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Interactive theorem provers are computer programs that check whether mathematical statements are correct. We show how the mathematics of theories in chemical physics can be written in the language of the Lean theorem prover, allowing chemical theory to be made even more rigorous and providing insight into the mathematics behind a theory. We use Lean to precisely define the assumptions and derivations of the Langmuir and BET theories of adsorption. We can also go further and create a network of definitions that build off of each other. This allows us to define a common basis for equations of motion or thermodynamics and derive many statements about them, like the kinematic equations of motion or gas laws such as Boyle's law. This approach could be extended beyond chemistry, and we propose the creation of a library of formally-proven theories in all fields of science. Furthermore, the rigorous logic of theorem provers complements the generative capabilities of AI models that generate code; we anticipate their integration to be valuable for automating the discovery of new scientific theories. 

Ethiopian mustard (Brassica carinata) is an ancient crop with remarkable stress resilience and a desirable seed fatty acid profile for biofuel uses. Brassica carinata is one of six Brassica species that share three major genomes from three diploid species (AA, BB, and CC) that spontaneously hybridized in a pairwise manner to form three allotetraploid species (AABB, AACC, and BBCC). Of the genomes of these species, that of B. carinata is the least understood. Here, we report a chromosome scale 1.31-Gbp genome assembly with 156.9-fold sequencing coverage for B. carinata, completing the reference genomes comprising the classic Triangle of U, a classical theory of the evolutionary relationships among these six species. Our assembly provides insights into the hybridization event that led to the current B. carinata genome and the genomic features that gave rise to the superior agronomic traits of B. carinata. Notably, we identified an expansion of transcription factor networks and agronomically important gene families. Completion of the Triangle of U comparative genomics platform has allowed us to examine the dynamics of polyploid evolution and the role of subgenome dominance in the domestication and continuing agronomic improvement of B. carinata and other Brassica species.

 

Despite early domestication around 3000 BC, the evolutionary history of the ancient allotetraploid speciesBrassica juncea(L.) Czern & Coss remains uncertain. Here, we report a chromosome-scale de novo assembly of a yellow-seededB. junceagenome by integrating long-read and short-read sequencing, optical mapping and Hi-C technologies. Nuclear and organelle phylogenies of 480 accessions worldwide supported thatB. junceais most likely a single origin in West Asia, 8,000–14,000 years ago, via natural interspecific hybridization. Subsequently, new crop types evolved through spontaneous gene mutations and introgressions along three independent routes of eastward expansion. Selective sweeps, genome-wide trait associations and tissue-specific RNA-sequencing analysis shed light on the domestication history of flowering time and seed weight, and on human selection for morphological diversification in this versatile species. Our data provide a comprehensive insight into the origin and domestication and a foundation for genomics-based breeding ofB. juncea.

 

Plants are often attacked by insects and other herbivores. As a result, they have evolved to defend themselves by producing many different chemicals that are toxic to these pests. As producing each chemical costs energy, individual plants often only produce one type of chemical that is targeted towards their main herbivore. Related species of plants often use the same type of chemical defense so, if a particular herbivore gains the ability to cope with this chemical, it may rapidly become an important pest for the whole plant family. To escape this threat, some plants have gained the ability to produce more than one type of chemical defense. Wallflowers, for example, are a group of plants in the mustard family that produce two types of toxic chemicals: mustard oils, which are common in most plants in this family; and cardenolides, which are an innovation of the wallflowers, and which are otherwise found only in distantly related plants such as foxglove and milkweed. The combination of these two chemical defenses within the same plant may have allowed the wallflowers to escape attacks from their main herbivores and may explain why the number of wallflower species rapidly increased within the last two million years. Züst et al. have now studied the diversity of mustard oils and cardenolides present in many different species of wallflower. This analysis revealed that almost all of the tested wallflower species produced high amounts of both chemical defenses, while only one species lacked the ability to produce cardenolides. The levels of mustard oils had no relation to the levels of cardenolides in the tested species, which suggests that the regulation of these two defenses is not linked. Furthermore, Züst et al. found that closely related wallflower species produced more similar cardenolides, but less similar mustard oils, to each other. This suggests that mustard oils and cardenolides have evolved independently in wallflowers and have distinct roles in the defense against different herbivores. The evolution of insect resistance to pesticides and other toxins is an important concern for agriculture. Applying multiple toxins to crops at the same time is an important strategy to slow the evolution of resistance in the pests. The findings of Züst et al. describe a system in which plants have naturally evolved an equivalent strategy to escape their main herbivores. Understanding how plants produce multiple chemical defenses, and the costs involved, may help efforts to breed crop species that are more resistant to herbivores and require fewer applications of pesticides. 

Many crops are polyploid or have a polyploid ancestry. Recent phylogenetic analyses have found that polyploidy often preceded the domestication of crop plants. One explanation for this observation is that increased genetic diversity following polyploidy may have been important during the strong artificial selection that occurs during domestication.

In order to test the connection between domestication and polyploidy, we identified and examined candidate genes associated with the domestication of the diverse crop varieties ofBrassica rapa. Like all ‘diploid’ flowering plants,B. rapahas a diploidized paleopolyploid genome and experienced many rounds of whole genome duplication (WGD). We analyzed transcriptome data of more than 100 cultivatedB. rapaaccessions.

Using a combination of approaches, we identified > 3000 candidate genes associated with the domestication of four majorB. rapacrop varieties. Consistent with our expectation, we found that the candidate genes were significantly enriched with genes derived from the Brassiceae mesohexaploidy. We also observed that paleologs were significantly more diverse than non‐paleologs.

Our analyses find evidence for that genetic diversity derived from ancient polyploidy played a key role in the domestication ofB. rapaand provide support for its importance in the success of modern agriculture.

 

Whole‐genome duplications (WGDs) are prevalent throughout the evolutionary history of plants. For example, dozens of WGDs have been phylogenetically localized across the order Brassicales, specifically, within the family Brassicaceae. A WGD event has also been identified in the Cleomaceae, the sister family to Brassicaceae, yet its placement, as well as that of WGDs in other families in the order, remains unclear.

Phylo‐transcriptomic data were generated and used to infer a nuclear phylogeny for 74 Brassicales taxa. Genome survey sequencing was also performed on 66 of those taxa to infer a chloroplast phylogeny. These phylogenies were used to assess and confirm relationships among the major families of the Brassicales and within Brassicaceae. Multiple WGD inference methods were then used to assess the placement of WGDs on the nuclear phylogeny.

Well‐supported chloroplast and nuclear phylogenies for the Brassicales and the putative placement of the Cleomaceae‐specific WGD event Th‐ɑ are presented. This work also provides evidence for previously hypothesized WGDs, including a well‐supported event shared by at least two members of the Resedaceae family, and a possible event within the Capparaceae.

Phylogenetics and the placement of WGDs within highly polyploid lineages continues to be a major challenge. This study adds to the conversation on WGD inference difficulties by demonstrating that sampling is especially important for WGD identification and phylogenetic placement. Given its economic importance and genomic resources, the Brassicales continues to be an ideal group for assessing WGD inference methods.

 

Green plants (Viridiplantae) include around 450,000–500,000 species of great diversity and have important roles in terrestrial and aquatic ecosystems. Here, as part of the One Thousand Plant Transcriptomes Initiative, we sequenced the vegetative transcriptomes of 1,124 species that span the diversity of plants in a broad sense (Archaeplastida), including green plants (Viridiplantae), glaucophytes (Glaucophyta) and red algae (Rhodophyta). Our analysis provides a robust phylogenomic framework for examining the evolution of green plants. Most inferred species relationships are well supported across multiple species tree and supermatrix analyses, but discordance among plastid and nuclear gene trees at a few important nodes highlights the complexity of plant genome evolution, including polyploidy, periods of rapid speciation, and extinction. Incomplete sorting of ancestral variation, polyploidization and massive expansions of gene families punctuate the evolutionary history of green plants. Notably, we find that large expansions of gene families preceded the origins of green plants, land plants and vascular plants, whereas whole-genome duplications are inferred to have occurred repeatedly throughout the evolution of flowering plants and ferns. The increasing availability of high-quality plant genome sequences and advances in functional genomics are enabling research on genome evolution across the green tree of life.