wide range of monovalent/divalent ion concentrations, and our analyses show that the thermally unfolding pathway of dsRNA is generally dependent on its length as well as its sequence. In addition, the model was employed to examine the salt-dependent flexibility of a dsRNA helix, and the calculated salt-dependent persistence lengths are in good accordance with experiments.

Interface Residues That Drive Allosteric Transitions Also Control the Assembly of l-Lactate Dehydrogenase

The allosteric enzyme, l-lactate dehydrogenase (LDH), is activated by fructose 1,6-metaphosphate (FBP) to reduce pyruvate to lactate. The molecular details of the FBP-driven transition from the low affinity T state to the high affinity R state in LDH, a tetramer composed of identical subunits, are not known. The dynamics of the T → R allosteric transition, investigated using Brownian dynamics (BD) simulations of the self-organized polymer (SOP) model, revealed that coordinated rotations of the subunits drive the T → R transition. We used the structural perturbation method (SPM), which requires only the static structure, to identify the allostery wiring diagram (AWD), a network of residues that transmits signals across the tetramer, as LDH undergoes the T → R transition. Interestingly, the residues that play a major role in the dynamics, which are predominantly localized at the interfaces, coincide with the AWD identified using the SPM. Although the allosteric pathways are highly heterogeneous, on the basis of our simulations, we surmise that predominantly the conformational changes in the T → R transition start from the region near the active site, comprised of helix αC, helix α1/2G, helix α3G, and helix α2F, and proceed to other structural units, thus completing the global motion. Brownian dynamics simulations of the tetramer assembly, triggered by a temperature quench from the fully disrupted conformations, show that the bottleneck for assembly is the formation of the correct orientational registry between the subunits, requiring contacts between the interface residues. Surprisingly, these residues are part of the AWD, which was identified using the SPM. Taken together, our results show that LDH, and perhaps other multidomain proteins, may have evolved to stabilize distinct states of allosteric enzymes using precisely the same AWD that also controls the functionally relevant allosteric transitions.

Sequence-Dependent Three Interaction Site Model for Single- and Double-Stranded DNA

We develop a robust coarse-grained model for single- and double-stranded DNA by representing each nucleotide by three interaction sites (TIS) located at the centers of mass of sugar, phosphate, and base. The resulting TIS model includes base-stacking, hydrogen bond, and electrostatic interactions as well as bond-stretching and bond angle potentials that account for the polymeric nature of DNA. The choices of force constants for stretching and the bending potentials were guided by a Boltzmann inversion procedure using a large representative set of DNA structures extracted from the Protein Data Bank. Some of the parameters in the stacking interactions were calculated using a learning procedure, which ensured that the experimentally measured melting temperatures of dimers are faithfully reproduced. Without any further adjustments, the calculations based on the TIS model reproduce the experimentally measured salt and sequence-dependence of the size of single-stranded DNA (ssDNA), as well as the persistence lengths of poly(dA) and poly(dT) chains. Interestingly, upon application of mechanical force, the extension of poly(dA) exhibits a plateau, which we trace to the formation of stacked helical domains. In contrast, the force-extension curve (FEC) of poly(dT) is entropic in origin and could be described by a standard polymer model. We also show that the persistence length of double-stranded DNA, formed from two complementary ssDNAs, is consistent with the prediction based on the worm-like chain. The persistence length, which decreases with increasing salt concentration, is in accord with the Odijk-Skolnick-Fixman theory intended for stiff polyelectrolyte chains near the rod limit. Our model predicts the melting temperatures of DNA hairpins with excellent accuracy, and we are able to recover the experimentally known sequence-specific trends. The range of applications, which did not require adjusting any parameter after the initial construction based solely on PDB structures and melting profiles of dimers, attests to the transferability and robustness of the TIS model for ssDNA and dsDNA.

Alchemical free energy calculations and umbrella sampling with local molecular field theory

Understanding the thermodynamic driving forces underlying any chemical process requires a description of the underlying free energy surface. However, computation of free energies is difficult, often requiring advanced sampling techniques. Moreover, these computations can be further complicated by the evaluation of any long-ranged interactions in the system of interest, such as Coulomb interactions in charged and polar media. Local molecular field theory is a promising approach to avoid many of the conceptual and computational difficulties associated with long-ranged interactions. We present frameworks for performing alchemical free energy calculations and non-Boltzmann sampling with local molecular field theory. We demonstrate that local molecular field theory can be used to perform these free energy calculations with accuracy comparable to traditional methodologies while eliminating the need for explicit treatment of long-ranged interactions in simulations.

How epigenome drives chromatin folding and dynamics, insights from efficient coarse-grained models of chromosomes

The 3D organization of chromosomes is crucial for regulating gene expression and cell function. Many experimental and polymer modeling efforts are dedicated to deciphering the mechanistic principles behind chromosome folding. Chromosomes are long and densely packed-topologically constrained-polymers. The main challenges are therefore to develop adequate models and simulation methods to investigate properly the multi spatio-temporal scales of such macromolecules. Here, we proposed a generic strategy to develop efficient coarse-grained models for self-avoiding polymers on a lattice. Accounting accurately for the polymer entanglement length and the volumic density, we show that our simulation scheme not only captures the steady-state structural and dynamical properties of the system but also tracks the same dynamics at different coarse-graining. This strategy allows a strong power-law gain in numerical efficiency and offers a systematic way to define reliable coarse-grained null models for chromosomes and to go beyond the current limitations by studying long chromosomes during an extended time period with good statistics. We use our formalism to investigate in details the time evolution of the 3D organization of chromosome 3R (20 Mbp) in drosophila during one cell cycle (20 hours). We show that a combination of our coarse-graining strategy with a one-parameter block copolymer model integrating epigenomic-driven interactions quantitatively reproduce experimental data at the chromosome-scale and predict that chromatin motion is very dynamic during the cell cycle.

Intrinsic Disorder in a Well-Folded Globular Protein

The folded structure of the heterodimeric sweet protein monellin mimics single-chain proteins with topology β1-α1-β2-β3-β4-β5 (chain A: β3-β4-β5; chain B: β1-α1-β2). Furthermore, like naturally occurring single-chain proteins of a similar size, monellin folds cooperatively with no detectable intermediates. However, the two monellin chains, A and B, are marginally structured in isolation and fold only upon binding to each other. Thus, monellin presents a unique opportunity to understand the design of intrinsically disordered proteins that fold upon binding. Here, we study the folding of a single-chain variant of monellin (scMn) using simulations of an all heavy-atom structure-based model. These simulations can explain mechanistic details derived from scMn experiments performed using several different structural probes. scMn folds cooperatively in our structure-based simulations, as is also seen in experiments. We find that structure formation near the transition-state ensemble of scMn is not uniformly distributed but is localized to a hairpin-like structure which contains one strand from each chain (β2, β3). Thus, the sequence and the underlying energetics of heterodimeric monellin promote the early formation of the interchain interface (β2-β3). By studying computational scMn mutants whose "interchain" interactions are deleted, we infer that this energy distribution allows the two protein chains to remain largely disordered when this interface is not folded. From these results, we suggest that cutting the protein backbone of a globular protein between residues which lie within its folding nucleus may be one way to construct two disordered fragments which fold upon binding.

Denaturants Alter the Flux through Multiple Pathways in the Folding of PDZ Domain

Although we understand many aspects of how small proteins (number of residues less than about hundred) fold, it is a major challenge to quantitatively describe how large proteins self-assemble. To partially overcome this challenge, we performed simulations using the self-organized polymer model with side chains (SOP-SC) in guanidinium chloride (GdmCl), using the molecular transfer model (MTM), to describe the folding of the 110-residue PDZ3 domain. The simulations reproduce the folding thermodynamics accurately including the melting temperature (T_m), the stability of the folded state with respect to the unfolded state. We show that the calculated dependence of ln k_obs (k_obs is the relaxation rate) has the characteristic chevron shape. The slopes of the chevron plots are in good agreement with experiments. We show that PDZ3 folds by four major pathways populating two metastable intermediates, in accord with the kinetic partitioning mechanism. The structure of one of the intermediates, populated after polypeptide chain collapse, is structurally similar to an equilibrium intermediate. Surprisingly, the connectivities between the intermediates and hence, the fluxes through the pathways depend on the concentration of GdmCl. The results are used to predict possible outcomes for unfolding of PDZ domain subject to mechanical forces. Our study demonstrates that, irrespective of the size or topology, simulations based on MTM and SOP-SC offer a theoretical framework for describing the folding of proteins, mimicking precisely the conditions used in experiments.

On the folding of a structurally complex protein to its metastable active state

For successful protease inhibition, the reactive center loop (RCL) of the two-domain serine protease inhibitor, α1-antitrypsin (α1-AT), needs to remain exposed in a metastable active conformation. The α1-AT RCL is sequestered in a β-sheet in the stable latent conformation. Thus, to be functional, α1-AT must always fold to a metastable conformation while avoiding folding to a stable conformation. We explore the structural basis of this choice using folding simulations of coarse-grained structure-based models of the two α1-AT conformations. Our simulations capture the key features of folding experiments performed on both conformations. The simulations also show that the free energy barrier to fold to the latent conformation is much larger than the barrier to fold to the active conformation. An entropically stabilized on-pathway intermediate lowers the barrier for folding to the active conformation. In this intermediate, the RCL is in an exposed configuration, and only one of the two α1-AT domains is folded. In contrast, early conversion of the RCL into a β-strand increases the coupling between the two α1-AT domains in the transition state and creates a larger barrier for folding to the latent conformation. Thus, unlike what happens in several proteins, where separate regions promote folding and function, the structure of the RCL, formed early during folding, determines both the conformational and the functional fate of α1-AT. Further, the short 12-residue RCL modulates the free energy barrier and the folding cooperativity of the large 370-residue α1-AT. Finally, we suggest experiments to test the predicted folding mechanism for the latent state.

Parsing the roles of neck-linker docking and tethered head diffusion in the stepping dynamics of kinesin

Kinesin walks processively on microtubules (MTs) in an asymmetric hand-over-hand manner consuming one ATP molecule per 16-nm step. The individual contributions due to docking of the approximately 13-residue neck linker to the leading head (deemed to be the power stroke) and diffusion of the trailing head (TH) that contributes in propelling the motor by 16 nm have not been quantified. We use molecular simulations by creating a coarse-grained model of the MT-kinesin complex, which reproduces the measured stall force as well as the force required to dislodge the motor head from the MT, to show that nearly three-quarters of the step occurs by bidirectional stochastic motion of the TH. However, docking of the neck linker to the leading head constrains the extent of diffusion and minimizes the probability that kinesin takes side steps, implying that both the events are necessary in the motility of kinesin and for the maintenance of processivity. Surprisingly, we find that during a single step, the TH stochastically hops multiple times between the geometrically accessible neighboring sites on the MT before forming a stable interaction with the target binding site with correct orientation between the motor head and the [Formula: see text] tubulin dimer.

Anisotropic Fluctuations in the Ribosome Determine tRNA Kinetics

The ribosome is a large ribonucleoprotein complex that is responsible for the production of proteins in all organisms. Accommodation is the process by which an incoming aminoacyl-tRNA (aa-tRNA) molecule binds the ribosomal A site, and its kinetics has been implicated in the accuracy of tRNA selection. In addition to rearrangements in the aa-tRNA molecule, the L11 stalk can undergo large-scale anisotropic motions during translation. To explore the potential impact of this protruding region on the rate of aa-tRNA accommodation, we used molecular dynamics simulations with a simplified model to evaluate the free energy as a function of aa-tRNA position. Specifically, these calculations describe the transition between A/T and elbow-accommodated (EA) configurations (∼20 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.

Reexamining the origin of the directionality of myosin V

The nature of the conversion of chemical energy to directional motion in myosin V is examined by careful simulations that include two complementary methods: direct Langevin Dynamics (LD) simulations with a scaled-down potential that provided a detailed time-resolved mechanism, and kinetic equations solution for the ensemble long-time propagation (based on information collected for segments of the landscape using LD simulations and experimental information). It is found that the directionality is due to the rate-limiting ADP release step rather than the potential energy of the lever arm angle. We show that the energy of the power stroke and the barriers involved in it are of minor consequence to the selectivity of forward over backward steps and instead suggest that the selective release of ADP from a postrigor myosin motor head promotes highly selective and processive myosin V. Our model is supported by different computational methods-LD simulations, Monte Carlo simulations, and kinetic equations solution-as well as by structure-based binding energy calculations.

Fast Protein Translation Can Promote Co- and Posttranslational Folding of Misfolding-Prone Proteins

Chemical kinetic modeling has previously been used to predict that fast-translating codons can enhance cotranslational protein folding by helping to avoid misfolded intermediates. Consistent with this prediction, protein aggregation in yeast and worms was observed to increase when translation was globally slowed down, possibly due to increased cotranslational misfolding. Observation of similar behavior in molecular simulations would confirm predictions from the simpler chemical kinetic model and provide a molecular perspective on cotranslational folding, misfolding, and the impact of translation speed on these processes. All-atom simulations cannot reach the timescales relevant to protein synthesis, and most conventional structure-based coarse-grained models do not allow for nonnative structure formation. Here, we introduce a protocol to incorporate misfolding using the functional forms of publicly available force fields. With this model we create two artificial proteins that are capable of undergoing structural transitions between a native and a misfolded conformation and simulate their synthesis by the ribosome. Consistent with the chemical kinetic predictions, we find that rapid synthesis of misfolding-prone nascent-chain segments increases the fraction of folded proteins by kinetically partitioning more molecules through on-pathway intermediates, decreasing the likelihood of sampling misfolded conformations. Novel to this study, to our knowledge, we observe that differences in protein dynamics, arising from different translation-elongation schedules, can persist long after the nascent protein has been released from the ribosome, and that a sufficient level of energetic frustration is needed for fast-translating codons to be beneficial for folding. These results provide further evidence that fast-translating codons can be as biologically important as pause sites in coordinating cotranslational folding.

Electron-transfer chain in respiratory complex I

Complex I is a part of the respiration energy chain converting the redox energy into the cross-membrane proton gradient. The electron-transfer chain of iron-sulfur cofactors within the water-soluble peripheral part of the complex is responsible for the delivery of electrons to the proton pumping subunit. The protein is porous to water penetration and the hydration level of the cofactors changes when the electron is transferred along the chain. High reaction barriers and trapping of the electrons at the iron-sulfur cofactors are prevented by the combination of intense electrostatic noise produced by the protein-water interface with the high density of quantum states in the iron-sulfur clusters caused by spin interactions between paramagnetic iron atoms. The combination of these factors substantially lowers the activation barrier for electron transfer compared to the prediction of the Marcus theory, bringing the rate to the experimentally established range. The unique role of iron-sulfur clusters as electron-transfer cofactors is in merging protein-water fluctuations with quantum-state multiplicity to allow low activation barriers and robust operation. Water plays a vital role in electron transport energetics by electrowetting the cofactors in the chain upon arrival of the electron. A general property of a protein is to violate the fluctuation-dissipation relation through nonergodic sampling of its landscape. High functional efficiency of redox enzymes is a direct consequence of nonergodicity.

A coarse-grained model for assisting the investigation of structure and dynamics of large nucleic acids by ion mobility spectrometry-mass spectrometry

Ion Mobility Spectrometry-Mass Spectrometry (IMS-MS) is a rapidly emerging tool for the investigation of nucleic acid structure and dynamics. IMS-MS determinations can provide valuable information regarding alternative topologies, folding intermediates, and conformational heterogeneities, which are not readily accessible to other analytical techniques. The leading strategies for data interpretation rely on computational and experimental approaches to correctly assign experimental observations to putative structures. A very effective strategy involves the application of molecular dynamics (MD) simulations to predict the structure of the analyte molecule, calculate its collision cross section (CCS), and then compare this computational value with the corresponding experimental data. While this approach works well for small nucleic acid species, analyzing larger nucleic acids of biological interest is hampered by the computational cost associated with capturing their extensive structure and dynamics in all-atom detail. In this report, we describe the implementation of a coarse graining (CG) approach to reduce the cost of the computational methods employed in the data interpretation workflow. Our framework employs a five-bead model to accurately represent each nucleotide in the nucleic acid structure. The beads are appropriately parameterized to enable the direct calculation of CCS values from CG models, thus affording the ability to pursue the analysis of larger, highly dynamic constructs. The validity of this approach was successfully confirmed by the excellent correlation between the CCS values obtained in parallel by all-atom and CG workflows.

Kinematics of the lever arm swing in myosin VI

Myosin VI (MVI) is the only known member of the myosin superfamily that, upon dimerization, walks processively toward the pointed end of the actin filament. The leading head of the dimer directs the trailing head forward with a power stroke, a conformational change of the motor domain exaggerated by the lever arm. Using a unique coarse-grained model for the power stroke of a single MVI, we provide the molecular basis for its motility. We show that the power stroke occurs in two major steps. First, the motor domain attains the poststroke conformation without directing the lever arm forward; and second, the lever arm reaches the poststroke orientation by undergoing a rotational diffusion. From the analysis of the trajectories, we discover that the potential that directs the rotating lever arm toward the poststroke conformation is almost flat, implying that the lever arm rotation is mostly uncoupled from the motor domain. Because a backward load comparable to the largest interhead tension in a MVI dimer prevents the rotation of the lever arm, our model suggests that the leading-head lever arm of a MVI dimer is uncoupled, in accord with the inference drawn from polarized total internal reflection fluorescence (polTIRF) experiments. Without any adjustable parameter, our simulations lead to quantitative agreement with polTIRF experiments, which validates the structural insights. Finally, in addition to making testable predictions, we also discuss the implications of our model in explaining the broad step-size distribution of the MVI stepping pattern.

Unraveling Mg2+-RNA binding with atomistic molecular dynamics

Interaction with divalent cations is of paramount importance for RNA structural stability and function. We report here a detailed molecular dynamics study of all the possible binding sites for Mg2+ on an RNA duplex, including both direct (inner sphere) and indirect (outer sphere) binding. In order to tackle sampling issues, we develop a modified version of bias-exchange metadynamics, which allows us to simultaneously compute affinities with previously unreported statistical accuracy. Results correctly reproduce trends observed in crystallographic databases. Based on this, we simulate a carefully chosen set of models that allows us to quantify the effects of competition with monovalent cations, RNA flexibility, and RNA hybridization. Our simulations reproduce the decrease and increase of Mg2+ affinity due to ion competition and hybridization, respectively, and predict that RNA flexibility has a site-dependent effect. This suggests a nontrivial interplay between RNA conformational entropy and divalent cation binding.

Coarse-Grained Prediction of Peptide Binding to G-Protein Coupled Receptors

In this study, we used the Martini Coarse-Grained model with no applied restraints to predict the binding mode of some peptides to G-Protein Coupled Receptors (GPCRs). Both the Neurotensin-1 and the chemokine CXCR4 receptors were used as test cases. Their ligands, NTS_8-13 and CVX15 peptides, respectively, were initially positioned in the surrounding water box. Using a protocol based on Replica Exchange Molecular Dynamics (REMD), both opening of the receptors and entry of the peptides into their dedicated pockets were observed on the μs time-scale. After clustering, the most statistically representative orientations were closely related to the X-ray structures of reference, sharing both RMSD lower than 3 Å and most of the native contacts. These results demonstrate that such a model, that does not require access to tremendous computational facilities, can be helpful in predicting peptide binding to GPCRs as well as some of the receptor's conformational changes required for this key step. We also discuss how such an approach can now help to predict, de novo, the interactions of GPCRs with other intra- or extracellular peptide/protein partners.

Van der Waals Perspective on Coarse-Graining: Progress toward Solving Representability and Transferability Problems

Low-resolution coarse-grained (CG) models provide the necessary efficiency for simulating phenomena that are inaccessible to more detailed models. However, in order to realize their considerable promise, CG models must accurately describe the relevant physical forces and provide useful predictions. By formally integrating out the unnecessary details from an all-atom (AA) model, "bottom-up" approaches can, at least in principle, quantitatively reproduce the structural and thermodynamic properties of the AA model that are observable at the CG resolution. In practice, though, bottom-up approaches only approximate this "exact coarse-graining" procedure. The resulting models typically reproduce the intermolecular structure of AA models at a single thermodynamic state point but often describe other state points less accurately and, moreover, tend to provide a poor description of thermodynamic properties. These two limitations have been coined the "transferability" and "representability" problems, respectively. Perhaps, the simplest and most commonly discussed manifestation of the representability problem regards the tendency of structure-based CG models to dramatically overestimate the pressure. Furthermore, when these models are adjusted to reproduce the pressure, they provide a poor description of the compressibility. More generally, it is sometimes suggested that CG models are fundamentally incapable of reproducing both structural and thermodynamic properties. After all, there is no such thing as a "free lunch"; any significant gain in computational efficiency should come at the cost of significant model limitations. At least in the case of structural and thermodynamic properties, though, we optimistically propose that this may be a false dichotomy. Accordingly, we have recently re-examined the "exact coarse-graining" procedure and investigated the intrinsic consequences of representing an AA model in reduced resolution. These studies clarify the origin and inter-relationship of representability and transferability problems. Both arise as consequences of transferring thermodynamic information from the high resolution configuration space and encoding this information into the many-body potential of mean force (PMF), that is, the potential that emerges from an exact coarse-graining procedure. At least in principle, both representability and transferability problems can be resolved by properly addressing this thermodynamic information. In particular, we have demonstrated that "pressure-matching" provides a practical and rigorous means for addressing the density dependence of the PMF. The resulting bottom-up models accurately reproduce the structure, equilibrium density, compressibility, and pressure equation of state for AA models of molecular liquids. Additionally, we have extended this approach to develop transferable potentials that provide similar accuracy for heptane-toluene mixtures. Moreover, these potentials provide predictive accuracy for modeling concentrations that were not considered in their parametrization. More generally, this work suggests a "van der Waals" perspective on coarse-graining, in which conventional structure-based methods accurately describe the configuration dependence of the PMF, while independent variational principles infer the thermodynamic information that is necessary to resolve representability and transferability problems.

Understanding protein domain-swapping using structure-based models of protein folding

In domain-swapping, two or more identical protein monomers exchange structural elements and fold into dimers or multimers whose units are structurally similar to the original monomer. Domain-swapping is of biotechnological interest because inhibiting domain-swapping can reduce disease-causing fibrillar protein aggregation. To achieve such inhibition, it is important to understand both the energetics that stabilize the domain-swapped structure and the protein dynamics that enable the swapping. Structure-based models (SBMs) encode the folded structure of the protein in their potential energy functions. SBMs have been successfully used to understand diverse aspects of monomer folding. Symmetrized SBMs model interactions between two identical protein chains using only intra-monomer interactions. Molecular dynamics simulations of such symmetrized SBMs have been used to correctly predict the domain-swapped structure and to understand the mechanism of domain-swapping. Here, we review such models and illustrate that monomer topology determines key aspects of domain-swapping. However, in some proteins, specifics of local energetic interactions modulate domain-swapping and these need to be added to the symmetrized SBMs. We then summarize some general principles of the mechanism of domain-swapping that emerge from the symmetrized SBM simulations. Finally, using our own results, we explore how symmetrized SBMs could be used to design domain-swapping in proteins.

Directly Modifying the Nonbonded Potential Based on the Standard Iterative Boltzmann Inversion Method for Coarse-Grained Force Fields

Effective potentials are of great importance for coarse-grained (CG) simulations, which can be obtained by the structure-based iterative Boltzmann inversion (IBI) method. However, the standard IBI method is incapable of maintaining the mechanical and thermodynamic properties of the CG model in agreement with those of the all-atom model. Unlike the existing techniques, such as introducing friction force as the dissipative force to reduce the superatom motion while keeping the conservative force arising from the CG potential intact, we directly modified the standard IBI nonbonded potential by adding an empirical function. According to an analysis of the dissipative particle dynamics, the additional function did compensate for the friction reduction of the standard IBI CG model. In this work, the thermal fluctuation information from the nonbonded radial distribution function was incorporated into the additional empirical function. As an illustration of the new CG force fields, we presented simulations of the stress-strain relation and thermodynamic properties in terms of cis-polyisoprene and compared the statistical structure information of the superatoms with those of the IBI CG model and the all-atom model. It should be emphasized that the additional empirical function contributed to compensating for the friction reduction, irrespective of the functional form it took. In this sense, the proposed method was easily operable.

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

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

The translation of mRNA by the ribosome is governed by a series of large-scale conformational transitions. Here the authors use MD simulations to demonstrate how the rate of dissociation of elongation factor Tu affects the dynamics of tRNA accommodation and proofreading.

Semiflexible macromolecules in quasi-one-dimensional confinement: Discrete versus continuous bond angles

The conformations of semiflexible polymers in two dimensions confined in a strip of width D are studied by computer simulations, investigating two different models for the mechanism by which chain stiffness is realized. One model (studied by molecular dynamics) is a bead-spring model in the continuum, where stiffness is controlled by a bond angle potential allowing for arbitrary bond angles. The other model (studied by Monte Carlo) is a self-avoiding walk chain on the square lattice, where only discrete bond angles (0° and ±90°) are possible, and the bond angle potential then controls the density of kinks along the chain contour. The first model is a crude description of DNA-like biopolymers, while the second model (roughly) describes synthetic polymers like alkane chains. It is first demonstrated that in the bulk the crossover from rods to self-avoiding walks for both models is very similar, when one studies average chain linear dimensions, transverse fluctuations, etc., despite their differences in local conformations. However, in quasi-one-dimensional confinement two significant differences between both models occur: (i) The persistence length (extracted from the average cosine of the bond angle) gets renormalized for the lattice model when D gets less than the bulk persistence length, while in the continuum model it stays unchanged. (ii) The monomer density near the repulsive walls for semiflexible polymers is compatible with a power law predicted for the Kratky-Porod model in the case of the bead-spring model, while for the lattice case it tends to a nonzero constant across the strip. However, for the density of chain ends, such a constant behavior seems to occur for both models, unlike the power law observed for flexible polymers. In the regime where the bulk persistence length ℓp is comparable to D, hairpin conformations are detected, and the chain linear dimensions are discussed in terms of a crossover from the Daoud/De Gennes "string of blobs"-picture to the flexible rod picture when D decreases and/or the chain stiffness increases. Introducing a suitable further coarse-graining of the chain contours of the continuum model, direct estimates for the deflection length and its distribution could be obtained.

The Power of Force: Insights into the Protein Folding Process Using Single-Molecule Force Spectroscopy

One of the major challenges in modern biophysics is observing and understanding conformational changes during complex molecular processes, from the fundamental protein folding to the function of molecular machines. Single-molecule techniques have been one of the major driving forces of the huge progress attained in the last few years. Recent advances in resolution of the experimental setups, aided by theoretical developments and molecular dynamics simulations, have revealed a much higher degree of complexity inside these molecular processes than previously reported using traditional ensemble measurements. This review sums up the evolution of these developments and gives an outlook on prospective discoveries.

Capturing Transition States for tRNA Hybrid-State Formation in the Ribosome

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.

Insights into Cotranslational Nascent Protein Behavior from Computer Simulations

Regulation of protein stability and function in vivo begins during protein synthesis, when the ribosome translates a messenger RNA into a nascent polypeptide. Cotranslational processes involving a nascent protein include folding, binding to other macromolecules, enzymatic modification, and secretion through membranes. Experiments have shown that the rate at which the ribosome adds amino acids to the elongating nascent chain influences the efficiency of these processes, with alterations to these rates possibly contributing to diseases, including some types of cancer. In this review, we discuss recent insights into cotranslational processes gained from molecular simulations, how different computational approaches have been combined to understand cotranslational processes at multiple scales, and the new scenarios illuminated by these simulations. We conclude by suggesting interesting questions that computational approaches in this research area can address over the next few years.

Capturing transition paths and transition states for conformational rearrangements in the ribosome

To reveal the molecular determinants of biological function, one seeks to characterize the interactions that are formed in conformational and chemical transition states. In other words, what interactions govern the molecule's energy landscape? To accomplish this, it is necessary to determine which degrees of freedom can unambiguously identify each transition state. Here, we perform simulations of large-scale aminoacyl-transfer RNA (aa-tRNA) rearrangements during accommodation on the ribosome and project the dynamics along experimentally accessible atomic distances. From this analysis, we obtain evidence for which coordinates capture the correct number of barrier-crossing events and accurately indicate when the aa-tRNA is on a transition path. Although a commonly used coordinate in single-molecule experiments performs poorly, this study implicates alternative coordinates along which rearrangements are accurately described as diffusive movements across a one-dimensional free-energy profile. From this, we provide the theoretical foundation required for single-molecule techniques to uncover the energy landscape governing aa-tRNA selection by the ribosome.

The impact of resolution upon entropy and information in coarse-grained models

By eliminating unnecessary degrees of freedom, coarse-grained (CG) models tremendously facilitate numerical calculations and theoretical analyses of complex phenomena. However, their success critically depends upon the representation of the system and the effective potential that governs the CG degrees of freedom. This work investigates the relationship between the CG representation and the many-body potential of mean force (PMF), W, which is the appropriate effective potential for a CG model that exactly preserves the structural and thermodynamic properties of a given high resolution model. In particular, we investigate the entropic component of the PMF and its dependence upon the CG resolution. This entropic component, SW, is a configuration-dependent relative entropy that determines the temperature dependence of W. As a direct consequence of eliminating high resolution details from the CG model, the coarsening process transfers configurational entropy and information from the configuration space into SW. In order to further investigate these general results, we consider the popular Gaussian Network Model (GNM) for protein conformational fluctuations. We analytically derive the exact PMF for the GNM as a function of the CG representation. In the case of the GNM, -TSW is a positive, configuration-independent term that depends upon the temperature, the complexity of the protein interaction network, and the details of the CG representation. This entropic term demonstrates similar behavior for seven model proteins and also suggests, in each case, that certain resolutions provide a more efficient description of protein fluctuations. These results may provide general insight into the role of resolution for determining the information content, thermodynamic properties, and transferability of CG models. Ultimately, they may lead to a rigorous and systematic framework for optimizing the representation of CG models.

Single-Molecule FRET Spectroscopy and the Polymer Physics of Unfolded and Intrinsically Disordered Proteins

The properties of unfolded proteins have long been of interest because of their importance to the protein folding process. Recently, the surprising prevalence of unstructured regions or entirely disordered proteins under physiological conditions has led to the realization that such intrinsically disordered proteins can be functional even in the absence of a folded structure. However, owing to their broad conformational distributions, many of the properties of unstructured proteins are difficult to describe with the established concepts of structural biology. We have thus seen a reemergence of polymer physics as a versatile framework for understanding their structure and dynamics. An important driving force for these developments has been single-molecule spectroscopy, as it allows structural heterogeneity, intramolecular distance distributions, and dynamics to be quantified over a wide range of timescales and solution conditions. Polymer concepts provide an important basis for relating the physical properties of unstructured proteins to folding and function.

Imprints of function on the folding landscape: functional role for an intermediate in a conserved eukaryotic binding protein

In the computational characterization of single domain protein folding, the effective free energies of numerous microstates are projected onto few collective degrees of freedom that in turn serve as well-defined reaction coordinates. In this regard, one-dimensional (1D) free energy profiles are widely used mainly for their simplicity. Since folding and functional landscapes are interlinked, how well can these reduced representations capture the structural and dynamic features of functional states while being simultaneously consistent with experimental observables? We investigate this issue by characterizing the folding of the four-helix bundle bovine acyl-CoA binding protein (bACBP), which exhibits complex equilibrium and kinetic behaviours, employing an Ising-like statistical mechanical model and molecular simulations. We show that the features of the 1D free energy profile are sufficient to quantitatively reproduce multiple experimental observations including millisecond chevron-like kinetics and temperature dependence, a microsecond fast phase, barrier heights, unfolded state movements, the intermediate structure and average ϕ-values. Importantly, we find that the structural features of the native-like intermediate (partial disorder in helix 1) are intricately linked to a unique interplay between packing and electrostatics in this domain. By comparison with available experimental data, we propose that this intermediate determines the promiscuous functional behaviour of bACBP that exhibits broad substrate specificity. Our results present evidence to the possibility of employing the statistical mechanical model and the resulting 1D free energy profile to not just understand folding mechanisms but to even extract features of functionally relevant states and their energetic origins.

Holliday Junction Thermodynamics and Structure: Coarse-Grained Simulations and Experiments

Holliday junctions play a central role in genetic recombination, DNA repair and other cellular processes. We combine simulations and experiments to evaluate the ability of the 3SPN.2 model, a coarse-grained representation designed to mimic B-DNA, to predict the properties of DNA Holliday junctions. The model reproduces many experimentally determined aspects of junction structure and stability, including the temperature dependence of melting on salt concentration, the bias between open and stacked conformations, the relative populations of conformers at high salt concentration, and the inter-duplex angle (IDA) between arms. We also obtain a close correspondence between the junction structure evaluated by all-atom and coarse-grained simulations. We predict that, for salt concentrations at physiological and higher levels, the populations of the stacked conformers are independent of salt concentration, and directly observe proposed tetrahedral intermediate sub-states implicated in conformational transitions. Our findings demonstrate that the 3SPN.2 model captures junction properties that are inaccessible to all-atom studies, opening the possibility to simulate complex aspects of junction behavior.

Diffusive dynamics of DNA unzipping in a nanopore

When an electric field is applied to an insulating membrane, movement of charged particles through a nanopore is induced. The measured ionic current reports on biomolecules passing through the nanopore. In this work, we explored the kinetics of DNA unzipping in a nanopore using our coarse-grained model (Stachiewicz and Molski, J. Comput. Chem. 2015, 36, 947). Coarse graining allowed a more detailed analysis for a wider range of parameters than all-atom simulations. Dependence of the translocation mode (unzipping or distortion) on the pore diameter was examined, and the threshold voltages were estimated. We determined the potential of mean force, position-dependent diffusion coefficient, and position-dependent effective charge for the DNA unzipping. The three molecular profiles were correlated with the ionic current and molecular events. On the unzipping/translocation force profile, two energy maxima were found, one of them corresponding to the unzipping, and the other to the translocation barriers. The unzipping kinetics were further explored using Brownian dynamics.

Steric interactions lead to collective tilting motion in the ribosome during mRNA-tRNA translocation

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.

During protein elongation, the translocation of mRNA and tRNA molecules across the 30S ribosomal subunit is associated with large-scale motions of the 30S head domain. Here the authors carry out MD simulations to probe the associated steric interactions and identify novel tilting motions during the late stages of translocation.

Using the folding landscapes of proteins to understand protein function

Proteins fold on a biologically-relevant timescale because of a funnel-shaped energy landscape. This landscape is sculpted through evolution by selecting amino-acid sequences that stabilize native interactions while suppressing stable non-native interactions that occur during folding. However, there is strong evolutionary selection for functional residues and these cannot be chosen to optimize folding. Their presence impacts the folding energy landscape in a variety of ways. Here, we survey the effects of functional residues on folding by providing several examples. We then review how such effects can be detected computationally and be used as assays for protein function. Overall, an understanding of how functional residues modulate folding should provide insights into the design of natural proteins and their homeostasis.