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

Abstract

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.

Dynamical modelling of secondary metabolism and metabolic switches in Streptomyces xiamenensis 318

“…Within our modelling platform, the fitness level or the robustness of each steady state can be accurately estimated and compared. In this regard, the requirement on the metabolic stability has been formulated into the said dynamical algorithm as a manifest of the real-world biological regulations [16]. As a metabolic network is intrinsically different from a gene regulation network due to the mass conservation constraint, it is intriguing to uncover how robustness in metabolic fluxes can be achieved under varying nutrient intakes and metabolic demands (figure 4 d ).…”

“…Since most biological reactions are catalysed by enzymes, one can construct the kinetic model based on a generic enzymatic rate equation. Central to our modelling methodology is a self-regulation algorithm that resembles real biological processes in maintaining metabolic stability and requires only a small set of boundary conditions [16–18]. We present below a brief summary of the methodology.…”

“…Equation (4.1) specifies the stoichiometry with an implicit enzyme(s) that applies to both directions of the reaction. Our simulation employs a generic enzymatic rate equation of the form [16,17]right left.5emthickmathspaceu([Ai],[Pj])=VFfalse∏i=1mfalse[Aifalse]/Ki−VnormalB∏ j=1n[Pj]/K′j f1false(VnormalF,VnormalBfalse)∏i=1m(1+false[Aifalse]/Ki)+f2false(VnormalF,VnormalBfalse)∏ j=1n(1+false[Pjfalse]/Knormal′j).where V F / V B is the forward/backward peak reaction rate and the...…”

“…Following the formal mathematical analysis developed previously [16,34–37], one can always define quite generally a monotonically decreasing Lyapunov function φfalse(xfalse(tfalse),Vfalse) for equation (4.6). The construction of the Lyapunov function is closely related to the diffusion matrix of the stochastic fluctuations.…”

A Gas Sensor Device for Oxygen and Carbon Dioxide Detection

“…Moreover, this sensor could be effective in several fields of applications (e.g., Bio-Medical, industrial, wearable), and in particular can also provide a quick estimation of metabolism parameters for discriminating glycolytic vs. oxidizing glucose metabolism. Additionally, as the tool can record in real-time a huge number of observations, it could provide data required for calculating the Ljapunov functions of non-equilibrium processes, like those occurring during metabolism in living systems [7] and pathological conditions, like cancer [8]. …”