Fast protein folding on downhill energy landscape

Downhill, Ultrafast and Fast Folding Proteins Revised

Research on the protein folding problem differentiates the protein folding process with respect to the duration of this process. The current structure encoded in sequence dogma seems to be clearly justified, especially in the case of proteins referred to as fast-folding, ultra-fast-folding or downhill. In the present work, an attempt to determine the characteristics of this group of proteins using fuzzy oil drop model is undertaken. According to the fuzzy oil drop model, a protein is a specific micelle composed of bi-polar molecules such as amino acids. Protein folding is regarded as a spherical micelle formation process. The presence of covalent peptide bonds between amino acids eliminates the possibility of free mutual arrangement of neighbors. An example would be the construction of co-micelles composed of more than one type of bipolar molecules. In the case of fast folding proteins, the amino acid sequence represents the optimal bipolarity system to generate a spherical micelle. In order to achieve the native form, it is enough to have an external force field provided by the water environment which directs the folding process towards the generation of a centric hydrophobic core. The influence of the external field can be expressed using the 3D Gaussian function which is a mathematical model of the folding process orientation towards the concentration of hydrophobic residues in the center with polar residues exposed on the surface. The set of proteins under study reveals a hydrophobicity distribution compatible with a 3D Gaussian distribution, taken as representing an idealized micelle-like distribution. The structure of the present hydrophobic core is also discussed in relation to the distribution of hydrophobic residues in a partially unfolded form.

Globular Protein Folding In Vitro and In Vivo

In vitro, computational, and theoretical studies of protein folding have converged to paint a rich and complex energy landscape. This landscape is sensitively modulated by environmental conditions and subject to evolutionary pressure on protein function. Of these environments, none is more complex than the cell itself, where proteins function in the cytosol, in membranes, and in different compartments. A wide variety of kinetic and thermodynamics experiments, ranging from single-molecule studies to jump kinetics and from nuclear magnetic resonance to imaging on the microscope, have elucidated how protein energy landscapes facilitate folding and how they are subject to evolutionary constraints and environmental perturbation. Here we review some recent developments in the field and refer the reader to some original work and additional reviews that cover this broad topic in protein science.

Kinetic Transition Networks for the Thomson Problem and Smale's Seventh Problem

The Thomson problem, arrangement of identical charges on the surface of a sphere, has found many applications in physics, chemistry and biology. Here, we show that the energy landscape of the Thomson problem for N particles with N=132, 135, 138, 141, 144, 147, and 150 is single funneled, characteristic of a structure-seeking organization where the global minimum is easily accessible. Algorithmically, constructing starting points close to the global minimum of such a potential with spherical constraints is one of Smale's 18 unsolved problems in mathematics for the 21st century because it is important in the solution of univariate and bivariate random polynomial equations. By analyzing the kinetic transition networks, we show that a randomly chosen minimum is, in fact, always "close" to the global minimum in terms of the number of transition states that separate them, a characteristic of small world networks.

Crowding effects on the small, fast-folding protein lambda6-85

The microsecond folder lambda6-85 is a small (9.2 kDa = 9200 amu) five helix bundle protein. We investigated the stability of lambda6-85 in two different low-fluorescence crowding matrices: the large 70 kDa carbohydrate Ficoll 70, and the small 14 kDa thermophilic protein SubL. The same thermal stability of secondary structure was measured by circular dichroism in aqueous buffer, and at a crowding fraction phi = 15 +/- 1% of Ficoll 70. Tryptophan fluorescence detection (probing a tertiary contact) yielded the same thermal stability in Ficoll, but 4 degrees C lower in aqueous buffer. Temperature-jump kinetics revealed that the relaxation rate, corrected for bulk viscosity, was very similar in Ficoll and in aqueous buffer. Thus viscosity, hydrodynamics and crowding seem to compensate one another. However, a new fast phase was observed in Ficoll, attributed to crowding-induced downhill folding. We also measured the stability of lambda6-85 in phi = 14 +/- 1% SubL, which acts as a smaller more rigid crowder. Significantly greater stabilization (7 to 13 degrees C depending on probe) was observed than in the Ficoll matrix. The results highlight the importance of crowding agent choice for studies of small, fast-folding proteins amenable to comparison with molecular dynamics simulations.

Combination of Markov state models and kinetic networks for the analysis of molecular dynamics simulations of peptide folding

Atomistic molecular dynamics simulations of the TZ1 beta-hairpin peptide have been carried out using an implicit model for the solvent. The trajectories have been analyzed using a Markov state model defined on the projections along two significant observables and a kinetic network approach. The Markov state model allowed for an unbiased identification of the metastable states of the system, and provided the basis for commitment probability calculations performed on the kinetic network. The kinetic network analysis served to extract the main transition state for folding of the peptide and to validate the results from the Markov state analysis. The combination of the two techniques allowed for a consistent and concise characterization of the dynamics of the peptide. The slowest relaxation process identified is the exchange between variably folded and denatured species, and the second slowest process is the exchange between two different subsets of the denatured state which could not be otherwise identified by simple inspection of the projected trajectory. The third slowest process is the exchange between a fully native and a partially folded intermediate state characterized by a native turn with a proximal backbone H-bond, and frayed side-chain packing and termini. The transition state for the main folding reaction is similar to the intermediate state, although a more native like side-chain packing is observed.

Probing the folding of mini-protein Beta3s by two-dimensional infrared spectroscopy; simulation study

We propose to use infrared coherent two-dimensional correlation spectroscopy (2DCS) to characterize the folding mechanism of the mini-protein Beta3s. In this study Beta3s was folded by molecular dynamics (MD) simulation and intermediate conformational ensembles were identified. The one and two-dimensional correlation spectrum was calculated for the intermediate and native states of the mini-protein. A direct structure-spectra relationship was determined by analysis of conformational properties and specific residue contributions. We identified the structural origin of diagonal and off-diagonal peaks in the 2DCS spectra for the native and intermediate conformational ensembles in the folding mechanism. This work supports the implementation of computational techniques in conjunction with experimental 2DCS to study the folding mechanism of proteins. In addition to exploring the folding mechanism the work presented here can be applied in combination with experiment to refine and validate current molecular dynamics force fields.

PACS Codes: 87.15.Cc, 87.15.hm, 87.15.hp

A conserved unfoldase activity for the p97 AAA-ATPase in proteasomal degradation

The multifunctional AAA-ATPase p97 is one of the most abundant and conserved proteins in eukaryotic cells. The p97/Npl4/Ufd1 complex dislocates proteins that fail the protein quality control in the endoplasmic reticulum to the cytosol where they are subject to degradation by the ubiquitin/proteasome system. Substrate dislocation depends on the unfoldase activity of p97. Interestingly, p97 is also involved in the degradation of specific soluble proteasome substrates but the exact mode of action of p97 in this process is unclear. Here, we show that both the central pore and ATPase activity of p97 are necessary for the degradation of cytosolic ubiquitin-fusion substrates. Addition of a flexible extended C-terminal peptide to the substrate relieves the requirement for p97. Deletion mapping reveals a conserved length dependency of 20 residues for the peptide, which allows p97-independent degradation to occur. Our results suggest that initiation of unfolding may be more complex than previously anticipated and that the 19S regulatory complex of the proteasome can require preprocessing of highly folded, ubiquitylated substrates by the p97(Ufd1/Npl4) complex. Our data provide an explanation for the observation that p97 is only essential for a subpopulation of soluble substrates and predict that a common characteristic of soluble p97-dependent substrates is the lack of an initiation site to facilitate unfolding by the 26S proteasome.

CHARMM: the biomolecular simulation program

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.

Folding pathways and rates for the three-stranded beta-sheet peptide Beta3s using discrete path sampling

The discrete path sampling method was used to investigate the folding of a three-stranded antiparallel beta-sheet peptide, Beta3s, described by an empirical potential and implicit solvent model. After application of a coarse-graining scheme that groups together sets of minima in local equilibrium, the calculated folding time was in reasonable agreement with other simulations and consistent with the experimental upper bound. The folding mechanism exhibited by the most significant discrete paths involves early formation of the C-terminal hairpin followed by docking of the N-terminal strand.

FACTS: Fast analytical continuum treatment of solvation

An efficient method for calculating the free energy of solvation of a (macro)molecule embedded in a continuum solvent is presented. It is based on the fully analytical evaluation of the volume and spatial symmetry of the solvent that is displaced from around a solute atom by its neighboring atoms. The two measures of solvent displacement are combined in empirical equations to approximate the atomic (or self) electrostatic solvation energy and the solvent accessible surface area. The former directly yields the effective Born radius, which is used in the generalized Born (GB) formula to calculate the solvent-screened electrostatic interaction energy. A comparison with finite-difference Poisson data shows that atomic solvation energies, pair interaction energies, and their sums are evaluated with a precision comparable to the most accurate GB implementations. Furthermore, solvation energies of a large set of protein conformations have an error of only 1.5%. The solvent accessible surface area is used to approximate the nonpolar contribution to solvation. The empirical approach, called FACTS (Fast Analytical Continuum Treatment of Solvation), is only four times slower than using the vacuum energy in molecular dynamics simulations of proteins. Notably, the folded state of structured peptides and proteins is stable at room temperature in 100-ns molecular dynamics simulations using FACTS and the CHARMM force field.

Simulating temperature jumps for protein folding

We present a new computational methodology aimed to calculate the thermodynamics and kinetics of peptide folding. We focus in particular on temperature jump experiments of folding rates and show how a combination of replica exchange molecular dynamics (REMD) followed by multiplexed molecular dynamics starting from structures taken from the REMD runs can be used to extract properties in line with experiments. A model system, alanine20, is studied in this article as a proof of principle and used to describe the methodology.

Folding time distributions as an approach to protein folding kinetics

A 27-residue lattice heteropolymer subject to Monte Carlo dynamics on a simple cubic lattice is studied over a range of temperatures. Folding time distributions are used to obtain information concerning the details of folding kinetics. The results are compared with those from methods based on mean force surfaces expressed in terms of a reduced set of variables and on a disconnectivity graph for the same system. A detailed analysis of the folding trajectories is given, and the importance of dead-end traps in determining the folding time is demonstrated. We show that the calculated folding kinetics can be modeled by a system of kinetic equations, with the essential rate constants determined from the Monte Carlo simulations and the resulting folding time distributions. The kinetic equations make possible an analysis of the variation of the importance of different channels with temperature. In particular, we show that the presence of intermediates may be masked in the folding time distributions, with the mean folding time being independent of the height of the barrier between the intermediates and collapsed globule state of the system. This and other results demonstrate that care has to be used in interpreting experimental folding data in terms of the underlying kinetics. Correspondingly, simulations are shown to have to satisfy certain requirements to obtain proper sampling of the dead-end traps.

Tuning lambda6-85 towards downhill folding at its melting temperature

The five-helix bundle lambda6-85* is a fast two-state folder. Several stabilized mutants have been reported to fold kinetically near-downhill or downhill. These mutants undergo a transition to two-state folding kinetics when heated. It has been suggested that this transition is caused by increased hydrophobicity at higher temperature. Here we investigate two histidine-containing mutants of lambda6-85* to see if a weaker hydrophobic core can extend the temperature range of downhill folding. The very stable lambdaHA is the fastest-folding lambda repressor to date (k(f)(-1) approximately k(obs)(-1)=2.3 micros at 44 degrees C). It folds downhill at low temperature, but transits back to two-state folding at its unfolding midpoint. lambdaHG has a weakened hydrophobic core. It is less stable than some slower folding mutants of lambda6-85*, and it has more exposed hydrophobic surface area in the folded state. This mutant nonetheless folds very rapidly, and has the non-exponential folding kinetics of an incipient downhill folder even at the unfolding midpoint (k(m)(-1) approximately 2 micros, k(a)(-1)=15 micros at 56 degrees C). We also compare the thermodynamic melting transition of lambdaHG with the nominal two-state folding mutant lambdaQG, which has a similar melting temperature. Unlike lambdaQG, lambdaHG yields fluorescence wavelength-dependent cooperativities and probe-dependent melting temperatures. This result combined with previous work shows that the energy landscapes of lambda repressor mutants support all standard folding mechanisms.

Recognition of LXXLL by Ligand Binding Domain of the Farnesoid X Receptor in Molecular Dynamics Simulation

The Farnesoid X receptor (FXR) has recently become a potential therapeutical target. The recruitment of coactivator protein (specified by LXXLL sequence) is the initial step in transcriptional activation of nuclear receptors (NRs). In this paper, the process of recognition of the LXXLL motif by the ligand binding domain (LBD) of FXR is observed in a 25 ns molecular dynamics simulation. The hydrophobic and hydrogen bonding interactions between the LBD and the coactivator are fully analyzed. This observation provides justification for the 'on deck' model proposed by Nettles and Greene. At last, insight to the protein-polypeptide interactions and protein conformational changes are discussed.

Quantifying Polypeptide Conformational Space: Sensitivity to Conformation and Ensemble Definition

Quantifying the density of conformations over phase space (the conformational distribution) is needed to model important macromolecular processes such as protein folding. In this work, we quantify the conformational distribution for a simple polypeptide (N-mer polyalanine) using the cumulative distribution function (CDF), which gives the probability that two randomly selected conformations are separated by less than a "conformational" distance and whose inverse gives conformation counts as a function of conformational radius. An important finding is that the conformation counts obtained by the CDF inverse depend critically on the assignment of a conformation's distance span and the ensemble (e.g., unfolded state model): varying ensemble and conformation definition (1 --> 2 A) varies the CDF-based conformation counts for Ala(50) from 10(11) to 10(69). In particular, relatively short molecular dynamics (MD) relaxation of Ala(50)'s random-walk ensemble reduces the number of conformers from 10(55) to 10(14) (using a 1 A root-mean-square-deviation radius conformation definition) pointing to potential disconnections in comparing the results from simplified models of unfolded proteins with those from all-atom MD simulations. Explicit waters are found to roughen the landscape considerably. Under some common conformation definitions, the results herein provide (i) an upper limit to the number of accessible conformations that compose unfolded states of proteins, (ii) the optimal clustering radius/conformation radius for counting conformations for a given energy and solvent model, (iii) a means of comparing various studies, and (iv) an assessment of the applicability of random search in protein folding.

Unfolding dynamics of the protein ubiquitin: insight from simulation

The temperature-induced unfolding pathway of ubiquitin has been investigated by molecular dynamics simulation at four different temperatures. It has been observed that the sequences of the unfolding events are same at all the temperatures. However, the time scale of the dynamics at different temperatures are different. The transition states at various temperatures also possess similar secondary structural elements. The intermediate conformations visited by the protein at different temperatures can help determination of the transition states. The well known " state" of ubiquitin, hitherto found to be stable only in methanol water mixture, have been observed to be a common transient intermediate conformation in the unfolding path of the protein in water. Our observation about the similarities of the unfolding process at different temperatures strongly recommend for a defined pathway for the unfolding process.

Estimation of protein folding probability from equilibrium simulations

The assumption that similar structures have similar folding probabilities (p(fold)) leads naturally to a procedure to evaluate p(fold) for every snapshot saved along an equilibrium folding-unfolding trajectory of a structured peptide or protein. The procedure utilizes a structurally homogeneous clustering and does not require any additional simulation. It can be used to detect multiple folding pathways as shown for a three-stranded antiparallel beta-sheet peptide investigated by implicit solvent molecular dynamics simulations.

Comparison of sequence-based and structure-based energy functions for the reversible folding of a peptide

We used computer simulations to compare the reversible folding of a 20-residue peptide, as described by sequence-based and structure-based energy functions. Sequence-based energy functions are transferable and can be used to describe the behavior of different proteins, since interactions are defined between atomic species. Conversely, structure-based energy functions are not transferable, since the interactions are defined relative to the native conformation, which is assumed to correspond to the global minimum of the energy. Our results indicate that the sequence-based and the structure-based descriptions are in qualitative agreement in characterizing the two-state behavior of the peptide that we studied. We also found, however, that several equilibrium properties, including the free-energy landscape, can be significantly different in the various models. These results suggest that the fact that a model describes the native state of a polypeptide chain does not necessarily imply that the thermodynamic and kinetic properties will also be reproduced correctly.

Folding thermodynamics of three beta-sheet peptides: a model study

We study the folding thermodynamics of a beta-hairpin and two three-stranded beta-sheet peptides using a simplified sequence-based all-atom model, in which folding is driven mainly by backbone hydrogen bonding and effective hydrophobic attraction. The native populations obtained for these three sequences are in good agreement with experimental data. We also show that the apparent native population depends on which observable is studied; the hydrophobicity energy and the number of native hydrogen bonds give different results. The magnitude of this dependence matches well with the results obtained in two different experiments on the beta-hairpin.

Barrier-limited, microsecond folding of a stable protein measured with hydrogen exchange: Implications for downhill folding

Folding experiments are conducted to test whether a covalently cross-linked coiled-coil folds so quickly that the process is no longer limited by a free-energy barrier. This protein is very stable and topologically simple, needing merely to "zipper up," while having an extrapolated folding rate of k(f) = 2 x 10(5) s(-1). These properties make it likely to attain the elusive "downhill folding" limit, at which a series of intermediates can be characterized. To measure the ultra-fast kinetics in the absence of denaturant, we apply NMR and hydrogen-exchange methods. The stability and its denaturant dependence for the hydrogen bonds in the central part of protein equal the values calculated for whole-molecule unfolding. Like-wise, their closing and opening rates indicate that these hydrogen bonds are broken and reformed in a single cooperative event representing the folding transition from the fully unfolded state to the native state. Additionally, closing rates for these hydrogen bonds agree with the extrapolated barrier-limited folding rate observed near the melting transition. Therefore, even in the absence of denaturant, where DeltaG(eq) approximately -6 kcal.mol(-1) (1 cal = 4.18 J) and tau(f) approximately 6 mus, folding remains cooperative and barrier-limited. Given that this prime candidate for downhill folding fails to do so, we propose that protein folding will remain barrier-limited for proteins that fold cooperatively.

Formation of the folding nucleus of an SH3 domain investigated by loosely coupled molecular dynamics simulations

The experimentally well-established folding mechanism of the src-SH3 domain, and in particular the phi-value analysis of its transition state, represents a sort of testing table for computational investigations of protein folding. Here, parallel molecular dynamics simulations of the src-SH3 domain have been performed starting from denatured conformations. By rescuing and restarting only trajectories approaching the folding transition state, an ensemble of conformations was obtained with a completely structured central beta-sheet and a native-like packing of residues Ile-110, Ala-121, and Ile-132. An analysis of the trajectories shows that there are several pathways leading to the formation of the central beta-sheet whereas its two hairpins form in a different but consistent way.

The protein folding network

The conformation space of a 20 residue antiparallel beta-sheet peptide, sampled by molecular dynamics simulations, is mapped to a network. Snapshots saved along the trajectory are grouped according to secondary structure into nodes of the network and the transitions between them are links. The conformation space network describes the significant free energy minima and their dynamic connectivity without requiring arbitrarily chosen reaction coordinates. As previously found for the Internet and the World-Wide Web as well as for social and biological networks, the conformation space network is scale-free and contains highly connected hubs like the native state which is the most populated free energy basin. Furthermore, the native basin exhibits a hierarchical organization, which is not found for a random heteropolymer lacking a predominant free-energy minimum. The network topology is used to identify conformations in the folding transition state (TS) ensemble, and provides a basis for understanding the heterogeneity of the TS and denatured state ensemble as well as the existence of multiple pathways.

Conformational transitions and glycation of serum albumin in patients with minimal-change glomerulopathy

BACKGROUND

There has been a lack of study on the structural changes of serum albumin in patients with minimal change disease (MCD). To determine whether glycation and/or conformational transitions of albumin are involved in the pathogenesis of albuminuria, nine patients with MCD were enrolled in a prospective follow-up study for comparison of these parameters in serum albumin during the remission and relapse of nephrotic syndrome.

METHODS

Circular dichroism measurements were made with purified albumin. Ellipticities at each wavelength were transformed to mean residue ellipticity. Monosaccharide composition was analyzed by high-pH anion-exchange chromatography with pulsed amperometric detection.

RESULTS

There was no difference in the proportions of alpha-helix, beta-conformation, and beta-turn of albumin between the sera of control patients and those with nephrotic syndrome. However, the proportion of the random configuration was slightly higher in the plasma albumin of patients in relapse than in those in remission. The proportion of the random configuration was lower in the albumin of the serum than in the urine of patients with nephrotic syndrome, but there was no difference in the proportions of alpha-helix, beta-conformation, and beta-tum of albumin between their plasma and urine.

CONCLUSION

Our results suggest that conformational changes in albumin are involved in albuminuria in patients with MCD.