Molecular dynamics simulation of the unfolding of barnase: characterization of the major intermediate

Motif-driven dynamics and intermediates during unfolding of multi-domain BphC enzyme

Understanding the folding mechanisms of multi-domain proteins is crucial for gaining insights into protein folding dynamics. The BphC enzyme, a key player in the degradation of polychlorinated biphenyls consists of eight identical subunits, each containing two domains, with each domain comprising two "βαβββ" motifs. In this study, we employed high-temperature molecular dynamics simulations to systematically analyze the unfolding dynamics of a BphC subunit. Our results reveal that the unfolding process of BphC is a complex, multi-intermediate, and multi-phased event. Notably, we identified a thermodynamically stable partially unfolded intermediate. The unfolding sequences, pathways, and rates of the motifs differ significantly. Motif D unfolds first and most rapidly, while Motif C initiates unfolding before Motifs A and B but completes it slightly later. The unfolding behavior of the motifs strongly influences the domain unfolding, leading to the early initiation of Domain 2 unfolding compared to Domain 1, although at a slower rate. The motifs and domains exhibit both independence and cooperativity during the unfolding process, which we interpret through proposed cascading effects. We hypothesize that the folding mechanism of BphC begins with local folding, which propagates through cooperative interactions across structural hierarchies to achieve the folded state. These findings provide new insights into the folding and unfolding mechanisms of multi-domain proteins.

From covalent transition states in chemistry to noncovalent in biology: from β- to Φ-value analysis of protein folding

Solving the mechanism of a chemical reaction requires determining the structures of all the ground states on the pathway and the elusive transition states linking them. 2024 is the centenary of Brønsted's landmark paper that introduced the β-value and structure-activity studies as the only experimental means to infer the structures of transition states. It involves making systematic small changes in the covalent structure of the reactants and analysing changes in activation and equilibrium-free energies. Protein engineering was introduced for an analogous procedure, Φ-value analysis, to analyse the noncovalent interactions in proteins central to biological chemistry. The methodology was developed first by analysing noncovalent interactions in transition states in enzyme catalysis. The mature procedure was then applied to study transition states in the pathway of protein folding - 'part (b) of the protein folding problem'. This review describes the development of Φ-value analysis of transition states and compares and contrasts the interpretation of β- and Φ-values and their limitations. Φ-analysis afforded the first description of transition states in protein folding at the level of individual residues. It revealed the nucleation-condensation folding mechanism of protein domains with the transition state as an expanded, distorted native structure, containing little fully formed secondary structure but many weak tertiary interactions. A spectrum of transition states with various degrees of structural polarisation was then uncovered that spanned from nucleation-condensation to the framework mechanism of fully formed secondary structure. Φ-analysis revealed how movement of the expanded transition state on an energy landscape accommodates the transition from framework to nucleation-condensation mechanisms with a malleability of structure as a unifying feature of folding mechanisms. Such movement follows the rubric of analysis of classical covalent chemical mechanisms that began with Brønsted. Φ-values are used to benchmark computer simulation, and Φ and simulation combine to describe folding pathways at atomic resolution.

Conserved patterns and interactions in the unfolding transition state across SH3 domain structural homologues

Proteins with similar structures are generally assumed to arise from similar sequences. However, there are more cases than not where this is not true. The dogma is that sequence determines structure; how, then, can very different sequences fold to the same structure? Here, we employ high temperature unfolding simulations to probe the pathways and specific interactions that direct the folding and unfolding of the SH3 domain. The SH3 metafold in the Dynameomics Database consists of 753 proteins with the same structure, but varied sequences and functions. To investigate the relationship between sequence and structure, we selected 17 targets from the SH3 metafold with high sequence variability. Six unfolding simulations were performed for each target, transition states were identified, revealing two general folding/unfolding pathways at the transition state. Transition states were also expressed as mathematical graphs of connected chemical nodes, and it was found that three positions within the structure, independent of sequence, were consistently more connected within the graph than any other nearby positions in the sequence. These positions represent a hub connecting different portions of the structure. Multiple sequence alignment and covariation analyses also revealed certain positions that were more conserved due to packing constraints and stabilizing long-range contacts. This study demonstrates that members of the SH3 domain with different sequences can unfold through two main pathways, but certain characteristics are conserved regardless of the sequence or unfolding pathway. While sequence determines structure, we show that disparate sequences can provide similar interactions that influence folding and lead to similar structures.

Edge Strand Dissociation and Conformational Changes in Transthyretin under Amyloidogenic Conditions

During amyloidogenesis, proteins undergo conformational changes that allow them to aggregate and assemble into insoluble, fibrillar structures. Soluble oligomers that form during this process typically contain 2-24 monomeric subunits and are cytotoxic. Before the formation of these soluble oligomers, monomeric species first adopt aggregation-competent conformations. Knowledge of the structures of these intermediate states is invaluable to the development of molecular strategies to arrest pathological amyloid aggregation. However, the highly dynamic and interconverting nature of amyloidogenic species limits biophysical characterization of their structures during amyloidogenesis. Here, we use molecular dynamics simulations to probe conformations sampled by monomeric transthyretin under amyloidogenic conditions. We show that certain β-strands in transthyretin tend to unfold and sample nonnative conformations and that the edge strands in one β-sheet (the DAGH sheet) are particularly susceptible to conformational changes in the monomeric state. We also find that changes in the tertiary structure of transthyretin can be associated with disruptions to the secondary structure. We evaluated the conformations produced by molecular dynamics by calculating how well molecular-dynamics-derived structures reproduced NMR-derived interatomic distances. Finally, we leverage our computational results to produce experimentally testable hypotheses that may aid experimental explorations of pathological conformations of transthyretin.

Visualizing Protein Folding and Unfolding

Protein folding/unfolding is a complicated process that defies high-resolution characterization by experimental methods. As an alternative, atomistic molecular dynamics simulations are now routinely employed to elucidate and magnify the accompanying conformational changes and the role of solvent in the folding process. However, the level of detail necessary to map the process at high spatial-temporal resolution provides an overwhelming amount of data. As more and better tools are developed for analysis of these large data sets and validation of the simulations, one is still left with the problem of visualizing the results in ways that provide insight into the folding/unfolding process. While viewing and interrogating static crystal structures has become commonplace, more and different approaches are required for dynamic, interconverting, unfolding, and refolding proteins. Here we review a variety of approaches, ranging from straightforward to complex and unintuitive for multiscale analysis and visualization of protein folding and unfolding.

Validating Molecular Dynamics Simulations against Experimental Observables in Light of Underlying Conformational Ensembles

Far from the static, idealized conformations deposited into structural databases, proteins are highly dynamic molecules that undergo conformational changes on temporal and spatial scales that may span several orders of magnitude. These conformational changes, often intimately connected to the functional roles that proteins play, may be obscured by traditional biophysical techniques. Over the past 40 years, molecular dynamics (MD) simulations have complemented these techniques by providing the "hidden" atomistic details that underlie protein dynamics. However, there are limitations of the degree to which molecular simulations accurately and quantitatively describe protein motions. Here we show that although four molecular dynamics simulation packages (AMBER, GROMACS, NAMD, and ilmm) reproduced a variety of experimental observables for two different proteins (engrailed homeodomain and RNase H) equally well overall at room temperature, there were subtle differences in the underlying conformational distributions and the extent of conformational sampling obtained. This leads to ambiguity about which results are correct, as experiment cannot always provide the necessary detailed information to distinguish between the underlying conformational ensembles. However, the results with different packages diverged more when considering larger amplitude motion, for example, the thermal unfolding process and conformational states sampled, with some packages failing to allow the protein to unfold at high temperature or providing results at odds with experiment. While most differences between MD simulations performed with different packages are attributed to the force fields themselves, there are many other factors that influence the outcome, including the water model, algorithms that constrain motion, how atomic interactions are handled, and the simulation ensemble employed. Here four different MD packages were tested each using best practices as established by the developers, utilizing three different protein force fields and three different water models. Differences between the simulated protein behavior using two different packages but the same force field, as well as two different packages with different force fields but the same water models and approaches to restraining motion, show how other factors can influence the behavior, and it is incorrect to place all the blame for deviations and errors on force fields or to expect improvements in force fields alone to solve such problems.

Mechanical Folding and Unfolding of Protein Barnase at the Single-Molecule Level

The unfolding and folding of protein barnase has been extensively investigated in bulk conditions under the effect of denaturant and temperature. These experiments provided information about structural and kinetic features of both the native and the unfolded states of the protein, and debates about the possible existence of an intermediate state in the folding pathway have arisen. Here, we investigate the folding/unfolding reaction of protein barnase under the action of mechanical force at the single-molecule level using optical tweezers. We measure unfolding and folding force-dependent kinetic rates from pulling and passive experiments, respectively, and using Kramers-based theories (e.g., Bell-Evans and Dudko-Hummer-Szabo models), we extract the position of the transition state and the height of the kinetic barrier mediating unfolding and folding transitions, finding good agreement with previous bulk measurements. Measurements of the force-dependent kinetic barrier using the continuous effective barrier analysis show that protein barnase verifies the Leffler-Hammond postulate under applied force and allow us to extract its free energy of folding, ΔG0. The estimated value of ΔG0 is in agreement with our predictions obtained using fluctuation relations and previous bulk studies. To address the possible existence of an intermediate state on the folding pathway, we measure the power spectrum of force fluctuations at high temporal resolution (50 kHz) when the protein is either folded or unfolded and, additionally, we study the folding transition-path time at different forces. The finite bandwidth of our experimental setup sets the lifetime of potential intermediate states upon barnase folding/unfolding in the submillisecond timescale.

Identification of putative unfolding intermediates of the mutant His-107-tyr of human carbonic anhydrase II in a multidimensional property space

In this article, we develop an extensive search procedure of the multi-dimensional folding energy landscape of a protein. Our aim is to identify different classes of structures that have different aggregation propensities and catalytic activity. Following earlier studies by Daggett et al. [Jong, D. D.; Riley, R.: Alonso, D.O.: Dagett, V. J. Mol. Biol. 2002, 319, 229], a series of high temperature all-atom classical molecular simulation studies has been carried out to derive a multi-dimensional property space. Dynamical changes in these properties are then monitored by projecting them along a one-dimensional reaction coordinate, dmean . We have focused on the application of this method to partition a wide array of conformations of wild type human carbonic anhydrase II (HCA II) and its unstable mutant His-107-Tyr along dmean by sampling a 35-dimensional property space. The resultant partitioning not only reveals the distribution of conformations corresponding to stable structures of HCA II and its mutant, but also allows the monitoring of several partially unfolded and less stable conformations of the mutant. We have investigated the population of these conformations at different stages of unfolding and collected separate sets of structures that are widely separated in the property space. The dynamical diversity of these sets are examined in terms of the loading of their respective first principal component. The partially unfolded structures thus collected are qualitatively mapped on to the experimentally postulated light molten globule (MGL) and molten globule (MG) intermediates with distinct aggregation propensities and catalytic activities. Proteins 2016; 84:726-743. © 2016 Wiley Periodicals, Inc.

Protein unfolding from free-energy calculations: integration of the Gaussian network model with bond binding energies

Motivated by single molecule experiments, we study thermal unfolding pathways of four proteins, chymotrypsin inhibitor, barnase, ubiquitin, and adenylate kinase, using bond network models that combine bond energies and elasticity. The protein elasticity is described by the Gaussian network model (GNM), to which we add prescribed bond binding energies that are assigned to all (nonbackbone) connecting bonds in the GNM of native state and assumed identical for simplicity. Using exact calculation of the Helmholtz free energy for this model, we consider bond rupture single events. The bond designated for rupture is chosen by minimizing the free-energy difference for the process, over all (nonbackbone) bonds in the network. Plotting the free-energy profile along this pathway at different temperatures, we observe a few major partial unfolding, metastable or stable, states, that are separated by free-energy barriers and change role as the temperature is raised. In particular, for adenylate kinase we find three major partial unfolding states, which is consistent with single molecule FRET experiments [Pirchi et al., Nat. Commun. 2, 493 (2011)] for which hidden Markov analysis reveals between three and five such states. Such states can play a major role in enzymatic activity.

Structure-affinity properties of a high-affinity ligand of FKBP12 studied by molecular simulations of a binding intermediate

With a view to explaining the structure-affinity properties of the ligands of the protein FKBP12, we characterized a binding intermediate state between this protein and a high-affinity ligand. Indeed, the nature and extent of the intermolecular contacts developed in such a species may play a role on its stability and, hence, on the overall association rate. To find the binding intermediate, a molecular simulation protocol was used to unbind the ligand by gradually decreasing the biasing forces introduced. The intermediate was subsequently refined with 17 independent stochastic boundary molecular dynamics simulations that provide a consistent picture of the intermediate state. In this state, the core region of the ligand remains stable, notably because of the two anchoring oxygen atoms that correspond to recurrent motifs found in all FKBP12 ligand core structures. Besides, the non-core regions participate in numerous transient intermolecular and intramolecular contacts. The dynamic aspect of most of the contacts seems important both for the ligand to retain at least a part of its configurational entropy and for avoiding a trapped state along the binding pathway. Since the transient and anchoring contacts contribute to increasing the stability of the intermediate, as a corollary, the dissociation rate constant of this intermediate should be decreased, resulting in an increase of the affinity constant . The present results support our previous conclusions and provide a coherent rationale for explaining the prevalence in high-affinity ligands of (i) the two oxygen atoms found in carbonyl or sulfonyl groups of dissimilar core structures and of (ii) symmetric or pseudo-symmetric mobile groups of atoms found as non-core moieties. Another interesting aspect of the intermediate is the distortion of the flexible 80 s loop of the protein, mainly in its tip region, that promotes the accessibility to the bound state.

Early steps in thermal unfolding of superoxide dismutase 1 are similar to the conformational changes associated with the ALS-associated A4V mutation

There are over 100 mutations in Cu/Zn superoxide dismutase (SOD1) that result in a subset of familial amyotrophic lateral sclerosis (fALS) cases. The hypothesis that dissociation of the dimer, misfolding of the monomer and subsequent aggregation of mutant SOD1 leads to fALS has been gaining support as an explanation for how these disparate missense mutations cause the same disease. These forms are only responsible for a fraction of the ALS cases; however, the rest are sporadic. Starting with a folded apo monomer, the species considered most likely to be involved in misfolding, we used high-temperature all-atom molecular dynamics simulations to explore the events of the wild-type protein unfolding through the denatured state. All simulations showed early loss of structure along the β5-β6 edge of the β-sandwich, supporting earlier findings of instability in this region. Transition state structures identified from the simulations are in good agreement with experiment, providing detailed, validated molecular models for this elusive state. Furthermore, we compare the process of thermal unfolding investigated here to that of the lethal A4V mutant-induced unfolding at physiological temperature and find that the pathways are very similar.

Cooperativity in thermal and force-induced protein unfolding: integration of crack propagation and network elasticity models

We investigate force-induced and temperature-induced unfolding of proteins using the combination of a gaussian network model and a crack propagation model based on "bond"-breaking independent events. We assume the existence of threshold values for the mean strain and strain fluctuations that dictate bond rupture. Surprisingly, we find that this stepwise process usually leads to a few cooperative, first-order-like, transitions in which several bonds break simultaneously, reminiscent of the "avalanches" seen in disordered networks.

Protein high-force pulling simulations yield low-force results

All-atom explicit-solvent molecular dynamics simulations are used to pull with extremely large constant force (750–3000 pN) on three small proteins. The introduction of a nondimensional timescale permits direct comparison of unfolding across all forces. A crossover force of approximately 1100 pN divides unfolding dynamics into two regimes. At higher forces, residues sequentially unfold from the pulling end while maintaining the remainder of the protein force-free. Measurements of hydrodynamic viscous stresses are made easy by the high speeds of unfolding. Using an exact low-Reynolds-number scaling, these measurements can be extrapolated to provide, for the first time, an estimate of the hydrodynamic force on low-force unfolding. Below 1100 pN, but surprisingly still at extremely large applied force, intermediate states and cooperative unfoldings as seen at much lower forces are observed. The force-insensitive persistence of these structures indicates that decomposition into unfolded fragments requires a large fluctuation. This finding suggests how proteins are constructed to resist transient high force. The progression of helix and sheet unfolding is also found to be insensitive to force. The force-insensitivity of key aspects of unfolding opens the possibility that numerical simulations can be accelerated by high applied force while still maintaining critical features of unfolding.

Efficient Construction of Mesostate Networks from Molecular Dynamics Trajectories

The coarse-graining of data from molecular simulations yields conformational space networks that may be used for predicting the system's long time scale behavior, to discover structural pathways connecting free energy basins in the system, or simply to represent accessible phase space regions of interest and their connectivities in a two-dimensional plot. In this contribution, we present a tree-based algorithm to partition conformations of biomolecules into sets of similar microstates, i.e., to coarse-grain trajectory data into mesostates. On account of utilizing an architecture similar to that of established tree-based algorithms, the proposed scheme operates in near-linear time with data set size. We derive expressions needed for the fast evaluation of mesostate properties and distances when employing typical choices for measures of similarity between microstates. Using both a pedagogically useful and a real-word application, the algorithm is shown to be robust with respect to tree height, which in addition to mesostate threshold size is the main adjustable parameter. It is demonstrated that the derived mesostate networks can preserve information regarding the free energy basins and barriers by which the system is characterized.

Protein folding pathways and state transitions described by classical equations of motion of an elastic network model

Protein topology defined by the matrix of residue contacts has proved to be a fruitful basis for the study of protein dynamics. The widely implemented coarse-grained elastic network model of backbone fluctuations has been used to describe crystallographic temperature factors, allosteric couplings, and some aspects of the folding pathway. In the present study, we develop a model of protein dynamics based on the classical equations of motion of a damped network model (DNM) that describes the folding path from a completely unfolded state to the native conformation through a single-well potential derived purely from the native conformation. The kinetic energy gained through the collapse of the protein chain is dissipated through a friction term in the equations of motion that models the water bath. This approach is completely general and sufficiently fast that it can be applied to large proteins. Folding pathways for various proteins of different classes are described and shown to correlate with experimental observations and molecular dynamics and Monte Carlo simulations. Allosteric transitions between alternative protein structures are also modeled within the DNM through an asymmetric double-well potential.

The folding transition-state ensemble of a four-helix bundle protein: helix propensity as a determinant and macromolecular crowding as a probe

The four-helix bundle protein Rd-apocyt b(562), a redesigned stable variant of apocytochrome b(562), exhibits two-state folding kinetics. Its transition-state ensemble has been characterized by Phi-value analysis. To elucidate the molecular basis of the transition-state ensemble, we have carried out high-temperature molecular dynamics simulations of the unfolding process. In six parallel simulations, unfolding started with the melting of helix I and the C-terminal half of helix IV, and followed by helix III, the N-terminal half of helix IV and helix II. This ordered melting of the helices is consistent with the conclusion from native-state hydrogen exchange, and can be rationalized by differences in intrinsic helix propensity. Guided by experimental Phi-values, a putative transition-state ensemble was extracted from the simulations. The residue helical probabilities of this transition-state ensemble show good correlation with the Phi-values. To further validate the putative transition-state ensemble, the effect of macromolecular crowding on the relative stability between the unfolded ensemble and the transition-state ensemble was calculated. The resulting effect of crowding on the folding kinetics agrees well with experimental observations. This study shows that molecular dynamics simulations combined with calculation of crowding effects provide an avenue for characterize the transition-state ensemble in atomic details.

A comprehensive multidimensional-embedded, one-dimensional reaction coordinate for protein unfolding/folding

The goal of the Dynameomics project is to perform, store, and analyze molecular dynamics simulations of representative proteins, of all known globular folds, in their native state and along their unfolding pathways. To analyze unfolding simulations, the location of the protein along the unfolding reaction coordinate (RXN) must be determined. Properties such as the fraction of native contacts and radius of gyration are often used; however, there is an issue regarding degeneracy with these properties, as native and nonnative species can overlap. Here, we used 15 physical properties of the protein to construct a multidimensional-embedded, one-dimensional RXN coordinate that faithfully captures the complex nature of unfolding. The unfolding RXN coordinates for 188 proteins (1534 simulations and 22.9 mus in explicit water) were calculated. Native, transition, intermediate, and denatured states were readily identified with the use of this RXN coordinate. A global native ensemble based on the native-state properties of the 188 proteins was created. This ensemble was shown to be effective for calculating RXN coordinates for folds outside the initial 188 targets. These RXN coordinates enable, high-throughput assignment of conformational states, which represents an important step in comparing protein properties across fold space as well as characterizing the unfolding of individual proteins.

Effect of interdomain linker length on an antagonistic folding-unfolding equilibrium between two protein domains

Fusion of one protein domain with another is a common event in both evolution and protein engineering experiments. When insertion is at an internal site (e.g., a surface loop or turn), as opposed to one of the termini, conformational strain can be introduced into both domains. Strain is manifested by an antagonistic folding-unfolding equilibrium between the two domains, which we previously showed can be parameterized by a coupling free-energy term (DeltaG(X)). The extent of strain is predicted to depend primarily on the ratio of the N-to-C distance of the guest protein to the distance between ends of the surface loop in the host protein. Here, we test that hypothesis by inserting ubiquitin (Ub) into the bacterial ribonuclease barnase (Bn), using peptide linkers from zero to 10 amino acids each. DeltaG(X) values are determined by measuring the extent to which Co(2+) binding to an engineered site on the Ub domain destabilizes the Bn domain. All-atom, unforced Langevin dynamics simulations are employed to gain structural insight into the mechanism of mechanically induced unfolding. Experimental and computational results find that the two domains are structurally and energetically uncoupled when linkers are long and that DeltaG(X) increases with decreasing linker length. When the linkers are fewer than two amino acids, strain is so great that one domain unfolds the other. However, the protein is able to refold as dimers and higher-order oligomers. The likely mechanism is a three-dimensional domain swap of the Bn domain, which relieves conformational strain. The simulations suggest that an effective route to mechanical unfolding begins with disruption of the hydrophobic core of Bn near the Ub insertion site.

Molecular simulations of peptides: a useful tool for the development of new drugs and for the study of molecular recognition

The study of the molecular recognition and self-organization properties of peptides has emerged in recent years as a very active and diverse field of research, ranging from biomedicine to biotechnology and even to material sciences. In the case of biomedicine, peptides can be used as ligands of biological receptors to gain insights into the structural, dynamical, and chemical determinants underlying the formation of complexes and identify new effectors of biological processes of interest. In the case of biotechnology and material science, short sequences have been used to understand the sequence determinants of the formation of ordered supra-molecular structures of nanoscale dimensions. In this work, we will describe our research activities in these two areas of modern chemical biology. In the first part, we will describe the development of a new, specific, potent, and selective anticancer peptide and its use to obtain the information needed to identify a non-peptidic small molecular lead to be used as an inhibitor of cancer growth. In the second part, we will describe the introduction of a new method for the description of the self-organization process at the basis of the growth of ordered supra-molecular structures held together by weak, non-covalent, yet specific interactions.

Microscopic reversibility of protein folding in molecular dynamics simulations of the engrailed homeodomain

The principle of microscopic reversibility states that at equilibrium the number of molecules entering a state by a given path must equal those exiting the state via the same path under identical conditions or, in structural terms, that the conformations along the two pathways are the same. There has been some indirect evidence indicating that protein folding is such a process, but there have been few conclusive findings. In this study, we performed molecular dynamics simulations of an ultrafast unfolding and folding protein at its melting temperature to observe, on an atom-by-atom basis, the pathways the protein followed as it unfolded and folded within a continuous trajectory. In a total of 0.67 micros of simulation in water, we found six transient denaturing events near the melting temperature (323 and 330 K) and an additional refolding event following a previously identified unfolding event at a high temperature (373 K). In each case, unfolding and refolding transition state ensembles were identified, and they agreed well with experiment on the basis of a comparison of S and Phi values. On the basis of several structural properties, these 13 transition state ensembles agreed very well with each other and with four previously identified transition states from high-temperature denaturing simulations. Thus, not only were the unfolding and refolding transition states part of the same ensemble, but in five of the seven cases, the pathway the protein took as it unfolded was nearly identical to the subsequent refolding pathway. These events provide compelling evidence that protein folding is a microscopically reversible process. In the other two cases, the folding and unfolding transition states were remarkably similar to each other but the paths deviated.

Protein unfolding behavior studied by elastic network model

Experimental and theoretical studies have showed that the native-state topology conceals a wealth of information about protein folding/unfolding. In this study, a method based on the Gaussian network model (GNM) is developed to study some properties of protein unfolding and explore the role of topology in protein unfolding process. The GNM has been successful in predicting atomic fluctuations around an energy minimum. However, in the GNM, the normal mode description is linear and cannot be accurate in studying protein folding/unfolding, which has many local minima in the energy landscape. To describe the nonlinearity of the conformational changes during protein unfolding, a method based on the iterative use of normal mode calculation is proposed. The protein unfolding process is mimicked through breaking the native contacts between the residues one by one according to the fluctuations of the distance between them. With this approach, the unfolding processes of two proteins, CI2 and barnase, are simulated. It is found that the sequence of protein unfolding events revealed by this method is consistent with that obtained from thermal unfolding by molecular dynamics and Monte Carlo simulations. The results indicate that this method is effective in studying protein unfolding. In this method, only the native contacts are considered, which implies that the native topology may play an important role in the protein unfolding process. The simulation results also show that the unfolding pathway is robust against the introduction of some noise, or stochastic characters. Furthermore, several conformations selected from the unfolding process are studied to show that the denatured state does not behave as a random coil, but seems to have highly cooperative motions, which may help and promote the polypeptide chain to fold into the native state correctly and speedily.

Characterization of protein-folding pathways by reduced-space modeling

Ab initio simulations of the folding pathways are currently limited to very small proteins. For larger proteins, some approximations or simplifications in protein models need to be introduced. Protein folding and unfolding are among the basic processes in the cell and are very difficult to characterize in detail by experiment or simulation. Chymotrypsin inhibitor 2 (CI2) and barnase are probably the best characterized experimentally in this respect. For these model systems, initial folding stages were simulated by using CA-CB-side chain (CABS), a reduced-space protein-modeling tool. CABS employs knowledge-based potentials that proved to be very successful in protein structure prediction. With the use of isothermal Monte Carlo (MC) dynamics, initiation sites with a residual structure and weak tertiary interactions were identified. Such structures are essential for the initiation of the folding process through a sequential reduction of the protein conformational space, overcoming the Levinthal paradox in this manner. Furthermore, nucleation sites that initiate a tertiary interactions network were located. The MC simulations correspond perfectly to the results of experimental and theoretical research and bring insights into CI2 folding mechanism: unambiguous sequence of folding events was reported as well as cooperative substructures compatible with those obtained in recent molecular dynamics unfolding studies. The correspondence between the simulation and experiment shows that knowledge-based potentials are not only useful in protein structure predictions but are also capable of reproducing the folding pathways. Thus, the results of this work significantly extend the applicability range of reduced models in the theoretical study of proteins.

Comparative unfolding studies of psychrophilic and mesophilic uracil DNA glycosylase: MD simulations show reduced thermal stability of the cold-adapted enzyme

Uracil DNA glycosylase (UDG) is a DNA repair enzyme involved in the base excision repair (BER) pathway, removing misincorporated uracil from the DNA strand. The native and mutant forms of Atlantic cod and human UDG have previously been characterized in terms of kinetic and thermodynamic properties as well as the determination of several crystal structures. This data shows that the cold-adapted enzyme is more catalytically efficient but at the same time less resistant to heat compared to its warm-active counterpart. In this study, the structure-function relationship is further explored by means of comparative molecular dynamics (MD) simulations at three different temperatures (375, 400 and 425K) to gain a deeper insight into the structural features responsible for the reduced thermostability of the cold-active enzyme. The simulations show that there are distinct structural differences in the unfolding pathway between the two homologues, particularly evident in the N- and C-terminals. Distortion of the mesophilic enzyme is initiated simultaneously in the N- and C-terminal, while the C-terminal part plays a key role for the stability of the psychrophilic enzyme. The simulations also show that at certain temperatures the cold-adapted enzyme unfolds faster than the warm-active homologues in accordance with the lower thermal stability found experimentally.

Retention of local conformational compactness in unfolding of barnase; Contribution of end-to-end interactions within quasi-modules

To understand how protein reduces the conformational space to be searched for the native structure, it is crucial to characterize ensembles of conformations on the way of folding processes, in particular ensembles of relatively long-range structures connecting between an extensively unfolded state and a state with a native-like overall chain topology. To analyze such intermediate conformations, we performed multiple unfolding molecular dynamics simulations of barnase at 498K. Some short-range structures such as part of helix and turn were well sustained while most of the secondary structures and the hydrophobic cores were eventually lost, which is consistent with the results by other experimental and computational studies. The most important novel findings were persistence of long-range relatively compact substructures, which was captured by exploiting the concept of module. Module is originally introduced to describe the hierarchical structure of a globular protein in the native state. Modules are conceptually such relatively compact substructures that are resulted from partitioning the native structure of a globular protein completely into several contiguous segments with the least extended conformations. We applied this concept of module to detect a possible hierarchical structure of each snapshot structure in unfolding processes as well. Along with this conceptual extension, such detected relatively compact substructures are named quasi-modules. We found almost perfect persistence of quasi-module boundaries that are positioned close to the native module boundaries throughout the unfolding trajectories. Relatively compact conformations of the quasi-modules seemed to be retained mainly by hydrophobic interactions formed between residues located at both terminal regions within each module. From these results, we propose a hypothesis that hierarchical folding with the early formation of quasi-modules effectively reduces search space for the native structure.

Identification and characterization of protein folding intermediates

In order to understand the mechanism by which a polypeptide chain folds into its functionally active native state it is necessary to characterize in detail all the species accumulated along the pathway. The elusive nature of protein folding intermediates poses their identification and characterization as an extremely difficult task in the protein folding field. In the case of small single domain proteins, the direct measurement of the thermodynamics and structural parameters of protein folding intermediates has provided new insights on the nature of the forces involved in the stabilization of nascent protein structures. Here we summarize some of the experimental approaches aimed at the detection and characterization of folding intermediates along with a discussion of some general structural features emerging from these studies.

Structural Analysis of Human Lysozyme Using Molecular Dynamics Simulations

In this study, various molecular dynamics simulations were conducted to investigate the effects of ethanol and temperature on the conformational changes of human lysozyme, which may lead insights into amyloidosis. The analyses of some important structural characteristics, such as backbone root-mean-square deviation, secondary structural stability, radius of gyration, accessible surface area, and hydrophobic contact of the hydrophobic core all show that ethanol tends to destabilize human lysozyme at high temperatures. It can be attributed to that higher temperatures result in the destruction of the native structure of this protein, leading to the exposure of the interior hydrophobic core. At this stage, ethanol plays a role to destroy this region by forming hydrophobic interactions between protein and solvent due to its lower polarity comparing to water. Such newly formed intermolecular interactions accelerate the unfolding of this protein, starting from the core between the alpha- and beta-domains. Our results are in good agreement with the previous hypothesis suggesting that the distortion of the hydrophobic core at the alpha- and beta-interface putatively results in the formation of the initial "seed" for amyloid fibril. Although the present results cannot directly be linked to fibril formation, they still provide valuable insights into amyloidosis of human lysozyme.

The role of plastic beta-hairpin and weak hydrophobic core in the stability and unfolding of a full sequence design protein

In this study, the thermal stability of a designed alpha/beta protein FSD (full sequence design) was studied by explicit solvent simulations at three moderate temperatures, 273 K, 300 K, and 330 K. The average properties of the ten trajectories at each temperature were analyzed. The thermal unfolding, as judged by backbone root-mean-square deviation and percentage of native contacts, was displayed with increased sampling outside of the native basin as the temperature was raised. The positional fluctuation of the hairpin residues was significantly higher than that of the helix residues at all three temperatures. The hairpin segment displayed certain plasticity even at 273 K. Apart from the terminal residues, the highest fluctuation was shown in the turn residues 7-9. Secondary structure analysis manifested the structural heterogeneity of the hairpin segment. It was also revealed by the simulation that the hydrophobic core was vulnerable to thermal denaturation. Consistent with the experiment, the I7Y mutation in the double mutant FSD-EY (FSD with mutations Q1E and I7Y) dramatically increased the protein stability in the simulation, suggesting that the plasticity of the hairpin can be partially compensated by a stronger hydrophobic core. As for the unfolding pathway, the breathing of the hydrophobic core and the separation of the two secondary structure elements (alpha helix and beta hairpin) was the initiation step of the unfolding. The loss of global contacts from the separation further destabilized the hairpin structure and also led to the unwinding of the helix.

Molecular simulations of cotranslational protein folding: fragment stabilities, folding cooperativity, and trapping in the ribosome

Although molecular simulation methods have yielded valuable insights into mechanistic aspects of protein refolding in vitro, they have up to now not been used to model the folding of proteins as they are actually synthesized by the ribosome. To address this issue, we report here simulation studies of three model proteins: chymotrypsin inhibitor 2 (CI2), barnase, and Semliki forest virus protein (SFVP), and directly compare their folding during ribosome-mediated synthesis with their refolding from random, denatured conformations. To calibrate the methodology, simulations are first compared with in vitro data on the folding stabilities of N-terminal fragments of CI2 and barnase; the simulations reproduce the fact that both the stability and thermal folding cooperativity increase as fragments increase in length. Coupled simulations of synthesis and folding for the same two proteins are then described, showing that both fold essentially post-translationally, with mechanisms effectively identical to those for refolding. In both cases, confinement of the nascent polypeptide chain within the ribosome tunnel does not appear to promote significant formation of native structure during synthesis; there are however clear indications that the formation of structure within the nascent chain is sensitive to location within the ribosome tunnel, being subject to both gain and loss as the chain lengthens. Interestingly, simulations in which CI2 is artificially stabilized show a pronounced tendency to become trapped within the tunnel in partially folded conformations: non-cooperative folding, therefore, appears in the simulations to exert a detrimental effect on the rate at which fully folded conformations are formed. Finally, simulations of the two-domain protease module of SFVP, which experimentally folds cotranslationally, indicate that for multi-domain proteins, ribosome-mediated folding may follow different pathways from those taken during refolding. Taken together, these studies provide a first step toward developing more realistic methods for simulating protein folding as it occurs in vivo.

Similarity and difference in the unfolding of thermophilic and mesophilic cold shock proteins studied by molecular dynamics simulations

Molecular dynamics simulations were performed to unfold a homologous pair of thermophilic and mesophilic cold shock proteins at high temperatures. The two proteins differ in just 11 of 66 residues and have very similar structures with a closed five-stranded antiparallel beta-barrel. A long flexible loop connects the N-terminal side of the barrel, formed by three strands (beta1-beta3), with the C-terminal side, formed by two strands (beta4-beta5). The two proteins were found to follow the same unfolding pathway, but with the thermophilic protein showing much slower unfolding. Unfolding started with the melting of C-terminal strands, leading to exposure of the hydrophobic core. Subsequent melting of beta3 and the beta-hairpin formed by the first two strands then resulted in unfolding of the whole protein. The slower unfolding of the thermophilic protein could be attributed to ion pair formation of Arg-3 with Glu-46, Glu-21, and the C-terminal. These ion pairs were also found to be important for the difference in folding stability between the pair of proteins. Thus electrostatic interactions appear to play similar roles in the difference in folding stability and kinetics between the pair of proteins.

Molecular simulations of cotranslational protein folding: fragment stabilities, folding cooperativity, and trapping in the ribosome

Although molecular simulation methods have yielded valuable insights into mechanistic aspects of protein refolding in vitro, they have up to now not been used to model the folding of proteins as they are actually synthesized by the ribosome. To address this issue, we report here simulation studies of three model proteins: chymotrypsin inhibitor 2 (CI2), barnase, and Semliki forest virus protein (SFVP), and directly compare their folding during ribosome-mediated synthesis with their refolding from random, denatured conformations. To calibrate the methodology, simulations are first compared with in vitro data on the folding stabilities of N-terminal fragments of CI2 and barnase; the simulations reproduce the fact that both the stability and thermal folding cooperativity increase as fragments increase in length. Coupled simulations of synthesis and folding for the same two proteins are then described, showing that both fold essentially post-translationally, with mechanisms effectively identical to those for refolding. In both cases, confinement of the nascent polypeptide chain within the ribosome tunnel does not appear to promote significant formation of native structure during synthesis; there are however clear indications that the formation of structure within the nascent chain is sensitive to location within the ribosome tunnel, being subject to both gain and loss as the chain lengthens. Interestingly, simulations in which CI2 is artificially stabilized show a pronounced tendency to become trapped within the tunnel in partially folded conformations: non-cooperative folding, therefore, appears in the simulations to exert a detrimental effect on the rate at which fully folded conformations are formed. Finally, simulations of the two-domain protease module of SFVP, which experimentally folds cotranslationally, indicate that for multi-domain proteins, ribosome-mediated folding may follow different pathways from those taken during refolding. Taken together, these studies provide a first step toward developing more realistic methods for simulating protein folding as it occurs in vivo.

A detailed unfolding pathway of a (beta/alpha)8-barrel protein as studied by molecular dynamics simulations

The (beta/alpha)(8)-barrel is the most common protein fold. Similar structural properties for folding intermediates of (beta/alpha)(8)-barrel proteins involved in tryptophan biosynthesis have been reported in a number of experimental studies; these intermediates have the last two beta-strands and three alpha-helices partially unfolded, with other regions of the polypeptide chain native-like in conformation. To investigate the detailed folding/unfolding pathways of these (beta/alpha)(8)-barrel proteins, temperature-induced unfolding simulations of N-(5'-phosphoribosyl)anthranilate isomerase from Escherichia coli were carried out using a special-purpose parallel computer system. Unfolding simulations at five different temperatures showed a sequential unfolding pathway comprised of several events. Early events in unfolding involved disruption of the last two strands and three helices, producing an intermediate ensemble similar to those detected in experimental studies. Then, denaturation of the first two betaalpha units and separation of the sixth strand from the fifth took place independently. The remaining central betaalphabetaalphabeta module persisted the longest during all simulations, suggesting an important role for this module as the incipient folding scaffold. Our simulations also predicted the presence of a nucleation site, onto which several hydrophobic residues condensed forming the foundation for the central betaalphabetaalphabeta module.

Thermal unfolding simulations of a multimeric protein--transition state and unfolding pathways

The folding of an oligomeric protein poses an extra challenge to the folding problem because the protein not only has to fold correctly; it has to avoid nonproductive aggregation. We have carried out over 100 molecular dynamics simulations using an implicit solvation model at different temperatures to study the unfolding of one of the smallest known tetramers, p53 tetramerization domain (p53tet). We found that unfolding started with disruption of the native tetrameric hydrophobic core. The transition state for the tetramer to dimer transition was characterized as a diverse ensemble of different structures using Phi value analysis in quantitative agreement with experimental data. Despite the diversity, the ensemble was still native-like with common features such as partially exposed tetramer hydrophobic core and shifts in the dimer-dimer arrangements. After passing the transition state, the secondary and tertiary structures continued to unfold until the primary dimers broke free. The free dimer had little secondary structure left and the final free monomers were random-coil like. Both the transition states and the unfolding pathways from these trajectories were very diverse, in agreement with the new view of protein folding. The multiple simulations showed that the folding of p53tet is a mixture of the framework and nucleation-condensation mechanisms and the folding is coupled to the complex formation. We have also calculated the entropy and effective energy for the different states along the unfolding pathway and found that the tetramerization is stabilized by hydrophobic interactions.

Comparative all-atomic study of unfolding pathways for proteins chymotrypsin inhibitor 2 and barnase

The features of transition states and intermediates are important in the study on protein folding. However, transition states and intermediates could not be obviously identified from trajectories obtained by dynamic simulations. In this work, a different method to identify and characterize the transition states and intermediates by combining the root mean square deviation of C(alpha) atoms and the similarity factor Q to the native state is proposed. The unfolding processes based on all-atomic simulations for proteins chymotrypsin inhibitor 2 and barnase are studied, and the related transition states and intermediates are identified by observing an unfolding factor U = 1-F. Comparisons between the conformational cluster analysis and experimental results are also made. The various analyses on the unfolding behaviors indicate that our method can well define the transition states and intermediates, and the factor U (or F) can be used as a reaction coordinate of the folding and unfolding process. It is also found that three-state folding proteins might experience more complicated pathways and have more rugged energy landscapes than two-state folding proteins.

Barnase thermal titration via molecular dynamics simulations: Detection of early denaturation sites

The thermal stability of barnase has been studied using constant pressure and temperature (CPT) molecular dynamics at different temperatures. Barnase X-ray coordinates were obtained from the Research Collaboratory for Structural Bioinformatics (RCSB) Protein Data Bank (PDB code:1rnb). Simulations were performed at 285, 295, 300, 335, 345, and 395 K in explicit water under periodic boundary conditions for 280 ps. For each simulation, conformations were saved every 0.2 ps. Root mean square deviation (RMSD) values were calculated relative to the starting structure at 300 K and at time t = 0. Root mean square fluctuation (RMSF) values were calculated relative to the average structure obtained from the 300K simulation. Both root mean square deviation and fluctuation analysis indicated the presence of discrete regions of hyper-sensitivity along the barnase polypeptide chain. These regions exhibited spikes in flexibility prior to any global structural changes. The specific changes in barnase backbone flexibility are accompanied by increased phi/psi angle fluctuations. These results suggest the presence of early denaturation sites or denaturation nuclei whose local structure is disrupted prior to global structure disruption. Identification of denaturation nuclei suggests that appropriate amino acid replacements at these sites may lead to the design and development of more stable barnase mutants. This strategy of identifying denaturation nuclei in protein structures may represent a first step in the design of more stable protein structures.

Symmetric connectivity of secondary structure elements enhances the diversity of folding pathways

The influence of native connectivity of secondary structure elements (SSE) on folding is studied using coarse-grained models of proteins with mixed alpha and beta structure and the analysis of the structural database of wild-type proteins. We found that the distribution of SSE along a sequence determines the diversity of folding pathways. If alpha and beta SSE are localized in different parts of a sequence, the diversity of folding pathways is restricted. An even (symmetric) distribution of alpha and beta SSE with respect to sequence midpoint favors multiple folding routes. Simulations are supplemented by the database analysis of the distribution of SSE in wild-type protein sequences. On an average, two-thirds of wild-type proteins with mixed alpha and beta structure have symmetric distribution of alpha and beta SSE. The propensity for symmetric distribution of SSE is especially evident for large proteins with the number of SSE > or = 10. We suggest that symmetric SSE distribution in protein sequences may arise due to nearly random allocation of alpha and beta structure along wild-type sequences. The tendency of long sequences to misfold is perhaps compensated by the enhanced pathway diversity. In addition, folding pathways are shown to progress via hierarchic assembly of SSE in accordance with their proximity along a sequence. We demonstrate that under mild denaturation conditions folding and unfolding pathways are similar. However, the reversibility of folding/unfolding pathways is shown to depend on the distribution of SSE. If alpha and beta SSE are localized in different parts of a sequence, folding and unfolding pathways are likely to coincide.

Repetitive pulling catalyzes co-translocational unfolding of barnase during import through a mitochondrial pore

We present a computational study of barnase unfolding during import into mitochondria through a model translocon. In contrast to thermal (or chemical) unfolding, the major intermediates of co-translocational unfolding are mainly mediated by non-native interactions accompanying the protein configurations induced by pulling forces. These energy contributions, combined with backbone topological constraints imposed by the model pore, result in milestones along the unfolding pathways which are significantly different not only from those experienced during thermal (or chemical) denaturation, but also from those observed in single-molecule pulling by both ends without pore constraints. Two on-pathway major translocation intermediates trapped in long-lived states by significantly high unfolding barriers are identified. A fraction of these pathways can, however, skip such local kinetic traps and result in extremely fast translocations, leading to a dramatic kinetic partitioning spanning approximately four orders of magnitude. The fraction of fast translocation events is shown to increase upon switching the pull off and on, when compared to pulling at constant force. This suggests a "catalytic" mechanism by which the mitochondrial import machinery regulates this partitioning by repetitively pulling in cycles. A number of mutation sites that alter the kinetic "flow" of the unfolding trajectories are suggested and tested.

Determination of the folding transition states of barnase by using PhiI-value-restrained simulations validated by double mutant PhiIJ-values

The protein barnase folds from the denatured state into its native conformation via a high-energy intermediate. Using PhiI-values determined experimentally from single-point mutations as restraints in all-atom molecular dynamics simulations, we have determined ensembles of structures corresponding to the transition states for the formation of the folding intermediate and its conversion into the native state. We have also introduced a stringent validation of the approach used to calculate such structures by predicting interaction PhiIJ-values determined experimentally from a series of double-mutant cycles. The ensembles that we have obtained illustrate the heterogeneity in the nucleation-condensation process by which barnase folds. Obligatory steps of this process include the sequential formation of two folding nuclei, which correspond to the two main hydrophobic cores of the protein. Nonobligatory steps include the elongation of the strand beta1 and the formation of the helix alpha2. The results confirm that the use of experimental observables such as PhiI-values as restraints in molecular dynamics simulations is a powerful general strategy to characterize the relatively heterogeneous structural ensembles that populate nonnative regions of the energy landscapes of proteins.

Simulation and experiment conspire to reveal cryptic intermediates and a slide from the nucleation-condensation to framework mechanism of folding

There is a change from three-state to two-state kinetics of folding across the homeodomain superfamily of proteins as the mechanism slides from framework to nucleation-condensation. The tendency for framework folding in this family correlates with inherent helical propensity. The cellular myeloblastis protein (c-Myb) falls in the mechanistic transition region. An earlier, preliminary report of protein engineering experiments and molecular dynamics simulations (MD) showed that the folding mechanism for this protein has aspects of both the nucleation-condensation and framework models. In the more in-depth analysis of the MD trajectories presented here, we find that folding may be attributed to both of these mechanisms in different regions of the protein. The folding of the loop, middle helix, and turn is best described by nucleation-condensation, whereas folding of the N and C-terminal helices may be described by the framework model. Experimentally, c-Myb folds by apparent two-state kinetics, but the MD simulations predict that the kinetics hide a high-energy intermediate. We stabilized this hypothetical folding intermediate by deleting a residue (P174) in the loop between its second and third helices, and the mutant intermediate is long-lived in the simulations. Equilibrium and kinetic experiments demonstrate that folding of the DeltaP174 mutant is indeed three-state. The presence and shape of the intermediate observed in the simulations were confirmed by small angle X-ray scattering experiments.

How well can simulation predict protein folding kinetics and thermodynamics?

Simulation of protein folding has come a long way in five years. Notably, new quantitative comparisons with experiments for small, rapidly folding proteins have become possible. As the only way to validate simulation methodology, this achievement marks a significant advance. Here, we detail these recent achievements and ask whether simulations have indeed rendered quantitative predictions in several areas, including protein folding kinetics, thermodynamics, and physics-based methods for structure prediction. We conclude by looking to the future of such comparisons between simulations and experiments.

The Structure of the Major Transition State for Folding of an FF Domain from Experiment and Simulation

We have analysed the transition state of folding of the four-helix FF domain from HYPA/FBP11 by high-resolution experiment and simulation as part of a continuing effort to understand the principles of folding and the refinement of predictive methods. The major transition state for folding was subjected to a Phi-value analysis utilising 50 mutants. The transition state contained a nucleus for folding centred around the end of helix 1 (H1) and the beginning of helix 2 (H2). Secondary structure in this region was fully formed (PhiF=0.9-1) and tertiary interactions were well developed. Interactions in the distal part of the native structure were weak (PhiF=0-0.2). The hydrophobic core and other parts of the protein displayed intermediate Phi-values, suggesting that interactions coalesce as the end of H1 and beginning of H2 are in the process of being formed. The distribution of Phi-values resembled that of barnase, which folds via an intermediate, rather than that of CI2 which folds by a concerted nucleation-condensation mechanism. The overall picture of the transition state structure identified in molecular dynamics simulations is in qualitative agreement, with the turn connecting H1 and H2 being formed, a loosened core, and H4 partially unfolded and detached from the core. There are some differences in the details and interpretation of specific Phi-values.