Parameter-Free Hydrogen-Bond Definition to ... - ACS Publications

Apr 12, 2016 - It is based on a hydrogen-bond definition with an energy cutoff. To assess whether hydrogen bonds defined in a parameter-free way may g...
1 downloads 3 Views 447KB Size
Download PDF
Article pubs.acs.org/JPCB

Parameter-Free Hydrogen-Bond Definition to Classify Protein Secondary Structure Hasti Haghighi,†,‡ Jonathan Higham,†,‡ and Richard H. Henchman*,†,‡ †

Manchester Institute of Biotechnology, The University of Manchester, 131 Princess Street, Manchester M1 7DN, United Kingdom School of Chemistry, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom

‡

ABSTRACT: DSSP is the most commonly used method to assign protein secondary structure. It is based on a hydrogen-bond definition with an energy cutoff. To assess whether hydrogen bonds defined in a parameter-free way may give more generality while preserving accuracy, we examine a series of hydrogen-bond definitions to assign secondary structure for a series of proteins. Assignment by the strongest-acceptor bifurcated definition with provision for unassigned donor hydrogens, termed the SABLE method, is found to match DSSP with 95% agreement. The small disagreement mainly occurs for helices, turns, and bends. While there is no absolute way to assign protein secondary structure, avoiding molecule-specific cutoff parameters should be advantageous in generalizing structure-assignment methods to any hydrogen-bonded system.

■

INTRODUCTION The assignment of secondary structure is an important tool in simplifying and characterizing the structure of a protein. Secondary structure motifs such as helices and beta sheets are distinguished by particular patterns of backbone hydrogen bonds (HBs),1−5 the backbone atoms,6,7 the Cα atoms,1,3,8−11 or Cα contacts.12 The most widely used algorithm for the assignment of the secondary structure of a protein from its 3D structures is DSSP, which makes use of HBs.2 HBs, like any intermolecular interaction, are strong at short-range and diminish continuously out to zero at infinity. To be useful in a simple classification scheme they must be treated as stepfunctions, either on or off. This introduces some arbitrariness as to where to put the cutoff. Different cutoffs can lead to different secondary structure assignments. The standard approach is to use fixed cutoff parameters in some measure of HB strength such as energy or geometry,1−3 which assumes that the cutoff parameters are suitable for all proteins and all conditions. DSSP implements a moderately simple HB definition. It assigns HBs according to the electrostatic energy between backbone carbonyl and amide groups. The electrostatic energy is summed over the interactions of the carbon (C) and oxygen (O) of the carbonyl group with the hydrogen (H) and nitrogen (N) of the amide group; the respective charges assigned for each atom are 0.42, −0.42, 0.2, and −0.2 in units of electron charge. The hydrogen atom, typically missing from X-ray crystal structures, is added in. For each amide group, only the two most stably interacting carbonyl groups are considered, a point not made explicitly clear in the original paper.2 This is justified because hydrogens may be bifurcated but rarely trifurcated. Of these two strongest interactions, an HB is assigned if the energy lies below the threshold of −0.5 kcal mol−1. Thus, there are © XXXX American Chemical Society

effectively four parameters in DSSP: the energy cutoff, the limit of two nearest-acceptors, and the two charge magnitudes. The details of the secondary-structure assignment can be found in the original paper.2 In brief, the rules are based on the relative numbering of consecutive stretches of HBs and priorities of secondary structure types. Priorities are applied if an amino acid has more than one possible secondary structure. The priorities of each type, from highest to lowest, together with their symbols, are α helix (H), single β bridge (B), β strand (E), 310 helix (G), π helix (I), turn (T), bend (S), or none. The only cutoff used in the assignment rules is for the bend, which requires the angle between three consecutive Cα atoms to be >70°. We have been examining the question of how to classify the structure of hydrogen-bonded systems without the use of cutoff parameters. The main advantage of this is generality; it avoids having to determine parameters for every type of HB under every kind of conditions. Our method to do this is the strongest-acceptor method13−15 whereby a donor donates to the acceptor with which it has the most attractive electrostatic force. The method can also detect hydrogens that are not assigned an acceptor if the donor−acceptor interaction is weaker than another donor−acceptor interaction involving the same two molecules.14 It also allows for the possibility of hydrogens bifurcating between two oxygens if the acceptor with which the donor has the second strongest interaction acceptor has fewer donors than the nearest acceptor.16 The method is Special Issue: J. Andrew McCammon Festschrift Received: March 11, 2016 Revised: April 8, 2016

A

DOI: 10.1021/acs.jpcb.6b02571 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

because stable HBs can form with these residues. This criterion also applies to any possible bifurcation previously described. This method was termed the Local Environment (LE) method. It was combined with the SA, SAB, and STA methods, giving 3 more methods and 12 in total. The method to determine an unassigned donor is based on the assignment of broken HBs in water.14 In the context of secondary structure assignment of a static protein, the term “broken” is inappropriate because there is no opportunity for HBs to change and because the donor may actually form an HB but to a nonbackbone atom not considered in the classification such as a side chain or water molecule. The methods were implemented by modifying the DSSP code,2 which was obtained from the Web site http://swift.cmbi. ru.nl/gv/dssp/ of the Centre for Molecular and Biomolecular Informatics.20 We used the same protein test set of 1594 X-ray proteins as in the study of Martin et al.,10 removing 51 duplicated proteins from their list of 1645. Coordinates for the protein structures were downloaded from the PDB. The files containing the modified code and list of proteins can be found at http://personalpages.manchester.ac.uk/staff/henchman/ software/. Every method was compared with DSSP by taking the secondary structure outputs for both DSSP and the new method and comparing the HB agreement and secondary structure assignment for each residue. The total number of residues that were assigned the same HBs or secondary structure was totalled in each case to give an overall percentage agreement. The combination of methods with the best agreement with DSSP was found to use the FOH measure and the SAB and LE methods, now denoted as SABLE. The percentage agreements of SABLE with DSSP with a range of different energy cutoffs from 0 to −4 kcal mol−1 were also calculated to assess the appropriateness of DSSP’s energy cutoff. A histogram of ECOHN for all HBs was calculated for DSSP and SABLE to assess the contributing HBs. To examine SABLE’s assignment as a function of secondary structure, we constructed a matrix of the percentage agreement as a function of secondary structure.

essentially a nearest-neighbor method and is based on the idea of resolving transition states that bound stable HB configurations rather than assuming a fixed kind of HB. The method has been applied to liquid water14,16−18 and aqueous solutions.13,15,19 Here we apply it to proteins, looking at the secondary assignment it generates according to the DSSP rules instead of the energy-based definition in standard DSSP. To help identify the contributing factors in this examination, we test 12 different definitions differing in force, energy, energy cutoff, choice of atoms, and the possibility of HB bifurcation or unassigned donors. In so doing, we span a range of methods that are systematically intermediate between the strongestacceptor definition and DSSP’s energy-cutoff definition. We apply the methods to 1594 proteins used in another secondary structure comparison elsewhere10 and compare the resulting secondary structure assignments to the those of the original DSSP.

■

METHODS The 12 methods to assign backbone HBs in proteins are the following. Three different variables to assess the HB are combined with four methods to allocate HBs. We first consider the three different variables with which to assess the HB: (1) FOH: The electrostatic force between O and H. This is equivalent to the inverse of OH distance because the O and H charges are fixed, making this method parameter-free. (2) FCOHN: The electrostatic force between CO and HN using the same charges as in DSSP. (3) ECOHN: The electrostatic energy between CO and HN using the same charges as in DSSP. We next consider three methods governing how to allocate HBs to a given donor: (1) Strongest Acceptor (SA): The donor forms a HB to the acceptor with which it has the most favorable interaction. (2) Strongest Acceptor plus Bifurcation (SAB): The donor forms an HB to its most favorable acceptor and possibly bifurcates to the next most favorable acceptor if that acceptor accepts fewer HBs than the acceptor with the donor’s most favorable interaction, ignoring any other bifurcation. Carbonyl oxygens may accept zero, one, or two HBs. On the basis of a previous study of water,16 the assumption is that a donor to an oxygen crowded with more donors prefers to bifurcate to a neighboring oxygen with fewer donors. (3) Strongest Two Acceptors (STA): The donor forms an HB to the two acceptors with which it has the most favorable interactions. These methods were chosen to provide a systematic progression from using FOH with no bifurcation (SA) to using ECOHN with full bifurcation forced between two acceptors (STA), which is equivalent to DSSP with an energy cutoff of 0 kcal mol−1. The variable EOH is not considered because it is equivalent to FOH when comparing relative values because both depend only on the OH distance. Finally, an additional mechanism was included to permit the possibility of unassigned donors because it was found to be necessary to cut down on spuriously long HBs. This was only implemented for interactions defined in terms of FOH, which was found to give the best agreement with DSSP. The amide hydrogen of residue n is an unassigned donor if the acceptor with which it has the most favorable interaction is the backbone carbonyl oxygen on the donor’s previous residue n − 1, with the numbering starting from the N-terminus. Exclusion was not based on other residues more distant along the protein chain

■

RESULTS The percentage agreements in HB assignment and secondarystructure assignment between DSSP and each of the 12 methods are shown in Tables 1 and 2, respectively. The Table 1. Percentage Agreement of Hydrogen Bonds between Each Method and DSSP hydrogen-bond variable hydrogen-bond method strongest acceptor strongest acceptor + bifurcation strongest two acceptors

ECOHN

FCOHN

FOH

FOH + local environment

80.7 62.1

80.4 62.9

78.8 55.1

88.9 85.0

42.0

41.5

39.2

76.8

agreement in HBs is comparable for all three variables ECOHN, FCOHN, and FOH but gets worse as more bifurcation is included going from SA to SAB to STA. Including the local-environment criterion to FOH improves the agreement noticeably, even for the bifurcated methods, although no bifurcation is still better. When considering the agreement based on secondary structure assignment, the trends are similar but less extreme, showing that the DSSP rules for structure assignment possess some B

DOI: 10.1021/acs.jpcb.6b02571 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

also be used to a high level of accuracy. Why DSSP and SABLE agree fairly closely can be further seen in the histograms of HB energies, which are plotted in Figure 2. Both methods detect

Table 2. Percentage Agreement of Total SecondaryStructure between Each Method and DSSP hydrogen-bond variable hydrogen-bond method strongest acceptor strongest acceptor + bifurcation strongest two acceptors

ECOHN

FCOHN

FOH

FOH + local environment

89.7 82.2

88.9 81.7

90.7 85.2

92.9 94.6

71.5

63.6

76.4

94.8

degree of robustness with respect to HB definition. FOH with the local environment criterion performs the best, but now bifurcation helps improve the agreement. Both SAB and STA share the highest secondary structure agreement of 95%. Given that the SAB method with FOH and the local environment criterion is free of parameters and does not have forced bifurcation, it is our preferred method. Even though the other methods are less accurate, they are insightful in explaining the contributions of each differing factor. The methods using ECOHN, FCOHN, and FOH without LE get progressively worse with increasing bifurcation, the opposite trend to FOH with LE. This can be attributed to their excessive inclusion of weak HBs that DSSP would disregard. This makes clear a weakness of these kinds of nearest-neighbor HB definitions for isolated protein molecules. In the absence of solvent and other molecules expected in typical condensedphase environments and with donors not being allowed to donate to side chains, such definitions predict excessive and unrealistically long HBs. A criterion for unassigned donors is essential because the donor’s actual acceptor, such as a side chain or water molecule, may not be being considered in the assignment. It may also be because the hydrogen actually does not have any nearby acceptor, as, for example, for donors at the air−water interface.19 As previously noted, the STA method with ECOHN is equivalent to DSSP with zero cutoff. To see how the STA method transitions to normal DSSP, Figure 1 shows the

Figure 2. Histogram of HB energies for SABLE (black) and DSSP (gray) with cutoff (dashed).

the large peak of strong, well-defined HBs but differ for the weak HBs. DSSP picks up some extra HBs just before the cutoff, again supporting the notion that DSSP’s cutoff is slightly generous,3 and that a cutoff around 1 kcal mol−1 might be more suitable. SABLE picks up a small peak of donor−acceptor interactions with unfavorable energy. SABLE uses only the OH interaction and yet the energies calculated here are COHN energies. The unfavorable energies are therefore due to the contribution of the C and N atoms, implying a misaligned HB. This may arise either because of strain in the protein or inaccuracy due to low resolution. Evidently, the local environment criterion used here to detect unassigned donors is not strict enough. Combining SABLE with DSSP’s −0.5 kcal mol−1 cutoff would eliminate the second trailing peak at the cost of introducing a cutoff. An alternative is to use a 0 kcal mol−1 cutoff, justified by the need for the HB to be favorable dipole−dipole interaction, which would not affect the generality of the HB definition. How the methods differ for each type of secondary structure can be seen in Table 3, which shows a matrix of the respective percentages of each assignment. The main diagonal represents agreement, whereas off-diagonal terms are disagreement. Also given are the secondary structure percentages for DSSP and SABLE in the respective column or row. Finally, the total percentage agreement of each type of secondary structure is given, which is defined as the value in the main diagonal divided by the percentage of DSSP secondary structure. The agreement for the main secondary structure elements of α helices and β sheets is very high at 97%. This is matched by the 97% agreement, where there is no secondary structure, and both methods assign the same overall amount of secondary structure. The agreement is slightly lower for bends (92%), turns (86%), and bridges (80%), of which the latter two are the respective building blocks of helices and sheets. The agreement is good for 310 helices at 94% but the worst for π helices at 69%. Looking at the largest off-diagonal elements, SABLE assigns more 310 helices than either turns or α helices. It assigns more turns than α helices or bends, although these trends are sometimes reversed. The methods do not always agree about bridges. DSSP picks up more π helices, although these are already low in number.

Figure 1. Percentage agreement between SABLE and DSSP whose HBs are calculated for a range of COHN energy cutoffs.

percentage agreement between SABLE and DSSP with a range of energy cutoffs. As expected, the agreement improves, equaling 95% agreement with SABLE in Table 1 at −0.5 kcal mol−1 but providing a maximum overlap of 97% at −0.65 kcal mol−1 before decreasing again. This does not mean that a cutoff of −0.65 kcal mol−1 is necessarily better than −0.5 kcal mol−1, given the success of DSSP, but it does suggest that SABLE can C

DOI: 10.1021/acs.jpcb.6b02571 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B Table 3. Percentage Agreement in Secondary Structure between SABLE and DSSP DSSP SABLE

■

H

E

T

S

G

B

I

none

secondary structure

H E T S G B I none

31.2 0.0 0.6 0.0 0.4 0.0 0.0 0.0

0.0 20.1 0.0 0.1 0.0 0.1 0.0 0.5

0.3 0.0 9.7 0.4 0.8 0.0 0.0 0.1

0.0 0.1 0.6 8.4 0.1 0.0 0.0 0.0

0.0 0.0 0.1 0.0 3.4 0.0 0.0 0.0

0.0 0.1 0.0 0.0 0.0 1.0 0.0 0.1

0.2 0.0 0.0 0.0 0.0 0.0 0.4 0.0

0.0 0.5 0.0 0.0 0.0 0.1 0.0 20.3

31.8 20.8 11.1 8.9 4.7 1.2 0.5 21.0

secondary structure agreement

32.3 96.7

20.8 96.8

11.3 85.7

9.2 91.5

3.6 94.2

1.3 79.6

0.6 69.2

20.9 96.9

100.0

flexible systems is the program DSSPCont,4 which combines assignments from a spectrum of energy cutoffs ranging from −0.2 to −1.0 kcal mol−1 at 0.1 kcal mol−1. A weakness of SABLE, though, is that it is more susceptible to missing atoms such as solvent and side chains that might actually be the strongest acceptor for a hydrogen, such that a hydrogen may be assigned a spuriously long HB. This is likely to be the reason for the extra bridges. Such a problem would largely disappear in a fully atomistic system. Nonetheless, the performance of SABLE and related variants bodes well for its application to any kind of hydrogen-bonded system such as water,24 organic molecules,25 carbohydrates,26 or RNA,27−29 not to mention any combination of these. Such generalization would require electrostatic charges of the donors and acceptors, but these are readily available in typical force fields.

DISCUSSION The results show that parameter-free HB definitions can be applied to the classification of protein secondary structure, yielding results that are comparable to DSSP with its energycutoff HB definition. Given the close similarity in assignment between SABLE and DSSP, the performance of SABLE compared with other secondary structure assignments is likely to be comparable to that of DSSP.10,21,22 While the simplest SA method using FOH still gives 91% agreement with DSSP, the inclusion of bifurcation and unassigned donors in the SABLE method has the best agreement at 95%. Even though SABLE produces a small yet undesirable number of spuriously weak HBs, the DSSP assignment rules appear robust with respect to these. There is no guarantee that the DSSP assignment is the best, and there are suggestions in this study indicating that its energy cutoff may be too generous. Nonetheless, its widespread popularity is a testament to its conformity with the experience of crystallographers.23 Regarding SABLE, it would be desirable to find a better way to more effectively leave donors unassigned; however, doing this more accurately for proteins is not obvious without introducing cutoff parameters, an energy cutoff in ECOHN of 0 kcal mol−1 being an obvious choice that could be justified in the general case. Nonetheless, the idea of having competing donor−acceptor interactions should be a viable approach in general because it is designed to identify the separating transition states as previously discussed. Another area for improvement is how bifurcation is implemented. Similar to the case of water,16 the method implemented here only works for identical kinds of acceptors. An advantage of SABLE is that its flexible way of defining HBs should give it a greater ability to detect distorted HBs, as may be found in the kinks or C-termini of helices or the bulges of sheets; however, there is no obvious manifestation of this in comparing the secondary structure assignments. The main difference between the methods is that DSSP predicts slightly more α-helical residues than SABLE, which instead predicts more 310 helices. A visual inspection showed these differences to mostly lie at the C-termini of the helices, which is typically their least stable part and thus the least-defined. The most likely explanation for the difference is bifurcation, which DSSP with its energy cutoff is better able to capture. This lets the terminal residues retain the necessary HBs to remain in the higherpriority α helix. Although not important to the single X-ray crystal structures studied here, SABLE’s flexibility should also help detect HBs in dynamic systems, especially important for more disordered proteins, and over a wide range of temperatures. A method that seeks to adapt DSSP to such

■

CONCLUSIONS A group of 12 DSSP-based methods have been tested to classify the secondary structure for a group of proteins. The methods use the same assignment rules as DSSP based on HBs but differ in how the HBs are defined. Instead of using an energy cutoff as in DSSP, donors either donate to their strongest acceptor, are given the option to also bifurcate to their next strongest acceptor, or to both their strongest two acceptors according to FOH, FCOHN, or ECOHN. In addition, in the case of FOH, donors can also be assigned no HB if their nearest acceptor is outcompeted by the oxygen on their previous residue. The definition that gives the best secondary structure agreement with DSSP of 95% uses FOH, the strongest acceptor plus bifurcation and local environment and is termed SABLE. Variations in the types of secondary structure are minor, being smallest for α helices and β sheets. An analysis of HB energies and energy cutoffs suggests that DSSP might benefit from a slightly more negative cutoff in the range −0.65 to −1 kcal mol−1. It also shows that SABLE could be further improved by having a greater ability to leave donor hydrogens unassigned, therefore preventing unusually long HBs being assigned for donors with no nearby acceptor. Nonetheless, it demonstrates that parameter-free HB definitions can be used in the assignment of protein secondary structure and are likely to be useful in all hydrogen-bonded systems.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +44 161-3065194. D

DOI: 10.1021/acs.jpcb.6b02571 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B Notes

(19) Irudayam, S. J.; Henchman, R. H. Long-range hydrogen-bond structure in aqueous solutions and the vapor-water interface. J. Chem. Phys. 2012, 137, 034508. (20) Touw, W. G.; Baakman, C.; Black, J.; te Beek, T. A. H.; Krieger, E.; Joosten, R. P.; Vriend, G. A series of PDB-related databanks for everyday needs. Nucleic Acids Res. 2015, 43, D364−D368. (21) Colloc'h, N.; Etchebest, C.; Thoreau, E.; Henrissat, B.; Mornon, J. P. Comparison of 3 algorithms for the assignment of secondary structure in proteins - the advantages of a consensus assignment. Protein Eng., Des. Sel. 1993, 6, 377−382. (22) Zhang, Y.; Sagui, C. Secondary structure assignment for conformationally irregular peptides: Comparison between DSSP, STRIDE and KAKSI. J. Mol. Graphics Modell. 2015, 55, 72−84. (23) Baker, E. N.; Hubbard, R. E. Hydrogen-bonding in globularproteins. Prog. Biophys. Mol. Biol. 1984, 44, 97−179. (24) Stillinger, F. H. Water revisited. Science 1980, 209, 451−457. (25) Etter, M. C. Encoding and decoding hydrogen-bond patterns of organic-compounds. Acc. Chem. Res. 1990, 23, 120−126. (26) Jeffrey, G. A.; Takagi, S. Hydrogen-bond structure in carbohydrate crystals. Acc. Chem. Res. 1978, 11, 264−270. (27) Yang, H. W.; Jossinet, F.; Leontis, N.; Chen, L.; Westbrook, J.; Berman, H.; Westhof, E. Tools for the automatic identification and classification of rna base pairs. Nucleic Acids Res. 2003, 31, 3450−3460. (28) Sarver, M.; Zirbel, C. L.; Stombaugh, J.; Mokdad, A.; Leontis, N. B. RNA 3D: finding local and composite recurrent structural motifs in RNA 3D structures. J. Math. Biol. 2007, 56, 215−252. (29) Zheng, G. H.; Lu, X. J.; Olson, W. K. Web 3DNA − a web server for the analysis, reconstruction, and visualization of threedimensional nucleic-acid structures. Nucleic Acids Res. 2009, 37, W240−W246.

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We acknowledge BBSRC grant BB/K001558/1 for funding and thank Andrew Doig and Rebecca Wade for thoughtful discussions.

■

REFERENCES

(1) Levitt, M.; Greer, J. Automatic identification of secondary structure in globular proteins. J. Mol. Biol. 1977, 114, 181−239. (2) Kabsch, W.; Sander, C. Dictionary of protein secondary structure: Pattern recognition of hydrogen-bonded and geometrical features. Biopolymers 1983, 22, 2577−2637. (3) Frishman, D.; Argos, P. Knowledge-based protein secondary structure assignment. Proteins: Struct., Funct., Genet. 1995, 23, 566− 579. (4) Andersen, C. A. F.; Palmer, A. G.; Brunak, S.; Rost, B. Continuum secondary structure captures protein flexibility. Structure 2002, 10, 175−184. (5) Fodje, M. N.; Al-Karadaghi, S. Occurrence, conformational features and amino acid propensities for the π-helix. Protein Eng., Des. Sel. 2002, 15, 353−358. (6) Sklenar, H.; Etchebest, C.; Lavery, R. Describing proteinstructure − a general algorithm yielding complete helicoidal parameters and a unique overall axis. Proteins: Struct., Funct., Genet. 1989, 6, 46−60. (7) King, S. M.; Johnson, W. C. Assigning secondary structure from protein coordinate data. Proteins: Struct., Funct., Genet. 1999, 35, 313− 320. (8) Richards, F. M.; Kundrot, C. E. Identification of structural motifs from protein coordinate data: Secondary structure and first-level supersecondary structure. Proteins: Struct., Funct., Genet. 1988, 3, 71− 84. (9) Labesse, G.; Colloch, N.; Pothier, J.; Mornon, J. P. P-SEA: A new efficient assignment of secondary structure from Cα trace of proteins. Bioinformatics 1997, 13, 291−295. (10) Martin, J.; Letellier, G.; Marin, A.; Taly, J. F.; de Brevern, A. G.; Gibrat, J. F. Protein secondary structure assignment revisited: a detailed analysis of different assignment methods. BMC Struct. Biol. 2005, 5, 17. (11) Hosseini, S. R.; Sadeghi, M.; Pezeshk, H.; Eslahchi, C.; Habibi, M. PROSIGN: A method for protein secondary structure assignment based on three-dimensional coordinates of consecutive C α atoms. Comput. Biol. Chem. 2008, 32, 406−411. (12) Dupuis, F.; Sadoc, J. F.; Mornon, J. P. Protein secondary structure assignment through Voronoi tessellation. Proteins: Struct., Funct., Genet. 2004, 55, 519−528. (13) Irudayam, S. J.; Plumb, R. D.; Henchman, R. H. Entropic trends in aqueous solutions of common functional groups. Faraday Discuss. 2010, 145, 467−485. (14) Henchman, R. H.; Irudayam, S. J. Topological hydrogen-bond definition to characterize the structure and dynamics of liquid water. J. Phys. Chem. B 2010, 114, 16792−16810. (15) Irudayam, S. J.; Henchman, R. H. Prediction and interpretation of the hydration entropies of monovalent cations and anions. Mol. Phys. 2011, 109, 37−48. (16) Henchman, R. H.; Cockram, S. J. Water’s non-tetrahedral side. Faraday Discuss. 2013, 167, 529−550. (17) Green, J. A.; Irudayam, S. J.; Henchman, R. H. Molecular interpretation of Trouton’s and Hildebrand’s rules for the entropy of vaporization of a liquid. J. Chem. Thermodyn. 2011, 43, 868−872. (18) Ma, Z. H.; Zhang, Y. L.; Tuckerman, M. E. Ab initio molecular dynamics study of water at constant pressure using converged basis sets and empirical dispersion corrections. J. Chem. Phys. 2012, 137, 044506. E

DOI: 10.1021/acs.jpcb.6b02571 J. Phys. Chem. B XXXX, XXX, XXX−XXX