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1. Competition-driven eco-evolutionary feedback reshapes bacteriophage lambda’s fitness landscape and enables speciation

   https://doi.org/10.1038/s41467-024-45008-5  

   Doud, Michael B.; Gupta, Animesh; Li, Victor; Medina, Sarah J.; De La Fuente, Caesar A.; Meyer, Justin R. (January 2024, Nature Communications)

   Abstract A major challenge in evolutionary biology is explaining how populations navigate rugged fitness landscapes without getting trapped on local optima. One idea illustrated by adaptive dynamics theory is that as populations adapt, their newly enhanced capacities to exploit resources alter fitness payoffs and restructure the landscape in ways that promote speciation by opening new adaptive pathways. While there have been indirect tests of this theory, to our knowledge none have measured how fitness landscapes deform during adaptation, or test whether these shifts promote diversification. Here, we achieve this by studying bacteriophage$$\lambda$$ $\lambda$, a virus that readily speciates into co-existing receptor specialists under controlled laboratory conditions. We use a high-throughput gene editing-phenotyping technology to measure$$\lambda$$ $\lambda$’s fitness landscape in the presence of different evolved-$$\lambda$$ $\lambda$competitors and find that the fitness effects of individual mutations, and their epistatic interactions, depend on the competitor. Using these empirical data, we simulate$$\lambda$$ $\lambda$’s evolution on an unchanging landscape and one that recapitulates how the landscape deforms during evolution.$$\lambda$$ $\lambda$heterogeneity only evolves in the shifting landscape regime. This study provides a test of adaptive dynamics, and, more broadly, shows how fitness landscapes dynamically change during adaptation, potentiating phenomena like speciation by opening new adaptive pathways. 

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2. Inferring the number and position of changes in selective regime in a non-equilibrium mutation-selection framework

   https://doi.org/10.1186/s12862-021-01770-4  

   Ritchie, Andrew M.; Stark, Tristan L.; Liberles, David A. (March 2021, BMC Ecology and Evolution)

   Abstract BackgroundRecovering the historical patterns of selection acting on a protein coding sequence is a major goal of evolutionary biology. Mutation-selection models address this problem by explicitly modelling fixation rates as a function of site-specific amino acid fitness values.However, they are restricted in their utility for investigating directional evolution because they require prior knowledge of the locations of fitness changes in the lineages of a phylogeny. ResultsWe apply a modified mutation-selection methodology that relaxes assumptions of equlibrium and time-reversibility. Our implementation allows us to identify branches where adaptive or compensatory shifts in the fitness landscape have taken place, signalled by a change in amino acid fitness profiles. Through simulation and analysis of an empirical data set of$$\beta $$ $\beta$-lactamase genes, we test our ability to recover the position of adaptive events within the tree and successfully reconstruct initial codon frequencies and fitness profile parameters generated under the non-stationary model. ConclusionWe demonstrate successful detection of selective shifts and identification of the affected branch on partitions of 300 codons or more. We successfully reconstruct fitness parameters and initial codon frequencies in simulated data and demonstrate that failing to account for non-equilibrium evolution can increase the error in fitness profile estimation. We also demonstrate reconstruction of plausible shifts in amino acid fitnesses in the bacterial$$\beta $$ $\beta$-lactamase family and discuss some caveats for interpretation. 

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3. Emergence of Escherichia coli critically buckled motile helices under stress

   https://doi.org/10.1073/pnas.1809374115  

   Phan, Trung V.; Morris, Ryan J.; Lam, Ho Tat; Hulamm, Phuson; Black, Matthew E.; Bos, Julia; Austin, Robert H. (November 2018, Proceedings of the National Academy of Sciences)

   Bacteria under external stress can reveal unexpected emergent phenotypes. We show that the intensely studied bacteriumEscherichia colican transform into long, highly motile helical filaments poized at a torsional buckling criticality when exposed to minimum inhibitory concentrations of several antibiotics. While the highly motile helices are physically either right- or left-handed, the motile helices always rotate with a right-handed angular velocity $\overrightarrow{\omega }$, which points in the same direction as the translational velocity ${\overrightarrow{v}}_T$of the helix. Furthermore, these helical cells do not swim by a “run and tumble” but rather synchronously flip their spin $\overrightarrow{\omega }$and thus translational velocity—backing up rather than tumbling. By increasing the translational persistence length, these dynamics give rise to an effective diffusion coefficient up to 20 times that of a normalE. colicell. Finally, we propose an evolutionary mechanism for this phenotype’s emergence whereby the increased effective diffusivity provides a fitness advantage in allowing filamentous cells to more readily escape regions of high external stress. 

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4. Vanishing of quartic and sextic twists of L-functions

   https://doi.org/10.1007/s40993-023-00499-x  

   Berg, Jennifer; Ryan, Nathan C.; Young, Matthew P. (February 2024, Research in Number Theory)

   Abstract LetEbe an elliptic curve over$${{\mathbb {Q}}}$$ $Q$. We conjecture asymptotic estimates for the number of vanishings of$$L(E,1,\chi )$$ $L(E,1,\chi )$as$$\chi $$ $\chi$varies over all primitive Dirichlet characters of orders 4 and 6, subject to a mild hypothesis onE. Our conjectures about these families come from conjectures about random unitary matrices as predicted by the philosophy of Katz-Sarnak. We support our conjectures with numerical evidence. Compared to earlier work by David, Fearnley and Kisilevsky that formulated analogous conjectures for characters of any odd prime order, in the composite order case, we need to justify our use of random matrix theory heuristics by analyzing the equidistribution of the squares of normalized Gauss sums. To do this, we introduce the notion of totally order$$\ell $$ $\ell$characters to quantify how quickly the quartic and sextic Gauss sums become equidistributed. Surprisingly, the rate of equidistribution in the full family of quartic (resp., sextic) characters is much slower than in the sub-family of totally quartic (resp., sextic) characters. We provide a conceptual explanation for this phenomenon by observing that the full family of order$$\ell $$ $\ell$twisted elliptic curveL-functions, with$$\ell $$ $\ell$even and composite, is a mixed family with both unitary and orthogonal aspects. 

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5. Low rank representations for quantum simulation of electronic structure

   https://doi.org/10.1038/s41534-021-00416-z  

   Motta, Mario; Ye, Erika; McClean, Jarrod R.; Li, Zhendong; Minnich, Austin J.; Babbush, Ryan; Chan, Garnet Kin-Lic (May 2021, npj Quantum Information)

   Abstract The quantum simulation of quantum chemistry is a promising application of quantum computers. However, forNmolecular orbitals, the$${\mathcal{O}}({N}^{4})$$ $O\left(N^4\right)$gate complexity of performing Hamiltonian and unitary Coupled Cluster Trotter steps makes simulation based on such primitives challenging. We substantially reduce the gate complexity of such primitives through a two-step low-rank factorization of the Hamiltonian and cluster operator, accompanied by truncation of small terms. Using truncations that incur errors below chemical accuracy allow one to perform Trotter steps of the arbitrary basis electronic structure Hamiltonian with$${\mathcal{O}}({N}^{3})$$ $O\left(N^3\right)$gate complexity in small simulations, which reduces to$${\mathcal{O}}({N}^{2})$$ $O\left(N^2\right)$gate complexity in the asymptotic regime; and unitary Coupled Cluster Trotter steps with$${\mathcal{O}}({N}^{3})$$ $O\left(N^3\right)$gate complexity as a function of increasing basis size for a given molecule. In the case of the Hamiltonian Trotter step, these circuits have$${\mathcal{O}}({N}^{2})$$ $O\left(N^2\right)$depth on a linearly connected array, an improvement over the$${\mathcal{O}}({N}^{3})$$ $O\left(N^3\right)$scaling assuming no truncation. As a practical example, we show that a chemically accurate Hamiltonian Trotter step for a 50 qubit molecular simulation can be carried out in the molecular orbital basis with as few as 4000 layers of parallel nearest-neighbor two-qubit gates, consisting of fewer than 10⁵non-Clifford rotations. We also apply our algorithm to iron–sulfur clusters relevant for elucidating the mode of action of metalloenzymes. 

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