Self-organization of primitive metabolic cycles and shape-shifting complexes due to non-reciprocal interactions

One of the greatest mysteries concerning the origin of life is how it has emerged so quickly after the formation of the earth. In particular, it is not understood how the intricate structures of metabolic cycles, which power the non-equilibrium activity of cells and support their functions under homeostatic conditions, have come into existence in the first instances. These structures have emerged from a dilute primordial soup of chemicals that have turned out to be suitable partners in certain reactions in the roles of reactants and catalysts. While it is generally expected that non-equilibrium conditions would have been necessary for the formation of these primitive metabolic structures, the focus has so far been on externally imposed non-equilibrium conditions, such as temperature or proton gradients. I introduce an alternative paradigm in which naturally occurring non-reciprocal interactions between catalysts that can potentially partner together in a cyclic reaction lead to their rapid recruitment into self-organized functional structures. Within this paradigm, we uncover different classes of self-organized cycles that form through exponentially rapid coarsening processes, depending on the parity of the cycle and the nature of the interaction motifs, which are all generic but have readily tuneable features. Our results also shed light on possibilities that may be explored in designing efficient synthetic cycles. Moreover, we identify programmable non-reciprocal interactions as a tool to achieve the ability to employ a common set of building blocks that can self-organize into a multitude of different structures. The design rule is composed of reciprocal interactions that lead to the equilibrium assembly of the different structures, through a process denoted as multifarious self-assembly, and non-reciprocal interactions that give rise to non-equilibrium dynamical transitions between the structures. The design of such self-organized shape-shifting structures can be implemented at different scales, from nucleic acids and peptides to proteins and colloids.