Correspondence between anomalous m- and DeltaCp-values in protein folding

Proteins folding according to a classical two-state system characteristically show V-shaped chevron plots. We have previously interpreted the symmetrically curved chevron plot of the protein U1A as denaturant-dependent movements in the position of the transition state ensemble (TSE). S6, a structural analog of U1A, shows a classical V-shaped chevron plot indicative of straightforward two-state kinetics, but the mutant LA30 has a curved unfolding limb, which is most consistent with TSE mobility. The kinetic m-values (derivatives of the rate constants with respect to denaturant concentration) in themselves depend on denaturant concentration. To obtain complementary information about putative mobile TSEs, we have carried out a thermodynamic analysis of the three proteins, based on data for refolding and unfolding over the range 10 degrees C to 70 degrees C. The data at all temperatures can be fitted to two-state model systems. Importantly, for all three proteins the activation heat capacities are, within error, identical to the heat capacities measured in independent experiments under equilibrium conditions. Although the equilibrium heat capacities are essentially invariant with regard to denaturant concentration, the activation heat capacities, similar to the structurally equivalent kinetic m-values, show marked denaturant dependence. Furthermore, the values of beta++ at different denaturant concentrations measured by m-values and by heat capacity values are very similar. These observations are consistent with significant transition state movements within the framework of two-state folding. The basis for TSE movement appears to be enthalpic rather than entropic, suggesting that the binding energy of denaturant-protein interactions is a major determinant of the response of energy landscape contours to changing environments.     

Physical characterization of MxiH and PrgI, the needle component of the type III secretion apparatus from Shigella and Salmonella

Shigella and Salmonella use similar type III secretion systems for delivering effector proteins into host cells. This secretion system consists of a base anchored in both bacterial membranes and an extracellular "needle" that forms a rod-like structure exposed on the pathogen surface. The needle is composed of multiple subunits of a single protein and makes direct contact with host cells to facilitate protein delivery. The proteins that make up the needle of Shigella and Salmonella are MxiH and PrgI, respectively. These proteins are attractive vaccine candidates because of their essential role in virulence and surface exposure. We therefore isolated, purified, and characterized the monomeric forms of MxiH and PrgI. Their far-UV circular dichroism spectra show structural similarities with hints of subtle differences in their secondary structure. Both proteins are highly helical and thermally unstable, with PrgI having a midpoint of thermal unfolding (Tm) near 37 degrees C and MxiH having a value near 42 degrees C. The two proteins also have comparable intrinsic stabilities as measured by chemically induced (urea) unfolding. MxiH, however, with a free energy of unfolding (DeltaG degrees 0,un) of 1.6 kcal/mol, is slightly more stable than PrgI (1.2 kcal/mol). The relatively low m-values obtained for the urea-induced unfolding of the proteins suggest that they undergo only a small change in solvent-accessible surface area. This argues that when MxiH and PrgI are incorporated into the needle complex, they obtain a more stable structural state through the introduction of protein-protein interactions.     

Metrics that differentiate the origins of osmolyte effects on protein stability: a test of the surface tension proposal

Osmolytes that are naturally selected to protect organisms against environmental stresses are known to confer stability to proteins via preferential exclusion from protein surfaces. Solvophobicity, surface tension, excluded volume, water structure changes and electrostatic repulsion are all examples of forces proposed to account for preferential exclusion and the ramifications exclusion has on protein properties. What has been lacking is a systematic way of determining which force(s) is(are) responsible for osmolyte effects. Here, we propose the use of two experimental metrics for assessing the abilities of various proposed forces to account for osmolyte-mediated effects on protein properties. Metric 1 requires prediction of the experimentally determined ability of the osmolyte to bring about folding/unfolding resulting from the application of the force in question (i.e. prediction of the m-value of the protein in osmolyte). Metric 2 requires prediction of the experimentally determined ability of the osmolyte to contract or expand the Stokes radius of the denatured state resulting from the application of the force. These metrics are applied to test separate claims that solvophobicity/solvophilicity and surface tension are driving forces for osmolyte-induced effects on protein stability. The results show clearly that solvophobic/solvophilic forces readily account for protein stability and denatured state dimensional effects, while surface tension alone fails to do so. The agreement between experimental and predicted m-values involves both positive and negative m-values for three different proteins, and as many as six different osmolytes, illustrating that the tests are robust and discriminating. The ability of the two metrics to distinguish which forces account for the effects of osmolytes on protein properties and which do not, provides a powerful means of investigating the origins of osmolyte-protein effects.     

The effect of increasing the stability of non-native interactions on the folding landscape of the bacterial immunity protein Im9

How stabilising non-native interactions influence protein folding energy landscapes is currently not well understood: such interactions could speed folding by reducing the conformational search to the native state, or could slow folding by increasing ruggedness. Here, we examine the influence of non-native interactions in the folding process of the bacterial immunity protein Im9, by exploiting our ability to manipulate the stability of the intermediate and rate-limiting transition state (TS) in the folding of this protein by minor alteration of its sequence or changes in solvent conditions. By analysing the properties of these species using Phi-value analysis, and exploration of the structural properties of the TS ensemble using molecular dynamics simulations, we demonstrate the importance of non-native interactions in immunity protein folding and demonstrate that the rate-limiting step involves partial reorganisation of these interactions as the TS ensemble is traversed. Moreover, we show that increasing the contribution to stability made by non-native interactions results in an increase in Phi-values of the TS ensemble without altering its structural properties or solvent-accessible surface area. The data suggest that the immunity proteins fold on multiple, but closely related, micropathways, resulting in a heterogeneous TS ensemble that responds subtly to mutation or changes in the solvent conditions. Thus, altering the relative strength of native and non-native interactions influences the search to the native state by restricting the pathways through the folding energy landscape.     

Microsecond hydrophobic collapse in the folding of Escherichia coli dihydrofolate reductase, an alpha/beta-type protein

Using small-angle X-ray scattering combined with a continuous-flow mixing device, we monitored the microsecond compaction dynamics in the folding of Escherichia coli dihydrofolate reductase, an alpha/beta-type protein. A significant collapse of the radius of gyration from 30 A to 23.2 A occurs within 300 micros after the initiation of refolding by a urea dilution jump. The subsequent folding after the major chain collapse occurs on a considerably longer time-scale. The protein folding trajectories constructed by comparing the development of the compactness and the secondary structure suggest that the specific hydrophobic collapse model rather than the framework model better explains the experimental observations. The folding trajectory of this alpha/beta-type protein is located between those of alpha-helical and beta-sheet proteins, suggesting that native structure determines the folding landscape.     

Theoretical investigation of the photoinitiated folding of HP-36

A computational model was developed to examine the phototriggered folding of a caged protein, a protein modified with an organic photolabile cross-linker. Molecular dynamics simulations of the modified 36-residue fragment of subdomain B of chicken villin head piece with a photolabile linker were performed, starting from both the caged and the uncaged structures. Construction of a free-energy landscape, based on principal components as well as on radius of gyration versus root-mean-square deviation, and circular dichroism calculations were employed to characterize folding behavior and structures. The folded structures observed in the molecular dynamics trajectories were found to be similar to that of the wild-type protein, in agreement with the published experimental results. The free-energy landscapes of the modified and wild-type proteins have similar topology, suggesting common thermodynamic/kinetic behavior. The existence of small differences in the free-energy surface of the modified protein from that of the native protein, however, indicates subtle differences in the folding behavior.     

Methods for the accurate estimation of confidence intervals on protein folding phi-values

Phi-values provide an important benchmark for the comparison of experimental protein folding studies to computer simulations and theories of the folding process. Despite the growing importance of phi measurements, however, formulas to quantify the precision with which phi is measured have seen little significant discussion. Moreover, a commonly employed method for the determination of standard errors on phi estimates assumes that estimates of the changes in free energy of the transition and folded states are independent. Here we demonstrate that this assumption is usually incorrect and that this typically leads to the underestimation of phi precision. We derive an analytical expression for the precision of phi estimates (assuming linear chevron behavior) that explicitly takes this dependence into account. We also describe an alternative method that implicitly corrects for the effect. By simulating experimental chevron data, we show that both methods accurately estimate phi confidence intervals. We also explore the effects of the commonly employed techniques of calculating phi from kinetics estimated at non-zero denaturant concentrations and via the assumption of parallel chevron arms. We find that these approaches can produce significantly different estimates for phi (again, even for truly linear chevron behavior), indicating that they are not equivalent, interchangeable measures of transition state structure. Lastly, we describe a Web-based implementation of the above algorithms for general use by the protein folding community.     

Radius of gyration as an indicator of protein structure compactness

Identification and study of the main principles underlying the kinetics and thermodynamics of protein folding generate a new insight into the factors that control this process. Statistical analysis of the radius of gyration for 3769 protein domains of four major classes (α, β, α/β, and α + β) showed that each class has a characteristic radius of gyration that determines the protein structure compactness. For instance, α proteins have the highest radius of gyration throughout the protein size range considered, suggesting a less tight packing as compared with β-and (α + β)-proteins. The lowest radius of gyration and, accordingly, the tightest packing are characteristic of α/β-proteins. The protein radius of gyration normalized by the radius of gyration of a ball with the same volume is independent of the protein size, in contrast to compactness and the number of contacts per residue.     

An all-atom force field for tertiary structure prediction of helical proteins

We have developed an all-atom free-energy force field (PFF01) for protein tertiary structure prediction. PFF01 is based on physical interactions and was parameterized using experimental structures of a family of proteins believed to span a wide variety of possible folds. It contains empirical, although sequence-independent terms for hydrogen bonding. Its solvent-accessible surface area solvent model was first fit to transfer energies of small peptides. The parameters of the solvent model were then further optimized to stabilize the native structure of a single protein, the autonomously folding villin headpiece, against competing low-energy decoys. Here we validate the force field for five nonhomologous helical proteins with 20-60 amino acids. For each protein, decoys with 2-3 A backbone root mean-square deviation and correct experimental Cbeta-Cbeta distance constraints emerge as those with the lowest energy.     

Radius of gyration is indicator of compactness of protein structure

Search and study of the general principles that govern kinetics and thermodynamics of protein folding generate a new insight into the factors controlling this process. Statistical analysis of radii of gyration for 3769 protein structures from four general structural classes (all-alpha, all-beta, alpha/beta, alpha + beta) demonstrates that each class of proteins has its own class-specific radius of gyration, which determines compactness of protein structures: alpha-proteins have the largest radius of gyration. This indicates that they are less tightly packed than beta- and alpha + beta-proteins. Finally, alpha/beta-proteins are the most tightly packed proteins with the least radius of gyration. It should be underlined that radius of gyration normalized on the radius of gyration of ball with the same volume, is independent of the length in comparison with such parameters as compactness and number of contacts per residue.     

Dissecting the Critical Factors for Thermodynamic Stability of Modular Proteins Using Molecular Modeling Approach

Repeat proteins have recently attracted much attention as alternative scaffolds to immunoglobulin antibodies due to their unique structural and biophysical features. In particular, repeat proteins show high stability against temperature and chaotic agents. Despite many studies, structural features for the stability of repeat proteins remain poorly understood. Here we present an interesting result from in silico analyses pursuing the factors which affect the stability of repeat proteins. Previously developed repebody structure based on variable lymphocytes receptors (VLRs) which consists of leucine-rich repeat (LRR) modules was used as initial structure for the present study. We constructed extra six repebody structures with varying numbers of repeat modules and those structures were used for molecular dynamics simulations. For the structures, the intramolecular interactions including backbone H-bonds, van der Waals energy, and hydrophobicity were investigated and then the radius of gyration, solvent-accessible surface area, ratio of secondary structure, and hydration free energy were also calculated to find out the relationship between the number of LRR modules and stability of the protein. Our results show that the intramolecular interactions lead to more compact structure and smaller surface area of the repebodies, which are critical for the stability of repeat proteins. The other features were also well compatible with the experimental results. Based on our observations, the repebody-5 was proposed as the best structure from the all repebodies in structure optimization process. The present study successfully demonstrated that our computer-based molecular modeling approach can significantly contribute to the experiment-based protein engineering challenge.     

Molecular dynamics simulation of intrinsically disordered proteins

Intrinsically disordered proteins are biomolecules that do not have a definite 3D structure; therefore, their dynamical simulation cannot start from a known list of atomistic positions, such as a Protein Data Bank file. We describe a method to start a computer simulation of these proteins. The first step of the procedure is the creation of a multi-rod configuration of the molecule, derived from its primary sequence. This structure is dynamically evolved in vacuo until its gyration radius reaches the experimental average value; at this point solvent molecules, in explicit or implicit implementation, are added to the protein and a regular molecular dynamics simulation follows. We have applied this procedure to the simulation of tau, one of the largest totally disordered proteins.     

Mixed osmolytes: the degree to which one osmolyte affects the protein stabilizing ability of another

Mixtures of organic osmolytes occur in cells of many organisms, raising the question of whether their actions on protein stability are independent or synergistic. To investigate this question it is desirable to develop a system that permits evaluation of the effect of one osmolyte on the efficacy of another to either force-fold or denature a protein. A means of evaluating the efficacy of an osmolyte is provided by its m-value, an experimental quantity that measures the ability of the osmolyte to force a protein to unfold or fold. An experimental system is presented that enables evaluations of the m-values of osmolytes in the presence and absence of a second osmolyte. The experimental system involves use of a marginally stable protein in 10 mM buffer (pH 7, 200 mM salt, and 34 degrees C) that is at the midpoint of its native to denatured transition. These conditions enable determination of m-values for protecting and denaturing osmolytes in the presence and absence of a second osmolyte, permitting assessment of the extent to which the two osmolytes affect each other's efficacy. The two osmolytes investigated in this work are the denaturing osmolyte, urea, and the protecting osmolyte, sarcosine. Results show unequivocally that neither osmolyte alters the efficacy of the other in forcing the protein to fold or unfold-the osmolytes act independently on the protein despite their combined concentrations being in the multi-molar range. These osmolytes avoid altering one another's efficacy at these high concentrations because the number of osmolyte interaction sites on the protein is large and the binding constants are quite small. Consequently, the site occupancies are low enough in number that the two osmolytes neither compete nor cooperate in interacting with the protein.     

Fast accurate evaluation of protein solvent exposure

Protein solvation energies are often taken to be proportional to solvent-accessible surface areas. Computation of these areas is numerically demanding and may become a bottleneck for folding and design applications. Fast graph-based methods, such as dead-end elimination (DEE), become possible if all energies, including solvation energies, are expressed as single-residue and pair-residue terms. To this end, Street and Mayo originated a pair-residue approximation for solvent-accessible surface areas (Street AG, Mayo SL. Pairwise calculation of protein solvent accessible surface areas. Fold Des 1998;3:253-258). The dominant source of error in this method is the overlapping burial of side-chain surfaces in the protein core. Here we report a new pair-residue approximation, which greatly reduces this overlap error by the use of optimized generic side-chains. We have tested the generic-side-chain method for the ten proteins studied by Street and Mayo and for 377 single-domain proteins from the CATH database (Orengo CA, Michie AD, Jones S, Jones DT, Swindells MB, Thornton JM. CATH-A hierarchic classification of protein domain structures. Structure 1997;5:1093-1108). With little additional cost in computation, the new method consistently reduces error for total areas and residue-by-residue areas by more than a factor of two. For example, the residue-by-residue error (for buried area) is reduced from 7.42 A(2) to 3.70 A(2). This difference translates into a solvation energy difference of approximately 0.2 kcal/mol per residue, amounting to a reduction in root-mean-square energy error of 2 kcal/mol for a 100 residue chain, a potentially critical difference for both protein folding and design applications.     

Tryptophan to Glycine mutation in the position 116 leads to protein aggregation and decreases the stability of the LITAF protein

Mutations in the gene-encoding vesicle lipopolysaccharide-induced tumor necrosis factor (LITAF) protein cause Charcot–Marie–Tooth type 1C (CMT1C) disease, a neurological disorder. The LITAF gene is mapped to chromosome number 16 and can be found at cytogenetic location 16p13 of the chromosome. CMT1C-linked small integral membrane protein of lysosome/late endosome mutants are loss-of-function mutants that act in a dominant negative manner to impair endosomal trafficking, leading to prolonged extracellular signal-regulated kinases 1/2 signaling downstream of ErbB activation. Mutation W116G in the LITAF decreases the stability of the protein and also interrupts the functioning of gene. We have analyzed the single nucleotide polymorphism (SNP) results of 28 nsSNPs obtained from dbSNP. We also carried out multiple molecular dynamics simulations of 200 ns and obtained results of root-mean-square deviation, root-mean-square fluctuation, radius of gyration, solvent-accessible surface area, H-bond, and principal component analysis to check and prove the stability of both the wild type and the mutant. The protein was then checked for its aggregation and the results showed loss of helix. The loss of helix leads to the instability of the protein.     

PROTERAN: animated terrain evolution for visual analysis of patterns in protein folding trajectory

The mechanism of protein folding remains largely a mystery in molecular biology, despite the enormous effort from many groups in the past decades. Currently, the protein folding mechanism is often characterized by calculating the free energy landscape versus various reaction coordinates such as the fraction of native contacts, the radius of gyration and so on. In this paper, we present an integrated approach towards understanding the folding process via visual analysis of patterns of these reaction coordinates. The three disparate processes (1) protein folding simulation, (2) pattern elicitation and (3) visualization of patterns, work in tandem. Thus as the protein folds, the changing landscape in the pattern space can be viewed via the visualization tool, PROTERAN, a program we developed for this purpose. We first present an incremental (on-line) trie-based pattern discovery algorithm to elicit the patterns and then describe the terrain metaphor based visualization tool. Using two example small proteins, a beta-hairpin and a designed protein Trp-cage, we next demonstrate that this combined pattern discovery and visualization approach extracts crucial information about protein folding intermediates and mechanism.     

Conformational plasticity in folding of the split beta-alpha-beta protein S6: evidence for burst-phase disruption of the native state

An increasing number of folding studies of two-state proteins shows that point mutations sometimes change the kinetic m-values, leading to kinks and curves in the chevron plots. The molecular origin of these changes is yet unclear although it is speculated that they are linked to structural rearrangement of the transition state or to accumulation of meta-stable intermediates. To shed more light on this issue, we present here a combined m and phi-value analysis of the split beta-alpha-beta protein S6. Wild-type S6 displays classical two-state kinetics with v-shaped chevron plot, but a majority of its mutants display distinct m-value changes or curved chevrons. We observe that this kinetic aberration of S6 is linked to mutations that are clustered in distinct regions of the native structure. The most pronounced changes, i.e. decrease in the m-value for the unfolding rate constant, are seen upon truncation of interactions between the N and C termini, whereas mutations in the centre of the hydrophobic core show smaller or even opposed effects. As a consequence, the calculated phi-values display a systematic increase upon addition of denaturant. In the case of S6, the phenomenon seems to arise from a general plasticity of the different species on the folding pathway. That is, the structure of the denatured ensemble, the transition state, and the native ground-state for unfolding seem to change upon mutation. From these changes, it is concluded that interactions spanning the centre of the hydrophobic core form early in folding, whereas the entropically disfavoured interactions linking the N and C termini consolidate very late, mainly on the down-hill-side of the folding barrier.     

Fast compaction of alpha-lactalbumin during folding studied by stopped-flow X-ray scattering

To monitor the fast compaction process during protein folding, we have used a stopped-flow small-angle X-ray scattering technique combined with a two-dimensional charge-coupled device-based X-ray detector that makes it possible to improve the signal-to-noise ratio of data dramatically, and measured the kinetic refolding reaction of alpha-lactalbumin. The results clearly show that the radius of gyration and the overall shape of the kinetic folding intermediate of alpha-lactalbumin are the same as those of the molten globule state observed at equilibrium. Thus, the identity between the kinetic folding intermediate and the equilibrium molten globule state is firmly established. The present results also suggest that the folding intermediate is more hydrated than the native state and that the hydrated water molecules are dehydrated when specific side-chain packing is formed during the change from the molten globule to the native state.     

The magnitude of changes in guanidine-HCl unfolding m-values in the protein, iso-1-cytochrome c, depends upon the substructure containing the mutation

Hydrophilic to hydrophobic mutations have been made at 11 solvent exposed sites on the surface of iso-1-cytochrome c. Most of these mutations involve the replacement of lysine with methionine, which is nearly isosteric with lysine. Minimal perturbation to the native structure is expected, and this expectation is confirmed by infrared amide I spectroscopy. Guanidine hydrochloride denaturation studies demonstrate that these variants affect the magnitude of the m-value, the rate of change of free energy with respect to denaturant concentration, to different degrees. Changes in m-values are indicative of changes in the equilibrium folding mechanism of a protein. Decreases in m-values are normally thought to result either from an increased population of intermediates during unfolding or from a more compact denatured state. When cytochrome c is considered in terms of its thermodynamic substructures, the changes in the m-value for a given variant appear to depend upon the substructure in which the mutation is made. These data indicate that the relative stabilities and physical properties of substructures of cytochrome c play an important determining role in the equilibrium folding mechanism of this protein.