The stretching of single poly-ubiquitin molecules: Static versus dynamic disorder in the non-exponential kinetics of chain unfolding

Static disorder has recently been implicated in the non-exponential kinetics of the unfolding of single molecules of poly-ubiquitin under a constant force Kuo, Garcia-Manyes, Li, Barel, Lu, Berne, Urbakh, Klafter, and Fernandez, Proc. Natl. Acad. Sci. U. S. A. 107, 11336 (2010)]. In the present paper, it is suggested that dynamic disorder may provide a plausible, alternative description of the experimental observations. This suggestion is made on the basis of a model in which the barrier to chain unfolding is assumed to be modulated by a control parameter r that evolves in a parabolic potential under the action of fractional Gaussian noise according to a generalized Langevin equation. The treatment of dynamic disorder within this model is pursued using Zwanzig's indirect approach to noise averaging Acc. Chem. Res. 23, 148 (1990)]. In conjunction with a self-consistent closure scheme developed by Wilemski and Fixman J. Chem. Phys. 58, 4009 (1973); ibid. 60, 866 (1974)], this approach eventually leads to an expression for the chain unfolding probability that can be made to fit the corresponding experimental data very closely. (C) 2011 American Institute of Physics.

Ligand-modulated Parallel Mechanical Unfolding Pathways of Maltose-binding Proteins

Protein folding and unfolding are complex phenomena, and it is accepted that multidomain proteins generally follow multiple pathways. Maltose-binding protein (MBP) is a large (a two-domain, 370-amino acid residue) bacterial periplasmic protein involved in maltose uptake. Despite the large size, it has been shown to exhibit an apparent two-state equilibrium unfolding in bulk experiments. Single-molecule studies can uncover rare events that are masked by averaging in bulk studies. Here, we use single-molecule force spectroscopy to study the mechanical unfolding pathways of MBP and its precursor protein (preMBP) in the presence and absence of ligands. Our results show that MBP exhibits kinetic partitioning on mechanical stretching and unfolds via two parallel pathways: one of them involves a mechanically stable intermediate (path I) whereas the other is devoid of it (path II). The apoMBP unfolds via path I in 62% of the mechanical unfolding events, and the remaining 38% follow path II. In the case of maltose-bound MBP, the protein unfolds via the intermediate in 79% of the cases, the remaining 21% via path II. Similarly, on binding to maltotriose, a ligand whose binding strength with the polyprotein is similar to that of maltose, the occurrence of the intermediate is comparable (82% via path I) with that of maltose. The precursor protein preMBP also shows a similar behavior upon mechanical unfolding. The percentages of molecules unfolding via path I are 53% in the apo form and 68% and 72% upon binding to maltose and maltotriose, respectively, for preMBP. These observations demonstrate that ligand binding can modulate the mechanical unfolding pathways of proteins by a kinetic partitioning mechanism. This could be a general mechanism in the unfolding of other large two-domain ligand-binding proteins of the bacterial periplasmic space.

Solvent Sensitivity of Protein Unfolding: Dynamical Study of Chicken Villin Headpiece Subdomain in Water Ethanol Binary Mixture

We carry out a series of long atomistic molecular dynamics simulations to study the unfolding of a small protein, chicken villin headpiece (HP-36), in water-ethanol (EtOH) binary mixture. The prime objective of this work is to explore the sensitivity of protein unfolding dynamics toward increasing concentration of the cosolvent and unravel essential features of intermediates formed in search of a dynamical pathway toward unfolding. In water ethanol binary mixtures, HP-36 is found to unfold partially, under ambient conditions, that otherwise requires temperature as high as similar to 600 K to denature in pure aqueous solvent. However, an interesting course of pathway is observed to be followed in the process, guided by the formation of unique intermediates. The first step of unfolding is essentially the separation of the cluster formed by three hydrophobic (phenylalanine) residues, namely, Phe-7, Phe-11, and Phe-18, which constitute the hydrophobic core, thereby initiating melting of helix-2 of the protein. The initial steps are similar to temperature-induced unfolding as well as chemical unfolding using DMSO as cosolvent. Subsequent unfolding steps follow a unique path. As water-ethanol shows composition-dependent anomalies, so do the details of unfolding dynamics. With an increase in cosolvent concentration, different partially unfolded intermediates are found to be formed. This is reflected in a remarkable nonmonotonic composition dependence of several order parameters, including fraction of native contacts and protein-solvent interaction energy. The emergence of such partially unfolded states can be attributed to the preferential solvation of the hydrophobic residues by the ethyl groups of ethanol. We further quantify the local dynamics of unfolding by using a Marcus-type theory.

Comparative Study of Protein Unfolding in Aqueous Urea and Dimethyl Sulfoxide Solutions: Surface Polarity, Solvent Specificity, and Sequence of Secondary Structure Melting

Elucidation of possible pathways between folded (native) and unfolded states of a protein is a challenging task, as the intermediates are often hard to detect. Here, we alter the solvent environment in a controlled manner by choosing two different cosolvents of water, urea, and dimethyl sulfoxide (DMSO) and study unfolding of four different proteins to understand the respective sequence of melting by computer simulation methods. We indeed find interesting differences in the sequence of melting of alpha helices and beta sheets in these two solvents. For example, in 8 M urea solution, beta-sheet parts of a protein are found to unfold preferentially, followed by the unfolding of alpha helices. In contrast, 8 M DMSO solution unfolds alpha helices first, followed by the separation of beta sheets for the majority of proteins. Sequence of unfolding events in four different alpha/beta proteins and also in chicken villin head piece (HP-36) both in urea and DMSO solutions demonstrate that the unfolding pathways are determined jointly by relative exposure of polar and nonpolar residues of a protein and the mode of molecular action of a solvent on that protein.

Investigation of thermal unfolding process of cyanic adduct of horseradish peroxidase by Fourier transform infrared and circular dichroism spectrometry

Detailed circular dichroism(CD) and Fourier transform infrared (FTIR) studies have been carried out to monitor thermal unfolding of horseradish peroxidase isoenzyme C(HRP) inhibited by CN(HRP-CN). The results suggest that HRP-CN is quite different from native HRP with different spin states of Fe of heme and different coordinated states. Cyanide becomes the sixth ligand of Fe(I) of heme and the hydrogen-binding network is destroyed partly at the same time, which cause the drastic decrease of thermal stability of HRP. The FTIR and Soret-CD spectra analysis demonstrate that during the heating process there is an intermediate state(I') which has both partly destroyed secondary and tertiary structures of native HRP, then it is the appearance of protein aggregation state(A) after fully unfolding. The unfolding pathway thus can be shown as follows: I -->I'-->U -->A.

Pressure-jump-induced kinetics reveals a hydration dependent folding/unfolding mechanism of ribonuclease A

Pressure-jump (p-jump)-induced relaxation kinetics was used to explore the energy landscape of protein folding/unfolding of Y115W, a fluorescent variant of ribonuclease A. Pressure-jumps of 40MPa amplitude (5ms dead-time) were conducted both to higher (unfolding) and to lower (folding) pressure, in the range from 100 to 500MPa, between 30 and 50°C. Significant deviations from the expected symmetrical protein relaxation kinetics were observed. Whereas downward p-jumps resulted always in single exponential kinetics, the kinetics induced by upward p-jumps were biphasic in the low pressure range and monophasic at higher pressures. The relative amplitude of the slow phase decreased as a function of both pressure and temperature. At 50°C, only the fast phase remained. These results can be interpreted within the framework of a two-dimensional energy surface containing a pressure- and temperature-dependent barrier between two unfolded states differing in the isomeric state of the Asn-113–Pro-114 bond. Analysis of the activation volume of the fast kinetic phase revealed a temperature-dependent shift of the unfolding transition state to a larger volume. The observed compensation of this effect by glycerol offers an explanation for its protein stabilizing effect

Grid warehousing of molecular dynamics protein unfolding data

With the increasing awareness of protein folding disorders, the explosion of genomic information, and the need for efficient ways to predict protein structure, protein folding and unfolding has become a central issue in molecular sciences research. Molecular dynamics computer simulations are increasingly employed to understand the folding and unfolding of proteins. Running protein unfolding simulations is computationally expensive and finding ways to enhance performance is a grid issue on its own. However, more and more groups run such simulations and generate a myriad of data, which raises new challenges in managing and analyzing these data. Because the vast range of proteins researchers want to study and simulate, the computational effort needed to generate data, the large data volumes involved, and the different types of analyses scientists need to perform, it is desirable to provide a public repository allowing researchers to pool and share protein unfolding data. This paper describes efforts to provide a grid-enabled data warehouse for protein unfolding data. We outline the challenge and present first results in the design and implementation of the data warehouse.

Isolation of a myoglobin molten globule by selective cobalt(III)-induced unfolding

Reaction of the Schiff-base complex [Co(acetylacetonate-ethylenediimine)(NH3)2]+ with metmyoglobin at pH 6.5 yields a partially folded protein containing six Co(III) complexes. Although half of its α-helical secondary structure is retained, absorption and CD spectra indicate that the tertiary structure in both B-F and AGH domains is disrupted in the partially folded protein. In analogy to proton-induced unfolding, it is likely that the loss of tertiary structure is triggered by metal-ion binding to histidines. Cobalt(III)-induced unfolding of myoglobin is unique in its selectivity (other proteins are unaffected) and in allowing the isolation of the partially folded macromolecule (the protein does not refold or aggregate upon removal of free denaturant).

Two-dimensional IR correlation spectroscopy: Sequential events in the unfolding process of the λ Cro-V55C repressor protein

A question often posed in protein folding/unfolding studies is whether the process is fully cooperative or whether it contains sequential elements. To address this question, one needs tools capable of resolving different events. It seems that, at least in certain cases, two-dimensional (2D) IR correlation spectroscopy can provide answers to this question. To illustrate this point, we have turned to the Cro-V55C dimer of the λ Cro repressor, a protein known to undergo thermal unfolding in two discrete steps through a stable equilibrium intermediate. The secondary structure of this intermediate is compatible with that of a partially unfolded protein and involves a reorganization of the N terminus, whereas the antiparallel β-ribbon formed by the C-terminal part of each subunit remains largely intact. To establish whether the unfolding process involves sequential events, we have performed a 2D correlation analysis of IR spectra recorded over the temperature range of 20–95°C. The 2D IR correlation analysis indeed provides evidence for a sequential formation of the stable intermediate, which is created in three (closely related) steps. A first step entails the unfolding of the short N-terminal β-strand, followed by the unfolding of the α-helices in a second step, and the third step comprises the reorganization of the remaining β-sheet and of some unordered segments in the protein. The complete unfolding of the stable intermediate at higher temperatures also undergoes sequential events that ultimately end with the breaking of the H bonds between the two β-strands at the dimer interface.

Stretching single-domain proteins: Phase diagram and kinetics of force-induced unfolding

Single-molecule force spectroscopy reveals unfolding of domains in titin on stretching. We provide a theoretical framework for these experiments by computing the phase diagrams for force-induced unfolding of single-domain proteins using lattice models. The results show that two-state folders (at zero force) unravel cooperatively, whereas stretching of non-two-state folders occurs through intermediates. The stretching rates of individual molecules show great variations reflecting the heterogeneity of force-induced unfolding pathways. The approach to the stretched state occurs in a stepwise “quantized” manner. Unfolding dynamics and forces required to stretch proteins depend sensitively on topology. The unfolding rates increase exponentially with force f till an optimum value, which is determined by the barrier to unfolding when f = 0. A mapping of these results to proteins shows qualitative agreement with force-induced unfolding of Ig-like domains in titin. We show that single-molecule force spectroscopy can be used to map the folding free energy landscape of proteins in the absence of denaturants.

NMR investigation of ferricytochrome c unfolding: Detection of an equilibrium unfolding intermediate and residual structure in the denatured state

Horse ferricytochrome c (cyt c) undergoes exchange of one of its axial heme ligands (Met-80) for one or more non-native ligands under denaturing conditions. We have used 1H NMR spectroscopy to detect two conformations of paramagnetic cyt c with non-native heme ligation through a range of urea concentrations. One non-native form is an equilibrium unfolding intermediate observed under partially denaturing conditions and is attributed to replacement of Met-80 with one or more Lys side chains. The second non-native form, in which the native Met ligand is replaced by a His, is observed under strongly denaturing conditions. Thermodynamic analysis of these data indicates a relatively small ΔG (17 kJ/mol) for the transition from native to the Lys-ligated intermediate and a significantly larger ΔG (47 kJ/mol) for the transition from native to the His-ligated species. Although CD and fluorescence data indicate that the equilibrium unfolding of cyt c is a two-state process, these NMR results implicate an intermediate with His-Lys ligation.

A general two-process model describes the hydrogen exchange behavior of RNase A in unfolding conditions.

When NMR hydrogen exchange was used previously to monitor the kinetics of RNase A unfolding, some peptide NH protons were found to show EX2 exchange (detected by base catalysis) in addition to the expected EX1 exchange, whose rate is limited by the kinetic unfolding process. In earlier work, two groups showed independently that a restricted two-process model successfully fits published hydrogen exchange rates of native RNase A in the range 0-0.7 M guanidinium chloride. We find that this model predicts properties that are very different from the observed properties of the EX2 exchange reactions of RNase A in conditions where guanidine-induced unfolding takes place. The model predicts that EX2 exchange should be too fast to measure by the technique used, whereas it is readily measurable. Possible explanations for the contradiction are considered here, and we show that removing the restriction from the earlier two-process model is sufficient to resolve the contradiction; instead of specifying that exchange caused by global unfolding occurs by the EX2 mechanism, we allow it to occur by the general mechanism, which includes both the EX1 and EX2 cases. It is logical to remove this restriction because global unfolding of RNase A is known to give rise to EX1 exchange in these unfolding conditions. Resolving the contradiction makes it possible to determine whether populated unfolding intermediates contribute to the EX2 exchange, and this question is considered elsewhere. The results and simulations indicate that moderate or high denaturant concentrations readily give rise to EX1 exchange in native proteins. Earlier studies showed that hydrogen exchange in native proteins typically occurs by the EX2 mechanism but that high temperatures or pH values above 7 may give rise to EX1 exchange. High denaturant concentrations should be added to the list of variables likely to cause EX1 exchange.

Stopped-flow NMR spectroscopy: real-time unfolding studies of 6-19F-tryptophan-labeled Escherichia coli dihydrofolate reductase.

Escherichia coli dihydrofolate reductase (DHFR; EC 1.5.1.3) contains five tryptophan residues that have been replaced with 6-19F-tryptophan. The 19F NMR assignments are known in the native, unliganded form and the unfolded form. We have used these assignments with stopped-flow 19F NMR spectroscopy to investigate the behavior of specific regions of the protein in real time during urea-induced unfolding. The NMR data show that within 1.5 sec most of the intensities of the native 19F resonances of the protein are lost but only a fraction (approximately 20%) of the intensities of the unfolded resonances appears. We postulate that the early disappearance of the native resonances indicates that most of the protein rapidly forms an intermediate in which the side chains have considerable mobility. Stopped-flow far-UV circular dichroism measurements indicate that this intermediate retains native-like secondary structure. Eighty percent of the intensities of the NMR resonances assigned to the individual tryptophans in the unfolded state appear with similar rate constants (k approximately 0.14 sec-1), consistent with the major phase of unfolding observed by stopped-flow circular dichroism (representing 80% of total amplitude). These data imply that after formation of the intermediate, which appears to represent an expanded structural form, all regions of the protein unfold at the same rate. Stopped-flow measurements of the fluorescence and circular dichroism changes associated with the urea-induced unfolding show a fast phase (half-time of about 1 sec) representing 20% of the total amplitude in addition to the slow phase mentioned above. The NMR data show that approximately 20% of the total intensity for each of the unfolded tryptophan resonances is present at 1.5 sec, indicating that these two phases may represent the complete unfolding of the two different populations of the native protein.

Interaction of GroEL with a highly structured folding intermediate: iterative binding cycles do not involve unfolding.

The GroE proteins are molecular chaperones involved in protein folding. The general mechanism by which they facilitate folding is still enigmatic. One of the central open questions is the conformation of the GroEL-bound nonnative protein. Several suggestions have been made concerning the folding stage at which a protein can interact with GroEL. Furthermore, the possibility exists that binding of the nonnative protein to GroEL results in its unfolding. We have addressed these issues that are basic for understanding the GroE-mediated folding cycle by using folding intermediates of an Fab antibody fragment as molecular probes to define the binding properties of GroEL. We show that, in addition to binding to an early folding intermediate, GroEL is able to recognize and interact with a late quaternary-structured folding intermediate (Dc) without measurably unfolding it. Thus, the prerequisite for binding is not a certain folding stage of a nonnative protein. In contrast, general surface properties of nonnative proteins seem to be crucial for binding. Furthermore, unfolding of a highly structured intermediate does not necessarily occur upon binding to GroEL. Folding of Dc in the presence of GroEL and ATP involves cycles of binding and release. Because in this system no off-pathway reactions or kinetic traps are involved, a quantitative analysis of the reactivation kinetics observed is possible. Our results indicate that the association reaction of Dc and GroEL in the presence of ATP is rather slow, whereas in the absence of ATP association is several orders of magnitude more efficient. Therefore, it seems that ATP functions by inhibiting reassociation rather than promoting release of the bound substrate.

Unfolding kernel embeddings of graphs:enhancing class separation through manifold learning

In this paper, we investigate the use of manifold learning techniques to enhance the separation properties of standard graph kernels. The idea stems from the observation that when we perform multidimensional scaling on the distance matrices extracted from the kernels, the resulting data tends to be clustered along a curve that wraps around the embedding space, a behavior that suggests that long range distances are not estimated accurately, resulting in an increased curvature of the embedding space. Hence, we propose to use a number of manifold learning techniques to compute a low-dimensional embedding of the graphs in an attempt to unfold the embedding manifold, and increase the class separation. We perform an extensive experimental evaluation on a number of standard graph datasets using the shortest-path (Borgwardt and Kriegel, 2005), graphlet (Shervashidze et al., 2009), random walk (Kashima et al., 2003) and Weisfeiler-Lehman (Shervashidze et al., 2011) kernels. We observe the most significant improvement in the case of the graphlet kernel, which fits with the observation that neglecting the locational information of the substructures leads to a stronger curvature of the embedding manifold. On the other hand, the Weisfeiler-Lehman kernel partially mitigates the locality problem by using the node labels information, and thus does not clearly benefit from the manifold learning. Interestingly, our experiments also show that the unfolding of the space seems to reduce the performance gap between the examined kernels.