Any species involved in a chemical system involving features of self-organization must be protected from a fast spontaneous decay leading rapidly to deactivated products or side products (Figure1). This means that every species involved in the proto-metabolic part of Figure1 must be located in a free energy well and protected by kinetic barriers to avoid its spontaneous fast conversion into close to equilibrium (inactivated) products. This is true for any metabolite that has a lifetime significant compared with the time scale at which the system progresses, a quantity that is related, in the case of metabolic loops, to the turnover frequency proposed as an essential parameter in the kinetic description of catalytic cycles[17]. Transition state theory[18] provides a relationship between the rate constant of the chemical reaction, the free energy of activation (kinetic barrier) and the absolute temperature. The Eyring equation (Equation 1) expresses the rate constant of the transformation of any reactant as a function of the barrier and absolute temperature.
(1)
This relation involves only three variables (the rate constant, the kinetic barrier and the absolute temperature) and universal constants of physics (namely the Boltzmann, Planck and gas constants). It can be transformed to express the height of the kinetic barrier as a function of the half-life of the reaction for a first-order (or pseudo-first order) reaction and of the temperature (Equation 2).
(2)
A linear plot corresponding to equation 2 is displayed in Figure2 using a logarithmic scale for half-lives covering the full range of chemical times representing ca. 30 orders of magnitude, from the duration of a vibration to the age of the Universe. Considering that the practical lifetime of an energy carrier or a metabolite that accumulates significantly in a metabolic or proto-metabolic pathway must be comprised between 1 s to 100 yr (more than 9 orders of magnitude) an assessment of the kinetic barriers needed for a system capable of self- organization at moderate temperature (300 K) can be given as a range of free energy of 74 to 129 kJ mol–1 (Figure2). Because of the logarithmic dependence, this range is astonishingly limited by comparison with the nine-orders in magnitude change in lifetimes so that the assessment of this range of kinetic barriers can be considered as representative of the self- organization process through proto-metabolic pathways. This range of about 100 kJ mol–1 can be compared with the bonding energies involved in chemical interactions and amounts to a significant fraction (about one fourth for a C-C bond) of the free energy of a covalent bond. It results that self-organization in systems based on simple molecules must be based on strong chemical bonding. It should not be achievable though weak chemical interactions (Van der Waals forces, hydrogen bonding, hydrophobic interactions…) except for the rare systems based on multivalent bonds and in which bonding energy could be additive[19], because of an adapted rigid structure implying that all bonds are broken in a concerted way. Long-lived species feeding the system in energy and that have to migrate in the environment from the location of their formation to that of the self-organizing chemical system must then be protected from a spontaneous deactivation into products or side-products by a free energy barrier ΔG≠ with a similar height (Figure1). Importantly, this condition also applies to the reverse transformation into their inactivated precursors (Figure1), which is actually identical to a condition for the process to be irreversible. In other words, the kinetic barrier of the reverse of the activation reaction must be high enough so that the proto-metabolism works as a one-way chemical system. An estimate of the free energy needed for biochemical carriers to enable the development of biochemistry has been made independently to a minimum value of ca. –50 kJ mol–1 (corresponding to ΔG in Figure1)[20]. The free energy source capable of driving the system must thus be capable of delivering a thermodynamic potential reaching the sum of the absolute values of ΔG≠ and ΔG, ca. 150 kJ mol–1, which establishes a severe constraint on the thermodynamics of proto-metabolic systems.
The driver process delivering energy and enabling the formation of an activated carrier in the first step of Figure1 may be physical (for instance photochemical and not being subject to microscopic reversibility as proposed in an analysis of autocatalytic models on the emergence of homochirality[21]) or chemical. However, its actual nature does not matter. The condition that the proto-metabolisms must work irreversibly (as a one-way flux of reactants) for coupling self-organization with an entropy producing process implies that this driver process is capable of bringing the system into an excited state with a free energy exceeding the level of the transition state of the reaction reverting the energy carrier into its precursors. As a result, this short-lived activated state either reverts back to the reactants or proceeds downhill in the forward direction until a free energy well is reached yielding a chemical carrier conserving a significant part of the free energy of the source. Irreversibility in the proto-metabolic process thus emerges from the kinetic barrier of a reverse reaction. This discussion helps in identifying processes enabling the formation of the energy carriers. Photochemical processes able to deliver the corresponding amount of energy (ca. 150 kJ mol–1) correspond to wavelength of ca. 0.8 μm meaning that light in the visible spectrum is needed. Few other physical processes are capable of driving such systems in a spontaneous way. Using the black body emission as a typical example of irreversible transformation of thermal energy, heating a solid to 3600 K enables the emission of electromagnetic radiations with a maximum at the wavelength of 0.8 μm. This can be a measurement of the temperature needed for thermal energy to generate activated chemical intermediates, though the system needs a quenching step to preserve the corresponding species from evolving back to equilibrium. The only obvious processes compatible with the effect of heat are lightning, as mimicked in the Miller experiment[22], and impact-shock syntheses[23]. These processes are capable of heating locally and transiently the atmosphere at temperatures exceeding several thousand of K needed to generate radicals and ions that have enough time to recombine after cooling within a fraction of second at the lower temperature of the high atmosphere. By contrast, finding means by which geothermal energy could directly play a similar role is more problematic.
In principle, having a chemical environment in which species are held far from equilibrium by kinetic barriers may enable certain catalysts to be amplified provided that the reaction network is additionally capable of producing them. These protometabolic cycles involving catalysts that are themselves reproduced by the system are likely to increase the rate of consumption of energy carriers so that they will tend to predominate in the environment–they are selected–, corresponding to the definition of dynamic kinetic stability, which is the main feature of living systems.