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The Bone Morphogenetic Protein (BMP) pathway, also known as the Smad pathway, is an essential cellular signaling cascade regulating various cellular functions such as differentiation and regeneration across multiple organisms. Its structure is highly conserved across biological species. It consists of a receptor that, upon receiving an input signal, triggers a cascade of biochemical reactions ultimately resulting in the transport of the active complex into the nucleus where it binds to DNA and regulates the transcription of numerous downstream genes [1].

While the structure of this pathway is conserved across species, the system displays flexible behavior, measured as different performance objectives (POs), which are adjusted through various non-conserved parameters (NCPs). As in the engineering world, a perfectly optimal system does not exist and there is a system of trade-offs between competing POs. The system must then be fine-tuned to fit the biological context. The minimum set of POs are the rise time to steady state, noise attenuation ratio (NAR), and the linear sensitivity of the output [2].

Along with the active trimeric complex, (pSmad1)2/(Smad4), there are other complexes of the Smad proteins, including the (pSmad1)/(Smad4) dimer and the pSmad1 monomer, that are transported into the nucleus, forming a multi-layered system where the signal is processed at multiple levels. Unlike a more straightforward scheme, this complex system can give rise to various behaviors desirable for cellular signal processing and interpretation.

To better understand how the multi-tiered system affects signal transduction, we created a mathematical model based on the generic BMP pathway. We used computational tools to analyze the dynamics of the various complexes within. By comparing the POs of several proteins in the pathway, we observed that the performance of the trimer is worse than that of the monomer and dimer. However, the trimer can display a greater range of possible POs in the NCP screen as well as a significantly more varied sensitivity coefficient. This can point to the trimer output as having some unique behavior, not described by the minimum set of POs, desirable for signal processing in the BMP pathway.

[1]Madamanchi A, Mullins MC, Umulis DM. Diversity and robustness of bone morphogenetic protein pattern formation. Development. 7, 148 (2021). Published 2021 Apr 6. https://doi.org/10.1242/dev.192344

[2]Shaikh, R., Larson, N.J., Kam, J. et al. Optimal performance objectives in the highly conserved bone morphogenetic protein signaling pathway. npj Syst Biol Appl. 10, 103 (2024). https://doi.org/10.1038/s41540-024-00430-9