Linear control analysis of the autocatalytic glycolysis system

Abstract

Abstract-Autocatalysis is necessary and ubiquitous in both engineered and biological systems but can aggravate control performance and cause instability. We analyze the properties of autocatalysis in the universal and well studied glycolytic pathway. A simple two-state model incorporating ATP autocatalysis and inhibitory feedback control captures the essential dynamics, including limit cycle oscillations, observed experimentally. System performance is limited by the inherent autocatalytic stoichiometry and higher levels of autocatalysis exacerbate stability and performance. We show that glycolytic oscillations are not merely a "frozen accident" but a result of the intrinsic stability tradeoffs emerging from the autocatalytic mechanism. This model has pedagogical value as well as appearing to be the simplest and most complete illustration yet of Bode's integral formula.

Compositional analysis of autocatalytic networks in biology

“…1. In this paper we explicitly account for the intermediate reactions in the model given by (2) and demonstrate the effect of the pathway size n on the stability of the pathway and computational complexity of verifying RoA properties around nominal operating conditions (i.e., fixed points). A direct application of a secant condition [9], [10], [12] gives an upper bound h d (n) on the feedback gainsĥ, that result in stable pathways of fixed size n and arbitrary (fixed) intermediate reaction rates.…”

“…This simple decomposition allows us to construct block diagonal Lyapunov functions (i.e., functions of the type U (x, y) = U 1 (x) + U 2 (y), x ∈ R n , y ∈ R) for (2). However this decomposition is not as useful for gains larger thanĥ d (n).…”

“…Additionally, the product of the pathway inhibits the enzyme that catalyzes the autocatalytic (first) reaction. An example of such a pathway is the glycolysis pathway [1], [2], [3].…”

Stability analysis of a class of biological network models

“…These reduced models usually contain the Hill functions. In this example, we consider the nominal regulated autocatalytic glycolysis model, which is studied in [1], as followṡ…”

“…In [1], the effect of autocatalysis in a glycolytic pathway model is studied by tools from linear control theory. The authors show that glycolytic oscillations are rather a result of the hard tradeoffs that emerges from the autocatalytic mechanism of glycolysis.…”