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Review
. 2023 Jul 5;145(26):14169-14183.
doi: 10.1021/jacs.2c12665. Epub 2023 Jun 21.

Non-equilibrium Steady States in Catalysis, Molecular Motors, and Supramolecular Materials: Why Networks and Language Matter

Ivan Aprahamian  1 , Stephen M Goldup  2
Affiliations
Review

Non-equilibrium Steady States in Catalysis, Molecular Motors, and Supramolecular Materials: Why Networks and Language Matter

Ivan Aprahamian et al. J Am Chem Soc. .

Abstract

All chemists are familiar with the idea that, at equilibrium steady state, the relative concentrations of species present in a system are predicted by the corresponding equilibrium constants, which are related to the free energy differences between the system components. There is also no net flux between species, no matter how complicated the reaction network. Achieving and harnessing non-equilibrium steady states, by coupling a reaction network to a second spontaneous chemical process, has been the subject of work in several disciplines, including the operation of molecular motors, the assembly of supramolecular materials, and strategies in enantioselective catalysis. We juxtapose these linked fields to highlight their common features and challenges as well as some common misconceptions that may be serving to stymie progress.

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Conflict of interest statement

The authors declare no competing financial interest.

Figures

Figure 1
Figure 1
(a) A cyclic equilibrium between A, B, and C. (b) A chemical example of a cyclic equilibrium. (c) Kelly’s helicene rotor 1(6) with a ratchet-like potential-energy surface that nonetheless fails to rotate unidirectionally at equilibrium.
Figure 2
Figure 2
Coupling MeI and ester hydrolysis. (a) The reactions that are coupled. (b) The reaction network established. (c) Annotated equation for the ratio of [RCO2Me] and [RCO2] at steady state (SS) (charges omitted in concentrations for clarity).
Figure 3
Figure 3
A “linear” network in which RCO2Me and R′CO2Me are in direct conformational exchange, but only RCO2Me is in exchange with RCO2–.
Figure 4
Figure 4
(a) A network in which ester formation/hydrolysis, and conformational exchange between RCO2Me and R′CO2Me are coupled to MeI hydrolysis. (b) Annotated equation for the ratcheting constant, r0.
Figure 5
Figure 5
Moberg’s MER strategy. (a) The coupled reactions that form the reaction network. (b) The simple network formed when the reactions are coupled. (c) MER reaction network in which the rate constants for the enantiomeric pathways are distinct (3, H2O, AcOH, and HCN omitted for clarity).
Figure 6
Figure 6
Information ratchet motor 6. (a) The reactions that are coupled to generate directional motion in 6. (b) The network that results from the coupling of these reactions. (c) Schematic representation of the operation of 6 (FmocCl, CO2, NEt3, and NEt3·HCl omitted for clarity).
Figure 7
Figure 7
(a) Switching of catenane 8 on protonation. (b) A reaction network in which switching of 8 is not coupled to the conversion of 9H to 10H. c) A cyclic network in which the switching of 8 is coupled to the conversion of 9H to 10H. (c) Energy ratchet molecular motor 12 that completes a full turn either on addition of CCl3CO2H (12H) or by sequential addition of acid then base (R = (CH2)3, R1 = NH-3,5-ditBu-benzoyl, R2 = 2,5-di-Me-benzyl).
Figure 8
Figure 8
Simplified models of actin polymerization at NESS. (a) The behavior of actin in solution with ATP; ATP-actin hydrolyzes slowly. (b) ATP-actin hydrolyzes rapidly when assembled in an actin filament. (c) The coupled processes involved in the assembly of ATP-actin to a preformed filament. (d) A simple reaction network that confirms the coupling of assembly and hydrolysis even when the details of the hydrolysis process are ignored. (e) An expanded model of ATP-actin self-assembly that can be used to account for treadmilling. (f) A schematic that demonstrates that the disassembly of aged actin filaments is qualitatively different from the disassembly of a simple supramolecular polymer; ADP-Pi-actin monomer units in the bulk are kinetically stable and strongly bound to the filament but can rapidly lose Pi at the termini, resulting in the dissociation of ADP-actin.
Figure 9
Figure 9
(a) Transient assembly of a gel by the conversion of 14 to 15 and 16. The results can be explained by two extreme reaction networks in which (b) assembly is not coupled to the hydrolysis of MeI (hydrolysis of 16 only in solution) or (c) it is strongly coupled (hydrolysis of 16 only in the gel state); the real network is likely to be intermediate between these extremes. Rate constants k±1 and k±2 refer to reaction of MeI to generate an ester and hydrolysis, respectively. MeI, I–, –OH, and MeOH are omitted from the majority of the network for clarity.
Figure 10
Figure 10
Comparison between (a) the standard representation of the reaction network in Figure 5b making use of equilibrium arrows (⇌) and (b) the equivalent network in which simple arrows (⇄) represent composite processes.
Figure 11
Figure 11
(a) Isomerization of hydrazone 17 and the associated equation for the E:Z ratio at PSS (ελ(E/Z) = extinction coefficient at wavelength of irradiation λ; ϕλ = quantum yield of indicated isomerization process at wavelength λ). (b) “Linear” network for the assembly of monomer B under continuous irradiation in which the supramolecular polymer is at equilibrium with the dispersed monomer. (c) Cyclic network for the assembly of monomer B under continuous irradiation in which the supramolecular polymer is at a NESS (primed kinetic constants refer to processes involving the aggregated state). (d) Schematic potential energy diagram for ester exchange reaction (Quantitative Descriptions of Simple Reaction Networks) 1. highlighting that the overall cycle is thermodynamically downhill and takes place on a single surface. (e) Schematic potential energy diagram for the isomerization of 17 highlighting that the conversion of Z-17 to E-17 is thermodynamically uphill and that the process takes place on two different surfaces (nrd = non-radiative decay).
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