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...
The amplitude of fluctuation-induced patterns might be expected to be proportional to the strength of the driving noise, suggesting that such patterns would be difficult to observe in nature. Here, we show that a large class of spatially-extended dynamical systems driven by intrinsic noise can exhibit giant amplification, yielding patterns whose amplitude is comparable to that of deterministic Turing instabilities. The giant amplification results from the interplay between noise and non-orthogonal eigenvectors of the linear stability matrix, yielding transients that grow with time, and which, when driven by the ever-present intrinsic noise, lead to persistent large amplitude patterns. This mechanism provides a robust basis for fluctuation-induced biological pattern formation based on the Turing mechanism, without requiring fine tuning of diffusion constants.
How are granular details of stochastic growth and division of individual cells reflected in smooth deterministic growth of population numbers? We provide an integrated, multiscale perspective of microbial growth dynamics by formulating a data-validated theoretical framework that accounts for observables at both single-cell and population scales. We derive exact analytical complete time-dependent solutions to cell-age distributions and population growth rates as functionals of the underlying interdivision time distributions, for symmetric and asymmetric cell division. These results provide insights into the surprising implications of stochastic single-cell dynamics for population growth. Using our results for asymmetric division, we deduce the time to transition from the reproductively quiescent (swarmer) to the replicationcompetent (stalked) stage of the Caulobacter crescentus life cycle. Remarkably, population numbers can spontaneously oscillate with time. We elucidate the physics leading to these population oscillations. For C. crescentus cells, we show that a simple measurement of the population growth rate, for a given growth condition, is sufficient to characterize the condition-specific cellular unit of time and, thus, yields the mean (single-cell) growth and division timescales, fluctuations in cell division times, the cell-age distribution, and the quiescence timescale.
The origin of homochirality, the observed single-handedness of biological amino acids and sugars, has long been attributed to autocatalysis, a frequently assumed precursor for early life self-replication. 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 autocatalytic prebiotic self-replicators that are maintained out of thermal equilibrium. Without chiral inhibition, the racemic state is the global attractor of the deterministic dynamics, but intrinsic multiplicative noise stabilizes the homochiral states. Moreover, we show that this noise-induced bistability is robust with respect to diffusion of molecules of opposite chirality, and systems of diffusively coupled autocatalytic chemical reactions synchronize their final homochiral states when the self-replication is the dominant production mechanism for the chiral molecules. We conclude that nonequilibrium autocatalysis is a viable mechanism for homochirality, without imposing additional nonlinearities such as chiral inhibition. DOI: 10.1103/PhysRevE.95.032407 Homochirality, the single-handedness of all biological amino acids and sugars, is one of two major universal features of life on Earth. The other is the canonical genetic code. Their universality transcends all categories of life, up to and including the three domains, and thus requires an explanation that transcends the idiosyncrasies of individual organisms and particular environments. The only universal process common to all life is, of course, evolution, and so it is natural to seek an explanation for biological homochirality in these terms, just as has been done to account for the universality and error-minimization aspects of the genetic code [1]. This paper is just such an attempt, using the simplest and most general commonly accepted attributes of living systems.The origin of biological homochirality has been one of the most debated topics since its discovery by Louis Pasteur in 1848 [2]. There are those who argue that homochirality must have preceded the first chemical systems undergoing Darwinian evolution, and there are those who believe homochirality is a consequence of life, but not a prerequisite [3]. There are even those who argue that homochirality is a consequence of underlying asymmetries from the laws of physics, invoking complicated astrophysical scenarios for the origin of chiral organic molecules [4] or even the violation of parity from the weak interactions [5,6]! In fact, explanations that are based on physical asymmetries can only predict an enantiomeric excess of one handedness over another, and not the 100% effect observed in nature [7]. * Corresponding author: fjafarpo@purdue.eduThe most influential class of theories for biological homochirality rest on an idea of F.C. Frank's, in which there is a kinetic instability of a racemic (50% right handed and 50% left handed) mi...
We study the effect of correlations in generation times on the dynamics of population growth of microorganisms. We show that any non-zero correlation that is due to cell-size regulation, no matter how small, induces long-term oscillations in the population growth rate. The population only reaches its steady state when we include the often-neglected variability in the growth rates of individual cells. We discover that the relaxation time scale of the population to its steady state is determined by the distribution of single-cell growth rates and is surprisingly independent of details of the division process such as the noise in the timing of division and the mechanism of cell-size regulation. We validate the predictions of our model using existing experimental data and propose an experimental method to measure single-cell growth variability by observing how long it takes for the population to reach its steady state or balanced growth.
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