Stochastic Modeling of BMP Heterodimer-Receptor Interactions Shows Emergence of Low-Pass Filtering Behavior

In developing tissues, signal transduction from morphogen gradients conveys positional information to cells, resulting in cell specification and differentiation. One such morphogen is bone morphogenetic protein (BMP), of the TGF-{beta} superfamily, whose signaling network is highly conserved across many species. In Danio rerio (zebrafish), this signaling pathway directs dorsoventral axis formation during early embryogenesis. Many of the molecules that play a role in this network are well-understood; however, the mechanisms through which they achieve noise attenuation and gradient robustness have not been fully defined. Specifically, the heterodimer-heterotetramer complex has been shown to be required for signal transduction[1], but current understanding and modeling of the BMP membrane receptors at this stage has not given any insight into evolutionary drivers of the requirement. In this study, we develop a stochastic model of receptor oligomerization with the published reports of binding kinetics of BMP ligand-receptor interactions to mechanistically assess zebrafish phenotype variability related to the distributions of noise and stochasticity. We can also analyze time-dependent signaling and frequency metrics that are not available in traditional, deterministic modeling. Fast Fourier Transform and cumulative energy spectral density visualization show that the heterodimer-heterotetramer complex may function as part of a low-pass filter mechanism in the dorsal-ventral axis formation process, specifically tuned to the noise of the system. Under dynamic conditions such as the mid-blastula transition (MBT), wherein the morphogen gradient rapidly changes shape, established metrics of noise and information transduction, such as coefficient of variation and mutual information, overlook important temporal effects that may be particularly relevant during development. As the BMP signaling pathway is highly conserved and has been implicated in human bone growth and wound healing, its study in simpler systems stands to accelerate our comprehension of BMP network structure and molecular mechanisms with potential application in regenerative medical studies.