Structural and functional robustness of the adaptive-sorting signaling network

摘要

A major task of study on ligand discrimination by T cells is the construction of a mechanistic model to account for threshold setting in response to variant ligands interacting with the same T-cell receptors. Recently, Lalanne and Francois in a seminal paper (2013 Phys. Rev. Lett. 110 218102) have addressed this question by constructing minimal core circuits such that the biological outputs can satisfy the essential properties of early T-cell activation. To make this core set of network topology a valuable tool for synthetic biologists to robustly engineer biological circuits, we are motivated to ask a general question: is adaptive response encoded by the proposed circuit topology structurally stable, regardless of the values of the kinetic parameters? This has particularly relevant effects for the network reliability, since failures in ligand discrimination result in either infection or autoimmune diseases. To the best of our knowledge, a rigorous and complete mathematical proof of this issue is still lacking in the literature. In this paper, by giving a rigorous mathematical proof, we have shown that this regulatory circuitry is appropriately designed and the existence, uniqueness, and globally asymptotic attractiveness of the steady state are preserved. Moreover, we further generalize the adaptive sorting module and undertake an extensive analysis on the trade-off between antagonism and sensitivity of T-cell ligand discrimination in various cellular conditions. Notably, the optimal phosphorylation step in which to place the regulatory motif is analytically obtained and numerically confirmed. Finally, relevant experimental facts and biological implications are discussed.