Protein collapse driven against solvation free energy without H‐bonds

Abstract

Proteins collapse and fold because intramolecular interactions and solvent entropy, which favor collapse, outweigh solute–solvent interactions that favor expansion. Since the protein backbone actively participates in protein folding and some intrinsically disordered proteins are glycine rich, oligoglycines are good models to study the protein backbone as it collapses, both during conformational changes in disordered proteins and during folding. The solvation free energies of short glycine oligomers become increasingly favorable as chain length increases. In contrast, the solubility limits of glycine oligomers decrease with increasing chain length, indicating that peptide–peptide, and potentially solvent–solvent interactions, overcome peptide–solvent interactions to favor aggregation at finite concentrations of glycine oligomers. We have recently shown that hydrogen‐ (H‐) bonds do not contribute significantly to the concentration‐based aggregation of pentaglycines but that dipole–dipole (CO) interactions between the amide groups on the backbone do. Here we demonstrate for the collapse of oligoglycines ranging in length from 15 to 25 residues similarly that H‐bonds do not contribute significantly to collapse but that CO dipole interactions do. These results illustrate that some intrapeptide interactions that determine the solubility limit of short glycine oligomers are similar to those that drive the collapse of longer glycine peptides.

Abbreviations

IDPs

intrinsically disordered proteins

NAMD

nanoscale molecular dynamics

R_g

radii of gyration

TIP3P

transferable intermolecular potential 3 point

vdW

Van der Waals interactions

Introduction

The collapse of an extended, disordered protein into a compact state is because of competition among intramolecular peptide–peptide interactions/associations, intermolecular peptide–water interactions, and solvent–solvent energies.1, 2, 3 Intrinsically disordered proteins (IDPs) form a class of proteins that do not assume a single stable conformation but assume a range of different, interconverting, disordered conformations, ranging from extended to collapsed states, while binding to different partners in the cell.4, 5 The role of competition among intramolecular peptide–peptide interactions, intermolecular peptide–water interactions, and solvent–solvent energies in the structural transitions in IDPs is of particular interest in defining their range of possible states.

Experiments have shown that the protein backbone is not a passive participant in protein folding and unfolding but contributes significantly via not only the Pauling H‐bonds6 but also by backbone‐solvent interactions,7, 8 the largest of which is the electrostatic contribution.9 Oligoglycine tracts appear in many IDP domains,4 especially in regulatory domains of nuclear transcription factors.10 Thus, oligoglycines offer a convenient model system to study the driving forces for collapse in functionally disordered states of proteins. Oligoglycines have also been observed to collapse both in simulation11, 12 and in experiment13 without forming any stable, regular structures, a behavior reminiscent of IDPs in solution.

Previous work has shown that at infinite dilution the solvation free energy of a single oligoglycine is favorable and decreases with increasing chain length.9 However, experiments have also shown that at finite concentrations the solubility of oligoglycines decreases with increasing chain length,14, 15 indicating that as more peptide–peptide interactions become available, fewer peptide–water interactions are formed. This observation has been corroborated by theoretical and experimental studies that have shown that oligoglycines of various chain lengths collapse in water.11, 12, 13

Experiments show that as the concentration of oligoglycines in solution is increased, a transition into a cloudy liquid state occurs.13, 14, 15 This phase separation in some ways resembles the dense liquid phase observed in the precrystallization stage in proteins,16, 17 indicating that the interactions stabilizing these two transitions may be similar. One mechanism that has been proposed to contribute to the collapse of proteins and the aggregation of glycine oligomers is the formation of hydrogen‐ (H‐) bonds.6 However, H‐bonds were not frequently observed during the collapse of oligoglycines.12 In studies involving the simulation of several hundred thousand to several million atoms, we showed that the solubility limit of theoretical models of Gly₅ is 0.016M and that aggregation of pentaglycines in water above the solubility limit is not driven by H‐bonds.18 Instead, we found that CO dipole‐dipole interactions between the amide groups on the backbone were more numerous and important.

Here, we consider simulations of single oligoglycines of varying chain lengths of 5 (Gly₅), 15 (Gly₁₅), and 25 (Gly25) in water and compare the mechanisms of collapse with that of aggregation in finite concentration solutions of pentaglycines. We demonstrate that the contribution to collapse from H‐bonds is small compared to that of CO interactions, just as in the aggregation of small glycine oligomers. We also compare these findings to those obtained from a simulation of N‐methylated decaglycine (NMe‐Gly₁₀), which, in contrast to oligoglycines, is soluble in water.

Results

Collapse of oligoglycines

The model Gly₁₅ and Gly₂₅ oligomers began to collapse during equilibration to assume a distribution of globule‐shaped structures. While the peptides were collapsed for the entire production run, they dynamically explored many structures without assuming any kinetically stable conformations or classical secondary structures. This finding is in accord with previous computational and experimental observations about the behavior of oligoglycines in water.11, 12, 13 Figure 1 shows the probability densities of the radii of gyration (R _g) of the oligoglycines and NMe‐Gly₁₀. Neuweiler and colleagues13 have examined a similar N‐methylated oligoglycine of twenty residues and found that it was more soluble and more extended in solution than similar oligoglycines. Figure 1 confirms this finding. The oligoglycines were more collapsed than NMe‐Gly₁₀. The longer oligoglycines did explore larger conformations, but with a very small probability. Borrowing from polymer physics concepts, R _g =  $a{N}^{\nu }$ (where a is the length of a single peptide unit and ν is a scaling exponent that depends on solvent quality).3 For all the oligoglycines $\nu \sim 0.3$, whereas for NMe‐Gly₁₀ $\nu \sim 0.4$, indicating that water is a better solvent for NMe‐Gly₁₀ than for oligoglycines. The scaling exponents are in agreement with those observed in the experimental comparisons of Gly₂₀ and NMe‐Gly_20. 13

Figure 1.

Probability distributions of the radius of gyration (R _g) for oligoglycines with 5 (Gly₅), 15 (Gly₁₅), and 25 (Gly₂₅) monomers and N‐methylated decaglycine (NMe‐Gly₁₀). Representative snapshots of Gly₁₅ (R _g of 7 Å) and NMe‐Gly₁₀ (R _g of 8 Å) are shown as a green model figure and cyan model figure respectively.

Dipole correlations

Let us consider the mechanism of stabilization of the modeled structures. Many interactions contribute to the collapse of proteins in solution. H‐bonds can form strong dipole–dipole interactions, but they are only one of the favorable dipole–dipole interactions possible between peptide units. We have previously observed that dipolar CO interactions led to the formation of distinctive patterns in dipole correlations ( $〈{\mu }_i·{\mu }_j\left(r\right)〉$) in aggregates of pentaglycines.18 In Figure 2, we find that the $〈{\mu }_i·{\mu }_j\left(r\right)〉$ for the single longer oligoglycines are similar to those we observed previously in aggregates of pentaglycines. In oligoglycine, $〈{\mu }_i·{\mu }_j\left(r\right)〉$ had a positive peak near 3 Å followed by a minimum at 4 Å. These extremes are because of correlations between adjacent dipoles on the same chain (Fig. 3), which are expected to be present in all peptides, in part because of the constraints created by the bonded peptide backbone. In quantum mechanics these interactions would be assigned as n $\to \pi$* interactions between an oxygen atom and the carbonyl group of the adjacent amide, and have been considered previously in the crystal structures of proteins.19

Figure 2.

Normalized dipole–dipole correlations ( $〈{\mu }_i·{\mu }_j\left(r\right)〉$) as functions of distance in single oligoglycines of varying lengths at infinite dilution and in phase‐separated clusters containing 625 pentaglycines. Note that the curve for the clustered pentaglycine system includes both intrapeptide and interpeptide correlations. Correlations in NMe‐Gly₁₀ are shown in cyan.

Figure 3.

Representative snapshot of Gly₁₅ with examples of peptide dipoles (shown as sticks) in conformations that lead to correlations observed in Figure 2. A pair of sequential residues with their dipole moments oriented parallel to each other are shown with C atoms colored magenta, a pair of sequential residues with their dipole moments oriented antiparallel to each other are shown with C atoms colored green, and two nonsequential residues that come together in a parallel orientation (separated by a distance of 4.4 Å) are shown with C atoms colored yellow.

An interesting feature of Figure 2 is the peak between 4 Å and 5 Å. For Gly₅, Gly₁₅, and Gly₂₅ this third feature is caused by dipoles that are far apart in the peptide sequence but which come together to form favorable interactions when the peptide collapses (Fig. 3). These dipolar interactions are similar chemically to the n $\to \pi$* interactions described above. In aggregates of pentaglycines this is the primary peak present in correlations between separate molecules, and the interactions between these atoms help stabilize the aggregates.

As observed in oligoglycines, the dipole correlation in NMe‐Gly₁₀ has a large peak at 3 Å. However beyond that point $〈{\mu }_i·{\mu }_j\left(r\right)〉$ degenerates into noise. No correlation is present between 4 Å and 5 Å, i.e. the correlations that contribute significantly to collapse and aggregation in oligoglycines are not present in NMe‐Gly₁₀.

Figure 2 shows that $〈{\mu }_i·{\mu }_j\left(r\right)〉$ for Gly₅, Gly₁₅, and Gly₂₅ are similar to those observed in aggregates of pentaglycine, although the peaks in $〈{\mu }_i·{\mu }_j\left(r\right)〉$ between 4 and 5 Å for the individual oligoglycines are slightly larger than those in the aggregates of pentaglycine. We suggest that although these single oligoglycine systems are at infinite dilution, the presence of the peptide covalent bonds forces them to behave as though they are at much higher concentrations, which we define as a local or constrained concentration. Consider that the solubility of Gly₁₅ is between micromolar and nanomolar, extrapolating from similar systems,13, 15 whereas the solubility of Gly₅ is millimolar, at best, experimentally and 0.016M computationally for model force fields.18 In these simulations Gly₁₅ has a mean radius of gyration of ∼7 Å. If Gly₁₅ is considered to be three five‐mers held together by peptide bonds, then the effective local concentration of these pentaglycines would be orders of magnitude more than their solubility limit,20 allowing them to form the associations and interactions observed to stabilize aggregated clusters of pentaglycines. The presence of the peptide bonds alters the entire free energy surface. We note that Gly₅'s must give up translational and rotational entropy in solution in forming longer oligomeric peptides, further enhancing the effects of effective concentration on the solubility.

Number of intrapeptide interactions

We next consider an analysis of the number of H‐bonds and CO dipolar interactions. H‐bonds are favorable intramolecular electrostatic interactions that are expected to favor the collapse of larger oligoglycines. In Figure 4 we plot the numbers of H‐bonds and CO interactions in oligoglycines at infinite dilution and in similarly sized aggregates of pentaglycines from the 0.3M solution. Note that the number of interactions in aggregates is the sum of intra‐ as well as interpeptide interactions. There are very few H‐bonds for dilute oligoglycines, irrespective of their chain length. In contrast, there are many more CO–CO interactions in both single oligoglycines and in the clusters. The numbers of both H‐bonds and CO–CO interactions are statistically similar to the numbers of interactions found in comparably sized clusters, once again suggesting that the mechanisms favoring collapse of oligoglycines at infinite dilution are similar to those favoring the aggregation of smaller oligoglycines. We have previously shown that the pair interaction energies of H‐bonds and CO–CO interactions differ only by about 1 kcal/mol (−4.0 kcal/mol for H‐bonds vs. −3.0 kcal/mol for CO–CO interactions),18 as measured for energy distributions calculated for distances up to several times the geometric criteria cutoffs (within 10 Å). The larger number of CO–CO interactions (around a factor of 6) indicates that they are more important than H‐bonds in driving aggregation and collapse.

Figure 4.

The numbers of hydrogen (H) bonds in oligoglycines (black filled circles) and in clusters of comparable sizes (cyan filled squares) and the numbers of dipole–dipole (CO) interactions between the amide groups in oligoglycine (red, open, inverted triangles) and in clusters of comparable sizes (blue asterisks). CO interactions in NMe‐Gly₁₀ are shown as a green cross.

In contrast to the oligoglycines, NMe‐Gly₁₀ cannot form intrapeptide H‐bonds because the N‐bonded H atom is absent. We calculated the number of intramolecular CO interactions, and the results are shown in Figure 4. On average there are fewer than 10 intramolecular CO interactions in NMe‐Gly₁₀. These interactions occur primarily between adjacent residues and result in the strong positive peak in $〈{\mu }_i·{\mu }_j\left(r\right)〉$ at 3 Å in Figure 2. There are few, if any, CO interactions, such as those observed to contribute to the peak between 3 and 4 Å in oligoglycines, between non‐neigboring residues in NMe‐Gly₁₀. The absence of favorable intramolecular H‐bonds and CO interactions to overcome the favorable solute–solvent interactions may help explain why NMe‐Gly₁₀ is more extended than the longer oligoglycines.

Potential energy

To consider further the mechanisms driving the collapse of these polymer chains, we considered the solute–solvent and solute–solute interaction energies for Gly₂₅ and NMe‐Gly₁₀. We plot both the intramolecular (peptide–peptide) and intermolecular (peptide–water) electrostatic components of the energies as functions of the solvent‐accessible surface area in Figure 5. If we use the average solute–solvent electrostatic interaction energy divided by 2 as a linear‐response‐theory estimate of the electrostatic solvation free energy ( $\Delta G_{\text{elec}}$), then we can see that $\Delta G_{\text{elec}}$ favors extended states for both oligoglycines and NMe‐Gly₁₀. However the oligoglycines collapse by a mechanism that is similar to that observed during aggregation, whereas NMe‐Gly₁₀ does not collapse, indicating that while those intra‐ and intermolecular interaction energies that increase with area and those that decrease with area are the same for both systems, small changes at the atomic level can shift the balance such that intramolecular intrapeptide interactions and possibly solvent‐solvent interactions become more favorable than intermolecular peptide‐water interactions. This phenomenon becomes more apparent when comparing how these interaction energies vary with area for Gly₂₅ and NMe‐Gly₁₀ to how they vary with area for other molecules, such as decaalanine. The implied electrostatic surface tension, or the derivative of $\Delta G_{\text{elec}}$ with respect to the solvent‐accessible surface area, is −80 cal/mol/Ų for Gly₂₅ and −62 cal/mol/Ų for NMe‐Gly₁₀, in comparison with −21 cal/mol/Ų for decaalanine, computed from the data in a previous paper.21 It is interesting to note that the electrostatic solvation free energy of NMe‐Gly₁₀ decreases more rapidly with the solvent‐accessible surface area than that of decaalanine, even though these two compounds are isomeric (each has one methyl per residue, but decaalanine also has the ability to make donor H‐bonds with itself). The intramolecular electrostatic energy, on the other hand, favors compact configurations more strongly for NMe‐Gly₁₀ and Gly₂₅ (45 cal/mol/Ų for both systems) than for decaalanine (20 cal/mol/Ų),21 yet NMe‐Gly₁₀ does not collapse significantly, oligoglycines collapse but not into any stable conformations, and decaalanine can and do form stable, compact α‐helices in water.22

Figure 5.

Average intrapeptide (A) and peptide–water (B) electrostatic energy components of Gly₂₅; and intramolecular (C) and solute–water (D) electrostatic energy components of NMe‐Gly₁₀ versus area respectively.

Discussion and Conclusions

The solubility limits of the isolated peptide units of oligoglycine through Gly₄ have been measured,14, 15 and oligoglycines of various lengths collapse to assume globule‐like structures, as has been observed previously, both in simulation11, 12 and experiment.13 Both the aggregation and collapse of oligoglycines occur in the absence of hydrophobic side chains. The decrease in solubility with respect to increasing the number of monomers is striking given that the solvation free energy decreases with the addition of each peptide unit.9 This apparent contradiction would be resolved if intrapeptide interactions overwhelm the increasingly favorable peptide–solvent interactions.

One intrapeptide interaction that could drive collapse and aggregation would be the formation of H‐bonds, and H‐bonds are often necessary for the stabilization of proteins near a single ordered conformation. Indeed, the disruption of a single H‐bond is sometimes enough to unfold an ordered protein.23 However, we found previously that the average energy of an H‐bond differed from that of a CO interaction by only about 1 kcal/mol and that H‐bonds are five to six times less numerous than CO interactions for both oligoglycines at infinite dilution and in aggregates of pentaglycine.18 These findings imply that the formation of CO interactions are more important than the formation of H‐bonds in the collapse and aggregation of oligoglycine. Given that the backbone is a feature of all proteins, CO interactions may also play a role in proteins of nontrivial sequence where structure is eventually determined by interior packing and the stabilizing effects of H‐bonds and CO–CO interactions.19, 24, 25

NMe‐Gly₁₀ makes an interesting control for the current study. One might consider that the addition of a methyl per residue and the concomitant lack of ability to make donor H‐bonds with solvent would render NMe‐Gly₁₀ insoluble. We note that experimentally the molecule is far more soluble than glycines of similar length.13 In agreement with previous findings,13 NMe‐Gly₁₀ was more extended than comparable oligoglycines at infinite dilution.13 It has been hypothesized that this occurs solely because the methyl groups prevent the formation of H‐bonds. If this were true the formation of CO–CO dipole interactions would not be affected. However as we see, the formation of interactions and correlations between CO–CO dipoles is disrupted significantly. NMe‐Gly₁₀'s methyls would prevent amide or N‐methyl amides from forming these sorts interactions and correlations. In addition, the solvation free energy of NMe‐Gly₁₀ favors staying in solution more than other similar molecules, such as decaalanine. Together, these observations may also help explain why NMe‐Gly₁₀ was less compact than oligoglycines.

Methods

Simulation protocol

We simulated single, capped oligoglycines with lengths in multiples of 5 (Gly₅, Gly₁₅, and Gly₂₅) in explicit water using molecular dynamics. The oligoglycines were built with the Chemistry at Harvard Molecular Mechanics (CHARMM) program26 and solvated using Visual Molecular Dynamics (VMD)27 with transferable intermolecular potential 3 point (TIP3P) water modified for use with the CHARMM force field.28 Each oligoglycine was surrounded by five solvation shells on all sides when they were at their most extended state. All the systems were minimized for 25 K steps with the peptide held fixed and then minimized for an additional 25 K steps with all molecules allowed to move freely. The systems were equilibrated in NPT (pressure = 1 atm, temperature = 300 K) for 2 ns and then in NVT (temperature = 300 K) for 1 ns. Gly₅ and Gly₁₅ were run for 100 ns, and Gly₂₅ was run for 350 ns in the NVE ensemble with a time step of 1 fs. We avoided a thermostat for the production run to avoid any artifacts associated with the artificial supply or removal of energy from various modes during the collapse. All systems showed minimal temperature variance, with mean temperatures of 300.64 ± 2.9 K, 299.65 ± 1.2 K, and 299.33 ± 0.7 K for Gly₅, Gly₁₅, and Gly₂₅ systems, respectively.

We used Nanoscale Molecular Dynamics (NAMD)29 to run the simulations with the CHARMM22 force field with the CMAP corrections.28, 30 Particle Mesh Ewald was used to calculate long‐range electrostatics.31 RATTLE was used to constrain all bonds involving hydrogen atoms.32 Van der Waals (vdW) interactions were truncated at 12 Å.

We used a replica exchange simulation to explore conformations of NMe‐Gly₁₀. We used 10 replicas where the large energy barrier in the cis–trans torsion angle was progressively reduced from 2.5 kcal/mol to 0.25 kcal/mol in increments of 0.25 kcal/mol. The initial structures were built and solvated with xLEaP in the Assisted Model Building with Energy Refinement (Amber) 12 package33 and TIP3P water.34 These simulations were run with NAMD29 and the generalized Amber force field.35 The replica exchange simulations were run with an NPT ensemble (pressure = 1 atm, temperature = 300 K), maintained with Langevin thermo‐ and baro‐stats.29 Particle Mesh Ewald was used to calculate long‐range electrostatics.31 The vdW interactions were truncated with a switching function beginning at 10 Å and terminated at 12 Å. RATTLE was used to constrain all bonds involving hydrogens.32 Attempts were made every 1 ps to swap ensembles. The replica exchange simulation ran for a total of 52 ns.

Dipole correlations

The dipole vector of the peptide with carbonyl in residue i and NH in residue i + 1 was defined as

$${\mu }_i({\mathbf{r}}_{\mathbf{i}})\hspace{0.17em}=\hspace{0.17em}{q}_{C_i}({\mathbf{r}}_{{\mathbf{C}}_{\mathbf{i}}}-\hspace{0.17em}{\mathbf{r}}_{\mathbf{i}})\hspace{0.17em}+\hspace{0.17em}{q}_{O_i}({\mathbf{r}}_{{\mathbf{O}}_{\mathbf{i}}}-\hspace{0.17em}{\mathbf{r}}_{\mathbf{i}})\hspace{0.17em}+\hspace{0.17em}{q}_{N_{i+1}}({\mathbf{r}}_{{\mathbf{N}}_{\mathbf{i}+1}}-\hspace{0.17em}{\mathbf{r}}_{\mathbf{i}})\hspace{0.17em}+\hspace{0.17em}{q}_{H_{i+1}}({\mathbf{r}}_{{\mathbf{H}}_{\mathbf{i}+1}}-\hspace{0.17em}{\mathbf{r}}_{\mathbf{i}}),$$

where $q_{C_i}$ and $q_{O_i}$ are the charges of the carbonyl carbon and carbonyl oxygen of residue i, $q_{N_{i+1}}$, and $q_{H_{i+1}}$ are the amide nitrogen and amide hydrogen of residue i + 1, ${\mathbf{r}}_{{\mathbf{C}}_{\mathbf{i}}},\hspace{0.17em}{\mathbf{r}}_{{\mathbf{O}}_{\mathbf{i}}},\hspace{0.17em}{\mathbf{r}}_{{\mathbf{N}}_{\mathbf{i}+1}}$, and ${\mathbf{r}}_{{\mathbf{H}}_{\mathbf{i}+1}}$ are the positions of those atoms, and

$${\mathbf{r}}_{\mathbf{i}}=(|q_{C_i}|{\mathbf{r}}_{{\mathbf{C}}_{\mathbf{i}}}+|q_{O_i}|{\mathbf{r}}_{{\mathbf{O}}_{\mathbf{i}}}+|q_{N_{i+1}}|{\mathbf{r}}_{{\mathbf{N}}_{\mathbf{i}+1}}+|q_{H_{i+1}}|{\mathbf{r}}_{{\mathbf{H}}_{\mathbf{i}+1}})/(|q_{C_i}|+|q_{O_i}|+|q_{N_{i+1}}|+|q_{H_{i+1}}|).$$

The correlation ( $〈{\mu }_i·{\mu }_j\left(r\right)〉$) between the dipole vectors of residues i and j was defined to be the dot product between them. Dipole correlations in NMe‐Gly₁₀ were calculated by substituting the C atom from the methyl group atoms for the amide hydrogen atom in the above equations.

Number of interactions

To compare the mechanisms of collapse with those of aggregation, we considered the number of intrapeptide interactions. An interaction between CO‐NH atom pairs, i.e. a H‐bond, was defined as present if the distance between donor atom H and acceptor atom O was $\le$ 2.4 Å. This is an extremely generous criterion, but even with this loose criterion we did not observe an appreciable number of H‐bonds in aggregates of pentaglycines.18 Interactions between CO atom pairs were considered to be present if the distance between either of the positive C atoms and negative O atoms was $\le$ 4.2 Å. Both distance cutoffs were taken from the first minimum of the radial distribution of the respective atoms about each other.

Potential energy

The potential energies were defined to be the sum of electrostatic and vdW potentials,

$$U_{\text{potential}}={\displaystyle \sum _{i,j}\frac{q_i{q}_j}{r_{ij}}}+4\epsilon {ϵ}_{ij}\left[{\left(\frac{{\sigma }_{ij}}{r_{ij}}\right)}^{12}-{\left(\frac{{\sigma }_{ij}}{r_{ij}}\right)}^6\right],$$

where the summation was taken over atom pairs in the peptide when computing intrapeptide potentials and over atom pairs with one member in the peptide and one in the solvent when computing solvent–solute potentials. Potentials were computed with NAMD.29 Solvent‐accessible surface areas were calculated using the DAlphaBall package using a solvent probe radius of 1.4 Å.36