Stability and response of polygenic traits to stabilizing selection and mutation

When polygenic traits are under stabilizing selection, many different combinations of alleles allow close adaptation to the optimum. If alleles have equal effects, all combinations that result in the same deviation from the optimum are equivalent. Furthermore, the genetic variance that is maintained by mutation-selection balance is $2 \mu/S$ per locus, where $\mu$ is the mutation rate and $S$ the strength of stabilizing selection. In reality, alleles vary in their effects, making the fitness landscape asymmetric, and complicating analysis of the equilibria. We show that that the resulting genetic variance depends on the fraction of alleles near fixation, which contribute by $2 \mu/S$, and on the total mutational effects of alleles that are at intermediate frequency. The interplay between stabilizing selection and mutation leads to a sharp transition: alleles with effects smaller than a threshold value of $2\sqrt{\mu / S}$ remain polymorphic, whereas those with larger effects are fixed. The genetic load in equilibrium is less than for traits of equal effects, and the fitness equilibria are more similar. We find that if the optimum is displaced, alleles with effects close to the threshold value sweep first, and their rate of increase is bounded by $\sqrt{\mu S}$. Long term response leads in general to well-adapted traits, unlike the case of equal effects that often end up at a sub-optimal fitness peak. However, the particular peaks to which the populations converge are extremely sensitive to the initial states, and to the speed of the shift of the optimum trait value.Comment: Accepted in Genetic

Determinism, Noise, and Spurious Estimations in a Generalised Model of Population Growth

We study a generalised model of population growth in which the state variable is population growth rate instead of population size. Stochastic parametric perturbations, modelling phenotypic variability, lead to a Langevin system with two sources of multiplicative noise. The stationary probability distributions have two characteristic power-law scales. Numerical simulations show that noise suppresses the explosion of the growth rate which occurs in the deterministic counterpart. Instead, in different parameter regimes populations will grow with ``anomalous'' stochastic rates and (i) stabilise at ``random carrying capacities'', or (ii) go extinct in random times. Using logistic fits to reconstruct the simulated data, we find that even highly significant estimations do not recover or reflect information about the deterministic part of the process. Therefore, the logistic interpretation is not biologically meaningful. These results have implications for distinct model-aided calculations in biological situations because these kinds of estimations could lead to spurious conclusions.Comment: Accepted in Physica A. Updated with [minor] observations from the reffere

Amino acid fermentation at the origin of the genetic code

There is evidence that the genetic code was established prior to the existence of proteins, when metabolism was powered by ribozymes. Also, early proto-organisms had to rely on simple anaerobic bioenergetic processes. In this work I propose that amino acid fermentation powered metabolism in the RNA world, and that this was facilitated by proto-adapters, the precursors of the tRNAs. Amino acids were used as carbon sources rather than as catalytic or structural elements. In modern bacteria, amino acid fermentation is known as the Stickland reaction. This pathway involves two amino acids: the first undergoes oxidative deamination, and the second acts as an electron acceptor through reductive deamination. This redox reaction results in two keto acids that are employed to synthesise ATP via substrate-level phosphorylation. The Stickland reaction is the basic bioenergetic pathway of some bacteria of the genus Clostridium. Two other facts support Stickland fermentation in the RNA world. First, several Stickland amino acid pairs are synthesised in abiotic amino acid synthesis. This suggests that amino acids that could be used as an energy substrate were freely available. Second, anticodons that have complementary sequences often correspond to amino acids that form Stickland pairs. The main hypothesis of this paper is that pairs of complementary proto-adapters were assigned to Stickland amino acids pairs. There are signatures of this hypothesis in the genetic code. Furthermore, it is argued that the proto-adapters formed double strands that brought amino acid pairs into proximity to facilitate their mutual redox reaction, structurally constraining the anticodon pairs that are assigned to these amino acid pairs. Significance tests which randomise the code are performed to study the extent of the variability of the energetic (ATP) yield. Random assignments can lead to a substantial yield of ATP and maintain enough variability, thus selection can act and refine the assignments into a proto-code that optimises the energetic yield. Monte Carlo simulations are performed to evaluate the establishment of these simple proto-codes, based on amino acid substitutions and codon swapping. In all cases, donor amino acids are assigned to anticodons composed of U+G, and have low redundancy (1-2 codons), whereas acceptor amino acids are assigned to the the remaining codons. These bioenergetic and structural constraints allow for a metabolic role for amino acids before their co-option as catalyst cofactors. Reviewers: this article was reviewed by Prof. William Martin, Prof. Eörs Szathmáry (nominated by Dr. Gáspár Jékely) and Dr. Ádám Kun (nominated by Dr. Sandor Pongor

Neuronal boost to evolutionary dynamics

Standard evolutionary dynamics is limited by the constraints of the genetic system. A central message of evolutionary neurodynamics is that evolutionary dynamics in the brain can happen in a neuronal niche in real time, despite the fact that neurons do not reproduce. We show that Hebbian learning and structural synaptic plasticity broaden the capacity for informational replication and guided variability provided a neuronally plausible mechanism of replication is in place. The synergy between learning and selection is more efficient than the equivalent search by mutation selection. We also consider asymmetric landscapes and show that the learning weights become correlated with the fitness gradient. That is, the neuronal complexes learn the local properties of the fitness landscape, resulting in the generation of variability directed towards the direction of fitness increase, as if mutations in a genetic pool were drawn such that they would increase reproductive success. Evolution might thus be more efficient within evolved brains than among organisms out in the wild

Evolutionary interplay between structure, energy and epistasis in the coat protein of the phi X174 phage family

Viral capsids are structurally constrained by interactions among the amino acids (AAs) of their constituent proteins. Therefore, epistasis is expected to evolve among physically interacting sites and to influence the rates of substitution. To study the evolution of epistasis, we focused on the major structural protein of the ϕX174 phage family by first reconstructing the ancestral protein sequences of 18 species using a Bayesian statistical framework. The inferred ancestral reconstruction differed at eight AAs, for a total of 256 possible ancestral haplotypes. For each ancestral haplotype and the extant species, we estimated, in silico, the distribution of free energies and epistasis of the capsid structure. We found that free energy has not significantly increased but epistasis has. We decomposed epistasis up to fifth order and found that higher-order epistasis sometimes compensates pairwise interactions making the free energy seem additive. The dN/dS ratio is low, suggesting strong purifying selection, and that structure is under stabilizing selection. We synthesized phages carrying ancestral haplotypes of the coat protein gene and measured their fitness experimentally. Our findings indicate that stabilizing mutations can have higher fitness, and that fitness optima do not necessarily coincide with energy minima