New Results

Experimentally-Determined Strengths of Atom-Atom (C, N, O) Interactions Responsible for Protein Self-Assembly in Water: Applications to Folding and Other Protein Processes

Xian Cheng, Irina A. Shkel, Kevin O’Connor, M. Thomas Record Jr.
doi: https://doi.org/10.1101/2020.05.26.104851

Abstract

Folding and other protein self-assembly processes are driven by favorable interactions between O, N, and C unified atoms of the polypeptide backbone and sidechains. These processes are perturbed by solutes that interact with these atoms differently than water does. C=O···HN hydrogen bonding and various π-system interactions have been better-characterized structurally or by simulations than experimentally in water, and unfavorable interactions are relatively uncharacterized. To address this situation, we previously quantified interactions of alkylureas with amide and aromatic compounds, relative to interactions with water. Analysis yielded strengths of interaction of each alkylurea with unit areas of different hybridization states of unified O, N, C atoms of amide and aromatic compounds. Here, by osmometry, we quantify interactions of ten pairs of amides selected to complete this dataset. A novel analysis yields intrinsic strengths of six favorable and four unfavorable atom-atom interactions, expressed per unit area of each atom and relative to interactions with water. The most favorable interactions are sp2O - sp2C (lone pair-π, presumably n-π*), sp2C - sp2C (π-π and/or hydrophobic), sp2O-sp2N (hydrogen bonding) and sp3C-sp2C (CH-π and/or hydrophobic). Interactions of sp3C with itself (hydrophobic) and with sp2N are modestly favorable, while sp2N interactions with sp2N and with amide/aromatic sp2C are modestly unfavorable. Amide sp2O-sp2O interactions and sp2O-sp3C interactions are more unfavorable, indicating the preference of amide sp2O to interact with water. These intrinsic interaction strengths are used to predict interactions of amides with proteins and chemical effects of amides (including urea, N-ethylpyrrolidone (NEP), and polyvinyl-pyrrolidone (PVP)) on protein stability.

Significance Quantitative information about strengths of amide nitrogen-amide oxygen hydrogen bonds and π-system and hydrophobic interactions involving amide-context sp2 and/or sp3 carbons is needed to assess their contributions to specificity and stability of protein folds and assemblies in water, as well as to predict or interpret how urea and other amides interact with proteins and affect protein processes. Here we obtain this information from thermodynamic measurements of interactions between small amide molecules in water and a novel analysis that determines intrinsic strengths of atom-atom interactions, relative to water and per unit area of each atom-type present in amide compounds. These findings allow prediction or interpretation of effects of any amide on protein processes from structure, and may be useful to analyze protein interfaces.

Introduction

Biopolymer self-assembly in water, including folding, binding, droplet formation, phase separation and formation of the functional protein and nucleic acid complexes of the cell, is driven by net-favorable interactions between C, N and O unified atoms of their biochemical functional groups, relative to interactions with water. To understand the energetics of these processes and relate thermodynamic and structural information, strengths of interaction of the different types of C, N and O unified atoms with one another, relative to their interactions with water, must be determined. Effects of biochemical solutes and noncoulombic effects of salts from the Hofmeister series on these biopolymer processes result from preferential interactions of the C, N, O atoms of the solute (and inorganic ions of the salt) with the C, N and O atoms of the biomolecule (1, 2). Quantitative information about preferential interactions of the various types of C, N and O atoms of biomolecules and solutes will therefore be useful in analyzing both self-assembly interactions and solute effects on these interactions.

Hydrogen bonding between amide sp2O and sp2N unified atoms (3-6) and the hydrophobic effect of reducing the exposure of sp2C and sp3C atoms to water (7-10), have long been recognized to be key determinants of specificity and stability of protein assemblies and complexes. In addition, n-π* interactions (a type of lone pair – π interaction (11)) between amide sp2O and amide or aromatic sp2C (12-17), π-π interactions of sp2C with sp2C (18, 19) and CH-π interactions of sp3C with sp2C (20-23) have been characterized by structural, spectroscopic and computational studies. Much less is known about the relative strengths of these and other amide atom-atom contacts in water, including interactions of amide sp2N with amide sp2N, sp3C and sp2C and interactions of amide sp2O with amide sp2O and sp3C.

Preferential interactions of biochemical solutes and Hofmeister salts with other solutes or biopolymers, relative to interactions with water, are quantified by chemical potential derivatives (∂µ2/∂m3)T,P,m2 = µ23, where the subscripts “2” and “3” refer to the two solutes, respectively, and µ23 = µ32.(1, 2). These µ23 values, related to transfer free energies, are determined by osmometry or solubility assays (20, 24-32). Integration of the radial distribution (33-36) of one solute in the vicinity of the other, obtained from molecular dynamics simulations (36-41), also yields µ23 (31).

Experimental research and analysis extending over the last decade (24-32) has shown that µ23 values are accurately described as a sum of contributions (α3,iASAi(2)) from interactions of solute 3 with the accessible surface of the different types of C, N, O atoms on solute 2: Embedded Image

The choice of which solute to designate as component 2 or 3 is arbitrary because µ23 = µ32.

In Eq. 1, each intensive quantity α3,i is a thermodynamic coefficient (called a one-way alpha value) that quantifies the strength of interaction of the amide compound designated component 3 (e.g. urea) with a unit area (1 Å2) of one of the i different types (i.e. hybridization states) of C, N and O atoms on the set of amide compounds (each designated component 2), relative to interactions with water. The extensive quantity ASAi(2) is the water-accessible surface area in Å2 of the i th atom type of the amide solute (component 2) whose interaction with amide solute 3 is quantified by μ23. Examples of Eq. 1 for the interaction of two amide compounds investigated here are provided in SI Eqs. S3-4.

Eq. 1 is based on the two hypotheses that contributions to µ23 from different weak solute-atom interactions are additive and increase in proportion to the ASA of that C, N or O atom. Additivity has been tested and validated by the analysis of sets of µ23 values using Eq. 1, because the size of the µ23 data sets greatly exceed the number of one-way alpha values determined from the analysis. ASA is found to be a better choice of extensive variable than the number of atoms or weighted number of atoms (31, 32). Using one-way alpha values α3,i, effects of solutes (species 3) on biopolymer (species 2) processes are predicted or interpreted in terms of the interaction of solute 3 with the different types of biopolymer surface area (ASAi(2)) exposed or buried in the process.

µ23 -Values can be interpreted as free energy changes for transfer of a solute from a two component solution to a three component solution in which the concentration of the other solute is 1 molal. Originally, effects of urea and osmolytes on protein stability were interpreted assuming additivity of transfer free energy contributions from the peptide backbone and each of the nineteen different amino acid side chains that are exposed to the solution in unfolding (42-46). These twenty side chain and backbone transfer free energies were obtained from amino acid and dipeptide solubility data, also assuming additivity. Analysis of urea effects on protein stability using Eq. 1 involves many fewer parameters (from as few as two (47) to four (31) or seven (26, 27) one-way alpha values (αurea,i), depending on the extent of coarse-graining of the ASA exposed in unfolding). One-way alpha values are interpretable in terms of the local accumulation or exclusion of the solute in the vicinity of a particular type of atom on the model compound or protein, using the solute partitioning model (SPM) (2, 20, 24-29, 48-52).

One-way alpha values are found to have fundamental chemical significance. For example, the one-way alpha value for interaction of urea with amide sp2O atoms (αurea,sp2O) is favorable (31) and of similar magnitude to (∼35% smaller than) that for the interaction of urea with carbonyl sp2O atoms of nucleobases (32). This observation indicates that hydrogen bonding interactions of the two urea sp2N unified atoms (hydrogen bond donors) with amide and nucleobase carbonyl sp2O (acceptor) must be of similar strength per unit area of sp2O surface and that these sp2N - sp2O interactions are more favorable than interactions of the separate atoms with water. It also indicates that these favorable sp2N - sp2O hydrogen bonding interactions contribute more to the observed one-way alpha value (αurea,sp2O) than interactions of urea sp2O with amide or nucleobase sp2O, which are expected to be quite unfavorable because these sp2O atoms hydrogen bond to water but have no way to interact favorably with each other.

Alkylation of urea reduces sp2N ASA, reducing its ability to hydrogen bond to amide and carbonyl sp2O, and introduces aliphatic sp3C which is expected to interact unfavorably with amide and carbonyl sp2O. Consistent with the above, as the extent of alkylation increases the one-way alpha value for interaction with amide and carbonyl sp2O becomes increasingly unfavorable. These trends extend to other one-way alkylurea alpha values, as discussed previously (31, 32).

The above examples lead to the hypothesis that one-way alpha values for amide compounds can be dissected into contributions from the interaction of the different types of atoms on amide solute 3 (e.g. amide sp2O, sp2N, sp2C for urea) with each type of atom on the set of amide solutes 2. Such a two-way dissection would quantify atom-atom interactions (designated simply as two-way alpha values) relative to water and per unit ASA of each atom.

The research reported here tests this hypothesis for the interactions of amide compounds with other amide compounds. These amide compounds display four of the most common types of unified atoms of proteins (amide sp2O, N, C; sp3C). Our previous study focused on the series of alkylated ureas, all of which have small water-accessible surface area of amide sp2C atoms. Here we extend the amide dataset by determining µ23 values for interactions of five other amides, including formamide and N-methyl formamide, which have large water-accessible surface areas (ASA) of amide sp2C, and malonamide and N-acetyl-alanine N-methylamide (aama), which have two amide groups and correspondingly larger ASA of amide sp2O.

Analysis of the combined µ23 dataset for amides (more than one hundred µ23-values) yields a set of ten two-way alpha values that quantify all possible pairwise interactions between amide sp2O, amide sp2N, sp2C and sp3C atoms of these amide compounds. We demonstrate the use of these two-way alpha values to predict µ23 values for interactions of any two amide compounds (with amide sp2O, N, C and aliphatic sp3C) in water from ASA information. Since proteins are of course polyamides, µ23 values for any amide-protein interaction (or protein-protein interaction involving only amide and hydrocarbon surface) can be predicted from these two-way alpha values, as can standard free energy derivatives Embedded Image called m-values (equal to Δµ23) that quantify the effect of any amide solute on any protein process in which the change in ASA is primarily from amide and hydrocarbon atoms (as is the case for protein folding). In addition, the rank order of two-way alpha values and relative strengths of these atom-atom preferential interactions should provide a useful starting point for assessing the contributions of different atom-atom contacts to the stability of a protein interface.

Results

Analysis to Determine Atom-atom Interactions from Solute-Atom Interactions

For interactions of a series of urea and alkyl ureas (component 3) with amide compounds (component 2), analyzed by Eq. 1 as summarized above, each of the solute (3) - atom (i) one-way alpha values (α3,i) exhibited a regular progression with increasing alkylation (and reduced exposure of amide nitrogen) of the urea (Fig. S1; (31)). Motivated by this observation, here we test the hypothesis that each of these one-way alpha values can be dissected into additive, ASA-based contributions from the interaction of the different types of atoms on amide solute 3 (sp2O, N, C and sp3C) with the i-th type of atom (also sp2O, N, C or sp3C) on amide solute 2. Embedded Image

Eq. 2 for the one-way alpha value α3,i is completely analogous to Eq. 1 for µ23. In Eq. 2, each intensive quantity αij is the strength of interaction of a unit area of atom j of solute 3 with a unit area of atom i of solute 2, and the corresponding extensive quantity ASAj(3) is the accessible surface area of atom type j on solute 3. For the amide-amide interactions of interest here, an example with all the individual terms in the sum in Eq. 2 is provided in SI Eqs. S5-6. The hypotheses of additivity and ASA-dependence of the contributions αij ASAj(3) to the one-way alpha value α3,i are tested concurrently with the determination of two-way alpha values (αij) because the number of equations (like Eq. 2) greatly exceeds the number of unknowns (αij) being determined (see below).

A straightforward test of Eq. 2 is provided by the comparison of one-way alpha-values α3,i for selected pairs of amide solutes that differ primarily in ASA of one atom type (j). For these situations, a semiquantitative estimate of the two way alpha value αij is obtained from the difference in one-way alpha values Δα3,i and the ASA difference for atom type j (ΔASAj(3)) Embedded Image

An example of this calculation is provided in SI (Eqs. S7-10) to clarify the notation.

Combination of Eqs. 1 and 2 gives the proposed dissection of any solute-model compound µ23 – value into contributions from the interactions of accessible atoms of the solute with accessible atoms of the model compound: Embedded Image where αij= αji. The complete set of terms in this double sum for the amide compounds investigated here is given in SI as Eq. S11.

As an interpretation of one term in Eq. 4, consider the contribution to µ23 from the interaction of amide sp2N of one amide solute (component 2) with amide sp2O on a second amide solute (component 3), relative to interactions with water, given by αsp2N−sp2OASA2,sp2NASA3,sp2O. The product of ASA values is proportional to the probability that a contact between the two solutes involves sp2N atom(s) of solute component 2 and sp2O atom(s) of solute component 3, and the two-way alpha value αsp2N−sp2O is the strength of that interaction per unit ASA of both atom types, again relative to water. These two-way alpha values are useful to predict or interpret µ23 values for interactions of amides for which one-way alpha values are not available, and to predict or interpret effects of these amides on protein processes in terms of structural information. Two-way alpha values may also be useful in analyses of atom-atom interactions in protein assemblies and in binding interfaces.

VPO Determinations of Interactions of Amides with Large ASA of Amide sp2C and sp2O

Previously we determined one-way alpha values α3,i (Eq 1) quantifying interactions of urea and six alkyl urea solutes with the types of unified atoms of amide (sp2O, sp2N, sp2C; sp3C) and aromatic hydrocarbon (sp2C) compounds using osmometric and solubility studies (31). Trends in these one-way alpha values with increasing alkylation of the urea showed which atom-atom interactions are favorable and which are unfavorable. However, preliminary tests of Eqs. 2 and 4 using the ninety-five μ23 values from this previous study revealed that these were insufficient to accurately quantify all atom-atom interactions (two-way alpha values) involving amide sp2O and/or sp2C.

Here we determine μ23 values by osmometry for an additional ten interactions of five amide compounds, including interactions of two amides with large ASA of amide sp2C (formamide, N-methylformamide) with one another and with two amides with large ASA of amide sp2O (malonamide, aama). Interactions of these four amides with propionamide are also determined. In addition to their significance for the two-way analysis proposed here, these measurements also permit the determination of one-way alpha values for the interactions of these five amides with amide sp2O, sp2N, sp2C and aliphatic sp3C atoms, increasing the number of amide compounds for which one-way alpha values (Eq 1) are available from seven to twelve.

For uncharged solutes at concentrations up to ∼1 molal, the difference ΔOsm = Osm(m2,m3) – Osm(m2) – Osm(m3) between the osmolality (Osm) of a three component solution and the two corresponding two-component solutions is proportional to the product of solute molal concentrations (m2m3) with proportionality constant μ23/RT (31). Embedded Image

If ΔOsm is negative, μ23 is negative, μ2 decreases with increasing m3, and the interaction of the two solutes is favorable.

For each of the ten pairs of amides investigated here, ΔOsm is plotted vs. m2m3 in the panels of Fig. 1. All µ23 values are negative, indicating favorable interactions between all ten pairs of amides investigated here. Values of µ23 at 23 °C obtained from these slopes are listed in Table S1. Of these, the interaction of malonamide and aama (middle panel of Fig. 1) is the least favorable(µ23 = - 8.6 ± 2.2 cal mol-1 molal-1) and the interaction of propionamide and N-methyl formamide (top panel of Fig. 1) is the most favorable (µ23 = - 102 ± 1.9 cal mol-1 molal-1). Though there is substantial scatter in the data for some pairs of amides, slopes µ23/RT are quite well determined (see Table S1) because the intercept is constrained to be zero.

Figure 1.
Figure 1. Osmometric Determinations of Preferential Interactions of Pairs of Amide Compounds in Water.

Osmolality differences ΔOsm = Osm(m2,m3) – (Osm(m2) + Osm(m3)) between a three-component solution of two amide compounds and the two corresponding two-component solutions, determined by VPO at 23 °C, are plotted vs. the product of molal concentrations (m2m3) of the two amides (Eq. 5). Slopes of linear fits with zero intercept yield chemical potential derivatives Embedded Image quantifying preferential interactions between the two amides. aama: N-Acetylalanine N-methylamide.

One-way Alpha values for Interactions of Five Amide Solutes with Amide O, N and C Atoms

Analysis of the ten µ23-values determined from Fig. 1 together with previous results for the interactions of these five amides with other amides (31) by Eq. 1 yields one-way alpha values α3,i for interactions of these five amides with each of the four types of unified atoms of amide compounds. These one-way alpha values are plotted as bar graphs in Fig. 2 and listed in Table S2. Fig S1 compares one-way alpha value one-way alpha values for all 12 amide compounds investigated to date. Figs. 2 and S1 show that all amide compounds investigated here and previously interact favorably with amide sp2C, amide sp2N, and aliphatic sp3C, and that all but urea and formamide interact unfavorably with amide sp2O.

Figure 2.
Figure 2.

A: Strengths of Interaction of Five Amides (formamide (fad), N-methylformamide (mfad), malonamide (mad), propionamide (ppa) and Acetyl-L-ala-methylamide (aama)) with Amide and Hydrocarbon Unified Atoms. Bar graphs compare interaction potentials (α-values; Table S2)) quantifying interactions of these five amide compounds with a unit area of amide sp2O, amide sp2N, aliphatic sp3C, and amide sp2C at 23°C. Favorable interactions have negative one-way alpha values while unfavorable interactions have positive one-way alpha values. B: Comparison of Predicted and Observed µ23 Values for Pairwise Interactions of these Five Amide Compounds at 23 °C. Predictions of µ23 use one-way alpha values for these five amide compounds with amide sp2O, amide sp2N, amide sp2C and aliphatic sp3 C from Panel A and Table S2. Color scheme is that of Panel A. Observed µ23 values are from Tables S1 and S3. The line represents equality of predicted and observed values.

Strengths of Pairwise Interactions of Amide sp2O, N, C and Aliphatic sp3C Unified Atoms

All one hundred and five µ23 values (Tables S3, S4) for interactions of twelve different amide compounds with each other, and in some cases with naphthalene and/or anthracene, were analyzed using Eq. 4 to obtain ten two-way alpha values (αsp2O,sp2O, αsp2O,sp2N, αsp2O, sp2C, αsp2O,sp3C; αsp2N,sp2N, αsp2N,sp2C, αsp2N,sp3C; αsp2C,sp2C, αsp2C,sp3C; αsp3C,sp3C). The previous one-way (31) analysis revealed that interactions of sp2C atoms of aromatic hydrocarbons and of amides are similar if not identical, and they are analyzed together here. (Alternative analyses of sp2C presented in SI and discussed below justify this treatment.) In this analysis of all amide-amide and amide-aromatic µ23 values, the number of equations (105 applications of Eq. 4) exceeds the number of unknowns (10 two-way alpha values) by more than ten-fold, making them highly overdetermined. The additivity and ASA-dependence of contributions to µ23 underlying Eq. 4 are tested quantitatively by comparison of predicted and observed µ23 values (Tables S3, S4, Fig. 3B), and semi-quantitatively from differences in one-way alpha values for amides differing primarily in ASA of one type of unified atom (see below).

Figure 3.
Figure 3. Amide Compound Atom-Atom Interaction Strengths and their Ability to Predict µ23 Values

A) Two-way alpha values (Table 1) quantifying interactions of pairs of amide atoms shown, relative to interactions with water at 23 °C. sp2C is for combined amide and aromatic sp2C. Negative alpha values indicate favorable interactions. B) Comparison of predicted and observed µ23 values for interactions of each pair of amide compounds investigated at 23 °C. Predictions of µ23 use two-way alpha values in Table 1. Observed µ23 values are from Tables S1 and S3. The line represents equality of predicted and observed values.

Results of this analysis (two-way alpha values) quantifying the pairwise interactions of amide sp2O, sp2N, sp2C and aliphatic sp3C unified atoms with one another are listed in Table 1. These ten two-way alpha values are also plotted in the bar graph of Fig. 3A in ranked order from the most negative (most favorable interactions relative to interactions with water) to the most positive (most unfavorable interactions). Uncertainties in these two-way alpha values range from 3% to 30% except for the small-magnitude interaction of sp2C with sp2N, where the uncertainty is larger (∼70%). These uncertainties do not affect the semi-quantitative conclusions of this research.

View this table:
Table 1. Ranked Intrinsic Strengths of Atom-Atom Interactions of Amide Compounds

Six of the ten atom-atom interactions in Table 1 are favorable, with negative two-way alpha values. The four most favorable interactions, of similar strength when expressed per unit area of each unified atom, are sp2O - sp2C, sp2C - sp2C, sp2O - sp2N and sp2C - sp3C. Two-way alpha values for these four interactions are about three times more negative than two-way alpha values for sp3C - sp3C and sp3C - sp2N interactions. The most unfavorable interaction in this set is sp2O - sp2O. Sp2O - sp3C and sp2N - sp2N interactions are modestly unfavorable, while the sp2N - sp2C interaction is slightly unfavorable. The signs and relative magnitudes of these interaction strengths, relative to interactions with water, make good chemical sense as discussed below and in SI. We therefore conclude that these two-way alpha values not only are useful to predict and interpret interactions of amide solutes and amide effects on protein processes, but also have fundamental chemical significance for understanding the weak interactions that drive self-assembly.

Comparison of Two-way Alpha Values Obtained by Fitting with Estimates from One-way Alpha Values for Amide Pairs Differing Primarily in ASA of One Atom Type

Ethylurea and 1,1-diethylurea differ from methylurea and 1,1-dimethylurea primarily in aliphatic sp3C ASA. The sp3C ASA difference between the dialkylated ureas (64 Å2) is about twice as large for the monoalkylated ureas (36 Å2). These sp3C ASA differences are 85-90% of the total magnitude of ASA differences for these pairs of compounds. Applying Eq. 3 to estimate two-way alpha values for the interactions of aliphatic sp3C atoms with amide sp2O, N and C atoms from differences in the corresponding one-way alpha values for these pairs of amide compounds and these differences in sp3C ASA yields the direct estimates in Table S5. For the dialkyl ureas, where the differences in one-way alpha values are larger and better determined, estimates of two-way alpha values for interactions of sp3C with all four atom types agree quantitatively with those obtained from global fitting, differing by less than the propagated uncertainty in the fitted values. For the monoalkyl ureas, agreement is semiquantitative, with deviations of 25-40%.

1,3-Diethylurea differs from proprionamide primarily in amide sp2N ASA (20 Å2, which is 84% of the total magnitude of ASA differences for this pair of compounds). Table S5 shows a range of agreement between estimates of two-way alpha values from Eq. 3 and best fit two-way alpha values. Near-quantitative agreement of two-way alpha values is obtained for interactions of amide sp2N with amide sp2O and aliphatic sp3C, while estimates for interactions with amide sp2N and amide sp2C agree with best-fit two-way alpha values in sign but not in magnitude. With the exception of the strongly favorable amide sp2N - amide sp2O interaction, atom-atom interactions involving amide sp2N are weak, which affects the ability to determine them by this difference approach. Finally, the diamide Acetyl-L-ala-methylamide (aama) differs from 1,3-diethylurea (1,3-deu) primarily in amide sp2O ASA (34 Å2, which is 63% of the total magnitude of ASA differences for this pair of compounds). Estimates of two-way alpha values for interactions of sp2O from differences in one-way alpha values (Eq. 3), listed in Table S5, agree with best-fit two-way alpha values within 10-30%. This level of agreement is obtained because interactions involving sp2O are the strongest of any atom type, and hence are dominant even for this situation where the ASA difference is only 63% sp2O.

Comparison of Observed µ23 Values with Predictions from Alpha Values and ASA

Fig. 3B compares observed µ23 values for interactions of the series of urea and amide solutes with each other with those predicted from two-way alpha values (Tables 1) and ASA information (31) using Eq.3. All observed and predicted µ23 values are listed in Tables S3 and S4. For amide-amide interactions, predicted and observed µ23 values are in good agreement within the combined uncertainties (± 1 SD, typically 15%) for about 90% of the interactions investigated (94 out of 105).

Table S3 also lists predicted µ23 values for the amide compounds in the dataset calculated from one-way alpha values of five amide solutes (formamide, N-methylformamide, malonamide, propionamide and Acetyl-L-ala-methylamide (aama)) with the four amide atoms (Table S2) and ASA information using Eq. 2. Comparison in Table S4 of predicted µ23 values for the interaction of two amides using two-way alpha values (Table 1) with predictions using the sets of one-way alpha values determined for the two amides (Table S3) reveals that agreement with experimental data is equally good for both sets of alpha values. Comparison in Figure S2 (one-way alpha values are calculated based on combination of amide and aromatic sp2C) and Table S6 of one-way alpha values which are calculated from µ23 values with predictions of one-way alpha values from two-way alpha values shows a good agreement with each other.

Discussion

Chemical Significance of Amide Two-way Alpha Values

Interactions of Aliphatic sp3C with Aliphatic sp3C, Amide/Aromatic sp2C and Amide sp2N, O

Interactions of aliphatic sp3C atoms of amide compounds with aliphatic sp3C, amide sp2C and amide sp2N atoms of other amides are favorable, while interactions with amide sp2O are unfavorable, relative to interactions with water. Strengths (two-way alpha values) of these preferential interactions, expressed per unit area of each atom type (Table 1), span a wide range. These two-way alpha values are well-determined from the global fitting, with uncertainties of 3-5%.

The preferential interaction of sp3C with sp2C, quantified per unit ASA of each atom type, is one of the four most favorable atom-atom interactions characterized here. This is often called a CH-π interaction, and should also involve a hydrophobic effect from the burial of sp3C and sp2C ASA when it occurs. From Table 1 two-way alpha values, the strength of a favorable sp3C - sp2C interaction is almost three times that of a sp3C-sp3C interaction, which is presumably driven by a hydrophobic effect from removing sp3C ASA from water. Interpreted most simply, this comparison indicates that the CH-π component of the favorable interaction of aliphatic sp3C with amide or aromatic sp2C contributes more than the hydrophobic component of this interaction.

Two-way alpha values in Table 1 also reveal that the sp3C - sp2N preferential interaction is about as favorable as the sp3C - sp3C interaction. Because sp2N unified atoms are expected to interact more favorably with water than sp3C atoms do, it follows that the intrinsic interaction of sp3C with sp2N (i.e. not relative to water) is more favorable than the intrinsic interaction of sp3C with sp3C.

The sp3C - sp2O interaction in water is highly unfavorable, with an α -value that is equal in magnitude and opposite in sign to the sp3C - sp2C interaction. An unfavorable interaction means that intrinsic interactions of the unified sp3C and sp2O atoms with water are more favorable than the intrinsic sp3C - sp2O interaction. The sp3C - sp2O interaction is unfavorable because the intrinsic interaction of water with sp2O is favorable while the intrinsic interaction of sp3C with amide sp2O is probably comparably unfavorable to its intrinsic interaction with water.

Amide/aromatic sp2C Interactions

From Table 1, interactions of amide/aromatic sp2C atoms with amide sp2O, aliphatic sp2C, and amide sp3C atoms of other amides are all very favorable, while interactions with amide sp2N are slightly unfavorable, relative to interactions with water. Overall, amide/aromatic sp2C atoms interact more favorably with the atoms of amide compounds than any other atom type in Table 1. These sp2C two-way alpha values are not as accurately known as sp3C two-way alpha values. Except for the sp2C - sp3C interaction (5% uncertainty), uncertainties are 27% for interactions with sp2O and sp2C and 70% for the very weak interaction with sp2N.

The sp2C-sp2O interaction is the most favorable interaction quantified here, with a two-way alpha values which is about 3 times as favorable as for hydrophobic sp3C - sp3C, which we take as a reference. In all likelihood the sp2C-sp2O interaction is a n – π* interaction (one example of a lone pair (lp) – π interaction (11)) involving n-shell electrons of amide sp2O and the π system of the amide group or aromatic ring, as characterized previously in structural and spectroscopic studies and MD simulations (12-17). The observation that a single two-way alpha value quantifies this interaction for both amide and aromatic sp2C is a compelling argument for the use of ASA in this analysis. This two-way alpha value is very similar to that deduced from the one-way alpha value for the interaction of naphthalene with amide sp2O ((31); see SI Table S7). Water forms hydrogen bonds to amide sp2O atoms and presumably participates in a lone pair – π interaction with sp2C atoms, so the strength of the sp2O - sp2C interaction in Table 1 is relative to these competitive interactions involving water.

Comparison of two-way alpha values in Table 1 reveals that the sp2C - sp2C interaction is about as favorable, per unit area of each participant, as the sp2C - sp3C interaction discussed above. Therefore it is likely that the π – π component of the sp2C - sp2C interaction, expressed per unit area of each participant, is similar in strength to the CH-π interaction and contributes about twice as much as the hydrophobic effect to the favorable sp2C - sp2C interaction.

The un-named interaction of amide/aromatic sp2C with amide sp2N is very marginally unfavorable. This interaction is not as favorable as the sp3C - sp2N interaction, probably because the intrinsic interaction of water oxygen lone pairs with the sp2C π system is more favorable than the interaction of water with sp3C. Even so, because it is only marginally unfavorable, there should be no significant free energy penalty for forming contacts between amide/aromatic sp2C and amide sp2N in a protein interface.

Amide sp2O Interactions

From Table 1, interactions of amide sp2O atoms with amide and aromatic sp2C and amide sp2N atoms are both very favorable while amide sp2O interactions with aliphatic sp3C and amide sp3O are very unfavorable, relative to interactions with water. Uncertainties in these two-way alpha values are moderate, ranging from 5% for sp2O - sp3C to 28% for sp2O - sp2C and sp2O - sp2O.

The favorable interaction of amide sp2O with amide-aromatic sp2C is discussed above. The similarly favorable interaction of amide sp2O with amide sp2N in water is almost certainly the NH—O=C hydrogen bond interaction in which the unified amide sp2N atom is the donor and the sp2O atom is the acceptor (3-6). The amide sp2O -amide sp2O interaction is almost twice as unfavorable as the amide sp2O – aliphatic sp3C interaction because of the very favourable intrinsic interaction of amide sp2O with water, which contributes twice as much in magnitude to the two-way alpha value for sp2O - sp2O as for sp2O - sp3C.

Amide sp2N Interactions

From Table 1, the amide sp2N-amide sp2O interaction is the most favorable interaction involving amide sp2N, while the amide sp2N-aliphatic sp3C interaction is modestly favorable, and the amide sp2N interactions with amide-aromatic sp2C and amide sp2N is slightly unfavorable, relative to interactions with water. Uncertainties in two-way alpha values for interactions involving amide sp2N are small (5% to 18%) except for the very weak interaction with sp2C. All these interactions except amide sp2N-amide sp2N are discussed above.

The amide sp2N - amide sp2N interaction, which very likely is the NH···N hydrogen bond, is modestly unfavorable, indicating that hydrogen bonding of amide sp2N with water is intrinsically more favorable. Consistent with this, NH···N hydrogen bonds are seldom observed in protein secondary structures, except involving proline (53). However, a hydrogen bond between unified N atoms of heterocyclic aromatic rings occurs in both AT (also AU) and GC base pairs of nucleic acid duplexes.

Using Two-Way Alpha Values to Predict Amide, Polyamide Effects on Biopolymer Processes

a) Predicting m-Values for Urea and other Amide Solutes

One of the significant applications of two-way alpha values for amide compound atom-atom interactions is to predict or interpret effects (m-values) of urea or any other amide solute on protein processes (26, 28) in terms of ASA information for the amide solute and ΔASA information for each type of unified protein atom using Eqs. 2 and 5. Recently, we analyzed urea m-values for unfolding of globular proteins using urea one-way alpha values for amide sp2O, amide sp2N, aliphatic sp3C and aromatic sp2C and ΔASA information assuming an extended chain model of the unfolded state. Generally good agreement is obtained between experimental m-values and m-values predicted either using these four major protein atom types or using all seven protein atom types (26). Figure S3 shows that use of two-way alpha values from Table 1 yields predicted m-values which agree well with the two one-way predictions and with experimental m-values.

b) Predicting Chemical Contributions to Interactions of the Polyamide PVP with Protein Surfaces and Effects of PVP on Protein Processes; Comparison with PEG

The water-soluble, flexibly-coiling polyamide polyvinylpyrrolidine (PVP), available in several different molecular weight ranges, has occasionally been used in place of the polyether PEG (polyethylene glycol) as a “macromolecular crowder” in studies of protein stability and interactions under conditions of high volume occupancy. The two-way alpha values from Table 1 are useful to predict the chemical interaction of PVP and its model monomer (N-ethyl pyrrolidone, NEP) with proteins and compare PVP with PEG. For PEG, where a wide range of molecular weights from monomer to oligomers and polymers is available, we previously determined the chemical interactions of end and interior groups of PEG with the different types of protein atoms (29) and separated chemical (preferential interaction) and physical (excluded volume) effects of PEG oligomers and polymers on protein (54) and nucleic acid (55) processes. Short oligomers of PVP are not commercially available to determine preferential interactions with protein atoms as done for PEG, but since NEP and PVP are amides, their chemical interactions with protein atoms and their chemical effects on protein processes can be predicted from the two-way alpha values obtained here and reported in Table 1.

For polymeric PVP with an average degree of polymerization N3 greater than about 20 residues, the per-residue interaction with another solute (component 2), i.e. Embedded Image, is well approximated as the interaction of an interior PVP residue, neglecting differences between end and interior residues: Embedded Image

The corresponding expression for PVP oligomers where contributions from the end groups should be treated separately is given in SI. In Eq. 6, αI,i quantifies the strength of interaction of an interior PVP residue with the i-th type of atom on solute 2, with accessible surface area ASAi(2). While neither these αI,i values for PVP nor the corresponding αNEP,i values for NEP have been determined directly, both are readily predicted using Eq. 2 from the two-way alpha values in Table 1 and ASA information for PVP interior residues and NEP. Table S8 summarizes this ASA information, and Table S9 lists predicted one-way alpha values (αI,i, αNEP,i and the PVP end-group one-way alpha value αE,i) and compares these PVP residue one-way alpha values with those obtained previously (29) for PEG residues.

Table S9 shows a similar pattern of interactions of PVP and PEG interior residues with the most common types of protein atoms. Chemical interactions of both PVP and PEG residues with protein aliphatic sp3C, amide sp2N and amide sp2C are favorable, while interactions with protein amide sp2O are unfavorable. Interactions of PVP interior residues with aliphatic sp3C and amide sp2O are about 2-fold stronger than for PEG, while PVP interactions with protein amide sp2C and amide sp2 N are about 1.6- and 1.2-fold stronger than for PEG.

Table S10 predicts that PVP monomer (NEP) destabilizes globular proteins, in agreement with its observed destabilization of CI2 (56). NEP is predicted to stabilize α-helices; this difference results from the very different composition of the ASA exposed in unfolding α-helices (predominantly amide, weighted toward amide sp2O) as compared to unfolding globular proteins (predominantly sp3C). By contrast, PEG monomer (ethylene glycol) and dimer (diethylene glycol) are predicted and observed to stabilize globular proteins, while tri- and tetraethylene glycol are destabilizing (29). Polymeric PVP is observed to stabilize CI2 (57, 58), which we conclude is because the predicted stabilizing excluded volume effect (54) counterbalances the predicted small destabilizing chemical effect (SI text and Table S10).

Hence PVP exerts chemical effects which differ only modestly from those of PEG. Since both PVP and PEG are flexible polymers with similar persistence lengths, their excluded volume contributions to μ23 are also expected to be similar. Since PEG is available at high purity over a much wider range of chain lengths than PVP, it is the better choice for these studies.

c) Applications of two-way alpha values to protein self-assembly interactions

Potential new directions of research using two-way alpha values include predicting or interpreting χ parameters of Flory-Huggins theory (59-61) in applications to aqueous polymer solutions. In this theory, χ quantifies the strength of segment-water interactions relative to segment-segment and water-water interactions. Extensions of this theory with “stickers and spacers” provide more realistic analyses of interactions of segments of flexible chain models of biopolymers (61, 62). It seem likely that two-way alpha values for amide atoms can be used to predict or interpret χ and noncoulombic “sticker” and “spacer” interaction parameters in analyses of the different behaviors of low-complexity polypeptides and unfolded proteins in chain expansion-collapse and aggregation (61, 63-65). Use of two-way alpha values would allow the sticker and spacer treatment to be extended to include a third type of region with net-unfavorable interactions (positive alpha values). Expansion of the set of two-way alpha values to include interactions of protein and nucleic acid unified atoms will allow their use in coarse-grained simulations and other analyses of interactions in liquid droplets formed by RNA and RNA binding proteins (61, 62, 65-67).

Conclusion

Average strengths of interaction of amide O, N and C unified atoms, quantified per unit of accessible area of each atom by two-way alpha values, provide important bridges between protein structural (ASA) information, molecular dynamics simulations, and experimental studies of protein-solute interactions and solute effects of protein processes, as well as a window into a new chemistry of weak interactions of these O, N and C unified atoms in water.

Supplementary Information

Materials and Methods

Chemicals

Formamide (>99.5%), N-methylformamide (>99%), and malonamide (>97%) were obtained from Sigma. Propionamide (>98%) was from Alfa Aesar and acetyl-L-ala-methylamide (aama, >99%) was from Bachem. All these amides were obtained in anhydrous form and used without further purification. All were dissolved in deionized water obtained from a Barnstead E-pure system (Thermo-Fischer Scientific).

Structures of Amide Compounds and ASA Calculations

Molecular structures of NEP (N-ethyl pyrrolidone) and of short oligomers of PVP (polyvinyl pyrrolidone) used for calculations of water-accessible surface areas (ASA) were predicted from NIH Cactus(1) website (https://cactus.nci.nih.gov/translate/) as described previously (2). Molecular structures of all other amide compounds investigated were analyzed previously (2). In all cases, a unified atom model was used in which hydrogens are treated as part of the C or N atom to which they are bonded. ASA information for NEP and PVP oligomers was calculated using the program Surface Racer (2) with the Richards set of van der Waals radii (3) and a 1.4 Å probe radius for water. As previously (2), ASA values were obtained for four coarse-grained atom types: amide sp2O, sp2N, sp2C and aliphatic sp3C. Alternative sources of structural information (PubChem ((4) and Biological Magnetic Resonance Bank (BMRB)(5)) and alternative ASA programs (VMD(6) and GetArea(7)) were compared with Cactus and Surface Racer previously (8, 9), and no significant differences were found.

Determination of ASA of End and interior Residues of PVP from Molecular Models of Short Oligomers

Water accessible surface areas (ASA) of the four types of unified atom (amide sp2O, sp2N, sp2C; aliphatic sp3C) of NEP and short PVP oligomers (number of residues N3 ≤ 5) were calculated using Surfracer program. Results are given in Table S8. To determine ASA contributions from the two end residues (ASA2E,i) and the N3-2 interior residues (ASAI,i) of a PVP oligomer, ASA values for each type of atom (i) were fitted to Eq.S1: Embedded Image

Values of ASA2E,i and ASAI,i obtained from these fits are also reported in Table S8.

Vapor Pressure Osmometry (VPO)

VPO is used to quantify thermodynamic interactions of small solutes which are soluble and nonvolatile in water by measuring osmolality differences ΔOsm(m2, m3) between three component (water, solute 2, and solute 3) and two component (water and solute 2, water and solute 3) solutions. Details of the osmolality analysis were described previously (9). Embedded Image

Preferential interactions (μ23 values) of a series of urea and alkyl ureas with one another and with other amide compounds were determined previously by VPO using Eq.S2 (9). Here μ23 values quantifying pairwise interactions in aqueous solution between five additional amide compounds (formamide, N-methylformamide, propionamide, malonamide and aama) are determined.

Analysis and Interpretation

One- and Two -Way Dissections of μ23 Values for Amide-Amide Interactions

In this section we provide specific expressions applying Eqs. 1-4 to the amides studied here. Embedded Image

Each contribution in this sum is composed of an intrinsic interaction strength (one-way alpha value) for the interaction of solute 3 with a unit area (1 A2) of accessible surface of one type of unified atom of the biopolymer or other solute 2. For the interactions of amide compounds investigated here, these atom types are amide sp2O, sp2N and sp2C, and aliphatic sp3C. Taking as a specific example the interaction of acetyl-L-ala-methylamide (aama, component 3) with the various amide atoms of proprionamide (ppa, component 2), for which μ23= μppa,aama = −43 ± 4 cal mol-1 molal-1 (Table S1): Embedded Image where the proprionamide ASA values in Eq. S3 (9) are in Å2 and the units of the one-way alpha values are cal mol-1 molal-1 Å-2.

Ten other equations like Eq. S3 are written to interpret experimental μ2,aama values for the interactions of aama with formamide, N-methylformamide, malonamide, urea, methylurea, and the remainder of the set of amide compounds (component 2) investigated. Solving these eleven equations in four unknowns Embedded Image determines best-fit values for the above four one-way aama alpha values (Table S2). Comparison of predicted and observed μ2,aama values for the full set of eleven aama-amide compound interactions (Fig. 2B, Table S3) tests the hypotheses of additivity and proportionality of contributions to ASA which are the basis of Eqs 1 and S3. Analogous sets of eleven equations are formulated and solved to obtain sets of four one-way alpha values quantifying the interactions of each other amide compound (formamide, N-methylformamide, malonamide, proprionamide) with a unit area of amide sp2O, sp2N, sp2C and aliphatic sp3C atoms (Table S2).

Since μ23= μ32 therefore Embedded Image

Ten other equations like Eq. S4 are written to interpret experimental μ2,ppa values for the interactions of proprionamide with formamide, N-methylformamide, malonamide, urea, methylurea, and the remainder of the set of amide compounds (component 2) investigated.

Solving these eleven equations in four unknowns Embedded Image determines best-fit values for the above four one-way proprionamide alpha values (Table S2). Embedded Image

Continuing with the above example for the ppa-aama interaction, Embedded Image Embedded Image where the units of the two-way alpha values are cal mol-1 molal-1 Å-4. Nine other equations like Eqs. S5-6 are written to interpret experimental α3,sp2O values for the interactions of formamide, N-methylformamide, malonamide, urea, methylurea, and the remainder of the set of amide compounds (component 2) with sp2O atoms. Solving these eleven equations in four unknowns (αSp2O,Sp2O, αSp2O,Sp2N, αSp2O,Sp2C, αSp2O,Np2C) determines best-fit values for these four two-way alpha values (Table 1). Comparison of predicted and observed μ23 values for the full set of eleven aama-amide compound interactions (Fig. 2B, Table S3) tests the hypotheses of additivity and proportionality of contributions to ASA which are the basis of Eqs 2 and S3-6. An analogous set of eleven equations is formulated and solved to obtain a set of four two-way alpha values quantifying the interactions of a unit area of each other type of unified atom (amide sp2N, sp2C and aliphatic sp3C) with a unit area of amide sp2O, sp2N, sp2C and aliphatic sp3C atoms (Table 1). Embedded Image

Here we illustrate the application of Eq. 3 to one of the four pairs of amides (methylurea and ethylurea) analyzed in the text. These amides differ primarily in amount of sp3C ASA. (See text for a discussion of all four amide pairs, based on the numerical analysis in Table S5.)

For methylurea (mu), the one-way α-value for the interaction with 1 Å2 of amide sp2O surface (0.78 cal mol-1 molal-1 Å-2; (9) is interpreted by Eq. 2 as the sum of ASA-weighted contributions from interactions of the methyl sp3C and amide sp2O, sp2N and sp2C atoms of methylurea (mu) with amide sp2O atoms of other compounds: Embedded Image

The corresponding equation for ethylurea (eu) is Embedded Image

Subtracting Eq. S7 from S8 yields a specific example of Δα3,i: Embedded Image

Because 87% of the ASA difference between ethylurea and methylurea is from sp3C, to a good approximation αeu,Sp2O - αmu,sp2O ≈ αsp3C,sp2OΔASA sp3C and Embedded Image which is a specific example of Eq. 3 in the text. Table S5 summarizes the results of this and three other difference analyses to estimate two-way alpha values, and compares these estimates with those in Table 1, obtained from global fitting. For the case of αNp2C,Sp2O analyzed above, the estimate from Eq. S10 is within 30% of the Table 1 value, as shown in Table S5. Embedded Image

As in sections A-C above, indices i and j refer to the four types of unified atom present in the amide compounds investigated (amide sp2O, sp2N, sp2C; aliphatic sp3C). Hence, for each of the one hundred and five pairs of amide compounds investigated: Embedded Image

Here, as in sections A-C above, ASAi(3) is the ASA of group i on solute 3 and ASAj(2) is the ASA of group j on solute 2.

Predicting One-Way Alpha Values for Interactions of Amide Solutes with the Types of Unified Atoms of Amide Compounds

As described in the main text, two-way alpha values can be used to predict one way alpha values quantifying how any amide solute interacts with amide sp2O, sp2N, sp2C and aliphatic sp3C unified atoms on any amide or polyamide molecule or surface (e.g. the surface exposed in protein unfolding). As an example, one-way alpha values for interactions of all twelve amide solutes investigated with unit areas of the four amide unified atoms may be predicted from two-way alpha values (Table 1) and ASA information (9) using Eqs. 2 (see Eqs. S5-6 for examples), and compared with observed one-way alpha values determined from µ23 values using Eq. 1 (see Eqs. S3-4 for examples) and ASA information. Results of these two methods to obtain one-way alpha values are shown in Table S6. Agreement within the combined 1 SD uncertainties is observed for 83% of these solute-atom interactions, and all but the interaction of N-methylformamide with sp2O agree within 2 SD.

Comparison of Two-way Alpha Values for Atom-Atom Interactions of Amides From Different Treatments of sp2C

One-way alpha values for interactions of urea and alkylureas with amide and aromatic sp2C were found to be similar (9). Two-way alpha values listed in Table 1 were determined by analysis of 105 µ23 values for amide interactions (85 amide compound-amide compound, 20 amide compound-aromatic compound) using Eq. 4, to obtain a combined two-way alpha value for amide and aromatic sp2C. To justify this analysis, here we extend it by global fitting all µ23 values (105 total, including 20 for amide-aromatic hydrocarbon interactions) to Eq. S12 which includes one global weighting factor Embedded Image quantifying the relative strength of interactions of amide sp2C as compared to aromatic sp2C. Clearly this is an oversimplification, since in principle a different weighting factor might be needed for interactions of sp2C with each other type of atom, but it provides a test of whether such corrections are significant. The revised version of Eq. 4 for μ23 is Embedded Image

In Eq. S12, the subscript Cam,ar stands for combined amide and aromatic sp2C, Cam stands for amide sp2C and Car is aromatic sp2C.

Two-way alpha values summarized in Table 1 were obtained for the unweighted case Embedded Image. In Table S7 these values are compared with those obtained from a global analysis using Eq. S12 and floating Embedded Image. Two-way alpha values obtained from this analysis are the same as in Table 1 within the uncertainty, although the percent difference in the interaction of sp2O with sp2O is about 80%. In this fit, the weighting coefficient Embedded Image, indicating that on average interactions of amide sp2C with the different atom types are about 82% as strong as for aromatic sp2C.

Table S7 also compares two-way alpha values obtained from analyses of subsets of μ23 values with those in Table 1 and from the fit with Embedded Image weighting. Fitting only the 64 amide-amide μ23 values obtained for amides with minimal amounts of amide sp2C to the variant of Eq. 4 with only six terms for interactions involving only sp2O, sp2N and sp3C yields six two-way alpha values which agree within the combined uncertainty with those of Table 1. Fitting only the 20 amide-aromatic μ23 values to another variant of Eq. 4 yields two-way alpha values for interactions of sp2C with sp2O, sp2N, sp2C and sp3C. Two-way alpha values for sp2C-sp2C and sp2C-sp3C agree with those in Table 1, while those for sp2C-sp2O, and sp2C-sp2N are both 20-30% larger in magnitude than their counterparts in Table 1, consistent with the finding of a weighting coefficient Embedded Image for interactions involving amide sp2C.

Additional Tests of Effect of Size of Dataset on Two-way Alpha Values

Table S7, discussed above, compared the separate determinations of four two-way alpha values from μ23 values for 20 amide-aromatic interactions and of six two-way alpha values for 85 amide-amide interactions with the ten two-way alpha values obtained from global analysis of the set of 105 μ23 values for amide-aromatic and amide-amide interactions, treating amide sp2C as the same as or differently from aromatic sp2C. Two-way alpha values obtained from these various approaches agree in most cases within the combined uncertainty. In Table S11 the effect of other reductions in the size of the μ23 data set are examined. This table shows there is little effect on two-way alpha values of removing all of the 14 to 26 μ23 values that quantify interactions of the more polar (urea, malonamide) and/or nonpolar (,3-diethylurea, aama) amides. The insensitivity of the two-way alpha values to these reductions in the set of μ23 values analyzed shows that even these subsets are large enough and diverse enough to determine all ten two-way alpha values.

Predicting the Chemical Interactions of PVP and its Model Monomer NEP with Amide and Hydrocarbon Atoms of Proteins

This section generalizes Eq. 6 for chemical (preferential interaction) contributions to μ23 values for interactions of PVP oligomers or polymers of any number of residues (N3) with the different hybridization states of O, N and C atoms of other solutes or proteins. For interactions of larger PVP oligomers and polymers with large solutes, an excluded volume term also contributes to μ23 and the chemical term in Eq. 6 may be reduced by a shielding term χ (10). Since any PVP has two end residues and N3-2 interior residues, the interaction of the average PVP residue with a solute 2 is therefore Embedded Image

For N3 > 20, Eq. S13 reduces to Eq. 6 of the main text. In Eq. S13, αE,i and αI,i are one-way alpha values that quantify the intrinsic strength of interactions of PVP end (E) and interior (I) residues with the i-th type of atom on another solute or protein. For PEG, where the end residues (as defined) are half the size of interior residues, we combined them (α2E,i) but for PVP it is more appropriate to treat each end residue separately. In Eq. 6 of the text for μ23 for high molecular weight PVP (N3 >> 1)), no distinction is made between end and interior residues.

By analogy with Eq. 2, each one-way αE,i and αI,i in Eq. S13 is itself a sum of contributions of interaction of the i-th type of protein atom with the j-th type of PVP atom (see Eq.3). Embedded Image

In Eq. S14, each two-way alpha value (αii) quantifies the interaction of 1 A2 atom type i of solute 2 with 1 A2 of PVP atom type j, ASAi(PVP,E) and ASAi(PVP,I) are areas (in A2) of atom type j on the end and interior residues of PVP. One-way alpha values for NEP and for PVP end and interior residues, calculated from two-way alpha values as in Eqs. 2 and S14, are listed in Table S9 and compared with the corresponding quantities for PEG.

As previously (10), we interpret the interaction of PVP (component 3) with a protein (component 2) as the sum of preferential interaction (abbreviated pi) and excluded volume (ev) contributions, Embedded Image

In Eq. S15, the quantity χ is the fractional accessibility of the average residue of PVP. For a PVP oligomer one expects χ ≈1, but for polymeric PVP one expects χ ≪ 1. (10)

Figure S1.
Figure S1. Comparison of One Way Alpha Values for Formamide, N-methyl Formamide, Malonamide, Proprionamide and N-acetylalanine N-methylamide (aama) with Other Amides

Amide compounds are listed arbitrarily in order of increasing aliphatic sp3C + amide sp2C ASA. Bar graphs compare interaction potentials (One-way alpha values; Table S1)) quantifying interactions of each amide compound with a unit area of a) amide sp2O, b) amide sp2N, c) amide-context sp3C, and d) amide/aromatic sp2C at 23 °C. Favorable interactions have negative α-values while unfavorable interactions have positive α-values. (aama: N-acetylalanine N-methylamide) α-Values for urea and alkyl ureas were reported previously (9).

Figure S2.
Figure S2.

Comparison of Predicted and Observed one-way alpha values (cal mol-1 m-1 Å-2) for Interactions of Urea and Alkylureas (urea, methylurea, ethylurea, 1,1-dimethylrea, 1,3-dimethylurea, 1,1-diethylurea and/or 1,3-diethylurea) with amide and aromatic functional groups (amide sp2O, amide sp2N, amide sp3C and combined aromatic and amide sp2C) at 23 °C; Observed one-way αi-values of these ureas were determined in reference (9) and predictions of one-way α-values use two-way alpha values of amide-amide interactions (Table 1) and the values are also tabulated in Table S6 above. The line represents equality of predicted and observed values.

Figure S3.
Figure S3.

Comparison of Predicted and Observed Urea m-values of Unfolding Globular Proteins. ΔASA Values for unfolding of these proteins are from reference (11). One-way alpha values of urea with 7 protein functional groups are from reference (12). One-way alpha values of urea with four unified atoms of amides were determined in reference (9); Two-way alpha values of atom-atom interactions are determined in this work (αij-values in Table 1). Purple: Previously-reported predictions of urea m-values using seven urea α-values (including hydroxyl O, carboxylate O and cationic N in addition to above amide and hydrocarbon unified atoms); Green: Predicted m-values were obtained from only four urea α-values (aromatic sp2C, aliphatic sp3C, amide sp2O and amide sp2N; reference (9). Yellow: Predicted m-values use two-way alpha values (Table 1) using Eq.3. Amide sp2C represents less than 1% of the ΔASA of unfolding and was not accounted for in these comparisons.

Supplemental Tables

View this table:
Table S1. Interactions of Amides with Relatively Large sp2C and/or sp2O Surface Area
View this table:
Table S2. One-way Alpha Values for Interactions of Formamide, Malonamide, N-methylformamide, Propionamide and aamaa With Amide sp2O, sp2N, sp2C and Aliphatic sp3C Atoms
View this table:
Table S3. Comparison of Observed µ23 Values (cal mol-1 molal-1; µ23 = µ32) for Amide Interactions at 23°C with Predictions of µ23 and µ32 from One-way Alpha Valuesa
View this table:
Table S4. Comparison of Observed µ23 Values (cal mol-1 molal-1) for Amide Interactions with Predictions from Two-Way Alpha Values (Table 1)
View this table:
Table S5. Comparison of Two-way Alpha Values Obtained by Fitting with Estimates from One-way Alpha Values for Amide Pairs Differing Primarily in ASA of One Atom Type
View this table:
Table S6. Comparison of One-way Alpha Values (cal mol-1 molal-1 Å-2) Calculated from µ23 Values with Predictions of One-way Alpha Values from Two-way Alpha Values
View this table:
Table S7. Comparison of Two-way Alpha Values for Atom-atom Interactions Using Different Treatments of Amide and Aromatic sp2C
View this table:
Table S8. PVP Oligomer ASA Values in Å2 from Cactus Models; Comparison with PubChem
View this table:
Table S9. PVP One-Way End and Interior Residue Alpha Values; Comparison with NEP and PEG
View this table:
Table S10. Predicted Chemical Contributions to m-Values Quantifying Effects of NEP (PVP Model Monomer) and PVP Polymer Residues on Protein and α-Helix Unfolding
View this table:
Table S11. Test of Dataset Size by Excluding µ23 Values for Selected Polar (urea, mad) and Nonpolar (1,3-deu, aama) Amidesa

Acknowledgments

We thank Emily Zytkiewicz for comments on the manuscript, and gratefully acknowledge support of NIH GM R35-118100 for this research.

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Posted May 27, 2020.
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Experimentally-Determined Strengths of Atom-Atom (C, N, O) Interactions Responsible for Protein Self-Assembly in Water: Applications to Folding and Other Protein Processes
Xian Cheng, Irina A. Shkel, Kevin O’Connor, M. Thomas Record Jr.
bioRxiv 2020.05.26.104851; doi: https://doi.org/10.1101/2020.05.26.104851
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