A Gibbs free energy formula for protein folding derived from quantum statistics

The fundamental law for protein folding is the thermodynamic principle. The amino acid sequence of a protein determines its native structure and the native structure has the minimum Gibbs free energy. Lacking of a Gibbs free energy formula is the reason that all ab initio protein structure prediction only empirical and various empirical energy surfaces or landscapes are introduced to fill the gap. We make a quantum mechanics derivation of the Gibbs free energy formula G(X) using quantum statistics for a single conformation X. For simplicity, only monomeric self folding globular proteins are considered.     

Protein folding as a stochastic process

In physiological conditions globular protein molecules assume a specific native conformation uniquely determined by its amino acid sequence. Upon environmental changes the protein molecules undergo reversible unfolding (order losing) and folding (order gaining) transitions, which is similar to the first-order phase transition. Pathways of folding have been intensively studied in the hope of deciphering the code that amino acid sequences carry as to the threedimensional structure of proteins. A strongly simplifiedlattice model of proteins has been found to be a powerful theoretical tool to simulate the dynamic process of the folding and unfolding transitions. The results of the simulation indicate the existence of stochastic pathways of folding.     

Relative partial photoionization cross-sections and photoelectron branching ratios of ethylene

Relative partial photoionization cross-sections and photoelectron branching ratios of the valence bands (~10–25 eV binding energy) of ethylene are reported over the photon energy ranges 18–100 eV and 21–100 eV, respectively. The four lowest ionization energy bands (1b⁻¹_1u, 1b⁻¹_1g, 3a⁻¹_g, and 1b⁻¹_2u) show monotonic cross-section decreases with photon energy from 33 eV, the 1b⁻¹_1u CC π band showing the least rapid decline. In contrast, the 2b⁻¹_3u and 2a⁻¹_g bands show almost constant cross-sections up to ~50 eV photon energy, followed by similar, although slower, monotonic decreases. This is attributed to the substantial carbon 2s character of the 2b_3u and 2a_g orbitais. The cross-section behaviour of all bands is interpreted with the aid of SCF-LCAO-MO calculations on the neutral molecule using the Gaussian-80 series of programs.     

Thermal activation measurement of positron binding energies at surfaces

The formation of positronium by low-energy positrons incident on “clean” metal surfaces is thermally activated by increasing temperature. The activation energy E_a has been measured for a number of surfaces. E_a is understood as the energy required to form positronium (binding energy 1/2Ry) from positrons bound at the surface by an energy E_b, E_a = E_b+φ_-? 1/2Ry, where φ_- is the electron work function. Representative values of E_b derived are Al(100):3.03(5) eV; Al(110):2.92(4) eV; Cu(111):2.80(5) eV.     

Structural changes during the unfolding of Bovine serum albumin in the presence of urea: A small-angle neutron scattering study

The native form of serum albumin is the most important soluble protein in the body plasma. In order to investigate the structural changes of Bovine serum albumin (BSA) during its unfolding in the presence of urea, a small-angle neutron scattering (SANS) study was performed. The scattering curves of dilute solutions of BSA with different concentrations of urea in D₂O at pH 7.2 ± 0.2 were measured at room temperature. The scattering profile was fitted to a prolate ellipsoidal shape (a, b, b) of the protein witha = 52.2 Å andb = 24.2 Å. The change in the dimensions of the protein as it unfolds was found to be anisotropic. The radius of gyration of the compact form of the protein in solution decreased as the urea concentration was increased.     

Disordered magnet near the percolation threshold

A disordered Potts magnet containing a random mixture of ferromagnetic exchange constants J_a and J_b (J_a?J_b) near the percolation threshold is considered. The scaling form for the free energy contains two crossover exponents. Duality arguments in two dimensions show that these exponents are equal. They are also shown to be equal to unity in d = 6 ? ? dimensions to order ?.     

Electronic structure of amino acids and ureas

The outer electronic levels of glycine, alanine, glycine ethyl ester, urea, and thiourea have been investigated by means of photoelectron spectroscopy using He I (584 Å) and He II (304 Å) radiation and CNDO/2 molecular orbital calculations. In the amino acids the molecular orbital (MO) ordering ha been found to be [σ core and carbonyl π > a″(O) a′(O) > a″(N)] with a first ionization potential of ～8.8 eV. Glycine and alanine are foun to exist as the undissociated amino carboxylic acids rather than zwitterions in the high temperature vapor. In urea the three lowest energy molecular o are near-degenerate [σ(4b₁) ～ π(1a₂) ～ π(2b₂)] while in thiourea only the two lowest energy MO's are near-degenerate [π(1a₂ σ(4b₁) ～ π(2b₂)]. The first ionization potentials of urea and thiourea are 9.7 and 7.9 eV respectively.     

Protein denaturation in vacuo: intrinsic unfolding pathways associated with the native tertiary structure of lysozyme

Using computer-simulated molecular dynamics, we study the effect of sequence mutation on the unfolding mechanism of a native fold. The system considered is the native fold of hen egg-white lysozyme, exposed to centrifugal unfolding in vacuo. This unfolding bias elicits configurational transitions that imitate the behaviour of anhydrous proteins diffusing after electrospraying from neutral-pH solutions. By changing the sequences threaded onto the native fold of lysozyme, we probe the role of disulfide bridges and the effect of a global mutation. We find that the initial denaturing steps share common characteristics for the tested sequences. Recurrent features are: (i) the presence of dumbbell conformers with significant residual secondary structure, (ii) the ubiquitous formation of hairpins and two-stranded β-sheets regardless of disulfide bridges, and (iii) an unfolding pattern where the reduction in folding complexity is highly correlated with the decrease in chain compactness. These findings appear to be intrinsic to the shape of the native fold, suggesting that similar unfolding pathways may be accessible to many protein sequences.     

Microwave spectrum of dimethylallene excited states and strong Coriolis coupling

The rotational spectra of six excited vibrational states of dimethylallene were measured and assigned to the corresponding vibrational levels, and for three more excited state spectra at least the rotational constants could be determined. Between the two lowest excited levels of symmetry species b₂ and b₁ of group C_2v a strong a-type Coriolis coupling was found to exist. The evaluation of the resulting perturbation by a diagonalization of the energy matrix yielded ζ^(a) = 0.36 and a precise value for the vibrational energy difference 48.761 GHz (1.6 cm^?1). The state b₂ is believed to be the first excited torsional substate (01, 10)₁ of methyl internal rotation, and the rotational transitions of this state as well as those of the strongly coupled state b₁ presented very irregular multiplet splittings. On the other hand, the splittings of the next-higher excited state of species a₂ which could be identified as the partner torsional substate (01, 10)₂, followed the regular pattern, yielding an internal rotation barrier V₃ (2079 cal/mole) not unlike that derived earlier from ground state splittings.     

Probing the sign-changeable interaction between dark energy and dark matter with current observations

We consider the models of vacuum energy interacting with cold dark matter in this study, in which the coupling can change sigh during the cosmological evolution. We parameterize the running coupling b by the form b(a) = b_0 a + b_e(1-a), where at the earlytime the coupling is given by a constant b_e and today the coupling is described by another constant b_0. We explore six specific models with(i) Q = b(a)H_0ρ_0,(ii) Q = b(a)H_0ρ_(de),(iii) Q = b(a)H_0ρ_c,(iv) Q = b(a)Hρ_0,(v) Q = b(a)Hρ_(de), and(vi) Q = b(a)Hρ_c.The current observational data sets we use to constrain the models include the JLA compilation of type Ia supernova data, the Planck 2015 distance priors data of cosmic microwave background observation, the baryon acoustic oscillations measurements,and the Hubble constant direct measurement. We find that, for all the models, we have b_0 0 and b_e 0 at around the 1σ level,and b_0 and b_e are in extremely strong anti-correlation. Our results show that the coupling changes sign during the evolution at about the 1σ level, i.e., the energy transfer is from dark matter to dark energy when dark matter dominates the universe and the energy transfer is from dark energy to dark matter when dark energy dominates the universe.     

Hybridized kinetic energy functional for orbital-free density functional method

We propose a hybridized kinetic energy functional, aTTF+bTvW, where TTF is the Thomas-Fermi functional and TvW the von Weizsäcker functional while a and b are adjustable parameters. The new functional is implemented in orbital-free plane-wave density functional method, in which a conjugate-gradient line-search scheme of electronic minimization is incorporated. Calculations with the fitted a and b show that this kinetic energy functional can describe the structures of small Si, Al and Si-Al alloy clusters with reasonable accuracy.     

On the problem of a linear complex H4

The energy minimum of a linear chain of four hydrogen atomsH₄ was investigated in dependence on the inner atomic distancea and the ?surface” distanceb. An energy minimum was obtained for somea ≠b. Some comments of methodological character are added.     

Effect of humidity on domain switching behaviors of BaTiO3 single crystal under sustained load

Domain switching behaviors of BaTiO₃ single crystal in humidity conditions were studied by polarized light microscopy (PLM) and atomic force microscopy (AFM). The results showed that the low humidity has no effect on both a-b domain configuration and a-c domain configuration under sustained load. However, the high humidity can promote a domain switching to c domain under sustained load. The difference of energy reduction induced by H₂O molecules between c domains and a(b) domains leads to this phenomenon.     

Effects of scalar and pseudoscalar Higgs bosons in the process e^ + e^ - \to b\bar bv\bar v at the LEP II collider

The possibility of setting constraints on the couplings of the scalar or pseudoscalar Higgs boson to b quarks on the basis of data on the process $e^ + e^ - \to b\bar bv\bar v$ at the LEP II collider is investigated. The mixing of the scalar and the hypothetical pseudoscalar Higgs boson in the $Hb\bar b$ vertex is parametrized in the form $\frac{{m_b }}{v}(a + i\gamma _5 b)$ . An analysis of the differential distributions for the process $e^ + e^ - \to b\bar bv\bar v$ reveals that the contribution of the fusion subprocess WW → H in the channel involving an electron neutrino enhances the sensitivity of data to the parameters under analysis. It is shown that the LEP II data at $\sqrt s = 200$ GeV and $\smallint \mathcal{L}dt = 600 pb^{ - 1} $ per experiment would make it possible to constrain the parameters Δa = a ? 1 and b as follows: ?0.75 ≤ Δa ≤ 1.4 at b = 0 and free Δa and ?0.97 ≤ b ≤ 0.97 at Δa = 0 and free b.     

ESR studies of europium ions in alkali chlorides and bromides

ESR studies of europium ions in alkali chlorides and bromides were performed at room and liquid nitrogen temperatures. There were first reported spin Hamiltonian parameters for NaBr: Eu²⁺ and RbBr: Eu²⁺ crystals and also for coagulated europium ions in NaCl, KCl, KBr and RbBr crystals. The dependence of b₂⁰ and b₂² on the lattice constant, a, of host crystals was discussed; a single relation b₂⁰αa^?2.6 was obtained, while relations for b₂² were treated seperately for Na, K and Rb halide series, respectively. From the relative values of b₂² and b₂⁰, displacements of the nearest neighbor anions surrounding the Eu²⁺-vacancy pair were estimated to be 0.083a for NaCl and NaBr, 0.081a for KC1, 0.080a for KBr, 0.074a for RbCl and 0.078a for RbBr.     

Steady State Fluorescence Studies of Wild Type Recombinant Cinnamoyl CoA Reductase (Ll-CCRH1) and its Active Site Mutants

Fluorescence quenching and time resolved fluorescence studies of wild type recombinant cinnamoyl CoA reductase (Ll-CCRH1), a multitryptophan protein from Leucaena leucocephala and 10 different active site mutants were carried out to investigate tryptophan environment. The enzyme showed highest affinity for feruloyl CoA (K _a ?=?3.72?×?10⁵ M^?1) over other CoA esters and cinnamaldehydes, as determined by fluorescence spectroscopy. Quenching of the fluorescence by acrylamide for wild type and active site mutants was collisional with almost 100 % of the tryptophan fluorescence accessible under native condition and remained same after denaturation of protein with 6 M GdnHCl. In wild type Ll-CCRH1, the extent of quenching achieved with iodide (f _a?=?1.0) was significantly higher than cesium ions (f _a?=?0.33) suggesting more density of positive charge around surface of trp conformers under native conditions. Denaturation of wild type protein with 6 M GdnHCl led to significant increase in the quenching with cesium (f _a?=?0.54), whereas quenching with iodide ion was decreased (f _a?=?0.78), indicating reorientation of charge density around trp from positive to negative and heterogeneity in trp environment. The Stern-Volmer plots for wild type and mutants Ll-CCRH1 under native and denatured conditions, with cesium ion yielded biphasic quenching profiles. The extent of quenching for cesium and iodide ions under native and denatured conditions observed in active site mutants was significantly different from wild type Ll-CCRH1 under the same conditions. Thus, single substitution type mutations of active site residues showed heterogeneity in tryptophan microenvironment and differential degree of conformation of protein under native or denatured conditions.     

How does the β-ionone effect the spectra of chlorophyll and the excitation energy transfer in solution

This paper presents the excitation spectra and fluorescence spectra of mixed solution containing chlorophyll a(Chla), chlorophyll b(Chlb) and β-ionone of different concentration, investigates the spectral changes of Chla and Chlb caused by β-ionone through optimizing the frontier orbital of Chl-β-ionone compound, and calculates the energy transfer rate between Chla and Chlb by means of the fluorescence Gauss decomposition. The results show that the β-ionone interacts with Chl mainly via the connection between the magnesium atom in Chl molecule and the carbonyl in β-ionone molecule. The formation of Chl-β-ionone compound changes the charge distribution of Chl so greatly that it leads to the red-shift of the excitation spectra and blue-shift of the fluorescence spectra of Chls. Also in the compound the electronic energy located on carbon double bond of β-ionone can be transferred to Chl molecule by the Mg…O bond, which enhances the fluorescence intensity greatly. The calculation of the excitation energy transfer (EET) rate indicates that a small amount of β-ionone can promote the EET between Chla and Chlb.     

Strong spin-spin coupling in the two-dimensional J-resolved 360-MHz 1H NMR spectra of the common amino acids

The two-dimensional J-resolved ^H NMR spectra at 360 MHz of the 20 common amino acids have been investigated. The characteristic features of strong coupling are described. Advantages and drawbacks of projections, cross sections, and contour plots for the presentation of spectra including strong coupling are illustrated with selected examples. On the basis of the amino acid data practical aspects of the use of two-dimensional J-resolved spectroscopy to improve the resolution of high-field ¹H NMR spectra of proteins are discussed.     

Multiport beam-splitter controlled transformations with postselection of superposition single-photon states

Two components of superposition single-photon state are entering into two different ports of multiport interferometer. Interference effects in which the inputs into the interferometer are controlling the outputs are studied. In particular we study a multiport beam-splitter (BS) configuration, in which eight input operators a₀, a₁, a₂…a₇ are mixed by 12 BS's to produce the output operators b₀, b₁, b₂…b₇. Multiport beam-splitter transformations of superposition single-photon states are analyzed with a possible use of postselection effects.