Non-Arrhenius kinetics for the loop closure of a DNA hairpin

Intramolecular chain diffusion is an elementary process in the conformational fluctuations of the DNA hairpin-loop. We have studied the temperature and viscosity dependence of a model DNA hairpin-loop by FRET (fluorescence resonance energy transfer) fluctuation spectroscopy (FRETfs). Apparent thermodynamic parameters were obtained by analyzing the correlation amplitude through a two-state model and are consistent with steady-state fluorescence measurements. The kinetics of closing the loop show non-Arrhenius behavior, in agreement with theoretical prediction and other experimental measurements on peptide folding. The fluctuation rates show a fractional power dependence (β = 0.83) on the solution viscosity. A much slower intrachain diffusion coefficient in comparison to that of polypeptides was derived based on the first passage time theory of SSS [Szabo, A., Schulten, K. & Schulten, Z. (1980) J. Chem. Phys. 72, 4350–4357], suggesting that intrachain interactions, especially stacking interaction in the loop, might increase the roughness of the free energy surface of the DNA hairpin-loop.

Quantification of the hydrophobic interaction by simulations of the aggregation of small hydrophobic solutes in water

The hydrophobic interaction, the tendency for nonpolar molecules to aggregate in solution, is a major driving force in biology. In a direct approach to the physical basis of the hydrophobic effect, nanosecond molecular dynamics simulations were performed on increasing numbers of hydrocarbon solute molecules in water-filled boxes of different sizes. The intermittent formation of solute clusters gives a free energy that is proportional to the loss in exposed molecular surface area with a constant of proportionality of 45 ± 6 cal/mol⋅Å2. The molecular surface area is the envelope of the solute cluster that is impenetrable by solvent and is somewhat smaller than the more traditional solvent-accessible surface area, which is the area transcribed by the radius of a solvent molecule rolled over the surface of the cluster. When we apply a factor relating molecular surface area to solvent-accessible surface area, we obtain 24 cal/mol⋅Å2. Ours is the first direct calculation, to our knowledge, of the hydrophobic interaction from molecular dynamics simulations; the excellent qualitative and quantitative agreement with experiment proves that simple van der Waals interactions and atomic point-charge electrostatics account for the most important driving force in biology.

Mechanism for nucleic acid chaperone activity of HIV-1 nucleocapsid protein revealed by single molecule stretching

The nucleocapsid protein (NC) of HIV type 1 is a nucleic acid chaperone that facilitates the rearrangement of nucleic acids into conformations containing the maximum number of complementary base pairs. We use an optical tweezers instrument to stretch single DNA molecules from the helix to coil state at room temperature in the presence of NC and a mutant form (SSHS NC) that lacks the two zinc finger structures present in NC. Although both NC and SSHS NC facilitate annealing of complementary strands through electrostatic attraction, only NC destabilizes the helical form of DNA and reduces the cooperativity of the helix-coil transition. In particular, we find that the helix-coil transition free energy at room temperature is significantly reduced in the presence of NC. Thus, upon NC binding, it is likely that thermodynamic fluctuations cause continuous melting and reannealing of base pairs so that DNA strands are able to rapidly sample configurations to find the lowest energy state. The reduced cooperativity allows these fluctuations to occur in the middle of complex double-stranded structures. The reduced stability and cooperativity, coupled with the electrostatic attraction generated by the high charge density of NC, is responsible for the nucleic acid chaperone activity of this protein.

Monitoring the GAP catalyzed H-Ras GTPase reaction at atomic resolution in real time

The molecular reaction mechanism of the GTPase-activating protein (GAP)-catalyzed GTP hydrolysis by Ras was investigated by time resolved Fourier transform infrared (FTIR) difference spectroscopy using caged GTP (P3-1-(2-nitro)phenylethyl guanosine 5′-O-triphosphate) as photolabile trigger. This approach provides the complete GTPase reaction pathway with time resolution of milliseconds at the atomic level. Up to now, one structural model of the GAP⋅Ras⋅GDP⋅AlFx transition state analog is known, which represents a “snap shot” along the reaction-pathway. As now revealed, binding of GAP to Ras⋅GTP shifts negative charge from the γ to β phosphate. Such a shift was already identified by FTIR in GTP because of Ras binding and is now shown to be enhanced by GAP binding. Because the charge distribution of the GAP⋅Ras⋅GTP complex thus resembles a more dissociative-like transition state and is more like that in GDP, the activation free energy is reduced. An intermediate is observed on the reaction pathway that appears when the bond between β and γ phosphate is cleaved. In the intermediate, the released Pi is strongly bound to the protein and surprisingly shows bands typical of those seen for phosphorylated enzyme intermediates. All these results provide a mechanistic picture that is different from the intrinsic GTPase reaction of Ras. FTIR analysis reveals the release of Pi from the protein complex as the rate-limiting step for the GAP-catalyzed reaction. The approach presented allows the study not only of single proteins but of protein–protein interactions without intrinsic chromophores, in the non-crystalline state, in real time at the atomic level.

Configurational diffusion down a folding funnel describes the dynamics of DNA hairpins

Elucidating the mechanism of folding of polynucleotides depends on accurate estimates of free energy surfaces and a quantitative description of the kinetics of structure formation. Here, the kinetics of hairpin formation in single-stranded DNA are measured after a laser temperature jump. The kinetics are modeled as configurational diffusion on a free energy surface obtained from a statistical mechanical description of equilibrium melting profiles. The effective diffusion coefficient is found to be strongly temperature-dependent in the nucleation step as a result of formation of misfolded loops that do not lead to subsequent zipping. This simple system exhibits many of the features predicted from theoretical studies of protein folding, including a funnel-like energy surface with many folding pathways, trapping in misfolded conformations, and non-Arrhenius folding rates.

Polarity and permeation profiles in lipid membranes

The isotropic 14N-hyperfine coupling constant, a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{o}^{N}}}\end{equation*}\end{document}, of nitroxide spin labels is dependent on the local environmental polarity. The dependence of a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{o}^{N}}}\end{equation*}\end{document} in fluid phospholipid bilayer membranes on the C-atom position, n, of the nitroxide in the sn-2 chain of a spin-labeled diacyl glycerophospholipid therefore determines the transmembrane polarity profile. The polarity variation in phospholipid membranes, with and without equimolar cholesterol, is characterized by a sigmoidal, trough-like profile of the form {1 + exp [(n − no)/λ]}−1, where n = no is the point of maximum gradient, or polarity midpoint, beyond which the free energy of permeation decreases linearly with n, on a characteristic length-scale, λ. Integration over this profile yields a corresponding expression for the permeability barrier to polar solutes. For fluid membranes without cholesterol, no ≈ 8 and λ ≈ 0.5–1 CH2 units, and the permeability barrier introduces an additional diffusive resistance that is equivalent to increasing the effective membrane thickness by 35–80%, depending on the lipid. For membranes containing equimolar cholesterol, no ≈ 9–10, and the total change in polarity is greater than for membranes without cholesterol, increasing the permeability barrier by a factor of 2, whereas the decay length remains similar. The permeation of oxygen into fluid lipid membranes (determined by spin-label relaxation enhancements) displays a profile similar to that of the transmembrane polarity but of opposite sense. For fluid membranes without cholesterol no ≈ 8 and λ ≈ 1 CH2 units, also for oxygen. The permeation profile for polar paramagnetic ion complexes is closer to a single exponential decay, i.e., no lies outside the acyl-chain region of the membrane. These results are relevant not only to the permeation of water and polar solutes into membranes and their permeabilities, but also to depth determinations of site-specifically spin-labeled protein residues by using paramagnetic relaxation agents.

Mimicry of the calcium-induced conformational state of troponin C by low temperature under pressure.

Calcium binding to the N-domain of troponin C initiates a series of conformational changes that lead to muscle contraction. Calcium binding provides the free energy for a hydrophobic region in the core of N-domain to assume a more open configuration. Fluorescence measurements on a tryptophan mutant (F29W) show that a similar conformational change occurs in the absence of Ca2+ when the temperature is lowered under pressure. The conformation induced by subzero temperatures binds the hydrophobic probe bis-aminonaphthalene sulfonate, and the tryptophan has the same fluorescence lifetime (7 ns) as in the Ca2+-bound form. The decrease in volume (delta V = -25.4 ml/mol) corresponds to an increase in surface area. Thermodynamic measurements suggest an enthalpy-driven conformational change that leads to an intermediate with an exposed N-domain core and a high affinity for Ca2+.

On the mechanism of action of ribonuclease A: relevance of enzymatic studies with a p-nitrophenylphosphate ester and a thiophosphate ester.

It has been reported that His-119 of ribonuclease A plays a major role as an imidazolium ion acid catalyst in the cyclization/cleavage of normal dinucleotides but that it is not needed for the cyclization/cleavage of 3'-uridyl p-nitrophenyl phosphate. We see that this is also true for simple buffer catalysis, where imidazole (as in His-12 of the enzyme), but not imidazolium ion, plays a significant catalytic role with the nitrophenyl substrate, but both are catalytic for normal dinucleotides such as uridyluridine. Rate studies show that the enzyme catalyzes the cyclization of the nitrophenylphosphate derivative 47,000,000 times less effectively (kcat/kuncat) than it does uridyladenosine, indicating that approximately 50% of the catalytic free energy change is lost with this substrate. This suggests that the nitrophenyl substrate is not correctly bound to take full advantage of the catalytic groups of the enzyme and is thus not a good guide to the mechanism used by normal nucleotides. The published data on kinetic effects with ribonuclease A of substituting thiophosphate groups for the phosphate groups of normal substrates has been discussed elsewhere, and it was argued that these effects are suggestive of the classical mechanism for ribonuclease action, not the novel mechanism we have recently proposed. The details of these rate effects, including stereochemical preferences in the thiophosphate series, can be invoked as support for our newer mechanism.

A thermodynamic coupling mechanism for GroEL-mediated unfolding.

Chaperonins prevent the aggregation of partially folded or misfolded forms of a protein and, thus, keep it competent for productive folding. It was suggested that GroEL, the chaperonin of Escherichia coli, exerts this function 1 unfolding such intermediates, presumably in a catalytic fashion. We investigated the kinetic mechanism of GroEL-induced protein unfolding by using a reduced and carbamidomethylated variant of RNase T1, RCAM-T1, as a substrate. RCAM-T1 cannot fold to completion, because the two disulfide bonds are missing, and it is, thus, a good model for long-lived folding intermediates. RCAM-T1 unfolds when GroEL is added, but GroEL does not change the microscopic rate constant of unfolding, ruling out that it catalyzes unfolding. GroEL unfolds RCAM-T1 because it binds with high affinity to the unfolded form of the protein and thereby shifts the overall equilibrium toward the unfolded state. GroEL can unfold a partially folded or misfolded intermediate by this thermodynamic coupling mechanism when the Gibbs free energy of the binding to GroEL is larger than the conformational stability of the intermediate and when the rate of its unfolding is high.

Persistent confusion of total entropy and chemical system entropy in chemical thermodynamics.

The change in free energy with temperature at constant pressure of a chemical reaction is determined by the sum (dS) of changes in entropy of the system of reagents, dS(i), and the additional entropy change of the surroundings, dS(H), that results from the enthalpy change, W. A faulty identification of the total entropy change on reaction with dS(i) has been responsible for the attribution of general validity to the expressions (d deltaG/dT)p = -deltaS(i) and d(deltaG/T)/d(1/T)= deltaH, which are found in most textbooks and in innumerable papers.

Interactions between tRNA identity nucleotides and their recognition sites in glutaminyl-tRNA synthetase determine the cognate amino acid affinity of the enzyme.

Sequence-specific interactions between aminoacyl-tRNA synthetases and their cognate tRNAs both ensure accurate RNA recognition and prevent the binding of noncognate substrates. Here we show for Escherichia coli glutaminyl-tRNA synthetase (GlnRS; EC 6.1.1.18) that the accuracy of tRNA recognition also determines the efficiency of cognate amino acid recognition. Steady-state kinetics revealed that interactions between tRNA identity nucleotides and their recognition sites in the enzyme modulate the amino acid affinity of GlnRS. Perturbation of any of the protein-RNA interactions through mutation of either component led to considerable changes in glutamine affinity with the most marked effects seen at the discriminator base, the 10:25 base pair, and the anticodon. Reexamination of the identity set of tRNA(Gln) in the light of these results indicates that its constituents can be differentiated based upon biochemical function and their contribution to the apparent Gibbs' free energy of tRNA binding. Interactions with the acceptor stem act as strong determinants of tRNA specificity, with the discriminator base positioning the 3' end. The 10:25 base pair and U35 are apparently the major binding sites to GlnRS, with G36 contributing both to binding and recognition. Furthermore, we show that E. coli tryptophanyl-tRNA synthetase also displays tRNA-dependent changes in tryptophan affinity when charging a noncognate tRNA. The ability of tRNA to optimize amino acid recognition reveals a novel mechanism for maintaining translational fidelity and also provides a strong basis for the coevolution of tRNAs and their cognate synthetases.

Long-time quantum simulation of the primary charge separation in bacterial photosynthesis.

Accurate quantum mechanical simulations of the primary charge transfer in photosynthetic reaction centers are reported. The process is modeled by three coupled electronic states corresponding to the photoexcited chlorophyll special pair (donor), the reduced bacteriopheophytin (acceptor), and the reduced accessory chlorophyll (bridge) that interact with a dissipative medium of protein and solvent degrees of freedom. The time evolution of the excited special pair is followed over 17 ps by using a fully quantum mechanical path integral scheme. We find that a free energy of the reduced accessory chlorophyll state approximately equal to 400 cm(-1) lower than that of the excited special pair state yields state populations in agreement with experimental results on wild-type and modified reaction centers. For this energetic configuration electron transfer is a two-step process.

Chaperonin-facilitated protein folding: optimization of rate and yield by an iterative annealing mechanism.

We develop a heuristic model for chaperonin-facilitated protein folding, the iterative annealing mechanism, based on theoretical descriptions of "rugged" conformational free energy landscapes for protein folding, and on experimental evidence that (i) folding proceeds by a nucleation mechanism whereby correct and incorrect nucleation lead to fast and slow folding kinetics, respectively, and (ii) chaperonins optimize the rate and yield of protein folding by an active ATP-dependent process. The chaperonins GroEL and GroES catalyze the folding of ribulose bisphosphate carboxylase at a rate proportional to the GroEL concentration. Kinetically trapped folding-incompetent conformers of ribulose bisphosphate carboxylase are converted to the native state in a reaction involving multiple rounds of quantized ATP hydrolysis by GroEL. We propose that chaperonins optimize protein folding by an iterative annealing mechanism; they repeatedly bind kinetically trapped conformers, randomly disrupt their structure, and release them in less folded states, allowing substrate proteins multiple opportunities to find pathways leading to the most thermodynamically stable state. By this mechanism, chaperonins greatly expand the range of environmental conditions in which folding to the native state is possible. We suggest that the development of this device for optimizing protein folding was an early and significant evolutionary event.

Prediction of the stability of DNA triplexes.

We present rules that allow one to predict the stability of DNA pyrimidine.purine.pyrimidine (Y.R.Y) triple helices on the basis of the sequence. The rules were derived from van't Hoff analysis of 23 oligonucleotide triplexes tested at a variety of pH values. To predict the enthalpy of triplex formation (delta H degrees), a simple nearest-neighbor model was found to be sufficient. However, to accurately predict the free energy of the triplex (delta G degrees), a combination model consisting of five parameters was needed. These parameters were (i) the delta G degrees for helix initiation, (ii) the delta G degrees for adding a T-A.T triple, (iii) the delta G degrees for adding a C(+)-G.C triple, (iv) the penalty for adjacent C bases, and (v) the pH dependence of the C(+)-G.C triple's stability. The fitted parameters are highly consistent with thermodynamic data from the basis set, generally predicting both delta H degrees and delta G degrees to within the experimental error. Examination of the parameters points out several interesting features. The combination model predicts that C(+) -G.C. triples are much more stabilizing than T-A.T triples below pH 7.0 and that the stability of the former increases approximately equal to 1 kcal/mol per pH unit as the pH is decreased. Surprisingly though, the most stable sequence is predicted to be a CT repeat, as adjacent C bases partially cancel the stability of one another. The parameters successfully predict tm values from other laboratories, with some interesting exceptions.

Dressed polyions, counterion condensation, and adsorption excess in polyelectrolyte solutions.

The phenomenon of Manning-Oosawa counterion condensation is given an explicit statistical mechanical and qualitative basis via a dressed polyelectrolyte formalism in connection with the topology of the electrostatic free-energy surface and is derived explicitly in terms of the adsorption excess of ions about the polyion via the nonlinear Poisson-Boltzmann equation. The approach is closely analogous to the theory of ion binding in micelles. Our results not only elucidate a Poisson-Boltzmann analysis, which shows that a fraction of the counterions lie within a finite volume around the polyion even if the volume of the system tends towards infinity, but also provide a direct link between Manning's theta-the number of condensed counterions for each polyion site-and a statistical thermodynamic quantity, namely, the adsorption excess per monomer.