Thermodynamics and Kinetics of Non-native Interactions in Protein Folding: A Single Point Mutant Significantly Stabilizes the N-terminal Domain of L9 by Modulating Non-native Interactions in the Denatured State

High-Accuracy Prediction of Stabilizing Surface Mutations to the Three-Helix Bundle, UBA(1), with EmCAST

The accurate modeling of energetic contributions to protein structure is a fundamental challenge in computational approaches to protein analysis and design. We describe a general computational method, EmCAST (empirical Cα stabilization), to score and optimize the sequence to the structure in proteins. The method relies on an empirical potential derived from the database of the Cα dihedral angle preferences for all possible four-residue sequences, using the data available in the Protein Data Bank. Our method produces stability predictions that naturally correlate one-to-one with the experimental results for solvent-exposed mutation sites. EmCAST predicted four mutations that increased the stability of a three-helix bundle, UBA(1), from 2.4 to 4.8 kcal/mol by optimizing residues in both helices and turns. For a set of eight variants, the predicted and experimental stabilizations correlate very well (R2 = 0.97) with a slope near 1 and with a 0.16 kcal/mol standard error for EmCAST predictions. Tests against literature data for the stability effects of surface-exposed mutations show that EmCAST outperforms the existing stability prediction methods. UBA(1) variants were crystallized to verify and analyze their structures at an atomic resolution. Thermodynamic and kinetic folding experiments were performed to determine the magnitude and mechanism of stabilization. Our method has the potential to enable the rapid, rational optimization of natural proteins, expand the analysis of the sequence/structure relationship, and supplement the existing protein design strategies.

Effects of Surface Tethering on the Thermodynamics and Kinetics of Frustrated Protein Folding

The interaction between the protein and surface plays an important role in biology and biotechnology. To understand how surface tethering influences the folding behavior of frustrated proteins, in this work, we systematically study the thermodynamics and folding kinetics of the bacterial immunity protein Im7 and Fyn SH3 domain tethered to a surface using Langevin dynamics simulations. Upon surface tethering, the stabilization often results from the entropic effect, whereas the destabilization is usually caused by either an energetic or entropic effect. For the Fyn SH3 domain with a two-state folding manner, the influence of nonnative interactions on thermodynamic stability is not significant, while nonnative interactions can weaken the effect of surface tethering on the change in the folding rate. By contrast, for the frustrated protein Im7, depending on where the protein is tethered, the surface tethering can promote or suppress misfolding by modulating specific nonnative contacts, thereby altering the folding rate and folding mechanism. Because surface tethering can change the intrachain diffusivity of unfolding, the kinetic stability cannot be well captured by the thermodynamic stability at some tether points. This study should be helpful in general to understand how surface tethering affects the folding energy landscape of frustrated proteins.

Denatured State Conformational Biases in Three-Helix Bundles Containing Divergent Sequences Localize near Turns and Helix Capping Residues

Rhodopseudomonas palustris cytochrome c', a four-helix bundle, and the second ubiquitin-associated domain, UBA(2), a three-helix bundle from the human homologue of yeast Rad23, HHR23A, deviate from random coil behavior under denaturing conditions in a fold-specific manner. The random coil deviations in each of these folds occur near interhelical turns and loops in their tertiary structures. Here, we examine an additional three-helix bundle with an identical fold to UBA(2), but a highly divergent sequence, the first ubiquitin-associated domain, UBA(1), of HHR23A. We use histidine-heme loop formation methods, employing eight single histidine variants, to probe for denatured state conformational bias of a UBA(1) domain fused to the N-terminus of iso-1-cytochrome c (iso-1-Cytc). Guanidine hydrochloride (GuHCl) denaturation shows that the iso-1-Cytc domain unfolds first, followed by the UBA(1) domain. Denatured state (4 and 6 M GuHCl) histidine-heme loop formation studies show that as the size of the histidine-heme loop increases, loop stability decreases, as expected for the Jacobson-Stockmayer relationship. However, loops formed with His35, His31, and His15, of UBA(1), are 0.6-1.1 kcal/mol more stable than expected from the Jacobson-Stockmayer relationship, confirming the importance of deviations of the denatured state from random coil behavior near interhelical turns of helical domains for facilitating folding to the correct topology. For UBA(1) and UBA(2), hydrophobic clusters on either side of the turns partially explain deviations from random coil behavior; however, helix capping also appears to be important.

A pH-dependent protein stability switch coupled to the perturbed pKa of a single ionizable residue

The contribution of electrostatic interactions in protein stability has not been fully understood. Burial of an ionizable amino acid inside the hydrophobic protein core can affect its ionization equilibrium and shift its pKa differentially in the native (N) and unfolded (U) states of a protein and this coupling between the folding/unfolding cycle and the ionization equilibria of the ionizable residue can substantially influence the protein stability. Here, we studied the coupling of the folding/unfolding cycle with the ionization of a buried ionizable residue in a multi-domain protein, Human Serum Albumin (HSA) using fluorescence spectroscopy. A pH-dependent change in the stability of HSA was observed in the near native pH range (pH 6.0-9.0). The protonation-deprotonation equilibrium of a single thiol residue that is buried in the protein structure was identified to give rise to the pH-dependent protein stability. We quantified the pKa of the thiol residue in the N and the U states. The mean pKa of the thiol in the N state was upshifted by 0.5 units to 8.7 due to the burial of the thiol in the protein structure. Surprisingly, the mean pKa of the thiol in the U state was observed to be downshifted by 1.3 units to 6.9. These results indicate that some charged residues are spatially proximal to the thiol group in the U state. Our results suggest that, in addition to the N state, electrostatic interactions in the U state are important determinants of protein stability.

Investigating the folding mechanism of the N-terminal domain of ribosomal protein L9

Protein folding is a popular topic in the life science. However, due to the limited sampling ability of experiments and simulations, the general folding mechanism is not yet clear to us. In this work, we study the folding of the N-terminal domain of ribosomal protein L9 (NTL9) in detail by a mixing replica exchange molecular dynamics method. The simulation results are close to previous experimental observations. According to the Markov state model, the folding of the protein follows a nucleation-condensation path. Moreover, after the comparison to its 39-residue β-α-β motif, we find that the helix at the C-terminal has a great influence on the folding process of the intact protein, including the nucleation of the key residues in the transition state ensemble and the packing of the hydrophobic residues in the native state.

Adaptive Markov state model estimation using short reseeding trajectories

In the last decade, advances in molecular dynamics (MD) and Markov State Model (MSM) methodologies have made possible accurate and efficient estimation of kinetic rates and reactive pathways for complex biomolecular dynamics occurring on slow time scales. A promising approach to enhanced sampling of MSMs is to use "adaptive" methods, in which new MD trajectories are "seeded" preferentially from previously identified states. Here, we investigate the performance of various MSM estimators applied to reseeding trajectory data, for both a simple 1D free energy landscape and mini-protein folding MSMs of WW domain and NTL9(1-39). Our results reveal the practical challenges of reseeding simulations and suggest a simple way to reweight seeding trajectory data to better estimate both thermodynamic and kinetic quantities.

Modeling pKas of unfolded proteins to probe structural models of unfolded state

Modeling unfolded states of proteins has implications for protein folding and stability. Since in unfolded state proteins adopt multiple conformations, any experimentally measured quantity is ensemble averaged, therefore the computed quantity should be ensemble averaged as well. Here, we investigate the possibility that one can model an unfolded state ensemble with the coil model approach, algorithm such as “flexible-meccano” [Ozenne V et al., Flexible-meccano: A tool for the generation of explicit ensemle descriptions of intrinsically disordered proteins and their associated experimental observables, Bioinformatics 28:1463–1470, 2012], developed to generate structures for intrinsically disordered proteins. We probe such a possibility by using generated structures to calculate pKas of titratable groups and compare with experimental data. It is demonstrated that even with a small number of representative structures of unfolded state, the average calculated pKas are in very good agreement with experimentally measured pKas. Also, predictions are made for titratable groups for which there is no experimental data available. This suggests that the coil model approach is suitable for generating 3D structures of unfolded state of proteins. To make the approach suitable for large-scale modeling, which requires limited number of structures, we ranked the structures according to their solvent accessible surface area (SASA). It is shown that in the majority of cases, the top structures with smallest SASA are enough to represent unfolded state.

Nonnative contact effects in protein folding

The folding simulations of three ββα-motifs and β-barrel structured proteins (NTL9, NuG2b, and CspA) were performed to determine the important roles of native and nonnative contacts in protein folding.

The Effect of Electrostatic Interactions on the Folding Kinetics of a 3-α-Helical Bundle Protein Family

The trio of protein segment repeats called spectrins diverges by more than 2 orders of magnitude in their folding and unfolding rates, despite having very similar stabilities and almost coincidental topologies. Experimental studies revealed that the mutation of five particular residues dramatically alters the kinetic rates in the slow folders, making them similar to the rates of the fast folder. This is considered to be an exceptional behavior which seems in principle to challenge the current understanding of the protein folding process. In this work, we analyze this scenario, using a simplified computational model, combined with state-of-the-art kinetic analysis techniques. Our model faithfully separates the kinetics of the fast and slow folders and captures the effect of the five mutations. We show that the inclusion of electrostatics in the model is necessary to explain the experimental findings.

Modulating charge patterning and ionic strength as a strategy to induce conformational changes in intrinsically disordered proteins

We present an analytical theory to describe conformational changes as a function of salt for polymers with a given sequence of charges. We apply this model to describe Intrinsically Disordered Proteins (IDPs) by explicitly accounting for charged residues and their exact placement in the primary sequence while approximating the effect of non-electrostatic interactions at a mean-field level by effective short-range (two body and three-body) interaction parameters. The effect of ions is introduced by treating electrostatic interactions within Debye-Huckle approximation. Using typical values of the short-range mean-field parameters derived from all-atom Monte Carlo simulations (at zero salt), we predict the conformational changes as a function of salt concentration. We notice that conformational transitions in response to changes in ionic strength strongly depend on sequence specific charge patterning. For example, globule to coil transition can be observed upon increasing salt concentration, in stark contrast to uniformly charged polyelectrolyte theories based on net charge only. In addition, it is possible to observe non-monotonic behavior with salt as well. Drastic differences in salt-induced conformational transitions is also evident between two doubly phosphorylated sequences-derived from the same wild type sequence-that only differ in the site of phosphorylation. Similar effects are also predicted between two sequences derived from the same parent sequence differing by a single site mutation where a negative charge is replaced by a positive charge. These effects are purely a result of charge decoration and can only be understood in terms of metrics based on specific placement of charges, and cannot be explained by models based on charge composition alone. Identifying sequences and hot spots within sequences-for post translational modification or charge mutation-using our high-throughput theory will yield fundamental insights into design and biological regulation mediated by phosphorylation and/or local changes in salt concentration.

Salt Effects on Protein Folding Thermodynamics

Salts differ in their ability to stabilize protein conformations, thereby affecting the thermodynamics and kinetics of protein folding. We developed a coarse-grained protein model that can predict salt-induced changes in protein properties by using the transfer free-energy data of various chemical groups from water to salt solutions. Using this model and molecular dynamics simulations, we probed the effect of seven different salts on the folding thermodynamics of the DNA binding domain of lac repressor protein ( lac-DBD) and N-terminal domain of ribosomal protein (NTL9). We show that a salt can act as a protein stabilizing or destabilizing agent depending on the protein sequence and folded state topology. The computed thermodynamic properties, especially the m values for various salts, which reveal the relative ability of a salt to stabilize the protein folded state, are in quantitative agreement with the experimentally measured values. The computations show that the degree of protein compaction in the denatured ensemble strongly depends on the salt identity, and for the same variation in salt concentration, the compaction in the protein dimensions varies from ∼4% to ∼30% depending on the salt. The transition-state ensemble (TSE) of lac-DBD is homogeneous and polarized, while the TSE of NTL9 is heterogeneous and diffusive. Salts induce subtle structural changes in the TSE that are in agreement with Hammond's postulate. The barrier to protein folding tends to disappear in the presence of moderate concentrations (∼3-4 m) of strongly stabilizing salts.

Collapse Transitions of Proteins and the Interplay Among Backbone, Sidechain, and Solvent Interactions

Proteins can collapse into compact globules or form expanded, solvent-accessible, coil-like conformations. Additionally, they can fold into well-defined three-dimensional structures or remain partially or entirely disordered. Recent discoveries have shown that the tendency for proteins to collapse or remain expanded is not intrinsically coupled to their ability to fold. These observations suggest that proteins do not have to form compact globules in aqueous solutions. They can be intrinsically disordered, collapsed, or expanded, and even form well-folded, elongated structures. This ability to decouple collapse from folding is determined by the sequence details of proteins. In this review, we highlight insights gleaned from studies over the past decade. Using a polymer physics framework, we explain how the interplay among sidechains, backbone units, and solvent determines the driving forces for collapsed versus expanded states in aqueous solvents.

Probing Denatured State Conformational Bias in a Three-Helix Bundle, UBA(2), Using a Cytochrome c Fusion Protein

Previous work with the four-helix-bundle protein cytochrome c' from Rhodopseudomonas palustris using histidine-heme loop formation methods revealed fold-specific deviations from random coil behavior in its denatured state ensemble. To examine the generality of this finding, we extend this work to a three-helix-bundle polypeptide, the second ubiquitin-associated domain, UBA(2), of the human DNA excision repair protein. We use yeast iso-1-cytochrome c as a scaffold, fusing the UBA(2) domain at the N-terminus of iso-1-cytochrome c. We have engineered histidine into highly solvent accessible positions of UBA(2), creating six single histidine variants. Guanidine hydrochloride denaturation studies show that the UBA(2)-cytochrome c fusion protein unfolds in a three-state process with iso-1-cytochrome c unfolding first. Furthermore, engineered histidine residues in UBA(2) strongly destabilize the iso-1-cytochrome c domain. Equilibrium and kinetic histidine-heme loop formation measurements in the denatured state at 4 and 6 M guanidine hydrochloride show that loop stability decreases as the size of the histidine-heme loop increases, in accord with the Jacobson-Stockmayer equation. However, we observe that the His27-heme loop is both more stable than expected from the Jacobson-Stockmayer relationship and breaks more slowly than expected. These results show that the sequence near His27, which is in the reverse turn between helices 2 and 3 of UBA(2), is prone to persistent interactions in the denatured state. Therefore, consistent with our results for cytochrome c', this reverse turn sequence may help to establish the topology of this fold by biasing the conformational distribution of the denatured state.

Helical Propensity Affects the Conformational Properties of the Denatured State of Cytochrome c'

Changing the helical propensity of a polypeptide sequence might be expected to affect the conformational properties of the denatured state of a protein. To test this hypothesis, alanines at positions 83 and 87 near the center of helix 3 of cytochrome c' from Rhodopseudomonas palustris were mutated to serine to decrease the stability of this helix. A set of 13 single histidine variants in the A83S/A87S background were prepared to permit assessment of the conformational properties of the denatured state using histidine-loop formation in 3 M guanidine hydrochloride. The data are compared with previous histidine-heme loop formation data for wild-type cytochrome c'. As expected, destabilization of helix 3 decreases the global stabilities of the histidine variants in the A83S/A87S background relative to the wild-type background. Loop stability versus loop size data yields a scaling exponent of 2.1 ± 0.2, similar to the value of 2.3 ± 0.2 obtained for wild-type cytochrome c'. However, the stabilities of all histidine-heme loops, which contain the helix 3 sequence segment, are increased in the A83S/A87S background compared to the wild-type background. Rate constants for histidine-heme loop breakage are similar for the wild-type and A83S/A87S variants. However, for histidine-heme loops that contain the helix 3 sequence segment, the rate constants for loop formation increase in the A83S/A87S background compared to the wild-type background. Thus, residual helical structure appears to stiffen the polypeptide chain slowing loop formation in the denatured state. The implications of these results for protein folding mechanisms are discussed.

Electrostatic Interactions in Protein Structure, Folding, Binding, and Condensation

Charged and polar groups, through forming ion pairs, hydrogen bonds, and other less specific electrostatic interactions, impart important properties to proteins. Modulation of the charges on the amino acids, e.g., by pH and by phosphorylation and dephosphorylation, have significant effects such as protein denaturation and switch-like response of signal transduction networks. This review aims to present a unifying theme among the various effects of protein charges and polar groups. Simple models will be used to illustrate basic ideas about electrostatic interactions in proteins, and these ideas in turn will be used to elucidate the roles of electrostatic interactions in protein structure, folding, binding, condensation, and related biological functions. In particular, we will examine how charged side chains are spatially distributed in various types of proteins and how electrostatic interactions affect thermodynamic and kinetic properties of proteins. Our hope is to capture both important historical developments and recent experimental and theoretical advances in quantifying electrostatic contributions of proteins.

Effect of an Imposed Contact on Secondary Structure in the Denatured State of Yeast Iso-1-cytochrome c

There is considerable evidence that long-range interactions stabilize residual protein structure under denaturing conditions. However, evaluation of the effect of a specific contact on structure in the denatured state has been difficult. Iso-1-cytochrome c variants with a Lys54 → His mutation form a particularly stable His-heme loop in the denatured state, suggestive of loop-induced residual structure. We have used multidimensional nuclear magnetic resonance methods to assign ¹H and ¹⁵N backbone amide and ¹³C backbone and side chain chemical shifts in the denatured state of iso-1-cytochrome c carrying the Lys54 → His mutation in 3 and 6 M guanidine hydrochloride and at both pH 6.4, where the His54-heme loop is formed, and pH 3.6, where the His54-heme loop is broken. Using the secondary structure propensity score, with the 6 M guanidine hydrochloride chemical shift data as a random coil reference state for data collected in 3 M guanidine hydrochloride, we found residual helical structure in the denatured state for the 60s helix and the C-terminal helix, but not in the N-terminal helix in the presence or absence of the His54-heme loop. Non-native helical structure is observed in two regions that form Ω-loops in the native state. There is more residual helical structure in the C-terminal helix at pH 6.4 when the loop is formed. Loop formation also appears to stabilize helical structure near His54, consistent with induction of helical structure observed when His-heme bonds form in heme-peptide model systems. The results are discussed in the context of the folding mechanism of cytochrome c.

The N-Terminal Domain of Ribosomal Protein L9 Folds via a Diffuse and Delocalized Transition State

The N-terminal domain of L9 (NTL9) is a 56-residue mixed α-β protein that lacks disulfides, does not bind cofactors, and folds reversibly. NTL9 has been widely used as a model system for experimental and computational studies of protein folding and for investigations of the unfolded state. The role of side-chain interactions in the folding of NTL9 is probed by mutational analysis. ϕ-values, which represent the ratio of the change in the log of the folding rate upon mutation to the change in the log of the equilibrium constant for folding, are reported for 25 point mutations and 15 double mutants. All ϕ-values are small, with an average over all sites probed of only 0.19 and a largest value of 0.4. The effect of modulating unfolded-state interactions is studied by measuring ϕ-values in second- site mutants and under solvent conditions that perturb unfolded-state energetics in a defined way. Neither of these alterations significantly affects the distribution of ϕ-values. The results, combined with those of earlier studies that probe the role of hydrogen-bond formation in folding and the burial of surface area, reveal that the transition state for folding contains extensive backbone structure and buries a significant fraction of hydrophobic surface area, but lacks well developed side-chain-side-chain interactions. The folding transition state for NTL9 does not contain a specific "nucleus" consisting of a few key residues; rather, it involves extensive backbone hydrogen bonding and partially formed structure delocalized over almost the entire domain. The potential generality of these observations is discussed.

The low populated folding intermediate of a mutant of the Fyn SH3 domain identified by a simple model

The low populated on-pathway folding intermediate of the A39V/N53P/V55L Fyn SH3 domain is captured by a native-centric model augmented by sequence-dependent nonnative hydrophobic interactions.

Role of Proteome Physical Chemistry in Cell Behavior

We review how major cell behaviors, such as bacterial growth laws, are derived from the physical chemistry of the cell’s proteins. On one hand, cell actions depend on the individual biological functionalities of their many genes and proteins. On the other hand, the common physics among proteins can be as important as the unique biology that distinguishes them. For example, bacterial growth rates depend strongly on temperature. This dependence can be explained by the folding stabilities across a cell’s proteome. Such modeling explains how thermophilic and mesophilic organisms differ, and how oxidative damage of highly charged proteins can lead to unfolding and aggregation in aging cells. Cells have characteristic time scales. For example, E. coli can duplicate as fast as 2–3 times per hour. These time scales can be explained by protein dynamics (the rates of synthesis and degradation, folding, and diffusional transport). It rationalizes how bacterial growth is slowed down by added salt. In the same way that the behaviors of inanimate materials can be expressed in terms of the statistical distributions of atoms and molecules, some cell behaviors can be expressed in terms of distributions of protein properties, giving insights into the microscopic basis of growth laws in simple cells.

NTL9 Folding at Constant pH: The Importance of Electrostatic Interaction and pH Dependence

The folding process of the N-terminal domain of ribosomal protein L9 (NTL9) was investigated at constant-pH computer simulations. Evaluation of the role of electrostatic interaction during folding was carried out by including a Debye-Hückel potential into a Cα structure-based model (SBM). In this study, the charges of the ionizable residues and the electrostatic potential are susceptible to the solution conditions, such as pH and ionic strength, as well as to the presence of charged groups. Simulations were performed under different pHs, and the results were validated by comparing them with experimental values of pKa and with denaturation experiment data. Also, the free energy profiles, Φ-values, and folding routes were calculated for each condition. It was shown how charges vary along the folding under different pH, which is subject to different scenarios. This study reveals how simplified models can capture essential physical features, reproducing experimental results, and presenting the role of electrostatic interactions before, during, and after the transition state.

Nascent β-Hairpin Formation of a Natively Unfolded Peptide Reveals the Role of Hydrophobic Contacts

Despite the important role of the unfolded states in protein stability, folding, and aggregation, they remain poorly understood due to the lack of residue-specific experimental data. Here, we explore features of the unfolded state of the NTL9 protein by applying all-atom replica-exchange simulations to the two fragment peptides NTL9(1–22) and NTL9(6–17). We found that while NTL9(6–17) is unstructured, NTL9(1–22) transiently folds as various β-hairpins, a fraction of which contain a native β-sheet. Interestingly, despite a large number of charged residues, the formation of backbone hydrogen bonds is concomitant with hydrophobic but not electrostatic contacts. Although the fragment peptides lack a proposed specific contact between Asp⁸ and Lys¹², the individually weak, nonspecific interactions with lysines together stabilize the charged Asp⁸, leading to a pK_a shift of nearly 0.5 units, in agreement with the NMR data. Taken together, our data suggest that the unfolded state of NTL9 likely contains a β-hairpin in segment 1–22 with sequence-distant hydrophobic contacts, thus lending support to a long-standing hypothesis that the unfolded states of proteins exhibit native-like topology with hydrophobic clusters.

Positioning the Intracellular Salt Potassium Glutamate in the Hofmeister Series by Chemical Unfolding Studies of NTL9

In vitro, replacing KCl with potassium glutamate (KGlu), the Escherichia coli cytoplasmic salt and osmolyte, stabilizes folded proteins and protein-nucleic acid complexes. To understand the chemical basis for these effects and rank Glu- in the Hofmeister anion series for protein unfolding, we quantify and interpret the strong stabilizing effect of KGlu on the ribosomal protein domain NTL9, relative to the effects of other stabilizers (KCl, KF, and K2SO4) and destabilizers (GuHCl and GuHSCN). GuHSCN titrations at 20 ° C, performed as a function of the concentration of KGlu or another salt and monitored by NTL9 fluorescence, are analyzed to obtain R-values quantifying the Hofmeister salt concentration (m3) dependence of the unfolding equilibrium constant K(obs) [r-value = −d ln K(obs)/dm3 = (1/RT) dΔG(obs) ° /dm3 = m-value/RT]. r-Values for both stabilizing K+ salts and destabilizing GuH+ salts are compared with predictions from model compound data. For two-salt mixtures, we find that contributions of stabilizing and destabilizing salts to observed r-values are additive and independent. At 20 ° C, we determine a KGlu r-value of 3.22 m(−1) and K2SO4, KF, KCl, GuHCl, and GuHSCN r-values of 5.38, 1.05, 0.64, −1.38, and −3.00 m(−1), respectively. The KGlu r-value represents a 25-fold (1.9 kcal) stabilization per molal KGlu added. KGlu is much more stabilizing than KF, and the stabilizing effect of KGlu is larger in magnitude than the destabilizing effect of GuHSCN. Interpretation of the data reveals good agreement between predicted and observed relative r-values and indicates the presence of significant residual structure in GuHSCN-unfolded NTL9 at 20 ° C.

Sequence- and Temperature-Dependent Properties of Unfolded and Disordered Proteins from Atomistic Simulations

We use all-atom molecular simulation with explicit solvent to study the properties of selected intrinsically disordered proteins and unfolded states of foldable proteins, which include chain dimensions and shape, secondary structure propensity, solvent accessible surface area, and contact formation. We find that the qualitative scaling behavior of the chains matches expectations from theory under ambient conditions. In particular, unfolded globular proteins tend to be more collapsed under the same conditions than charged disordered sequences of the same length. However, inclusion of explicit solvent in addition naturally captures temperature-dependent solvation effects, which results in an initial collapse of the chains as temperature is increased, in qualitative agreement with experiment. There is a universal origin to the collapse, revealed in the change of hydration of individual residues as a function of temperature: namely, that the initial collapse is driven by unfavorable solvation free energy of individual residues, which in turn has a strong temperature dependence. We also observe that in unfolded globular proteins, increased temperature also initially favors formation of native-like (rather than non-native-like) structure. Our results help to establish how sequence encodes the degree of intrinsic disorder or order as well as its response to changes in environmental conditions.

Conformational Dynamics of Two Natively Unfolded Fragment Peptides: Comparison of the AMBER and CHARMM Force Fields

Physics-based force fields are the backbone of molecular dynamics simulations. In recent years, significant progress has been made in the assessment and improvement of commonly used force fields for describing conformational dynamics of folded proteins. However, the accuracy for the unfolded states remains unclear. The latter is however important for detailed studies of protein folding pathways, conformational transitions involving unfolded states, and dynamics of intrinsically disordered proteins. In this work, we compare the three commonly used force fields, AMBER ff99SB-ILDN, CHARMM22/CMAP, and CHARMM36, for modeling the natively unfolded fragment peptides, NTL9(1-22) and NTL9(6-17), using explicit-solvent replica-exchange molecular dynamics simulations. All three simulations show that NTL9(6-17) is completely unstructured, while NTL9(1-22) transiently samples various β-hairpin states, reminiscent of the first β-hairpin in the structure of the intact NTL9 protein. The radius of gyration of the two peptides is force field independent but likely underestimated due to the current deficiency of additive force fields. Compared to the CHARMM force fields, ff99SB-ILDN gives slightly higher β-sheet propensity and more native-like residual structures for NTL9(1-22), which may be attributed to its known β preference. Surprisingly, only two sequence-local pairs of charged residues make appreciable ionic contacts in the simulations of NTL9(1-22), which are sampled slightly more by the CHARMM force fields. Taken together, these data suggest that the current CHARMM and AMBER force fields are globally in agreement in modeling the unfolded states corresponding to β-sheet in the folded structure, while differing in details such as the native-likeness of the residual structures and interactions.

A molecular interpretation of 2D IR protein folding experiments with Markov state models

The folding mechanism of the N-terminal domain of ribosomal protein L9 (NTL91-39) is studied using temperature-jump (T-jump) amide I' two-dimensional infrared (2D IR) spectroscopy in combination with spectral simulations based on a Markov state model (MSM) built from millisecond-long molecular dynamics trajectories. The results provide evidence for a compact well-structured folded state and a heterogeneous fast-exchanging denatured state ensemble exhibiting residual secondary structure. The folding rate of 26.4 μs(-1) (at 80°C), extracted from the T-jump response of NTL91-39, compares favorably with the 18 μs(-1) obtained from the MSM. Structural decomposition of the MSM and analysis along the folding coordinate indicates that helix-formation nucleates the global folding. Simulated difference spectra, corresponding to the global folding transition of the MSM, are in qualitative agreement with measured T-jump 2D IR spectra. The experiments demonstrate the use of T-jump 2D IR spectroscopy as a valuable tool for studying protein folding, with direct connections to simulations. The results suggest that in addition to predicting the correct native structure and folding time constant, molecular dynamics simulations carried out with modern force fields provide an accurate description of folding mechanisms in small proteins.

Energetically significant networks of coupled interactions within an unfolded protein

Unfolded and partially unfolded proteins participate in a wide range of biological processes from pathological aggregation to the regulation of normal cellular activity. Unfolded states can be populated under strongly denaturing conditions, but the ensemble which is relevant for folding, stability, and aggregation is that populated under physiological conditions. Characterization of nonnative states is critical for the understanding of these processes, yet comparatively little is known about their energetics and their structural propensities under native conditions. The standard view is that energetically significant coupled interactions involving multiple residues are generally not present in the denatured state ensemble (DSE) or in intrinsically disordered proteins. Using the N-terminal domain of the ribosomal protein L9, a small α-β protein, as an experimental model system, we demonstrate that networks of energetically significant, coupled interactions can form in the DSE of globular proteins, and can involve residues that are distant in sequence and spatially well separated in the native structure. X-ray crystallography, NMR, dynamics studies, native state pKa measurements, and thermodynamic analysis of more than 25 mutants demonstrate that residues are energetically coupled in the DSE. Altering these interactions by mutation affects the stability of the domain. Mutations that alter the energetics of the DSE can impact the analysis of cooperativity and folding, and may play a role in determining the propensity to aggregate.

Denatured state ensembles with the same radii of gyration can form significantly different long-range contacts

Defining the structural, dynamic, and energetic properties of the unfolded state of proteins is critical for an in-depth understanding of protein folding, protein thermodynamics, and protein aggregation. Here we analyze long-range contacts and compactness in two apparently fully unfolded ensembles of the same protein: the acid unfolded state of the C-terminal domain of ribosomal protein L9 in the absence of high concentrations of urea as well as the urea unfolded state at low pH. Small angle X-ray scattering reveals that the two states are expanded with values of Rg differing by <7%. Paramagnetic relaxation enhancement (PRE) nuclear magnetic resonance studies, however, reveal that the acid unfolded state samples conformations that facilitate contacts between residues that are distant in sequence while the urea unfolded state ensemble does not. The experimental PRE profiles for the acid unfolded state differ significantly from these predicted using an excluded volume limit ensemble, but these long-range contacts are largely eliminated by the addition of 8 M urea. The work shows that expanded unfolded states can sample very different distributions of long-range contacts yet still have similar radii of gyration. The implications for protein folding and for the characterization of unfolded states are discussed.

Salt effects on hydrophobic-core formation in folding of a helical miniprotein studied by molecular dynamics simulations

We have investigated effects of salt ions on folding events of a helical miniprotein chicken villin headpiece subdomain HP36. Low concentrations of ions alter electrostatic interactions between charged groups of a protein and can change the populations of conformers. Here, we compare two data sets of folding simulations of HP36 in explicit water solvent with or without ions. For efficient sampling of the conformational space of HP36, the multicanonical replica-exchange molecular dynamics method was employed. Our analyses suggest that salt alters salt-bridging nature of the protein at later stages of folding at room temperature. Especially, more nonnative, nonlocal salt bridges are formed at near-native conformations in pure water. Our analyses also show that such salt-bridge formation hinders the fully native hydrophobic-core packing at the final stages of folding.

cDNA, genomic sequence cloning and overexpression of ribosomal protein gene L9 (rpL9) of the giant panda (Ailuropoda melanoleuca)

The ribosomal protein L9 (RPL9), a component of the large subunit of the ribosome, has an unusual structure, comprising two compact globular domains connected by an α-helix; it interacts with 23 S rRNA. To obtain information about rpL9 of Ailuropoda melanoleuca (the giant panda) we designed primers based on the known mammalian nucleotide sequence. RT-PCR and PCR strategies were employed to isolate cDNA and the rpL9 gene from A. melanoleuca; these were sequenced and analyzed. We overexpressed cDNA of the rpL9 gene in Escherichia coli BL21. The cloned cDNA fragment was 627 bp in length, containing an open reading frame of 579 bp. The deduced protein is composed of 192 amino acids, with an estimated molecular mass of 21.86 kDa and an isoelectric point of 10.36. The length of the genomic sequence is 3807 bp, including six exons and five introns. Based on alignment analysis, rpL9 has high similarity among species; we found 85% agreement of DNA and amino acid sequences with the other species that have been analyzed. Based on topology predictions, there are two N-glycosylation sites, five protein kinase C phosphorylation sites, one casein kinase II phosphorylation site, two tyrosine kinase phosphorylation sites, three N-myristoylation sites, one amidation site, and one ribosomal protein L6 signature 2 in the L9 protein of A. melanoleuca. The rpL9 gene can be readily expressed in E. coli; it fuses with the N-terminal GST-tagged protein, giving rise to the accumulation of an expected 26.51-kDa polypeptide, which is in good agreement with the predicted molecular weight. This expression product could be used for purification and further study of its function.

A residue in helical conformation in the native state adopts a β-strand conformation in the folding transition state despite its high and canonical Φ-value

Delineating structures of the transition states in protein folding reactions has provided great insight into the mechanisms by which proteins fold. The most common method for obtaining this information is Φ-value analysis, which is carried out by measuring the changes in the folding and unfolding rates caused by single amino acid substitutions at various positions within a given protein. Canonical Φ-values range between 0 and 1, and residues displaying high values within this range are interpreted to be important in stabilizing the transition state structure, and to elicit this stabilization through native-like interactions. Although very successful in defining the general features of transition state structures, Φ-value analysis can be confounded when non-native interactions stabilize this state. In addition, direct information on backbone conformation within the transition state is not provided. In the work described here, we have investigated structure formation at a conserved β-bulge (with helical conformation) in the Fyn SH3 domain by characterizing the effects of substituting all natural amino acids at one position within this structural motif. By comparing the effects on folding rates of these substitutions with database-derived local structure propensity values, we have determined that this position adopts a non-native backbone conformation in the folding transition state. This result is surprising because this position displays a high and canonical Φ-value of 0.7. This work emphasizes the potential role of non-native conformations in folding pathways and demonstrates that even positions displaying high and canonical Φ-values may, nevertheless, adopt a non-native conformation in the transition state.

Differential ordering of the protein backbone and side chains during protein folding revealed by site-specific recombinant infrared probes

The time scale for ordering of the polypeptide backbone relative to the side chains is a critical issue in protein folding. The interplay between ordering of the backbone and ordering of the side chains is particularly important for the formation of β-sheet structures, as the polypeptide chain searches for the native stabilizing cross-strand interactions. We have studied these issues in the N-terminal domain of protein L9 (NTL9), a model protein with mixed α/β structure. We have developed a general approach for introducing site-specific IR probes for the side chains (azide) and backbone ((13)C═(18)O) using recombinant protein expression. Temperature-jump time-resolved IR spectroscopy combined with site-specific labeling enables independent measurement of the respective backbone and side-chain dynamics with single residue resolution. We have found that side-chain ordering in a key region of the β-sheet structure occurs on a slower time scale than ordering of the backbone during the folding of NTL9, likely as a result of the transient formation of non-native side-chain interactions.

Rational and computational design of stabilized variants of cyanovirin-N that retain affinity and specificity for glycan ligands

Cyanovirin-N (CVN) is an 11 kDa pseudosymmetric cyanobacterial lectin that has been shown to inhibit infection by the human immunodeficiency virus by binding to high-mannose oligosaccharides on the surface of the viral envelope glycoprotein gp120. In this work, we describe rationally designed CVN variants that stabilize the protein fold while maintaining high affinity and selectivity for their glycan targets. Poisson-Boltzmann calculations and protein repacking algorithms were used to select stabilizing mutations in the protein core. By substituting the buried polar side chains of Ser11, Ser20, and Thr61 with aliphatic groups, we stabilized CVN by nearly 12 °C against thermal denaturation, and by 1 M GuaHCl against chemical denaturation, relative to a previously characterized stabilized mutant. Glycan microarray binding experiments confirmed that the specificity profile of carbohydrate binding is unperturbed by the mutations and is identical for all variants. In particular, the variants selectively bound glycans containing the Manα(1→2)Man linkage, which is the known minimal binding unit of CVN. We also report the slow denaturation kinetics of CVN and show that they can complicate thermodynamic analysis; in particular, the unfolding of CVN cannot be described as a fixed two-state transition. Accurate thermodynamic parameters are needed to describe the complicated free energy landscape of CVN, and we provide updated values for CVN unfolding.

Physical limits of cells and proteomes

What are the physical limits to cell behavior? Often, the physical limitations can be dominated by the proteome, the cell's complement of proteins. We combine known protein sizes, stabilities, and rates of folding and diffusion, with the known protein-length distributions P(N) of proteomes (Escherichia coli, yeast, and worm), to formulate distributions and scaling relationships in order to address questions of cell physics. Why do mesophilic cells die around 50 °C? How can the maximal growth-rate temperature (around 37 °C) occur so close to the cell-death temperature? The model shows that the cell's death temperature coincides with a denaturation catastrophe of its proteome. The reason cells can function so well just a few degrees below their death temperature is because proteome denaturation is so cooperative. Why are cells so dense-packed with protein molecules (about 20% by volume)? Cells are packed at a density that maximizes biochemical reaction rates. At lower densities, proteins collide too rarely. At higher densities, proteins diffuse too slowly through the crowded cell. What limits cell sizes and growth rates? Cell growth is limited by rates of protein synthesis, by the folding rates of its slowest proteins, and--for large cells--by the rates of its protein diffusion. Useful insights into cell physics may be obtainable from scaling laws that encapsulate information from protein knowledge bases.

Analysis of electrostatic interactions in the denatured state ensemble of the N-terminal domain of L9 under native conditions

The pH dependence of protein stability is defined by the difference in the number of protons bound to the folded state and to the denatured state ensemble (DSE) as a function of pH. In many cases, the protonation behavior can be described as the sum of a set of independently titrating residues; in this case, the pH dependence of stability reflects differences in folded and DSE pK(a)'s. pH dependent stability studies have shown that there are energetically important interactions involving charged residues in the DSE of the N-terminal domain of L9 (NTL9), which affect significantly the stability of the protein. The DSE of wild type NTL9 cannot be directly characterized under native conditions because of its high stability. A destabilized double mutant of NTL9, V3AI4A, significantly populates the folded state and the DSE in the absence of denaturant. The two states are in slow exchange on the nuclear magnetic resonance time scale, and diffusion measurements indicate that the DSE is compact. The DSE pK(a)'s of all of the acidic residues were directly determined. The DSE pK(a) of Asp8 and Asp23 are depressed relative to model compounds values. Use of the mutant DSE pK(a)'s together with known native state pK(a)'s leads to a significantly improved agreement between the measured pH dependent stability and that predicted by the Tanford-Wyman linkage relationship. An analysis of the literature suggests that DSE interactions involving charged residues are relatively common and should be considered in discussions of protein stability.

How do thermophilic proteins and proteomes withstand high temperature?

We attempt to understand the origin of enhanced stability in thermophilic proteins by analyzing thermodynamic data for 116 proteins, the largest data set achieved to date. We compute changes in entropy and enthalpy at the convergence temperature where different driving forces are maximally decoupled, in contrast to the majority of previous studies that were performed at the melting temperature. We find, on average, that the gain in enthalpy upon folding is lower in thermophiles than in mesophiles, whereas the loss in entropy upon folding is higher in mesophiles than in thermophiles. This implies that entropic stabilization may be responsible for the high melting temperature, and hints at residual structure or compactness of the denatured state in thermophiles. We find a similar trend by analyzing a homologous set of proteins classified based only on the optimum growth temperature of the organisms from which they were extracted. We find that the folding free energy at the temperature of maximal stability is significantly more favorable in thermophiles than in mesophiles, whereas the maximal stability temperature itself is similar between these two classes. Furthermore, we extend the thermodynamic analysis to model the entire proteome. The results explain the high optimal growth temperature in thermophilic organisms and are in excellent quantitative agreement with full thermal growth rate data obtained in a dozen thermophilic and mesophilic organisms.

pK(a) values for the unfolded state under native conditions explain the pH-dependent stability of PGB1

Understanding the role of electrostatics in protein stability requires knowledge of these interactions in both the folded and unfolded states. Electrostatic interactions can be probed experimentally by characterizing ionization equilibria of titrating groups, parameterized as pK(a) values. However, pK(a) values of the unfolded state are rarely accessible under native conditions, where the unfolded state has a very low population. Here, we report pK(a) values under nondenaturing conditions for two unfolded fragments of the protein G B1 domain that mimic the unfolded state of the intact protein. pK(a) values were determined for carboxyl groups by monitoring their pH-dependent (13)C chemical shifts. Monte Carlo simulations using a Gaussian chain model provide corrections for changes in electrostatic interactions that arise from fragmentation of the protein. Most pK(a) values for the unfolded state agree well with model values, but some residues show significant perturbations that can be rationalized by local electrostatic interactions. The pH-dependent stability was calculated from the experimental pK(a) values of the folded and unfolded states and compared to experimental stability data. The use of experimental pK(a) values for the unfolded state results in significantly improved agreement with experimental data, as compared to calculations based on model data alone.

Manifestations of native topology in the denatured state ensemble of Rhodopseudomonas palustris cytochrome c'

To provide insight into the role of local sequence in the nonrandom coil behavior of the denatured state, we have extended our measurements of histidine-heme loop formation equilibria for cytochrome c' to 6 M guanidine hydrochloride. We observe that there is some reduction in the scatter about the best fit line of loop stability versus loop size data in 6 M versus 3 M guanidine hydrochloride, but the scatter is not eliminated. The scaling exponent, ν(3), of 2.5 ± 0.2 is also similar to that found previously in 3 M guanidine hydrochloride (2.6 ± 0.3). Rates of histidine-heme loop breakage in the denatured state of cytochrome c' show that some histidine-heme loops are significantly more persistent than others at both 3 and 6 M guanidine hydrochloride. Rates of histidine-heme loop formation more closely approximate random coil behavior. This observation indicates that heterogeneity in the denatured state ensemble results mainly from contact persistence. When mapped onto the structure of cytochrome c', the histidine-heme loops with slow breakage rates coincide with chain reversals between helices 1 and 2 and between helices 2 and 3. Molecular dynamics simulations of the unfolding of cytochrome c' at 498 K show that these reverse turns persist in the unfolded state. Thus, these portions of the primary structure of cytochrome c' set up the topology of cytochrome c' in the denatured state, predisposing the protein to fold efficiently to its native structure.

Energetics and mechanisms of folding and flipping the myristoyl switch in the {beta}-trefoil protein, hisactophilin

Myristoylation, the covalent linkage of a saturated, C(14) fatty acyl chain to the N-terminal glycine in a protein, plays a vital role in reversible membrane binding and signaling by the modified proteins. Currently, little is known about the effects of myristoylation on protein folding and stability, or about the energetics and molecular mechanisms of switching involving states with sequestered versus accessible myristoyl group. Our analysis of these effects in hisactophilin, a histidine-rich protein that binds cell membranes and actin in a pH-dependent manner, shows that myristoylation significantly increases hisactophilin stability, while also markedly increasing global protein folding and unfolding rates. The switching between sequestered and accessible states is pH dependent, with an apparent pK(switch) of 6.95, and an apparent free energy change of 2.0 kcal·mol(-1). The myristoyl switch is linked to the reversible uptake of ∼1.5 protons, likely by histidine residues. This pH dependence of switching appears to be the physical basis of the sensitive, pH-dependent regulation of membrane binding observed in vivo. We conclude that an increase in protein stability upon modification and burial of the attached group is likely to occur in numerous proteins modified with fatty acyl or other hydrophobic groups, and that the biophysical effects of such modification are likely to play an important role in their functional switches. In addition, the increased global dynamics caused by myristoylation of hisactophilin reveals a general mechanism whereby hydrophobic moieties can make nonnative interactions or relieve strain in transition states, thereby increasing the rates of interconversion between different states.

Nonnative interactions in coupled folding and binding processes of intrinsically disordered proteins

Proteins function by interacting with other molecules, where both native and nonnative interactions play important roles. Native interactions contribute to the stability and specificity of a complex, whereas nonnative interactions mainly perturb the binding kinetics. For intrinsically disordered proteins (IDPs), which do not adopt rigid structures when being free in solution, the role of nonnative interactions may be more prominent in binding processes due to their high flexibilities. In this work, we investigated the effect of nonnative hydrophobic interactions on the coupled folding and binding processes of IDPs and its interplay with chain flexibility by conducting molecular dynamics simulations. Our results showed that the free-energy profiles became rugged, and intermediate states occurred when nonnative hydrophobic interactions were introduced. The binding rate was initially accelerated and subsequently dramatically decreased as the strength of the nonnative hydrophobic interactions increased. Both thermodynamic and kinetic analysis showed that disordered systems were more readily affected by nonnative interactions than ordered systems. Furthermore, it was demonstrated that the kinetic advantage of IDPs (“fly-casting” mechanism) was enhanced by nonnative hydrophobic interactions. The relationship between chain flexibility and protein aggregation is also discussed.

Propensities of aromatic amino acids versus leucine and proline to induce residual structure in the denatured-state ensemble of iso-1-cytochrome c

Histidine-heme loop formation in the denatured state of a protein is a sensitive means for probing residual structure under unfolding conditions. In this study, we use a host-guest approach to investigate the relative tendencies of different amino acids to promote residual structure under denaturing conditions. The host for this work is a 6-amino-acid insert of five alanines, followed by a lysine engineered immediately following a unique histidine near the N-terminus of yeast iso-1-cytochrome c. We substitute the fourth alanine in this sequence HAAAXAK (with X=Trp, Phe, Tyr, and Leu). The effects of proline are tested with substitutions at positions 1 and 5 in the insert (HPAAAAK and HAAAAPK, respectively). Thermodynamic studies on His-heme loop formation in 3 M guanidine hydrochloride reveal significant stabilization of residual structure by aromatic amino acids, particularly Trp and Phe, and minimal stabilization of residual structure by Leu. Prolines slightly disfavor His-heme loop formation, presumably due to enhanced chain stiffness. Kinetic studies reveal that much of the change in His-heme loop stability for the aromatic amino acids is caused by a slowdown in the rate of His-heme loop breakage, indicating that residual structure is preferentially stabilized in the closed-loop form of the denatured state.

Uncovering specific electrostatic interactions in the denatured states of proteins

The stability and folding of proteins are modulated by energetically significant interactions in the denatured state that is in equilibrium with the native state. These interactions remain largely invisible to current experimental techniques, however, due to the sparse population and conformational heterogeneity of the denatured-state ensemble under folding conditions. Molecular dynamics simulations using physics-based force fields can in principle offer atomistic details of the denatured state. However, practical applications are plagued with the lack of rigorous means to validate microscopic information and deficiencies in force fields and solvent models. This study presents a method based on coupled titration and molecular dynamics sampling of the denatured state starting from the extended sequence under native conditions. The resulting denatured-state pK(a)s allow for the prediction of experimental observables such as pH- and mutation-induced stability changes. I show the capability and use of the method by investigating the electrostatic interactions in the denatured states of wild-type and K12M mutant of NTL9 protein. This study shows that the major errors in electrostatics can be identified by validating the titration properties of the fragment peptides derived from the sequence of the intact protein. Consistent with experimental evidence, our simulations show a significantly depressed pK(a) for Asp(8) in the denatured state of wild-type, which is due to a nonnative interaction between Asp(8) and Lys(12). Interestingly, the simulation also shows a nonnative interaction between Asp(8) and Glu(48) in the denatured state of the mutant. I believe the presented method is general and can be applied to extract and validate microscopic electrostatics of the entire folding energy landscape.