Folding with downhill behavior and low cooperativity of proteins

Understanding the Folding Mediated Assembly of the Bacteriophage MS2 Coat Protein Dimers

The capsids of RNA viruses such as MS2 are great models for studying protein self-assembly because they are made almost entirely of multiple copies of a single coat protein (CP). Although CP is the minimal repeating unit of the capsid, previous studies have shown that CP exists as a homodimer (CP2) even in an acid-disassembled system, indicating that CP2 is an obligate dimer. Here, we investigate the molecular basis of this obligate dimerization using coarse-grained structure-based models and molecular dynamics simulations. We find that, unlike monomeric proteins of similar size, CP populates a single partially folded ensemble whose "foldedness" is sensitive to denaturing conditions. In contrast, CP2 folds similarly to single-domain proteins populating only the folded and the unfolded ensembles, separated by a prominent folding free energy barrier. Several intramonomer contacts form early, but the CP2 folding barrier is crossed only when the intermonomer contacts are made. A dissection of the structure of CP2 through mutant folding simulations shows that the folding barrier arises both from the topology of CP and the interface contacts of CP2. Together, our results show that CP2 is an obligate dimer because of kinetic stability, that is, dimerization induces a folding barrier and that makes it difficult for proteins in the dimer minimum to partially unfold and access the monomeric state without completely unfolding. We discuss the advantages of this obligate dimerization in the context of dimer design and virus stability.

EspcTM: Kinetic Transition Network Based on Trajectory Mapping in Effective Energy Rescaling Space

The transition network provides a key to reveal the thermodynamic and kinetic properties of biomolecular systems. In this paper, we introduce a new method, named effective energy rescaling space trajectory mapping (EspcTM), to detect metastable states and construct transition networks based on the simulation trajectories of the complex biomolecular system. It mapped simulation trajectories into an orthogonal function space, whose bases were rescaled by effective energy, and clustered the interrelation between these trajectories to locate metastable states. By using the EspcTM method, we identified the metastable states and elucidated interstate transition kinetics of a Brownian particle and a dodecapeptide. It was found that the scaling parameters of effective energy also provided a clue to the dominating factors in dynamics. We believe that the EspcTM method is a useful tool for the studies of dynamics of the complex system and may provide new insight into the understanding of thermodynamics and kinetics of biomolecular systems.

Unfolding Transitions of Peripheral Subunit Binding Domains Show Cooperative Behavior

Characterization of native, intermediate, and denatured states is crucial for understanding the factors influencing the stability of proteins. We have carried out molecular dynamics simulations to study the unfolding of three peripheral subunit binding domains (PSBDs): E. coli BBL, Bacillus stearothermophilus E3BD, and human hbSBD, at three different temperatures: 300, 330, and 400 K, and in the presence of two solvents: water and 5 M guanidinium hydrochloride (GndCl) solution. These proteins share similar folds, with two parallel helices, maintained via a hydrophobic core comprising residues from their interconnecting loop. BBL is more sensitive to thermal and chemical denaturation in comparison to hbSBD, and E3BD is the most stable of all of the three proteins. The effect of temperature on the stability of these proteins is more pronounced in "water-only" simulations compared to that in the presence of guanidium hydrochloride in high concentrations. Our results show cooperative unfolding transitions of these proteins, which are triggered by an initial melting of the C-terminal helix H2. The consequent loss of interhelical interactions or native contacts, as observed, leads to the subsequent melting of the N-terminal helix H1.

pH-Dependent cooperativity and existence of a dry molten globule in the folding of a miniprotein BBL

Solution pH plays an important role in protein dynamics, stability, and folding; however, detailed mechanisms remain poorly understood. Here we use continuous constant pH molecular dynamics in explicit solvent with pH replica exchange to describe the pH profile of the folding cooperativity of a miniprotein BBL, which has drawn intense debate in the past. Our data reconciled the two opposing hypotheses (downhill vs. two-state) and uncovered a sparsely populated unfolding intermediate. As pH is lowered from 7 to 5, the folding barrier vanishes. As pH continues to decrease, the unfolding barrier lowers and denaturation is triggered by the protonation of Asp162, consistent with experimental evidence. Interestingly, unfolding proceeded via an intermediate, with intact secondary structure and a compact, unlocked hydrophobic core shielded from solvent, lending support to the recent hypothesis of a universal dry molten globule in protein folding. Our work demonstrates that constant pH molecular dynamics is a unique tool for testing this and other hypotheses to advance the knowledge in protein dynamics, stability, and folding.

Roles of conformational disorder and downhill folding in modulating protein-DNA recognition

Transcription factors are thought to efficiently search for their target DNA site via a combination of conventional 3D diffusion and 1D diffusion along the DNA molecule mediated by non-specific electrostatic interactions. This process requires the DNA-binding protein to quickly exchange between a search competent and a target recognition mode, but little is known as to how these two binding modes are encoded in the conformational properties of the protein. Here, we investigate this issue on the engrailed homeodomain (EngHD), a DNA-binding domain that folds ultrafast and exhibits a complex conformational behavior consistent with the downhill folding scenario. We explore the interplay between folding and DNA recognition using a coarse-grained computational model that allows us to manipulate the folding properties of the protein and monitor its non-specific and specific binding to DNA. We find that conformational disorder increases the search efficiency of EngHD by promoting a fast gliding search mode in addition to sliding. When gliding, EngHD remains loosely bound to DNA moving linearly along its length. A partially disordered EngHD also binds more dynamically to the target site, reducing the half-life of the specific complex via a spring-loaded mechanism. These findings apply to all conditions leading to partial disorder. However, we also find that at physiologically relevant temperatures EngHD is well folded and can only obtain the conformational flexibility required to accelerate 1D diffusion when it folds/unfolds within the downhill scenario (crossing a marginal free energy barrier). In addition, the conformational flexibility of native downhill EngHD enables its fast reconfiguration to lock into the specific binding site upon arrival, thereby affording finer control of the on- and off-rates of the specific complex. Our results provide key mechanistic insights into how DNA-binding domains optimize specific DNA recognition through the control of their conformational dynamics and folding mechanism.

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

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

Native state dynamics affects the folding transition of porcine pancreatic phospholipase A2

Porcine pancreatic phospholipase A2, a small and disulfide rich protein, is extremely resistant against chemically or thermally induced unfolding. Despite this marked resistance, the protein displays broad unfolding transitions resulting in comparatively low apparent thermodynamic stability. Broad unfolding transitions may result from undetected folding intermediates, residual structures in the unfolded state or an inhomogeneity of the native state. Using circular dichroism, fluorescence, and NMR spectroscopy, we ruled out the existence of stably populated folding intermediates, whereas UV absorbance measurements hinted at stable residual structures in the unfolded state. These residual structures proved, however, to have no impact on the folding parameters. Studies by limited proteolysis, CD, and NMR spectroscopy under non-denaturing conditions suggested pronounced dynamics of the protein in the native state, which as long as unrestrained by acidic pH or bound Ca(2+) ions exert considerable influence on the unfolding transition.

Modularity in protein structures: study on all-alpha proteins

Modularity is known as one of the most important features of protein's robust and efficient design. The architecture and topology of proteins play a vital role by providing necessary robust scaffolds to support organism's growth and survival in constant evolutionary pressure. These complex biomolecules can be represented by several layers of modular architecture, but it is pivotal to understand and explore the smallest biologically relevant structural component. In the present study, we have developed a component-based method, using protein's secondary structures and their arrangements (i.e. patterns) in order to investigate its structural space. Our result on all-alpha protein shows that the known structural space is highly populated with limited set of structural patterns. We have also noticed that these frequently observed structural patterns are present as modules or "building blocks" in large proteins (i.e. higher secondary structure content). From structural descriptor analysis, observed patterns are found to be within similar deviation; however, frequent patterns are found to be distinctly occurring in diverse functions e.g. in enzymatic classes and reactions. In this study, we are introducing a simple approach to explore protein structural space using combinatorial- and graph-based geometry methods, which can be used to describe modularity in protein structures. Moreover, analysis indicates that protein function seems to be the driving force that shapes the known structure space.

COMPARING FOLDING MECHANISMS OF DIFFERENT PRION PROTEINS BY Gō MODEL

Prions are associated with neurodegenerative diseases induced by transmissible spongiform encephalopathies. The infectious scrapie form is referred to as PrP Sc , which has conformational change from normal prion with predominant α-helical conformation to the abnormal PrP Sc that is rich in β-sheet content. Neurodegenerative diseases have been found from both human and bovine sources, but there are no reports about infected by transmissible spongiform encephalopathies from rabbit, canine and horse sources. Here we used coarse-grained Gō model to compare the difference among human, bovine, rabbit, canine, and horse normal (cellular) prion proteins. The denatured state of normal prion has relation with the conversion from normal to abnormal prion protein, so we used all-atom Gō model to investigate the folding pathway and energy landscape for human prion protein. Through using coarse-grained Gō model, the cooperativity of the five prion proteins was characterized in terms of calorimetric criterion, sigmoidal transition, and free-energy profile. The rabbit and horse prion proteins have higher folding free-energy barrier and cooperativity, and canine prion protein has slightly higher folding free-energy barrier comparing with human and bovine prion proteins. The results from all-atom Gō model confirmed the validity of C α-Gō model. The correlations of our results with previous experimental and theoretical researches were discussed.

Designing cooperativity into the designed protein Top7

The topology of the designed protein Top7 is not found in natural proteins. Top7 shows signatures of non-cooperative folding in both experimental studies and computer simulations. In particular, molecular dynamics of coarse-grained structure-based models of Top7 show a well-populated C-terminal folding-intermediate. Since most similarly sized globular proteins are cooperative folders, the non-natural topology of Top7 has been suggested as a reason for its non-cooperative folding. Here, we computationally examine the folding of Top7 with the intent of making it cooperative. We find that its folding cooperativity can be increased in two ways: (a) Optimization of packing interactions in the N-terminal half of the protein enables further folding of the C-terminal intermediate. (b) Reduction in the packing density of the C-terminal region destabilizes the intermediate. In practice, these strategies are implemented in our Top7 model through modifications to the contact-map. These modifications do not alter the topology of Top7 but result in cooperative folding. Amino-acid mutations that mimic these modifications also lead to a significant increase in folding cooperativity. Finally, we devise a method to randomize the sizes of amino-acids within the same topology, and confirm that the structure of Top7 makes its folding sensitive to packing interactions. In contrast, the ribosomal protein S6, which has secondary structure similar to Top7, has folding which is much less sensitive to packing perturbations. Thus, it should be possible to make a sequence fold cooperatively to the structure of Top7, but to do so its side-chain packing needs to be carefully designed.

Exact partition function zeros of the Wako-Saitô-Muñoz-Eaton protein model

I compute exact partition function zeros of the Wako-Saitô-Muñoz-Eaton model for various secondary structural elements and for two proteins, 1BBL and 1I6C, by using both analytic and numerical methods. Two-state and barrierless downhill folding transitions can be distinguished by a gap in the distribution of zeros at the positive real axis.

Using VIPT-jump to distinguish between different folding mechanisms: application to BBL and a Trpzip

Protein folding involves a large number of sequential molecular steps or conformational substates. Thus, experimental characterization of the underlying folding energy landscape for any given protein is difficult. Herein, we present a new method that can be used to determine the major characteristics of the folding energy landscape in question, e.g., to distinguish between activated and barrierless downhill folding scenarios. This method is based on the idea that the conformational relaxation kinetics of different folding mechanisms at a given final condition will show different dependences on the initial condition. We show, using both simulation and experiment, that it is possible to differentiate between disparate kinetic folding models by comparing temperature jump (T-jump) relaxation traces obtained with a fixed final temperature and varied initial temperatures, which effectively varies the initial potential (VIP) of the system of interest. We apply this method (hereafter refer to as VIPT-jump) to two model systems, tryptophan zipper (Trpzip)-2c and BBL, and our results show that BBL exhibits characteristics of barrierless downhill folding, whereas Trpzip-2c folding encounters a free energy barrier. In addition, using the T-jump data of BBL we are able to provide, via Langevin dynamics simulations, a realistic estimate of its conformational diffusion coefficient.

Is it possible to stabilize a thermophilic protein further using sequences and structures of mesophilic proteins: a theoretical case study concerning DgAS

Incorporating structural elements of thermostable homologs can greatly improve the thermostability of a mesophilic protein. Despite the effectiveness of this method, applying it is often hampered. First, it requires alignment of the target mesophilic protein sequence with those of thermophilic homologs, but not every mesophilic protein has a thermophilic homolog. Second, not all favorable features of a thermophilic protein can be incorporated into the structure of a mesophilic protein. Furthermore, even the most stable native protein is not sufficiently stable for industrial applications. Therefore, creating an industrially applicable protein on the basis of the thermophilic protein could prove advantageous. Amylosucrase (AS) can catalyze the synthesis of an amylose-like polysaccharide composed of only α-1,4-linkages using sucrose as the lone energy source. However, industrial development of AS has been hampered owing to its low thermostability. To facilitate potential industrial applications, the aim of the current study was to improve the thermostability of Deinococcus geothermalis amylosucrase (DgAS) further; this is the most stable AS discovered to date. By integrating ideas from mesophilic AS with well-established protein design protocols, three useful design protocols are proposed, and several promising substitutions were identified using these protocols. The successful application of this hybrid design method indicates that it is possible to stabilize a thermostable protein further by incorporating structural elements of less-stable homologs.

Folding and association of a homotetrameric protein complex in an all-atom Go model

The 84-residue homotetrameric BBAT1 is one of the smallest stable protein complexes and therefore is a good test system to study the self-assembly of multimeric proteins. We have researched for this protein the interplay between the folding of monomers and their assembly into tetramers. Replica exchange molecular dynamics simulations relying on a Go model are compared with earlier simulations that use the physics-based coarse-grained UNRES model.

Modeling Structural Flexibility of Proteins with Go-Models

Structure-based models are an efficient tool for folding studies of proteins since by construction their energy landscape is only minimal frustrated. However, their intrinsic drawback is a lack of structural flexibility as usually only one target structure is employed to construct the potentials. Hence, a Go-model may not capture differences in mutation-induced protein dynamics, if - as in the case of the disease-related A629P mutant of the Menkes protein ATP7A - the structural differences between mutant and wild type are small. In this work, we introduced three implementations of Go-models that take into account the flexibility of proteins in the NMR ensemble. Comparing the wild type and the mutant A629P of the 75-residue large 6th domain Menkes protein, we find that these new Go-potentials lead to broader distributions than Go-models relying on a single member of the NMR-ensemble. This allows us to detect the transient unfolding of a loosely formed β1β4-sheet in the mutant protein. Our results are consistent with previous simulations using physical force field and an explicit solvent, and suggests a mechanism by which these mutations cause Menkes disease. In addition, the improved Go-models suggest differences in the folding pathway between wild type and mutant, an observation that was not accessible to simulations of this 75-residue protein with a physical all-atom force field and explicit solvent.

Configuration-dependent diffusion dynamics of downhill and two-state protein folding

Configuration-dependent diffusion (CDD) is important for protein folding kinetics with small thermodynamic barriers. CDD can be even more crucial in downhill folding without thermodynamic barriers. We explored the CDD of a downhill protein (BBL), and a two-state protein (CI2). The hidden kinetic barriers due to CDD were revealed. The increased ~1 k(B)T kinetic barrier is in line with experimental value based on other fast folding proteins. Compared to that of CI2, the effective free-energy profile of BBL is found to be significantly influenced by CDD, and the kinetics are totally determined by diffusion. These findings are consistent with both earlier bulk and single-molecule fluorescence measurements. In addition, we found the temperature dependence of CDD. We also found that the ratio of folding transition temperature against optimal kinetic folding temperature can provide both a quantitative measure for the underlying landscape topography and an indicator for the possible appearance of downhill folding. Our study can help for a better understanding of the role of diffusion in protein folding dynamics.

Tertiary DNA structure in the single-stranded hTERT promoter fragment unfolds and refolds by parallel pathways via cooperative or sequential events

The discovery of G-quadruplexes and other DNA secondary elements has increased the structural diversity of DNA well beyond the ubiquitous double helix. However, it remains to be determined whether tertiary interactions can take place in a DNA complex that contains more than one secondary structure. Using a new data analysis strategy that exploits the hysteresis region between the mechanical unfolding and refolding traces obtained by a laser-tweezers instrument, we now provide the first convincing kinetic and thermodynamic evidence that a higher order interaction takes place between a hairpin and a G-quadruplex in a single-stranded DNA fragment that is found in the promoter region of human telomerase. During the hierarchical unfolding or refolding of the DNA complex, a 15-nucleotide hairpin serves as a common species among three intermediates. Moreover, either a mutant that prevents this hairpin formation or the addition of a DNA fragment complementary to the hairpin destroys the cooperative kinetic events by removing the tertiary interaction mediated by the hairpin. The coexistence of the sequential and the cooperative refolding events provides direct evidence for a unifying kinetic partition mechanism previously observed only in large proteins and complex RNA structures. Not only does this result rationalize the current controversial observations for the long-range interaction in complex single-stranded DNA structures, but also this unexpected complexity in a promoter element provides additional justification for the biological function of these structures in cells.

Observation of two families of folding pathways of BBL

BBL is an independent folding domain of a large multienzyme complex, 2-oxoglutarate dehydrogenase. The folding mechanism of BBL is under debate between the views of noncooperative downhill-type and classical two-state. Extensive replica exchange molecular dynamics simulations of BBL in explicit solvent have shown some non-two-state behaviors despite no definitive evidence of downhill folding. In this work, we postprocess the replica exchange data using our roadmap-based MaxFlux reaction path algorithm to reveal atomically detailed folding pathways. A connected graph is used to organize and visualize the folding pathways initiated from random coils. High structural and transition heterogeneity is seen in the early stage of folding. Two main parallel folding pathways emerge in the later stage; one path shows that tertiary contact and helix formation develop at different stages of folding, whereas the other path exhibits concurrence of secondary and tertiary structure formation to some extent. Because the native state of BBL is sensitive to experimental conditions, we speculate that the relative predominance of the two pathways may vary with the protein construct and solvent conditions, possibly leading to the seeming discrepancy of experimental results. Our roadmap-based reaction path algorithm is a general tool to extract path information from replica exchange.

The native ensemble and folding of a protein molten-globule: functional consequence of downhill folding

The continually emerging functional significance of intrinsic disorder and conformational flexibility in proteins has challenged the long-standing dogma of a well-defined structure contributing to a specific function. Molten-globular states, a class of proteins with significant secondary-structure but a fluid hydrophobic core, is one such example. They have however been difficult to characterize due to the complexity of experimental data and lack of computational avenues. Here, we dissect the folding mechanism of the α-helical molten-globular protein NCBD from three fundamentally different approaches: statistical-mechanical variable barrier model, C(α)-based Gō-model and explicit water all-atom molecular dynamics (MD) simulations. We find that NCBD displays the characteristics of a one-state globally downhill folder but is significantly destabilized. Using simulation techniques, we generate a highly constrained but a heterogeneous native ensemble of the molten-globule for the first time that is consistent with experimental data including small angle X-ray scattering (SAXS), circular dichroism (CD), and nuclear magnetic resonance (NMR). The resulting native ensemble populates conformations reported in other bound-forms providing direct evidence to the mechanism of conformational selection for binding multiple partners in this domain. Importantly, our simulations reveal a connection between downhill folding and large conformational flexibility in this domain that has been evolutionarily selected and functionally exploited resulting in large binding promiscuity. Finally, the multimodel approach we employ here serves as a powerful methodology to study mechanisms and suggests that the thermodynamic features of molten-globules fall within the array of folding mechanisms available to small single-domain proteins.

Unifying model for two-state and downhill protein folding

A protein-folding model is proposed at the amino acid level, in which the folding process is divided into two successive stages: the rate-determining step, dominated by the "stochastic interactions"of solvent molecules, and the rapid phase, dominated by the "order interactions"among atoms in polypeptide. The master equation approach is used to investigate the folding kinetics, and an analytical treatment of the master equation yields a simple three-parameter expression for folding time. It is found that both two-state and downhill protein-folding kinetics can be described by a unifying model.

Navigating the downhill protein folding regime via structural homologues

Proteins that fold over free-energy barriers <or= 3RT are classified as downhill folders. This regime is characterized by equilibrium unfolding that is proportionally broader and more complex the lower the folding barrier. Downhill proteins are also expected to fold up in a few microseconds. However, the relationship between rate and equilibrium signatures is affected by other factors such as protein size and folding topology. Here we perform a direct comparison of the kinetics and equilibrium unfolding of two structural homologues: BBL and PDD. BBL folds-unfolds in just approximately 1 micros at 335 K and displays the equilibrium signatures expected for a protein at the bottom of the downhill folding regime. PDD, which has the same 3D structure and size, folds-unfolds approximately 8 times more slowly and, concomitantly, exhibits all the downhill equilibrium signatures to a lesser degree. Our results demonstrate that the equilibrium signatures of downhill folding are proportional to the changes in folding rate once structural and size-scaling effects are factored out. This conclusion has two important implications: (1) it confirms that the quantitative analysis of equilibrium experiments in ultrafast folding proteins does provide direct information about free-energy barriers, a result that is incompatible with the conventional view of protein folding as a highly activated process, and (2) it advocates for equilibrium-kinetic studies of homologous proteins as a powerful tool to navigate the downhill folding regime via comparative analysis. The latter should prove extremely useful for the investigation of sequence, functional, and evolutionary determinants of protein folding barriers.

Evidence, from simulations, of a single state with residual native structure at the thermal denaturation midpoint of a small globular protein

The folding of the B-domain of staphylococcal protein A has been studied by coarse-grained canonical and multiplexed replica-exchange molecular dynamics simulations with the UNRES force field in a broad range of temperatures (270 K < or = T < or = 350 K). In canonical simulations, the folding was found to occur either directly to the native state or through kinetic traps, mainly the topological mirror image of the native three-helix bundle. The latter folding scenario was observed more frequently at low temperatures. With increase of temperature, the frequency of the transitions between the folded and misfolded/unfolded states increased and the folded state became more diffuse with conformations exhibiting increased root-mean-square deviations from the experimental structure (from about 4 A at T = 300 K to 8.7 A at T = 325 K). An analysis of the equilibrium conformational ensemble determined from multiplexed replica exchange simulations at the folding-transition temperature (T(f) = 325 K) showed that the conformational ensemble at this temperature is a collection of conformations with residual secondary structures, which possess native or near-native clusters of nonpolar residues in place, and not a 50-50% mixture of fully folded and fully unfolded conformations. These findings contradict the quasi-chemical picture of two- or multistate protein folding, which assumes an equilibrium between the folded, unfolded, and intermediate states, with equilibrium shifting with temperature but with the native conformations remaining essentially unchanged. Our results also suggest that long-range hydrophobic contacts are the essential factor to keep the structure of a protein thermally stable.

Multiscale methods for protein folding simulations

Inherently hierarchic nature of proteins makes multiscale computational methods especially useful in the studies of folding and other functional dynamics. With the multiscale strategies, one can achieve improved accuracy and efficiency by coupling the atomistic and the coarse grained simulations. Depending on the problems studied, very different implementation protocols can be used to realize the multiscale idea. Here, we give detailed introductions to the currently used multiscale protocols, together with some recent applications to the protein folding simulations in our group. The advantages and weakness, as well as the application scopes of these multiscale protocols are discussed. The directions for the future developments are also proposed.

Effect of solvation-related interaction on the low-temperature dynamics of proteins

The effect of solvation-related interaction on the low-temperature dynamics of proteins is studied by taking into account the desolvation barriers in the interactions of native contacts. It is found out that about the folding transition temperature, the protein folds in a cooperative manner, and the water molecules are expelled from the hydrophobic core at the final stage in the folding process. At low temperature, however, the protein would generally be trapped in many metastable conformations with some water molecules frozen inside the protein. The desolvation takes an important role in these processes. The number of frozen water molecules and that of frozen states of proteins are further analyzed with the methods based on principal component analysis (PCA) and the clustering of conformations. It is found out that both the numbers of frozen water molecules and the frozen states of the protein increase quickly below a certain temperature. Especially, the number of frozen states of the protein increases exponentially following the decrease in the temperature, which resembles the basic features of glassy dynamics. Interestingly, it is observed that the freezing of water molecules and that of protein conformations happen at almost the same temperature. This suggests that the solvation-related interaction performs an important role for the low-temperature dynamics of the model protein.

Competition between native topology and nonnative interactions in simple and complex folding kinetics of natural and designed proteins

We compared folding properties of designed protein Top7 and natural protein S6 by using coarse-grained chain models with a mainly native-centric construct that accounted also for nonnative hydrophobic interactions and desolvation barriers. Top7 and S6 have similar secondary structure elements and are approximately equal in length and hydrophobic composition. Yet their experimental folding kinetics were drastically different. Consistent with experiment, our simulated folding chevron arm for Top7 exhibited a severe rollover, whereas that for S6 was essentially linear, and Top7 model kinetic relaxation was multiphasic under strongly folding conditions. The peculiar behavior of Top7 was associated with several classes of kinetic traps in our model. Significantly, the amino acid residues participating in nonnative interactions in trapped conformations in our Top7 model overlapped with those deduced experimentally. These affirmations suggest that the simple ingredients of native topology plus sequence-dependent nonnative interactions are sufficient to account for some key features of protein folding kinetics. Notably, when nonnative interactions were absent in the model, Top7 chevron rollover was not correctly predicted. In contrast, nonnative interactions had little effect on the quasi linearity of the model folding chevron arm for S6. This intriguing distinction indicates that folding cooperativity is governed by a subtle interplay between the sequence-dependent driving forces for native topology and the locations of favorable nonnative interactions entailed by the same sequence. Constructed with a capability to mimic this interplay, our simple modeling approach should be useful in general for assessing a designed sequence's potential to fold cooperatively.

Understanding protein folding cooperativity based on topological consideration

The folding cooperativity is an important issue of protein folding dynamics. Since the native topology plays a significant role in determining the folding behavior of proteins, we believe that it also has close relationship with the folding cooperativity. In the present work, we perform simulations on proteins Naf-BBL, QNND-BBL, CI2, and SH3 with the Gō model and compare their different folding behaviors. By analyzing the weak cooperative folding of protein Naf-BBL in detail, we found that the folding of Naf-BBL shows relatively weak thermodynamic coupling between residues, and such weak coupling is found mainly between the nonlocal native contacts. This finding complements our understandings on the source of barrierless folding of Naf-BBL and promotes us to analyze the topological origins of the poor thermodynamic coupling of Naf-BBL. Then, we further extend our analysis to other two-state and multistate proteins. Based on the considerations of the thermodynamic coupling and kinetic coupling, we conclude that the fraction of scattered native contacts, the difference in loop entropy of contacts, and the long range relative contact order are the major topological factors that influence the folding cooperativity. The combination of these three tertiary structural features shows significant correlations with the folding types of proteins. Moreover, we also discuss the topological factors related to downhill folding. Finally, the generic role of tertiary structure in determining the folding cooperativity is summarized.

Native topology of the designed protein Top7 is not conducive to cooperative folding

Many single-domain proteins with <100 residues fold cooperatively; but the recently designed 92-residue Top7 protein exhibits clearly non-two-state behaviors. In apparent agreement with experiment, we found that coarse-grained, native-centric chain models, including potentials with and without elementary desolvation barriers, predicted that Top7 has a stable intermediate state in which the C-terminal fragment is folded while the rest of the chain remains disordered. We observed noncooperative folding in Top7 models that incorporated nonnative hydrophobic interactions as well. In contrast, free energy profiles deduced from models with desolvation barriers for a set of thirteen natural proteins with similar chain lengths and secondary structure elements suggested that they fold much more cooperatively than Top7. Buttressed by related studies on smaller natural proteins with chain lengths of approximately 40 residues, our findings argue that the de novo native topology of Top7 likely imposed a significant restriction on the cooperativity achievable by any design for this target structure.

Effect of the ordered water on protein folding: an off-lattice Gō-like model study

Recent experiments and numerical simulations have shown that the water molecules confined on the surfaces of some substrates, including the surfaces of cellular components in tissues and cells, form icelike ordered structures. If a protein folds in an environment with those icelike ordered water molecules, its behavior may be different from that in bulk water. Here, the effect of this ordered water environment on protein folding is studied by using an off-lattice Gō-like model. It is found that the ordered water environment significantly improves the native state stability and greatly speeds up the folding rate of the proteins.

Insights from coarse-grained Gō models for protein folding and dynamics

Exploring the landscape of large scale conformational changes such as protein folding at atomistic detail poses a considerable computational challenge. Coarse-grained representations of the peptide chain have therefore been developed and over the last decade have proved extremely valuable. These include topology-based Gō models, which constitute a smooth and funnel-like approximation to the folding landscape. We review the many variations of the Gō model that have been employed to yield insight into folding mechanisms. Their success has been interpreted as a consequence of the dominant role of the native topology in folding. The role of local contact density in determining protein dynamics is also discussed and is used to explain the ability of Gō-like models to capture sequence effects in folding and elucidate conformational transitions.

Dynamics of one-state downhill protein folding

The small helical protein BBL has been shown to fold and unfold in the absence of a free energy barrier according to a battery of quantitative criteria in equilibrium experiments, including probe-dependent equilibrium unfolding, complex coupling between denaturing agents, characteristic DSC thermogram, gradual melting of secondary structure, and heterogeneous atom-by-atom unfolding behaviors spanning the entire unfolding process. Here, we present the results of nanosecond T-jump experiments probing backbone structure by IR and end-to-end distance by FRET. The folding dynamics observed with these two probes are both exponential with common relaxation times but have large differences in amplitude following their probe-dependent equilibrium unfolding. The quantitative analysis of amplitude and relaxation time data for both probes shows that BBL folding dynamics are fully consistent with the one-state folding scenario and incompatible with alternative models involving one or several barrier crossing events. At 333 K, the relaxation time for BBL is 1.3 micros, in agreement with previous folding speed limit estimates. However, late folding events at room temperature are an order of magnitude slower (20 micros), indicating a relatively rough underlying energy landscape. Our results in BBL expose the dynamic features of one-state folding and chart the intrinsic time-scales for conformational motions along the folding process. Interestingly, the simple self-averaging folding dynamics of BBL are the exact dynamic properties required in molecular rheostats, thus supporting a biological role for one-state folding.

Probing possible downhill folding: native contact topology likely places a significant constraint on the folding cooperativity of proteins with approximately 40 residues

Experiments point to appreciable variations in folding cooperativity among natural proteins with approximately 40 residues, indicating that the behaviors of these proteins are valuable for delineating the contributing factors to cooperative folding. To explore the role of native topology in a protein's propensity to fold cooperatively and how native topology might constrain the degree of cooperativity achievable by a given set of physical interactions, we compared folding/unfolding kinetics simulated using three classes of native-centric C(alpha) chain models with different interaction schemes. The approach was applied to two homologous 45-residue fragments from the peripheral subunit-binding domain family and a 39-residue fragment of the N-terminal domain of ribosomal protein L9. Free-energy profiles as functions of native contact number were computed to assess the heights of thermodynamic barriers to folding. In addition, chevron plots of folding/unfolding rates were constructed as functions of native stability to facilitate comparison with available experimental data. Although common Gō-like models with pairwise Lennard-Jones-type interactions generally fold less cooperatively than real proteins, the rank ordering of cooperativity predicted by these models is consistent with experiment for the proteins investigated, showing increasing folding cooperativity with increasing nonlocality of a protein's native contacts. Models that account for water-expulsion (desolvation) barriers and models with many-body (nonadditive) interactions generally entail higher degrees of folding cooperativity indicated by more linear model chevron plots, but the rank ordering of cooperativity remains unchanged. A robust, experimentally valid rank ordering of model folding cooperativity independent of the multiple native-centric interaction schemes tested here argues that native topology places significant constraints on how cooperatively a protein can fold.

Folding of proteins with an all-atom Go-model

The Go-like potential at a residual level has been successfully applied to the folding of proteins in many previous works. However, taking into consideration more detailed structural information in the atomic level, the definition of contacts used in these traditional Go-models may not be suitable for all-atom simulations. Here, in this work, we develop a rational definition of contacts considering the screening effect in the crowded intramolecular environment. In such a scheme, a large amount of screened atom pairs are excluded and the number of contacts is decreased compared to the case of the traditional definition. These contacts defined by such a new definition are compatible with the all-atom representation of protein structures. To verify the rationality of the new definition of contacts, the folding of proteins CI2 and SH3 is simulated by all-atom molecular dynamics simulations. A high folding cooperativity and good correlation of the simulated Phi-values with those obtained experimentally, especially for CI2, are found. This suggests that the all-atom Go-model is improved compared to the traditional Go-model. Based on the comparison of the Phi-values, the roles of side chains in the folding are discussed, and it is concluded that the side-chain structures are more important for local contacts in determining the transition state structures. Moreover, the relations between side chain and backbone orderings are also discussed.

Coevolution of function and the folding landscape: correlation with density of native contacts

The relationship between the folding landscape and function of evolved proteins is explored by comparison of the folding mechanisms for members of the flavodoxin fold. CheY, Spo0F, and NtrC have unrelated functions and low sequence homology but share an identical topology. Recent coarse-grained simulations show that their folding landscapes are uniquely tuned to properly suit their respective biological functions. Enhanced packing in Spo0F and its limited conformational dynamics compared to CheY or NtrC lead to frustration in its folding landscape. Simulation as well as experimental results correlate with the local density of native contacts for these and a sample of other proteins. In particular, protein regions of low contact density are observed to become structured late in folding; concomitantly, these dynamic regions are often involved in binding or conformational rearrangements of functional importance. These observations help to explain the widespread success of Gō-like coarse-grained models in reproducing protein dynamics.

Observation of noncooperative folding thermodynamics in simulations of 1BBL

One of the predictions of the energy landscape theory of protein folding is the possibility of barrierless, "downhill" folding under certain conditions. The protein 1BBL has been proposed to fold by such a downhill mechanism, though this is a matter of some dispute. We carried out extensive replica exchange molecular dynamics simulations on 1BBL in explicit solvent to address this controversy and provide a microscopic picture of its folding thermodynamics. Our simulations show two distinct structural transitions in the folding of 1BBL. A low-temperature transition involves a disordering of the protein's tertiary structure without loss of secondary structure. A distinct, higher temperature transition involves the complete loss of secondary structure and dissolution of the hydrophobic core. In contrast, control simulations of the 1BBL homolog E3BD show a single high temperature unfolding transition. Further simulations of 1BBL at high ionic strength show a significant destabilization of helix II but not helix I, suggesting that the apparent folding cooperativity of 1BBL may be highly dependent on experimental conditions. Although our simulations cannot provide definitive evidence of downhill folding in 1BBL, they clearly show evidence of a complex, non-two-state folding process.

Origins of barriers and barrierless folding in BBL

In contrast to classical chemical phenomenology, theory suggests that proteins may undergo downhill folding without an activation barrier under certain thermodynamic conditions. Recently, the BBL protein was proposed to fold by such a downhill scenario, but discrepancies between experimental results found in different groups argue against this. After briefly reviewing the major experimental studies of the BBL folding mechanism, we show that simulations of both coarse-grained and atomistic models can reconcile the seemingly conflicting observations.