Probing Position-Dependent Diffusion in Folding Reactions Using Single-Molecule Force Spectroscopy

Folding of proteins and nucleic acids involves a diffusive search over a multidimensional conformational energy landscape for the minimal-energy structure. When examining the projection of conformational motions onto a one-dimensional reaction coordinate, as done in most experiments, the diffusion coefficient D is generally position dependent. However, it has proven challenging to measure such position-dependence experimentally. We investigated the position-dependence of D in the folding of DNA hairpins as a simple model system in two ways: first, by analyzing the round-trip time to return to a given extension in constant-force extension trajectories measured by force spectroscopy, and second, by analyzing the fall time required to reach a given extension in force jump measurements. These methods yielded conflicting results: the fall time implied a fairly constant D, but the round-trip time implied variations of over an order of magnitude. Comparison of experiments with computational simulations revealed that both methods were strongly affected by experimental artifacts inherent to force spectroscopy measurements, which obscured the intrinsic position-dependence of D. Lastly, we applied Kramers’s theory to the kinetics of hairpins with energy barriers located at different positions along the hairpin stem, as a crude probe of D at different stem positions, and we found that D did not vary much as the barrier was moved along the reaction coordinate. This work underlines the difficulties faced when trying to deduce position-dependent diffusion coefficients from experimental folding trajectories.     

Single-Molecule TPM Studies on the Conversion of Human Telomeric DNA

Human telomere contains guanine-rich (G-rich) tandem repeats of single-stranded DNA sequences at its 3′ tail. The G-rich sequences can be folded into various secondary structures, termed G-quadruplexes (G4s), by Hoogsteen basepairing in the presence of monovalent cations (such as Na⁺ and K⁺). We developed a single-molecule tethered particle motion (TPM) method to investigate the unfolding process of G4s in the human telomeric sequence AGGG(TTAGGG)₃ in real time. The TPM method monitors the DNA tether length change caused by formation of the G4, thus allowing the unfolding process and structural conversion to be monitored at the single-molecule level. In the presence of its antisense sequence, the folded G4 structure can be disrupted and converted to the unfolded conformation, with apparent unfolding time constants of 82 s and 3152 s. We also observed that the stability of the G4 is greatly affected by different monovalent cations. The folding equilibrium constant of G4 is strongly dependent on the salt concentration, ranging from 1.75 at 5 mM Na⁺ to 3.40 at 15 mM Na⁺. Earlier spectral studies of Na⁺- and K⁺-folded states suggested that the spectral conversion between these two different folded structures may go through a structurally unfolded intermediate state. However, our single-molecule TPM experiments did not detect any totally unfolded intermediate within our experimental resolution when sodium-folded G4 DNA molecules were titrated with high-concentration, excess potassium ions. This observation suggests that a totally unfolding pathway is likely not the major pathway for spectral conversion on the timescale of minutes, and that interconversion among folded states can be achieved by the loop rearrangement. This study also demonstrates that TPM experiments can be used to study conformational changes in single-stranded DNA molecules.     

Protein-ligand interactions measured by 15N-filtered diffusion experiments

NMR diffusion coefficient measurements have been shown to be sensitive to the conformational and oligomeric states of proteins. Recently, heteronuclear-filtered diffusion experiments have been proposed [Dingley et al. (1997) J. Biomol. NMR, 10, 1–8]. Several new heteronuclear-filtered diffusion pulse sequences are proposed which are shown to have superior sensitivity to those previously proposed. One of these new heteronuclear-filtered diffusion experiments has been used to study the binding of an SH3 domain to a peptide. Using this system, we show that it is possible to measure binding constants from diffusion coefficient measurements.     

Hexamer oligonucleotide topology and assembly under solution phase NMR and theoretical modeling scrutiny

The entire family of noncomplementary hexamer oligodeoxyribonucleotides d(GCXYGC) (X and Y = A, G, C, or T) were assessed for topological indicators and equilibrium thermodynamics using a priori molecular modeling and solution phase NMR spectroscopy. Feasible modeled hairpin structures formed a basis from which solution structure and equilibria for each oligonucleotide were considered. ¹H and ³¹P variable temperature‐dependent (VT) and concentration‐dependent NMR data, NMR signal assignments, and diffusion parameters led to d(GCGAGC) and d(GCGGGC) being understood as exceptions within the family in terms of self‐association and topological character. A mean diffusion coefficient D_{298 K} = (2.0 ± 0.07) × 10^?10 m² s^?1 was evaluated across all hexamers except for d(GCGAGC) (D_{298 K} = 1.7 × 10^?10 m² s^?1) and d(GCGGGC) (D_{298 K} = 1.2 × 10^?10 m² s^?1). Melting under VT analysis (T_m = 323 K) combined with supporting NMR evidence confirmed d(GCGAGC) as the shortest tandem sheared GA mismatched duplex. Diffusion measurements were used to conclude that d(GCGGGC) preferentially exists as the shortest stable quadruplex structure. Thermodynamic analysis of all data led to the assertion that, with the exception of XY = GA and GG, the remaining noncomplementary oligonucleotides adopt equilibria between monomer and duplex, contributed largely by monomer random‐coil forms. Contrastingly, d(GCGAGC) showed preference for tandem sheared GA mismatch duplex formation with an association constant K = 3.9 × 10⁵M^?1. No direct evidence was acquired for hairpin formation in any instance although its potential existence is considered possible for d(GCGAGC) on the basis of molecular modeling studies. © 2010 Wiley Periodicals, Inc. Biopolymers 93: 1023–1038, 2010. This article was originally published online as an accepted preprint. The “Published Online” date corresponds to the preprint version. You can request a copy of the preprint by emailing the Biopolymers editorial office at biopolymers@wiley.com     

Determining Intrachain Diffusion Coefficients for Biopolymer Dynamics from Single-Molecule Force Spectroscopy Measurements

The conformational diffusion coefficient for intrachain motions in biopolymers, D, sets the timescale for structural dynamics. Recently, force spectroscopy has been applied to determine D both for unfolded proteins and for the folding transitions in proteins and nucleic acids. However, interpretation of the results remains unsettled. We investigated how instrumental effects arising from the force probes used in the measurement can affect the value of D recovered via force spectroscopy. We compared estimates of D for the folding of DNA hairpins found from measurements of rates and energy landscapes made using optical tweezers with estimates obtained from the same single-molecule trajectories via the transition path time. The apparent D obtained from the rates was much lower than the result found from the same data using transition time analysis, reflecting the effects of the mechanical properties of the force probe. Deconvolution of the finite compliance effects on the measurement allowed the intrinsic value to be recovered. These results were supported by Brownian dynamics simulations of the effects of force-probe compliance and bead size.     

Determining Intrachain Diffusion Coefficients for Biopolymer Dynamics from Single-Molecule Force Spectroscopy Measurements

The conformational diffusion coefficient for intrachain motions in biopolymers, D, sets the timescale for structural dynamics. Recently, force spectroscopy has been applied to determine D both for unfolded proteins and for the folding transitions in proteins and nucleic acids. However, interpretation of the results remains unsettled. We investigated how instrumental effects arising from the force probes used in the measurement can affect the value of D recovered via force spectroscopy. We compared estimates of D for the folding of DNA hairpins found from measurements of rates and energy landscapes made using optical tweezers with estimates obtained from the same single-molecule trajectories via the transition path time. The apparent D obtained from the rates was much lower than the result found from the same data using transition time analysis, reflecting the effects of the mechanical properties of the force probe. Deconvolution of the finite compliance effects on the measurement allowed the intrinsic value to be recovered. These results were supported by Brownian dynamics simulations of the effects of force-probe compliance and bead size.     

Characterization of the overall and local dynamics of a protein with intermediate rotational anisotropy: Differentiating between conformational exchange and anisotropic diffusion in the B3 domain of protein G

Because the overall tumbling provides a major contribution to protein spectral densities measured in solution, the choice of a proper model for this motion is critical for accurate analysis of protein dynamics. Here we study the overall and backbone dynamics of the B3 domain of protein G using ¹⁵N relaxation measurements and show that the picture of local motions is markedly dependent on the model of overall tumbling. The main difference is in the interpretation of the elevated R ₂ values in the -helix: the isotropic model results in conformational exchange throughout the entire helix, whereas no exchange is predicted by anisotropic models that place the longitudinal axis of diffusion tensor almost parallel to the helix axis. Due to small size (fast tumbling) of the protein, the T ₁ values have low sensitivity to NH bond orientation. The diffusion tensor derived from orientation dependence of R ₂/R ₁ is anisotropic (D _par/D _perp=1.4), with a small rhombic component. In order to distinguish the correct picture of motion, we apply model-independent methods that are sensitive to conformational exchange and do not require knowledge of protein structure or assumptions about its dynamics. A comparison of the CSA/dipolar cross-correlation rate constants with ¹⁵N relaxation rates and the estimation of R _ex terms from relaxation data at 9.4 and 14.1 T indicate no conformational exchange in the helix, in support of the anisotropic models. The experimentally derived diffusion tensor is in excellent agreement with theoretical predictions from hydrodynamic calculations; a detailed comparison with various hydrodynamic models revealed optimal parameters for hydrodynamic calculations.     

High-Bandwidth Protein Analysis Using Solid-State Nanopores

High-bandwidth measurements of the ion current through hafnium oxide and silicon nitride nanopores allow the analysis of sub-30 kD protein molecules with unprecedented time resolution and detection efficiency. Measured capture rates suggest that at moderate transmembrane bias values, a substantial fraction of protein translocation events are detected. Our dwell-time resolution of 2.5 μs enables translocation time distributions to be fit to a first-passage time distribution derived from a 1D diffusion-drift model. The fits yield drift velocities that scale linearly with voltage, consistent with an electrophoretic process. Further, protein diffusion constants (D) are lower than the bulk diffusion constants (D₀) by a factor of ∼50, and are voltage-independent in the regime tested. We reason that deviations of D from D₀ are a result of confinement-driven pore/protein interactions, previously observed in porous systems. A straightforward Kramers model for this inhibited diffusion points to 9- to 12-kJ/mol interactions of the proteins with the nanopore. Reduction of μ and D are found to be material-dependent. Comparison of current-blockage levels of each protein yields volumetric information for the two proteins that is in good agreement with dynamic light scattering measurements. Finally, detection of a protein-protein complex is achieved.     

High-Bandwidth Protein Analysis Using Solid-State Nanopores

High-bandwidth measurements of the ion current through hafnium oxide and silicon nitride nanopores allow the analysis of sub-30 kD protein molecules with unprecedented time resolution and detection efficiency. Measured capture rates suggest that at moderate transmembrane bias values, a substantial fraction of protein translocation events are detected. Our dwell-time resolution of 2.5 μs enables translocation time distributions to be fit to a first-passage time distribution derived from a 1D diffusion-drift model. The fits yield drift velocities that scale linearly with voltage, consistent with an electrophoretic process. Further, protein diffusion constants (D) are lower than the bulk diffusion constants (D₀) by a factor of ∼50, and are voltage-independent in the regime tested. We reason that deviations of D from D₀ are a result of confinement-driven pore/protein interactions, previously observed in porous systems. A straightforward Kramers model for this inhibited diffusion points to 9- to 12-kJ/mol interactions of the proteins with the nanopore. Reduction of μ and D are found to be material-dependent. Comparison of current-blockage levels of each protein yields volumetric information for the two proteins that is in good agreement with dynamic light scattering measurements. Finally, detection of a protein-protein complex is achieved.     

Diffusion NMR-based comparison of electrostatic influences of DNA on various monovalent cations

Counterions are important constituents for the structure and function of nucleic acids. Using ⁷Li and ¹³³Cs nuclear magnetic resonance (NMR) spectroscopy, we investigated how ionic radii affect the behavior of counterions around DNA through diffusion measurements of Li⁺ and Cs⁺ ions around a 15-bp DNA duplex. Together with our previous data on ²³Na⁺ and ¹⁵NH₄⁺ ions around the same DNA under the same conditions, we were able to compare the dynamics of four different monovalent ions around DNA. From the apparent diffusion coefficients at varied concentrations of DNA, we determined the diffusion coefficients of these cations inside and outside the ion atmosphere around DNA (D_b and D_f, respectively). We also analyzed ionic competition with K⁺ ions for the ion atmosphere and assessed the relative affinities of these cations for DNA. Interestingly, all cations (i.e., Li⁺, Na⁺, NH₄⁺, and Cs⁺) analyzed by diffusion NMR spectroscopy exhibited nearly identical D_b/D_f ratios despite the differences in their ionic radii, relative affinities, and diffusion coefficients. These results, along with the theoretical relationship between diffusion and entropy, suggest that the entropy change due to the release of counterions from the ion atmosphere around DNA is also similar regardless of the monovalent ion types. These findings and the experimental diffusion data on the monovalent ions are useful for examination of computational models for electrostatic interactions or ion solvation.     

1,3-Di(quinolin-2-yl)guanidine binds to GGCCCC hexanucleotide repeat DNA in C9ORF72

Aberrant expansion of GGGGCC (G4C2) hexanucleotide repeat (HNR) in the first intron of C9ORF72 has been found in frontotemporal dementia and amyotrophic lateral sclerosis (FTD/ALD). The non-canonical DNA structures of the expanded repeats are causative to repeat instability leading to contraction and expansion. We demonstrate that 1,3-di(quinolin-2-yl)guanidine (DQG) binds to GGCCCC/GGCCCC (G2C4/G2C4) motif in double stranded DNA and also antisense G2C4 HNR DNA in C9ORF72. Large increase in the melting temperature of dsDNA containing the G2C4/G2C4 motif was confirmed by the binding of DQG. The marked CD spectral changes indicated structural transition of d(G2C4)₉ from i-motifs and/or hairpins to DQG-stabilized d(G2C4)₉ structures.     

Cyclohexenyl nucleic acids: conformationally flexible oligonucleotides

Cyclohexenyl nucleic acid (CeNA) is a nucleic acid mimic, where the (deoxy)ribose sugar has been replaced by cyclohexenyl moieties. In order to study the conformation of cyclohexenyl nucleosides by NMR, the HexRot program was developed to calculate conformations from scalar coupling constants of cyclohexenyl compounds, analogous to the methods applied for (deoxy)ribose nucleosides. The conformational equilibria and the values of the thermodynamic parameters are very similar between a cyclohexenyl nucleoside [energy difference between ₂H³ (N-type) and ²H₃ (S-type) is 1.8 kJ/mol and equilibrium occurs via the eastern hemisphere with a barrier of 10.9 kJ/mol] and a natural ribose nucleoside (energy difference between N-type and S-type is 2 kJ/mol and equilibrium occurs via the eastern hemisphere with a barrier of 4–20 kJ/mol). The flexibility of the cyclohexenyl nucleoside was demonstrated by the fast equilibrium between two conformational states that was observed in a CeNA-U monomer, combined with the ₂H³ conformation of the cyclohexene moiety when incorporated into a Dickerson dodecamer and the ²H₃ conformation when incorporated in a d(5′-GCGT*GCG-3′)/d(5′-CGCACGC-3′) duplex, as determined by the NMR spectroscopy. This represents the first example of a synthetic nucleoside that adopts different conformations when incorporated in different double-stranded DNA sequences.     

Analysis of conformationally-linked dissociation of proteins

Conformationally-linked dissociation equilibria of dimeric proteins have been examined to determine how experimentally obtainable parameters, such as the apparent dissociation constant, k_D, and the apparent conformational transition constant, K_conf, are related to intrinsic subunit interaction constants, K_A or K_B, and intrinsic isomerization constants, K₁ or k₂. Limiting models are considered in which either the conformational change occurs before dissociation or in which the dissociation occurs before the conformational change, as well as a general model including both possibilities. Models are also considered in which three conformations are allowed or in which four subunits (tetramers) are involved. Simulated data for the dimer equilibria are presented to show how variation of protein concentration and variation of certain constants affect the proportion of various molecular species, the weight-average molecular weight, and the overall extent of conformational change. Methods are suggested to distinguish between the different limiting cases based upon the dependence of K_D and/or K_conf on protein concentration, perturbant concentration, and temperature. It is concluded that methods used to calculate self-dissociation constants oligomeric proteins include linked isomerization reactions such that the equilibrium constant obtained should not be considered as a true subunit interaction term. Indeed, dissociation can occur under the influence of a perturbant with no change in the intrinsic affinity of the subunits but with the sole effect of the perturbant being on a linked conformational change. Additional experiments on the thermodynamics of the conformational change are required to determine the actual relationship. Depending on the complexity of the equilibria involved and the relative value of the equilibrium constants, the extent of the conformational change can vary directly with, vary inversely with, or he independent of the total protein concentration. Even when intrinsic subunit affinities are not affected by the perturbant, the extent of conformational change can vary with protein concentration. Interpretation of data from proteins which may be involved in conformationally-linked dissociation reactions, therefore, must be made with caution.     

High-throughput thermal stability assessment of DNA hairpins based on high resolution melting

On the basis of high-resolution melting, a high-throughput approach to measure melting temperatures (T_ms) of short DNA hairpins was developed. With this method, T_ms of thousands of triloop, tetraloop, and pentaloop hairpins involving various loop sequences and various closing base pairs (cbp) were obtained in hours. The stability of triloop hairpins decreased with the change of cbp (5′–3′) in the order of c-g > g-c > t-a ≥ a-t, showing that the cbp of 5′-Pyr-Pur-3′ (Pyr = pyrimidine, Pur = purine) contributed more stability than 5′-Pur-Pyr-3′. For tetraloop hairpins, GNNA, GNAB, and CNNG (N = A, G, C, or T; B = G, C, or T) were found to be highly stable irrespective of the cbp type. TNNA was also stable in both g-c and a-t families, while CGNA only in the c-g family. Pentaloop hairpins of cTGNAGg, cGNYNAg (Y = T or C) and cCGNNAg were exceptionally stable motifs. In most cases, pyrimidine-rich loops were more favorable to stabilize the whole structure than purine-rich ones. The present approach showed a good performance in assessing the thermal stability of large amounts of DNA hairpins comprehensively. These data are useful to understand the sequence dependence of the stability of DNA secondary structures and promising to improve the structure simulation by consummating basic databases.     

Conformational analysis of two novel cytotoxic C2-substituted pyrrolo[2,3-f]quinolines in aqueous media,organic solvents,membrane bilayers and at the putative active site

We have performed: (i) conformational analysis of two novel cytotoxic C2-substituted pyrrolo[2,3-f]quinolines 5e and 5g in deuterated dimethylsulfoxide (DMSO-d₆) utilizing NOE results from NMR spectroscopy; (ii) molecular dynamics (MD) calculations in water, DMSO and dimyristoyl phosphatidylcholine bilayers and (iii) molecular docking and MD calculations on DNA nucleotide sequences. The obtained results for the two similar in structure molecules showed differences in: (i) their conformational properties in silico and in media that reasonably simulate the biological environment; (ii) the way they are incorporated into the lipid bilayers and therefore their diffusion ability and (iii) molecular docking capacity as it is depicted from their different binding scores.     

13C spin relaxation measurements in RNA: Sensitivity and resolution improvement using spin-state selective correlation experiments

A set of new NMR pulse sequences has been designed for the measurement of ¹³C relaxation rate constants in RNA and DNA bases: the spin-lattice relaxation rate constant R(C_z), the spin-spin relaxation rate constant R(C₊), and the CSA-dipolar cross-correlated relaxation rate constant . The use of spin-state selective correlation techniques provides increased sensitivity and spectral resolution. Sensitivity optimised C-C filters are included in the pulse schemes for the suppression of signals originating from undesired carbon isotopomers. The experiments are applied to a 15% ¹³C-labelled 33-mer RNA–theophylline complex. The measured ratios indicate that ¹³C CSA tensors do not vary significantly for the same type of carbon (C₂, C₆, C₈), but that they differ from one type to another. In addition, conformational exchange effects in the RNA bases are detected as a change in the relaxation decay of the narrow ¹³C doublet component when varying the spacing of a CPMG pulse train. This new approach allows the detection of small exchange effects with a higher precision compared to conventional techniques.     

Structure dissection of zebrafish progranulins identifies a well‐folded granulin/epithelin module protein with pro‐cell survival activities

The ancient and pluripotent progranulins contain multiple repeats of a cysteine‐rich sequence motif of ∼60 amino acids, called the granulin/epithelin module (GEM) with a prototypic structure of four β‐hairpins zipped together by six inter‐hairpin disulfide bonds. Prevalence of this disulfide‐enforced structure is assessed here by an expression screening of 19 unique GEM sequences of the four progranulins in the zebrafish genome, progranulins 1, 2, A and B. While a majority of the expressed GEM peptides did not exhibit uniquely folded conformations, module AaE from progranulin A and AbB from progranulin B were found to fold into the protopypic 4‐hairpin structure along with disulfide formation. Module AaE has the most‐rigid three‐dimensional structure with all four β‐hairpins defined using high‐resolution (H–¹⁵N) NMR spectroscopy, including 492 inter‐proton nuclear Overhauser effects, 23 ³J(HN,H_α) coupling constants, 22 hydrogen bonds as well as 45 residual dipolar coupling constants. Three‐dimensional structure of AaE and the partially folded AbB re‐iterate the conformational stability of the N‐terminal stack of two beta‐hairpins and varying degrees of structural flexibility for the C‐terminal half of the 4‐hairpin global fold of the GEM repeat. A cell‐based assay demonstrated a functional activity for the zebrafish granulin AaE in promoting the survival of neuronal cells, similarly to what has been found for the corresponding granulin E module in human progranulin. Finally, this work highlights the remaining challenges in structure‐activity studies of proteins containing the GEM repeats, due to the apparent prevalence of structural disorder in GEM motifs despite potentially a high density of intramolecular disulfide bonds.     

Synthesis and conformational analysis of carbasugar bioisosteres of α-l-iduronic acid and its methyl glycoside

The synthesis of two novel carbasugar analogues of α-l-iduronic acid is described in which the ring-oxygen is replaced by a methylene group. In analogy with the conformational equilibrium described for α-l-IdopA, the conformation of the carbasugars was investigated by ¹H and ¹³C NMR spectroscopy. Hadamard transform NMR experiments were utilised for rapid acquisition of ¹H,¹³C-HSQC spectra and efficient measurements of heteronuclear long-range coupling constants. Analysis of ¹H NMR chemical shifts and J_H,H coupling constants extracted by a total-lineshape fitting procedure in conjunction with J_H,C coupling constants obtained by three different 2D NMR experiments, viz., ¹H,¹³C-HSQC-HECADE, J-HMBC and IPAP-HSQC-TOCSY-HT, as well as effective proton-proton distances from 1D ¹H,¹H T-ROE and NOE experiments showed that the conformational equilibrium ⁴C₁?²S_5a?¹C₄ is shifted towards ⁴C₁ as the predominant or exclusive conformation. These carbasugar bioisosteres of α-l-iduronic acid do not as monomers show the inherent flexibility that is anticipated to be necessary for biological activity.     

The effect of hydrostatic pressure on the thermal stability of DNA hairpins

DNA hairpins consist of two distinct structural domains: a double stranded stem and a single-stranded loop that connect the two strands of the stem. Previous studies of short DNA hairpins have revealed that loop and stem sequences can significantly affect the thermodynamic stability of short DNA hairpins. In this work we present the effect of hydrostatic pressure on the helix-coil transition temperature (T_M) for 11 16-base, hairpin-forming DNA oligonucleotides. All of the samples form a hairpin with a 6-base pair stem and a four-base loop. In addition, the four base pairs at the end of the stem distal from the loop are the same for every molecule. We have varied loop sequence and identity of the two duplex base pairs adjacent to the loop. Using the change in UV absorption to monitor the conformational state of the oligonucleotide the hairpin-coil transition temperature of these molecules was studied as a function of sodium ion concentration and pressure. From these data we calculated the volume change accompanying the transition. Model-dependent (van't Hoff) transition parameters such as ΔH_vH and transition volume (ΔV) were estimated from the analysis of conformational transitions. Experiments revealed that the ΔV for denaturation of these molecules range from − 2.35 to + 6.74 cm³ mol⁻¹. The expansibility (ΔΔV/ΔT) and the pressure dependence of cation release are also presented. The difference in the volume change for this transition is related to the differences in the hydration of these molecules.     

NMR studies on DNA hairpin structures with a five nucleotide loop

One- and two-dimensional NMR experiments have been undertaken to investigate the structure of DNA hairpins with a five nucleotide loop. Analysis of proton NMR spectra suggests that the four hairpin structures examined have some common structural features; B-type conformation in the stem region and the same stacking pattern, 5' (XXX-turn-XX) 3', in the loop region. The phosphorus NMR spectra suggest that the conformational changes in the loop region affect the backbone conformation of the stem duplex.