1,720,961 research outputs found
Calculation of site affinity constants and cooperativity coefficients for binding of ligands and/or protons to macromolecules. II. Relationships between chemical model and partition function algorithm
No full textThe relationships between the chem. properties of a system and the partition function algorithm as applied to the description of multiple equil. in soln. are explained. The partition functions ZM, ZA, and ZH are obtained from powers of the binary generating functions Jj = (1 + Kjγj,i[Y]i,j, where itj = ptj, qtj, or rtj represent the max. no. of sites in class j, for Y = M, A, or H, resp. Each term of the generating function can be considered an element {ij} of a vector Jj and each power of the cooperativity factor γj,ii can be considered an element of a diagonal cooperativity matrix Γj. The vectors Jj are combined in tensor product matrixes Ll = {J1} [J2] ... [Jj] ..., thus representing different receptor-ligand combinations. The partition functions are obtained by summing elements of the tensor matrixes. The relationship of the partition functions with the total chem. amts. TM, TA, and TH has been found. The aim is to describe the total chem. amts. TM, TA, and TH as functions of the site affinity consts. kj and cooperativity coeffs. bj. The total amts. are calcd. from the sum of elements of tensor matrixes Ll. Each set of indexes {pj ..., qj ..., rj ...} represents one element of a tensor matrix Ll and defines each term of the summation. Each term corresponds to the concn. of a chem. microspecies. The distinction between microspecies MpjAqjHrj with ligands bound on specific sites and macrospecies MpAQHR corresponding to a chem. stoichiometric compn. is shown. The translation of the properties of chem. model schemes into the algorithms for the generation of partition functions is illustrated with ref. to a series of examples of gradually increasing complexity. The equil. examd. concern: (1) a unique class of sites; (2) the protonation of a base with 2 classes of sites; (3) the simultaneous binding of ligand A and proton H to a macromol. or receptor M with 4 classes of sites; and (4) the binding to a macromol. M of ligand A which is in turn a receptor for proton H. With ref. to a specific example, it is shown how a computer program for least-squares refinement of variables kj and bj can be organized. The chem. model from the free components M, A, and H to the satd. macrospecies MPAQHR, with possible complex macrospecies MPAQ and AHR, is defined first. Subsequently, the binary functions compatible with the model, along with the initial values of the site affinity const. kj, the no. of sites in each class, and the cooperativity coeffs. bj, are entered. The chem. model controls the type of tensor product matrixes Ll which are generated and the limits of the lower-case letter indexes pj, qj and rj which define the terms (microspecies) contributing to the total chem. amts. TM, TA, TH
Probability, thermodynamics, and dispersion space for a statistical model of equilibria in solution. 1. Quantum levels and thermodynamic functions in grand canonical and canonical ensembles
No full textThe relative or excess grand canonical partition function, ZM, represents the probability relative to free M of finding any species MAi in a soln. contg. receptor M and ligand A. On a mol. scale, the partition function can be seen as the distribution of population among levels i of a quantized model. The properties of the model are here defined. The distribution of species can be modulated from outside either by changing diln. or temp. On a molar scale, the relation between the partition function, ZM, and the probability factors for free energy, exp(-ΔG/RT), enthalpy, exp(-Δ4H/RT), and entropy, exp(ΔS/R), resp., can be represented in probability space, which is suited to relate partition function (probability) to the exptl. domains of concn. and diln. The probability space can be transformed into the affinity thermodn. space suited to the representation of heat exchange (calorimetric domain) and chem. work (cratic domain). This formal anal. is employed to explain why the heat exchanged in a reaction (-ΔH/RT) in grand canonical ensembles can be measured by detns. of concns. in the cratic domain without any direct calorimetric detn. The heat effect is due to the existence of an intrinsic enthalpy difference in the quantized model of the reaction. Cryscopic (-ΔmH/RT) and ebullioscopic (-ΔebH/RT) properties are explained by the same principle, in the affinity thermodn. space. No outstanding enthalpy level is present in canonical ensembles, where no reaction takes place. The anal. shows how the enthalpy and entropy changes upon the temp. are indistinguishable and can be transformed into each other by calcn. Therefore, the isobaric heat capacity Cp apparently conveys the same thermodn. information either as Cp dT = dH or as Cp d nT = dS, in canonical ensembles. The distinction between grand canonical and canonical ensembles based on the enthalpy difference is a starting point for their studies and for the interpretation of exptl. data
Molecular thermodynamic model for the solubility of noble gases in water
No full textThe thermodn. model based on the distributions of mol. populations among energy levels was employed for the anal. of the soly. of noble gases in water at different temps. The soly. is expressed in polynomial form. The apparent thermodn. quantities are obtained from the given expression. The whole system is considered as the convoluted ensemble (gc*c)e formed by a grand canonical ensemble, gce, and a canonical ensemble, ce, the latter corresponding to the solvent. The statistical distribution is described by a convoluted partition function, (GC*C)PF, which is the product of a grand canonical partition function, GCPF, and a canonical partition function, CPF. The apparent thermodn. functions can be decompd. into the contributions of the sep. partition functions. In particular, the apparent enthalpy {-ΔHapp}T = -ΔH° - nwCp,wT is the sum of the enthalpy change due to the reaction between gas and water, -ΔH°, and the heat absorbed by the water mols. involved in the reaction ΔHw = NwCp,wT. The enthalpy term ΔHw, which varies linearly with the temp., was calcd. by using the relation of thermal equiv. diln. valid for the canonical ensemble. By plotting the apparent enthalpy{-ΔHapp}T vs. T, the value nw can be obtained from the slope of the line. Sets of data from different sources were analyzed and yield congruent values of -ΔH° and nw. The values nw ranging from 1.5 for helium to 3.3 for xenon clearly depend on the size of the atoms of the noble gas and can be related to the formation of a cavity of water mols. in the solvent
Probability, thermodynamics, and dispersion space for a statistical model of equilibria in solution. 3. Aqueous solutions of monocarboxylic acids at different temperatures
No full textThe thermal moments of the grand canonical partition function for solutes are related to the coeffs. of a Taylor-McLaurin expansion because the solutes form a statistical ensemble distributed according to the Boltzmann law. When treating equil. in soln., the solvent is present in large excess and its concn. is in general assumed as const. The mols. of solvent can be considered to form a canonical subsystem. For this subsystem, the change of temp. d ln T produces a change of entropy dS = Cp,w d ln T, where Cp,w is the molar heat capacity of H2O, exactly equiv. to the change of entropy produced by a change of diln. dS = -d ln [W]. The properties of the canonical subsystem combined with those of the grand canonical system explain the variation of the apparent protonation const. of carboxylic acids with the temp. The curve for ethanolic acid plotted as the function of 1/T shows a min. at T = 295.4 K and can be expressed as a polynomial. By changing the ref. temp., θ, a set of values of apparent enthalpy is obtained which plotted against T = θ yields a line of intercept -ΔH0/R and slope nwCp,wθ/R. The no. of H2O mols. involved in the reaction, nw can be calcd. For the protonation of several carboxylic acids that can be represented by a normalized equation, the authors obtain nw = 2.1. By considering the H2O mols. as part of the reaction, the true equil. const. k0 can be calcd. The values of the true enthalpy, -ΔHγ and true std. entropy, -ΔSγ of the protonation-dehydration process come out to be very different from the apparent values, -ΔHappγ and -ΔSappγ, resp. because of enthalpy-entropy compensation concerning the nw H2O mols. involved
Probability, thermodynamics and dispersion space for a statistical model of equilibria in solution. 2. Concentration and temperature moments of partition function
No full textThe derivs. of the excess grand canonical partition function, ZM, or the abs. grand canonical partition function, ΞM = [M]ZM correspond to means and variances of thermodn. functions. The 1st deriv. with respect to ligand concn., δ ln Zm/δ ln [A], corresponds in thermodn. space to the formation function of Bjerrun, n (mean entropy change), the 2nd deriv. to the buffer capacity, ΔB/pA (entropy variance or dispersion). The latter can be represented in a concn.-dispersion space. In systems where no chem. reaction is taking place, the relations ΔGγ/RT = 0, ZM = 1, and ΞM = [M] hold. Analogs relations hold for each species MAi assocd. to energy level i. The distribution of the population among the sublevels j of each level i can be represented by intralevel canonical partition function, ζi whose 1st deriv. with respect to 1/T, δ ln ζi/δ(1/T) is the mean enthalpy -〈ΔHj,i/R〉 of the level i whereas the deriv. δ in ζi-1/δ ln T is the mean entropy 〈ΔSj,i/R〉 of the level. The higher derivs. of ln ζi with respect to 1/T and the higher derivs. of ln ζi-1 with respect to ln T are related to the higher moments of enthalpy and entropy distribution, resp. The 2nd moment (variance) can be exptl. detd. by measurements of the molar isobaric heat capacity, Cp. The diagram Cp = f(ln T) can be considered as thermal-dispersion space. Analogs relations were found between derivs. of ln ΞM or ln ZM with respect to 1/T or ln T and moments of the free energy distribution for grand canonical ensembles. The set of derivs. can be introduced as the coeffs. in a Taylor-McLaurin series reproducing the logarithms of equil. consts. at different temps. up to the limit of stochastic error. The level model with Boltzmann statistical distribution of populations is correct for the description of the properties of systems in equil. in soln. The concn. and thermal dispersion spaces are parallel. Mixed concn.-temp. derivs. can be calcd. for grand canonical ensembles. In particular, new expressions for the apparent isobaric heat capacity, Cp,app can be obtained from mixed concn.-temp. moments
Calculation of site enthalpy for binding of ligands and protons to macromolecules
No full textA special algorithm has been developed by which the heat evolved can be expressed as a function of sp. site enthalpy and sp. cooperative enthalpies for each class of sites. The algorithms represents the math. analog of the interconnections between components in some types of complex macrospecies of the chem. model assumed and their deconvolution into microspecies. A computer program was also developed; flow chart is not presented
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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