Theoretical investigation of the relationship between four-carbon d -sugars and five l -amino acids

Tetrahedron xxx (2016) 1e5

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Theoretical investigation of the relationship between four-carbon D-sugars and five L-amino acids Dan Zhao a, Qi-Qi Zhao a, Hua-Jie Zhu a, *, Li Liu b a b

Chinese Center for Chirality, School of Pharmacy, Hebei University, 071002, Baoding, China Health Science Center, Hebei University, 071002, Baoding, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 4 July 2016 Accepted 15 July 2016 Available online xxx

This study constructed the relationship between L-amino acids and four-carbon D-sugar using quantum theory. Theoretically, an L-amino acid could react with the ketone to afford the corresponding Schiff base which may take place an Aldol reaction with a molecule of formaldehyde. An assumption is proposed that the Aldol addition products with (R) or (S) configuration could have different quantity due to the effect from stereogenic center of L-amino acid. By hydrolysis of the Aldol addition, different D- or L-sugar would form. Thus, B3LYP, WP1MPW91 and wB97XD theories were used for the energy difference computations at the 6-311þþG(2d,p) level in the gas phase, or in water using PCM and SMD model, respectively. The predicted ee value sequence agrees well to the experimental result in the asymmetric synthesis of 3-carbon sugar using five L-amino acids. Further theoretical study exhibited that 4-carbon D sugar should form if the corresponding L-amino acid is used. The ee values of the 4-carbon sugar are bigger than those of 3-carbon D-sugars catalyzed by the same L-amino acids. This looks like the chiral amplification in the procedure. Ó 2016 Elsevier Ltd. All rights reserved.

Keywords: D-Sugar L-Amino acids Conformational study Energy difference DFT

1. Introduction Until now, researchers don’t know the relationship between an acid and a four-carbon D-sugar. An L-amino acid is the key synthetic unit to protein, and the D-sugar is the important material to afford cellulose, also the energy sources for life use. Formation of both L-amino acids and D-sugars in the origin of life has puzzled and attracted many scientists to explore it, such as Cech’s study (RNA first, where RNA can act as a substrate and/or an enzyme);1 and protein-mediated for evolution et al.2 It is reported that five (S)-a-methyl amino acids (L-type) with ee values from 2.8% to 15.2% were found in meteorites that landed on Earth near Murchison Australia in 1969,3 they have a chiral quaternary carbon instead of tertiary carbon, which exhibits the stereogenic center could not take racemization. The abnormal amino acids may play a role in formation of normal L-amino acids or Dsugars due to its weak catalysis.4 Other discoveries included the right polarized UV light from the universal led to selective destruction of D-amino acids, resulting in a mixture with a few percent excess of the L-enantiomer,5 or the polarized UV from neutron stars.6 Breslow and co-workers studied the conversion of (S)-amethyl amino acids to normal L-amino acids with about 1% ee values catalyzed by Cu(II),7 and this small ee of L-amino acids may L-amino

* Corresponding author. E-mail address: [email protected] (H.-J. Zhu).

be enriched by amplification,8 for example, via different solubility of salts of D-, L-amino acid crystals; or the different solubility of ribonucleosides produced the chiral amplifications.9 Recently, Breslow and co-workers reported that some meteoritic components can be used to furnish normal L-amino acids, D-sugars and nucleosides, in high chiral excess under sensible prebiotic conditions.4,10 For example, when a pure L-valine (4) was used, 5.4% ee of three-carbon D-sugar (8) formed from formaldehyde (6) (Scheme 1), this ee value increased to 19.2% under the pH

Scheme 1. (left in dash frame) Formation of three-carbon sugar (8) from CHO; (right) L-amino acids used in the chiral catalytic formation of 8.

http://dx.doi.org/10.1016/j.tet.2016.07.047 0040-4020/Ó 2016 Elsevier Ltd. All rights reserved.

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values of 2.9e4.2. L-Glutamic acid (5) led to 21.4% ee formation of 8 or 34.8% under the same acidic conditions. Under the prebiotic conditions, the atmosphere contained huge CO2, which could dissolve in water and lead to water having about pH value of 5.6. This datum is smaller than 4.2 but larger than 6.5. Thus, this weak acidic condition could be a good benefit to synthesize D-sugar in prebiotic environment. This discovery is extremely important and valid. A logical question then rises: should the other D-sugars such as 4-carbon sugar could form via the similar procedure? However, there is no any experimental or theoretical investigation to show asymmetric formation of four-carbon sugar (C4H8O4, 9) or others catalyzed by Lamino acids. In this study, we investigate the asymmetric formation of four-carbon sugar catalyzed by different L-amino acids. The prediction clearly exhibits that high ee values of four-carbon sugar, theoretically, could be obtained using the corresponding L-amino acids, such as phenylalanine. 2. Theoretical section Theoretically, an L-amino acid could react with hydroxyl acetaldehyde (7) to form the corresponding Schiff base 12 (Scheme 2). The second CHO molecule would react with the intermediate 12 to afford 13 with either (R) or (S) configuration at C-2 in different ratio, which would depend on the both of (1) their relative energy differences and the (2) Aldol reaction activation energy barrier. Base on the reports from Breslow,4,10 the Aldol reaction could take place at room temperature to afford 13, that means the activation energies (DG1 and DG2 in Fig. 1) are not high. Therefore, this Aldol reaction is reversible at room temperature. The distributions of products (2R,20 S)-13 and (2S,20 S)-13 should majorly depend on their energy differences (DE in Fig. 1). The bigger the relative energy difference is, the bigger the quantity difference of (2R,20 S)-13 and (2S,20 S)-13 should be. Namely, the higher the de value will be. After

the Aldol addition, this intermediate 13 could decompose into the corresponding D- or L-sugar 8 and the L-amino acid in water, respectively. Thus, the de values of 13 should be the same as ee values of the sugar 8. In this report, activation energy barriers are not considered since the reaction could take place at room temperature. For a clear statement, (R)-13 and (S)-13 are used, respectively, to representative (2R,20 S)-13 and (2S,20 S)-13, and the de values of the intermediate 13 should be regarded as the ee values of the corresponding D-sugar.

3. Computational section and discussion The calculations were performed using density functional theory (DFT),11 because energies,12 analytic gradients, and true analytic frequencies,13 are available for all DFT models. We used the B3LYP,14 WP1MPW91,15 and wB97XD16 theories at the bases sets of 6311þþG(2d,p) in calculations.17 Frequency calculations were also performed.18 Solvent effects were modeled through the use of the polarizable continuum model (PCM)19 and solvation model density (SMD),20 respectively. In our recent study, the methods mentioned above exhibited valid data to explain the experimental data by conformational study.21 The conformations of (R)-13 and (S)-13 were searched using different conformational search packages, such as ComputeVOA, Barista, respectively, via MMFF94S force field. All conformations that were found were used in optimizations at the B3LYP/6-31G(d) level in the gas phase first. These geometries with relative energy from 0 to 2.5 Kcal/mol were used for further optimizations using five different quantum methods. The first one is to optimize the B3LYP/6-31G(d)-conformations at the B3LYP/6-311þþG(2d,p) level in the gas phase (method 1). The second one is to use the B3LYP/6311þþG(2d,p)-optimized geometries in optimizations at the same level in water using PCM model (method 2). The third method is to optimize the B3LYP/6-31G(d)-geometries at the WP1PW91/6311þþG(2d,p) level in the gas phase (method 3), and then these WP1PW91/6-311þþG(2d,p)-optimized conformers were recomputed at the same level in water using PCM model (method 4). Finally, the geometries were then optimized at the wB97XD/6311þþG(2d,p) level in water using SMD model (method 5). The smallest energy differences between (R)-13 and (S)-13 were then computed using the lowest energy of (R)-13 and (S)-13. Every method can afford its corresponding smallest energy difference. Then, the differences were used for quantity computations of (R)-13 and (S)-13, respectively, using Arrhenius Eq. 1.

Q ¼ keDE=RT

Scheme 2. Formation of three-carbon sugar (8) catalyzed by L-amino acids.

(1)

where Q is the quantity of intermediate (R)-13 or (S)-13, k is a constant, R is the gas constant (8.314 J mol1 k1), T is the absolute temperature, 298 K is used in the calculations. DE is the

Fig. 1. Coordinates for plausible reaction paths from mixture of 12 and CH2O to 13. Herein, (R)-13 and (S)-13 are used, respectively, to representative (2R,20 S)-13 and (2S,20 S)-13. Two cases exist in the procedure. Case 1: the reaction barrier (DG2) to (S)-13 is higher than that to (R)-13 (DG1); case 2: the reaction barrier (DG2) to (S)-13 is smaller than that to (R)-13 (DG1). Since the sugar obtained has D-type of AC, the product (S)-13 should have lower relative energetics than (R)-13.

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energy difference. Then, the ratio of (S)-13 to (R)-13 should be computed using Eq. 2:

QS eDES =RT ¼ DE =RT ¼ eðDES DER Þ=RT R QR e

(2)

On the other hand, the sum of fractions of (R) and (S)-isomers should be 1 (Eq. 3):

QS þ QR ¼ 1

(3)

Combinational uses of Eqs. 2 and 3, we can compute the de values for (R)-13 and (S)-13 for each method. The results are summarized in Table 1. Table 1 The relative energy of intermediate (R)-13 and (S)-13 and the predicted ee for D-sugar 8 and experimental ee values Entry Amino Method DE(SeR) of 13 (kcal/mol) acid DETa DE0 DG

Calcd ee (%) for 8e

DET

DE0

DG

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

32.3 11.1 8.3 11.6 18.4 83.9 79.2 84.4 85.7 75.6 48.0 43.3 100.0 49.7 53.4 18.3 15.0 22.4 12.1 23.0 93.3 91.3 89.0 98.2 98.0

36.2 10.7 23.4 12.9 12.1 73.8 48.0 72.7 60.3 64.9 40.2 41.3 44.4 40.7 282 18.6 12.1 11.7 22.1 29.1 93.9 90.2 93.8 92.5 98.0

13.3 13.9 34.4 20.8 54.4 70.0 44.7 24.9 31.8 50.0 7.7 54.6 53.5 63.4 32.1 10.7 32.2 36.3 6.2 24.3 90.2 75.9 90.7 82.6 98.5

1

2

3

4

5

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

0.396 0.132 0.098 0.138 0.220 1.439d 1.273 1.459 1.515 1.168 0.618 0.548 0.898 0.645 0.705 0.219 0.178 0.269 0.144 0.277 1.993 1.829 1.680 2.767 2.726

0.448 0.126 0.282 0.153 0.144 1.119 0.618 1.091 0.825 0.916 0.504 0.520 0.564 0.511 0.343 0.222 0.143 0.139 0.265 0.355 2.048 1.757 2.037 1.920 2.730

0.158 0.165 0.424 0.250 0.420 1.027 0.569 0.301 0.390 0.649 0.091 0.725 0.707 0.884 0.393 0.127 0.395 0.450 0.074 0.294 1.757 1.176 1.785 1.392 2.875

Exp. ee (%) 1.6b

0.6b

5.4b

5.4b 19.0c

21.4b 34.8c

a DET: Total electronic energy difference. DE0: Zero-point energy difference. DG: Gibbs free energy difference. b See Ref. 10 for details, the pH values were not mentioned in this reference. c pH values in reactions were from 2.9 to 4.3. See Ref. 4 for more details. d The italic data means the results do not agree to the experiments. e The ee values of D-sugar 8 equal to the de values of 13.

As mentioned above, the de values of 13 should be the same as the ee value of sugar 8 obtained in experiments. Therefore, the de values of 13 should be used as the ee values of D-sugar in the following discussion. The best prediction is to use method 2 to predict the ee values of sugar 8 catalyzed by L-valine. The predicted ee

3

values were 12.1%, 22.1% and 6.2% using the total electronic energy, zero point energy and Gibbs free energy, respectively. The experimental ee was 5.4%, or 19% under the acidic condition (pH¼2.9e4.2). Method 4 predicted well for (R)-13 using L-valine (4) using the three kind of energies, especially using Gibbs free energy in ee predictions (6.2% predicted vs 5.4% in experiments). Another good prediction way is method 1 by using Gibbs free energy, the predicted ee value is 7.7% (entry 11), and the experimental ee was 5.4%. Methods 1 and 3 cannot predict the accurate energy differences. Among all five computational methods, method 5 gave the poorest prediction, for example, only the predicted ee value (smallest ee is 12.1%) for L-alanine (1) closed to the experimental ee % (1.6%), other predictions did not match the experimental results (Table 1, entries 10, 15, 20 and 25). It was found that L-type sugar might produce under weak basic condition (pH¼8e9) or neutron condition (pH¼6.5e7.5) with a small ee value.4 However, this reaction system could be of a weak acidic environment since the formation of Schiff base (12) led to the relative strong conjugation formation of lone pair of electrons of N atom to the sp2 C, which can reduce the base of N atom. Thus, the whole molecule should exhibit weak acidic. This is helpful formation of D-type sugar. It is amazing that the predicted product should be L-sugar using L-glutamic amino acid and L-serine (Table 1, entries 6e10 and 21e25). These are conflict to the experimental results. Why only the two predictions disagree with the experimental results? The possible reason may be the characteristics of the two amino acids. For example, serine (5) has a terminal eOH and glutamic amino acid (5) has a eCOOH. Both groups easily form H-bonds with other terminal eOH in intermediate 13, affording a big head-tail connection cyclic structure when conformational search is performed (Fig. 2). Such a big cyclic structure is not easily formed under water since the huge number of water molecules could break down the head-tail connected circle. For example, it should be a 9-atom ring structure in the intermediate 13 using L-serine and 11-atom ring structure using L-glutamic amino acid, respectively (Fig. 2). The formation of H-bonds may change the energy sequence of (R)-13 and (S)-13. Other amino acids, such as L-alanine (1) L-phenylalanine (3) and L-valine (4) had no any terminal eOH or eCOOH, they could not form such big head-tail connected structures in 13. The energy sequences predicted using these L-amino acids agree to the experimental results. Therefore, the real head-tail connection structure may not exist in real case. To examine the assumption, the lowest energy geometries of (R)-13 and (S)-13 using L-glutamic amino acid and L-serine were analyzed (Fig. 2). As the expected, both (R)-13 and (S)-13 using L-glutamic amino acid formed the headetail connected circle with two H-bonds. (R)-13 using L-serine formed head-tail connected structure with one H-bond while (S)13 did not form H-bond using L-serine. Obviously, the ring sizes of 9-atom could be easily broken in water environment. If all of the head-tail connected structures using L-serine and Lglutamic acid are removed from the energy computations and

Fig. 2. The cyclic head-tail connection structures of (R)-13 and (S)-13 catalyzed by L-glutamic amino acid and L-serine.

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analysis, the energy difference sequence of (R)-13 and (S)-13 may reversed. Therefore, all of the conformations without the head-tail connections were used in the computations using the four methods. The calculation results are listed in Table 2. Fortunately, the predicted sugar should be D-type using L-serine now, its ee value was 11% (entry 3, Table 2), the experimental value is only 0.6. The D-sugar was also predicted with ee values of 34e95% catalyzed Table 2 The relative energy differences of intermediate 13 with (R) or (S) configuration at C-2 catalyzed by L-glutamic amino acid and L-serine, respectively Entry Amino Method DE(SeR) of 13 (kcal/mol) acid DET DE0 DG 1 2 3 4 5 6 7 8 9 10 a b c

2

5

1 2 3 4 5 1 2 3 4 5

0.913 0.785 1.298 0.873 1.776 0.053 0.216c 0.028 0.175 0.371

0.800 0.746 1.217 0.777 1.080 0.069 0.358 0.055 0.233 0.242

0.349 0.452 0.656 0.331 0.452 0.624 0.527 0.218 0.355 0.274

Calcd ee (%) for 8

DET

DE0

DG

64.8 58.1 79.9 62.8 90.5 4.5 18.0 2.3 14.7 30.4

58.9 55.8 77.3 57.6 72.2 5.8 29.4 4.7 19.5 20.1

28.7 36.4 50.4 27.3 36.4 48.4 41.8 18.2 29.1 22.8

Exp. ee (%) 0.6a

21.4a 34.8b

See Ref. 10 for details, the pH values were not mentioned in this reference. pH values in reactions was from 2.9 to 4.3. See Ref. 4 for details. The italic number means the major product should be (R)-13 instead of (S)-13.

by L-glutamic acid using methods 1 and 3. The experimental ee values were 21.4% or 34.8% under an acidic condition. Unfortunately, the methods 2 and 4 predicted the L-sugar should form instead of D-sugar when catalyzed by L-glutamic acid. Method 5 now predicted close to the experimental results (Table 2, entries 5 and 10). This clearly exhibited the head-tail connection with a big ring structure is not available in water. Among all calculation methods, method 2 is recommended for further computations in relative energy computation. Similarly, L- or D-type of 4-carbon sugar (10) could form via the corresponding intermediates (3R,20 S)-15 and (3S,20 S)-15 (Scheme 3). After conformational searches for 15, all conformers

15, respectively, for each computational method. The results are summarized in Table 3. Table 3 Predicted relative energy of (R)-15 and (S)-15 and their ee values for D-sugar 10 catalyzed by the five L-amino acids Entry Amino acid Method DE(SeR) of 15 (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

1

2

3

4

5

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

Calcd ee (%) for 10b

DET

DE0

DG

DET

DE0

DG

0.628 1.956 0.564 1.885 1.251 0.038 0.107 0.788 0.486 1.296 1.221 1.336 0.769 0.726 0.386 0.240 1.750 0.091 1.501 0.137 1.428 0.274 1.878 0.513 1.108

0.331 1.653 0.330 1.600 0.873 0.049 0.116 0.651 0.415 1.394 1.087 1.216 0.973 0.967 0.435 0.193 1.260 0.312 1.034 0.339 1.584 0.298 2.028 0.367 0.893

0.564 0.389 0.670 0.469 0.247 0.759 0.639 0.108 0.120 1.289 1.209 0.104 1.740 1.784 0.067 0.377 0.116 0.709 0.440 0.661 0.535 1.459 0.772 1.359 0.873

48.6 92.9 44.4 92.1 78.5 3.3 9.0 58.2 38.9 79.9 77.5 81.1 57.2 54.7 31.5 20.0 90.1 7.7 85.3 11.6 83.6 22.8 92.0 40.8 73.4

27.3 88.5 27.2 87.5 62.8 4.2 9.8 50.1 33.7 83.7 72.5 77.3 67.7 67.4 35.2 16.2 78.8 25.8 70.4 27.9 87.1 24.7 93.7 30.1 63.8

44.4a 31.7 51.3 37.7 20.6 56.6 49.3 9.2 10.1 79.7 77.1 8.8 90.0 90.6 5.6 30.9 9.8 53.6 35.6 50.7 42.3 84.3 57.3 81.7 62.8

a The italic numbers mean the major product should be (R)-15 instead of the expected (S)-15. b The de values of 15 should be the same as the ee values of 10, and therefore, the ee values are used here.

Intermediate (S)-15 can decompose into the corresponding fourcarbon D-sugar, this case is similar to the one that (S)-13 can decompose into the corresponding three-carbon D-sugar. The de

Scheme 3. (left in dash frame) Formation of four-carbon sugar (10) from CHO; (right) L-amino acids used in chiral catalytic formation of 10.

that were recorded by MMFF94S force field were then used in optimizations at the B3LYP/6-31G(d) level in the gas phase. Then, the five methods mentioned above were used for optimizations of all conformers of 15 with relative energy from 0 to 2.5 Kcal/mol. Again for clarity, (R)-15 and (S)-15 were, respectively, used to representative (3R,20 S)-15 and (3S,20 S)-15 in the following discussions. The quantity differences were then calculated between the lowest energy conformer of (S)-15 and the lowest energy conformer (R)-

values of 15 should be also equal to the ee values of the four-carbon D-sugar 10. Thus, as mentioned above, the de values predicted for 15 should equal to the ee of four-carbon D-sugar in the following discussions. It is found that the method 2 predicted all the sugar formed should be D-type catalyzed by the five L-amino acids except for L-4 as a catalyst when Gibbs free energy values were used (entry 17). More importantly, the most predicted ee values for D type of

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4-carbon sugar are bigger than those of 3-carbon sugar using the same L amino acid. For a clear comparison, the energy differences and ee values of 10 catalyzed by L-1 and L-4 are copied, respectively, to Table 4. The ee values for D-type sugar 10 could reach about 31% predicted by Gibbs free energy, or 88% by zero-point energy catalyzed by L-1 (entry 2), or 78% using zero-point energy catalyzed by L-4 if the method 2 has the same reliability as used in the predicted ee values for D-sugar 8. Considering this reality, as two parallel of computations, it could be concluded that method 2 should be more reliable in the predictions of ee for 13 using the same amino acid. Table 4 Comparison of the de values predicted for (R)-13 and (S)-13, (R)-15 and (S)-15 using L-1 and L-4, respectively, as the catalysts Orig. Entry Amino acid Method DE(SeR) of 13 (kcal/mol)

2 4 14 16

1

2 4 14 16

1

4

2 4 2 4

DET

DE0

DG

DET

DE0

DG

0.132 0.138 0.178 0.144

0.126 0.153 0.143 0.265

0.165 0.250 d d

11.1 11.6 15.0 12.1

10.7 12.9 12.1 22.1

13.9 20.8 d d

Calcd 92.9 92.1 90.1 85.3

ee (%) 88.5 87.5 78.8 70.4

for 10a 31.7 37.7 d d

DE(SeR) of 15 (kcal/mol) 4

2 4 2 4

Calcd ee (%) for 8a

1.9565 1.8850 1.7507 1.5010

1.653 1.600 1.260 1.034

0.389 0.469 d d

a Intermediate (S)-13 and (S)-15 could decomposed into the corresponding Dsugar, thus, their de values should equal to the ee values of the corresponding sugars, therefore, the de values of (S)-13 and (S)-15 are regarded as the ee values of 8 and 10, respectively.

4. Summary This report investigated the ee values of the sugars (8 and 10), which derived from the Aldol reaction of Schiff bases formed from 2-hydroxyacetaldehyde and 1,3-dihydroxypropan-2-one with five L-amino acids, with CHO, respectively. The best method used in predictions of ee data of D-sugars is the level of B3LYP/6311þþG(2d,p) in water using PCM model based on the experimental and theoretical data. Acknowledgements H. J. Zhu thanks the financial supports from Hebei University, and the High Performance Computer Center of Hebei University.

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Please cite this article in press as: Zhao, D.; et al., Tetrahedron (2016), http://dx.doi.org/10.1016/j.tet.2016.07.047