Best practices for the execution, analysis, and data storage of plant single-cell/nucleus transcriptomics.

Single-cell and single-nucleus RNA-sequencing technologies capture the expression of plant genes at an unprecedented resolution. Therefore, these technologies are gaining traction in plant molecular and developmental biology for elucidating the transcriptional changes across cell types in a specific tissue or organ, upon treatments, in response to biotic and abiotic stresses, or between genotypes. Despite the rapidly accelerating use of these technologies, collective and standardized experimental and analytical procedures to support the acquisition of high-quality data sets are still missing. In this commentary, we discuss common challenges associated with the use of single-cell transcriptomics in plants and propose general guidelines to improve reproducibility, quality, comparability, and interpretation and to make the data readily available to the community in this fast-developing field of research.

Biologically meaningful regulatory logic enhances the convergence rate in Boolean networks and bushiness of their state transition graph.

Boolean models of gene regulatory networks (GRNs) have gained widespread traction as they can easily recapitulate cellular phenotypes via their attractor states. Their overall dynamics are embodied in a state transition graph (STG). Indeed, two Boolean networks (BNs) with the same network structure and attractors can have drastically different STGs depending on the type of Boolean functions (BFs) employed. Our objective here is to systematically delineate the effects of different classes of BFs on the structural features of the STG of reconstructed Boolean GRNs while keeping network structure and biological attractors fixed, and explore the characteristics of BFs that drive those features. Using $10$ reconstructed Boolean GRNs, we generate ensembles that differ in BFs and compute from their STGs the dynamics' rate of contraction or 'bushiness' and rate of 'convergence', quantified with measures inspired from cellular automata (CA) that are based on the garden-of-Eden (GoE) states. We find that biologically meaningful BFs lead to higher STG 'bushiness' and 'convergence' than random ones. Obtaining such 'global' measures gets computationally expensive with larger network sizes, stressing the need for feasible proxies. So we adapt Wuensche's $Z$-parameter in CA to BFs in BNs and provide four natural variants, which, along with the average sensitivity of BFs computed at the network level, comprise our descriptors of local dynamics and we find some of them to be good proxies for bushiness. Finally, we provide an excellent proxy for the 'convergence' based on computing transient lengths originating at random states rather than GoE states.

Leveraging developmental landscapes for model selection in Boolean gene regulatory networks.

Boolean models are a well-established framework to model developmental gene regulatory networks (DGRNs) for acquisition of cellular identities. During the reconstruction of Boolean DGRNs, even if the network structure is given, there is generally a large number of combinations of Boolean functions that will reproduce the different cell fates (biological attractors). Here we leverage the developmental landscape to enable model selection on such ensembles using the relative stability of the attractors. First we show that previously proposed measures of relative stability are strongly correlated and we stress the usefulness of the one that captures best the cell state transitions via the mean first passage time (MFPT) as it also allows the construction of a cellular lineage tree. A property of great computational importance is the insensitivity of the different stability measures to changes in noise intensities. That allows us to use stochastic approaches to estimate the MFPT and thereby scale up the computations to large networks. Given this methodology, we revisit different Boolean models of Arabidopsis thaliana root development, showing that a most recent one does not respect the biologically expected hierarchy of cell states based on relative stabilities. We therefore developed an iterative greedy algorithm that searches for models which satisfy the expected hierarchy of cell states and found that its application to the root development model yields many models that meet this expectation. Our methodology thus provides new tools that can enable reconstruction of more realistic and accurate Boolean models of DGRNs.

SeSAM: software for automatic construction of order-robust linkage maps.

BACKGROUND: Genotyping and sequencing technologies produce increasingly large numbers of genetic markers with potentially high rates of missing or erroneous data. Therefore, the construction of linkage maps is more and more complex. Moreover, the size of segregating populations remains constrained by cost issues and is less and less commensurate with the numbers of SNPs available. Thus, guaranteeing a statistically robust marker order requires that maps include only a carefully selected subset of SNPs. RESULTS: In this context, the SeSAM software allows automatic genetic map construction using seriation and placement approaches, to produce (1) a high-robustness framework map which includes as many markers as possible while keeping the order robustness beyond a given statistical threshold, and (2) a high-density total map including the framework plus almost all polymorphic markers. During this process, care is taken to limit the impact of genotyping errors and of missing data on mapping quality. SeSAM can be used with a wide range of biparental populations including from outcrossing species for which phases are inferred on-the-fly by maximum-likelihood during map elongation. The package also includes functions to simulate data sets, convert data formats, detect putative genotyping errors, visualize data and map quality (including graphical genotypes), and merge several maps into a consensus. SeSAM is also suitable for interactive map construction, by providing lower-level functions for 2-point and multipoint EM analyses. The software is implemented in a R package including functions in C++. CONCLUSIONS: SeSAM is a fully automatic linkage mapping software designed to (1) produce a framework map as robust as desired by optimizing the selection of a subset of markers, and (2) produce a high-density map including almost all polymorphic markers. The software can be used with a wide range of biparental mapping populations including cases from outcrossing. SeSAM is freely available under a GNU GPL v3 license and works on Linux, Windows, and macOS platforms. It can be downloaded together with its user-manual and quick-start tutorial from ForgeMIA (SeSAM project) at https://forgemia.inra.fr/gqe-acep/sesam/-/releases.

Enhancing backcross programs through increased recombination.

BACKGROUND: Introgression of a quantitative trait locus (QTL) by successive backcrosses is used to improve elite lines (recurrent parent) by introducing alleles from exotic material (donor parent). In the absence of selection, the proportion of the donor genome decreases by half at each generation. However, since selection is for the donor allele at the QTL, elimination of the donor genome around that QTL will be much slower than in the rest of the genome (i.e. linkage drag). Using markers to monitor the genome around the QTL and in the genetic background can accelerate the return to the recurrent parent genome. Successful introgression of a locus depends partly on the occurrence of crossovers at favorable positions. However, the number of crossovers per generation is limited and their distribution along the genome is heterogeneous. Recently, techniques have been developed to modify these two recombination parameters. RESULTS: In this paper, we assess, by simulations in the context of Brassicaceae, the effect of increased recombination on the efficiency of introgression programs by studying the decrease in linkage drag and the recovery of the recurrent genome. The simulated selection schemes begin by two generations of foreground selection and continue with one or more generations of background selection. Our results show that, when the QTL is in a region that initially lacked crossovers, an increase in recombination rate can decrease linkage drag by nearly ten-fold after the foreground selection and improves the return to the recurrent parent. However, if the QTL is in a region that is already rich in crossovers, an increase in recombination rate is detrimental. CONCLUSIONS: Depending on the recombination rate in the region targeted for introgression, increasing it can be beneficial or detrimental. Thus, the simulations analysed in this paper help us understand how an increase in recombination rate can be beneficial. They also highlight the best methods that can be used to increase recombination rate, depending on the situation.

Recombination suppression in heterozygotes for a pericentric inversion induces the interchromosomal effect on crossovers in Arabidopsis.

During meiosis, recombination ensures allelic exchanges through crossovers (COs) between the homologous chromosomes. Advances in our understanding of the rules of COs have come from studies of mutations including structural chromosomal rearrangements that, when heterozygous, are known to impair COs in various organisms. In this work, we investigate the effect of a large heterozygous pericentric inversion on male and female recombination in Arabidopsis. The inversion was discovered in the Atmcc1 mutant background and was characterized through genetic and next-generation sequencing analysis. Reciprocal backcross populations, each consisting of over 400 individuals, obtained from the mutant and the wild type, both crossed with Landsberg erecta, were analyzed genome-wide by 143 single-nucleotide polymorphisms. The negative impact of inversion became evident in terms of CO loss in the rearranged chromosome in both male and female meiosis. No single-CO event was detected within the inversion, consistent with a post-meiotic selection operating against unbalanced gametes. Cytological analysis of chiasmata in F1 plants confirmed that COs were reduced in male meiosis in the chromosome with inversion. Crossover suppression on the rearranged chromosome is associated with a significant increase of COs in the other chromosomes, thereby maintaining unchanged the number of COs per cell. The CO pattern observed in our study is consistent with the interchromosomal (IC) effect as first described in Drosophila. In contrast to male meiosis, in female meiosis no IC effect is visible. This may be related to the greater strength of interference that constrains the CO number in excess of the minimum value imposed by CO assurance in Arabidopsis female meiosis.

Amplifying recombination genome-wide and reshaping crossover landscapes in Brassicas.

Meiotic recombination by crossovers (COs) is tightly regulated, limiting its key role in producing genetic diversity. However, while COs are usually restricted in number and not homogenously distributed along chromosomes, we show here how to disrupt these rules in Brassica species by using allotriploid hybrids (AAC, 2n = 3x = 29), resulting from the cross between the allotetraploid rapeseed (B. napus, AACC, 2n = 4x = 38) and one of its diploid progenitors (B. rapa, AA, 2n = 2x = 20). We produced mapping populations from different genotypes of both diploid AA and triploid AAC hybrids, used as female and/or as male. Each population revealed nearly 3,000 COs that we studied with SNP markers well distributed along the A genome (on average 1 SNP per 1.25 Mbp). Compared to the case of diploids, allotriploid hybrids showed 1.7 to 3.4 times more overall COs depending on the sex of meiosis and the genetic background. Most surprisingly, we found that such a rise was always associated with (i) dramatic changes in the shape of recombination landscapes and (ii) a strong decrease of CO interference. Hybrids carrying an additional C genome exhibited COs all along the A chromosomes, even in the vicinity of centromeres that are deprived of COs in diploids as well as in most studied species. Moreover, in male allotriploid hybrids we found that Class I COs are mostly responsible for the changes of CO rates, landscapes and interference. These results offer the opportunity for geneticists and plant breeders to dramatically enhance the generation of diversity in Brassica species by disrupting the linkage drag coming from limits on number and distribution of COs.

Feedback between environment and traits under selection in a seasonal environment: consequences for experimental evolution.

Batch cultures are frequently used in experimental evolution to study the dynamics of adaptation. Although they are generally considered to simply drive a growth rate increase, other fitness components can also be selected for. Indeed, recurrent batches form a seasonal environment where different phases repeat periodically and different traits can be under selection in the different seasons. Moreover, the system being closed, organisms may have a strong impact on the environment. Thus, the study of adaptation should take into account the environment and eco-evolutionary feedbacks. Using data from an experimental evolution on yeast Saccharomyces cerevisiae, we developed a mathematical model to understand which traits are under selection, and what is the impact of the environment for selection in a batch culture. We showed that two kinds of traits are under selection in seasonal environments: life-history traits, related to growth and mortality, but also transition traits, related to the ability to react to environmental changes. The impact of environmental conditions can be summarized by the length of the different seasons which weight selection on each trait: the longer a season is, the higher the selection on associated traits. Since phenotypes drive season length, eco-evolutionary feedbacks emerge. Our results show how evolution in successive batches can affect season lengths and strength of selection on different traits.

High-throughput measurement of recombination rates and genetic interference in Saccharomyces cerevisiae.

Allelic recombination owing to meiotic crossovers is a major driver of genome evolution, as well as a key player for the selection of high-performing genotypes in economically important species. Therefore, we developed a high-throughput and low-cost method to measure recombination rates and crossover patterning (including interference) in large populations of the budding yeast Saccharomyces cerevisiae. Recombination and interference were analysed by flow cytometry, which allows time-consuming steps such as tetrad microdissection or spore growth to be avoided. Moreover, our method can also be used to compare recombination in wild-type vs. mutant individuals or in different environmental conditions, even if the changes in recombination rates are small. Furthermore, meiotic mutants often present recombination and/or pairing defects affecting spore viability but our method does not involve growth steps and thus avoids filtering out non-viable spores.

Recombination patterns in maize reveal limits to crossover homeostasis.

During meiotic recombination, double-strand breaks (DSBs) are formed in chromosomal DNA and then repaired as either crossovers (COs) or non-crossovers (NCOs). In most taxa, the number of DSBs vastly exceeds the number of COs. COs are required for generating genetic diversity in the progeny, as well as proper chromosome segregation. Their formation is tightly controlled so that there is at least one CO per pair of homologous chromosomes whereas the maximum number of COs per chromosome pair is fairly limited. One of the main mechanisms controlling the number of recombination events per meiosis is CO homeostasis, which maintains a stable CO number even when the DSB number is dramatically altered. The existence of CO homeostasis has been reported in several species, including mouse, yeast, and Caenorhabditis elegans. However, it is not known whether homeostasis exists in the same form in all species. In addition, the studies of homeostasis have been conducted using mutants and/or transgenic lines exhibiting fairly severe meiotic phenotypes, and it is unclear how important homeostasis is under normal physiological conditions. We found that, in maize, CO control is robust only to ensure one CO per chromosome pair. However, once this limit is reached, the CO number is linearly related to the DSB number. We propose that CO control is a multifaceted process whose different aspects have a varying degree of importance in different species.

Crossover localisation is regulated by the neddylation posttranslational regulatory pathway.

Crossovers (COs) are at the origin of genetic variability, occurring across successive generations, and they are also essential for the correct segregation of chromosomes during meiosis. Their number and position are precisely controlled, however the mechanisms underlying these controls are poorly understood. Neddylation/rubylation is a regulatory pathway of posttranslational protein modification that is required for numerous cellular processes in eukaryotes, but has not yet been linked to homologous recombination. In a screen for meiotic recombination-defective mutants, we identified several axr1 alleles, disrupting the gene encoding the E1 enzyme of the neddylation complex in Arabidopsis. Using genetic and cytological approaches we found that axr1 mutants are characterised by a shortage in bivalent formation correlated with strong synapsis defects. We determined that the bivalent shortage in axr1 is not due to a general decrease in CO formation but rather due to a mislocalisation of class I COs. In axr1, as in wild type, COs are still under the control of the ZMM group of proteins. However, in contrast to wild type, they tend to cluster together and no longer follow the obligatory CO rule. Lastly, we showed that this deregulation of CO localisation is likely to be mediated by the activity of a cullin 4 RING ligase, known to be involved in DNA damage sensing during somatic DNA repair and mouse spermatogenesis. In conclusion, we provide evidence that the neddylation/rubylation pathway of protein modification is a key regulator of meiotic recombination. We propose that rather than regulating the number of recombination events, this pathway regulates their localisation, through the activation of cullin 4 RING ligase complexes. Possible targets for these ligases are discussed.

Constrained Allocation Flux Balance Analysis.

New experimental results on bacterial growth inspire a novel top-down approach to study cell metabolism, combining mass balance and proteomic constraints to extend and complement Flux Balance Analysis. We introduce here Constrained Allocation Flux Balance Analysis, CAFBA, in which the biosynthetic costs associated to growth are accounted for in an effective way through a single additional genome-wide constraint. Its roots lie in the experimentally observed pattern of proteome allocation for metabolic functions, allowing to bridge regulation and metabolism in a transparent way under the principle of growth-rate maximization. We provide a simple method to solve CAFBA efficiently and propose an "ensemble averaging" procedure to account for unknown protein costs. Applying this approach to modeling E. coli metabolism, we find that, as the growth rate increases, CAFBA solutions cross over from respiratory, growth-yield maximizing states (preferred at slow growth) to fermentative states with carbon overflow (preferred at fast growth). In addition, CAFBA allows for quantitatively accurate predictions on the rate of acetate excretion and growth yield based on only 3 parameters determined by empirical growth laws.

Combined fluorescent and electron microscopic imaging unveils the specific properties of two classes of meiotic crossovers.

Crossovers (COs) shuffle genetic information and allow balanced segregation of homologous chromosomes during the first division of meiosis. In several organisms, mutants demonstrate that two molecularly distinct pathways produce COs. One pathway produces class I COs that exhibit interference (lowered probability of nearby COs), and the other pathway produces class II COs with little or no interference. However, the relative contributions, genomic distributions, and interactions of these two pathways are essentially unknown in nonmutant organisms because marker segregation only indicates that a CO has occurred, not its class type. Here, we combine the efficiency of light microscopy for revealing cellular functions using fluorescent probes with the high resolution of electron microscopy to localize and characterize COs in the same sample of meiotic pachytene chromosomes from wild-type tomato. To our knowledge, for the first time, every CO along each chromosome can be identified by class to unveil specific characteristics of each pathway. We find that class I and II COs have different recombination profiles along chromosomes. In particular, class II COs, which represent about 18% of all COs, exhibit no interference and are disproportionately represented in pericentric heterochromatin, a feature potentially exploitable in plant breeding. Finally, our results demonstrate that the two pathways are not independent because there is interference between class I and II COs.

Phenotypic innovation through recombination in genome-scale metabolic networks.

Recombination is an important source of metabolic innovation, especially in prokaryotes, which have evolved the ability to survive on many different sources of chemical elements and energy. Metabolic systems have a well-understood genotype-phenotype relationship, which permits a quantitative and biochemically principled understanding of how recombination creates novel phenotypes. Here, we investigate the power of recombination to create genome-scale metabolic reaction networks that enable an organism to survive in new chemical environments. To this end, we use flux balance analysis, an experimentally validated computational method that can predict metabolic phenotypes from metabolic genotypes. We show that recombination is much more likely to create novel metabolic abilities than random changes in chemical reactions of a metabolic network. We also find that phenotypic innovation is more likely when recombination occurs between parents that are genetically closely related, phenotypically highly diverse, and viable on few rather than many carbon sources. Survival on a new carbon source preferentially involves reactions that are superessential, that is, essential in many metabolic networks. We validate our observations with data from 61 reconstructed prokaryotic metabolic networks. Our systematic and quantitative analysis of metabolic systems helps understand how recombination creates innovation.

Statistical Physics Methods Provide the Exact Solution to a Long-Standing Problem of Genetics.

Analytic and computational methods developed within statistical physics have found applications in numerous disciplines. In this Letter, we use such methods to solve a long-standing problem in statistical genetics. The problem, posed by Haldane and Waddington [Genetics 16, 357 (1931)], concerns so-called recombinant inbred lines (RILs) produced by repeated inbreeding. Haldane and Waddington derived the probabilities of RILs when considering two and three genes but the case of four or more genes has remained elusive. Our solution uses two probabilistic frameworks relatively unknown outside of physics: Glauber's formula and self-consistent equations of the Schwinger-Dyson type. Surprisingly, this combination of statistical formalisms unveils the exact probabilities of RILs for any number of genes. Extensions of the framework may have applications in population genetics and beyond.

Crossover rate between homologous chromosomes and interference are regulated by the addition of specific unpaired chromosomes in Brassica.

Recombination is a major mechanism generating genetic diversity, but the control of the crossover rate remains a key question. In Brassica napus (AACC, 2n = 38), we can increase the homologous recombination between A genomes in AAC hybrids. Hypotheses for this effect include the number of C univalent chromosomes, the ratio between univalents and bivalents and, finally, which of the chromosomes are univalents. To test these hypotheses, we produced AA hybrids with zero, one, three, six or nine additional C chromosomes and four different hybrids carrying 2n = 32 and 2n = 35 chromosomes. The genetic map lengths for each hybrid were established to compare their recombination rates. The rates were 1.4 and 2.7 times higher in the hybrids having C6 or C9 alone than in the control (0C). This enhancement reached 3.1 and 4.1 times in hybrids carrying six and nine C chromosomes, and it was also higher for each pair of hybrids carrying 2n = 32 or 2n = 35 chromosomes, with a dependence on which chromosomes remained as univalents. We have shown, for the first time, that the presence of one chromosome, C9 , affects significantly the recombination rate and reduces crossover interference. This result will have fundamental implications on the regulation of crossover frequency.

Genome-wide crossover distribution in Arabidopsis thaliana meiosis reveals sex-specific patterns along chromosomes.

In most species, crossovers (COs) are essential for the accurate segregation of homologous chromosomes at the first meiotic division. Their number and location are tightly regulated. Here, we report a detailed, genome-wide characterization of the rate and localization of COs in Arabidopsis thaliana, in male and female meiosis. We observed dramatic differences between male and female meiosis which included: (i) genetic map length; 575 cM versus 332 cM respectively; (ii) CO distribution patterns: male CO rates were very high at both ends of each chromosome, whereas female CO rates were very low; (iii) correlations between CO rates and various chromosome features: female CO rates correlated strongly and negatively with GC content and gene density but positively with transposable elements (TEs) density, whereas male CO rates correlated positively with the CpG ratio. However, except for CpG, the correlations could be explained by the unequal repartition of these sequences along the Arabidopsis chromosome. For both male and female meiosis, the number of COs per chromosome correlates with chromosome size expressed either in base pairs or as synaptonemal complex length. Finally, we show that interference modulates the CO distribution both in male and female meiosis.

Preponderance of generalized chain functions in reconstructed Boolean models of biological networks.

Boolean networks (BNs) have been extensively used to model gene regulatory networks (GRNs). The dynamics of BNs depend on the network architecture and regulatory logic rules (Boolean functions (BFs)) associated with nodes. Nested canalyzing functions (NCFs) have been shown to be enriched among the BFs in the large-scale studies of reconstructed Boolean models. The central question we address here is whether that enrichment is due to certain sub-types of NCFs. We build on one sub-type of NCFs, the chain functions (or chain-0 functions) proposed by Gat-Viks and Shamir. First, we propose two other sub-types of NCFs, namely, the class of chain-1 functions and generalized chain functions, the union of the chain-0 and chain-1 types. Next, we find that the fraction of NCFs that are chain-0 (also holds for chain-1) functions decreases exponentially with the number of inputs. We provide analytical treatment for this and other observations on BFs. Then, by analyzing three different datasets of reconstructed Boolean models we find that generalized chain functions are significantly enriched within the NCFs. Lastly we illustrate that upon imposing the constraints of generalized chain functions on three different GRNs we are able to obtain biologically viable Boolean models.

Two types of meiotic crossovers coexist in maize.

We apply modeling approaches to investigate the distribution of late recombination nodules in maize (Zea mays). Such nodules indicate crossover positions along the synaptonemal complex. High-quality nodule data were analyzed using two different interference models: the "statistical" gamma model and the "mechanical" beam film model. For each chromosome, we exclude at a 98% significance level the hypothesis that a single pathway underlies the formation of all crossovers, pointing to the coexistence of two types of crossing-over in maize, as was previously demonstrated in other organisms. We estimate the proportion of crossovers coming from the noninterfering pathway to range from 6 to 23% depending on the chromosome, with a cell average of approximately 15%. The mean number of noninterfering crossovers per chromosome is significantly correlated with the length of the synaptonemal complex. We also quantify the intensity of interference. Finally, we develop inference tools that allow one to tackle, without much loss of power, complex crossover interference models such as the beam film. The lack of a likelihood function in such models had prevented their use for parameter estimation. This advance will allow more realistic mechanisms of crossover formation to be modeled in the future.

A preference for link operator functions can drive Boolean biological networks towards critical dynamics.

Boolean modelling is a powerful framework to understand the operating principles of biological networks. The regulatory logic between biological entities in these networks is expressed as Boolean functions (BFs). There exist various types of BFs (and thus regulatory logic rules) which are meaningful in the biological context. In this contribution, we explore one such type, known as link operator functions (LOFs). We theoretically enumerate these functions and show that, among all BFs and even within the biologically consistent effective and unate functions (EUFs), the LOFs form a tiny subset. We then find that the AND-NOT LOFs are particularly abundant in reconstructed biological Boolean networks. By leveraging these facts, namely, the tiny representation of LOFs in the space of EUFs and their presence in the biological dataset, we show that the space of acceptable models can be shrunk by applying steady-state constraints to BFs, followed by the choice of LOFs which satisfy those constraints. Finally, we demonstrate that among a wide range of BFs, the LOFs drive biological network dynamics towards criticality.