Towards stable kinetics of large metabolic networks: Nonequilibrium potential function approach

While the biochemistry of metabolism in many organisms is well studied, details of the metabolic dynamics are not fully explored yet. Acquiring adequate in vivo kinetic parameters experimentally has always been an obstacle. Unless the parameters of a vast number of enzyme-catalyzed reactions happened to fall into very special ranges, a kinetic model for a large metabolic network would fail to reach a steady state. In this work we show that a stable metabolic network can be systematically established via a biologically motivated regulatory process. The regulation is constructed in terms of a potential landscape description of stochastic and nongradient systems. The constructed process draws enzymatic parameters towards stable metabolism by reducing the change in the Lyapunov function tied to the stochastic fluctuations. Biologically it can be viewed as interplay between the flux balance and the spread of workloads on the network. Our approach allows further constraints such as thermodynamics and optimal efficiency. We choose the central metabolism of Methylobacterium extorquens AM1 as a case study to demonstrate the effectiveness of the approach. Growth efficiency on carbon conversion rate versus cell viability and futile cycles is investigated in depth.