Analysis of stochastic receptor signaling in BMP pathways
Many patterning processes that produce an intricate body pattern from a single cell embryo rely on the precise interpretation of the local concentration of a class of secreted molecules known as morphogens. Morphogens play a crucial role in organismal development by specifying cell fate organization in developing tissues. Patterns of gene expressions or signalling immediately downstream of many morphogens such as the Bone Morphogenetic Proteins(BMPs) are highly reproducible despite the presence of various forms of perturbations. This starkly contrasts with our expectation of a noisy interpretation due to stochastic fluctuations that would arise due to biophysical reasons such as: 1) experimentally determined low concentration (approximately picomolar) BMP activity, 2) tight receptor binding, and 3) very slow kinetic rates. To investigate mechanisms by which this intrinsic noise can be attenuated in BMP-mediated patterning, we focus on a class of secreted molecules that bind to BMPs extracellularly and play an active role in the mediation of BMP/receptor interactions. We developed a stochastic model of BMP signaling in Drosophila melanogaster and used the model to quantify the extent that stochastic fluctuations would lead to errors in spatial patterning. The model was extended to investigate how a surface–associated BMP binding protein (SBP) like Crossveinless-2 (Cv-2) may buffer out signaling noise in the context of BMP signaling. We find that in the presence of SBPs, fluctuations in the level of ligand-bound receptor can be reduced by more than 2-fold depending on the associated dynamics for the intermediate transition states. In order to screen the model based on the parameter values of intermediate transition rates, we developed a comparatively easy, yet efficient and accurate, way of finding the steady-state(SS) distribution of ligand-bound receptor assuming the existence of a unique deterministic SS (unimodal) of the system. To find the approximate SS, we first use the truncated-state space representation to reduce the system to a finite dimension, and subsequently reformulate an eigenvalue problem into a linear system. We used this approach to 1) estimate the steady state probability distribution, 2) calculate the standard deviation (σ) and mean of all the interacting species and 3) quantify the dynamic properties of SBP-mediated receptor regulation. Screening of the network yields three primary qualitative subclasses for Cv-2 behavior in the regulation of extracellular BR (C) fluctuation amplitude: i) reduced amplitude ii) increased amplitude and iii) mixed amplitude behavior . Regulation of receptor-ligand interactions by SBPs may also increase the frequency of stochastic fluctuations providing a separation of time-scales between high frequency receptor equilibration and slower morphogen patterning. High frequency noise generated by SBP regulation is easily attenuated by the intracellular pMad network creating a system that imitates the performance of a simple low pass filter common in audio and communication applications. Together, these data indicate that one of the benefits of receptor-ligand regulation by secreted non-receptors may be greater reliability of BMP-mediated signaling.^
David M. Umulis, Purdue University.