Self-assembly of protein amyloid: a competition between amorphous and ordered aggregation

Protein aggregation in the form of amyloid fibrils has important biological and technological implications. Although the self-assembly process is highly efficient, aggregates not in the fibrillar form would also occur and it is important to include these disordered species when discussing the thermodynamic equilibrium behavior of the system. Here, we initiate such a task by considering a mixture of monomeric proteins and the corresponding aggregates in the disordered form (micelles) and in the fibrillar form (amyloid fibrils). Starting with a model on the respective binding free energies for these species, we calculate their concentrations at thermal equilibrium. We then discuss how the incorporation of the disordered structure furthers our understanding on the various amyloid promoting factors observed empirically, and on the kinetics of fibrilization.Comment: Minor changes in the presentatio

Formation of an Icosahedral Structure during the Freezing of Gold Nanoclusters: Surface-Induced Mechanism

The freezing behavior of gold nanoclusters was studied by employing molecular dynamics simulations based on a semi-empirical embedded-atom method. Investigations of the gold nanoclusters revealed that, just after freezing, ordered nano-surfaces with a fivefold symmetry were formed with interior atoms remaining in the disordered state. Further lowering of temperatures induced nano-crystallization of the interior atoms that proceeded from the surface towards the core region, finally leading to an icosahedral structure. These dynamic processes explain why the icosahedral cluster structure is dominantly formed in spite of its energetic metastability.Comment: 9 pages, 4 figures(including 14 eps-files

On Some Properties Of The Two-dimensional Phases Condensed On A Foreign Substrate. Ii. Surface Roughness Of Condensed Layers And Variation Of The Surface Free Energy During Multiple Layer Adsorption

The roughness of the surface resulting from a multiple-layer adsorption is treated as a function of the temperature and the supersaturation. It is shown that the supersaturation Δμ(i) v7, at which the number of vacancies and admolecules of the i-th top-layer are equal, is the arithmetic mean of the equilibrium supersaturations Δμ(i) 0 and Δμ(i + 1) 0 of the i-th and (i + 1)-th layers respectively, contrary to a three-dimensional phase, where Δμv7 and Δμ0 are identical (nil). The further use of Δμ(i) v7, as origin for the supersaturation scale, leads to reduced equations, permitting to calculate easily roughness and surface free energy variations in the stability range (Δμ(i) 0 < Δμ < Δμ(i + 1) 0) of the i-th layer. The total free surface energy variation due to multiple layer adsorption is decomposed into two parts: the first, due to the deposition of i compact layers, and the second, due to the roughness of the top monomolecular layer. A method is proposed for determining the absolute specific adhesion energy between two substances (A and B) in the case when only the positions of the steps of the experimental step-wise isotherm of A on B are known. The method is applied to the adhesion energy xenon/graphite. © 1976.61193108Mutaftschiev, (1976) Surface Sci., 60Champion, Halsey, (1953) J. Phys. Chem., 57, p. 646Singleton, Halsey, (1954) J. Phys. Chem., 58, p. 1011Hill, (1946) J. Chem. Phys., 14, p. 263Mutaftschiev, (1965) Adsorption et Croissance Cristalline, p. 231. , CNRS, ParisTemkin, (1966) Crystallization Processes, p. 15. , Consultants Bureau, New YorkFrumkin, (1925) Z. Physik. Chem., 116, p. 466Fowler, Guggenheim, (1960) Statistical Thermodynamics, p. 466. , CambridgeBragg, Williams, The Effect of Thermal Agitation on Atomic Arrangement in Alloys (1934) Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 145, p. 699Bragg, Williams, The Effect of Thermal Agitation on Atomic Arrangement in Alloys. II (1935) Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 151, p. 540Born, Stern, (1919) Sitz. Ber. Preuss. Akad. Wiss., 48, p. 901Thomy, Duval, (1965) Adsorption et Croissance Cristalline, p. 81. , CNRS, ParisQuentel, Rickard, Kern, (1973) Vide, 28, p. 65J. Regnier and B. Mutaftschiev, to be publishe

STRUCTURE ET FONCTION DE PARTITION DE TRÈS PETITS AGRÉGATS DE GAZ RARES ET LEUR INFLUENCE SUR LA CINÉTIQUE DE LA NUCLÉATION HOMOGÈNE

Ce travail traite la structure et l'énergie libre de petits agrégats d'une substance monoatomique. La théorie de la nucléation est reconsidérée dans le but d'obtenir une nouvelle expression de la fréquence de nucléation. Cette dernière évite la plupart des paramètres dont on se sert dans la théorie classique, tels que le germe critique, la forme d'équilibre, l'énergie de surface, de même que l'introduction assez ambiguë dans les équations des facteurs entropiques, telle qu'elle est faite dans la théorie de Lothe et Pound. La vapeur sursaturée est supposée constituée d'agrégats de toutes tailles considérés comme différentes espèces chimiques. La condensation apparaît alors comme une chaîne de réactions au travers des différentes tailles d'agrégats. Les paramètres entrant dans la fréquence de nucléation sont la fonction de partition interne d'un i-mère et la constante de la réaction bi-moléculaire entre un (i - 1) mère et un monomère en supposant que c'est la seule réaction produisant un i-mère. Cette dernière est évaluée à partir du rayon effectif de la section efficace de collision du (i - 1) mère. Pour déterminer la fonction de partition interne on peut utiliser 2 méthodes : la première, bien connue, consiste à calculer les fonctions de partition des vibrations de rotation et de translation pour les agrégats d'une manière indépendante en utilisant les méthodes de la thermodynamique chimique. L'agrégat est considéré comme une géante molécule dont la structure est déterminée à l'aide de modèles dont on minimise l'énergie. L'un des résultats les plus importants de cette méthode est la mise en évidence de symétries d'ordre 5 dans les structures les plus stables. Cependant il est difficile d'appliquer ce calcul à des agrégats de plus de 13 atomes car le type de structure qu'il convient d'adopter devient arbitraire. C'est pourquoi une nouvelle méthode est proposée pour déterminer les fonctions de partition interne, en utilisant la méthode statistique de Monte Carlo. Cette méthode permet le calcul d'intégrales multiples, ce qui correspond bien au cas de la fonction de partition. Jusqu'à présent cette méthode a été appliquée au cas d'agrégats unidimensionnels de 2 à 7 atomes. Les résultats sont en total accord avec ceux obtenus par la méthode chimique. Le calcul de la fonction de partition d'agrégats mono-atomiques de 2 à 13 molécules, ainsi que de leur section efficace de collision, permettent de déterminer la fréquence de nucléation J pour des sursaturations élevées. La courbe obtenue est comparée aux courbes données par la théorie classique corrigées ou non du facteur de Lothe et Pound. La comparaison entre la théorie classique et celle de Lothe-Pound révèle un désaccord de l'ordre de 1013 pour les fréquences de nucléation. Les résultats de la méthode chimique comparés à ceux de la théorie classique permettent de prévoir une transition de phase entre structures polytétraédriques et cristallines pour des tailles intermédiaires.This work is concerning the structure and free energy of the small clusters of a monoatomic substance. The theory of nucleation is reconsidered, in view of obtaining a new expression for the nucleation frequency. The latter avoids the greatest part of parameters used in the classical theory, as critical nucleous, equilibrium form, surface energy, as well as the quite ambiguous introduction in the classical equations of entropy factors, as done in the Lothe-Pound theory. The supersaturated vapour is considered as a mixture of clusters of all sizes, considered as different chemical specy. The condensation appears than as a chain of chemical reactions, all along the different sizes of clusters. The parameters entering the nucleation rate equation are the internal partition function of a i-mer and the rate constant of the bi-molecular reaction between an (i - 1) mer and a monomer, considered as the only reaction producing a i-mer. The latter is evaluated from the effective radius of the collision cross section of the (i - 1) mer. For the internal partition function, two methods can be used : the first, and now well known one, consists in calculating the vibrational, rotational and translational partition functions of the clusters independently, by means of the methods of the chemical thermodynamics. The cluster is considered as a big molecule, the structure of which is determined from model considerations, and by a energy minimization. One of the main results obtained from this method is the existence of five-fold symetries in the most stable structures. However, it cannot be applied for clusters much bigger than 13 atomic, because the choice of the structures to be considered becomes arbitrary and very difficult. So, a new method is proposed to evaluate the internal partition functions of the clusters by means of the Monte Carlo statistical method. This method allows calculation of high order multiple integrals, which is exactly the case of the partition function. Up to now, this latter method has been applied to unidimensional clusters including two to seven atoms. The results are in perfect agreement with those obtained by the chemical method. The calculation of the partition function for 2 to 13 molecular monoatomic clusters as well as their collision cross section allows the determination of the nucleation rate J for high supersaturations. The curve obtained is compared with those given by the classical theory corrected or not by the Lothe-Pound factor. The comparison between the classical and Lothe-Pound theory shows a disagreement of some 1013, in the nucleation rates and the comparison between the classical theory and the results of the chemical method allows to expect a phase transition from polytetrahedral structures into crystalline ones, at intermediate sizes

SOME PROPERTIES OF 2-DIMENSIONAL PHASES CONDENSED ON FOREIGN SUBSTRATE .1. STRUCTURAL ASPECTS

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MULTISITE ADSORPTION AND ORDER-DISORDER TRANSITIONS IN ONE- AND TWO-DIMENSIONAL PHASES CONDENSED ON FOREIGN SUBSTRATE

On calcule pour des modèles unidimensionnels les isothermes et les variations d'énergie libre dans le cas d'adsorption multisite "un pour n" (c'est-à-dire l'occupation moyenne de n sites d'adsorption par une molécule adsorbée). On montre qu'aucune transition du premier ordre ne peut être attendue entre une phase désordonnée condensée (un pour n) et la phase solide ordonnée (un pour un). L'entropie de configuration d'une phase adsorbée bidimensionnelle un pour n est calculée numériquement par une simulation de remplissage séquentielle au hasard. Dans ce cas, la phase bidimensionnelle est construite d'une manière désordonnée et le système peut basculer d'un état désordonné à un état ordonné.Isotherms and free energy variations at equilibnum in the case of fixed one-to-n adsorption (i.e. the average occupation of n adsorption sites by one adsorbed molecule) are calculated for one-dimensional models and their properties are discussed. It proceeds that no first order transition can be expected between a condensed (one-to-n) disordered phase and the ordered (one-to-one) solid phase. Configurational entropy of an adsorbed two-dimensional one-to-n phase is computed numerically during a random sequential filling simulation. Since in this case, the two-dimensional phase is built in a disordered manner, the system can swing abruptly from disordered to ordered state

Thermal behavior of c ( 2 × 2 ) layers in the Pb/Cu(110) system and the influence of surface defects on the order-disorder transition

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