Protonation/deprotonation effects on the stability of the Trp-cage miniprotein

The Trp-cage miniprotein is a 20 amino acid peptide that exhibits many of the properties of globular proteins. In this protein, the hydrophobic core is formed by a buried Trp side chain. The folded state is stabilized by an ion pair between aspartic acid and an arginine side chain. The effect of protonating the aspartic acid on the Trp-cage miniprotein folding/unfolding equilibrium is studied by explicit solvent molecular dynamics simulations of the protein in the charged and protonated Asp9 states. Unbiased Replica Exchange Molecular Dynamics (REMD) simulations, spanning a wide temperature range, are carried out to the microsecond time scale, using the AMBER99SB forcefield in explicit TIP3P water. The protein structural ensembles are studied in terms of various order parameters that differentiate the folded and unfolded states. We observe that in the folded state the root mean square distance (rmsd) from the backbone of the NMR structure shows two highly populated basins close to the native state with peaks at 0.06 nm and 0.16 nm, which are consistent with previous simulations using the same forcefield. The fraction of folded replicas shows a drastic decrease because of the absence of the salt bridge. However, significant populations of conformations with the arginine side chain exposed to the solvent, but within the folded basin, are found. This shows the possibility to reach the folded state without formation of the ion pair. We also characterize changes in the unfolded state. The equilibrium populations of the folded and unfolded states are used to characterize the thermodynamics of the system. We find that the change in free energy difference due to the protonation of the Asp amino acid is 3 kJ mol(-1) at 297 K, favoring the charged state, and resulting in ΔpK(1) = 0.5 units for Asp9. We also study the differences in the unfolded state ensembles for the two charge states and find significant changes at low temperature, where the protonated Asp side chain makes multiple hydrogen bonds to the protein backbone.     

Free-energy landscape for beta hairpin folding from combined parallel tempering and metadynamics

We develop a new free-energy method, based on the combination of parallel tempering and metadynamics, and apply this method to the calculation of the free-energy landscape of the folding beta hairpin in explicit water. We show that the combined method greatly improves the performance of both parallel tempering and metadynamics. In particular, we are able to sample the high free-energy regions, which are not accessible with conventional parallel tempering. We use our results to calculate the difference in entropy and enthalpy between the folded and the unfolded state and to characterize the most populated configurations in the relevant free-energy basins.     

Understanding the folding rates and folding nuclei of globular proteins

The first part of this paper contains an overview of protein structures, their spontaneous formation ("folding"), and the thermodynamic and kinetic aspects of this phenomenon, as revealed by in vitro experiments. It is stressed that universal features of folding are observed near the point of thermodynamic equilibrium between the native and denatured states of the protein. Here the "two-state" ("denatured state" <--> "native state") transition proceeds without accumulation of metastable intermediates, but includes only the unstable "transition state". This state, which is the most unstable in the folding pathway, and its structured core (a "nucleus") are distinguished by their essential influence on the folding/unfolding kinetics. In the second part of the paper, a theory of protein folding rates and related phenomena is presented. First, it is shown that the protein size determines the range of a protein's folding rates in the vicinity of the point of thermodynamic equilibrium between the native and denatured states of the protein. Then, we present methods for calculating folding and unfolding rates of globular proteins from their sizes, stabilities and either 3D structures or amino acid sequences. Finally, we show that the same theory outlines the location of the protein folding nucleus (i.e., the structured part of the transition state) in reasonable agreement with experimental data.     

Fast folding of a four-helical bundle protein

The FK506-FKBP12 binding-domain of the kinase FRAP (FRB) forms a classic up-down four-helical bundle. The folding pathway of this protein has been investigated using a combination of equilibrium and kinetic studies. The native state of the protein is stable with respect to the unfolded state by some 7 kcal mol(-1) at pH 6.0, 10 degrees C. A kinetic analysis of unfolding and refolding rate constants as a function of chemical denaturant concentration suggests that an intermediate state may be populated during folding at low concentrations of denaturant. The presence of this intermediate state is confirmed by refolding experiments performed in the presence of the hydrophobic dye 8-anilinonaphthalene-1 sulfonate (ANS). ANS binds to the partially folded intermediate state populated during the folding of FRB and undergoes a large change in fluorescence that can be detected using stopped-flow techniques. Analysis of the kinetic data suggests that the intermediate state is compact and it may even be a misfolded species that has to partially unfold before it can reach the transition state. Folding and unfolding rate constants in water are approximately 150-200 s(-1) and 0.005-0.06 s(-1), respectively, at neutral pH and 10 degrees C. The folding of FRB is somewhat slower than for other all-helical proteins, probably as a consequence of the formation of a metastable intermediate state. The folding rate constant in the absence of any populated intermediate can be estimated to be 8800 s(-1). Despite the presence of an intermediate state, which effectively slows folding, the protein still folds rapidly with a half-life of 5 ms at 10 degrees C. The dependence of the rate constants on denaturant concentration indicates that the transition state for folding is compact with some 80% of the surface area exposed in the unfolded state buried in the transition state. Data presented for FRB is compared with kinetic data obtained for other all-helical proteins.     

Protein stability at a carbon nanotube interface

The interactions of proteins with solid surfaces occur in a variety of situations. Motivated by the many nanoengineering applications of protein-carbon nanotube hybrids, we investigate the conformational transitions of hen egg white lysozyme adsorbed on a carbon nanotube. Using a C(α) structure-based model and replica exchange molecular dynamics, we show how the folding/unfolding equilibrium of the adsorbed protein varies with the strength of its coupling to the surface. The stability of the native state depends on the balance between the favorable entropy and unfavorable enthalpy change on adsorption. In the case of a weakly attractive surface when the former dominates, the protein is stabilized. In this regime, the protein can fold and unfold while maintaining the same binding fraction. With increasing surface attraction, the unfavorable enthalpic effect dominates, the native state is destabilized, and the protein has to extensively unbind before changing states from unfolded to folded. At the highest surface coupling, the entropic penalty of folding vanishes, and a folding intermediate is strongly stabilized. In this intermediate state, the α-domain of lysozyme is disrupted, while the β-sheet remains fully structured. We rationalize the relative stability of the two domains on the basis of the residue contact order.     

Effect of urea on the β-hairpin conformational ensemble and protein denaturation mechanism

Despite the daily use of urea to influence protein folding and stability, the molecular mechanism with which urea acts is still not well understood. Here the use of combined parallel tempering and metadynamics simulation allows us to study the free-energy landscape associated with the folding/unfolding of β-hairpin GB1 equilibrium in 8 M urea and pure water. The nature of the unfolded state in both solutions has been analyzed: in urea solution the addition of denaturants acts to expand the denatured state, while in pure water solution the unfolded state is noticeably more compact. For what concerns the mechanism by which urea acts as a denaturant, a preferential direct interaction between urea molecules and protein backbone has been found. However, the bias toward urea solvation is largest at intermediate values of the gyration radius.     

Probing the transition state ensemble of a protein folding reaction by pressure-dependent NMR relaxation dispersion

The F61A/A90G mutant of a redesigned form of apocytochrome b562 folds by an apparent two-state mechanism. We have used the pressure dependence of 15N NMR relaxation dispersion rate profiles to study the changes in volumetric parameters that accompany the folding reaction of this protein at 45 degrees C. The experiments were performed under conditions where the folding/unfolding equilibrium could be studied at each pressure without addition of denaturants. The exquisite sensitivity of the methodology to small changes in folding/unfolding rates facilitated the use of relatively low-pressure values (between 1 and 270 bar) so that pressure-induced changes to the unfolded state ensemble could be minimized. A volume change for unfolding of -81 mL/mol is measured (at 1 bar), a factor of 1.4 larger (in absolute value) than the volume difference between the transition state ensemble (TSE) and the unfolded state. Notably, the changes in the free energy difference between folded and unfolded states and in the activation free energy for folding were not linear with pressure. Thus, the difference in the isothermal compressibility upon unfolding (-0.11 mL mol(-1) bar(-1)) and, for the first time, the compressibility of the TSE relative to the unfolded state (0.15 mL mol(-1) bar(-1)) could be calculated. The results argue for a TSE that is collapsed but loosely packed relative to the folded state and significantly hydrated, suggesting that the release of water occurs after the rate-limiting step in protein folding. The notion of a collapsed and hydrated TSE is consistent with expectations based on earlier temperature-dependent folding studies, showing that the barrier to folding at 45 degrees C is entropic (Choy, W. Y.; Zhou, Z.; Bai, Y.; Kay, L. E. J. Am. Chem. Soc. 2005, 127, 5066-5072).     

Thermodynamics of Go-type models for protein folding

Go-type potentials, based on the inter-residue contacts present in the native structure of a protein, are frequently used to predict dynamic and structural features of the folding pathways through computer simulations. However, the mathematical form used to define the model interactions includes several arbitrary choices, whose consequences are not usually analyzed. In this work, we use a simple off-lattice protein model and a parallel tempering Monte Carlo simulation technique to carry out such analysis, centered in the thermodynamic characteristics of the folding transition. We show how the definition of a native contact has a deep impact on the presence of simple or complex transitions, with or without thermodynamic intermediates. In addition, we have checked that the width of the attractive wells has a profound effect on the free-energy barrier between the folded and unfolded states, mainly through its influence on the entropy of the denatured state.     

A lattice protein with an amyloidogenic latent state: stability and folding kinetics

We have designed a model lattice protein that has two stable folded states, the lower free energy native state and a latent state of somewhat higher energy. The two states have a sizable part of their structures in common (two "alpha-helices") and differ in the content of "alpha-helices" and "beta-strands" in the rest of their structures; i.e. for the native state, this part is alpha-helical, and for the latent state it is composed of beta-strands. Thus, the lattice protein free energy surface mimics that of amyloidogenic proteins that form well organized fibrils under appropriate conditions. A Go-like potential was used and the folding process was simulated with a Monte Carlo method. To gain insight into the equilibrium free energy surface and the folding kinetics, we have combined standard approaches (reduced free energy surfaces, contact maps, time-dependent populations of the characteristic states, and folding time distributions) with a new approach. The latter is based on a principal coordinate analysis of the entire set of contacts, which makes possible the introduction of unbiased reaction coordinates and the construction of a kinetic network for the folding process. The system is found to have four characteristic basins, namely a semicompact globule, an on-pathway intermediate (the bifurcation basin), and the native and latent states. The bifurcation basin is shallow and consists of the structure common to the native and latent states, with the rest disorganized. On the basis of the simulation results, a simple kinetic model describing the transitions between the characteristic states was developed, and the rate constants for the essential transitions were estimated. During the folding process the system dwells in the bifurcation basin for a relatively short time before it proceeds to the native or latent state. We suggest that such a bifurcation may occur generally for proteins in which native and latent states have a sizable part of their structures in common. Moreover, there is the possibility of introducing changes in the system (e.g., mutations), which guide the system toward the native or misfolded state.     

A free-energy landscape for coupled folding and binding of an intrinsically disordered protein in explicit solvent from detailed all-atom computations

The N-terminal repressor domain of neural restrictive silencer factor (NRSF) is an intrinsically disordered protein (IDP) that binds to the paired amphipathic helix (PAH) domain of mSin3. An NMR experiment revealed that the minimal binding unit of NRSF is a 15-residue segment that adopts a helical structure upon binding to a cleft of mSin3. We computed a free-energy landscape of this system by an enhanced conformational sampling method, all-atom multicanonical molecular dynamics. The simulation started from a configuration where the NRSF segment was fully disordered and distant from mSin3 in explicit solvent. In the absence of mSin3, the disordered NRSF segment thermally fluctuated between hairpins, helices, and bent structures. In the presence of mSin3, the segment bound to mSin3 by adopting the structures involved in the isolated state, and non-native and native complexes were formed. The free-energy landscape comprised three superclusters, and free-energy barriers separated the superclusters. The native complex was located at the center of the lowest free-energy cluster. When NRSF landed in the largest supercluster, the generated non-native complex moved on the landscape to fold into the native complex, by increasing the interfacial hydrophobic contacts and the helix content. When NRSF landed in other superclusters, the non-native complex overcame the free-energy barriers between the various segment orientations in the binding cleft of mSin3. Both population-shift and induced-fit (or induced-folding) mechanisms work cooperatively in the coupled folding and binding. The diverse structural adaptability of NRSF may be related to the hub properties of the IDP.     

Detection of the equilibrium folding intermediate of beta-lactoglobulin in the presence of trifluoroethanol by mass spectrometry

Nano-electrospray ionization mass spectrometry (nano-ESI-MS) was used to monitor the effect of trifluoroethanol (TFE) on the conformational properties of beta-lactoglobulin (BLG). TFE stabilizes protein secondary structure, particularly alpha-helices. However, it also acts as a denaturant above critical concentrations. In the case of BLG, TFE at low concentrations is known to induce formation of an equilibrium intermediate that contains non-native helical structure. Such an intermediate is thought to form also under physiological conditions, playing a role in BLG folding in vivo by preventing aggregation. This well-characterized system was chosen in order to test species distributions obtained by nano-ESI-MS. BLG spectra at increasing concentrations of TFE at pH 2 indicate transient accumulation of a conformer whose charge-state distribution (CSD) falls between that of the native and that of the denatured protein, indicating that the TFE-induced, partially folded form can be selectively monitored by this technique. The condition of its maximum accumulation corresponds to 16% TFE, in excellent agreement with results from solution experiments. In contrast, titrations with methanol or acetonitrile (ACN) reveal apparent two-state transitions from native to fully unfolded BLG. At 10% TFE, the protein appears to be still fully folded at room temperature but, if unfolding is elicited by the combination with other denaturing agents, e.g. heat or low concentrations of ACN, it proceeds via formation of the intermediate. Thus, TFE can also induce formation of the BLG intermediate in synergism with generic denaturing agents. This study indicates good agreement between ESI-MS and other biophysical methods monitoring protein conformational transitions in the presence of TFE.     

脲和盐酸胍诱导过氧化氢酶去折叠的研究

用荧光相图法分别研究了脲和盐酸胍诱导牛肝过氧化氢酶去折叠的过程。当脲 浓度从0依次增大至0.50,4.5和8.0 mol/L时,过氧化氢酶从天然四聚体依次转变 为蓬松的四聚体、部分折叠的无活性二聚体和去折叠态,而当盐酸胍浓度从0依次 变化至0.65,2.5和6.0 mol/L时,过氧化氢酶则从天然四聚体集资转变为部分折叠 的激活二聚体、部分折叠的单体和去折叠态,这表明无论是用脲还是用盐酸胍作为 变性剂,该蛋白的变性过程都符合“四态模型”,但这两种变性剂诱导该蛋白去折 叠的途径和机制有较大差异。实验结果表明荧光相图法可以检测蛋白质去折叠的中 间态。用等温滴定量去热法研究了盐酸胍诱导过氧化氢酶去折叠过程的热力学, 25.0 ℃时低浓度盐酸胍诱导该蛋白从天然四聚体转变为部分折叠的激活二聚体的 本征摩尔构象变化焓、Gibbs自由能和熵分别为-69.2 kJ·mol~(-1),6.43 kJ· mol~(-1)和-254 J·K~(-1)·mol~(-1),据此推断盐酸胍通过熵效应和静电效应来 稳定和激活该二聚体。     

Measurement of electrostatic interactions in protein folding with the use of protein charge ladders

This paper describes a new method for the measurement of the role of interactions between charged groups on the energetics of protein folding. This method uses capillary electrophoresis (CE) and protein charge ladders (mixtures of protein derivatives that differ incrementally in number of charged groups) to measure, in a single set of electrophoresis experiments, the free energy of unfolding (DeltaG(D-N)) of alpha-lactalbumin (alpha-LA) as a function of net charge. These same data also yield the hydrodynamic radius, R(H), and net charge measured by CE, Z(CE), of the folded and denatured proteins. Alpha-LA unfolds to a compact denatured state under mildly alkaline conditions; a small increase in R(H) (11%, 2 A) coincides with a large increase in Z(CE) (71%, -4 charge units), relative to the folded state. The increase in Z(CE), in turn, predicts a large pH dependence of free energy of unfolding (-22 kJ/mol per unit increase in pH), due to differences in proton binding in the folded and denatured states. The free energy of unfolding correlates with the square of net charge of the members of the charge ladder. The differential dependence of DeltaG(D-N) on net charge for holo-alpha-LA, (partial differential) DeltaG(D-N)/(partial differential)Z = -0.14Z kJ/mol per unit of charge. This dependence of DeltaG(D-N) on net charge is a result of a net electrostatic repulsion among charge groups on the protein. These results, together with data from pH titrations, show that both the effects of electrostatic repulsion and differences in proton binding in the folded and denatured states can play an important role in the pH dependence of this protein; the relative magnitude of these effects varies with pH. The combination of charge ladders and CE is a rapid and efficient tool that measures the contributions of electrostatics to the energetics of protein folding, and the size and charge of proteins as they unfold. All this information is obtained from a single set of electrophoresis experiments.     

New scenarios of protein folding can occur on the ribosome

Identifying and understanding the differences between protein folding in bulk solution and in the cell is a crucial challenge facing biology. Using Langevin dynamics, we have simulated intact ribosomes containing five different nascent chains arrested at different stages of their synthesis such that each nascent chain can fold and unfold at or near the exit tunnel vestibule. We find that the native state is destabilized close to the ribosome surface due to an increase in unfolded state entropy and a decrease in native state entropy; the former arises because the unfolded ensemble tends to behave as an expanded random coil near the ribosome and a semicompact globule in bulk solution. In addition, the unfolded ensemble of the nascent chain adopts a highly anisotropic shape near the ribosome surface and the cooperativity of the folding-unfolding transition is decreased due to the appearance of partially folded structures that are not populated in bulk solution. The results show, in light of these effects, that with increasing nascent chain length folding rates increase in a linear manner and unfolding rates decrease, with larger and topologically more complex folds being the most highly perturbed by the ribosome. Analysis of folding trajectories, initiated by temperature quench, reveals the transition state ensemble is driven toward compaction and greater native-like structure by interactions with the ribosome surface and exit vestibule. Furthermore, the diversity of folding pathways decreases and the probability increases of initiating folding via the N-terminus on the ribosome. We show that all of these findings are equally applicable to the situation in which protein folding occurs during continuous (non-arrested) translation provided that the time scales of folding and unfolding are much faster than the time scale of monomer addition to the growing nascent chain, which results in a quasi-equilibrium process. These substantial ribosome-induced perturbations to almost all aspects of protein folding indicate that folding scenarios that are distinct from those of bulk solution can occur on the ribosome.     

Molecular simulation of protein dynamics in nanopores. I. Stability and folding

Discontinuous molecular dynamics simulations, together with the protein intermediate resolution model, an intermediate-resolution model of proteins, are used to carry out several microsecond-long simulations and study folding transition and stability of alpha-de novo-designed proteins in slit nanopores. Both attractive and repulsive interaction potentials between the proteins and the pore walls are considered. Near the folding temperature T(f) and in the presence of the attractive potential, the proteins undergo a repeating sequence of folding/partially folding/unfolding transitions, with T(f) decreasing with decreasing pore sizes. The unfolded states may even be completely adsorbed on the pore's walls with a negative potential energy. In such pores the energetic effects dominate the entropic effects. As a result, the unfolded state is stabilized, with a folding temperature T(f) which is lower than its value in the bulk and that, compared with the bulk, the folding rate decreases. The opposite is true in the presence of a repulsive interaction potential between the proteins and the walls. Moreover, for short proteins in very tight pores with attractive walls, there exists an unfolded state with only one alpha-helical hydrogen bond and an energy nearly equal to that of the folded state. The proteins have, however, high entropies, implying that they cannot fold onto their native structure, whereas in the presence of repulsive walls the proteins do attain their native structure. There is a pronounced asymmetry between the two termini of the protein with respect to their interaction with the pore walls. The effect of a variety of factors, including the pore size and the proteins' length, as well as the temperature, is studied in detail.     

Atomistic folding simulations of the five-helix bundle protein λ(6−85)

Protein folding is a classic grand challenge that is relevant to numerous human diseases, such as protein misfolding diseases like Alzheimer’s disease. Solving the folding problem will ultimately require a combination of theory, simulation, and experiment, with theory and simulation providing an atomically detailed picture of both the thermodynamics and kinetics of folding and experimental tests grounding these models in reality. However, theory and simulation generally fall orders of magnitude short of biologically relevant time scales. Here we report significant progress toward closing this gap: an atomistic model of the folding of an 80-residue fragment of the λ repressor protein with explicit solvent that captures dynamics on a 10 milliseconds time scale. In addition, we provide a number of predictions that warrant further experimental investigation. For example, our model’s native state is a kinetic hub, and biexponential kinetics arises from the presence of many free-energy basins separated by barriers of different heights rather than a single low barrier along one reaction coordinate (the previously proposed incipient downhill folding scenario).     

Folding of human telomerase RNA pseudoknot using ion-jump and temperature-quench simulations

Globally RNA folding occurs in multiple stages involving chain compaction and subsequent rearrangement by a number of parallel routes to the folded state. However, the sequence-dependent details of the folding pathways and the link between collapse and folding are poorly understood. To obtain a comprehensive picture of the thermodynamics and folding kinetics we used molecular simulations of coarse-grained model of a pseudoknot found in the conserved core domain of the human telomerase (hTR) by varying both temperature (T) and ion concentration (C). The phase diagram in the [T,C] plane shows that the boundary separating the folded and unfolded state for the finite 47-nucleotide system is relatively sharp, implying that from a thermodynamic perspective hTR behaves as an apparent two-state system. However, the folding kinetics following single C-jump or T-quench is complicated, involving multiple channels to the native state. Although globally folding kinetics triggered by T-quench and C-jump are similar, the kinetics of chain compaction are vastly different, which reflects the role of initial conditions in directing folding and collapse. Remarkably, even after substantial reduction in the overall size of hTR, the ensemble of compact conformations are far from being nativelike, suggesting that the search for the folded state occurs among the ensemble of low-energy fluidlike globules. The rate of unfolding, which occurs in a single step, is faster upon C-decrease compared to a jump in temperature. To identify "hidden" states that are visited during the folding process we performed simulations by periodically interrupting the approach to the folded state by lowering C. These simulations show that hTR reaches the folded state through a small number of connected clusters that are repeatedly visited during the pulse sequence in which the folding or unfolding is interrupted. The results from interrupted folding simulations, which are in accord with non-equilibrium single-molecule folding of a large ribozyme, show that multiple probes are needed to reveal the invisible states that are sampled by RNA as it folds. Although we have illustrated the complexity of RNA folding using hTR as a case study, general arguments and qualitative comparisons to time-resolved scattering experiments on Azoarcus group I ribozyme and single-molecule non-equilibrium periodic ion-jump experiments establish the generality of our findings.     

Mapping tertiary interactions in protein folding reactions: a novel mass spectrometry- and chemical synthesis-based approach

A novel mass spectrometry- and chemical synthesis-based approach for studying protein folding reactions is described, and its initial application to study the folding/unfolding reaction of a homo-hexameric enzyme 4-oxalocrotonate (4OT) is reported. This new approach involves the application of total chemical synthesis to prepare protein analogues that contain a photoreactive amino acid site-specifically incorporated into their primary amino acid sequence. To this end, a photoreactive amino acid-containing analogue of 4OT in which Pro-1 was replaced with p-benzoyl-l-phenylalanine (Bpa) was prepared. This analogue can be used to map structurally specific protein-protein interactions in 4OT's native folded state. These photocrosslinking studies and peptide mapping results with (PlBpa)4OT indicate that this construct is potentially useful for probing the structural properties of equilibrium and kinetic intermediates in 4OT's folding reaction.