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), a highly conserved member of the TGF-β superfamily. In Danio rerio (zebrafish), BMP signaling directs dorsoventral axis formation during early embryogenesis. Although many of the components of this network are well-understood, the mechanisms that ensure noise attenuation and gradient robustness remain unclear. Specifically, the heterodimer-heterotetramer receptor complex is required for signal transduction, but current modeling has not explained why this architecture is necessary. In this study, we develop a stochastic model of receptor oligomerization using published BMP ligand-receptor binding kinetics to assess zebrafish phenotype variability arising from noise and stochasticity. Unlike traditional deterministic modeling, we can analyze time-dependent signaling and frequency. Fast Fourier Transform and cumulative energy spectral density analysis suggest that the heterodimer-heterotetramer complex acts as part of a low-pass filter during dorsal-ventral axis patterning, specifically tuned to the noise of the system. As the BMP signaling pathway is highly conserved and linked to bone growth and wound healing, these results improve understanding of BMP network structure and molecular mechanisms with potential relevance to regenerative medicine.