<i>An Introduction to Statistical Thermodynamics</i>

Hill, Terrell L.; Gillis, J. J.

doi:10.1063/1.3057470

Cited by 694 publications

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“…The translational partition function in two dimensions, q tr,2D q , is 40 where A is the area occupied by one naphthalene molecule in the saturated layer, A ) 6.45 × 10 -19 m 2 , and m is the mass of the molecule.…”

Section: Discussionmentioning

confidence: 99%

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Heat of Adsorption of Naphthalene on Pt(111) Measured by Adsorption Calorimetry

et al. 2006

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The heat of adsorption of naphthalene on Pt(111) at 300 K was measured with single-crystal adsorption calorimetry. The heat of adsorption on the ideal, defect-free surface is estimated to be (300 -34Θ -199Θ 2 ) kJ/mol. From this, a C-Pt bond energy for aromatic hydrocarbons on Pt(111) of ∼30 kJ/mol is estimated, consistent with earlier results for benzene on Pt(111). There is higher heat of adsorption at very low coverage, attributed to step sites where the adsorption heat is g330 kJ/mol. Saturation coverage, Θ ) 1 ML, corresponds to 1.55 × 10 14 molecules/cm 2 . Sticking probability measurements of naphthalene on Pt (111) give a high initial value of 1.0 and a Kisliuk-type coverage dependence that implies precursor-mediated sticking. The ratio of the hopping rate to the desorption rate of this precursor is ∼51. Naphthalene adsorbs transiently on top of chemisorbed naphthalene molecules with a heat of adsorption of 83-87 kJ/mol.

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Section: Discussionmentioning

confidence: 99%

“…The rotational partition function in three dimensions, q rot,3D q , is expressed as 40 with the symmetry factor σ (σ ) 4 for naphthalene), the velocity of light c 0 , and the rotational constants B A , B B , and B C for naphthalene (in m -1 ). 41 Now, we consider two limiting cases for the state of the adsorbate.…”

Section: Discussionmentioning

confidence: 99%

Heat of Adsorption of Naphthalene on Pt(111) Measured by Adsorption Calorimetry

et al. 2006

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“…Knowing the depth, , for a square well allows us to calculate second virial coefficients exactly. The second virial coefficient, defined as the coefficient of the leading term in the expansion of the osmotic equation of state, is given in terms of an integral of the pair potential 22 where V(r) is the protein pair potential. Using the square well model for V(r), B 2 follows exactly from eq 4 as This gives us B 2 as a function of salt concentration through its dependence on the concentration dependent well depth.…”

Section: Modelmentioning

confidence: 99%

Liquid−Liquid Coexistence Surface for Lysozyme: Role of Salt Type and Salt Concentration

Wentzel

Gunton

2007

J. Phys. Chem. B

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The liquid-liquid phase separation curves for lysozyme in a salt solution are known to depend on salt type and salt concentration. For the case of monovalent cations, the cloud point temperature typically increases with increasing salt concentration, for fixed lysozyme concentration. For the case of divalent cations, however, a maximum in the cloud point temperature is observed that has been interpreted as being due to ion binding to the protein surface and subsequent water structuring. In this paper, we use a simple square well model due to Grigsby et al. (Biophys. Chem. 2001, 91, 231-243), whose well depth depends on salt type and salt concentration, to determine the phase coexistence surfaces from experimental data. The surfaces are shown as a function of temperature, salt concentration, and protein concentration for two typical salts, NaCl and MgCl 2 . These surfaces are calculated using the results of a single standard Monte Carlo simulation and a simple scaling argument and are in reasonably good agreement with known experimental results.

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“…Here, we argue that the same approximation can be made for gJ(E). It is known that the energy distribution of the denatured state, p(E), can be well approximated by a Gaussian function, as is true for almost any thermally equilibrated system (Hill, 1986). so that…”

Section: Relationship Of Zmisfijlds To Experimental Quantitiesmentioning

confidence: 99%

What should the Z‐score of native protein structures be?

Zhang

Skolnick

1998

Protein Science

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The Z-score of a protein is defined as the energy separation between the native fold and the average of an ensemble of misfolds in the units of the standard deviation of the ensemble. The Z-score is often used as a way of testing the knowledge-based potentials for their ability to recognize the native fold from other alternatives. However, it is not known what range of values the Z-scores should have if one had a correct potential. Here, we offer an estimate of Z-scores extracted from calorimetric measurements of proteins. The energies obtained from these experimental data are compared with those from computer simulations of a lattice model protein. It is suggested that the Z-scores calculated from different knowledge-based potentials are generally too small in comparison with the experimental values. Keywords: knowledge-based potentials; protein folding; Z-scoresIn protein folding studies, knowledge-based potentials derived from a statistical analysis of known protein structures (Ueda et al., 1978;Maiorov & Crippen, 1992;Kolinski & Skolnick, 1994;Sippl, 1995; Mimy & Domany, 1996;Miyazawa & Jernigan, 1996;Liwo et al., 1997;Park et al., 1997) are frequently used in simplified models of proteins. The quality of such potentials is often assessed by socalled Z-scores, which test how well the potentials differentiate the native fold of a protein from an ensemble of misfolded structures. These Z-scores are calculated by (Bowie et al., 1991;Sippl, 1993): where Enotive is the energy of the native structure of a protein, is the average energy of an ensemble of misfolded structures, and arn,,f;,/ds is the standard deviation of the energy in this ensemble.However, it is not known what range of values of Z-scores should be expected for real proteins with exact potentials. Table 1 lists the Z-score ranges calculated from several typical knowledgebased potentials reported in the literature. The Z-scores vary tremendously from protein to protein. The widest spread of Z-scores was found for hydrophobic fitness potentials (Huang et al., 1996), which give a range between 1 and 24 for similar sized proteins, although on average the Z-score is quite high, around 11. In fact, because many approximations are introduced in the derivation of the knowledge-based potentials, there is a great deal of uncertainty as to the validity of these potentials (Jones & Thornton, 1996; Reprint requests to: Jeffrey Skolnick, Department of Molecular Biology. TPC-5, The Scripps Research Institute, 10550 North Torrey Pines Road, La Jolla, California 92037; e-mail: skolnick@scripps.edu.Pereira & Pochapsky, 1996;Thomas & Dill, 1996;Skolnick et al., 1997;Wang & Ben-Naim, 1997). This conflicting situation calls for examination of the physical meaning of the Z-scores.In this paper, we suggest a means of extracting Z-scores from the experimental data of proteins. Such Z-scores are defined differently than Zmr,,f,,,d.y, but it is possible to relate the two quantities. Thus, it is hoped that the results presented here can provide guidance into reaso...

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An Introduction to Statistical Thermodynamics

Cited by 694 publications

References 0 publications

Heat of Adsorption of Naphthalene on Pt(111) Measured by Adsorption Calorimetry

Heat of Adsorption of Naphthalene on Pt(111) Measured by Adsorption Calorimetry

Liquid−Liquid Coexistence Surface for Lysozyme: Role of Salt Type and Salt Concentration

What should the Z‐score of native protein structures be?

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