Design of conditions for emergence of self-replicators

A self-replicator is usually understood to be an object of definite form that promotes the conversion of materials in its environment into a nearly identical copy of itself. The challenge of engineering novel, micro- or nano-scale self-replicators has attracted keen interest in recent years, both because exponential amplification is an attractive method for generating high yields of specific products, and also because self-reproducing entities have the potential to be optimized or adapted through rounds of iterative selection. Substantial steps forward have been achieved both in the engineering of particular self-replicating molecules, and also in characterizing the physical basis for possible mechanisms of self-replication. At present, however, there is need for a theoretical treatment of what physical conditions are most conducive to the emergence of novel self-replicating structures from a reservoir of building blocks on a desired time-scale. Here we report progress in addressing this need. By analyzing the dynamics of a generic class of heterogeneous particle mixtures whose reaction rates emerge from basic physical interactions, we demonstrate that the spontaneous discovery of self-replication is controlled by relatively generic features of the chemical space, namely: the dispersion in the distribution of reaction timescales and bound-state energies. Based on this analysis, we provide quantitative criteria that may aid experimentalists in designing a system capable of producing self-replicators, and in estimating the likely timescale for exponential growth to start.Comment: Supplementary Information is under the Ancillary Files ---

Information-theoretic bound on the entropy production to maintain a classical nonequilibrium distribution using ancillary control

There are many functional contexts where it is desirable to maintain a mesoscopic system in a nonequilibrium state. However, such control requires an inherent energy dissipation. In this article, we unify and extend a number of works on the minimum energetic cost to maintain a mesoscopic system in a prescribed nonequilibrium distribution using ancillary control. For a variety of control mechanisms, we find that the minimum amount of energy dissipation necessary can be cast as an information-theoretic measure of distinguishability between the target nonequilibrium state and the underlying equilibrium distribution. This work offers quantitative insight into the intuitive idea that more energy is needed to maintain a system farther from equilibrium.Comment: 6 pages, 2 figure

Morphogen Gradient from a Noisy Source

We investigate the effect of time-dependent noise on the shape of a morphogen gradient in a developing embryo. Perturbation theory is used to calculate the deviations from deterministic behavior in a simple reaction-diffusion model of robust gradient formation, and the results are confirmed by numerical simulation. It is shown that such deviations can disrupt robustness for sufficiently high noise levels, and the implications of these findings for more complex models of gradient-shaping pathways are discussed.Comment: Four pages, three figure

Self-Organized Resonance during Search of a Diverse Chemical Space

Recent studies of active matter have stimulated interest in the driven self-assembly of complex structures. Phenomenological modeling of particular examples has yielded insight, but general thermodynamic principles unifying the rich diversity of behaviors observed have been elusive. Here, we study the stochastic search of a toy chemical space by a collection of reacting Brownian particles subject to periodic forcing. We observe the emergence of an adaptive resonance in the system matched to the drive frequency, and show that the increased work absorption by these resonant structures is key to their stabilization. Our findings are consistent with a recently proposed thermodynamic mechanism for far-from-equilibrium self-organization

Spontaneous fine-tuning to environment in many-species chemical reaction networks

A chemical mixture that continually absorbs work from its environment may exhibit steady-state chemical concentrations that deviate from their equilibrium values. Such behavior is particularly interesting in a scenario where the environmental work sources are relatively difficult to access, so that only the proper orchestration of many distinct catalytic actors can power the dissipative flux required to maintain a stable, far-from-equilibrium steady state. In this article, we study the dynamics of an in silico chemical network with random connectivity in an environment that makes strong thermodynamic forcing available only to rare combinations of chemical concentrations. We find that the long-time dynamics of such systems are biased toward states that exhibit a fine-tuned extremization of environmental forcing. Keywords: nonequilibrium thermodynamics; adaptation; chemical reaction networks; self-organization; energy seekingGordon and Betty Moore Foundation (Grant GBMF4343

Far-from-equilibrium distribution from near-steady-state work fluctuations

A long-standing goal of nonequilibrium statistical mechanics has been to extend the conceptual power of the Boltzmann distribution to driven systems. We report some new progress towards this goal. Instead of writing the nonequilibrium steady-state distribution in terms of perturbations around thermal equilibrium, we start from the linearized driven dynamics of observables about their stable fixed point, and expand in the strength of the nonlinearities encountered during typical fluctuations away from the fixed point. The first terms in this expansion retain the simplicity of known expansions about equilibrium, but can correctly describe the statistics of a certain class of systems even under strong driving. We illustrate this approach by comparison with a numerical simulation of a sheared Brownian colloid, where we find that the first two terms in our expansion are sufficient to account for the shear thinning behavior at high shear rates.American Society for Engineering Education. National Defense Science and Engineering Graduate Fellowship (32 CRF 168a

Statistical Physics of Self-Replication

Self-replication is a capacity common to every species of living thing, and simple physical intuition dictates that such a process must invariably be fueled by the production of entropy. Here, we undertake to make this intuition rigorous and quantitative by deriving a lower bound for the amount of heat that is produced during a process of self-replication in a system coupled to a thermal bath. We find that the minimum value for the physically allowed rate of heat production is determined by the growth rate, internal entropy, and durability of the replicator, and we discuss the implications of this finding for bacterial cell division, as well as for the pre-biotic emergence of self-replicating nucleic acids.Comment: 4+ pages, 1 figur

Statistical Physics of Adaptation

Whether by virtue of being prepared in a slowly relaxing, high-free energy initial condition, or because they are constantly dissipating energy absorbed from a strong external drive, many systems subject to thermal fluctuations are not expected to behave in the way they would at thermal equilibrium. Rather, the probability of finding such a system in a given microscopic arrangement may deviate strongly from the Boltzmann distribution, raising the question of whether thermodynamics still has anything to tell us about which arrangements are the most likely to be observed. In this work, we build on past results governing nonequilibrium thermodynamics and define a generalized Helmholtz free energy that exactly delineates the various factors that quantitatively contribute to the relative probabilities of different outcomes in far-from-equilibrium stochastic dynamics. By applying this expression to the analysis of two examples—namely, a particle hopping in an oscillating energy landscape and a population composed of two types of exponentially growing self-replicators—we illustrate a simple relationship between outcome-likelihood and dissipative history. In closing, we discuss the possible relevance of such a thermodynamic principle for our understanding of self-organization in complex systems, paying particular attention to a possible analogy to the way evolutionary adaptations emerge in living things.United States. Air Force Office of Scientific Research (32 CFR 168a