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

Molecular basis for the dissociation dynamics of protein A-immunoglobulin G1 complex

Staphylococcus aureus protein A (SpA) is the most popular affinity ligand for immunoglobulin G1 (IgG1). However, the molecular basis for the dissociation dynamics of SpA-IgG1 complex is unclear. Herein, coarse-grained (CG) molecular dynamics (MD) simulations with the Martini force field were used to study the dissociation dynamics of the complex. The CG-MD simulations were first verified by the agreement in the structural and interactional properties of SpA and human IgG1 (hIgG1) in the association process between the CG-MD and all-atom MD at different NaCl concentrations. Then, the CG-MD simulation studies focused on the molecular insight into the dissociation dynamics of SpA-hIgG1 complex at pH 3.0. It is found that there are four steps in the dissociation process of the complex. First, there is a slight conformational adjustment of helix II in SpA. This is followed by the phenomena that the electrostatic interactions provided by the three hot spots (Glu143, Arg146 and Lys154) of helix II of SpA break up, leading to the dissociation of helix II from the binding site of hIgG1. Subsequently, breakup of the hydrophobic interactions between helix I (Phe132, Tyr133 and His137) in SpA and hIgG1 occurs, resulting in the disengagement of helix I from its binding site of hIgG1. Finally, the non-specific interactions between SpA and hIgG1 decrease slowly till disappearance, leading to the complete dissociation of the SpA-hIgG1 complex. This work has revealed that CG-MD coupled with the Martini force field is an effective method for studying the dissociation dynamics of protein-protein complex.

Modelling of crowded polymers elucidate effects of double-strand breaks in topological domains of bacterial chromosomes

Using numerical simulations of pairs of long polymeric chains confined in microscopic cylinders, we investigate consequences of double-strand DNA breaks occurring in independent topological domains, such as these constituting bacterial chromosomes. Our simulations show a transition between segregated and mixed state upon linearization of one of the modelled topological domains. Our results explain how chromosomal organization into topological domains can fulfil two opposite conditions: (i) effectively repulse various loops from each other thus promoting chromosome separation and (ii) permit local DNA intermingling when one or more loops are broken and need to be repaired in a process that requires homology search between broken ends and their homologous sequences in closely positioned sister chromatid.

On the role of thermal backbone fluctuations in myoglobin ligand gate dynamics

We construct an energy function that describes the crystallographic structure of sperm whale myoglobin backbone. As a model in our construction, we use the Protein Data Bank entry 1ABS that has been measured at liquid helium temperature. Consequently, the thermal B-factor fluctuations are very small, which is an advantage in our construction. The energy function that we utilize resembles that of the discrete nonlinear Schrödinger equation. Likewise, ours supports topological solitons as local minimum energy configurations. We describe the 1ABS backbone in terms of topological solitons with a precision that deviates from 1ABS by an average root-mean-square distance, which is less than the experimentally observed Debye-Waller B-factor fluctuation distance. We then subject the topological multi-soliton solution to extensive numerical heating and cooling experiments, over a very wide range of temperatures. We concentrate in particular to temperatures above 300 K and below the Θ-point unfolding temperature, which is around 348 K. We confirm that the behavior of the topological multi-soliton is fully consistent with Anfinsen's thermodynamic principle, up to very high temperatures. We observe that the structure responds to an increase of temperature consistently in a very similar manner. This enables us to characterize the onset of thermally induced conformational changes in terms of three distinct backbone ligand gates. One of the gates is made of the helix F and the helix E. The two other gates are chosen similarly, when open they provide a direct access route for a ligand to reach the heme. We find that out of the three gates we investigate, the one which is formed by helices B and G is the most sensitive to thermally induced conformational changes. Our approach provides a novel perspective to the important problem of ligand entry and exit.

Understanding the folding-function tradeoff in proteins

When an amino-acid sequence cannot be optimized for both folding and function, folding can get compromised in favor of function. To understand this tradeoff better, we devise a novel method for extracting the "function-less" folding-motif of a protein fold from a set of structurally similar but functionally diverse proteins. We then obtain the β-trefoil folding-motif, and study its folding using structure-based models and molecular dynamics simulations. CompariA protein sequence serves two purpson with the folding of wild-type β-trefoil proteins shows that function affects folding in two ways: In the slower folding interleukin-1β, binding sites make the fold more complex, increase contact order and slow folding. In the faster folding hisactophilin, residues which could have been part of the folding-motif are used for function. This reduces the density of native contacts in functional regions and increases folding rate. The folding-motif helps identify subtle structural deviations which perturb folding. These may then be used for functional annotation. Further, the folding-motif could potentially be used as a first step in the sequence design of function-less scaffold proteins. Desired function can then be engineered into these scaffolds.

Where soft matter meets living matter--protein structure, stability, and folding in the cell

A protein is a biopolymer that self-assembles through the process of protein folding. A cell is a crowded space where the surrounding macromolecules of a protein can limit the number of ways of folding. These crowding macromolecules can also affect the shape and the size of a physically malleable, or 'soft, squishy', protein with regulatory purposes. In this review, we focus on the in silico approaches of coarse-grained molecular simulations that enable the investigation of protein folding in a cell-like environment. When these simulation results were compared with experimentally measured properties of a protein, such joint effort has yielded new ideas on the specific function of a protein in cells. We also highlighted the recent developments of computer modeling and simulations that encompass the importance of the shape of a macromolecule, the interactions between macromolecules, and the hydrodynamic interactions on the kinetics and thermodynamics of a protein in a high concentration of protein solution and in cytoplasmic environments.

Structure-based molecular simulations reveal the enhancement of biased Brownian motions in single-headed kinesin

Kinesin is a family of molecular motors that move unidirectionally along microtubules (MT) using ATP hydrolysis free energy. In the family, the conventional two-headed kinesin was experimentally characterized to move unidirectionally through “walking” in a hand-over-hand fashion by coordinated motions of the two heads. Interestingly a single-headed kinesin, a truncated KIF1A, still can generate a biased Brownian movement along MT, as observed by in vitro single molecule experiments. Thus, KIF1A must use a different mechanism from the conventional kinesin to achieve the unidirectional motions. Based on the energy landscape view of proteins, for the first time, we conducted a set of molecular simulations of the truncated KIF1A movements over an ATP hydrolysis cycle and found a mechanism exhibiting and enhancing stochastic forward-biased movements in a similar way to those in experiments. First, simulating stand-alone KIF1A, we did not find any biased movements, while we found that KIF1A with a large friction cargo-analog attached to the C-terminus can generate clearly biased Brownian movements upon an ATP hydrolysis cycle. The linked cargo-analog enhanced the detachment of the KIF1A from MT. Once detached, diffusion of the KIF1A head was restricted around the large cargo which was located in front of the head at the time of detachment, thus generating a forward bias of the diffusion. The cargo plays the role of a diffusional anchor, or cane, in KIF1A “walking.”

It is one of the major issues in biophysics how molecular motors such as conventional two-headed kinesin convert the chemical energy released at ATP hydrolysis into mechanical work. While most molecular motors move with more than one catalytic domain working in coordinated fashions, there are some motors that can move with only a single catalytic domain, which provides us a possibly simpler case to understand. A single-headed kinesin, KIF1A, with only one catalytic domain, has been characterized by in vitro single-molecule assay to generate a biased Brownian movement along the microtubule. Here, we conducted a set of structure-based coarse-grained molecular simulations for KIF1A system over an ATP hydrolysis cycle for the first time to our knowledge. Without cargo the simulated stand-alone KIF1A could not generate any directional movement, while a large-friction cargo-analog linked to the C-terminus of KIF1A clearly enhanced the forward-biased Brownian movement of KIF1A significantly. Interestingly, the cargo-analog here is not merely load but an important promoter to enable efficient movements of KIF1A.

Allosteric activation transitions in enzymes and biomolecular motors: insights from atomistic and coarse-grained simulations

The chemical step in enzymes is usually preceded by a kinetically distinct activation step that involves large-scale conformational transitions. In "simple" enzymes this step corresponds to the closure of the active site; in more complex enzymes, such as biomolecular motors, the activation step is more complex and may involve interactions with other biomolecules. These activation transitions are essential to the function of enzymes and perturbations in the scale and/or rate of these transitions are implicated in various serious human diseases; incorporating key flexibilities into engineered enzymes is also considered a major remaining challenge in rational enzyme design. Therefore it is important to understand the underlying mechanism of these transitions. This is a significant challenge to both experimental and computational studies because of the allosteric and multi-scale nature of such transitions. Using our recent studies of two enzyme systems, myosin and adenylate kinase (AK), we discuss how atomistic and coarse-grained simulations can be used to provide insights into the mechanism of activation transitions in realistic systems. Collectively, the results suggest that although many allosteric transitions can be viewed as domain displacements mediated by flexible hinges, there are additional complexities and various deviations. For example, although our studies do not find any evidence for "cracking" in AK, our results do underline the contribution of intra-domain properties (e.g., dihedral flexibility) to the rate of the transition. The study of mechanochemical coupling in myosin highlights that local changes important to chemistry require stabilization from more extensive structural changes; in this sense, more global structural transitions are needed to activate the chemistry in the active site. These discussions further emphasize the importance of better understanding factors that control the degree of co-operativity for allosteric transitions, again hinting at the intimate connection between protein stability and functional flexibility. Finally, a number of topics of considerable future interest are briefly discussed.

Exploring the nature of the translocon-assisted protein insertion

The elucidation of the molecular nature of the translocon-assisted protein insertion is a challenging problem due to the complexity of this process. Furthermore, the limited availability of crucial structural information makes it hard to interpret the hints about the insertion mechanism provided by biochemical studies. At present, it is not practical to explore the insertion process by brute force simulation approaches due to the extremely lengthy process and very complex landscape. Thus, this work uses our previously developed coarse-grained model and explores the energetics of the membrane insertion and translocation paths. The trend in the calculated free-energy profiles is verified by evaluating the correlation between the calculated and observed effect of mutations as well as the effect of inverting the signal peptide that reflects the "positive-inside" rule. Furthermore, the effect of the tentative opening induced by the ribosome is found to reduce the kinetic barrier. Significantly, the trend of the forward and backward energy barriers provides a powerful way to analyze key energetics information. Thus, it is concluded that the insertion process is most likely a nonequilibrium process. Moreover, we provided a general formulation for the analysis of the elusive apparent membrane insertion energy, ΔG(app), and conclude that this important parameter is unlikely to correspond to the free-energy difference between the translocon and membrane. Our formulation seems to resolve the controversy about ΔG(app) for Arg.

Sensing proteins through nanopores: fundamental to applications

Proteins subjected to an electric field and forced to pass through a nanopore induce blockades of ionic current that depend on the protein and nanopore characteristics and interactions between them. Recent advances in the analysis of these blockades have highlighted a variety of phenomena that can be used to study protein translocation and protein folding, to probe single-molecule catalytic reactions in order to obtain kinetic and thermodynamic information, and to detect protein-antibody complexes, proteins with DNA and RNA aptamers, and protein-pore interactions. Nanopore design is now well controlled, allowing the development of future biotechnologies and medicine applications.

RNA under tension: Folding Landscapes, Kinetic partitioning Mechanism, and Molecular Tensegrity

Non-coding RNA sequences play a great role in controlling a number of cellular functions, thus raising the need to understand their complex conformational dynamics in quantitative detail. In this perspective, we first show that single molecule pulling when combined with with theory and simulations can be used to quantitatively explore the folding landscape of nucleic acid hairpins, and riboswitches with tertiary interactions. Applications to riboswitches, which are non-coding RNA elements that control gene expression by undergoing dynamical conformational changes in response to binding of metabolites, lead to an organization principle that assembly of RNA is determined by the stability of isolated helices. We also point out the limitations of single molecule pulling experiments, with molecular extension as the only accessible parameter, in extracting key parameters of the folding landscapes of RNA molecules.

The origin of minus-end directionality and mechanochemistry of Ncd motors

Adaptation of molecular structure to the ligand chemistry and interaction with the cytoskeletal filament are key to understanding the mechanochemistry of molecular motors. Despite the striking structural similarity with kinesin-1, which moves towards plus-end, Ncd motors exhibit minus-end directionality on microtubules (MTs). Here, by employing a structure-based model of protein folding, we show that a simple repositioning of the neck-helix makes the dynamics of Ncd non-processive and minus-end directed as opposed to kinesin-1. Our computational model shows that Ncd in solution can have both symmetric and asymmetric conformations with disparate ADP binding affinity, also revealing that there is a strong correlation between distortion of motor head and decrease in ADP binding affinity in the asymmetric state. The nucleotide (NT) free-ADP (φ-ADP) state bound to MTs favors the symmetric conformation whose coiled-coil stalk points to the plus-end. Upon ATP binding, an enhanced flexibility near the head-neck junction region, which we have identified as the important structural element for directional motility, leads to reorienting the coiled-coil stalk towards the minus-end by stabilizing the asymmetric conformation. The minus-end directionality of the Ncd motor is a remarkable example that demonstrates how motor proteins in the kinesin superfamily diversify their functions by simply rearranging the structural elements peripheral to the catalytic motor head domain.

Proteins belonging to the kinesin superfamily are responsible for vesicle or organelle transport, spindle morphogenesis, and chromosome sorting during cell division. Interestingly, while most proteins in kinesin superfamily that share the common catalytic motor head domain have plus-end directionality along microtubules, kinesin-14 (Ncd) exhibits minus-end directionality. Despite the several circumstantial evidences on the determining factors for the motor directionality in the last decade, a comprehensive understanding of the mechanism governing the Ncd minus-end directionality is still missing. Our studies provide a clear explanation for this minus-end directionality and the associated mechanochemical cycle. Here, we modeled an Ncd motor by employing structural details available in the literature to simulate its conformational dynamics. Simulations using our structure-based model of Ncd assert that the dynamics due to a simple rearrangement of structural elements, peripheral to the catalytic motor domain, is the key player in determining both the directionality and mechanochemistry unique to Ncd motors. Although Ncd has a different directionality, it uses a similar strategy to kinesin-1 of structural adaptation of the catalytic motor domain. Therefore using the same physical principle of protein folding and very similar structural elements, motors in the kinesin superfamily are able to achieve a variety of biological function.

Hybrid molecular mechanics/coarse-grained simulations for structural prediction of G-protein coupled receptor/ligand complexes

Understanding how ligands bind to G-protein coupled receptors (GPCRs) provides insights into a myriad of cell processes and is crucial for drug development. Here we extend a hybrid molecular mechanics/coarse-grained (MM/CG) approach applied previously to enzymes to GPCR/ligand complexes. The accuracy of this method for structural predictions is established by comparison with recent atomistic molecular dynamics simulations on the human β2 adrenergic receptor, a member of the GPCRs superfamily. The results obtained with the MM/CG methodology show a good agreement with previous all-atom classical dynamics simulations, in particular in the structural description of the ligand binding site. This approach could be used for high-throughput predictions of ligand poses in a variety of GPCRs.

Realistic simulations of the coupling between the protomotive force and the mechanical rotation of the F0-ATPase

The molecular origin of the action of the F(0) proton gradient-driven rotor presents a major puzzle despite significant structural advances. Although important conceptual models have provided guidelines of how such systems should work, it has been challenging to generate a structure-based molecular model using physical principles that will consistently lead to the unidirectional proton-driven rotational motion during ATP synthesis. This work uses a coarse-grained (CG) model to simulate the energetics of the F(0)-ATPase system in the combined space defined by the rotational coordinate and the proton transport (PTR) from the periplasmic side (P) to the cytoplasmic side (N). The model establishes the molecular origin of the rotation, showing that this effect is due to asymmetry in the energetics of the proton path rather than only the asymmetry of the interaction of the Asp on the c-ring helices and Arg on the subunit-a. The simulation provides a clear conceptual background for further exploration of the electrostatic basis of proton-driven mechanochemical systems.

Crucial role of dynamic linker histone binding and divalent ions for DNA accessibility and gene regulation revealed by mesoscale modeling of oligonucleosomes

Monte Carlo simulations of a mesoscale model of oligonucleosomes are analyzed to examine the role of dynamic-linker histone (LH) binding/unbinding in high monovalent salt with divalent ions, and to further interpret noted chromatin fiber softening by dynamic LH in monovalent salt conditions. We find that divalent ions produce a fiber stiffening effect that competes with, but does not overshadow, the dramatic softening triggered by dynamic-LH behavior. Indeed, we find that in typical in vivo conditions, dynamic-LH binding/unbinding reduces fiber stiffening dramatically (by a factor of almost 5, as measured by the elasticity modulus) compared with rigidly fixed LH, and also the force needed to initiate chromatin unfolding, making it consistent with those of molecular motors. Our data also show that, during unfolding, divalent ions together with LHs induce linker-DNA bending and DNA–DNA repulsion screening, which guarantee formation of heteromorphic superbeads-on-a-string structures that combine regions of loose and compact fiber independently of the characteristics of the LH–core bond. These structures might be important for gene regulation as they expose regions of the DNA selectively. Dynamic control of LH binding/unbinding, either globally or locally, in the presence of divalent ions, might constitute a mechanism for regulation of gene expression.

Denaturant-dependent folding of GFP

We use molecular simulations using a coarse-grained model to map the folding landscape of Green Fluorescent Protein (GFP), which is extensively used as a marker in cell biology and biotechnology. Thermal and Guanidinium chloride (GdmCl) induced unfolding of a variant of GFP, without the chromophore, occurs in an apparent two-state manner. The calculated midpoint of the equilibrium folding in GdmCl, taken into account using the Molecular Transfer Model (MTM), is in excellent agreement with the experiments. The melting temperatures decrease linearly as the concentrations of GdmCl and urea are increased. The structural features of rarely populated equilibrium intermediates, visible only in free energy profiles projected along a few order parameters, are remarkably similar to those identified in a number of ensemble experiments in GFP with the chromophore. The excellent agreement between simulations and experiments show that the equilibrium intermediates are stabilized by the chromophore. Folding kinetics, upon temperature quench, show that GFP first collapses and populates an ensemble of compact structures. Despite the seeming simplicity of the equilibrium folding, flux to the native state flows through multiple channels and can be described by the kinetic partitioning mechanism. Detailed analysis of the folding trajectories show that both equilibrium and several kinetic intermediates, including misfolded structures, are sampled during folding. Interestingly, the intermediates characterized in the simulations coincide with those identified in single molecule pulling experiments. Our predictions, amenable to experimental tests, show that MTM is a practical way to simulate the effect of denaturants on the folding of large proteins.

Biomolecular dynamics: order-disorder transitions and energy landscapes

While the energy landscape theory of protein folding is now a widely accepted view for understanding how relatively weak molecular interactions lead to rapid and cooperative protein folding, such a framework must be extended to describe the large-scale functional motions observed in molecular machines. In this review, we discuss (1) the development of the energy landscape theory of biomolecular folding, (2) recent advances toward establishing a consistent understanding of folding and function and (3) emerging themes in the functional motions of enzymes, biomolecular motors and other biomolecular machines. Recent theoretical, computational and experimental lines of investigation have provided a very dynamic picture of biomolecular motion. In contrast to earlier ideas, where molecular machines were thought to function similarly to macroscopic machines, with rigid components that move along a few degrees of freedom in a deterministic fashion, biomolecular complexes are only marginally stable. Since the stabilizing contribution of each atomic interaction is on the order of the thermal fluctuations in solution, the rigid body description of molecular function must be revisited. An emerging theme is that functional motions encompass order-disorder transitions and structural flexibility provides significant contributions to the free energy. In this review, we describe the biological importance of order-disorder transitions and discuss the statistical-mechanical foundation of theoretical approaches that can characterize such transitions.

Influence of the shape of crowding particles on the structural transitions in a polymer

We investigate the structural transitions in a polymer induced by spherical and nonspherical crowding particles over a wide range of conditions. The polymer conformations are specified by the radius of gyration and the quality of the solvent in the absence of crowding particles. In the presence of crowding particles, the structures are altered by the volume fraction, size, shape, and polydispersity of the crowders. We show that crowding induces an array of structural changes, ranging from helix, helical hairpin (HH), and multiple helix bundles (HBs), depending on the interplay of multiple length and energy scales including the solvent quality, length of the polymer, temperature, and the characteristics of the crowding agents. In nearly good solvents, the polymer undergoes coil-helix transition in accord with the predictions based on the entropic stabilization mechanism. Higher-order (HH and HB) structures are obtained in poor or moderately poor solvents. In a binary mixture of spherical crowders, the effect of the two components is largely additive with the polymer undergoing greater compaction at higher volume fraction. In contrast to spherical crowders, spherocylinder-like crowders have a dramatically different effect on the diagram of states of the polymer. In the presence of spherocylinders, the polymer prefers to form a nearly ideal helix, especially at low temperatures and high aspect ratios of the crowders, at volume fractions that are not large enough for nematic order. Surprisingly, there is a complete absence of HH and HB in the range of conditions explored here. The dominant formation of spherocylinder-induced helix formation is due to the tendency of the spherocylinders and the polymer to align along the director formed by an increase in nematic order only in the vicinity of the polymer. Our study, which has produced several testable predictions, shows that only by probing the effects of crowding on a polymer (or a protein and RNA) over a wide range of conditions can the diagram of states be quantitatively described.

A physics-based approach of coarse-graining the cytoplasm of Escherichia coli (CGCYTO)

We have investigated protein stability in an environment of Escherichia coli cytoplasm using coarse-grained computer simulations. To coarse-grain a small slide of E. coli's cytoplasm consisting of over 16 million atoms, we have developed a self-assembled clustering algorithm (CGCYTO). CGCYTO uses the shape parameter and asphericity as well as a parameter λ (ranging from 0 to 1) that measures the covolume of a test protein and a macromolecule against the covolume of a test protein and a sphere of equal volume as that of a macromolecule for the criteria of coarse-graining a cytoplasmic model. A cutoff λ(c) = 0.8 was chosen based on the size of a test protein and computational resources and it determined the resolution of a coarse-grained cytoplasm. We compared the results from a polydisperse cytoplasmic model (PD model) produced by CGCYTO with two other coarse-grained hard-sphere cytoplasmic models: 1), F70 model, macromolecules in the cytoplasm were modeled by homogeneous hard spheres with a radius of 55 Å, the size of Ficoll70 and 2), HS model, each macromolecule in the cytoplasm was modeled by a hard sphere of equal volume. It was found that the folding temperature T(f) of a test protein (apoazurin) in a PD model is ~5° greater than that in a F70 model. In addition, the deviation of T(f) in a PD model is twice as much as that in a HS model when an apoazurin is randomly placed at different voids formed by particle fluctuations in PD models.

A structural perspective on the dynamics of kinesin motors

Despite significant fluctuation under thermal noise, biological machines in cells perform their tasks with exquisite precision. Using molecular simulation of a coarse-grained model and theoretical arguments, we envisaged how kinesin, a prototype of biological machines, generates force and regulates its dynamics to sustain persistent motor action. A structure-based model, which can be versatile in adapting its structure to external stresses while maintaining its native fold, was employed to account for several features of kinesin dynamics along the biochemical cycle. This analysis complements our current understandings of kinesin dynamics and connections to experiments. We propose a thermodynamic cycle for kinesin that emphasizes the mechanical and regulatory role of the neck linker and clarify issues related to the motor directionality, and the difference between the external stalling force and the internal tension responsible for the head-head coordination. The comparison between the thermodynamic cycle of kinesin and macroscopic heat engines highlights the importance of structural change as the source of work production in biomolecular machines.

Link between allosteric signal transduction and functional dynamics in a multisubunit enzyme: S-adenosylhomocysteine hydrolase

S-adenosylhomocysteine hydrolase (SAHH), a cellular enzyme that plays a key role in methylation reactions including those required for maturation of viral mRNA, is an important drug target in the discovery of antiviral agents. While targeting the active site is a straightforward strategy of enzyme inhibition, evidence of allosteric modulation of active site in many enzymes underscores the molecular origin of signal transduction. Information of co-evolving sequences in SAHH family and the key residues for functional dynamics that can be identified using native topology of the enzyme provide glimpses into how the allosteric signaling network, dispersed over the molecular structure, coordinates intra- and intersubunit conformational dynamics. To study the link between the allosteric communication and functional dynamics of SAHHs, we performed Brownian dynamics simulations by building a coarse-grained model based on the holo and ligand-bound structures. The simulations of ligand-induced transition revealed that the signal of intrasubunit closure dynamics is transmitted to form intersubunit contacts, which in turn invoke a precise alignment of active site, followed by the dimer-dimer rotation that compacts the whole tetrameric structure. Further analyses of SAHH dynamics associated with ligand binding provided evidence of both induced fit and population shift mechanisms and also showed that the transition-state ensemble is akin to the ligand-bound state. Besides the formation of enzyme-ligand contacts at the active site, the allosteric couplings from the residues distal to the active site are vital to the enzymatic function.