Observation via one-dimensional 13Calpha NMR of local conformational substates in thermal unfolding equilibria of a synthetic analog of the GCN4 leucine zipper.

Synthesis of a 33-residue, capped leucine zipper analogous to that in GCN4 is reported. Histidine and arginine residues are mutated to lysine to reduce the unfolding temperature. CD and ultracentrifugation studies indicate that the molecule is a two-stranded coiled coil under benign conditions. Versions of the same peptide are made with 99% 13Calpha at selected sites. One-dimensional 13C NMR spectra are assigned by inspection and used to study thermal unfolding equilibria over the entire transition from 8 to 73 degrees C. Spectra at the temperature extremes establish the approximate chemical shifts for folded and unfolded forms at each labeled site. Resonances for each amino acid appear at both locations at intermediate T, indicating that folded and unfolded forms interconvert slowly (> >2 ms) on the NMR time scale. Moreover, near room temperature, the structured form's resonance is double at several, but not all, sites, indicating at least two slowly interconverting, structured, local conformational substates. Analysis of the dynamics is possible. For example, near room temperature at the Val-9, Ala-24, and Gly-31 positions, the equilibrium constant for interconversion of the two structured forms is near unity and the time scale is > or= 10-20 ms.

A method for distance determination in proteins using a designed metal ion binding site and site-directed spin labeling: evaluation with T4 lysozyme.

The use of molecular genetics to introduce both a metal ion binding site and a nitroxide spin label into the same protein opens the use of paramagnetic metalnitroxyl interactions to estimate intramolecular distances in a wide variety of proteins. In this report, a His-Xaa3-His metal ion binding motif was introduced at the N terminus of the long interdomain helix of T4 lysozyme (Lys-65 --> His/Gln-69 --> His) of three mutants, each containing a single nitroxide-labeled cysteine residue at position 71, 76, or 80. The results show that Cu(II)-induced relaxation effects on the nitroxide can be quantitatively analyzed in terms of interspin distance in the range of 10-25 A using Redfield theory, as first suggested by Leigh [Leigh, J.S. (1970) J. Chem. Phys. 52, 2608-2612]. Of particular interest is the observation that distances can be determined both under rigid lattice conditions in frozen solution and in the presence of motion of the spins at room temperature under physiological conditions. The method should be particularly attractive for investigating structure in membrane proteins that are difficult to crystallize. In the accompanying paper, the technique is applied to a polytopic membrane protein, lactose permease.

Distance determination in proteins using designed metal ion binding sites and site-directed spin labeling: application to the lactose permease of Escherichia coli.

As shown in the accompanying paper, the magnetic dipolar interaction between site-directed metal-nitroxide pairs can be exploited to measure distances in T4 lysozyme, a protein of known structure. To evaluate this potentially powerful method for general use, particularly with membrane proteins that are difficult to crystallize, both a paramagnetic metal ion binding site and a nitroxide side chain were introduced at selected positions in the lactose permease of Escherichia coli, a paradigm for polytopic membrane proteins. Thus, three individual cysteine residues were introduced into putative helix IV of a lactose permease mutant devoid of native cysteine residues containing a high-affinity divalent metal ion binding site in the form of six contiguous histidine residues in the periplasmic loop between helices III and IV. In addition, the construct contained a biotin acceptor domain in the middle cytoplasmic loop to facilitate purification. After purification and spin labeling, electron paramagnetic resonance spectra were obtained with the purified proteins in the absence and presence of Cu(II). The results demonstrate that positions 103, 111, and 121 are 8, 14, and > 23 A from the metal binding site. These data are consistent with an alpha-helical conformation of transmembrane domain IV of the permease. Application of the technique to determine helix packing in lactose permease is discussed.

Determination of the distance between two spin labels attached to a macromolecule.

An EPR "spectroscopic ruler" was developed using a series of alpha-helical polypeptides, each modified with two nitroxide spin labels. The EPR line broadening due to electron-electron dipolar interactions in the frozen state was determined using the Fourier deconvolution method. These dipolar spectra were then used to estimate the distances between the two nitroxides separated by 8-25 A. Results agreed well with a simple alpha-helical model. The standard deviation from the model system was 0.9 A in the range of 8-25 A. This technique is applicable to complex systems such as membrane receptors and channels, which are difficult to access with high-resolution NMR or x-ray crystallography, and is expected to be particularly useful for systems for which optical methods are hampered by the presence of light-interfering membranes or chromophores.

Temperature chaos in 3D Ising spin glasses is driven by rare events

Temperature chaos has often been reported in the literature as a rare-event–driven phenomenon. However, this fact has always been ignored in the data analysis, thus erasing the signal of the chaotic behavior (still rare in the sizes achieved) and leading to an overall picture of a weak and gradual phenomenon. On the contrary, our analysis relies on a largedeviations functional that allows to discuss the size dependences. In addition, we had at our disposal unprecedentedly large configurations equilibrated at low temperatures, thanks to the Janus computer. According to our results, when temperature chaos occurs its effects are strong and can be felt even at short distances.

Correspondence between long-range and short-range spin glasses

We compare the critical behavior of the short-range Ising spin glass with a spin glass with long-range interactions which fall off as a power σ of the distance. We show that there is a value of σ of the long-range model for which the critical behavior is very similar to that of the short range model in four dimensions. We also study a value of σ for which we find the critical behavior to be compatible with that of the three-dimensional model, although we have much less precision than in the four-dimensional case.

Thermodynamic glass transition in a spin glass without time-reversal symmetry

Spin glasses are a longstanding model for the sluggish dynamics that appear at the glass transition. However, spin glasses differ from structural glasses in a crucial feature: they enjoy a time reversal symmetry. This symmetry can be broken by applying an external magnetic field, but embarrassingly little is known about the critical behavior of a spin glass in a field. In this context, the space dimension is crucial. Simulations are easier to interpret in a large number of dimensions, but one must work below the upper critical dimension (i.e., in d < 6) in order for results to have relevance for experiments. Here we show conclusive evidence for the presence of a phase transition in a four-dimensional spin glass in a field. Two ingredients were crucial for this achievement: massive numerical simulations were carried out on the Janus special-purpose computer, and a new and powerful finite-size scaling method.

Sample-to-sample fluctuations of the overlap distributions in the three-dimensional Edwards-Anderson spin glass

We study the sample-to-sample fluctuations of the overlap probability densities from large-scale equilibrium simulations of the three-dimensional Edwards-Anderson spin glass below the critical temperature. Ultrametricity, stochastic stability, and overlap equivalence impose constraints on the moments of the overlap probability densities that can be tested against numerical data. We found small deviations from the Ghirlanda Guerra predictions, which get smaller as system size increases. We also focus on the shape of the overlap distribution, comparing the numerical data to a mean-field-like prediction in which finite-size effects are taken into account by substituting delta functions with broad peaks.

Finite-size scaling analysis of the distributions of pseudo-critical temperatures in spin glasses

Using the results of large scale numerical simulations we study the probability distribution of the pseudo critical temperature for the three dimensional Edwards Anderson Ising spin glass and for the fully connected Sherrington-Kirkpatrick model. We find that the behaviour of our data is nicely described by straightforward finitesize scaling relations.

Static versus dynamic heterogeneities in the D=3 Edwards-Anderson-ising spin glass

We numerically study the aging properties of the dynamical heterogeneities in the Ising spin glass. We find that a phase transition takes place during the aging process. Statics-dynamics correspondence implies that systems of finite size in equilibrium have static heterogeneities that obey finite-size scaling, thus signaling an analogous phase transition in the thermodynamical limit. We compute the critical exponents and the transition point in the equilibrium setting, and use them to show that aging in dynamic heterogeneities can be described by a finite-time scaling ansatz, with potential implications for experimental work.

Nature of the spin-glass phase at experimental length scales

We present a massive equilibrium simulation of the three-dimensional Ising spin glass at low temperatures. The Janus special-purpose computer has allowed us to equilibrate, using parallel tempering, L = 32 lattices down to T ≈ 0.64Tc. We demonstrate the relevance of equilibrium finite-size simulations to understand experimental non-equilibrium spin glasses in the thermodynamical limit by establishing a time-length dictionary. We conclude that non-equilibrium experiments performed on a time scale of one hour can be matched with equilibrium results on L ≈ 110 lattices. A detailed investigation of the probability distribution functions of the spin and link overlap, as well as of their correlation functions, shows that Replica Symmetry Breaking is the appropriate theoretical framework for the physically relevant length scales. Besides, we improve over existing methodologies to ensure equilibration in parallel tempering simulations.

Spin glasses on the hypercube

We present a mean field model for spin glasses with a natural notion of distance built in, namely, the Edwards-Anderson model on the diluted D-dimensional unit hypercube in the limit of large D. We show that finite D effects are strongly dependent on the connectivity, being much smaller for a fixed coordination number. We solve the nontrivial problem of generating these lattices. Afterward, we numerically study the nonequilibrium dynamics of the mean field spin glass. Our three main findings are the following: i the dynamics is ruled by an infinite number of time sectors, ii the aging dynamics consists of the growth of coherent domains with a nonvanishing surface-volume ratio, and iii the propagator in Fourier space follows the p4 law. We study as well the finite D effects in the nonequilibrium dynamics, finding that a naive finite size scaling ansatz works surprisingly well.

Phase transition in the three dimensional Heisenberg spin glass: Finite-size scaling analysis

We have investigated the phase transition in the Heisenberg spin glass using massive numerical simulations to study very large sizes, 483. A finite-size scaling analysis indicates that the data are compatible with the most economical scenario: a common transition temperature for spins and chiralities.

Spin glass phase in the four-state three-dimensional Potts model

We perform numerical simulations, including parallel tempering, a four-state Potts glass model with binary random quenched couplings using the JANUS application-oriented computer. We find and characterize a glassy transition, estimating the critical temperature and the value of the critical exponents. Nevertheless, the extrapolation to infinite volume is hampered by strong scaling corrections. We show that there is no ferromagnetic transition in a large temperature range around the glassy critical temperature. We also compare our results with those obtained recently on the “random permutation” Potts glass.