Phenotypic switching of populations of cells in a stochastic environment

In biology phenotypic switching is a common bet-hedging strategy in the face of uncertain environmental conditions. Existing mathematical models often focus on periodically changing environments to determine the optimal phenotypic response. We focus on the case in which the environment switches randomly between discrete states. Starting from an individual-based model we derive stochastic differential equations to describe the dynamics, and obtain analytical expressions for the mean instantaneous growth rates based on the theory of piecewise deterministic Markov processes. We show that optimal phenotypic responses are non-trivial for slow and intermediate environmental processes, and systematically compare the cases of periodic and random environments. The best response to random switching is more likely to be heterogeneity than in the case of deterministic periodic environments, net growth rates tend to be higher under stochastic environmental dynamics. The combined system of environment and population of cells can be interpreted as host-pathogen interaction, in which the host tries to choose environmental switching so as to minimise growth of the pathogen, and in which the pathogen employs a phenotypic switching optimised to increase its growth rate. We discuss the existence of Nash-like mutual best-response scenarios for such host-pathogen games.Comment: 17 pages, 6 figure

ANNOTATION AND EXPRESSION OF FDM-LIKE GENES IN SEXUAL AND APOMICTIC H. PERFORATUM ACCESSIONS

Apomixis is an asexual reproductive strategy that permits to the inheritance of the maternal genome over generations without genetic recombination events. From a biological point of view, this modality of asexual reproduction by seed could be the consequence of heterocronic expression of genes involved in fundamental aspects of sexual reproduction, such as meiosis and spore selection, leading to the formation of functional un-reduced gametes which retain the ability to form an embryo eventually bypassing double fertilization. Although this process is well documented in many flowering plants, and despite its revolutionary potentials in plant breeding strategies, the genetic control of apomixes is still not properly understood. Recently, a number of independent studies on sexual model species provided experimental evidences linking single components of apomixis to the deregulation of genes involved in the RNA-directed DNA methylation pathway (RdDM). RNA-directed DNA methylation refers to a specific process in which small interfering RNAs produced by the RNA interference pathway guide de novo methylation of cytosines at the homologous DNA region, thereby regulating the expression of specific genes. Remarkably, gene expression studies in the apomictic model species Hypericum perforatum corroborate the hypothesis that miss expression of genes involved in this pathway is functionally associated with early events of apomixes in this species. The aim of the present research is a better understanding of the role of a class of genes involved in the RdDM known as Factor of DNA Methylation (FDM), in the frame of ovule cell fate change, megagametogenesis and, ultimately, aposporous apomixis. To this end, computational investigations were performed in order to annotate the H. perforatum FDM genes. The expression of these genes in H. perforatum pistils and ovules was studied by qPCR and ISH assays on sexual and apomictic accessions. Furthermore, Arabidopsis thaliana knock out lines were characterized in order to elucidate the role of specific genes in relation to gametophyte and/or seed formation. All data will be presented and critically discussed as they prove a better understanding of molecular bases of apomixes in H. perforatum

Intrinsic noise in systems with switching environments

We study individual-based dynamics in finite populations, subject to randomly switching environmental conditions. These are inspired by models in which genes transition between on and off states, regulating underlying protein dynamics. Similarly switches between environmental states are relevant in bacterial populations and in models of epidemic spread. Existing piecewise-deterministic Markov process (PDMP) approaches focus on the deterministic limit of the population dynamics while retaining the randomness of the switching. Here we go beyond this approximation and explicitly include effects of intrinsic stochasticity at the level of the linear-noise approximation. Specifically we derive the stationary distributions of a number of model systems, in good agreement with simulations. This improves existing approaches which are limited to the regimes of fast and slow switching.Comment: 15 pages, 11 figure

Dynamics of adaptive agents with asymmetric information

We apply path-integral techniques to study the dynamics of agent-based models with asymmetric information structures. In particular, we devise a batch version of a model proposed originally by Berg et al. [Quant. Fin. 1 (2001) 203], and convert the coupled multi-agent processes into an effective-agent problem from which the dynamical order parameters in ergodic regimes can be derived self-consistently together with the corresponding phase structure. Our dynamical study complements and extends the available static theory. Results are confirmed by numerical simulations.Comment: minor revision of text, accepted by JSTA

TRANSCRIPTOMIC ANALYSIS OF OVULE-SPECIFIC CELL LINEAGES TO IDENTIFY GENES RELATED TO APOSPOROUS APOMIXIS IN HYPERICUM PERFORATUM L.

The medicinal plant St. John\u2019s wort (Hypericum perforatum L.) is an attractive model system for the study of aposporous apomixis. The key biological features of apomixis in this species are the by-passing of meiosis, the differentiation of aposporous initials into embryo sacs containing unreduced egg cells, their autonomous development in functional embryos without fertilization, and the formation of viable endosperm either via fertilization-independent means or following fertilization with a sperm nucleus. The aim of this research is to define gene expression changes occurring in the nucellar cell types of the ovules primarily involved in the differentiation of the megaspore mother cells and aposporous initials. To this end, a laser-capture microdissection approach was adopted in combination with the RNA-seq technology in order to restrict the frame of our investigations to a specific portion of the ovule, i.e. the nucellus, at developmental stages preceding the differentiation of aposporous initials. Overall, our gene expression analysis identified 270 and 81 unigenes that were found significantly up- and down-regulated between ovules collected from sexual and apomictic accessions. Ontological annotation of differentially expressed genes indicated that genes up-regulated in apomictic ovules were significantly enriched in ontological terms related to the RNA-directed DNA polymerase activity and the RNA binding. Among these genes, several actors of the RdDM pathway were found, suggesting that the phenotypic expression of early events of aposporous apomixis is associated to changes in de novo DNA methylation mediated by small RNAs. Furthermore, as deregulation of single components of the sexual developmental pathway is believed to be a trigger of the apomictic reproductive program, genes involved in sporogenesis, gametogenesis and response to hormonal stimuli were annotated and investigated in great detail. The expression analysis of candidate genes was performed not only by Real-Time qPCR but also by ISH assays in order to verify the temporal and spatial expression patterns of selected transcripts in the ovule. Finally, the activity of specific genes in relation to embryo sac and/or embryo formation was investigated by using A. thaliana knock-out lines. Overall, our data suggest that phenotypic expression of aposporous apomixis is concomitant with the modulation of key genes involved in the sexual reproductive pathway, hormones and other actors likely playing a crucial role in the RNA-directed DNA methylation pathway

Annotation and Expression of IDN2-like and FDM-like genes in sexual and aposporous hypericum perforatum L. Accessions

The protein IDN2, together with the highly similar interactors FDM1 and FDM2, is required for RNA-directed DNA methylation (RdDM) and siRNA production. Epigenetic regulation of gene expression is required to restrict cell fate determination in A. thaliana ovules. Recently, three transcripts sharing high similarity with the A. thaliana IDN2 and FDM1-2 were found to be differentially expressed in ovules of apomictic Hypericum perforatum L. accessions. To gain further insight into the expression and regulation of these genes in the context of apomixis, we investigated genomic, transcriptional and functional aspects of the gene family in this species. The H. perforatum genome encodes for two IDN2-like and 7 FDM-like genes. Differential and heterochronic expression of FDM4-like genes was found in H. perforatum pistils. The involvement of these genes in reproduction and seed development is consistent with the observed reduction of the seed set and high variability in seed size in A. thaliana IDN2 and FDM-like knockout lines. Differential expression of IDN2-like and FDM-like genes in H. perforatum was predicted to affect the network of potential interactions between these proteins. Furthermore, pistil transcript levels are modulated by cytokinin and auxin but the effect operated by the two hormones depends on the reproductive phenotype

Random replicators with asymmetric couplings

Systems of interacting random replicators are studied using generating functional techniques. While replica analyses of such models are limited to systems with symmetric couplings, dynamical approaches as presented here allow specifically to address cases with asymmetric interactions where there is no Lyapunov function governing the dynamics. We here focus on replicator models with Gaussian couplings of general symmetry between p>=2 species, and discuss how an effective description of the dynamics can be derived in terms of a single-species process. Upon making a fixed point ansatz persistent order parameters in the ergodic stationary states can be extracted from this process, and different types of phase transitions can be identified and related to each other. We discuss the effects of asymmetry in the couplings on the order parameters and the phase behaviour for p=2 and p=3. Numerical simulations verify our theory. For the case of cubic interactions numerical experiments indicate regimes in which only a finite number of species survives, even when the thermodynamic limit is considered.Comment: revised version, removed some mathematical parts, discussion of negatively correlated couplings added, figures adde

ANNOTATION AND EXPRESSION OF FDM-LIKE GENES IN SEXUAL AND APOMICTIC MODEL SPECIES

Aposporous apomixis is a reproductive strategy that leads to seed production by avoiding female sporogenesis and, eventually, fertilization. In this peculiar reproductive strategy, embryo and endosperm are formed from unreduced gametes developing from somatic cells belonging to the ovule nucellus. Recently gained information on ovule gene expression in the apomictic model species Hypericum perforatum L. demonstrated that a few genes involved in the RNA-directed DNA methylation pathway (RdDM) are differentially expressed in ovules collected from apomictic accessions at pre-meiotic stages. In A. thaliana, the protein Involved in De Novo 2 (IDN2), together with members of the gene family Factors of DNA Methylation (FDM1, FDM2), acts downstream of the RdDM. In this pathway, IDN2/FDM complex are recruited to the chromatin by the ra-siRNAPol V transcript duplex, and then bind the un-methylated DNA to promote DNA methylation of both transposons and protein coding genes. Remarkably, the knock-out of genes involved in the RdDM in sexually reproducing species such as A. thaliana and Z. mays results in phenotypes mimicking early events of aposporous apomixis. Taken together, these findings let us to hypothesize that RNA-directed DNA methylation might be involved in correct patterning of cell fate determination in the ovule in sexual and apomictic species. This research focuses on genes belonging to the gene family known as Factors of DNA Methylation (FDM1-5) and their closely related IDN2 (Involved in De Novo 2). Our research aim is a better understanding of roles played by these genes in the frame of ovule cell fate determination and gametes formation. Bioinformatics analyses were performed in order to identify and annotate all gene family members expressed in H. perforatum ovules. Gene expression differences between pistils collected from sexual and apomictic accessions were confirmed by qPCR and ISH. Correlated experiments were performed by taking advantage of mutant lines available for A. thaliana. IDN2 and FDM1-5 knockout lines were analyzed for alterations in total seed set and plant habits. Mutant lines displayed overlapping phenotypes, including the reduction of seed set. Overall, our phenotypic data are in line with a sporophytic effect resulting in the ovule abortion in A. thaliana. GUS reporter lines were adopted to visualize the FDM promoter activity in ovules at different developmental time points. Furthermore, the development of a protocol suitable for whole-mount qPCR assays allowed rapid and reliable quantification of gene expression in micro-dissected ovules. Our results elucidate the role of FDM and IDN2 genes in both sexual and apomicts plants and add new factors affecting the complex events involved in ovule and gametes formation that should be further investigated

TRANSCRIPTOMIC ANALYSIS OF OVULE-SPECIFIC CELL LINEAGES TO IDENTIFY GENES RELATED TO APOSPOROUS APOMIXIS IN HYPERICUM PERFORATUM L.

Apomixis defines a plant reproductive strategy that, unlike sexual reproduction, permits the inheritance of the maternal genome without genetic recombination and syngamy. Earliest phenotypical symptoms of the aposporous developmental program in ovules are the avoidance of meiosis (i.e., apomeiosis) and the differentiation of functional unreduced embryo sacs from somatic cells of the nucellus (i.e., aposporous initials). Apospory deviates from sexuality as, in this latter case, the commitment to develop an embryo sac is strictly restricted to the reduced functional megaspore (FM) and failure of the meiotic program is typically not accompanied by the initiation of embryo sac development from cell lineages of the ovule other than the FM. Our research goal is a better understanding on gene expression changes accompanying the onset of aposporous apomixis in the ovule of the model species H. perforatum L. To this purpose, gene expression analyses were performed by adopting the RNA-seq technology on Laser-Capture Microdissected (LCM) ovule cells collected from sexual and apomictic genotypes at pre-meiotic developmental stages. We identified 402 differentially expressed genes (DEGs) (Bonferroni p-value 64 0.05) between ovules belonging to sexual and apomictic genotypes. Among these, 97 transcripts were only found in apomictic libraries, suggesting apomictic-specific expression. At the same time, 25 transcripts were only detected in sexual libraries. Differential expression was validated by RealTime qPCR and in-situ hybridization assay. Among identified DEGs, we found several RNAs whose products are related to biological processes modulated in other aposporous apomictic model species. Ontological annotation revealed an enrichment of the following biological processes in apomictic ovules: RNA binding, RNA splicing and RNA-directed DNA polymerase activity, this latter being associated to putative non-LTR retroelements. The massive expression of TEs in apomictic ovules suggested that DNA methylation is compromised in these cells. To address this question, we investigated the promoter and gene body DNA methylation level of a subset of DEGs by chop-PCR assays. Gene body methylation level of DEGs annotated as putative non-LTR retroelements supports the idea that transcriptomic changes for these genes might be epigenetically controlled. Furthermore, several genes involved in auxin and cytokinin (CK) homeostasis and signalling were found differentially expressed, implying that apomictic ovules might be subjected to alternative hormonal interplays. This let us hypothesise that hormonal response and DNA methylation might be connected to the transcriptional changes observed in apomictic ovules. To address this question, gene expression and promoter methylation studies were performed on flowers treated with synthetic CK and its antagonist PI-55. Gene expression and DNA methylation data will be presented and critically discussed in the frame of ovule and gamete development. Overall, our data suggest that phenotypic expression of early events of aposporous apomixis in H. perforatum is concomitant with the modulation of key genes involved in hormonal homeostasis, DNA methylation and cell cycle progression