(26f) Stochastic Analysis of Information Transduction Via BMP Receptor Oligomerization during Embryogenesis

Introduction: In developing tissues the interpretation of morphogen gradients provides cells with positional information and determines cell fate specification. Bone morphogenetic protein (BMP) signaling gradient directs patterning and dorsoventral axis formation during early embryogenesis. Published experimental evidence indicates that dorsoventral patterning during zebrafish embryogenesis requires signaling of the BMP2-7 ligand heterodimer through a hetero-tetrameric receptor complex comprising of one Alk3/6 and one Alk8 type I receptor and two type II receptors. However the evolutionary basis for the requirement of this specific combination of ligand and receptor tetramer during embryogenesis remains unclear.

Methods: To explore this question, we developed a stochastic model of BMP ligand binding and receptor tetramerization. We used GillesPy, an open-source Python interface for the StochKit2 software for simulation of stochastic biochemical systems. The StochKit2 system incorporates tau-leaping and Gillespie’s stochastic simulation algorithm to efficiently calculate trajectories that reflect the stochasticity of biochemical systems. Our model of BMP ligand binding and receptor tetramerization was informed by published reports of binding kinetics of BMP ligand-receptor interactions in cell-free systems. Our stochastic model was deployed in simple one-dimensional models of the BMP morphogen gradient to assess the intrinsic noise and information transduction properties of different ligand-receptor tetramer complexes.

Results: Unexpectedly we observe that the BMP2-7:Alk3:Alk8:RII:RII complex, the active ligand-receptor tetramer complex during zebrafish embryogenesis, has greater noise at steady state than other BMP ligand-receptor tetramer complexes across a broad range of ligand levels. However, spectral analysis indicates that at steady state, BMP2-7:Alk3:Alk8:RII:RII has less contribution of low-frequency oscillation than other ligand-receptor tetramer complexes. Consequently, the BMP2-7:Alk3:Alk8:RII:RII complex reaches steady state after changes in ligand levels more quickly than other BMP ligand-receptor tetramer complexes. Further, despite greater noise as measured by coefficient of variation, the BMP2-7:Alk3:Alk8:RII:RII complex offers greater temporal fidelity than other BMP ligand-receptor tetramer complexes.

Conclusions: Our study suggests that there is an information-theoeretic advantage for signaling through BMP2-7:Alk3:Alk8:RII:RII which may provide the evolutionary basis for its role during embryogenesis. Further our work suggests that established metrics of noise and information transduction such as coefficient of variation and mutual information overlook important temporal effects which may be particularly relevant during development.