Quantitative Modeling of Scaling of Patterns and Receptor Signaling in Morphogenesis

Md Shahriar Karim, Purdue University


Organs and tissue development often experience perturbations, but developmental processes seem to replicate a common body template to maintain appropriate proportions and positions. The key signaling factors that guide a number of those processes are known as morphogens. Developing cells sense their respective positional information from a graded morphogen profile, and differentiate into patterns. Remarkably, patterns are highly robust and reproducible among species, and the underlying mechanisms associated with such high degrees of precision are still enigmatic. In addition, details of the signal, such as the Bone Morphogenetic Protein (BMP) signal, that transmit patterning information to a group of homogenous cells to differentiate is not well understood. Determining how developmental processes ensure robust patterning in the presence of perturbations maintain structural precision by scaling, and what regulatory mechanisms act to ensure robust and reproducible patterning are two longstanding questions that need unraveling. Moreover, determining the mechanisms by which BMP homodimers dominate signaling in developing zebrafish embryos and other contexts is a key factor in understanding developmental regulation for a classic morphogen patterning. To answer these questions, this work has developed a set of mathematical models to evaluate and interrogate potential signaling networks and regulatory motifs. These models identify scaling mechanisms, test hypotheses on heterodimer dominance during signal transduction, and show how patterning systems function. For the scaling problem, this research proposes a Two Component System (TCS) mechanism, where a morphogen (m) and a modulator (M) interact reciprocally to alter the transport and reaction properties of each other spatially. An exhaustive parametric and network motif screen is conducted for several TCS variants under the reaction-diffusion-advection paradigm with spatially varying coefficients. Our analysis revealed a number of candidate networks and minimal regulatory motifs that achieve the precision needed for a developing species to ensure perfect development. Computational models of patterning signals, namely the Bone Morphogenetic Protein (BMP) mediated signal, were developed to analyze the receptor oligomerization that forms heterotetrameric receptor associations in BMP signaling. The oligomerization model disproves previous kinetic based hypotheses of heterodimer dominance, and identify other theoretical conditions to acquire it. Finally, the model predicts that heterodimer dominance provides a larger dynamic range and a higher concentration of morphogen activity, making it a robust sensor responding wide ranges of morphogen concentrations fundamental to a morphogen gradient system. Moreover, stochastic analysis of oligomerization steps reveal that recruitment of type II receptors during the receptor oligomerization by itself does not tend to lower noise in receptor signaling, an outcome that can be applied later in developing a complete probabilistic model of receptor oligomerization events. The computational arrangements and frameworks developed in this research have wider applications-- for instance, illustration of a large-scale screen of a reaction-diffusion-advection systems with spatially varying coefficients is a novel strategy to perform a large-scale screen of such system and could have wider applications in other areas. Additionally, our mathematical framework on the dynamics of a tetrameric complex formation and oligomerization steps could be applicable to other signaling pathways that require trimeric/tetrameric complex formation on the cell surface to elicit signaling.




Umulis, Purdue University.

Subject Area

Biomedical engineering|Developmental biology|Biophysics

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