Preliminary Oligomerization in a Glycolic AcidâGlycine Mixture: A Free

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Preliminary Oligomerization in a Glycolic Acid – Glycine Mixture: A Free Energy Map Jeremy Kua, and Lauren M Sweet J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b08076 • Publication Date (Web): 08 Sep 2016 Downloaded from http://pubs.acs.org on September 11, 2016

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The Journal of Physical Chemistry

Preliminary Oligomerization in a Glycolic Acid – Glycine Mixture: A Free Energy Map Jeremy Kua* and Lauren M. Sweet Department of Chemistry and Biochemistry, University of San Diego, 5998 Alcala Park, San Diego, CA 92110. * Corresponding author e-mail address and phone: [email protected]

(619) 260-7970

Abstract Glycolic acid and glycine can potentially self-oligomerize or co-oligomerize in solution by forming ester and amide bonds. Using density functional theory with implicit solvent, we have mapped a baseline free energy landscape to compare the relative stability of monomers, dimers and trimers in solution. We find that amide bond formation is favored over ester bond formation both kinetically and thermodynamically, although the differences decrease when zwitterionic species are taken into account. The replacement of ester linkages by amide bonds is favored over lengthening the oligomer, suggesting that one route to oligopeptide formation is utilizing oligoesters as a starting point. We also find that diketopiperazine, the cyclic dimer of glycine, is favored over the linear dimer, however the linear trimers are favored over their cyclic counterparts. Since glycolic acid and glycine are dominant products from a Strecker synthesis starting from formaldehyde and HCN, this study sheds light on potential pathways to prebiotic formation of oligopeptides via oligoesters.

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Introduction In 1953, Stanley Miller published a landmark paper on the synthesis of amino acids from simple substances (CH4, NH3, H2, H2O) thought to constitute Earth’s early atmosphere;1 the spark discharge experiment is credited with jump-starting research into the chemical origins of life. In early quantification of the soluble organics synthesized, glycine (2.1%) was the most abundant amino acid followed by alanine (1.7%).2 Their corresponding α-hydroxy acids, glycolic acid (1.9%) and lactic acid (1.6%) were synthesized in roughly similar amounts. This similarity is not surprising given the Strecker synthesis was established as the route to both the amino and αhydroxy acid via CH2O and HCN as intermediates.3 Both glycine and glycolic acid are also found among the water-soluble organics in both the GRA 95229 and Murchison meteorites, in higher yield than their larger molecular weight counterparts.4 While the formation of amino acids such as glycine seems likely under plausible prebiotic conditions, subsequent oligomerization to peptides, the precursors to protein catalysts, is not at all straightforward. Under standard conditions, the formation of an amide (peptide) bond between two amino acids is thermodynamically unfavorable in aqueous solution. In the case of glycine, the free energy difference is reported as 3.6 kcal/mol in favor of two glycine monomers over diglycine,5 i.e., in a 1 M solution of glycine, the relative amount of diglycine would be ~2.9 x 10-3. Concentrations of glycine are likely to be much lower under prebiotic conditions, disfavoring the accumulation of oligopeptides, at least in a prebiotic soup or broth. There are several strategies that yield oligopeptides. Early experiments involved the dry heating of amino acids to form thermal copolymers,6 but the cross-linked products do not resemble proteins in extant life. Other strategies include alternating hydration and dehydration cycles simulating a tide pool,7 simulating hydrothermal conditions in the presence of CuCl2,8 varying pH and temperature,9 and employing activation agents such as N-carboxyanhydrides (NCAs).10 These studies and more are summarized in recent reviews by Brack11 and Pascal et al.12 Some are plausibly prebiotic, while others require conditions or catalysts unlikely to be present on the early Earth. Recently, a different approach to peptide bond formation utilized polyesters as a starting material. When a mixture of lactic acid and either alanine or glycine was subject to wet-dry cycles, mixed oligomers consisting of lactic acid and amino acid monomeric units were produced; but more importantly, as the number of cycles was increased the proportion of amino 2 ACS Paragon Plus Environment

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acids in the oligomers increased.13 Since polyesters are generated when lactic acid is the sole monomer in wet-dry cycles, but no polyamides are observed under similar conditions with amino acid monomers, Forsythe et al. concluded that what was happening in a mixture of hydroxy and amino acids is the successive replacement of hydroxy acid subunits with amino acids – they called it “ester-mediated amide bond formation”.13 This was the starting point motivation for the present study, a free energy map for the preliminary steps of oligomerization in the presence of both monomers. Our group has developed a relatively fast protocol to calculate the relative free energies of small molecules in aqueous solution relevant to origin-of-life scenarios, to produce a baseline thermodynamic and kinetic map for oligomerization reactions. These include the selfoligomerization of formaldehyde14 and glycolaldehyde,15 the co-oligomerization of formaldehyde and ammonia,16 and most recently including HCN into the mix.17 We have found generally good agreement between our calculations and available experimental results for the relative free energies of “stable” species (i.e., molecules in local energy minima), but there is a systematic overestimating of activation barriers by 2-3 kcal/mol in general.15 Further details are provided in the Computational Methods section. In our present study, we have chosen glycolic acid and glycine as the monomers, as these are the simplest α-hydroxy and α-amino acids respectively. Ongoing work, not included in the present study, suggests that similar relative energies are obtained when glycine is replaced by alanine. The scope of the present work is to generate a free energy map of the dimers and trimers relative to the monomers. Homo and hetero-oligomers and ring systems are included, although we restricted our calculation of transition states and corresponding activation barriers to reactions involving dimer formation only. Since our protocol is aimed at generating baseline thermodynamics and kinetics in a reaction network, we have so far restricted our “conditions” to standard conditions, 1 atm, 298 K, pH 7, and neutral molecules (although we have one previous study involving cationic species18). Under these conditions, we find that (i) formation of new amide bonds is both thermodynamically and kinetically favored over ester bonds, (ii) diketopiperazine (DKP), the cyclic dimer of glycine, is the thermodynamic sink, and (iii) the replacement of an ester linkage by an amide is not only thermodynamically favored, it has the lowest barriers. However the presence of potential zwitterionic species complicates the free energy map by stabilizing molecules containing both 3 ACS Paragon Plus Environment


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carboxylic acid and amine functional groups, such as glycine and diglycine. This perturbs the baseline map in significant ways, and exposes limitations in our current protocol as we extend it to a wider network of reactions. Ester-mediated amide formation is still favored, but the overall picture becomes more complicated. Computational Methods The protocol described below is similar to our previous studies and much of the text in this section is reproduced from earlier work for clarity and reading ease.14-16 All calculations were carried out using Jaguar 6.019 at the B3LYP20-23 flavor of density functional theory (DFT) with the 6-311G** basis set. A comparison of our chosen level of theory, basis set, and implicit solvent scheme, with other methods can be found in our previous work.24 To increase the probability of finding global minima, multiple conformers of each species were calculated. Conformers were generated with the Conformer Distribution tool on Spartan ’04 using the Merck Molecular Force Field (MMFF).25-26 Starting with the lowest energy conformer, we typically selected 8-24 conformers (depending on system size) for optimization using the full protocol. In particular, we made sure to include starting structures with a variety of intramolecular hydrogen bonds in addition to more “open” extended structures. The Poisson-Boltzmann (PB) continuum approximation27-28 was used to describe the effect of water acting as an implicit solvent with a dielectric constant of 80.4 and a probe radius of 1.40 Å. As in previous work, the solvation energy was calculated at the optimized gas-phase geometry for the neutral molecules because in most cases there is practically no change between the gasphase and implicit solvent optimized geometries. For zwitterions, geometry optimization was performed in solution to prevent proton-hopping back to the non-zwitterionic structure in the gas phase. Even so, we had to use initial conformations with Cs symmetry and in some cases bond constraints to retain the zwitterionic structure. These are discussed in more detail in the Results and Discussion section. The electronic energies of the optimized structures and the solvation energy are designated Eelec and Esolv respectively in Table 1. Even though the solvation energy contribution is to some extent a free-energy correction, it certainly does not account for all of the free energy. The analytical Hessian was calculated for each optimized structure, and the electronic energy corrected for zero-point vibrations. Negative eigenvalues in transition state calculations were not 4 ACS Paragon Plus Environment

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included in the zero-point energy (ZPE). The temperature-dependent enthalpy correction term is straightforward to calculate from statistical mechanics where we assume that translational and rotational corrections are a constant times kT, that low frequency vibrational modes will generally cancel out when calculating enthalpy differences, and that the vibrational frequencies do not change appreciably in solution. The combined ZPE and enthalpy corrections to 298 K are designated Hcorr and the corresponding gas-phase Gibbs free energy correction to 298 K is designated Gcorr in Table 1. The corresponding free-energy corrections in solution are much less reliable.29-31 Changes in free energy terms for translation and rotation are poorly defined in solution, particularly as the size of the molecule increases. Additional corrections to the free energy for concentration differentials among species (to obtain the chemical potential) can be significant, especially if the solubility varies among the different species in solution. Furthermore, since the reactions being studied are in solution, the free energy being accounted for comes from two different sources: thermal corrections and implicit solvation. Neither of these parameters is easily separable, nor do they constitute all the required parts of the free energy under our approximations of the system. To estimate the free energy, we followed the approach of Lau and Deubel32 who assigned the solvation entropy of each species as half (or 0.5) of its gas-phase entropy. This was based on work by Wertz and Abraham proposing that upon dissolving in water, molecules lose a constant fraction of their entropy, typically close to 0.5. Wertz33 had originally proposed a factor of 0.46 based on a small suite of molecules, but as the diversity of molecules was expanded, Abraham34 found a wider range between 0.4 and 0.6. Since our protocol uses a factor of 0.5 for the entropic correction, this is designated -0.5TScorr in Table 1 and calculated as 0.5 x (Gcorr − Hcorr). We are not the only ones using this approach; there are other recent computational studies using a similar factor of 0.5 in unrelated systems.35-37 Although our most recent study exposed the inadequacy of the 0.5 factor for certain tautomerizations,17 the reactions under consideration here do not fall under this category – and in fact the 0.5 factor was shown to work well. The free energy of each species, designated G298 in Table 1, is the sum of Eelec, Esolv, Hcorr and -0.5TScorr. Only the most stable conformer for each unique molecular species (both minima and transition states) is reported in our free energy map. ΔG values are calculated from the difference in G298 between the reactants and products, and therefore include the ZPE, enthalpic, and entropic corrections to 298 K, for a reaction in aqueous solution. Although water as a solvent also 5 ACS Paragon Plus Environment


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participates explicitly in condensation reactions, concentration corrections are not included in this landscape, the advantages and disadvantages of which are discussed in our previous work.15 For transition state calculations, additional water molecules were explicitly added to the system to find the lowest energy barrier. We found, in agreement with previous work,15-17 that the addition of two water molecules yields optimal structures with the lowest barriers. All calculated transition states have one large negative eigenvalue corresponding to the reaction coordinate involving bond breaking/forming and accompanying proton transfer. The corresponding energy components of the transition states are listed in Table 2. In our previous study examining the equilibrium distribution of glycolaldehyde and its oligomers in solution,15 we found that this protocol for calculating free energies and estimating equilibrium concentrations showed good agreement with NMR experimental results. The activation barriers compared to experiment are reasonable but the agreement is not as close, and our protocol typically overestimated transition state barriers by 2-3 kcal/mol. On the other hand, our protocol performs well in calculating the relative free energies of stable species, typically within 0.5 kcal/mol of experimental results, or an uncertainty of within a factor of 2.3 in terms of equilibrium constant ratios. The barriers were calculated in reference to the separated reactants rather than a pre-associated complex, because in previous cases we found differences of 0-2 kcal/mol between the two methods,16 and we were willing to tolerate this error in favor of a cleaner protocol that simplified the task of determining relative free energies in a network of chemical species and reactions between them. Results and Discussion Notation and Overview of Reaction Network. To ease reading the text, without constantly referring to the reaction scheme, we designate glycolic acid A and glycine B. In the main scheme (Figure 1), these are represented by solid red and blue circles respectively. An “open” dimer is represented by a line connecting the two circles; two curved lines indicate a six-membered ring; the equilateral triangle of three circles represents a nine-membered ring. The carboxylic acid end of a molecule is always on the left. Hence, in an open dimer, a left red circle has an ester linkage, while a left blue circle has an amide linkage, i.e., the dimers AA and AB have ester linkages, while BA and BB have amide 6 ACS Paragon Plus Environment

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linkages. A right red circle has a free alcohol, while a right blue circle is a free amine. Thus, AA and BA have a free alcohol, while AB and BB have a free amine. To ensure there is no confusion, these circles are shown next to their respective structures and notations in subsequent Figures. Six-membered and nine-membered rings include designations of 6 and 9 respectively. For example, DKP, the six-membered ring of diglycine, is BB6. Tetrahedral intermediates have a tet suffix, and the transition states before and after the intermediate have ts1 and ts2 suffixes respectively. An x is included for ester-to-amide replacements in the form of AxB to indicated that A is being replaced by B. In Figure 1, overall reaction thermodynamics are shown using black arrows and numerical values. No zwitterionic species are considered in this scheme. Water, not shown, is a byproduct in condensation reactions. Monomers added are also not shown in Figure 1 to maintain the clarity of the overall picture (since reaction details are shown in subsequent Figures). There is basically only one type of reaction that takes place. This two-step reaction involves nucleophilic attack on the carboxylic acid by a free alcohol or amine generating a tetrahedral intermediate; the subsequent elimination reaction leads to the product. In dimerization reactions, the numerical value in red is the higher of the two energy barriers. We did not explicitly calculate the barriers for trimerizations since they are similar to dimerizations, and their reaction free energies forming both tetrahedral intermediates and products are in the same range as the dimerizations. The rest of this section is laid out as follows: We first present the detailed results for dimerization reactions, including ring formation and ester-mediated amide bond formation; these correspond to the left half of Figure 1. We then discuss reactions involving trimers. Finally, we present a modified version of Figure 1 that takes into account zwitterionic species (via a correction factor) and discuss the limitations and caveats of our current protocol. Dimer Formation. Figure 2 shows the reaction when the free hydroxyl of A attacks the carbonyl of either A or B to form a dimer with an ester linkage. The reaction is slightly endergonic: AA is uphill 4.0 kcal/mol and AB is uphill 3.5 kcal/mol. The addition step has a lower overall barrier compared to the elimination step relative to monomers. These values are slightly lower for AA formation, in 7 ACS Paragon Plus Environment


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line with the lower energy of its intermediate AAtet (15.4 kcal/mol) compared to ABtet (18.5 kcal/mol). On the other hand, formation of a dimer with an amide linkage is exergonic, as shown in Figure 3. Formation of BA and BB are downhill 4.2 and 3.4 kcal/mol respectively relative to monomers. The relative free energies of the first transition state and the intermediate are similar to the reaction forming the ester. The second step activation barrier, while still overall higher than the first step, is lower for amide formation compared to ester formation – this fits well with amide formation being overall exergonic. The two 8-center transition states for BA formation from its monomers (with two assisting water molecules) are shown in Figure 4; the transition states for the other dimerization reactions are similar. Figures 5 and 6 show the ring closure reactions for the four dimers. The formation of AA6 (glycolide) from AA is uphill 9.3 kcal/mol; a new ester linkage is made in the ring-closure reaction. The ring closure of BA to BA6 also makes a new ester linkage and is uphill 5.9 kcal/mol. On the other hand, making a new amide linkage is exergonic. Formation of AB6 from AB is downhill 2.5 kcal/mol (note that AB6 and BA6 are identical, although the intermediates and transition states are different because the reactants AB and BA are not identical). The ring closure of BB to BB6 (DKP) is downhill 5.6 kcal/mol. For three of the four reactions, the first step has a lower overall barrier compared to the second step. The exception is AA to AA6 where the barriers are similar, but it is unclear why even after optimizing several different transition state structures. The only noticeable difference from the lowest energy transition state is that AA6ts1 has an anomalously low solvation energy compared to AA6ts2, while in the other three reactions these solvation energies are similar between the two transition states. The two transition states for BB ring closure to BB6 are shown in Figure 7; the transition states for the other ring closures are similar. The open dimers can interconvert by replacing an ester linkage with an amide linkage, i.e., AA into BA or AB into BB. In Figure 8, we see that both these reactions are exergonic (-8.1 and -6.9 kcal/mol respectively), i.e., the reverse reaction of replacing an amide with an ester is thermodynamically unfavorable. The overall barrier is marginally higher for the second step compared to the first step, but is noticeably lower (+26.7 and +26.5 kcal/mol) than dimerization of monomers and ring formation – with one exception, the conversion of BB into BB6 is 8 ACS Paragon Plus Environment

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comparable in magnitude (+26.6 kcal/mol). The two transition states for conversion of AA into BA are shown in Figure 9; the analagous AB to BB conversion has a similar transition state. Our results suggest that when we consider neutral non-zwitterionic species, ester-mediated amide bond formation is kinetically favored over addition/removal of a monomer or forming a six-membered ring (with the exception of DKP). It is also the most thermodynamically favored, e.g., conversion of AA to BA is -8.1 kcal/mol, while AA to AA6 is +9.3 kcal/mol and AA to 2 A is -4.0 kcal/mol. Later, we will discuss how the picture changes when zwitterions are taken into account. Trimer Formation. In Figure 1, we see that each of the open dimers (AA, BA, AB, BB) can add a monomer A or B to the left (i.e. nucleophilic attack on the carboxylic acid end), thus growing the oligomer chain. Similar to what we found when two monomers condensed to form a dimer, the addition of A to form a trimer (AAA, ABA, AAB, ABB) is endergonic ranging from +3.2 to +4.2 kcal/mol. Addition of B to form a trimer (BAA, BBA, BAB, BBB) is exergonic ranging from -2.9 to -4.4 kcal/mol. The tetrahedral intermediates range from +15.6 to +17.9 kcal/mol (see Figure S1 in Supporting Information for structures and energies). Given the similar overall thermodynamics of these reactions to the previously discussed addition of two monomers to form a dimer, we did not calculate the energy barriers. All else being equal, we expect similar reaction profiles with overall barriers ranging from 29-34 kcal/mol. If instead the new monomer was added to the ester or amide carbonyl in the middle of the dimer, this would lead to tetrahedral intermediates similar to those in Figure 8. Leaving of a monomer moiety leads back to the dimer. While a potential side reaction of the tetrahedral intermediate is dehydration with water as a leaving group, the imino esters formed are higher in energy compared to the tetrahedral intermediates (see Figure S2 in Supporting Information) and thus unlikely to contribute significantly. In Figure 8 we see that the first step (with the lower barrier) for the branched addition is 25 kcal/mol, similar in range to the first steps for the linear addition (Figures 2-3) of 25-27 kcal/mol. It is the second rate-determining step where the substitution of a monomer in the branched addition (barriers of 26-27 kcal/mol) is kinetically favored over condensation in the linear trimer (barriers of 29-34 kcal/mol). Therefore we expect 9 ACS Paragon Plus Environment


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some competition between substitution and addition reactions, depending on where the incoming monomer attacks the oligomer. The linear trimer can undergo several intramolecular transformations: (1) Elimination of a monomer leads to the six-membered ring dimer; (2) Condensation of terminal groups leads to a nine-membered ring trimer; and (3) Trimers with a six-membered or five-membered ring can be formed via condensation. These possibilities are illustrated starting from linear triglycine (BBB) in Figure 10. A second intramolecular cyclization leads to a structure with fused six- and fivemembered rings. Starting from BBB, the elimination of a monomer to form the ring dimer is the thermodynamically favored route if no zwitterions are considered. The reaction BBB à BB6 + B (shown in blue in Figure 10) is exergonic by 1.6 kcal/mol, as indicated by the bottom left arrow in Figure 1. This value can also be determined from Hess’ Law since BB à BB6 is -5.6 kcal/mol and BB + B à BBB is -4.0 kcal/mol. Figure 1 has arrows showing three other monomer elimination reactions to form six-membered rings – the elimination of B from BAB, BBA and BAA, all of which are endergonic. There are four analogous reactions involving the elimination of leftmost A from linear trimers (reaction arrows not shown). If instead the terminal groups of BBB self-condense to form a new amide linkage, a ninemembered ring BBB9 is formed (shown in red in Figure 10). This cyclization reaction is endergonic by 9.0 kcal/mol. Energies for the cyclization of the other seven linear trimers range from +7.6 to +12.2 for amide linkage and +17.1 to +25.4 for ester linkage (see Figure S3 in Supporting Information). Two other cyclic products shown in Figure 10 are BB6B (green) and BB5B (gold). The six-membered ring BB6B is +9.3 kcal/mol compared to linear BBB, while the five-membered ring with the imine BB5B is even less stable at +15.3 kcal/mol compared to BBB. (In Figure 1, only the lower +9.3 kcal/mol value is displayed.) The single-ring trimers can undergo a second intramolecular cyclization to form the fused-ring structure B6B5B (see Figure 10) however this structure is still +6.9 kcal/mol higher in energy than BBB. Thus, cyclization of the trimer is unfavorable except for the elimination to the cyclic dimer DKP as described in the previous paragraph. Accounting for Zwitterions 10 ACS Paragon Plus Environment

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One problem with the free energy map shown in Figure 1 is that zwitterionic species were not taken into account. There are several reasons for this. First, there are significant difficulties with cleanly locating a transition state starting from the zwitterions, and the calculated barriers would be suspect. Second, while our protocol has been tested significantly on neutral polar organics, none of these contained zwitterions; the solvation free energies and the entropic contributions may contribute further errors. Third, even converging the zwitterionic structures into stable minima proved challenging, as the protons would hop reverting to non-optimal nonzwitterionic structures.38 Since zwitterions play a role in less than half the structures (mainly in the bottom half of Figure 1), and our goal in concert with previous work is to provide baseline free energy maps that are connected to a larger network of reactions,14-17 we chose to treat zwitterions as a perturbation to the main scheme. Zwitterions become significant when a species has both a free carboxylic acid and an amine group. These species would be the monomer B, the dimers AB and BB, and the trimers AAB, BAB, ABB and BBB. These are the non-ring structures in the bottom half of Figure 1. One issue we encountered when attempting to calculate these zwitterions using our protocol was proton hopping away from the zwitterionic structure. We were unable to prevent proton hopping in glycine even when running the optimization directly in (the dielectric) solution, unless we maintained the mirror plane throughout the calculation. Starting with a glycine conformer with Cs symmetry, the optimized glycine zwitterion zB is calculated to be 3.4 kcal/mol lower in free energy than B. Under standard conditions this corresponds to an equilibrium constant of ~370 in favor of the zwitterion. We are not aware of an experimentally measured equilibrium constant between B and zB for comparison. Even when applying Cs symmetry to diglycine and optimizing directly in solution, we still observed proton hopping. After several failed approaches, we finally settled on constraining the two problematic N–H bonds at 1.02 Å. This constrained optimization leads to the zwitterion zBB also being 3.5 kcal/mol lower in energy than its corresponding non-zwitterionic conformer of BB. (The most stable conformer of BB has a twist. Calculating its zwitterion would have required more N–H bond constraints, and our goal was to minimize the number of bond constraints used since the structure isn’t fully and freely optimized.) For the depsipeptide AB, we did not need any N–H bond constraints, but also started with a conformer with Cs symmetry. The 11 ACS Paragon Plus Environment


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zwitterion zAB was calculated to be 3.6 kcal/mol lower in energy than its corresponding nonzwitterionic conformer of AB. Based on these results, we decided to apply a standard correction factor of 3.5 kcal/mol to species that have a significant zwitterionic contribution. Calculating the zwitterionic trimer structures would have required additional constraints, making the corresponding factors even less reliable. While our approach of a blanket correction factor is not the best approximation, it is in line with keeping our protocol streamlined, and we are willing to tolerate this margin of error for the purposes of this preliminary study. Detailed structures and energies for the zwitterions and their corresponding conformers are found in Figure S4 and Table S2 in Supporting Information. A better approach would be to utilize a full QM/MM treatment with explicit solvent, which is beyond the scope of this paper. The use of a few explicit water molecules with implicit solvent, or employing diffuse functions in the basis set, has other drawbacks as discussed in Supporting Information. As we extend this work in a future study, we will likely need to refine the correction factor(s) to take into account further differences in molecular species. Figure 11 shows the updated reaction scheme with all structures that can form zwitterions stabilized by 3.5 kcal/mol. If a reaction involves an equal number of zwitterions comparing reactants to products, it will have the same free energy change as shown in Figure 1. For example, for the reaction A + B à AB + H2O, B and AB are both stabilized by the same amount and therefore the reaction free energy (coincidentally +3.5 kcal/mol) is the same in both Figures 1 and 11. However, the barrier for the rate-determining step increases since the transition state is not stabilized; it is now +37.0 instead of +33.5 kcal/mol. If a reaction has a different number of zwitterions comparing reactants to products, then the reaction free energies will change. For example, in B + B à BB + H2O, both monomers in B on the reactant side are stabilized for a total of 7.0 kcal/mol. The single product BB is stabilized by 3.5 kcal/mol. Thus, the reaction free energy is shifted to being +3.5 kcal/mol more endergonic; in Figure 11 it is +0.1 kcal/mol instead of -3.4 kcal/mol in Figure 1. Since the barrier is calculated with the reactants as the reference state, it increases by 7.0 kcal/mol to +38.3 instead of +31.3 kcal/mol. (Transition states do not involve zwitterions as discussed above, and are therefore not stabilized.) A recent extensive computational study using a variety of methods (MP2, B3LYP, CCSD) reported barriers ranging from 32-39 kcal/mol for glycine dimerization, albeit in the gas phase.39 12 ACS Paragon Plus Environment

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There are two important implications of applying an energy correction when zwitterions are taken into account. Firstly, this leads to a much higher barrier for the dimerization of glycine. In fact, the dimerization of glycolic acid into AA now has the lowest barrier (+32.3 kcal/mol) of the four possible dimerization reactions. This echoes the experimental finding that the dry-cycle onset of lactic acid (i.e., methyl glycolic acid) oligomerization was observed starting at a lower temperature of 55°C, compared to glycine oligomerization with an onset temperature of 65°C.13 This difference of 6 kcal/mol between the calculated barriers corresponds to a reduction in the rate constant by four orders of magnitude at 55°C assuming the same pre-exponential factor. Secondly, the overall equilibrium constant for the dimerization of glycine has now shifted in favor of the monomers, albeit the difference is only 0.1 kcal/mol. As mentioned in the Introduction, the experimental equilibrium constant in a solution of 1 M glycine is ~340, corresponding to a 3.6 kcal/mol energy gap, favoring the monomers. Since this is a condensation reaction with water, the solvent, as a product in the reaction, the concentration correction ( –RT ln 55.56) is 2.4 kcal/mol at room temperature. Applying this, the calculated gap is 2.5 kcal/mol corresponding to an equilibrium constant of ~70 favoring the monomers; not identical to the experimental results, but at least in the right direction and in the right ballpark quantitatively. We have showed how using this concentration correction factor perturbs the free energy map in previous work on the oligomerization of methylglyoxal.24 However, there are caveats with applying this approach as the concentrations of a wide variety of species may change over time in a complex oligomerization reaction with many intermediates.15, 24 Thus, we have chosen to present the baseline free energy map without concentration corrections. Other than these two main differences, the overall map in Figure 11 has many similarities to Figure 1. Adding a monomer to form a new ester linkage (endergonic) is still less favorable thermodynamically than adding a new amide linkage, although the latter is now only slightly exergonic or the free energy change is close to zero. DKP is still the thermodynamic sink without concentration corrections, although less favorably so. Barriers are slightly higher when zwitterionic species are involved, but overall the substitution of a monomer by replacing an ester linkage with an amide is still kinetically favored over the addition of a new bond (forming a new amide linkage is slow with barriers of 37-38 kcal/mol), but once formed amide hydrolysis is also slow compared to ester hydrolysis as expected. 13 ACS Paragon Plus Environment


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Conclusion A broad goal of our study is to extend the free energy map we have been developing for small polar organic molecules in solution. Some of the most interesting chemistry occurs in complex mixtures, and we want to understand how such systems change in molecular composition as the chemical environment changes. Thus, we have been mapping the thermodynamic and kinetic landscapes for neutral molecules at pH 7 under standard conditions. Ongoing work includes varying the “environment” to investigate changes to the system. As we have extended the suite of molecules, we are also learning the limits of our previously established protocol. While our relatively quick protocol worked well for aldehydes, ketones, and alcohols, we started to see some issues as imino esters, amides and carboxylic acids were introduced into the mix.17 In the present work with amino acids, we have found that zwitterions need to be taken into consideration, however there are challenges in optimizing and accurately calculating the relative free energies and activation barriers. The application of a standard zwitterion stabilization factor goes some way to mitigating the error of locating the appropriate reference energy for species that form stable zwitterions in solution (such as glycine and its oligomers), but is likely to be too crude for a more extensive and general protocol. Thus the perturbed energy map in Figure 11 should be taken as a qualitative and very rough approximation of how the free energies may change due to the presence of stable zwitterions. One motivation of our study was the experimental work of Forsythe et al. on “ester-mediated amide bond formation driven by wet-dry cycles”.13 Since the chemistry of life’s origins is likely to involve a complex solution of organic molecules, this caught our interest as an extension of our previous work on generating a free energy map for formaldehyde, glycolaldehyde, HCN and ammonia reacting in solution.14-17 (At present, our non-dynamic baseline map is limited, as it does not include concentration corrections for wet-dry cycles, nor temperature variations for cool-warm cycles. Energy maps excluding solvation energy to mimic a dry cycle and accompanying discussion can be found in Supporting Information.) Although we have only detailed the thermodynamics and kinetics for the interconversion of ester and amide linkages in dimers, our calculation of the free energies of the linear trimers allows us to locate their relative stabilities on the same scale. In Figure 12, we have assigned AAA a relative free energy of zero, and the relative energies of the other linear trimers are calculated using Hess’ Law based on the values in Figure 11. We see that successive replacement of A with B lowers the free energy. The 14 ACS Paragon Plus Environment

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network of reactions (involving many more transition states and tetrahedral intermediates) connecting these eight structures in Figure 12 is beyond the scope of the present study, and we look forward to teasing out the details in future work. Acknowledgements This research was supported by a Camille and Henry Dreyfus Teacher-Scholar award. Shared computing facilities were provided by the saber1 high-performance computer at the University of San Diego. Supporting Information Supporting Information includes (1) additional structural information and energies of trimer intermediates, imino esters and ring structures, (2) detailed structures and energies of zwitterions, (3) energy maps excluding solvation energy, and (4) XYZ coordinates of all optimized structures. References 1. Miller, S. L. A Production of Amino Acids under Possible Primitive Earth Conditions. Science 1953, 117, 528-529. 2. Miller, S. L.; Urey, H. C. Organic Compound Synthesis on the Primitive Earth. Science 1959, 130, 245-251. 3. Miller, S. L. The Atmosphere of the Primitive Earth and the Prebiotic Synthesis of Amino Acids. Orig Life 1974, 5, 139-151. 4. Pizzarello, S.; Huang, Y.; Alexandre, M. R. Molecular Asymmetry in Extraterrestrial Chemistry: Insights from a Pristine Meteorite. Proc Natl Acad Sci USA 2008, 105, 3700-3704. 5. Martin, R. B. Free Energies and Equilibria of Peptide Bond Hydrolysis and Formation. Biopolymers 1998, 45, 351-353. 6. Fox, S. W. H., K. Thermal Copolymerization of Amino Acids to a Product Resembling Protein. Science 1958, 128, 1214. 7. Yanagawa, H.; Kojima, K.; Ito, M.; Handa, N. Synthesis of Polypeptides by Microwave Heating I. Formation of Polypeptides During Repeated Hydration-Dehydration Cycles and Their Characterization. J Mol Evol 1990, 31, 180-186. 8. Imai, E.; Honda, H.; Hatori, K.; Brack, A.; Matsuno, K. Elongation of Oligopeptides in a Simulated Submarine Hydrothermal System. Science 1999, 283, 831-833. 9. Sakata, K.; Kitadai, N.; Yokoyama, T. Effects of pH and Temperature on Dimerization Rate of Glycine: Evaluation of Favorable Environmental Conditions for Chemical Evolution of Life. Geochim. Cosmochim. Acta 2010, 74, 6841-6851.



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10. Biron, J. P.; Pascal, R. Amino Acid N-Carboxyanhydrides: Activated Peptide Monomers Behaving as Phosphate-Activating Agents in Aqueous Solution. J. Am. Chem. Soc. 2004, 126, 9198-9199. 11. Brack, A. From Interstellar Amino Acids to Prebiotic Catalytic Peptides: A Review. Chem Biodivers 2007, 4, 665-679. 12. Danger, G.; Plasson, R.; Pascal, R. Pathways for the Formation and Evolution of Peptides in Prebiotic Environments. Chem. Soc. Rev. 2012, 41, 5416-29. 13. Forsythe, J. G.; Yu, S. S.; Mamajanov, I.; Grover, M. A.; Krishnamurthy, R.; Fernandez, F. M.; Hud, N. V. Ester-Mediated Amide Bond Formation Driven by Wet-Dry Cycles: A Possible Path to Polypeptides on the Prebiotic Earth. Angew. Chem. Int. Ed. Engl. 2015, 54, 9871-9875. 14. Kua, J.; Avila, J. E.; Lee, C. G.; Smith, W. D. Mapping the Kinetic and Thermodynamic Landscape of Formaldehyde Oligomerization under Neutral Conditions. J. Phys. Chem. A 2013, 117, 12658-12667. 15. Kua, J.; Galloway, M. M.; Millage, K. D.; Avila, J. E.; De Haan, D. O. Glycolaldehyde Monomer and Oligomer Equilibria in Aqueous Solution: Comparing Computational Chemistry and NMR Data. J. Phys. Chem. A 2013, 117, 2997-3008. 16. Kua, J.; Rodriguez, A. A.; Marucci, L. A.; Galloway, M. M.; De Haan, D. O. Free Energy Map for the Co-Oligomerization of Formaldehyde and Ammonia. J. Phys. Chem. A 2015, 119, 2122-2131. 17. Kua, J.; Thrush, K. L. HCN, Formamidic Acid, and Formamide in Aqueous Solution: A Free Energy Map. J. Phys. Chem. B 2016, 120, 8175-8185. 18. Kua, J.; Krizner, H. E.; De Haan, D. O. Thermodynamics and Kinetics of Imidazole Formation from Glyoxal, Methylamine, and Formaldehyde: A Computational Study. J. Phys. Chem. A 2011, 115, 1667-1675. 19. Jaguar v6.0; Schrodinger, LLC: Portland, OR, 2005. 20. Vosko, S. H.; Wilk, L.; Nusair, M. Accurate Spin-Dependent Electron Liquid Correlation Energies for Local Spin Density Calculations: A Critical Analysis. Can. J. Phys. 1980, 58, 12001211. 21. Becke, A. D. Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys. Rev. A 1988, 38, 3098-3100. 22. Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785-789. 23. Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648-5652. 24. Krizner, H. E.; De Haan, D. O.; Kua, J. Thermodynamics and Kinetics of Methylglyoxal Dimer Formation: A Computational Study. J. Phys. Chem. A 2009, 113, 6994-7001. 25. Spartan '04; Wavefunction, Inc: Irvine, CA, 2004. 26. Halgren, T. A. Merck Molecular Force Field. I. Basis, Form, Scope, Parameterization, and Performance of Mmff94. J. Comput. Chem. 1996, 17, 490-519. 27. Tannor, D. J.; Marten, B.; Murphy, R.; Friesner, R. A.; Sitkoff, D.; Nicholls, A.; Honig, B.; Ringnalda, M.; Goddard, W. A., III Accurate First Principles Calculation of Molecular Charge Distributions and Solvation Energies from Ab Initio Quantum Mechanics and Continuum Dielectric Theory. J. Am. Chem. Soc. 1994, 116, 11875-11882. 28. Marten, B.; Kim, K.; Cortis, C.; Friesner, R. A.; Murphy, R. B.; Ringnalda, M. N.; Sitkoff, D.; Honig, B. A New Model for Calculation of Solvation Free Energies: Correction of 16 ACS Paragon Plus Environment

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Self-Consistent Reaction Field Continuum Dielectric Theory for Short Range HydrogenBonding Effects. J. Phys. Chem. 1996, 100, 11775-11788. 29. Warshel, A.; Florian, J. Computer Simulations of Enzyme Catalysis: Finding out What Has Been Optimized by Evolution. Proc. Natl. Acad. Sci. 1998, 95, 5950-5955. 30. Wiberg, K. B.; Bailey, W. F. Chiral Diamines 4: A Computational Study of the Enantioselective Deprotonation of Boc-Pyrrolidine with an Alkyllithium in the Presence of a Chiral Diamine. J. Am. Chem. Soc. 2001, 123, 8231-8238. 31. Nielsen, R. J.; Keith, J. M.; Stoltz, B. M.; Goddard, W. A., 3rd A Computational Model Relating Structure and Reactivity in Enantioselective Oxidations of Secondary Alcohols by (-)Sparteine-Pd(II) Complexes. J. Am. Chem. Soc. 2004, 126, 7967-7974. 32. Deubel, D. V.; Lau, J. K. In Silico Evolution of Substrate Selectivity: Comparison of Organometallic Ruthenium Complexes with the Anticancer Drug Cisplatin. Chem. Commun. 2006, 2451-2453. 33. Wertz, D. H. Relationship between the Gas-Phase Entropies of Molecules and Their Entropies of Solvation in Water and 1-Octanol. J. Am. Chem. Soc. 1980, 102, 5316-5322. 34. Abraham, M. H. Relationship between Solution Entropies and Gas Phase Entropies of Nonelectrolytes. J. Am. Chem. Soc. 1981, 103, 6742-6744. 35. Liang, Y.; Liu, S.; Xia, Y.; Li, Y.; Yu, Z. X. Mechanism, Regioselectivity, and the Kinetics of Phosphine-Catalyzed [3+2] Cycloaddition Reactions of Allenoates and ElectronDeficient Alkenes. Chem. Eur. J. 2008, 14, 4361-4373. 36. Huang, F.; Lu, G.; Zhao, L.; Li, H.; Wang, Z. X. The Catalytic Role of N-Heterocyclic Carbene in a Metal-Free Conversion of Carbon Dioxide into Methanol: A Computational Mechanism Study. J. Am. Chem. Soc. 2010, 132, 12388-12396. 37. Liu, W. G.; Sberegaeva, A. V.; Nielsen, R. J.; Goddard, W. A.; Vedernikov, A. N. Mechanism of O-2 Activation and Methanol Production by (Di(2Pyridyl)Methanesulfonate)(PtMe)-Me-II(OHn)((2-N)-) Complex from Theory with Validation from Experiment. J. Am. Chem. Soc. 2014, 136, 2335-2341. 38. Nandini, G.; Sathyanarayana, D. N. Ab Initio Studies of Solvent Effects on Molecular Conformation and Vibrational Spectra of Diglycine Zwitterion. J. Phys. Chem. A 2003, 107, 11391-11400. 39. Van Dornshuld, E.; Vergenz, R. A.; Tschumper, G. S. Peptide Bond Formation Via Glycine Condensation in the Gas Phase. J. Phys. Chem. B 2014, 118, 8583-8590.



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Figure 1. Overall Reaction Scheme. All free energies are in kcal/mol.


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Figure 2. Formation of an Ester Dimer from Monomers. All free energies are in kcal/mol.



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Figure 3. Formation of an Amide Dimer from Monomers. All free energies are in kcal/mol.


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Figure 4. Transition States for BA Formation from Monomers.



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Figure 5. Ring Closure of AA and AB. All free energies are in kcal/mol.


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Figure 6. Ring Closure of BA and BB. All free energies are in kcal/mol.



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Figure 7. Transition States for Ring Closure of BB to BB6.


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Figure 8. Ester-Mediated Amide Bond Formation in Dimers. All free energies are in kcal/mol.



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Figure 9. Transition States for Conversion of AA to BA.


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Figure 10. Reactions of triglycine.



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Figure 11. Modified Reaction Scheme with Zwitterion Stabilization. All free energies are in kcal/mol.


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Figure 12. Relative Free Energies of Linear Trimers. All energies are in kcal/mol.



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Table 1. Energies of Stable Species. All energies are in kcal/mol except where indicated (Eelec is in a.u.). Eelec (a.u.) H2 O -76.44744 A -304.38813 B -284.51808 Dimers AA -532.32237 BA -512.45665 AB -512.45245 BB -492.59001 AA6 -455.84157 BA6/AB6 -435.98542 BB6 -416.12627 Tetrahedral Intermediates AAtet -608.77223 ABtet -588.90098 BAtet -588.90163 BBtet -569.02714 AA6tet -532.29678 BA6tet -512.43828 AB6tet -512.42391 BB6tet -492.56499 AxBAtet -816.83781 AxBBtet -796.96507 Trimers AAA -760.25704 BAA -740.39491 ABA -740.39387 BBA -720.52651 AAB -740.38704 BAB -720.52173 ABB -720.52486 BBB -700.66109 BB6B -624.17927 BB5B -624.17515 BBB9 -624.17662 B6B5B -547.71445

Esolv

Hcorr

Gcorr

-0.5TScorr

G298

-8.11 -10.98 -12.13

15.74 45.93 54.15

2.30 23.75 31.81

-6.72 -11.09 -11.17

-47970.59 -190982.61 -178506.98

-14.18 -20.68 -15.43 -18.47 -10.67 -15.64 -19.87

75.53 83.85 83.68 91.71 56.88 65.63 73.32

46.29 54.08 53.89 61.55 32.82 40.92 49.22

-14.62 -14.89 -14.90 -15.08 -12.03 -12.36 -12.05

-333990.67 -321523.18 -321515.48 -309046.80 -286010.78 -273547.40 -261081.83

-18.34 -16.65 -19.94 -21.02 -14.99 -18.74 -18.95 -22.81 -23.22 -23.44

93.92 101.84 102.15 110.28 75.63 83.74 83.91 92.11 131.61 140.52

64.03 71.26 72.37 80.09 49.41 57.21 57.41 65.60 95.74 103.73

-14.95 -15.29 -14.89 -15.10 -13.11 -13.27 -13.25 -13.26 -17.94 -18.40

-381949.78 -369471.12 -369474.11 -356995.83 -333973.81 -321508.21 -321499.21 -309033.21 -512483.11 -500004.55

-17.20 -21.10 -23.18 -29.10 -18.47 -23.05 -21.72 -26.41 -23.89 -20.52 -27.89 -21.81

104.50 112.44 112.80 120.72 113.26 120.75 121.43 129.47 111.07 110.91 112.02 92.76

70.03 76.68 77.99 84.95 75.99 84.49 84.17 92.15 79.17 79.05 82.18 64.91

-17.24 -17.88 -17.41 -17.89 -18.64 -18.13 -18.63 -18.66 -15.95 -15.93 -14.92 -13.93

-476998.53 -464531.45 -464532.05 -452063.57 -464523.82 -452054.73 -452055.19 -439587.16 -391607.25 -391601.44 -391607.61 -343639.05


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Table 2. Transition State Energies. All energies are in kcal/mol except where indicated (Eelec is in a.u.). Eelec (a.u.) AAts1 AAts2 ABts1 ABts2 BAts1 BAts2 BBts1 BBts2 AA6ts1 AA6ts2 AB6ts1 AB6ts2 BA6ts1 BA6ts2 BB6ts1 BB6ts2 AxBAts1 AxBAts2 AxBBts1 AxBBts2

-761.68360 -761.67917 -741.80423 -741.80232 -741.81035 -741.80393 -721.94214 -721.93125 -685.20157 -685.19591 -665.34265 -665.32986 -665.34223 -665.33443 -645.48515 -645.47343 -969.73746 -969.74327 -949.87213 -949.87119

Esolv -21.90 -21.50 -27.14 -25.40 -27.02 -23.79 -26.03 -25.31 -20.71 -24.24 -22.05 -22.82 -26.50 -28.38 -26.29 -25.91 -33.51 -29.83 -32.29 -32.05

Hcorr 123.11 125.74 130.86 133.25 132.82 130.34 140.97 139.00 104.77 104.06 114.83 112.16 112.74 112.33 123.05 121.57 160.48 162.47 169.11 170.09

Gcorr 86.25 90.92 94.51 98.29 97.60 93.51 105.43 101.44 72.44 72.76 83.99 79.13 80.57 80.38 92.15 89.10 117.93 119.28 126.91 127.00

-0.5TScorr -18.43 -17.41 -18.18 -17.48 -17.61 -18.42 -17.77 -18.78 -16.17 -15.65 -15.42 -16.52 -16.09 -15.98 -15.45 -16.24 -21.28 -21.60 -21.10 -21.55

G298 -477880.99 -477874.16 -465403.73 -465397.71 -465404.93 -465400.95 -452928.45 -452923.88 -429902.67 -429902.84 -417431.54 -417428.05 -417438.48 -417435.77 -404966.82 -404961.35 -608413.87 -608412.17 -595938.16 -595936.80



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Preliminary Oligomerization in a Glycolic AcidâGlycine Mixture: A Free

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