On the Entropy of a One-Dimensional Gas with and without Mixing Using Sinai Billiard.

A one-dimensional gas comprising N point particles undergoing elastic collisions within a finite space described by a Sinai billiard generating identical dynamical trajectories are calculated and analyzed with regard to strict extensivity of the entropy definitions of Boltzmann-Gibbs. Due to the collisions, trajectories of gas particles are strongly correlated and exhibit both chaotic and periodic properties. Probability distributions for the position of each particle in the one-dimensional gas can be obtained analytically, elucidating that the entropy in this special case is extensive at any given number N. Furthermore, the entropy obtained can be interpreted as a measure of the extent of interactions between molecules. The results obtained for the non-mixable one-dimensional system are generalized to mixable one- and two-dimensional systems, the latter by a simple example only providing similar findings.

Molecular features toward high photo-CIDNP hyperpolariztion explored through the oxidocyclization of tryptophan.

Photo-chemically induced dynamic nuclear polarization (photo-CIDNP) is a promising solution to the inherent lack of sensitivity in NMR spectroscopy. It is particularly interesting in biological systems since it operates in water, at room temperature, and it can be repeated if the bleaching of the system can be controlled. However, the photo-CIDNP signal enhancement is well below those of other hyperpolarization techniques. While DNP, PHIP, and SABRE reach polarization enhancements of 103 to 104-fold, photo-CIDNP enhancement is typically only one order of magnitude for 1H and two orders of magnitude for 13C in the amino-acids tryptophan and tyrosine. Here we report on a photo-oxidation product of tryptophan that is strongly photo-CIDNP active under continuous wave light irradiation. In conjunction with the dye Atto Thio 12, a 1H signal enhancement of 120-fold was observed on a 600 MHz spectrometer, while at 200 MHz the enhancement was 380-fold. These enhancements in signal to noise correspond to a reduction in measurement time of 14 400-fold and 144 400-fold, respectively. The enhancement for 13C is estimated to be over 1200-fold at 600 MHz which corresponds to an impressive measurement time reduction of 1 440 000-fold. This photo-CIDNP active oxidation product of tryptophan has been identified to be 3α-hydroxypyrroloindole. The reasons for its improved signal enhancement compared to tryptophan have been further investigated.

Atto Thio 12 as a promising dye for photo-CIDNP.

Photo-CIDNP is one among different promising techniques to improve nuclear magnetic resonance (NMR) sensitivity. Being sensitive to particular amino acids makes it a promising candidate with respect to biological NMR. Our goal is to exploit new sensitizers and compare them to the present working horses flavin mononucleotide, bipyridyl, and the recently applied fluorescein. Among the investigated dyes, we found a new and very efficient one, Atto Thio 12, conveniently used in fluorescence microscopy with 2-3 fold enhanced polarization when compared to the established ones. We also show that diode lasers which are now available from near UV to IR can be efficiently used in photo-CIDNP. Results are obtained with the amino acids tyrosine and tryptophan.

Nuclear Magnetic Resonance Solution Structure and Functional Behavior of the Human Proton Channel.

The human voltage-gated proton channel [Hv1(1) or VSDO(2)] plays an important role in the human innate immune system. Its structure differs considerably from those of other cation channels. It is built solely of a voltage-sensing domain and thus lacks the central pore domain, which is essential for other cation channels. Here, we determined the solution structure of an N- and C-terminally truncated human Hv1 (Δ-Hv1) in the resting state by nuclear magnetic resonance (NMR) spectroscopy. Δ-Hv1 comprises the typical voltage-sensing antiparallel four-helix bundle (S1-S4) preceded by an amphipathic helix (S0). The solution structure corresponds to an intermediate state between resting and activated forms of voltage-sensing domains. Furthermore, Zn2+-induced closing of proton channel Δ-Hv1 was studied with two-dimensional NMR spectroscopy, which showed that characteristic large scale dynamics of open Δ-Hv1 are absent in the closed state of the channel. Additionally, pH titration studies demonstrated that a higher H+ concentration is required for the protonation of side chains in the Zn2+-induced closed state than in the open state. These observations demonstrate both structural and dynamical changes involved in the process of voltage gating of the Hv1 channel and, in the future, may help to explain the unique properties of unidirectional conductance and the exceptional ion selectivity of the channel.

15N transverse relaxation measurements for the characterization of µs-ms dynamics are deteriorated by the deuterium isotope effect on 15N resulting from solvent exchange.

15N R2 relaxation measurements are key for the elucidation of the dynamics of both folded and intrinsically disordered proteins (IDPs). Here we show, on the example of the intrinsically disordered protein α-synuclein and the folded domain PDZ2, that at physiological pH and near physiological temperatures amide-water exchange can severely skew Hahn-echo based 15N R2 relaxation measurements as well as low frequency data points in CPMG relaxation dispersion experiments. The nature thereof is the solvent exchange with deuterium in the sample buffer, which modulates the 15N chemical shift tensor via the deuterium isotope effect, adding to the apparent relaxation decay which leads to systematic errors in the relaxation data. This results in an artificial increase of the measured apparent 15N R2 rate constants-which should not be mistaken with protein inherent chemical exchange contributions, Rex, to 15N R2. For measurements of 15N R2 rate constants of IDPs and folded proteins at physiological temperatures and pH, we recommend therefore the use of a very low D2O molar fraction in the sample buffer, as low as 1%, or the use of an external D2O reference along with a modified 15N R2 Hahn-echo based experiment. This combination allows for the measurement of Rex contributions to 15N R2 originating from conformational exchange in a time window from µs to ms.

Quantitative Studies on the Structure of Molten Binary Potassium Molybdates by in Situ Raman Spectroscopy and Quantum Chemistry ab Initio Calculations.

The quantitative distribution of different species ( Q ijklm and H ijklmno) in binary potassium molybdate melts has been investigated by in situ high temperature Raman spectroscopy in conjunction with quantum chemistry (QC) ab initio calculations. The symmetric stretching vibrational wavenumbers of molybdenum nonbridging oxygen bonds in high wavenumber range and their respectively corresponding Raman scattering cross sections were determined and analyzed. Deconvolution of the stretching bands of molybdenum nonbridging oxygen bonds of molten Raman spectra by using the Voigt function was carried out. The six-coordinated molybdenum oxygen octahedra [MoO6]6- have been proposed to be present in molten molybdates, apart from the well-known existence of the four-coordinated [MoO4]2- tetrahedra. The quantitative analysis of different species in the molten K2MoO4-MoO3 system and their dependence on the content of MoO3, as well as the relationship with the viscosities of the melts, were also discussed. The quantitative results have been integrated with published data on physical and chemical properties of the melts.

In-Situ Studies of Structure Transformation and Al Coordination of KAl(MoO4)2 during Heating by High Temperature Raman and 27Al NMR Spectroscopies.

Recent interest in optimizing composition and synthesis conditions of functional crystals, and the further exploration of new possible candidates for tunable solid-state lasers, has led to significant research on compounds in this family MIMIII(MVIO4)2 (MI = alkali metal, MIII = Al, In, Sc, Fe, Bi, lanthanide; MVI = Mo, W). The vibrational modes, structure transformation, and Al coordination of crystalline, glassy, and molten states of KAl(MoO4)2 have been investigated by in-situ high temperature Raman scattering and 27Al magic angle spinning nuclear magnetic resonance (MAS NMR) spectroscopy, together with first principles density functional simulation of room temperature Raman spectrum. The results showed that, under the present fast quenching conditions, Al is present predominantly in [AlO6] octahedra in both KAl(MoO4)2 glass and melt, with the tetrahedrally coordinated Al being minor at approximately 2.7%. The effect of K⁺, from ordered arrangement in the crystal to random distribution in the melt, on the local chemical environment of Al, was also revealed. The distribution and quantitative analysis of different Al coordination subspecies are final discussed and found to be dependent on the thermal history of the glass samples.

Towards Prebiotic Catalytic Amyloids Using High Throughput Screening.

Enzymes are capable of directing complex stereospecific transformations and of accelerating reaction rates many orders of magnitude. As even the simplest known enzymes comprise thousands of atoms, the question arises as to how such exquisite catalysts evolved. A logical predecessor would be shorter peptides, but they lack the defined structure and size that are apparently necessary for enzyme functions. However, some very short peptides are able to assemble into amyloids, thereby forming a well-defined tertiary structure called the cross-ß-sheet, which bestows unique properties upon the peptides. We have hypothesized that amyloids could have been the catalytically active precursor to modern enzymes. To test this hypothesis, we designed an amyloid peptide library that could be screened for catalytic activity. Our approach, amenable to high-throughput methodologies, allowed us to find several peptides and peptide mixtures that form amyloids with esterase activity. These results indicate that amyloids, with their stability in a wide range of conditions and their potential as catalysts with low sequence specificity, would indeed be fitting precursors to modern enzymes. Furthermore, our approach can be efficiently expanded upon in library size, screening conditions, and target activity to yield novel amyloid catalysts with potential applications in aqueous-organic mixtures, at high temperature and in other extreme conditions that could be advantageous for industrial applications.

Quantitative determination of NOE rates in perdeuterated and protonated proteins: practical and theoretical aspects.

Precision and accuracy are the limiting factors in extracting structural and dynamic information from experimental NOEs. In this study, error sources at all stages of such an analysis are identified and errors are estimated. The data set of H(N)-H(N) cross-relaxation rates obtained from triple-labeled ubiquitin presented in [B. Vögeli, T.F. Segawa, D. Leitz, A. Sobol, A. Choutko, D. Trzesniak, W. van Gunsteren, R. Riek, J. Am. Chem. Soc. 131 (47) (2009) 17215-17225] is extended to rates obtained from a double-labeled sample. Analog data sets are presented for GB3. It is shown that quantitative NOE rates can be determined with high accuracy from both triple-labeled as well as double-labeled samples. The quality of experimental cross-relaxation rates obtained from 3D HXQC-NOESY and NOESY-HXQC experiments is discussed. It is shown that NOESY-HXQC experiments provide rates of the same quality as HXQC-NOESY if both diagonal and cross peaks for a spin pair can be resolved. Expressions for cross-relaxation rates for anisotropically tumbling molecules exhibiting fast and slow motion are derived. The impact of anisotropy on the prediction of cross-relaxation rates and on the conversion of experimental rates into effective distances is discussed. For molecules with anisotropy D(II)/D( perpendicular) up to five the distance error is smaller than 2%. Finally, "averaged order parameters" are calculated for specific secondary-structural elements showing similar trends for ubiquitin and GB3.

Exact distances and internal dynamics of perdeuterated ubiquitin from NOE buildups.

It is proposed to convert nuclear Overhauser effects (NOEs) into relatively precise distances for detailed structural studies of proteins. To this purpose, it is demonstrated that the measurement of NOE buildups between amide protons in perdeuterated human ubiquitin using a designed (15)N-resolved HMQC-NOESY experiment enables the determination of (1)H(N)-(1)H(N) distances up to 5 A with high accuracy and precision. These NOE-derived distances have an experimental random error of approximately 0.07 A, which is smaller than the pairwise rmsd (root-mean-square deviation) of 0.24 A obtained with corresponding distances extracted from either an NMR or an X-ray structure (pdb codes: 1D3Z and 1UBQ), and also smaller than the pairwise rmsd between distances from X-ray and NMR structures (0.15 A). Because the NOE contains both structural and dynamical information, a comparison between the 3D structures and NOE-derived distances may also give insights into through-space dynamics. It appears that the extraction of motional information from NOEs by comparison to the X-ray structure or the NMR structure is challenging because the motion may be masked by the quality of the structures. Nonetheless, a detailed analysis thereof suggests motions between beta-strands and large complex motions in the alpha-helix of ubiquitin. The NOE-derived motions are, however, of smaller amplitude and possibly of a different character than those present in a 20 ns molecular dynamic simulation of ubiquitin in water using the GROMOS force field. Furthermore, a recently published set of structures representing the conformational distribution over time scales up to milliseconds (pdb: 2K39) does not satisfy the NOEs better than the single X-ray structure. Hence, the measurement of possibly thousands of exact NOEs throughout the protein may serve as an excellent probe toward a correct representation of both structure and dynamics of proteins.

Simultaneous measurement of residual dipolar couplings for proteins in complex using the isotopically discriminated NMR approach.

One-bond residual dipolar couplings (RDCs) measured for the amide groups of proteins partially aligned in a magnetic field provide valuable information regarding the relative orientation of protein units. In order for RDCs obtained for individual proteins to be useful in the structure determination of heterodimer complexes, they should be measured for exactly the same alignment of the complex. Here, an isotopically discriminated IDIS-RDC-TROSY NMR experiment is proposed, which enables the measurement of HN RDCs for two proteins simultaneously and independently, but in the same sample, while they are part of the same complex. The signals for both proteins, one of which should be labeled with (15)N and the other with (15)N and (13)C, are observed in different subspectra, thus reducing spectral overlap. The approach uniquely ensures that RDCs measured for both proteins relate to exactly the same alignment tensor, allowing accurate measurement of the relative angle between the two proteins. The method is also applicable for complexes containing three or more protein components. The experiment can speed up and lead to automation of protein-protein docking on the basis of angular restraints.

Spatial structure of the dimeric transmembrane domain of the growth factor receptor ErbB2 presumably corresponding to the receptor active state.

Proper lateral dimerization of the transmembrane domains of receptor tyrosine kinases is required for biochemical signal transduction across the plasma membrane. The spatial structure of the dimeric transmembrane domain of the growth factor receptor ErbB2 embedded into lipid bicelles was obtained by solution NMR, followed by molecular dynamics relaxation in an explicit lipid bilayer. ErbB2 transmembrane segments associate in a right-handed alpha-helical bundle through the N-terminal tandem GG4-like motif Thr652-X3-Ser656-X3-Gly660, providing an explanation for the pathogenic power of some oncogenic mutations.

Conformation and mode of membrane interaction in cyclotides. Spatial structure of kalata B1 bound to a dodecylphosphocholine micelle.

Cyclotides are a family of bioactive plant peptides that are characterized by a circular protein backbone and three conserved tightly packed disulfide bonds. The antimicrobial and hemolytic properties of cyclotides, along with the relative hydrophobicity of the peptides, point to the biological membrane as a target for cyclotides. To assess the membrane-induced conformation and orientation of cyclotides, the interaction of the Möbius cyclotide, kalata B1, from the African perennial plant Oldenlandia affinis, with dodecylphosphocholine micelles was studied using NMR spectroscopy. Under conditions where the cyclotide formed a well-defined complex with micelles, the spatial structure of kalata B1 was calculated from NOE and J couplings data, and the model for the peptide-micelle complex was built using 5- and 16-doxylstearate relaxation probes. The binding of divalent cations to the peptide-micelle complex was quantified by Mn2+ titration. The results show that the peptide binds to the micelle surface, with relatively high affinity, via two hydrophobic loops (loop 5, Trp19-Val21; and loop6, Leu27-Val29). The charged residues (Glu3 and Arg24), along with the cation-binding site (near Glu3) are segregated on the other side of the molecule and in contact with polar head groups of detergent. The spatial structure of kalata B1 is only slightly changed during incorporation into micelles and represents a distorted triple-stranded beta-sheet cross-linked by a cystine knot. Detailed structural analysis and comparison with other knottins revealed structural conservation of the two-disulfide motif in cyclic and acyclic peptides. The results thus obtained provide the first model for interaction of cyclotides with membranes and permit consideration of the cyclotides as membrane-active cationic antimicrobial peptides.

From structure and dynamics of protein L7/L12 to molecular switching in ribosome.

Based on the (1)H-(15)N NMR spectroscopy data, the three-dimensional structure and internal dynamic properties of ribosomal protein L7 from Escherichia coli were derived. The structure of L7 dimer in solution can be described as a set of three distinct domains, tumbling rather independently and linked via flexible hinge regions. The dimeric N-terminal domain (residues 1-32) consists of two antiparallel alpha-alpha-hairpins forming a symmetrical four-helical bundle, whereas the two identical C-terminal domains (residues 52-120) adopt a compact alpha/beta-fold. There is an indirect evidence of the existence of transitory helical structures at least in the first part (residues 33-43) of the hinge region. Combining structural data for the ribosomal protein L7/L12 from NMR spectroscopy and x-ray crystallography, it was suggested that its hinge region acts as a molecular switch, initiating "ratchet-like" motions of the L7/L12 stalk with respect to the ribosomal surface in response to elongation factor binding and GTP hydrolysis. This hypothesis allows an explanation of events observed during the translation cycle and provides useful insights into the role of protein L7/L12 in the functioning of the ribosome.