Dynamics robustness of cascading systems.

Jonathan T Young,Tetsuhiro S Hatakeyama,Kunihiko Kaneko,Sergei Maslov

doi:10.1371/journal.pcbi.1005434

Jonathan T Young, Tetsuhiro S Hatakeyama + Show 2 more

Open Access

https://doi.org/10.1371/journal.pcbi.1005434

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Abstract

A most important property of biochemical systems is robustness. Static robustness, e.g., homeostasis, is the insensitivity of a state against perturbations, whereas dynamics robustness, e.g., homeorhesis, is the insensitivity of a dynamic process. In contrast to the extensively studied static robustness, dynamics robustness, i.e., how a system creates an invariant temporal profile against perturbations, is little explored despite transient dynamics being crucial for cellular fates and are reported to be robust experimentally. For example, the duration of a stimulus elicits different phenotypic responses, and signaling networks process and encode temporal information. Hence, robustness in time courses will be necessary for functional biochemical networks. Based on dynamical systems theory, we uncovered a general mechanism to achieve dynamics robustness. Using a three-stage linear signaling cascade as an example, we found that the temporal profiles and response duration post-stimulus is robust to perturbations against certain parameters. Then analyzing the linearized model, we elucidated the criteria of when signaling cascades will display dynamics robustness. We found that changes in the upstream modules are masked in the cascade, and that the response duration is mainly controlled by the rate-limiting module and organization of the cascade’s kinetics. Specifically, we found two necessary conditions for dynamics robustness in signaling cascades: 1) Constraint on the rate-limiting process: The phosphatase activity in the perturbed module is not the slowest. 2) Constraints on the initial conditions: The kinase activity needs to be fast enough such that each module is saturated even with fast phosphatase activity and upstream changes are attenuated. We discussed the relevance of such robustness to several biological examples and the validity of the above conditions therein. Given the applicability of dynamics robustness to a variety of systems, it will provide a general basis for how biological systems function dynamically.

Highlights

Robustness is one of the most important concepts in biological systems
Past experiments have shown that cells’ internal signaling networks are sophisticated enough to process and encode temporal information such as the length of time a ligand is bound to a receptor
Little research has been done to verify whether information encoded onto temporal profiles can be made robust

Summary

Introduction

Robustness is one of the most important concepts in biological systems It is the ability of an organism to maintain a state or behavior against external or internal perturbations, and many frameworks of robustness have emerged [1,2,3,4,5,6,7]. In developmental biology, differentiated cellular states are known to be robust to disturbances, as was pioneered in the study by Waddington, who described the cell differentiation process as a ball rolling down an epigenetic landscape to settle into a stable valley [8] This is a metaphorical representation of robustness often used, while in terms of dynamical systems theory, one mathematical formulation for static robustness can be described as an orbit being pulled into a stable attractor. The robustness discussed therein is concerned about the stationary state, and is regarded as static robustness

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