Multilayered substructures of a non-enzymatic chemical reaction network for synthesizing sugars

The formose reaction performed using γ-Al₂O₃ and phosphates catalysts

The overlapping behavior of multiple substructures within the formose reaction was investigated using γ-Al₂O₃ and PB. Experiments were conducted in batch reactors, where time-course data for pH, as well as concentrations of the substrate (HCHO) and products, were collected. The reaction mixture contained aqueous methanol (10 vol%) as the solvent, 300 mM HCHO as the substrate, 3 mM C2 as the initiator, and either γ-Al₂O₃ (50 mg mL⁻¹) or γ-Al₂O₃ with PB (γ-Al₂O₃-PB), where γ-Al₂O₃ was combined with 50 mM PB. The reaction was heated at 80 °C for 72 h (Fig. 2a).

a Reaction conditions of the time-course experiments using a batch reactor. γ-Al₂O₃ or γ-Al₂O₃-PB were applied as a single and multiple catalysts, respectively. b Chromatograms of the HPLC analysis for sugars. Analyses were performed after the reaction with γ-Al₂O₃ (black line) and γ-Al₂O₃-PB (red line) for 15 h and 6 h, respectively. c, d Time courses of pH (i), concentration of HCHO (ii), and concentrations of reaction intermediates of the formose reaction (iii-vii) using γ-Al₂O₃ (c) and γ-Al₂O₃-PB (d) as catalysts. The chromatograms in (b) correspond to the reaction times indicated by the black and red dotted lines in (c, b), respectively. Plots and error bars represent the means of three trials and the 95% confidence intervals, respectively.

Quantitative analyses of the substrate and products during the reaction were performed using high-performance liquid chromatography (HPLC) systems. A reverse-phase column was used for analyzing HCHO and sugars with four or fewer carbon atoms, while a second HPLC system (Chromaster®, Hitachi) was used for the analysis of sugars containing five or six carbon atoms (C5 and C6, respectively). Product quantification was carried out using calibration curves generated with commercially available standards (details are provided in the Method section and Supplementary Fig. 2)²⁹. Figure 2b presents HPLC chromatograms for sugar analysis in the presence of γ-Al₂O₃ (black line) and γ-Al₂O₃-PB (red line) at reaction times of 15 h and 6 h, respectively, chosen as the time at which the peak with the highest intensity in the chromatogram (around 10 min retention time) reached its maximum. Additional chromatograms illustrating the progression of the reaction are shown in Supplementary Fig. 3. As depicted in Fig. 2b, the peaks between retention times of 15-23 min corresponded to sorbose and fructose (ketohexoses, C6k), as well as mannose, glucose, and galactose (aldohexoses, C6a). The peak associated with ketopentoses (C5k) was unsuitable for quantification due to overlap with several other peaks with similar retention times. Peaks attributed to 1,3,4-trihydroxy-3-(hydroxymethyl)butan-2-one (C5b) and 3-ketohexose (C6k’) were assigned based on prior reports²⁹ though they were not quantified owing to the unavailability of commercial standards.

The time-course profiles of pH and the concentrations of HCHO, C2, glyceraldehyde (C3a), C3k, aldotetroses (C4a), erythrulose (C4k), C6k, and C6a are shown in Fig. 2c, d for reactions using γ-Al₂O₃ and γ-Al₂O₃-PB, respectively. The pH and compound concentration profiles exhibited distinct behaviors for γ-Al₂O₃ and γ-Al₂O₃-PB. In the presence of γ-Al₂O₃-PB, the pH of the reaction mixture during the initial 6 h remained between 8.0 and 9.5, after which it stabilized in the neutral range (7.0 to 8.0) (Fig. 2d (i)). This suggests that OH⁻ ions may have acted as additional base catalysts, complementing the oxygen atoms on the surface of γ-Al₂O₃ during the early phase of the reaction. In contrast, the pH of the reaction solution containing only γ-Al₂O₃ dropped to 3.9 (Fig. 2c (i)). The time-course of HCHO concentration revealed that its consumption was faster in the presence of γ-Al₂O₃-PB compared to γ-Al₂O₃ (Fig. 2c, d, panel (ii)). With γ-Al₂O₃, HCHO concentration plateaued after 48 h, leaving 12.5% unreacted, while γ-Al₂O₃-PB resulted in nearly complete consumption (>99.9%) of HCHO within 15 h. Maximum concentrations of C2, C3a, C3k, C4a, and C4k were reached at 6 h in the γ-Al₂O₃-PB system, compared to 15 h with γ-Al₂O₃, aligning with the faster HCHO consumption observed in γ-Al₂O₃-PB.

As shown in panels (ii)-(v) of Fig. 2c, d, the time-course behavior of product concentrations in reactions using γ-Al₂O₃ and γ-Al₂O₃-PB followed similar trends, except for reaction rates. However, C6k (vi) and C6a (vii) exhibited differing behavior depending on the catalyst. With γ-Al₂O₃-PB, the concentration of C6k peaked at 15 h and then declined steadily (Fig. 2d (vi)). In contrast, the maximum glucose concentration with γ-Al₂O₃ was only 0.05 mM after 72 h, remaining consistently low throughout the reaction. With γ-Al₂O₃-PB, however, the maximum glucose concentration was 0.48 mM at 15-24 h, approximately 10 times higher than in the γ-Al₂O₃ reaction (Fig. 2c, d, panel (vii)). These findings suggest that γ-Al₂O₃-PB activates dissimilar substructures from those activated by γ-Al₂O₃, leading to the formation of an integrated CRN as depicted in Fig. 1c when both catalysts are used. To further explore this, we conducted the experiments described in Figs. 3–6 to determine the factors underlying the differences between the catalytic behaviors of γ-Al₂O₃ and γ-Al₂O₃-PB.

a Spline interpolated data of time-course experiments for γ-Al₂O₃ (blue line) and γ-Al₂O₃-PB (red line); plot regions for γ-Al₂O₃ (0–72.0 h) and γ-Al₂O₃-PB (0–36.3 h) were determined to maximize the means of cross-correlation coefficients. b Table of cross-correlation coefficients for the concentrations of compounds calculated from the data in (a).

a Substructure of the formose CRN connecting to C6k. The numbers appended to the compounds indicate the number of reaction steps to produce C6k from the corresponding compounds. b Reaction condition of Fig. 4c and d. c, d Concentration of compounds following reactions using (i) 40 mM fructose, (ii) 40 mM glucose, (iii) 90 mM C3a, (iv) 150 mM C2, and (v) 40 mM C4k and 50 mM C2 as substrates in 10 vol% aqueous methanol at 80 °C for 1 h together with γ-Al₂O₃, PB, or γ-Al₂O₃-PB, and without catalyst. e Calculated cause scores that combine the cross-correlation coefficients (Fig. 3b) with the CRN structure (a).

a Side and top view images of 2 × 2 super cells for Al₂O₃, 1P/Al₂O₃, and 4P/Al₂O₃ obtained by DFT calculations. The hydrogen atoms contained in the structure originate from the solvent water. b Range of negative charges on oxygen atoms on Al₂O₃, 1P/Al₂O₃, and 4P/Al₂O₃ surface within the square area enclosed by purple dashed line in the side views of Fig. 5a. The charges on oxygen atoms are calculated values. Boxes represent middle quartiles, their middle lines represent the median, crosses represent the average, and whiskers represent outlying quartiles. c Reaction condition for the preparation of P-Al₂O₃. d Solid state ³¹P NMR (400 MHz) spectra of P-Al₂O₃ and P-Al₂O₃ prepared with HCHO and C2 (purple and red lines, respectively). e Proposed structure of the integrated CRN synergistically activated by γ-Al₂O₃, PB, and Cat 3. f Concentration of compounds following reactions under the same condition of (i) in Fig. 4c and d using P-Al₂O₃ (50 mg mL⁻¹) without or with 50 mM PB.

a Schematic illustration of the experiments to prove the multilayered structure of substructures. b Reaction condition for the experiments shown in Fig. 6c. c pH and concentrations of sugars reacted for 2, 4, and 24 h after adding NaOH (red line) or PB (blue line) after the reaction with γ-Al₂O₃ at 80 °C for 63.5 h. The data for the case without additives is shown for comparison (gray line). The concentration before addition is shown at 0 h on the time axis. d Schematic illustration of the properties of γ-Al₂O₃, PB, and Cat 3 (P-Al₂O₃) in the γ-Al₂O₃-PB system.

Statistical analysis of reaction pathways using cross-correlation coefficients

In this section, we applied statistical analysis to identify differences in the substructures of the CRN activated by γ-Al₂O₃ and γ-Al₂O₃-PB, respectively, based on the experimental data shown in Fig. 2c, d. The complex CRN of the formose reaction, depicted in Fig. 1a, consists of multiple interconnected compounds and reaction pathways. This complexity makes it difficult to calculate the rate constants of individual pathways and compare them between substructures using conventional reaction kinetics.

As an alternative approach, we employed cross-correlation analysis of the time-course data for the concentrations of various compounds in the CRN, obtained under different reaction conditions³⁵. To do this, we first adjusted the time scales of the data in Fig. 2c, d to calculate the cross-correlation coefficients. By applying the algorithm described in the Method section, we determined the time range that maximized the average cross-correlation coefficient across all compound concentrations. The maximum average value of the cross-correlation coefficient was found when using the data from 0–72.0 h for γ-Al₂O₃ and 0–36.3 h for γ-Al₂O₃-PB.

If γ-Al₂O₃-PB uniformly accelerates all reaction pathways in the CRN as compared to γ-Al₂O₃, then the time-course data for all compound concentrations should exhibit a positive correlation when the difference in time scale are adjusted using the above conditions. Moreover, the cross-correlation coefficient provides insights into the variations in reaction rate balances between different catalysts. Specifically, significant deviations in the cross-correlation coefficients for certain compounds indicate that the reaction pathways involving those compounds are selectively accelerated or decelerated by γ-Al₂O₃-PB, as compared to γ-Al₂O₃.

Based on this rationale, we calculated the cross-correlation coefficients for the concentration changes over time for each compound, using the data from Fig. 2c, d. To calculate the cross-correlation coefficients, we performed spline interpolation on the time-course data, covering the intervals of 0–72.0 h for γ-Al₂O₃ and 0–36.3 h for γ-Al₂O₃-PB. This resulted in 200 evenly spaced data points for each dataset, allowing for consistent analysis. The interpolated data were plotted as blue lines for γ-Al₂O₃ and red lines for γ-Al₂O₃-PB, with the time scale normalized to a range of 0–72.0 h for both cases (Fig. 3a). The cross-correlation coefficients, \({r}_{{xy}}\), representing the correlation between the time-dependent concentrations of compounds under γ-Al₂O₃ and γ-Al₂O₃-PB, were calculated using Eq. (1):

where \({x}_{n}\) and \({y}_{n}\) are the n-th concentration values of each compound for γ-Al₂O₃ and γ-Al₂O₃-PB, respectively, and \(\bar{x}\) and \(\bar{y}\) represent the mean values of \({x}_{n}\) and \({y}_{n}\). A cross-correlation coefficient between 0 and 1 indicates a positive linear correlation, while a coefficient between −1 and 0 indicates an inverse linear correlation. A value around 0 suggests weak or no linear correlation between the two data sets. The resulting cross-correlation coefficients, \({r}_{{xy}}\), are summarized in Fig. 3b. The values, which range from 0 to 1, suggest that certain reaction pathways within the CRN are differentially influenced by γ-Al₂O₃ and γ-Al₂O₃-PB³⁶.

Elucidation of substructures by experimental approaches

We observed that the cross-correlation coefficient for fructose was 0.120, a value notably close to zero compared to the coefficients for other compounds. This near-zero correlation coefficient strongly suggests that the contributions of γ-Al₂O₃ and γ-Al₂O₃-PB to fructose-related reactions are significantly different (Fig. 3a, panel (viii)). In contrast, the values of the correlation coefficients for C3a, C3k, C4a, and C4k were all 0.9 or higher, suggesting that the reaction pathways involving these reactions show similar behavior in γ-Al₂O₃ and γ-Al₂O₃-PB (Fig. 3a, panel (iii)-(vi)). To validate this observation, we analyzed the results of other experiments that were designed to evaluate the differential effects of γ-Al₂O₃ and γ-Al₂O₃-PB on these reactions (Fig. 4a, b). The compounds involved in the CRN substructures linked to fructose in one- or two-step reactions, as illustrated in Fig. 4a, were anticipated to play critical roles in the production or consumption of fructose. For example, C6a and C6k’ are connected to fructose through one-step proton-transfer pathways, while C3a and C3k are connected to fructose via one-step aldol or retro-aldol reactions. Additionally, C2, C4a, and C4k are linked to fructose through two-step pathways that proceed via intermediates such as C6a, C6k’, C3a, or C3k. We hypothesized that analyzing the reaction state shortly after its initiation, using the compounds in Fig. 4a as substrates, would enable us to identify the fastest-reacting pathways. In these experiments, C2, C3a, C4k glucose, and fructose were used as substrates, and the resulting compounds were quantified one hour after the reaction onset. For comparison, PB alone used as a catalyst and without catalysts were also tested alongside γ-Al₂O₃ and γ-Al₂O₃-PB (Fig. 4b).

The concentrations of C2, C3a, C3k, C4a, and C4k after 1 h of reaction are presented in Fig. 4c, while Fig. 4d shows the concentrations of sorbose and fructose (C6k), along with mannose, glucose, and galactose (C6a). The differences between γ-Al₂O₃ and γ-Al₂O₃-PB were particularly evident in experiments where fructose (i), glucose (ii), C2 (iv), and the combination of C2 + C4k (v) were used as substrates. It was confirmed that there was little change in pH regardless of which catalyst was used under the applied reaction conditions (Supplementary Table 1). In the absence of a catalyst, the presence of products was confirmed for fructose (i), C3a (iii), and C2 (iv) in Fig. 4c, while no consumption of the substrate was observed in other cases, (ii) and (v) (Fig. 4c). On the other hand, when PB was applied alone, products were observed for all substrates except glucose (ii), and more C3k was formed from C3a (Fig. 4c, panel (iii)). Furthermore, the product yield obtained with γ-Al₂O₃-PB was not simply the sum of the yields obtained with γ-Al₂O₃ and PB individually.

The results described below showed that there are two types of reaction pathway related to fructose: one of which clearly shows the difference between γ-Al₂O₃ and γ-Al₂O₃-PB, and the other of which shows little difference. Results from panels (i) and (ii) in Fig. 4c, d showed that the reaction pathway connecting fructose and glucose was significantly accelerated by γ-Al₂O₃-PB compared to γ-Al₂O₃. Moreover, the enhanced formation of C6k under the conditions shown in panel (v), where C2 and C4k were applied as substrates, indicates that the conversion of C6k’ to C6k was also catalytically favored by γ-Al₂O₃-PB. This is consistent with the presence of a reaction pathway through which C6k’ is formed from C2 and C4k. In contrast, despite C3a being directly connected to fructose in a one-step reaction, no significant difference was observed between γ-Al₂O₃ and γ-Al₂O₃-PB in experiment (iii). These findings suggest that the lower cross-correlation coefficient may reflect the fact that the effects on the reaction pathways related to fructose production or consumption differ between γ-Al₂O₃ and γ-Al₂O₃-PB. In the case of glucose and galactose, the amount produced by γ-Al₂O₃ was about one-tenth and one-fifth of the amount produced by γ-Al₂O₃-PB, and the small change in concentration, as shown in Fig. 3a, panels (x) and (xi), was not thought to be fully reflected in the cross-correlation coefficient.

The aforementioned discussions suggest that differences between γ-Al₂O₃ and γ-Al₂O₃-PB are related to not only the cross-correlation coefficients but also the CRN structure. To investigate the differences associated with the CRN structure, we propose the cause score that combines the cross-correlation coefficients with the CRN structure. The cause score is obtained via the following algorithm. Let us consider N compounds denoted by c₁, c₂,…, and c_N. Let us define \({s}_{0,i}=1-{r}_{i}\) called the resulting difference score that is high if the cross-correlation coefficient r_i of c_i is small and vice versa. The value of this score s_0,i is propagated according to the reaction pathways; If c_i and c_j are a reactant and product of a reaction pathway p_k, respectively, then the score s_0,j of c_j is propagated into c_i and we denote this propagation by the coefficient a_k,i,j = 1. Otherwise, we set a_k,i,j = 0. The propagated value of s_0,j from c_j is defined as \({s}_{0,j}f/{n}_{j}\) where f < 1 is a decay rate and n_j is the number of propagated compounds from c_j that is given by

The sum of propagated values from all compounds to a compound c_i is called the one-step backtracking score of c_i that is given as follows:

In the same manner, the two-step backtracking score s_2,i denotes the sum of propagated values of s_1,j as follows:

For every t, the t-step backtracking score s_t,i is given by

Consequently, the cause score s_*,i is defined as the sum of the backtracking scores at all steps:

Practically, we can calculate the cause score easily based on a technique of Neumann series³⁷ (see its proof in Method section):

where I denotes the identity matrix and the matrix A is given by

where A_i,j denotes the component in the ith row and jth column of A.

We suggest that compounds having high cause scores contribute to the differences between γ-Al₂O₃ and γ-Al₂O₃-PB. Figure 4e shows the cause scores of the compounds calculated via the proposed algorithm, where the decay rate is set to f = 0.9. Setting the decay rate to such a large value emphasizes the impact of the CRN structure on the cause score while the decay rate must be less than 1.0 to avoid the divergence of the cause score. The resulting difference score \({s}_{0,i}=1-{r}_{i}\) of C6a is calculated using the cross-correlation coefficient \({r}_{i}\) of mannose that is minimal among those of compounds included in C6a. In the same manner, the cross-correlation coefficient \({r}_{i}\) of fructose is utilized for the resulting difference score of C6k. We found that the scores of C6k, C2, and C6k’ are greater and C5k’ is smaller than those of the others, indicating that these scores reflect information from both the cross-correlation coefficient and the substructures well.

Discussion of the third catalytic species

It is important to highlight that the distinctive catalytic behavior observed with γ-Al₂O₃-PB was not replicated by either γ-Al₂O₃ or PB alone. This observation suggests the formation of a novel catalytic species in the reaction system containing both γ-Al₂O₃ and PB, which could explain the unique catalytic properties seen in γ-Al₂O₃-PB. To further investigate this, we examined the structure and properties of this new catalytic species using both computational chemistry and experimental data, as discussed in the following section.

Given that phosphate ions are known to adsorb onto the surface of Al₂O₃, we hypothesized that the third catalytic species in the reaction system would be phosphate-adsorbed Al₂O₃^38,39. To explore this, we first assessed the catalytic activity of phosphate-adsorbed Al₂O₃ using plane-wave density functional theory (DFT) calculations. These calculations were performed with the Vienna Ab initio Simulation Package (VASP)^40,41,42 employing the Perdew-Burke-Ernzerhof exchange-correlation functional⁴³ with dispersion corrections based on the Grimme (PBE-D3)⁴⁴ and using projector-augmented wave (PAW) pseudopotentials⁴⁵. The computational study was conducted independently of experimental data, as described below.

We used a previously proposed bulk model for γ-Al₂O₃ in these calculations (Fig. 1d, γ-Al₂O₃)^46,47. The charge values on the oxygen atoms in the Al₂O₃, one phosphate group (1 P/Al₂O₃), and four phosphate groups (4 P/Al₂O₃) were evaluated by performing the Bader charge analysis previously implemented by Henkelman’s group⁴⁸. The results for surface oxygen atoms (enclosed by the purple dashed line in Fig. 5a) showed that the overall negative charge on these atoms increased with greater phosphate coverage (Fig. 5b). Oxygen atoms directly bonded to phosphorus had the highest negative charge, while other surface oxygen atoms also exhibited increasing negative charges as phosphate coverage rose (Supplementary Fig. 4). These findings suggest that phosphate-adsorbed Al₂O₃ has a more basic surface than pure Al₂O₃ and is likely to display distinct catalytic properties, potentially forming a unique CRN.

To experimentally investigate these changes, we synthesized γ-Al₂O₃ with phosphate adsorbed on its surface under the reaction conditions used in previous experiments. This involved heating an aqueous solution of 10 vol% methanol, γ-Al₂O₃ (50 mg mL⁻¹), and PB (50 mM) at 80 °C for 72 h. Since the solid-state sample prepared under these conditions may not perfectly replicate the catalytic sites in the aqueous solution, we refer to it as P-Al₂O₃. The concentration of free phosphate before and after the synthesis of P-Al₂O₃ was measured via inductively coupled plasma atomic emission spectroscopy (ICP-AES), yielding values of 53.3 mM and 20.4 mM, respectively. This corresponds to approximately 0.658 mmol of phosphate adsorbed per gram of γ-Al₂O₃. The P-Al₂O₃ solid was recovered by centrifugation, washed with ethanol and water, and dried (Fig. 5c). Solid-state ³¹P nuclear magnetic resonance (NMR) and attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR) of the P-Al₂O₃ sample confirmed the chemisorption of phosphate on the γ-Al₂O₃ surface. The ³¹P NMR spectrum displayed a broad signal between −20 and 0 ppm (purple line in Fig. 5d), which is consistent with bidentate phosphate chemisorbed on γ-Al₂O₃, as reported in the literature^49,50. ATR-FTIR spectra further corroborated the presence of bidentate phosphate species (Supplementary Fig. 5)^51,52 additionally, when the formose reaction components—HCHO (300 mM) and C2 (3 mM)—were introduced, the P-Al₂O₃ sample exhibited similar ³¹P NMR and ATR-FTIR spectra (red lines in Fig. 5d and Supplementary Fig. 5). Stability tests confirmed that the ³¹P NMR spectrum of P-Al₂O₃ remained nearly unchanged after heating in aqueous methanol for 72 h at 80 °C (Supplementary Fig. 6). These results suggest that P-Al₂O₃, containing bidentate phosphate complexes, is a critical component of the γ-Al₂O₃-PB reaction system.

Finally, we propose that the predicted third catalytic species (Cat 3) exhibits properties similar to those of P-Al₂O₃ and plays a role in activating unique CRN substructures, including pathways for glucose formation (Fig. 5e). Notably, the product distribution from reactions using fructose as a substrate with P-Al₂O₃ alone, or P-Al₂O₃ with PB, resembled that of reactions using γ-Al₂O₃-PB (Fig. 5f, and panels (i) in Fig. 4c, d). These findings provide strong evidence that P-Al₂O₃ formed in the γ-Al₂O₃-PB system acts as a third catalytic species, Cat 3. Furthermore, when C2 and C4k were used as substrates, the proton-transfer pathway between C6k’ and C6k was also enhanced by this third species (Supplementary Fig. 7). These results suggest that substructures activated by γ-Al₂O₃, PB, and Cat 3 interact synergistically, contributing to the formation of an integrated CRN in the γ-Al₂O₃-PB system.

Synergestic effect of the superimposed CRNs

We now revisit the formose reaction using HCHO as the substrate and C2 as the initiator, as illustrated in Fig. 2c, d. In Fig. 2c (ii), the time course of HCHO consumption by γ-Al₂O₃ did not display the typical sigmoidal pattern, which is characteristic of autocatalytic cycles in CRNs. However, when the reaction was performed without C2, a sigmoidal curve emerged (Supplementary Fig. 8), suggesting that γ-Al₂O₃ participates in an autocatalytic reaction cycle, as previously reported. Nonetheless, 11.9% of HCHO remained unreacted in the presence of C2, and 42.7% remained unreacted in its absence. These findings imply that the consumption of HCHO is somehow suppressed in environments lacking PB, despite the autocatalytic nature of the reaction cycle that should otherwise continuously consume HCHO.

The suppression of HCHO consumption by γ-Al₂O₃ is likely due to the protonation of oxygen atoms on the catalyst surface, which serve as basic catalytic sites⁵³ This suppression is consistent with the decrease in the solution’s pH, as shown in Fig. 2c (i). The decline in pH could be attributed to the formation of carboxylic acids through reactions with oxygen in the system⁵⁴, or to the crossed Cannizzaro reaction^55,56 both of which are known side reactions of the formose reaction. In contrast, continuous sugar production from HCHO was not achieved with PB alone and 88.4% of HCHO remained unreacted after the reaction at 80 °C for 66.5 h (Supplementary Fig. 9), and 7.1% of HCHO remained unreacted when using P-Al₂O₃ alone (Supplementary Fig. 10). However, when P-Al₂O₃ and PB were used together, HCHO was consumed efficiently (>99.8%) (Supplementary Fig. 10). Thus, PB not only promotes the aldol reaction but also serves as a buffer, helping maintain the catalytic activity of γ-Al₂O₃ and/or Cat 3.

To further verify roles of PB, experiments were conducted with γ-Al₂O₃, PB, and Cat 3 in a stepwise reaction process (Fig. 6a). If PB functions as a buffer, the catalytic activity of γ-Al₂O₃, which partially remains should recover after the addition of PB, leading to an increase in HCHO consumption. Additionally, the formation of Cat 3 after addition of PB would be expected to enhance glucose production. In one experiment, the reaction catalyzed by γ-Al₂O₃ was stopped at 63.5 h, and the solution contained 52.4 mM unreacted HCHO. To this mixture, either NaOH or PB was added, adjusting the pH to 7.5 or 7.0, respectively, after which the reaction was heated at 80 °C for 24 h (Fig. 6b). The results, shown in Fig. 6c, reveal that HCHO consumption, which had previously stalled, resumed once the pH was neutralized by the addition of PB or NaOH (Fig. 6c (ii)). This indicates that γ-Al₂O₃ regained catalytic activity when the pH was brought into the neutral range, where the effects of free H⁺ or OH⁻ ions were minimized. With PB, pH was buffered within this neutral range (Fig. 6c (i)), and nearly all HCHO was consumed within 24 h after its addition (Fig. 6c (ii)). In contrast, when NaOH was added, HCHO consumption resumed similarly to that with γ-Al₂O₃ but slowed after 2 h due to a gradual decrease in pH, as the effect of NaOH weakened. The decrease in C2 and the increase in C4a and C4k after PB addition indicated that PB (or Cat 3) facilitated the aldol reaction between two C2 molecules (Fig. 6c (v, viii, ix)). These results indicate that PB is responsible for maintaining the activity of γ-Al₂O₃ and/or Cat 3 for retro-aldol reactions, which is essential for the formation of the autocatalytic reaction cycle, as well as promoting aldol reactions. Furthermore, these experiments support the hypothesis that the fructose-to-glucose pathway was activated by Cat 3 formed in the reaction system, as previously discussed. After the addition of PB, fructose concentrations decreased while glucose concentrations increased, while little difference was obtained than no additive after the addition of NaOH (Fig. 6c (iii), (iv)). Figure 6d presents the properties of γ-Al₂O₃, PB, and Cat 3 in the γ-Al₂O₃-PB system, as estimated by the DFT calculations (Fig. 5a) and supported by the experimental results. A more detailed discussion on the proton transfer of fructose and glucose based on the experiments using 3-(N-morpholino)propanesulfonic acid (MOPS) as a buffer instead of PB and DFT calculations is provided in the Supplementary discussion and Supplementary Figs. 11–14.

Finally, we consider the structure of the autocatalytic reaction cycles formed by γ-Al₂O₃-PB. In the Breslow cycle⁵⁷, a well-known autocatalytic cycle associated with the formose reaction, the retro-aldol reaction of C4a (C4a → 2 C2) is thought to proceed via the proton transfer of C4k to C4a (Supplementary Fig. 15. However, our experiments suggest that these processes occurred only minimally when C4k was used as the substrate (Supplementary Fig. 16a). Interestingly, when xylulose (a ketopentose, C5k) was used as the substrate with γ-Al₂O₃, a different retro-aldol reaction occurred (Supplementary Fig. 17), suggesting that the retro-aldol cleavage of C5k (C5k → C2 + C3k) was active in the CRN. Moreover, C2 and C3k formation in reactions using C4k and HCHO as substrates supports the hypothesis that the retro-aldol reaction of C5k proceeds through an aldol reaction between C4k and HCHO (C4k + HCHO → C5k’, 3-ketopentose) followed by proton transfer of the product (C5k’ → C5k) (Supplementary Fig. 16b). These results support that γ-Al₂O₃ or Cat 3 promotes additional retro-aldol reactions beyond the Breslow cycle, contributing to the formation of autocatalytic reaction cycles in the integrated CRN (Supplementary Fig. 18).