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Shoot apical meristems (SAMs) are populations of dividing, undifferentiated cells that generate organs at the tips of stems and branches throughout the life of the plant. As they define the number, type and position of lateral organs, meristems are the basis of plant architecture, allowing plants to adapt their development to their environment. SAMs are essential determinants of major agronomic traits such as, for example, biomass, fruit size, flowering time, branching patterns, or leaf numbers. Since they interact with their environment, their activity depends on the temperature, light intensity or humidity. Therefore, a better understanding of meristem function is an essential basis for the development of varieties that are better adapted to a range of environments, particularly important in view of the expected changes in global climate.
Research on meristems has also an impact on animal stem cell research, as meristems afford a unique opportunity for extensive research on stem cell biology that is much less constrained than animal stem cell research.
This project aims at:
Our group thereby focuses on the following:
As a basis for our work a model with a suitable level of detail to follow gene regulatory processes within a tissue like the SAM has to be implemented, in this case an ordinary differential equation (ODE) model with cellular resolution. A spatial component, namely diffusion and active transport of gene products, will be included using an implicit representation where the spatial component is treated like an intra cellular contribution. Still, these spatial components in principle demand for a representation in terms of partial differential equations (PDE), which would make simulations using the model computationally intense. Since the model is intended for high-throughput simulations within an optimization framework, this additional computation time will be avoided by approximating the PDE fractions with ODEs.
Due to the implicitness of the considered spatial component, the ODE representation has to be embedded into a spatial context explicitly stating which cells are interacting with which. For this purpose a graph-based agent based model (ABMs) appears to be well-suited. The idea of ABMs dates back to the 1940s and some work of J. von Neumann and S. Ulam on the idea of cellular automaton - a concept improved over the years by J. Conway. Nowadays this kind of modeling approach enjoys growing popularity in several simulation disciplines in social sciences as well as natural sciences. The two key concepts of this class of models are the mere simplicity of the constituents and the possibility to incorporate arbitrary interaction topologies connecting the agents. In effect, these models are well suited to study emergent behavior like the one assumed to control pattern formation in plant tissue.
Parameter estimation in presence of quantitative data usually is performed using well established statistical methods. Since for the setup we are focusing only qualitative data is currently available, the fit of the model to the data or knowledge about the system's function is a bit more difficult and has to be done using different techniques: Using the qualitative data available which is given by putative gene expression domains within the SAM and the interactions between the involved genes, identifying suitable parameters can be seen as an optimization task aiming at maximizing the overlap of spatial gene expression domains known from experiments and those formed by the model during simulations. To assess the level of overlap between observed patterns and simulated patterns at least the following three criteria should be taken into account:
Since the size of the parameter space scales exponentially with the number of involved genes, exhaustive search for suitable parameters during the optimization becomes intractable. In addition the behavior of the underlying ODE systems is dominated by a relatively small set of fixed points which results in a relative robustness against parameter perturbations and therefore the mapping between parameter space and system behavior divides the parameter space into distinct larger levels associated with the fixed points of the system which makes optimization of parameters rather difficult.
To cope with these difficulties, for this optimization it is planned to employ an evolutionary algorithm (EA) - an optimization known to be well suited for such tasks. Either a custom-designed EA or an of-the-shelve EA using an objective function considering at least the above described criteria will be implemented for this task.
Additionally, it has to be noted that the SAM of Arabidopsis thaliana tolerates significant changes in expression levels of certain genes. Although this robustness might already be covered by the mentioned model properties or the fact that the stochastic nature of EAs favors robust solutions, robustness considerations should be explicitly included in the optimization process. But at this point it has to be mentioned that the robustness of the in vivo example might not be achievable: Since the robustness in the plant could in principle stem from at least two different origins (1) inherently robust reactions and (2) redundancies in the system, where especially robustness properties stemming from redundancies often are hard to transfer into the simulation due to incomplete knowledge.
Whereas the first two work packages provide the basis to investigate spatially gene expression phenomena in the SAM of Arabidopsis thaliana, this part of the thesis will deal with implementing techniques to systematically explore the space of possible interacting gene expression networks. Whereas for the previous packages the types of interactions, gene product production and degradation types and transportability properties were defined by a human expert and only the parameters for these terms had to be optimized, in this part the assembly of terms and types as well as the number of involved genes shall be determined by an automated procedure.
As a possible implementation for this idea it is planned to use an EA, iteratively adding, deleting or changing genes in the model. Possible target function for this method are on the one hand side the fit of the simulated patterns on the target patterns observed in experiments and on the other hand the mere complexity of the produced model. Following Ockhams Razor, it seems to be reasonable to search for the most simple model generating the desired pattern. So, this optimization process has to deal with at least two different objectives for which it is unclear a priori how they are to be aggregated into a single objective. Therefore it seems to be promising to employ a multi objective evolutionary algorithm to this task.
Whilst the procedure up to now does not involve domain knowledge, in a concurrent step it is planned to include further information about the system under investigation: In line with this idea, e.g., information about initial gene product concentration distributions could be used as starting point for the optimization instead of a homogeneous distributions with small perturbations. Additionally, instead of simulating the behavior of a given system for only one environment, the test of the system could be expanded onto a set of simulations for different environments and thereby evaluating the behavior of the system for whole series of, e.g., biological experiments.
