Two-state Manner Research Articles

Single molecule magnetic tweezers for unfolding dynamics of Acyl-CoA binding protein

There are significant differences in mechanical stability and unfolding dynamics among proteins with different structural compositions. Compared with proteins with β-sheets and subjected to shearing forces, proteins that are composed entirely of α-helices often undergo rapid unfolding under low stretching forces, thus requiring quantitative studies by using experimental tools that can precisely control forces on a pico-Newton scale. Magnetic tweezers with intrinsic force-control capability and great stability for long-time continuous measurement are suitable to measure force-induced conformation transitions of protein subjected to low forces of several pico-Newton. Acyl-CoA binding protein (ACBP) is a model protein used to study the folding/unfolding kinetics of complete α-helices protein. It is composed of 86 amino acid residues, forming a helical bundle of four α-helices. When its N- and C-terminal are stretched, the first and last α-helix are subjected to shear force in parallel. Previous biochemical studies showed that ACBP folding and unfolding in a two-state manner. In this paper, we use magnetic tweezers to stretch ACBP from its N- and C-end and obtain the distribution of the unfolding force at different loading rates ranging from 0.25 pN/s to 4 pN/s. The most probable unfolding forces are all less than 10 pN, which confirms that ACBP is not mechanically stable. At a constant loading rate, the unfolding force distribution and the most probable unfolding force as a function of loading rate have well-defined analytical formulas based on Bell’s model. Therefore, the experimental results of unfolding force can be fitted directly to obtain the important kinetic parameter of unfolding distance which is defined as the difference in extension between the native state and the transition state. Data analysis shows that ACBP has an extraordinarily long unfolding distance of 7.8 nm. Steered molecular dynamics simulations of ACBP stretching gives the transition state with N-terminal α-helix fully unfolded and C-terminal α-helix partially unfolded, which is consistent with the long unfolding distance obtained in the experiment on magnetic tweezers. According to the simulation results, the unfolding of α-helices is less cooperative than that of β-sheet structures. This characteristic makes α-helix proteins sensitive to mechanical forces, rendering them suitable as force sensors in cells. This study shows that single-molecule stretching experiment combined with molecular dynamics simulations is a reliable method to reveal the molecular mechanism of protein conformationtransitions under stretching forces.

Enhanced statistical sampling reveals microscopic complexity in the talin mechanosensor folding energy landscape.

Statistical mechanics can describe the major conformational ensembles determining the equilibrium free-energy landscape of a folding protein. The challenge is to capture the full repertoire of low-occurrence conformations separated by high kinetic barriers that define complex landscapes. Computationally, enhanced sampling methods accelerate the exploration of molecular rare events. However, accessing the entire protein's conformational space in equilibrium experiments requires technological developments to enable extended observation times. We developed single-molecule magnetic tweezers to capture over a million individual transitions as a single talin protein unfolds and refolds under force in equilibrium. When observed at classically-probed timescales, talin folds in an apparently uncomplicated two-state manner. As the sampling time extends from minutes to days, the underlying energy landscape exhibits gradually larger signatures of complexity, involving a finite number of well-defined rare conformations. A fluctuation analysis allows us to propose plausible structures of each low-probability conformational state. The physiological relevance of each distinct conformation can be connected to the binding of the cytoskeletal protein vinculin, suggesting an extra layer of complexity in talin-mediated mechanotransduction. More generally, our experiments directly test the fundamental notion that equilibrium dynamics depend on the observation timescale.

Flexible Target Recognition of the Intrinsically Disordered DNA-Binding Domain of CytR Monitored by Single-Molecule Fluorescence Spectroscopy.

The intrinsically disordered DNA-binding domain of cytidine repressor (CytR-DBD) folds in the presence of target DNA and regulates the expression of multiple genes in E. coli. To explore the conformational rearrangements in the unbound state and the target recognition mechanisms of CytR-DBD, we carried out single-molecule Förster resonance energy transfer (smFRET) measurements. The smFRET data of CytR-DBD in the absence of DNA show one major and one minor population assignable to an expanded unfolded state and a compact folded state, respectively. The population of the folded state increases and decreases upon titration with salt and denaturant, respectively, in an apparent two-state manner. The peak FRET efficiencies of both the unfolded and folded states change continuously with denaturant concentration, demonstrating the intrinsic flexibility of the DNA-binding domain and the deviation from a strict two-state transition. Remarkably, the CytR-DBD exhibits a compact structure when bound to both the specific and nonspecific DNA; however, the peak FRET efficiencies of the two structures are slightly but consistently different. The observed conformational heterogeneity highlights the potential structural changes required for CytR to bind variably spaced operator sequences.

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.

Unfolding of CBP21, a lytic polysaccharide monooxygenase, without dissociation of its copper ion cofactor.

Chitin-binding protein 21 (CBP21) from Serratia marcescens is a lytic polysaccharide monooxygenase that contains a copper ion as a cofactor. We aimed to elucidate the unfolding mechanism of CBP21 and the effects of Cu2+ on its structural stability at pH 5.0. Thermal unfolding of both apo- and holoCBP21 was reversible. ApoCBP21 unfolded in a simple two-state transition manner. The peak temperature of the DSC curve, tp , for holoCBP21 (74.4°C) was about nine degrees higher than that for apoCBP21 (65.6°C). The value of tp in the presence of excess Cu2+ was around 75°C, indicating that Cu2+ does not dissociate from the protein molecule during unfolding. The unfolding mechanism of holoCBP21 was considered to be as follows: N∙Cu2+ ⇌ U∙Cu2+ , where N and U represent the native and unfolded states, respectively. Urea-induced equilibrium unfolding analysis showed that holoCBP21 was stabilized by 35 kJ mol-1 in terms of the Gibbs energy change for unfolding (pH 5.0, 25°C), compared with apoCBP21. The increased stability of holoCBP21 was considered to result from the structural stabilization of the protein-Cu2+ complex itself.

Mechanical Unfolding and Folding of a Complex Slipknot Protein Probed by Using Optical Tweezers.

Knotted and slipknotted proteins are topologically complex. Understanding their folding and unfolding mechanism has attracted considerable interest. Here we combined protein engineering, single-molecule optical tweezers, and steered molecular dynamics (SMD) simulations to investigate the mechanical unfolding and folding of a slipknotted protein pyruvoyl-dependent arginine decarboxylase (PADC). In its slipknotted structure, PADC contains a long threaded loop (85 residues), which is almost twice the size of the knotting loop. When stretched from its N- and C-termini, the majority of PADC can be readily unfolded in a two-state manner, and the slipknotted structure was untied. A small percentage of PADC unfolded following a three-state pathway involving the formation of an unfolding intermediate state. These unfolding intermediate states showed a broad distribution of contour length increments, suggesting that they did not have a well-defined specific structure. SMD simulations revealed the main free energy barrier to the unfolding of PADC and suggested that the unfolding intermediate states may originate from the frication of polypeptide chain sliding during the process of pulling the threaded loop out of the knotting loop. Upon relaxation, a small percentage of the unfolded and untied PADC polypeptide chain can refold back to its native slipknotted conformation, but a large fraction can only reach a misfolded state. Our results revealed the complexity of the mechanical unfolding and refolding of a slipknotted protein with a long threaded loop.

Exploring the Folding Mechanism of Small Proteins GB1 and LB1.

The computational atomistic description of the folding reactions of the B1 domains, GB1 and LB1, of protein G and protein L, respectively, is an important challenge in current protein folding studies. Although the two proteins have overall very similar backbone structures (β-hairpin-α-helix-β-hairpin), their apparent folding behaviors observed experimentally were remarkably different. LB1 folds in a two-state manner with the single-exponential kinetics, whereas GB1 folds in a more complex manner with an early stage intermediate that may exist on the folding pathway. Here, we used a new method of all-atom molecular dynamics simulations to investigate the folding mechanisms of GB1 and LB1. With the Lorentzian energy term derived from the native structure, we successfully observed frequent folding and unfolding events in the simulations at a high temperature (414 K for GB1 or 393 K for LB1) for both the proteins. Three and two transition-state structures were predicted for the GB1 and LB1 folding, respectively, at the high temperature. Two of the three transition-state structures of GB1 have a better formed second β-hairpin. One of the LB1 transition states has a better formed first hairpin, and the other has both hairpins equally formed. The structural features of these transition states are in good agreement with experimental transition-state analysis. At 300 K, more complex folding processes were observed in the simulations for both the proteins. Several intermediate structures were predicted for the two proteins, which led to the conclusion that both the proteins folded through similar mechanisms. However, the intermediate state accumulated in a sufficient amount only in the GB1 folding, which led to the double-exponential feature of its folding kinetics. On the other hand, the LB1 folding kinetics were well fitted by a single-exponential function. These results are fully consistent with those previously observed experimentally.

Modulating long-range energetics via helix stabilization: A case study using T4 lysozyme.

Cooperative protein folding requires distant regions of a protein to interact and provide mutual stabilization. The mechanism of this long-distance coupling remains poorly understood. Here, we use T4 lysozyme (T4L*) as a model to investigate long-range communications across two subdomains of a globular protein. T4L* is composed of two structurally distinct subdomains, although it behaves in a two-state manner at equilibrium. The subdomains of T4L* are connected via two topological connections: the N-terminal helix that is structurally part of the C-terminal subdomain (the A-helix) and a long helix that spans both subdomains (the C-helix). To understand the role that the C-helix plays in cooperative folding, we analyzed a circularly permuted version of T4L* (CP13*), whose subdomains are connected only by the C-helix. We demonstrate that when isolated as individual fragments, both subdomains of CP13* can fold autonomously into marginally stable conformations. The energetics of the N-terminal subdomain depend on the formation of a salt bridge known to be important for stability in the full-length protein. We show that the energetic contribution of the salt bridge to the stability of the N-terminal fragment increases when the C-helix is stabilized, such as occurs upon folding of the C-terminal subdomain. These results suggest a model where long-range energetic coupling is mediated by helix stabilization and not specific tertiary interactions.

Quantitative measurements of protein−surface interaction thermodynamics

Whereas proteins generally remain stable upon interaction with biological surfaces, they frequently unfold on and adhere to artificial surfaces. Understanding the physicochemical origins of this discrepancy would facilitate development of protein-based sensors and other technologies that require surfaces that do not compromise protein structure and function. To date, however, only a small number of such artificial surfaces have been reported, and the physics of why these surfaces support functional biomolecules while others do not has not been established. Thus motivated, we have developed an electrochemical approach to determining the folding free energy of proteins site-specifically attached to chemically well-defined, macroscopic surfaces. Comparison with the folding free energies seen in bulk solution then provides a quantitative measure of the extent to which surface interactions alter protein stability. As proof-of-principle, we have characterized the FynSH3 domain site-specifically attached to a hydroxyl-coated surface. Upon guanidinium chloride denaturation, the protein unfolds in a reversible, two-state manner with a free energy within 2 kJ/mol of the value seen in bulk solution. Assuming that excluded volume effects stabilize surface-attached proteins, this observation suggests there are countervening destabilizing interactions with the surface that, under these conditions, are similar in magnitude. Our technique constitutes an unprecedented experimental tool with which to answer long-standing questions regarding the molecular-scale origins of protein-surface interactions and to facilitate rational optimization of surface biocompatibility.

Single molecule study on the mechanical response of the sixth domain of adseverin

Adseverin is a member of the calcium-regulated gelsolin superfamily that can sever, cap and uncap actin filaments. Force will be generated when adseverin regulates the architecture of the actin cytoskeleton. Thus, the mechanical properties of adseverin should be investigated. In this work, we systematically studied the mechanical response of the sixth domain of adseverin (A6) in the absence and presence of different concentrations of calcium ions using single-molecule force spectroscopy (SMFS) based on atomic force microscopy (AFM) and magnetic tweezers (MT), respectively. AFM results showed that the A6 mainly unfolded in a two-state unfolding manner. By contrast, MT results showed that A6 mainly unfolded in a three-state unfolding pathway. The unfolding force of A6 gradually increased with increase in calcium concentration. In addition, the mechanical unfolding force of A6 was more likely to occur in a two-state manner at a higher external force.

Structural Stability of the Coiled-Coil Domain of Tumor Susceptibility Gene (TSG)-101.

The tumor susceptibility gene-101 coiled coil domain (TSG101cc) is an integral component of the endosomal maturation machinery and cytokinesis, and also interacts with several transcription factors. The TSG101cc has been crystallized as a homotetramer but is known to interact with two of its binding partners as a heterotrimer. To investigate this apparent discrepancy, we examined the solution thermodynamics of the TSG101cc. Here, we use circular dichroism, differential scanning calorimetry, analytical ultracentrifugation, fluorescence, and structural thermodynamic analysis to investigate the structural stability and the unfolding of the TSG101cc. We demonstrate that TSG101cc exists in solution primarily as a tetramer, which unfolds in a two-state manner. Surprisingly, no homodimeric or homotrimeric species were detected. Structural thermodynamic analysis of the homotetrameric structure and comparison with known oligomeric coiled-coils suggests that the TSG101cc homotetramer is comparatively unstable on a per residue basis. Furthermore, the homotrimeric coiled-coil is predicted to be much less stable than the functional heterotrimeric coiled-coil in the endosomal sorting complex required for transport 1 (ESCRT1). These results support a model whereby the tetramer–monomer equilibrium of TSG101 serves as the cellular reservoir of TSG101, which is effectively outcompeted when its binding partners are present and the heteroternary complex can form.

Light-Induced Conformational Changes of LOV2-Kinase and the Linker Region in Arabidopsis Phototropin2.

Phototropins (phots) are blue light sensors found in a variety of higher plants and algae. The photochemical reactions of this family of proteins have attracted much attention since their discovery. Phots have two light sensor domains called light-oxygen-voltage 1 (LOV1) and LOV2. After the formation of the characteristic adduct of the LOV domain, a conformational change of the C-terminal region of the LOV2 domain occurs, and characterizing this change is important for understanding biological function, that is, kinase activation. Here, the reaction dynamics of the Jα-helix and the extended region adjacent to the Jα-helix (connector) have been investigated. The conformation of the connector part and the Jα-helix were found to alter significantly in a two-state manner. Furthermore, the conformational change of the kinase domain was also successfully detected as a change in translational diffusion, although the CD intensity due to the kinase domain movement was almost silent. These observations indicate that the tertiary structure of the kinase domain changes. The rate of the kinase domain change is almost the same as that of the change for the LOV2-linker, suggesting that the conformational change of the linker is the rate-determining step for kinase activation.

Perplexing cooperative folding and stability of a low-sequence complexity, polyproline 2 protein lacking a hydrophobic core

The burial of hydrophobic side chains in a protein core generally is thought to be the major ingredient for stable, cooperative folding. Here, we show that, for the snow flea antifreeze protein (sfAFP), stability and cooperativity can occur without a hydrophobic core, and without α-helices or β-sheets. sfAFP has low sequence complexity with 46% glycine and an interior filled only with backbone H-bonds between six polyproline 2 (PP2) helices. However, the protein folds in a kinetically two-state manner and is moderately stable at room temperature. We believe that a major part of the stability arises from the unusual match between residue-level PP2 dihedral angle bias in the unfolded state and PP2 helical structure in the native state. Additional stabilizing factors that compensate for the dearth of hydrophobic burial include shorter and stronger H-bonds, and increased entropy in the folded state. These results extend our understanding of the origins of cooperativity and stability in protein folding, including the balance between solvent and polypeptide chain entropies.

Folding Mechanisms of Small Proteins GB1 and LB1

The B1 domains of protein G (GB1) and protein L (LB1) are two small proteins that binds to antibody immunoglobulin G (IgG). GB1 and LB1 are similar in size (about 60 residues), and also have an overall similar structure (β-hairpin--α-helix--β-hairpin). However their sequences are very different, possessing only 15% identity in a structure-based alignment. Therefore, there are interesting similarity and differences in their folding mechanisms. Experimental evidence indicated that LB1 folds in a two-state manner; while GB1 folds in a more complex way -- an early stage intermediate may exist in the folding path. Till now, the folding mechanisms are still under extensive experimental and computational study. Structure-based modeling is one of the less costly computational methods. It has a simple formulated potential energy function summing over various geometrical restraints from one or more targeted structures. Here, we used a new all-atom structure-based method to investigate the folding mechanisms of GB1 and LB1. In this approach, folded structures of the two proteins were used to construct the restraints and they are stabilized by Lorentzian attractive term instead of conventional harmonic term.3 Our model is able to identify two-state and non-two-state proteins, and gives us more insights of the their folding pathways.1. Scalley, M. L., Yi, Q., Gu, H., McCormack, A., Yates, 3rd, J. R., and Baker, D. Biochemistry 36: 3373-82, 1997.2. McCallister, E., Alm, E., and Baker, D. Nat. Struct. Biol. 7: 669-673, 2000.3. Lee, J., Joo, K., Brooks, B., and Lee, J. J. Chem. Theory Comput. 11: 3211-3224, 2015.

Using High Pressure NMR to Study Folding Cooperativity and Kinetics of Protein L9

The ribosomal protein L9 is comprised of two globular domains, the N-terminal (NTL9) and C-terminal (CTL9) domains, connected by a rigid linker. The folding properties of the two domains have been investigated extensively with a variety of denaturants, including urea, GdnHCl, temperature, and pH. Both NTL9 and CTL9 have exhibited cooperative folding in a two-state manner. Pressure perturbation, as a relatively new denaturing factor, has been proved to unfold proteins locally by targeting their packing defects, and to slow protein folding due to the positive activation volume of folding. Conventional NMR spectroscopy is too slow to characterize the folding transition state of most single domain proteins. When combined with NMR spectroscopy, which provides residue-specific resolution, high pressure (HP) could reveal sequence based information regarding protein folding cooperativity and conformational dynamics. Hence we applied HP-NMR to NTL9, CTL9 and their variants, seeking to gain more insights on their folding mechanism. To study their folding equilibria, 1H-15N HSQC spectra were recorded as a function of pressure, and the intensity of each amide proton resonance was analyzed as a function of pressure. We combined HP with 15N ZZ-exchange NMR experiments to determine residue-specific folding and unfolding rate constants. Our thermodynamic and kinetic results reveal that NTL9 folding is very close to two-state, while small deviations from two-state behavior were observed for CTL9. The volumetric properties of these domains indicate that most of the solvent excluded voids in the hydrophobic cores of the folded structures are formed in their respective transition states.

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

Experimental studies indicate that the A39V/N53P/V55L Fyn SH3 domain folds from the unfolded state to the native state via a low-populated on-pathway intermediate, whereas the folding of the wildtype is two-state-like. To get insights into the biophysical basis of their different folding mechanisms, we used native-centric models with and without additional transferrable, sequence-dependent nonnative hydrophobic interactions to study the folding behaviors of the Fyn SH3 domain and its mutant. The pure native-centric model predicts that both the wildtype and the mutant fold in a two-state manner, without any detectable intermediate. However, in the simulated trajectories based on the model with sequence-dependent nonnative hydrophobic interactions, a low populated on-pathway intermediate was identified for the mutant, but not for the wild type, although it is not sufficient to induce chevron rollover. In the modelling intermediate, the topology of strands β1 to β4 followed by the helix turn is native-like, while strand β5 is mostly unstructured, which is in good agreement with experiments. Meanwhile, the nonnative contacts in the intermediate overlapped largely with those identified experimentally. Further investigation implies that different folding mechanisms between the wildtype and the mutant might arise from the distinction of the nonnative contact patterns at the transition states. In addition, we predicted that nonnative interactions led to deceleration or acceleration of the folding largely depending on whether they could destabilize or stabilize the transition state relative to the unfolded state. This study implies that the simple native-centric model augmented by sequence-dependent nonnative hydrophobic interactions should be useful in general to predict the folding of proteins with a low-populated intermediate.

Detailing Protein Landscapes under Pressure

Natural protein molecules are remarkable physical objects. Despite the astronomical number of competing structural forms, these systems self-organize into beautiful structural ensembles in biologically short timescales, puzzling out the feat of specifically bringing together thousands of atoms interacting by a myriad of weak forces. Moreover, most protein domains appear to fold with ease in a deceptively simple two-state manner, populating either the fully folded or fully unfolded ensembles. This is certainly not a property of random amino acid chains…how do proteins do it?

Folding and assembly of the large molecular machine Hsp90 studied in single-molecule experiments

Folding of small proteins often occurs in a two-state manner and is well understood both experimentally and theoretically. However, many proteins are much larger and often populate misfolded states, complicating their folding process significantly. Here we study the complete folding and assembly process of the 1,418 amino acid, dimeric chaperone Hsp90 using single-molecule optical tweezers. Although the isolated C-terminal domain shows two-state folding, we find that the isolated N-terminal as well as the middle domain populate ensembles of fast-forming, misfolded states. These intradomain misfolds slow down folding by an order of magnitude. Modeling folding as a competition between productive and misfolding pathways allows us to fully describe the folding kinetics. Beyond intradomain misfolding, folding of the full-length protein is further slowed by the formation of interdomain misfolds, suggesting that with growing chain lengths, such misfolds will dominate folding kinetics. Interestingly, we find that small stretching forces applied to the chain can accelerate folding by preventing the formation of cross-domain misfolding intermediates by leading the protein along productive pathways to the native state. The same effect is achieved by cotranslational folding at the ribosome in vivo.

Dissecting Ubiquitin Folding Using the Self-Organized Polymer Model.

Folding of Ubiquitin (Ub), a functionally important protein found in eukaryotic organisms, is investigated at low and neutral pH at different temperatures using simulations of the coarse-grained self-organized-polymer model with side chains (SOP-SC). The melting temperatures (Tm's), identified with the peaks in the heat capacity curves, decrease as pH decreases, in qualitative agreement with experiments. The calculated radius of gyration, showing dramatic variations with pH, is in excellent agreement with scattering experiments. At Tm, Ub folds in a two-state manner at low and neutral pH. Clustering analysis of the conformations sampled in equilibrium folding trajectories at Tm, with multiple transitions between the folded and unfolded states, shows a network of metastable states connecting the native and unfolded states. At low and neutral pH, Ub folds with high probability through a preferred set of conformations resulting in a pH-dependent dominant folding pathway. Folding kinetics reveal that Ub assembly at low pH occurs by multiple pathways involving a combination of nucleation-collapse and diffusion collision mechanism. The mechanism by which Ub folds is dictated by the stability of the key secondary structural elements responsible for establishing long-range contacts and collapse of Ub. Nucleation collapse mechanism holds if the stability of these elements are marginal, as would be the case at elevated temperatures. If the lifetimes associated with these structured microdomains are on the order of hundreds of microseconds, then Ub folding follows the diffusion-collision mechanism with intermediates, many of which coincide with those found in equilibrium. Folding at neutral pH is a sequential process with a populated intermediate resembling that sampled at equilibrium. The transition state structures, obtained using a Pfold analysis, are homogeneous and globular with most of the secondary and tertiary structures being native-like. Many of our findings for both the thermodynamics and kinetics of folding are not only in agreement with experiments but also provide missing details not resolvable in standard experiments. The key prediction that folding mechanism varies dramatically with pH is amenable to experimental tests.

Folding Rates from Thermodynamics Simulations: Apoazurin as an Example

In this work we employed the approach of the Mean First Passage Time (MFPT) to calculate protein-folding rates from the thermodynamic simulations according to the Energy Landscape Theory developed by Bryngelson and Wolynes. The folding rates from MPFT depend on a single reaction coordinate on the energy landscape. Here we applied this technique with the aid of coarse-grained molecular simulations for the computation of folding rates of protein Apoazurin. Experimentally, apoazurin folds in a two-state manner that allows for the use of a structure-based model attributable to a smooth funnel-like energy landscape. Based on the fraction of native contacts as the choice of a single reaction coordinates, we computed the folding rates of Apoazurin at several cellular conditions that perturb the population shift of the energy landsape.