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Shimizu S, Matubayasi N. Sorption Hysteresis: A Statistical Thermodynamic Fluctuation Theory. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2024; 40:11504-11515. [PMID: 38780491 PMCID: PMC11155257 DOI: 10.1021/acs.langmuir.4c00606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2024] [Revised: 05/03/2024] [Accepted: 05/06/2024] [Indexed: 05/25/2024]
Abstract
Hysteresis is observed commonly in sorption isotherms of porous materials. Still, there has so far been no unified approach that can both model hysteresis and assess its underlying energetics. Standard approaches, such as capillary condensation and isotherms based on interfacial equations of state, have not proved to be up to the task. Here, we show that a statistical thermodynamic approach can achieve the following needs simultaneously: (i) showing why adsorption and desorption transitions may be sharp yet continuous; (ii) providing a simple (analytic) isotherm equation for hysteresis branches; (iii) clarifying the energetics underlying sorption hysteresis; and (iv) providing macroscopic and nanoscopic perspectives to understanding hysteresis. This approach identifies the two pairs of parameters (determinable by fitting experimental data) that are required to describe the hysteresis: the free energy per molecule within the pore clusters and the cluster size in the pores. The present paper focuses on providing mechanistic insights to IUPAC hysteresis types H1, H2(a), and H2(b) and can also be applied to the isotherm types IV and V.
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Affiliation(s)
- Seishi Shimizu
- York
Structural Biology Laboratory, Department of Chemistry, University of York, Heslington, York YO10 5DD, United Kingdom
| | - Nobuyuki Matubayasi
- Division
of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
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2
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Shimizu S, Matubayasi N. Replacing the Langmuir Isotherm with the Statistical Thermodynamic Fluctuation Theory. J Phys Chem Lett 2024; 15:3683-3689. [PMID: 38536016 PMCID: PMC11000240 DOI: 10.1021/acs.jpclett.4c00281] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2024] [Revised: 03/13/2024] [Accepted: 03/15/2024] [Indexed: 04/05/2024]
Abstract
In the age of all-atom simulations, primitive isotherm models, such as Langmuir, BET, and GAB, are still used widely for analyzing experimental data. However, their routine applications to complex materials are not in line with their underlying assumptions (i.e., statistically independent adsorption sites with no interfacial structural changes), which manifests as the temperature dependence of the monolayer capacity. Our proposal is to replace these models with the statistical thermodynamic fluctuation theory because the ABC isotherm derived from it (i) contains these primitive models as its special cases, (ii) is applicable to any interfacial geometry, and (iii) is linked to molecular distribution functions, sharing the same language as simulations. Rectifying the inability of the primitive isotherm models to handle attractive and repulsive interactions consistently leads to a reconsideration of how physical interpretations should be attributed to the isotherms of empirical origin (e.g., Freundlich).
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Affiliation(s)
- Seishi Shimizu
- York
Structural Biology Laboratory, Department of Chemistry, University of York, Heslington, York YO10 5DD, United Kingdom
| | - Nobuyuki Matubayasi
- Division
of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
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3
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Shimizu S, Matubayasi N. Understanding Sorption Mechanisms Directly from Isotherms. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2023; 39:6113-6125. [PMID: 37071933 PMCID: PMC10157891 DOI: 10.1021/acs.langmuir.3c00256] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Currently, more than 100 isotherm models coexist for the six IUPAC isotherm types. However, no mechanistic insights can be reached when several models, each claiming a different mechanism, fit an experimental isotherm equally well. More frequently, popular isotherm models [such as the site-specific models like Langmuir, Brunauer-Emmett-Teller (BET), and Guggenheim-Anderson-de Boer (GAB)] have been applied to real and complex systems that break their basic assumptions. To overcome such conundrums, we establish a universal approach to model all isotherm types, attributing the difference to the sorbate-sorbate and sorbate-surface interactions in a systematic manner. We have generalized the language of the traditional sorption models (such as the monolayer capacity and the BET constant) to the model-free concepts of partitioning and association coefficients that can be applied across the isotherm types. Through such a generalization, the apparent contradictions, caused by applying the site-specific models alongside with cross-sectional area of sorbates for the purpose of surface area determination, can be eliminated straightforwardly.
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Affiliation(s)
- Seishi Shimizu
- York Structural Biology Laboratory, Department of Chemistry, University of York, Heslington, York YO10 5DD, United Kingdom
| | - Nobuyuki Matubayasi
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
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4
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Nishikawa K. The Solution Chemistry of Mixing States Probed via Fluctuations: a Direct Description of Inhomogeneity in Mixing. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 2021. [DOI: 10.1246/bcsj.20210205] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Keiko Nishikawa
- Toyota Physical & Chemical Research Institute, Nagakute, Aichi 480-1192, Japan
- Department of Chemistry, Graduate School of Science, Chiba University, Chiba 263-8522, Japan
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5
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Chialvo AA, Crisalle OD. Osmolyte-Induced Effects on the Hydration Behavior and the Osmotic Second Virial Coefficients of Alkyl-Substituted Urea Derivatives: Critical Assessment of Their Structure-Making/Breaking Behavior. J Phys Chem B 2021; 125:6231-6243. [PMID: 34086462 DOI: 10.1021/acs.jpcb.1c01855] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
We analyzed the hydration behavior of alkyl-substituted urea osmolytes in terms of their deviation from Lewis-Randall solution ideality and characterized their structure-making/breaking tendency according to a proposed solvation formalism that provides a rigorous cause-effect connection between the system microstructure and its solution thermodynamic nonidealities. After a brief introduction of the rationale behind the use of Lewis-Randall over alternative solution ideality references, we (i) assessed the effect of the nature and type of alkyl substitution on the osmolyte-induced perturbation of the solution microstructure as a function of composition, (ii) analyzed their microstructural responses to changes in temperature and pressure, and (iii) demonstrated the structure-breaking nature of urea and the magnifying behavior of its alkyl-substituted osmolytes, whose trend follows the increasingly positive deviation of the osmolyte solutions from Lewis-Randall ideality. Then, we discussed the falsifiability of a pair of frequently used conjectured structure-making/breaking criteria, supported by the derived exact relationships between the structure-making/breaking parameter, the solution thermodynamic nonideality, and the osmotic second virial coefficient of the aqueous osmolytes. Finally, we provided an outlook on how the proposed approach could guide the quest for a truly (microstructural to free energy) causative explanation for the denaturation mechanism of proteins.
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Affiliation(s)
| | - Oscar D Crisalle
- Department of Chemical Engineering, University of Florida, Gainesville, Florida 32611, United States
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6
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Ploetz EA, Karunaweera S, Bentenitis N, Chen F, Dai S, Gee MB, Jiao Y, Kang M, Kariyawasam NL, Naleem N, Weerasinghe S, Smith PE. Kirkwood-Buff-Derived Force Field for Peptides and Proteins: Philosophy and Development of KBFF20. J Chem Theory Comput 2021; 17:2964-2990. [PMID: 33878263 DOI: 10.1021/acs.jctc.1c00075] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
A new classical nonpolarizable force field, KBFF20, for the simulation of peptides and proteins is presented. The force field relies heavily on the use of Kirkwood-Buff theory to provide a comparison of simulated and experimental Kirkwood-Buff integrals for solutes containing the functional groups common in proteins, thus ensuring intermolecular interactions that provide a good balance between the peptide-peptide, peptide-solvent, and solvent-solvent distributions observed in solution mixtures. In this way, it differs significantly from other biomolecular force fields. Further development and testing of the intermolecular potentials are presented here. Subsequently, rotational potentials for the ϕ/ψ and χ dihedral degrees of freedom are obtained by analysis of the Protein Data Bank, followed by small modifications to provide a reasonable balance between simulated and observed α and β percentages for small peptides. This, the first of two articles, describes in detail the philosophy and development behind KBFF20.
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Affiliation(s)
- Elizabeth A Ploetz
- Department of Chemistry, Kansas State University, 213 CBC Building, 1212 Mid-Campus Drive North, Manhattan, Kansas 66506, United States
| | - Sadish Karunaweera
- Department of Chemistry, Kansas State University, 213 CBC Building, 1212 Mid-Campus Drive North, Manhattan, Kansas 66506, United States
| | - Nikolaos Bentenitis
- Department of Chemistry, Kansas State University, 213 CBC Building, 1212 Mid-Campus Drive North, Manhattan, Kansas 66506, United States
| | - Feng Chen
- Department of Chemistry, Kansas State University, 213 CBC Building, 1212 Mid-Campus Drive North, Manhattan, Kansas 66506, United States
| | - Shu Dai
- Department of Chemistry, Kansas State University, 213 CBC Building, 1212 Mid-Campus Drive North, Manhattan, Kansas 66506, United States
| | - Moon B Gee
- Department of Chemistry, Kansas State University, 213 CBC Building, 1212 Mid-Campus Drive North, Manhattan, Kansas 66506, United States
| | - Yuanfang Jiao
- Department of Chemistry, Kansas State University, 213 CBC Building, 1212 Mid-Campus Drive North, Manhattan, Kansas 66506, United States
| | - Myungshim Kang
- Department of Chemistry, Kansas State University, 213 CBC Building, 1212 Mid-Campus Drive North, Manhattan, Kansas 66506, United States
| | - Nilusha L Kariyawasam
- Department of Chemistry, Kansas State University, 213 CBC Building, 1212 Mid-Campus Drive North, Manhattan, Kansas 66506, United States
| | - Nawavi Naleem
- Department of Chemistry, Kansas State University, 213 CBC Building, 1212 Mid-Campus Drive North, Manhattan, Kansas 66506, United States
| | | | - Paul E Smith
- Department of Chemistry, Kansas State University, 213 CBC Building, 1212 Mid-Campus Drive North, Manhattan, Kansas 66506, United States
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Ploetz EA, Smith PE. Gas or Liquid? The Supercritical Behavior of Pure Fluids. J Phys Chem B 2019; 123:6554-6563. [DOI: 10.1021/acs.jpcb.9b04058] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Elizabeth A. Ploetz
- Department of Chemistry, Kansas State University, 213 CBC Building, 1212 Mid Campus Dr. North, Manhattan, Kansas 66506-0401, United States
| | - Paul E. Smith
- Department of Chemistry, Kansas State University, 213 CBC Building, 1212 Mid Campus Dr. North, Manhattan, Kansas 66506-0401, United States
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Jaganade T, Chattopadhyay A, Pazhayam NM, Priyakumar UD. Energetic, Structural and Dynamic Properties of Nucleobase-Urea Interactions that Aid in Urea Assisted RNA Unfolding. Sci Rep 2019; 9:8805. [PMID: 31217494 PMCID: PMC6584539 DOI: 10.1038/s41598-019-45010-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2019] [Accepted: 05/28/2019] [Indexed: 01/21/2023] Open
Abstract
Understanding the structure-function relationships of RNA has become increasingly important given the realization of its functional role in various cellular processes. Chemical denaturation of RNA by urea has been shown to be beneficial in investigating RNA stability and folding. Elucidation of the mechanism of unfolding of RNA by urea is important for understanding the folding pathways. In addition to studying denaturation of RNA in aqueous urea, it is important to understand the nature and strength of interactions of the building blocks of RNA. In this study, a systematic examination of the structural features and energetic factors involving interactions between nucleobases and urea is presented. Results from molecular dynamics (MD) simulations on each of the five DNA/RNA bases in water and eight different concentrations of aqueous urea, and free energy calculations using the thermodynamic integration method are presented. The interaction energies between all the nucleobases with the solvent environment and the transfer free energies become more favorable with respect to increase in the concentration of urea. Preferential interactions of urea versus water molecules with all model systems determined using Kirkwood-Buff integrals and two-domain models indicate preference of urea by nucleobases in comparison to water. The modes of interaction between urea and the nucleobases were analyzed in detail. In addition to the previously identified hydrogen bonding and stacking interactions between urea and nucleobases that stabilize the unfolded states of RNA in aqueous solution, NH-π interactions are proposed to be important. Dynamic properties of each of these three modes of interactions have been presented. The study provides fundamental insights into the nature of interaction of urea molecules with nucleobases and how it disrupts nucleic acids.
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Affiliation(s)
- Tanashree Jaganade
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Hyderabad, 500032, India
| | - Aditya Chattopadhyay
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Hyderabad, 500032, India
| | - Nila M Pazhayam
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Hyderabad, 500032, India
| | - U Deva Priyakumar
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Hyderabad, 500032, India.
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9
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Pallewela GN, Ploetz EA, Smith PE. Experimental Investigation of Triplet Correlation Approximations for Fluid Water. FLUID PHASE EQUILIBRIA 2018; 470:38-50. [PMID: 29915448 PMCID: PMC6003674 DOI: 10.1016/j.fluid.2017.10.028] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Triplet correlations play a central role in our understanding of fluids and their properties. Of particular interest is the relationship between the pair and triplet correlations. Here we use a combination of Fluctuation Solution Theory and experimental pair radial distribution functions to investigate the accuracy of the Kirkwood Superposition Approximation (KSA), as given by integrals over the relevant pair and triplet correlation functions, at a series of state points for pure water using only experimental quantities. The KSA performs poorly, in agreement with a variety of other studies. Several additional approximate relationships between the pair and triplet correlations in fluids are also investigated and generally provide good agreement for the fluid thermodynamics for regions of the phase diagram where the compressibility is small. A simple power law relationship between the pair and triplet fluctuations is particularly successful for state points displaying low to moderately high compressibilities.
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Affiliation(s)
- Gayani N Pallewela
- Department of Chemistry, 213 CBC Building, 1212 Mid Campus Dr. North, Kansas State University, Manhattan, KS 66506
| | - Elizabeth A Ploetz
- Department of Chemistry, 213 CBC Building, 1212 Mid Campus Dr. North, Kansas State University, Manhattan, KS 66506
| | - Paul E Smith
- Department of Chemistry, 213 CBC Building, 1212 Mid Campus Dr. North, Kansas State University, Manhattan, KS 66506
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10
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Shimizu S, Smith PE. How Osmolytes Counteract Pressure Denaturation on a Molecular Scale. Chemphyschem 2017; 18:2243-2249. [PMID: 28678423 PMCID: PMC5626881 DOI: 10.1002/cphc.201700503] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2017] [Revised: 05/30/2017] [Indexed: 11/08/2022]
Abstract
Life in the deep sea exposes enzymes to high hydrostatic pressure, which decreases their stability. For survival, deep sea organisms tend to accumulate various osmolytes, most notably trimethylamine N-oxide used by fish, to counteract pressure denaturation. However, exactly how these osmolytes work remains unclear. Here, a rigorous statistical thermodynamics approach is used to clarify the mechanism of osmoprotection. It is shown that the weak, nonspecific, and dynamic interactions of water and osmolytes with proteins can be characterized only statistically, and that the competition between protein-osmolyte and protein-water interactions is crucial in determining conformational stability. Osmoprotection is driven by a stronger exclusion of osmolytes from the denatured protein than from the native conformation, and water distribution has no significant effect on these changes at low osmolyte concentrations.
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Affiliation(s)
- Seishi Shimizu
- York Structural Biology Laboratory, Department of Chemistry, University of York, Heslington, York, YO10 5DD, UK
| | - Paul E Smith
- Department of Chemistry, Kansas State University, 213 CBC Building, Manhattan, Kansas, 66506-0401, USA
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11
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Ploetz EA, Smith PE. Simulated pressure denaturation thermodynamics of ubiquitin. Biophys Chem 2017; 231:135-145. [PMID: 28576277 DOI: 10.1016/j.bpc.2017.04.006] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2016] [Revised: 04/14/2017] [Accepted: 04/17/2017] [Indexed: 01/09/2023]
Abstract
Simulations of protein thermodynamics are generally difficult to perform and provide limited information. It is desirable to increase the degree of detail provided by simulation and thereby the potential insight into the thermodynamic properties of proteins. In this study, we outline how to analyze simulation trajectories to decompose conformation-specific, parameter free, thermodynamically defined protein volumes into residue-based contributions. The total volumes are obtained using established methods from Fluctuation Solution Theory, while the volume decomposition is new and is performed using a simple proximity method. Native and fully extended ubiquitin are used as the test conformations. Changes in the protein volumes are then followed as a function of pressure, allowing for conformation-specific protein compressibility values to also be obtained. Residue volume and compressibility values indicate significant contributions to protein denaturation thermodynamics from nonpolar and coil residues, together with a general negative compressibility exhibited by acidic residues.
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Affiliation(s)
- Elizabeth A Ploetz
- Department of Chemistry, 213 CBC Building, 1212 Mid Campus Dr. North, Kansas State University, Manhattan, KS 66506-0401, United States
| | - Paul E Smith
- Department of Chemistry, 213 CBC Building, 1212 Mid Campus Dr. North, Kansas State University, Manhattan, KS 66506-0401, United States.
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12
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Affiliation(s)
- Elizabeth A. Ploetz
- Department of Chemistry, 213 CBC Building, 1212 Mid Campus Dr North,
Kansas State University, Manhattan, Kansas 66506-0401,
USA
| | - Gayani N. Pallewela
- Department of Chemistry, 213 CBC Building, 1212 Mid Campus Dr North,
Kansas State University, Manhattan, Kansas 66506-0401,
USA
| | - Paul E. Smith
- Department of Chemistry, 213 CBC Building, 1212 Mid Campus Dr North,
Kansas State University, Manhattan, Kansas 66506-0401,
USA
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13
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Pallewela GN, Smith PE. Preferential Solvation in Binary and Ternary Mixtures. J Phys Chem B 2015; 119:15706-17. [DOI: 10.1021/acs.jpcb.5b10139] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Gayani N. Pallewela
- Department
of Chemistry, Kansas State University, 213 CBC Building, Manhattan, Kansas 66506, United States
| | - Paul E. Smith
- Department
of Chemistry, Kansas State University, 213 CBC Building, Manhattan, Kansas 66506, United States
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14
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Vafaei S, Tomberli B, Gray CG. McMillan-Mayer theory of solutions revisited: simplifications and extensions. J Chem Phys 2015; 141:154501. [PMID: 25338903 DOI: 10.1063/1.4897980] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
Abstract
McMillan and Mayer (MM) proved two remarkable theorems in their paper on the equilibrium statistical mechanics of liquid solutions. They first showed that the grand canonical partition function for a solution can be reduced to one with an effectively solute-only form, by integrating out the solvent degrees of freedom. The total effective solute potential in the effective solute grand partition function can be decomposed into components which are potentials of mean force for isolated groups of one, two, three, etc., solute molecules. Second, from the first result, now assuming low solute concentration, MM derived an expansion for the osmotic pressure in powers of the solute concentration, in complete analogy with the virial expansion of gas pressure in powers of the density at low density. The molecular expressions found for the osmotic virial coefficients have exactly the same form as the corresponding gas virial coefficients, with potentials of mean force replacing vacuum potentials. In this paper, we restrict ourselves to binary liquid solutions with solute species A and solvent species B and do three things: (a) By working with a semi-grand canonical ensemble (grand with respect to solvent only) instead of the grand canonical ensemble used by MM, and avoiding graphical methods, we have greatly simplified the derivation of the first MM result, (b) by using a simple nongraphical method developed by van Kampen for gases, we have greatly simplified the derivation of the second MM result, i.e., the osmotic pressure virial expansion; as a by-product, we show the precise relation between MM theory and Widom potential distribution theory, and (c) we have extended MM theory by deriving virial expansions for other solution properties such as the enthalpy of mixing. The latter expansion is proving useful in analyzing ongoing isothermal titration calorimetry experiments with which we are involved. For the enthalpy virial expansion, we have also changed independent variables from semi-grand canonical, i.e., fixed {N(A), μ(B), V, T}, to those relevant to the experiment, i.e., fixed {N(A), N(B), p, T}, where μ denotes chemical potential, N the number of molecules, V the volume, p the pressure, and T the temperature.
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Affiliation(s)
- Shaghayegh Vafaei
- Department of Physics and Biophysics Interdepartmental Group, University of Guelph, Guelph, Ontario N1G2W1, Canada
| | - Bruno Tomberli
- Department of Physics, Capilano University, Vancouver, British Columbia V7J3H5, Canada
| | - C G Gray
- Department of Physics, University of Guelph, Guelph, Ontario N1G2W1, Canada
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15
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Ploetz EA, Smith PE. Particle and Energy Pair and Triplet Correlations in Liquids and Liquid Mixtures from Experiment and Simulation. J Phys Chem B 2015; 119:7761-77. [DOI: 10.1021/acs.jpcb.5b00741] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Elizabeth A. Ploetz
- Department
of Chemistry, Kansas State University, 213 CBC Building, Manhattan, Kansas 66506, United States
| | - Paul E. Smith
- Department
of Chemistry, Kansas State University, 213 CBC Building, Manhattan, Kansas 66506, United States
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16
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Ploetz EA, Karunaweera S, Smith PE. Experimental triplet and quadruplet fluctuation densities and spatial distribution function integrals for pure liquids. J Chem Phys 2015; 142:044502. [PMID: 25637990 PMCID: PMC4312347 DOI: 10.1063/1.4905562] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2014] [Accepted: 12/22/2014] [Indexed: 11/14/2022] Open
Abstract
Fluctuation solution theory has provided an alternative view of many liquid mixture properties in terms of particle number fluctuations. The particle number fluctuations can also be related to integrals of the corresponding two body distribution functions between molecular pairs in order to provide a more physical picture of solution behavior and molecule affinities. Here, we extend this type of approach to provide expressions for higher order triplet and quadruplet fluctuations, and thereby integrals over the corresponding distribution functions, all of which can be obtained from available experimental thermodynamic data. The fluctuations and integrals are then determined using the International Association for the Properties of Water and Steam Formulation 1995 (IAPWS-95) equation of state for the liquid phase of pure water. The results indicate small, but significant, deviations from a Gaussian distribution for the molecules in this system. The pressure and temperature dependence of the fluctuations and integrals, as well as the limiting behavior as one approaches both the triple point and the critical point, are also examined.
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Affiliation(s)
- Elizabeth A Ploetz
- Department of Chemistry, Kansas State University, 213 CBC Building, Manhattan, Kansas 66506, USA
| | - Sadish Karunaweera
- Department of Chemistry, Kansas State University, 213 CBC Building, Manhattan, Kansas 66506, USA
| | - Paul E Smith
- Department of Chemistry, Kansas State University, 213 CBC Building, Manhattan, Kansas 66506, USA
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17
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Ploetz EA, Smith PE. Infinitely dilute partial molar properties of proteins from computer simulation. J Phys Chem B 2014; 118:12844-54. [PMID: 25325571 PMCID: PMC4234426 DOI: 10.1021/jp508632h] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A detailed understanding of temperature and pressure effects on an infinitely dilute protein's conformational equilibrium requires knowledge of the corresponding infinitely dilute partial molar properties. Established molecular dynamics methodologies generally have not provided a way to calculate these properties without either a loss of thermodynamic rigor, the introduction of nonunique parameters, or a loss of information about which solute conformations specifically contributed to the output values. Here we implement a simple method that is thermodynamically rigorous and possesses none of the above disadvantages, and we report on the method's feasibility and computational demands. We calculate infinitely dilute partial molar properties for two proteins and attempt to distinguish the thermodynamic differences between a native and a denatured conformation of a designed miniprotein. We conclude that simple ensemble average properties can be calculated with very reasonable amounts of computational power. In contrast, properties corresponding to fluctuating quantities are computationally demanding to calculate precisely, although they can be obtained more easily by following the temperature and/or pressure dependence of the corresponding ensemble averages.
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Affiliation(s)
- Elizabeth A Ploetz
- Department of Chemistry, Kansas State University , 213 CBC Building, Manhattan, Kansas 66506-0401, United States
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18
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Mijaković M, Polok KD, Kežić B, Sokolić F, Perera A, Zoranić L. A comparison of force fields for ethanol–water mixtures. MOLECULAR SIMULATION 2014. [DOI: 10.1080/08927022.2014.923567] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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