Abstract
Early steps in the origin of life were necessarily connected to the unlikely formation of self-reproducing structures from chaotic chemistry. Simulations of chemical kinetics based on the graded autocatalysis replication domain (GARD) model demonstrate the ability of a micellar system to become self-reproducing units away from equilibrium. Even though they may be very rare in the initial state of the system, the property of their endogenous mutually catalytic networks being dynamic attractors greatly enhanced reproduction propensity, revealing their potential for selection and Darwinian evolution processes. In parallel, order and complexity have been shown to be crucial parameters in successful evolution. Here, we probe these parameters in the dynamics of GARD-governed entities in an attempt to identify characteristic mechanisms of their development in non-covalent molecular assemblies. Using a virtual random walk perspective, a value for consecutive order is defined based on statistical thermodynamics. The complexity, on the other hand, is determined by the size of a minimal algorithm fully describing the statistical properties of the random walk. By referring to a previously published diagonal line in an order/complexity diagram that represents the progression of evolution, it is shown that the GARD model has the potential to advance in this direction. These results can serve as a solid foundation for identifying general criteria for future analyses of evolving systems.