On the Emergence of Autonomous Chemical Systems through Dissipation Kinetics

Abstract

This work addresses the kinetic requirements for compensating the entropic cost of self-organization and natural selection, thereby revealing a fundamental principle in biology. Metabolic and evolutionary features of life cannot therefore be separated from an origin of life perspective. Growth, self-organization, evolution and dissipation processes need to be metabolically coupled and fueled by low-entropy energy harvested from the environment. The evolutionary process requires a reproduction cycle involving out-of-equilibrium intermediates and kinetic barriers that prevent the reproductive cycle from proceeding in reverse. Model analysis leads to the unexpectedly simple relationship that the system should be fed energy with a potential exceeding a value related to the ratio of the generation time to the transition state lifetime, thereby enabling a process mimicking natural selection to take place. Reproducing life's main features, in particular its Darwinian behavior, therefore requires satisfying constraints that relate to time and energy. Irreversible reaction cycles made only of unstable entities reproduce some of these essential features, thereby offering a physical/chemical basis for the possible emergence of autonomy. Such Emerging Autonomous Systems (EASs) are found to be capable of maintaining and reproducing their kind through the transmission of a stable kinetic state, thereby offering a physical/chemical basis for what could be deemed an epigenetic process.

Keywords: autocatalysis; dynamic kinetic stability; emerging autonomous systems; evolution; irreversibility; origin of life.

Figure 1

In addition to the synthesis of the cell’s molecular components, its metabolism ensures a functional coupling between, on the one hand, the dissipation of the potential of energy sources and, on the other hand, the development, the reproduction and the evolution of living entities, all of which require them occurring in an irreversible manner in order that evolution remains a historical process directed towards increasing DKS. In this work, lightning bolts are used to picture an input of free energy into the system. In biology, energy carriers are built though catabolism, photosynthesis or the utilization of redox potentials. In abiotic chemistry, the activation process can be of a physical nature (resulting, for instance, from spark discharges or of the absorption of photons), which brings the system to a high-energy state that is quenched at ambient temperature impeding the system to relax to the equilibrium state. Alternatively, chemical activation can take place by reaction with high-energy species, which are held in a far-from-equilibrium state by kinetic barriers [28,29,30,31]. These activated chemicals can be considered to store the potential reached through a prior physical or geophysical activation process within an energy well surrounded by kinetic barriers. The nitrile triple bond can indeed correspond to this definition and its specific reaction with thiols provides an example of how chemical energy can be harvested in a synthetic way [32].

Figure 2

Development and reproduction of a living cell fed from a free energy source (e.g., nutrients in a disequilibrium state present in the environment). The cell cycle contributes to dissipate the energy potential into degraded forms corresponding to an energy sink (e.g., heat or inactivated waste). Note that recycling a cell into its initial state only results in dissipation and that chemical work is realized through the cell cycle just because one extra copy of the living being is produced per round of the cycle. By intimately coupling dissipation with the entropy loss associated with the reproduction of a thermodynamically unstable entity, the cell cycle avoids any violation of the Second Law.

Figure 3

Activating a chemical system can lead to different situations depending on the free energy difference ΔG between the activated state R* (in this work, the asterisk indicates that the molecular entity is not thermodynamically stable and therefore absent at equilibrium) and the inactivated reactant R and on the kinetic barrier separating the two states. (A) It may lead to an unstable state with no significant lifetime, or (B) to a kinetically stable state depending on the height of the barrier separating the activated state from the equilibrium state. (C) The existence of kinetic barriers opens the possibility of alternative pathways depending on the presence of additional reactants, as for instance a catalyst C forming a complex C·R* with the activated state R* thereby stabilizing the transition state TS^≠ leading to product.

Figure 4

Dissipation associated with chemical processes of increasing complexity occurring in a disequilibrium context involving an energy source and a sink (for simplicity, the addition of reactants and the release of inactivated products have been omitted from this scheme and can be considered as belonging, respectively to the source or the sink). (A) The activation of a reagent R can lead to the thermodynamically unstable form R* in a kinetically stable state that reverts to the reactant by releasing its energy content as heat. Apart from its energy content, chemical work can be produced and stored in the system only if the activated form R* is specifically subject to an additional process such as polymerization (dissipative self-assembly). (B) Process involving a chemically stable catalyst C, which, in principle, can be totally regenerated through a catalytic cycle. The activated intermediates I₁* and I₂* are formed in a DKS state with the cleavage of these species releasing heat, inactivated products and regenerating the stable catalyst C. The whole system cannot be considered as being in a DKS state since C corresponds to a ground state and energy is stored in the system only to maintain the DKS concentration of intermediates I₁* and I₂*. (C) Process involving an unstable catalyst C*. In this case, the usual non-quantitative character of chemical reactions would lead to a breakdown of the catalyst leading to limited turnover numbers except if an energized (activated) initiator Init* is continuously provided into the system. Init* can in principle be any one of the components of the catalytic cycle, C*, I₁* or I₂* since reconstituting the whole cycle needs only one of its components. Interestingly, differentiating the initiator from the catalyst illustrates the fact that most of the energy stored in the process does not mandatorily come from the energy source but also from the activated initiator Init*. (D) A self-maintained catalytic system corresponding to the definition of an Emerging Autonomous System (EAS) in which the initiator Init* is produced in one extra copy through a reaction cycle which is effectively autocatalytic. In this case, the whole catalytic cycle (including C*, I₁* and I₂*), rather than specific individual intermediates, becomes a rudimentary autonomous system (at least autonomous from the initiator) and is both DKS-stable and able to store energy derived from some source and to grow at its expense in a way similar to the cell cycle of Figure 2. Interestingly, the activated initiator Init* constitutes a true initiator that needs only to be added once, though the entire system would end up collapsing if the non-equilibrium environment was to dissipate. Restarting the system would then require a new initiation using the activated initiator Init*.

Figure 5

The potential that needs to be dissipated in order that the system becomes irreversible is assessed by considering a hypothetical reproduction cycle corresponding to the definition of an EAS in which the irreversible process (dissipation) is separated from the equilibrium synthesis of two copies of the catalyst C*. (A) Dissipation takes place during the formation of an intermediate I* from a catalyst C*. The intermediate I* carries the chemical potential needed for the formation of two copies of the unstable catalytic entity C*. R and R’ constitute non-activated reactants. (B) Irreversibility can be accounted for by uniquely considering the transformation from the intermediate I* back to the transition state TS^≠, which must be slower than the rate at which the whole cycle proceeds in the forward direction. It is independent of the values of free energy (omitted) characterizing states preceding the transition state TS^≠, as the reactant state (R + C*, depicted in grey), which have been intentionally ignored to make this point unambiguous. The kinetic barrier ΔG_r^≠ is related to the ratio of the forward and reverse reaction rates (K^≠ = k_r/k^≠) and therefore to that of the times needed for these processes to take place, namely τ^≠ the lifetime of the transition state (defined as τ^≠ = 1/k^≠) and τ_r the timescale of the backward process (defined as τ_r = 1/k_r).