Main

Biological anabolism is the construction of large, often functional-group-rich, molecules from simpler available building blocks. These structurally complex products typically have a higher chemical potential than the starting materials1, meaning that ‘contra-thermodynamic’2 transformations need to be coupled to exergonic processes to satisfy the conservation of energy3,4,5. Many synthetic schemes in biology involve the energy-demanding reaction being chemically orthogonal to the energy-releasing reaction that drives it5,6,7,8,9. This ubiquitous ‘chemical fuelling’ strategy allows both the synthesis of adenosine triphosphate (ATP) from chemically unrelated redox reactions6,7, and the subsequent use of ATP as a universal energy currency to drive numerous transformations9 in biological metabolism. Energy transduction between two unrelated chemical reactions becomes possible when the endergonic process is a catalyst3,10 for the exergonic process. In this way a ratchet mechanism11,12,13,14,15,16,17,18,19,20 provides the means of transducing an energy input into the chemical work necessary for endergonic synthesis3,4,10,20. In molecular-level machinery, ratchet mechanisms rectify stochastic fluctuations to accomplish directional motion10,11,12,13,14. In this Article, we demonstrate that an autonomous chemical reaction that proceeds through thermal activation back-and-forth across transition states21,22,23 can also be rectified by a ratchet mechanism to enable a thermodynamically unfavourable reaction outcome (Fig. 1b)3.

Fig. 1: Endergonic synthesis using ratchet mechanisms.
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a, Typical endergonic chemical transformation, for example, a deracemization or isomerization reaction, driven by light. Differences in the rates of photon absorption and excited-state relaxation lead to kinetic asymmetry in the reaction cycle, driving the system away from equilibrium. b, Chemical fuelling of an energetically uphill chemical transformation. An endergonic process in reaction coordinate 1 can be driven by orthogonal chemical fuelling along reaction coordinate 2. In a continuous process, energy transduction is driven by an information ratchet mechanism that relies on kinetic asymmetry in the rates of the fuel-to-waste reactions (F1 → W1 and F2 → W2). c, An endergonic Diels–Alder reaction between 2-furanacetic acid and acrylic acid. No Diels–Alder adducts (neither 5 nor other possible regio- and stereoisomers) were detected by 1H NMR or mass spectrometry from an initial concentration of 12.5 mM 1/2. The equilibrium constant, K, determined for 1 + 2 ⇌ 5 was 0.31 M−1 (Supplementary Information Section 2), meaning that at 12.5 mM the ratio (1 + 2):5 is ~250:1. d, Free energy of fuel-to-waste reaction; the hydration of DIC (DIC + H2O → DIU)62. e, Driving the endergonic Diels–Alder reaction of 1 and 2 thermodynamically uphill under autonomous chemical fuelling.

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Light energy has been used to power a number of endergonic chemical transformations2,24, including deracemizations25,26,27 and double-bond isomerizations28,29,30 (Fig. 1a). However, light-driven endergonic reactions are restricted to substrates that can interact with light, generally through energy transfer or photoredox interactions2,24, and the transduction of energy to the driven reaction is generally inefficient (a typical blue-light deracemization requires only +1.7 kJ mol−1 of energy2 yet consumes ~270 kJ mol−1 per photon). Even the most exquisite example of light-driven endergonic synthesis, photosynthesis, has an energy efficiency of just 3–6% (ref. 31).

Chemical fuelling15,16,17,18,19,20,32 (Fig. 1b) mediates many synthetic processes in biology5,6,7,8,9,33,34, can be energy efficient20 and scalable, and is amenable to many different classes of substrates. However, aside from a small number of deracemization reactions35,36,37, and a stepwise synthesis of a hydrazone using ATP38, artificial autonomous chemically fuelled endergonic synthesis has remained elusive. We sought to explore whether an endergonic example of a classical chemical transformation, the Diels–Alder reaction39, could be driven by chemical fuelling. The transduction of chemical energy from carbodiimide hydration through catalysis has recently been used to deracemize atropisomeric 1-(6′-substituted-phenyl)pyrrole 2,2′-dicarboxylic acid derivatives (and directionally drive rotation of the corresponding 6′-unsubstituted molecular motor)35. Transient tethering of the two carboxylic acids of the biaryl catalyst to form an anhydride enables atropisomer interconversion, with kinetic asymmetry10,13,14,15,16,17,18,19,20 in the fuelling cycle (generated by the use of a chiral carbodiimide and chiral hydrolysis promoter) driving the endergonic deracemization35. We hypothesized that similar transient tethering could be used to bring a diene and dienophile into close proximity40, promoting an otherwise endergonic Diels–Alder reaction by organizing the reactants for the cycloaddition and substantially increasing the effective concentration. In an energy ratchet mechanism (which cyclically switches the relative heights and depths of energy minima and maxima11) this could produce a power stroke that thermodynamically favoured the Diels–Alder reaction in the tethered state; in an information ratchet mechanism11, any kinetic asymmetry in the rates that the starting materials and product react with the fuel (and/or waste) would drive the Diels–Alder:retro-Diels–Alder ratio away from the equilibrium value3,10,20. Transiently organizing the reactants through fuelling also has the potential to exert regio- and/or stereocontrol in the driven reaction41.

Results and discussion

The Diels–Alder reaction is a synthetically important transformation in which six-membered rings are formed with up to four new stereocentres39. The cycloaddition can be accelerated and the stereochemical outcome controlled by catalysts42; however the yield and regio- and stereoselectivity of the reaction can all be limited by unfavourable thermodynamics41,43. Temporary tethering groups have been used to improve the regio- and stereochemical outcome of Diels–Alder reactions, but adding and removing the tether requires an additional two or three synthetic steps41,44,45. The intermolecular Diels–Alder reaction of furans and acrylates often favours the diene and dienophile, leading to low levels of the Diels–Alder adduct at equilibrium46,47. Furthermore, the symmetry of the furan offers little electronic polarization, leading to poor regioselectivity in reactions that do proceed46,47. Carrying out the reaction at elevated temperatures is also problematic due to the propensity of furans to thermally decompose. As such, this class of substrates provides a good testing ground to explore the effects and efficacy of chemical fuelling on a challenging endergonic reaction.

We chose 2-furanacetic acid (1) and acrylic acid (2) as diene and dienophile respectively (Fig. 1c). Each building block contains a carboxylic acid for forming an intermolecular anhydride, and molecular modelling suggested that the length between the diene and dienophile when tethered would not be strained when adopting the tricyclic transition state required for the cycloaddition. (Indeed, in preliminary experiments chemical fuelling of analogous acid pairs with one fewer or one more carbon atom in the chains did not lead to the formation of Diels–Alder adducts.) The transient formation of anhydrides and esters by carbodiimides in the presence of water has been exploited in nonequilibrium and systems chemistry40,48,49,50,51,52, and we have previously proposed3 that such a fuelling reaction could be suitable for driving coupled reactions out-of-equilibrium.

Mixing 1 and 2 in CD3CN:D2O 3:1 (v/v) at 12.5 mM, led to no detectable (by 1H nuclear magnetic resonance (NMR) spectroscopy or mass spectrometry) Diels–Alder adduct 5 after 21 days at either 20 °C or 100 °C (Fig. 1c and Supplementary Information Section 2). Experimental determination of the 1 + 2 ⇌ 5 equilibrium constant (Supplementary Information Section 2) at various concentrations indicated that the ratio of (1 + 2):5 is ~250:1 (that is, 0.4% 5) at equilibrium at 12.5 mM, which corresponds to ΔG° = +2.8 kJ mol−1.

Addition of diisopropylcarbodiimide (DIC, 1 equiv.) to the non-reacting mixture of 1 and 2 led to the rapid formation of both symmetrical and mixed (3) anhydrides (Fig. 1d,e; DIC was chosen as the fuel due to its modest tendency for N-acyl urea formation53). Over the course of several hours, the Diels–Alder adduct 4 was observed to form, presumably from intramolecular cycloaddition of the mixed anhydride, 3, the cycloaddition that did not proceed between the two carboxylic acids (1 and 2) under the same conditions of solvent, temperature and concentration. Concomitant hydrolysis of the anhydrides led to Diels–Alder adduct 5 in 10% yield (Fig. 2a,c). The structure of 5 was confirmed by two-dimensional NMR and high-resolution mass spectrometry (Supplementary Information Section 3.5). Addition of 2 equiv. (at the start of the reaction) of DIC improved the yield of 5 to 12%. Retro-Diels–Alder of the adduct 5 to reform 1 and 2 occurred spontaneously after the consumption of fuel, with a half-life of 16 days at 20 °C, confirming the endergonic nature of the Diels–Alder cycloaddition of 1 and 2 in the absence of chemical fuelling, and the kinetic stability of the Diels–Alder cycloadduct 5 (Fig. 2a–e and Supplementary Information Section 4.1).

Fig. 2: Ratcheted synthesis of 5.
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a, Ratcheted synthesis of 5 and, in the absence of the chemical fuel, its relaxation to the equilibrium distribution under the same conditions. b, Partial 1H NMR (600 MHz, CD3CN:D2O 3:1 (v/v), 298 K) stackplot showing the consumption of DIC (blue) and the formation of 4 (purple) and 5 (teal) over time. DIC addition at t = 0. c, Kinetics of the formation of 4 (triangles) and 5 (diamonds) and the subsequent retro-Diels–Alder of 5 to 1 and 2 at 20 °C or 40 °C beginning at time t. Thermal relaxation t1/220°C ~ 16 days, t1/240°C = 25 h. d, Kinetics of carbodiimide hydration catalysed by the endergonic reaction 1 + 2 ⇌ 5 (circles) and the uncatalysed background (squares). e, Kinetics of mixed (3, circles) and symmetrical (6, crosses; 7, squares) anhydride formation and hydrolysis. Symmetrical anhydrides are consumed through hydrolysis, whereas 3 either hydrolyses or reacts to form 4. Formation and hydrolysis of 3 constitutes an energy-consuming futile cycle. f, Free energy profile of ground state species of the anhydride chemical state calculated using (B3LYP/6-31 + G(d,p)/GD3BJ) level of theory with corrections for solvation (PCM in acetonitrile (ε = 35.688)). Free energy profile of the diacid chemical state based on experiment. Energies in kJ mol−1. Error bars refer to the measurement of ratios of NMR integrals (±0.5% relative to starting materials).

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Having confirmed that the cycloaddition of 1 and 2 was thermodynamically unfavourable at this concentration (without fuelling), we compared the concentrations of 1, 2 and 5 at equilibrium with those following chemical fuelling. Calculations54 (Fig. 3a and Supplementary Information Section 5) indicated that the Diels–Alder cycloaddition (ΔG° = +2.8 kJ mol−1) is ratcheted thermodynamically uphill by ΔG = +0.63 kJ mol−1 (that is, ΔGstored) when 1 equiv. DIC was added. The energy stored over the course of the ratcheted synthesis was quantified using an information thermodynamics approach. As the energy released by the hydration of DIC is ~80 kJ mol−1, 0.8% of the energy input is transduced into chemical work in the chemically fuelled cycloaddition to form 5. The efficiency of energy transduction in the chemically fuelled cycloaddition compares favourably to light and chemically fuelled deracemizations24,35.

Fig. 3: Progressive work and energy storage.
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a, The contribution of each species to the energy stored in the out-of-equilibrium reaction network54. The vertical axis is non-linear, increasing in increments of y2. Reaction conditions: [1]0 = [2]0 = [DIC]0 = 12.5 mM, CD3CN:D2O 3:1 (v/v), 298 K. b, Repeat fuelling of the ratcheted synthesis. Repetition of the fuelling cycle does cumulative chemical work. Reaction conditions: [1]0 = [2]0 = [DIC]0 = 12.5 mM, CD3CN:D2O 3:1 (v/v), 298 K. Second equivalent of DIC added at t = 90 h. Error bars refer to the measurement of ratios of NMR integrals (±0.5% relative to starting materials).

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Under the reaction conditions, the rate of hydrolysis of the anhydride is rate-limiting for the carbodiimide-to-urea reaction. This results in a fuelling regime in which the system is globally dehydrating for the initial phases of the reaction, followed by globally hydrating once little or no DIC remains. Varying the global conditions of a system over time in order to perform work is characteristic of an energy ratchet mechanism11. Another feature of ratchet mechanisms is that they are repetitive and progressive11, meaning that the fuelling cycle can be repeated to do cumulative work. Indeed, refuelling the endergonic product mixture with a second equivalent of DIC after 90 h (following complete hydrolysis of the anhydride intermediates but before complete thermal relaxation of 5 had occurred; Fig. 3b) increased the yield of 5 to 15% (ΔGstored = +1.05 kJ mol−1; Supplementary Information Section 5.1). This corresponds to two cycles of an energy ratchet mechanism. Following hydrolysis and the relaxation of 1, 2 and 5 back to equilibrium, repeating the fuelling cycle with a further equivalent of DIC reformed 5 in 7% yield, the reduced conversion due to N-acyl urea formation53 (Supplementary Information Section 4.3).

In addition to being thermodynamically uphill, the ratcheted synthesis of the Diels–Alder adduct 5 also proved to be both regio- and stereoselective (Fig. 4a). We could not detect the formation of either meta regioisomer of 5 by 1H NMR, indicating that the ratcheted synthesis is >99% regioselective for the ortho-adduct. Furthermore, we found that 5 is formed under fuelling with 92% stereoselectivity for the exo-adduct (Supplementary Information Section 3.6). Molecular modelling suggests that the high selectivity of the ratcheted synthesis for the exo- and ortho-isomer results from anhydride ring strain disfavouring the endo and meta Diels–Alder transition states.

Fig. 4: Reaction selectivity and mechanistic insights.
figure 4

a, Partial 1H NMR stackplot (600 MHz, CD3CN:D2O 3:1 (v/v), 293 K) showing the regioselectivity, stereoselectivity and yield of the unfuelled reaction (top) and the ratcheted synthesis under the same conditions (middle), in comparison with a thermal synthesis (bottom). Numbers denote the relative proportions (%) of the exo–ortho- (5, teal), endo–ortho- (purple) and meta- (grey) isomers. b, Ratcheting synthesis through an information ratchet mechanism. An orthogonal fuel (F1 → W1 and F2 → W2) reacting along reaction coordinate 2 can drive an endergonic reaction in reaction coordinate 1, so long as there is kinetic asymmetry (Kr > 1) in the fuelling cycle. A thermodynamic preference (a power stroke) in the ‘fuelled’ (that is, the tethered) state is insufficient to drive the reaction through an information ratchet mechanism (that is, at a chemically fuelled steady state). Kinetic asymmetry is present if the ratio of [R]:[P] varies from the equilibrium distribution under chemostatted conditions (constant fuel and waste concentrations)15,16,57. Kr, ratcheting constant15,16,57; R, reactants; P, product; t, time. c, Partial 1H NMR stackplot (600 MHz, CD3CN:D2O 3:1 (v/v), 293 K) after addition of 2 equiv. DIC showing the formation of 5 before the complete consumption of both fuels (DIC and D2O). Times are approximate; percentages refer to [DIC] relative to [DIC]0. Reaction conditions: [1] = [2] = 12.5 mM, [DIC]0 = 25.0 mM, CD3CN:D2O 3:1 (v/v), 298 K. d, The formation of the Diels–Alder adduct 5 under chemostatted conditions. DIC added continually at 0.7 equiv. per day. Reaction conditions: [1] = [2] = 12.5 mM, CD3CN:D2O 3:1 (v/v), 298 K. The concentration of 5 increases over time before reaching a steady state (4%), indicative of an information ratchet mechanism15,16,57. Error bars refer to the measurement of ratios of NMR integrals (±0.5% relative to starting materials).

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To confirm that one of the effects of fuelling is to increase the effective concentration of the diene and dienophile, we heated a neat mixture of 1 and 2 in the absence of solvent at 40 °C for 7 days (Fig. 4a and Supplementary Information Section 7). This resulted in a mixture of the four possible isomeric (endo-/exo-/ortho-/meta-) Diels–Alder adducts, in 39% total yield (Supplementary Information Section 8). However, 1H NMR indicated that the thermal solvent-free reaction afforded poor regio- and stereoselectivity, with only 10% of the cycloaddition products formed corresponding to the exo- and ortho-isomer 5, a 4% yield from 1 and 2. The substantial increase in the regio- and stereoselectivity of 5 under chemical fuelling compared with the neat thermal synthesis demonstrates that ratcheting can also be used to distinguish between energetically similar reaction outcomes. This is reminiscent of the way that biology uses kinetic proofreading to distinguish similar monomers in sequence-specific polymer synthesis3,4,8.

As carbodiimides can also drive information ratchet mechanisms35,50,51,55, we explored whether the carbodiimide fuelling cycle in Fig. 1d could promote the formation of 5 at a steady state under fuelling (Fig. 4b). Maintaining a constant concentration of fuel to 1 and 2 by continual addition of DIC to the reaction at a rate of 0.7 equiv. per day led to a steady state of 5 (~4%) in the presence of DIC (Fig. 4d and Supplementary Information Section 9). This is effectively a chemostatted15,16,56,57 regime, since the concentrations of DIC and D2O are kept constant and the presence of diisopropyl urea (DIU) does not affect the rate of any of the other processes. As the amount of 5 is below the NMR detection limit at equilibrium (Fig. 1c and Supplementary Information Sections 2 and 4), but is formed under the effectively chemostatted conditions, the fuelling cycle must15,16,57 possess modest kinetic asymmetry and proceed through an information ratchet11,13 mechanism (Supplementary Information Section 10). Under non-chemostatted conditions, where the chemical fuel is all added at time zero, the slow hydrolysis step means that the majority of 5 is produced after the consumption of fuel, effectively through an energy ratchet11 mechanism.

Conclusions

The use of ratchet mechanisms to directionally bias stochastic processes is a key principle that underpins the operation of molecular machines11,12,13,14,35,50,51,55. The endergonic synthesis of 5 demonstrates how chemically fuelled ratchet mechanisms can also modulate and direct the outcome of organic chemical transformations, just as they do in biology3. The chemically fuelled transformation of 1 and 2 to 5 involves a transiently formed tether between the reactants, which favourably organizes them to bring about the desired transformation. In the energy ratchet mechanism this requires the addition of fuel for each cycle, with the organization of the building blocks causing a power stroke (an energetically downhill reaction) in the tethered intermediate. In the information ratchet pathway, the key to a higher yield is to generate as large a kinetic asymmetry as possible by maximizing the differences in the reaction rates through Curtin–Hammett-type57 principles. Despite the modest chemically fuelled yield of 5, the efficiency of energy transduction from the carbodiimide-to-urea reaction to the Diels–Alder reaction is ~3–30× greater than the efficiency of a number of previously reported25,26 light-driven deracemization processes (Supplementary Information Section 13). In addition to making the endergonic transformation possible, the steric and chemical constraints necessary for ratcheting also result in improved regio- and stereochemical control in the chemically fuelled Diels–Alder synthesis of 5.

Like ATP, 5 is thermodynamically unstable under the conditions of its chemically fuelled synthesis. However, the kinetic stability of 5 is higher than that of ATP (t1/25 = 16 days versus t1/2ATP ≈ 6 h)20. We note that catalysis of the exergonic retro-Diels–Alder reaction of 5 could allow a suitable molecular machine to harness the chemical energy generated by the ratcheted synthesis to do useful work, rendering 5 a regenerable chemical fuel. However, even though every step of the thermally activated chemically fuelled cycle that makes 5 from 1 and 2 is subject to microreversibility, that does not mean that the products of chemically fuelled endergonic synthesis must necessarily have modest kinetic stability. That simply depends on whether the fastest (fuelled or non-fuelled) reverse pathway has a sufficiently high activation barrier. Such is the case, for example, for the chemically fuelled deracemization of 1-(6′-substituted-phenyl)pyrrole 2,2′-dicarboxylic acid derivatives, where the t1/2 of enantiomers of the 6′-ethyl biaryl system is ~22,000 years (ref. 35). As such, chemically fuelled ratcheted synthesis should prove useful for the endergonic synthesis of products with a range of kinetic stabilities, as well as recyclable fuels20, in sequence-specific synthesis33,34,58,59, dissipative materials40,48,49,52,60,61 and endergonic supramolecular structures17,18,19. The simplicity of the reactants and fuelling cycle of 5 provides a minimalist demonstration of chemically fuelled ratcheted synthesis that aids its understanding in biology and potential utility in synthesis.

Methods

Stock solutions

Stock solutions of reagents (in CD3CN) were used when stated: 2-furanacetic acid (1, 0.5 M), acrylic acid (2, 0.5 M), mesitylene (0.05 M) and DIC (0.5 M). All stock solutions were stored at 5 °C, except acrylic acid, which was freshly distilled immediately before use. Stock solutions were checked for composition and purity before use.

Autonomous fuelling (all of the fuel added at time zero)

Reactions were carried out in a 5 mm NMR tube. Reagents were added from stock solutions, following which CD3CN and D2O were added. A ‘pre-fuelling’ 1H NMR was recorded; then DIC was added (defined as t = 0) from a stock solution, resulting in a 0.5 ml solution. Reactions were monitored periodically by 1H NMR. The experiments carried out at 20 °C were kept in the temperature-controlled laboratory and analysed at 20 °C. The reactions carried out at 25 °C were kept within the temperature-controlled NMR probe for the duration of the experiment.

Pseudo-chemostated fuelling

In a 250-ml flask under a N2 atmosphere, freshly distilled acrylic acid (2) (216 mg, 2.50 mmol, 1 equiv.), 2-furanacetic acid (1) (315 mg, 2.50 mmol, 1 equiv.) and mesitylene (30 mg, 0.25 mmol, 10 mol%) were dissolved in CD3CN:D2O 3:1 (v/v) (12.5 mM, 200 ml). The solution was stirred at 20 °C, and DIC (0.5 M in CD3CN) (0.7 equiv. per day) was added continuously over a period of 6 days using a syringe pump. Care was taken to ensure no large drops formed by positioning the needle against the wall of the flask. Samples (0.5 ml) were taken periodically and analysed by 1H NMR.