Self-replication with magnetic dipolar colloids

On the exclusion of exponential autocatalysts by sub-exponential autocatalysts

Selection among autocatalytic species fundamentally depends on their growth law: exponential species, whose number of copies grows exponentially, are mutually exclusive, while sub-exponential ones, whose number of copies grows polynomially, can coexist. Here we consider competitions between autocatalytic species with different growth laws and make the simple yet counterintuitive observation that sub-exponential species can exclude exponential ones while the reverse is, in principle, impossible. This observation has implications for scenarios pertaining to the emergence of natural selection.

Onset of natural selection in populations of autocatalytic heteropolymers

Reduction of information entropy along with ever-increasing complexity is among the key signatures of life. Understanding the onset of such behavior in the early prebiotic world is essential for solving the problem of the origin of life. Here we study a general problem of heteropolymers capable of template-assisted ligation based on Watson-Crick-like hybridization. The system is driven off-equilibrium by cyclic changes in the environment. We model the dynamics of 2-mers, i.e., sequential pairs of specific monomers within the heteropolymer population. While the possible number of them is Z ² (where Z is the number of monomer types), we observe that most of the 2-mers get extinct, leaving no more than 2Z survivors. This leads to a dramatic reduction of the information entropy in the sequence space. Our numerical results are supported by a general mathematical analysis of the competition of growing polymers for constituent monomers. This natural-selection-like process ultimately results in a limited subset of polymer sequences. Importantly, the set of surviving sequences depends on initial concentrations of monomers and remains exponentially large (2 ^L down from Z ^L for length L) in each of realizations. Thus, an inhomogeneity in initial conditions allows for a massively parallel search of the sequence space for biologically functional polymers, such as ribozymes. We also propose potential experimental implementations of our model in the contexts of either biopolymers or artificial nano-structures.

Mutation at Expanding Front of Self-Replicating Colloidal Clusters

We construct a scheme for self-replicating square clusters of particles in two spatial dimensions, and validate it with computer simulations in a finite-temperature heat bath. We find that the self-replication reactions propagate through the bath in the form of Fisher waves. Our model reflects existing colloidal systems, but is simple enough to allow simulation of many generations and thereby the first study of evolutionary dynamics in an artificial system. By introducing spatially localized mutations in the replication rules, we show that the mutated cluster population can survive and spread with the expanding front in circular sectors of the colony.

Orientational dynamics of colloidal ribbons self-assembled from microscopic magnetic ellipsoids

We combine experiments and theory to investigate the orientational dynamics of dipolar ellipsoids, which self-assemble into elongated ribbon-like structures due to the presence of a permanent magnetic moment, perpendicular to the long axis in each particle. Monodisperse hematite ellipsoids are synthesized via the sol-gel technique and arrange into ribbons in the presence of static or time-dependent magnetic fields. We find that under an oscillating field, the ribbons reorient perpendicular to the field direction, in contrast with the behaviour observed under a static field. This observation is explained theoretically by treating a chain of interacting ellipsoids as a single particle with orientational and demagnetizing field energy. The model allows us to describe the orientational behaviour of the chain and captures well its dynamics at different strengths of the actuating field. The understanding of the complex dynamics and assembly of anisotropic magnetic colloids is a necessary step for controlling the structure formation, which has direct applications in different fluid-based microscale technologies.