Two-state Exchange Research Articles

A Closed-Form Expression for Analysis of Dark State Exchange Saturation Transfer (DEST) NMR Experiments.

Closed-form expressions for the analysis of Dark state Exchange Saturation Transfer (DEST) NMR experiments, a powerful experimental tool for characterizing exchange processes involving the interaction of NMR visible species with very high molecular weight partners, is presented. Essentially identical exchange and relaxation parameters are derived from the analytical and numerical best fits of the DEST profiles obtained for a protein construct derived from huntingtin exon-1, comprising the N-terminal amphiphilic sequence followed by a seven-residue glutamine repeat, httNTQ7, in the presence of small (SUV) and large (LUV) unilamellar lipid vesicles. The use of analytical expressions significantly speeds up the fitting of experimental DEST profiles to a two-state exchange model and simplifies the analysis of the DEST effects.

Analyzing paramagnetic NMR data on target DNA search by proteins using a discrete-state kinetic model for translocation.

Before reaching their targets, sequence-specific DNA-binding proteins nonspecifically bind to DNA through electrostatic interactions and stochastically change their locations on DNA. Investigations into the dynamics of DNA-scanning by proteins are nontrivial due to the simultaneous presence of multiple translocation mechanisms and many sites for the protein to nonspecifically bind to DNA. Nuclear magnetic resonance (NMR) spectroscopy can provide information about the target DNA search processes at an atomic level. Paramagnetic relaxation enhancement (PRE) is particularly useful to study how the proteins scan DNA in the search process. Previously, relatively simple two-state or three-state exchange models were used to explain PRE data reflecting the target search process. In this work, using more realistic discrete-state stochastic kinetics models embedded into an NMR master equation, we analyzed the PRE data for the HoxD9 homeodomain interacting with DNA. The kinetic models that incorporate sliding, dissociation, association, and intersegment transfer can reproduce the PRE profiles observed at some different ionic strengths. The analysis confirms the previous interpretation of the PRE data and shows that the protein's probability distribution among nonspecific sites is nonuniform during the target DNA search process.

NMR lineshape analysis using analytical solutions of multi-state chemical exchange with applications to kinetics of host–guest systems

Nuclear magnetic resonance (NMR) lineshape analysis is a powerful tool for the study of chemical kinetics. Here we provide techniques for analysis of the relationship between experimentally observed spin kinetics (transitions between different environments A,B,dots) and corresponding chemical kinetics (transitions between distinct chemical species; e.g., free host and complexed host molecule). The advantages of using analytical solutions for two-, three- or generally N-state exchange lineshapes (without J-coupling) over the widely used numerical calculation for NMR spectral fitting are presented. Several aspects of exchange kinetics including the generalization of coalescence conditions in two-state exchange, the possibility of multiple processes between two states, and differences between equilibrium and steady-state modes are discussed. ‘Reduced equivalent schemes’ are introduced for spin kinetics containing fast-exchanging states, effectively reducing the number of exchanging states. The theoretical results have been used to analyze a host–guest system containing an oxoporphyrinogen complexed with camphorsulfonic acid and several other literature examples, including isomerization, protein kinetics, or enzymatic reactions. The theoretical treatment and experimental examples present an expansion of the systematic approach to rigorous analyses of systems with rich chemical kinetics through NMR lineshape analysis.

Retrospective study for the universal applicability of the residue-based linear free energy relationship in the two-state exchange of protein molecules

Multiprobe measurements, such as NMR and hydrogen exchange studies, can provide the equilibrium constant, K, and rate constants for forward and backward processes, k and k′, of the two-state structural changes of a polypeptide on a per-residue basis. We previously found a linear relationship between log K and log k and between log K and log k′ for the topological exchange of a 27-residue bioactive peptide. To test the general applicability of the residue-based linear free energy relationship (rbLEFR), we performed a literature search to collect residue-specific K, k, and k′ values in various exchange processes, including folding-unfolding equilibrium, coupled folding and binding of intrinsically disordered peptides, and structural fluctuations of folded proteins. The good linearity in a substantial number of the log–log plots proved that the rbLFER holds for the structural changes in a wide variety of protein-related phenomena. Among the successful cases, the hydrogen exchange study of apomyoglobin folding intermediates is particularly interesting. We found that the residues that deviated from the linear relationship corresponded to the α-helix, for which transient translocation had been identified by other experiments. Thus, the rbLFER is useful for studying the structures and energetics of the dynamic states of protein molecules.

The Importance of Mg2+ -Free State in Nucleotide Exchange of Oncogenic K-Ras Mutants.

For efficient targeting of oncogenic K-Ras interaction sites, a mechanistic picture of the Ras-cycle is necessary. Herein, we used NMR relaxation techniques and molecular dynamics simulations to decipher the role of slow dynamics in wild-type and three oncogenic P-loop mutants of K-Ras. Our measurements reveal a dominant two-state conformational exchange on the ms timescale in both GDP- and GTP-bound K-Ras. The identified low-populated higher energy state in GDP-loaded K-Ras has a conformation reminiscent of a nucleotide-bound/Mg2+ -free state characterized by shortened β2/β3-strands and a partially released switch-I region preparing K-Ras for the interaction with the incoming nucleotide exchange factor and subsequent reactivation. By providing insight into mutation-specific differences in K-Ras structural dynamics, our systematic analysis improves our understanding of prolonged K-Ras signaling and may aid the development of allosteric inhibitors targeting nucleotide exchange in K-Ras.

On the potentially spurious contributions of cosolutes in protein 15N relaxation dispersion measurements

A rigorous quantification of the thermodynamics, kinetic and structural changes can be approached by relaxation dispersion methods, when such motions are in the microsecond to millisecond timescale. Albeit some past efforts, it is still unclear how cosolutes modulate the fitted parameters extracted from relaxation dispersion analyses. Here, we have studied how the systematic measurement of 15N relaxation dispersion on a well-studied enzyme, undergoing two-state chemical exchange, are affected in terms of the populations of the minor state (thermodynamics) and the exchange rates (kinetics) in the presence of different cosolutes, from ions to denaturants. The cosolute-induced changes are modest but can significantly affect protein function. Specifically, exchange rates can be associated to a subtle leverage in the exchange rates. For most canonical residues, i.e. without spurious effects caused by the cosolute, the chemical shift difference (Δω) between both states is essentially unaffected with respect to the expected shift of water resonance. Yet, solvent exposed residues do not always follow this canonical trend. Instead, residue-cosolute interactions are large enough to induce a residue specific shift that ultimately modulates the fitted parameter Δω. Unfortunately, solvent accessibility analysis is not accurate enough to a priori discriminate between canonical and non-canonical residues and a full experimental analysis at varying concentrations of the cosolute is required. This observation aims to act as a word of caution for measurements of relaxation dispersion at a single-solvent condition that contains large amounts of cosolutes.

The time-zero HSQC method improves the linear free energy relationship of a polypeptide chain through the accurate measurement of residue-specific equilibrium constants.

EXSY (exchange spectroscopy) NMR provides the residue-specific equilibrium constants, K, and residue-specific kinetic rate constants, k, of a polypeptide chain in a two-state exchange in the slow exchange regime. A linear free energy relationship (LFER) discovered in a log k versus log K plot is considered to be a physicochemical basis for smooth folding and conformational changes of protein molecules. For accurate determination of the thermodynamic and kinetic parameters, the measurement bias arising from state-specific differences in the R1 and R2 relaxation rates of 1H and other nuclei in HSQC and EXSY experiments must be minimized. Here, we showed that the time-zero HSQC acquisition scheme (HSQC0) is effective for this purpose, in combination with a special analytical method (Π analysis) for EXSY. As an example, we applied the HSQC0 + Π method to the two-state exchange of nukacin ISK-1 in an aqueous solution. Nukacin ISK-1 is a 27-residue lantibiotic peptide containing three mono-sulfide linkages. The resultant bias-free residue-based LFER provided valuable insights into the transition state of the topological interconversion of nukacin ISK-1. We found that two amino acid residues were exceptions in the residue-based LFER relationship. We inferred that the two residues could adopt special conformations in the transition state, to allow the threading of some side chains through a ring structure formed by one of the mono-sulfide linkages. In this context, the two residues are a useful target for the manipulation of the physicochemical properties and biological activities of nukacin ISK-1.

Residue-Specific Kinetic Insights into the Transition State in Slow Polypeptide Topological Isomerization by NMR Exchange Spectroscopy.

The characterization of the transition state is a central issue in biophysical studies of protein folding. NMR is a multiprobe measurement technique that provides residue-specific information. Here, we used exchange spectroscopy to characterize the transition state of the two-state slow topological isomerization of a 27-residue lantibiotic peptide. The exchange kinetic rates varied on a per-residue basis, indicating the reduced kinetic cooperativity of the two-state exchange, as well as the previously observed reduced thermodynamic cooperativity. Furthermore, temperature-dependent measurements revealed large variations in the activation enthalpy and entropy terms among residues. Interestingly, we found a linear relationship between the logarithm of the equilibrium constants and that of the exchange rates. Because the data points are derived from amino acid residues in one polypeptide chain, we refer to the linear relationship as the residue-based linear free energy relationship (rbLFER). The rbLFER offers information about the transition state of the two-state exchange.

Paramagnetic NMR Spectroscopy of a Tri-Nuclear Copper Center from a Multicopper Oxidase, Laccase

Among metalloproteins multicopper oxidases and especially laccases are noteworthy because of their wide application in the fields of green chemistry, medicine, bioremediation and enzymatic biofuel cells. Laccases have a type 1 (T1) copper site for oxidation of substrates and a tri-nuclear copper center (TNC) for oxygen reduction reaction. The TNC comprises a binuclear type 3 (T3) site and a mononuclear type 2 (T2) site. We report the paramagnetic NMR spectra of a laccase from Streptomyces coelicolor, in which the Fermi-contact shifted (FCS) resonances were assigned to the coordinating histidine Nδ1/Hδ1 nuclei using tailored 1H-1H EXSY and 1H-15N HMQC experiments. The pNMR spectra of the resting oxidized state and the native intermediate state are shown. The FCS resonances from the NI state display two-state chemical exchange with exchange rates in the order of 100 s−1. This is supported by the observation of two different gz values from the EPR spectra. It is proposed that the exchange processes reflect rotational motion of histidine imidazole rings that coordinate the coppers in the TNC. To our knowledge this is the first report that shows multidimensional paramagnetic NMR spectra of the tri-nuclear copper center and the presence of chemical exchange in the tri-nuclear copper centre of a laccase. The potential catalytic relevance is under study.

Two-State Exchange Dynamics in Membrane-Embedded Oligosaccharyltransferase Observed in Real-Time by High-Speed AFM

Oligosaccharyltransferase (OST) is a membrane-bound enzyme that catalyzes the transfer of oligosaccharide chains from lipid-linked oligosaccharides (LLO) to asparagine residues in polypeptide chains. Using high-speed atomic force microscopy (AFM), we investigated the dynamic properties of OST molecules embedded in biomembranes. An archaeal single-subunit OST protein was immobilized on a mica support via biotin–avidin interactions and reconstituted in a lipid bilayer. The distance between the top of the protein molecule and the upper surface of the lipid bilayer was monitored in real-time. The height of the extramembranous part exhibited a two-step variation with a difference of 1.8 nm. The high and low states are designated as state 1 and state 2, respectively. The transition processes between the two states fit well to single exponential functions, suggesting that the observed dynamic exchange is an intrinsic property of the archaeal OST protein. The two sets of cross peaks in the NMR spectra of the protein supported the conformational changes between the two states in detergent-solubilized conditions. Considering the height values measured in the AFM measurements, state 1 is closer to the crystal structure, and state 2 has a more compact form. Subsequent AFM experiments indicated that the binding of the sugar donor LLO decreased the structural fluctuation and shifted the equilibrium almost completely to state 1. This dynamic behavior is likely necessary for efficient catalytic turnover. Presumably, state 2 facilitates the immediate release of the bulky glycosylated polypeptide product, thus allowing OST to quickly prepare for the next catalytic cycle.

Chemical Exchange at the Trinuclear Copper Center of Small Laccase from Streptomyces coelicolor

The trinuclear copper center (TNC) of laccase reduces oxygen to water with very little overpotential. The arrangement of the coppers and ligands in the TNC is known to be from many crystal structures, yet information about possible dynamics of the ligands is absent. Here, we report dynamics at the TNC of small laccase from Streptomyces coelicolor using paramagnetic NMR and electron paramagnetic resonance spectroscopy. Fermi contact-shifted resonances tentatively assigned to histidine Hδ1 display a two-state chemical exchange with exchange rates in the order of 100 s−1. In the electron paramagnetic resonance spectra, at least two forms are observed with different gz-values. It is proposed that the exchange processes reflect the rotational motion of histidine imidazole rings that coordinate the coppers in the TNC.

Conformational Dynamics in the Core of Human Y145Stop Prion Protein Amyloid Probed by Relaxation Dispersion NMR.

Microsecond to millisecond timescale backbone dynamics of the amyloid core residues in Y145Stop human prion protein (PrP) fibrils were investigated by using 15 N rotating frame (R1ρ ) relaxation dispersion solid-state nuclear magnetic resonance spectroscopy over a wide range of spin-lock fields. Numerical simulations enabled the experimental relaxation dispersion profiles for most of the fibril core residues to be modelled by using a two-state exchange process with a common exchange rate of 1000 s-1 , corresponding to protein backbone motion on the timescale of 1 ms, and an excited-state population of 2 %. We also found that the relaxation dispersion profiles for several amino acids positioned near the edges of the most structured regions of the amyloid core were better modelled by assuming somewhat higher excited-state populations (∼5-15 %) and faster exchange rate constants, corresponding to protein backbone motions on the timescale of ∼100-300 μs. The slow backbone dynamics of the core residues were evaluated in the context of the structural model of human Y145Stop PrP amyloid.

Differential Ubiquitin Binding by the Acidic Loops of Ube2g1 and Ube2r1 Enzymes Distinguishes Their Lys-48-ubiquitylation Activities

The ubiquitin E2 enzymes, Ube2g1 and Ube2r1, are able to synthesize Lys-48-linked polyubiquitins without an E3 ligase but how that is accomplished has been unclear. Although both E2s contain essential acidic loops, only Ube2r1 requires an additional C-terminal extension (184-196) for efficient Lys-48-ubiquitylation activity. The presence of Tyr-102 and Tyr-104 in the Ube2g1 acidic loop enhanced both ubiquitin binding and Lys-48-ubiquitylation and distinguished Ube2g1 from the otherwise similar truncated Ube2r1(1-183) (Ube2r1C). Replacement of Gln-105-Ser-106-Gly-107 in the acidic loop of Ube2r1C (Ube2r1C(YGY)) by the corresponding residues from Ube2g1 (Tyr-102-Gly-103-Tyr-104) increased Lys-48-ubiquitylation activity and ubiquitin binding. Two E2∼UB thioester mimics (oxyester and disulfide) were prepared to characterize the ubiquitin binding activity of the acidic loop. The oxyester but not the disulfide derivative was found to be a functional equivalent of the E2∼UB thioester. The ubiquitin moiety of the Ube2r1C(C93S)-[(15)N]UB(K48R) oxyester displayed two-state conformational exchange, whereas the Ube2r1C(C93S/YGY)-[(15)N]UB(K48R) oxyester showed predominantly one state. Together with NMR studies that compared UB(K48R) oxyesters of the wild-type and the acidic loop mutant (Y102G/Y104G) forms of Ube2g1, in vitro ubiquitylation assays with various mutation forms of the E2s revealed how the intramolecular interaction between the acidic loop and the attached donor ubiquitin regulates Lys-48-ubiquitylation activity.

Characteristics of Sn segregation in Ge/GeSn heterostructures

We report an investigation of Sn segregation in Ge/GeSn heterostructures occurred during the growth by molecular beam epitaxy. The measured Sn profile in the Ge layer shows that: (a) the Sn concentration decreases rapidly near the Ge/GeSn interface, and (b) when moving away from the interface, the Sn concentration reduced with a much slower rate. The 1/e decay lengths of the present system are much longer than those of the conventional group IV system of Ge segregation in the Si overlayer because of the smaller kinetic potential as modeled by a self-limited two-state exchange scheme. The demonstration of the Sn segregation shows the material characteristics of the heterostructure, which are needed for the investigation of its optical properties.

A Folded Excited State of Ligand-Free Nuclear Coactivator Binding Domain (NCBD) Underlies Plasticity in Ligand Recognition

Intrinsically disordered proteins are renowned for their structural plasticity when they undergo coupled folding and binding to partner proteins. The nuclear coactivator binding domain of CBP is a remarkable example of this adaptability as it folds into two different conformations depending on the binding partner. To understand the role of the conformational ensemble for plasticity in ligand recognition, we investigated the millisecond dynamics of this domain using relaxation dispersion NMR spectroscopy. All NMR signals originating from the domain are broadened, demonstrating that the whole domain experience conformational exchange. The dispersion data can be described by a global two-state exchange process between a ground state and an excited state populated to 8%. The three helices are still folded in the excited state but have a different packing from the ground state; the contact between helices 2 and 3 found in the ground state is broken in the excited state, and a new one is formed between helices 1 and 3. This suggests that while NCBD in the ground state has a structure similar to the complex with the ligand ACTR, the conformation of NCBD in the excited state has some similarity with that of NCBD in complex with the ligand IRF-3. The energy landscape of this domain is thus proposed to resemble the fold-switching proteins that have two coexisting native states, which may serve as a starting point for binding via conformational selection.

Mechanisms of Allosteric Gene Regulation by NMR Quantification of Microsecond–Millisecond Protein Dynamics

The trp RNA-binding attenuation protein (TRAP) is a paradigmatic allosteric protein that regulates the tryptophan biosynthetic genes associated with the trp operon in bacilli. The ring-shaped 11-mer TRAP is activated for recognition of a specific trp-mRNA target by binding up to 11 tryptophan molecules. To characterize the mechanisms of tryptophan-induced TRAP activation, we have performed methyl relaxation dispersion (MRD) nuclear magnetic resonance (NMR) experiments that probe the time-dependent structure of TRAP in the microsecond-to-millisecond “chemical exchange” time window. We find significant side chain flexibility localized to the RNA and tryptophan binding sites of the apo protein and that these dynamics are dramatically reduced upon ligand binding. Analysis of the MRD NMR data provides insights into the structural nature of transiently populated conformations sampled in solution by apo TRAP. The MRD data are inconsistent with global two-state exchange, indicating that conformational sampling in apo TRAP is asynchronous. These findings imply a temporally heterogeneous population of structures that are incompatible with RNA binding and substantiate the study of TRAP as a paradigm for probing and understanding essential dynamics in allosteric, regulatory proteins.

Analyzing Protein Folding Cooperativity by Differential Scanning Calorimetry and NMR Spectroscopy

Some marginally stable proteins undergo microsecond time scale folding reactions that involve significant populations of partly ordered forms, making it difficult to discern individual steps in their folding pathways. It has been suggested that many of these proteins fold non-cooperatively, with no significant barriers to separate the energy landscape into distinct thermodynamic states. Here we present an approach for studying the cooperativity of rapid protein folding with a combination of differential scanning calorimetry (DSC), nuclear magnetic resonance (NMR) relaxation dispersion experiments, and an analysis of the temperature dependence of amide (1)H and (15)N chemical shifts. We applied this method to the PBX homeodomain (PBX-HD), which folds on the microsecond time scale and produces a broad DSC thermogram with an elevated and steeply sloping native-state heat capacity baseline, making it a candidate for barrierless folding. However, by globally fitting the NMR thermal melt and DSC data, and by comparing these results to those obtained from the NMR relaxation dispersion experiments, we show that the native form of the protein undergoes two-state exchange with a small population of the thermally denatured form, well below the melting temperature. This result directly demonstrates the coexistence of distinct folded and unfolded forms and firmly establishes that folding of PBX-HD is cooperative. Further, we see evidence of large-scale structural and dynamical changes within the native state by NMR, which helps to explain the broad and shallow DSC profile. This study illustrates the potential of combining calorimetry with NMR dynamics experiments to dissect mechanisms of protein folding.

Ultrafast Protonation/Deprotonation Dynamics of N,N-Dimethylacetamide in Hydrochloric Acid As Studied by Raman Band Shape Analysis

The protonation/deprotonation dynamics of N,N-dimethylacetamide (DMAA) in hydrochloric acid has been studied with a Raman band shape analysis based on the two-state dynamic exchange model. The observed Raman band shape changes of the symmetric and antisymmetric CC/CN stretch modes with acid concentration have been successfully interpreted in terms of the ultrafast dynamic exchange between DMAA and its protonated form DMAAH+. It is confirmed that the protonation takes place on the oxygen atom rather than on the nitrogen atom. Quantitative information on the exchange dynamics between DMAA and DMAAH+ has been obtained from the curve fitting of the observed band shapes. The protonation process follows the first-order kinetics with a rate constant of k1 = (10.1 ± 0.2) × 1010 s−1 M−1, which is slightly larger than the value expected for a simple diffusion-controlled reaction and which can be explained in terms of the proton transfer through the hydrogen-bonding network. The mean lifetime of the protonated form DMAAH+ is strongly dependent on the acid concentration; it is several picoseconds in concentration lower than 0.5 mol dm−1 but is prolonged to a few tens of picoseconds in concentrations higher than 2 mol dm−1. It is also shown that the static equilibrium model, which corresponds to the slow exchange limit, fails to explain the observed band shape changes with acid concentration and that they can be explained if and only if the effect of ultrafast exchange is taken into account.

Ultrafast generation/annihilation dynamics of the tert-butyl carbocation in sulfuric acid as studied by Raman band shape analysis

The ultrafast generation/annihilation dynamics of the tert-butyl carbocation (ultrafast dehydration/hydration dynamics of tert-butyl alcohol) in sulfuric acid has been studied quantitatively by Raman band shape analysis. The two-state exchange model successfully explains the change of the Raman band shape with increasing proton concentration and hence with increasing the rate of dehydration. Highly dynamic nature of the carbocation has been elucidated; in 1 mol dm −3 sulfuric acid, it is generated in timescales of 10 ps, and is annihilated with lifetimes of about 500 fs.

Probing the Conformational Features of a Phage Display Polypeptide Sequence Directed against Single-Walled Carbon Nanohorn Surfaces

Single-walled carbon nanohorns (SWNHs) are interesting carbon nanostructures that have applications to science and technology. Using M13 phage display technology, polypeptides directed again SWNHs surfaces have been created for a number of nanotechnology and pharmaceutical purposes, yet the molecular mechanism of polypeptide sequence interaction and binding to SWNHs surfaces is not known. Recently, we identified a linear 12-AA M13 phage pIII sequence, NH-12-5-2 (DYFSSPYYEQLF), that binds with high affinity to SWNHs surfaces. To probe the structure of this pIII tail polypeptide further, we investigated the conformation of a model peptide representing the 12 AA NH-12-5-2 sequence. At neutral pH, the NH-12-5-2 model polypeptide is conformationally labile and exhibits two-state conformational exchange involving the D1-S5 N-terminal segment. Simultaneous with this conformational exchange process is the observation that the P6 residue exhibits imido ring conformational variation. In the presence of the structure-stabilizing solvent, TFE, or at pH 2.5, both the exchange process and Pro ring motion phenomena disappear, indicating that the structure of this peptide sequence can be stabilized by extrinsic factors. Interestingly, we observe NMR parameters (ROEs, (3)J coupling constants) for NH-12-5-2 in 90% v/v TFE that are consistent with the presence of a partial helical structure, similar to what was observed at low pH in our earlier CD experiments. We conclude that the NH-12-5-2 model polypeptide sequence possesses an inherent conformational instability that involves the D1-S5 sequence segment and the P6 residue but that this instability can be offset by extrinsic factors (e.g., charge neutralization, imido ring interconversion, and hydrophobic-hydrophobic interactions). These nonbonding interactions may play a role in the recognition and binding of this phage sequence region to SWNHs surfaces.