Mathematical modeling of nitrogen regulated biological systems

• Autores: Pau Casanova Ferrer
• Directores de la Tesis: Saúl Ares García (dir. tes.) , Javier Manuel Muñoz Garcia (codir. tes.)
• Lectura: En la Universidad Carlos III de Madrid ( España ) en 2023
• Idioma: inglés
• Tribunal Calificador de la Tesis: Luis Guillermo Morelli (presid.) , María del Pilar Guerrero Contreras (secret.) , Vicente Mariscal Romero (voc.)
• Enlaces
  • Tesis en acceso abierto en: e-Archivo
• Resumen

  • This thesis studies the genetic regulatory network underlying the responses of two different organisms to environmental changes. We particularly study the reaction of both the cyanobacteria Anabaena and the rice plants to variation in the available nitrogen in their environment. But the regimes of nitrogen considered for these two systems during this thesis are quite different.

    For the Anabaena system, we study the activation of its nitrogen fixation capabilities when it is put under nitrogen deprivation conditions. This filamentous cyanobacterium undergoes a dynamical differentiation process that differentiates roughly one in every ten cells into nitrogen-fixing heterocyst, in a quasi-regular pattern that is maintained as the filament keeps growing.

    This study is initiated with an exhaustive revision of the state of the art of both experimental and theoretical modeling approaches. From this compilation of models, we observe that several Turing-like minimal 3 gene models can capture the formation of the pattern even in a discrete growing domain such as this.

    Then, we provide additional insight over this minimal models through a stability study over a 2-element system with simple diffusible inhibitor (patS) and a localized activator (hetR) from (Muñoz-García and Ares, 2016). We use the XPP-AUTO to obtain the bifurcation diagrams for all the parameter models for a two cell system. These diagrams show that this 2 cell present homogeneous, heterogeneous and biestable regimes for parameter values close to the WT parameters. Finally, we validate the results for the basal and regulated production of hetR with simulations of a 100 cell filaments. We show that this reduced system is already capable of shifting the filament between homogeneous and pattern-like heterogeneous regimes with small changes in the parameter values of the model.

    Later, we expand the existing model in order to reproduce the ¿patA phenotype, which presents heterocysts mostly on the filament ends without forming and internal pattern, we present an expantion of the model that includes both patA and hetF. This model proposes a maturation step for HetR necessary to habilitate its function as a transcription factor. Then, we hypothesize that HetF is essential for this maturation, and PatA would enhance it. The role of this genes is still not well-defined in the literature, but recent experimental studies seem to confirm both the existence of an HetR maturation process (Xiaomei Xu et al., 2020) and an indirect activator role of hetF (W.-Y. Xing et al., 2022). But there is still no evidence connecting these two mechanisms, as they seem to be mediated by different genes, hetL and patU3, whose role is still somewhat obscure. To simulate the biochemical interactions, we introduce the Langevin equations resulting from this model in a custom C++ object-oriented platform and use a simulated annealing algorithm to adjust the free parameters. This analysis of the patA mutant is especially relevant because it is a clear example that one can disrupt the formation of the pattern by affecting the intensity of the feedback loops controlled by HetR. Here, patA is hypothesized to have a reinforcing role in hetR regulation. Then, without patA the fraction of HetR that gets activated is reduced with respect to the wild type, this mutant seems to lose the compounding effect that allowed the formation of the pattern. Due to this, the ¿patA mutant is much less susceptible to sudden spikes of HetR production, and therefore most of the stochastic fluctuations get buffered without impacting the overall homogeneity of the filament. This indicates that the filament is capable to transition between the pattern forming and homogeneous regimes through the modulation of patA transcription.

    To finalize the study on Anabaena, simulations of much longer filaments (with an initial length of 5000 cells) were performed in order to study the correlations between cells. By obtaining the Pearson coefficient between the concentrations in cells at a certain distance, we obtained the profile of correlations between cells for different intercellular distances. Through this study we observe a similar initial homogenization effect for the ¿patS mutant which is corrected with the posterior apparition of heterocysts and the HetN production. Additionally, we use the correlations of both the diffusible inhibitor and the level of regulatory activity of HetR to propose a new two staged selection method of future heterocysts. This novel mechanism considers an initial short-ranged selection between groups of 5 cells and a later competition between those established ¿neighborhoods¿. This selection process is consistent with the available experimental evidence. Furthermore, it is capable to explain the existence of a pattern with a characteristic length much larger than the experimentally observed cell to cell correlation, without the need for an initial intrinsic spatial organization.

    Alternatively, for the rice plants, we study the effect that an increase of nitrogen fertilization has over the formation of lateral branches. To do so, we analyze the mechanism of growth regulation mediated by the GID1-GA complex in rice. This complex links vertical plant growth (mediated through DELLAs) with lateral growth or tillering (mediated by NGR5). The main objective of this model is to characterize this relationship between these two types of growth, as well as to study the response in plant tillering in response to changes in the level of fertilization for different genetic variants. This model was programmed in a Python simulation and, as in the previous system, a Simulated Anneling algorithm was used to adjust the free parameters using experimental data available in the literature. And, an exhaustive study of the parameter space was performed to study the robustness of the parameter set obtained above. Subsequently, a study of the stability of the equilibrium point of this model with respect to changes in the level of fertilization and the severity of multiple genetic mutations was performed. The results obtained with this model suggest that the regulatory mechanism that controls both the inhibition of vertical growth and the induction of tillering is evolutionary tuned to prioritize the inhibition of vertical growth over the increased tillering. This happens due to the preferential targeting for degradation of the tillering inducer NGR5 over the growth inhibitors DELLA. Then, if we were capable to invert this preference, we could have crops that prioritize the formation of new tillers over the reduction of height. If validated experimentally, this could open a new possibility to further enhance tiller response to increase of nitrogen fertilization. This is especially relevant given that we also observed in our model that the nitrogen fertilization seems to have diminishing returns in all the strains considered.

    The thesis ends with a brief discussion of recent studies that combine this two biological system to design new high efficient crops to incorporate the nitrogen fixation from cyanobacteria through and artificial symbiosis.