Abstract
Stability in a metabolic system may not be obtained if incorrect amounts of enzymes are used. Without stability, some metabolites may accumulate or deplete leading to the irreversible loss of the desired operating point. Even if initial enzyme amounts achieve a stable steady state, changes in enzyme amount due to stochastic variations or environmental changes may move the system to the unstable region and lose the steady-state or quasi-steady-state flux. This situation is distinct from the phenomenon characterized by typical sensitivity analysis, which focuses on the smooth change before loss of stability. Here we show that metabolic networks differ significantly in their intrinsic ability to attain stability due to the network structure and kinetic forms, and that after achieving stability, some enzymes are prone to cause instability upon changes in enzyme amounts. We use Ensemble Modelling for Robustness Analysis (EMRA) to analyze stability in four cell-free enzymatic systems when enzyme amounts are changed. Loss of stability in continuous systems can lead to lower production even when the system is tested experimentally in batch experiments. The predictions of instability by EMRA are supported by the lower productivity in batch experimental tests. The EMRA method incorporates properties of network structure, including stoichiometry and kinetic form, but does not require specific parameter values of the enzymes.
Highlights
Metabolic systems typically operate either under a stable steady state or an oscillatory mode
Some network structures are shown to be prone to instability
Ensemble Modelling for Robustness Analysis (EMRA) is a valuable tool for pathway design, synthetic pathways which are uncontrolled and not stabilized through evolution
Summary
Metabolic systems typically operate either under a stable steady state or an oscillatory mode. While systems with stable steady states or sustained oscillation have been studied extensively [1,2,3,4,5,6], to our knowledge metabolic systems prone to instability have not been investigated as much. Both stable (Fig 1A) or unstable (Fig 1B) system have a mathematical steady state (or fixed point), but the unstable steady state is not realizable in the physical world because any deviations from the steady state are amplified. The issue of stability is important when engineering a novel pathway or altering an existing one
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