Noise-Induced Mechanism for Biological Homochirality of Early Life Self-Replicators

Abstract

The observed single-handedness of biological amino acids and sugars has long been attributed to autocatalysis. However, the stability of homochiral states in deterministic autocatalytic systems relies on cross inhibition of the two chiral states, an unlikely scenario for early life self-replicators. Here, we present a theory for a stochastic individual-level model of autocatalysis due to early life selfreplicators. Without chiral inhibition, the racemic state is the global attractor of the deterministic dynamics, but intrinsic multiplicative noise stabilizes the homochiral states, in both well-mixed and spatially-extended systems. We conclude that autocatalysis is a viable mechanism for homochirality, without imposing additional nonlinearities such as chiral inhibition.PACS numbers: 87.23. Kg, 87.18.Tt, One of the very few universal features of biology is homochirality: every naturally occurring amino acid is left-handed ( L-chiral) while every sugar is right-handed (d-chiral) [1, 2]. Although such unexpected broken symmetries are well-known in physics, for example in the weak interaction, complete biological homochirality still defies explanation. In 1953, Charles Frank suggested that homochirality could be a consequence of chemical autocatalysis [3], frequently presumed to be the mechanism associated with the emergence of early life selfreplicators. Frank introduced a model in which the d and L enantiomers of a chiral molecule are autocatalytically produced from an achiral molecule A in reactions A + d → 2d and A + L → 2 L, and are consumed in a chiral inhibition reaction, d + L → 2A [4]. The state of this system can be described by the chiral order parameter ω defined as ω ≡ (d − l)/(d + l), where d and l are the concentrations of d and L. The order parameter ω is zero at the racemic state, and ±1 at the homochiral states. Frank's model has three deterministic fixed points of the dynamics; the racemic state is an unstable fixed point, and the two homochiral states are stable fixed points. Starting from almost everywhere in the d-L plane, the system converges to one of the homochiral fixed points (Fig. 1a).In the context of biological homochirality, extensions of Frank's idea have essentially taken two directions. On the one hand, the discovery of a synthetic chemical system of amino alcohols that amplifies an initial excess of one of the chiral states [5] has motivated several autocatalysisbased models (see [6] and references therein). On the other hand, ribozyme-driven catalyst experiments [7], have inspired theories based on polymerization and chiral inhibition that minimize [8-10] or do not include at all [11,12] autocatalysis. In contrast, a recent experimental realization of RNA replication using a novel ribozyme shows such efficient autocatalytic behavior that chiral inhibition does not arise [13]. Further extensions accounting for both intrinsic noise [6,14] and diffusion [15][16][17][18] build further upon Frank's work.Regardless of the specific model details, all these models share the three-fixed-po...

Necessary conditions for the emergence of homochirality via autocatalytic self-replication

“…32 This is so because first, the total number of molecules is conserved by our reaction scheme, hence so is the total concentration n = a + d + l. Second, the total chiral matter χ = d + l is a fast degree of freedom relative to the enantiomeric excess θ. 33 Simulations of the fully reversible scheme Eqs.…”

“…In this respect, Goldenfeld and co-workers recently reported that reaction noise in a closed model involving strictly irreversible enantioselective autocatalysis coupled with the uncatalyzed, reversible production of the enantiomers stabilizes the homochiral states, making these the most probable outcome of the system. 14 The purpose of this paper is to analyze in more detail the role of reaction noise in asymmetric autocatalytic reaction networks in the context of this proposal. In Sec.…”

“…This point has been discussed most frequently in the context of principles of chemical thermodynamics governing the reversibility of reactions. 12,13 Most recently, a modeling study by Goldenfeld and co-workers 14 developed an extension of the Frank model aiming to show that the original model's inhibition criterion is unnecessary. They reported that in a non-equilibrium steadystate system, homochirality may emerge from the racemic state by a noise-induced mechanism.…”

Motif analysis for small-number effects in chemical reaction dynamics

“…For example, similar biochemical reactions to motif I have been studied in several biological contexts. 12,17,[33][34][35] The list of motifs provided herein should be helpful in searching for other candidates of biochemical reactions in which the small-number effect is expected to play an important role within a cell. Furthermore, considering recent advances in synthetic biology, [36][37][38] the list is also expected to be useful for designing a system that shows the small-number effect.…”

Path integral approach to nonequilibrium potentials in multiplicative Langevin dynamics

“…Multiplicative noise naturally describes inhomogeneous diffusion in which fluctuations depend on the state of the system. Concrete applications are very diverse, covering a broad range of interest as, for instance, micromagnetism [10] and early life biology [11]. On the other hand, extended multiplicative systems present challenging phenomena, such as noiseinduced phase transitions (NIPT), stochastic resonance and pattern formation [12,13].…”