Modelling and pathway identification involving the transport mechanism of a complex metabolic system in batch culture

• We propose a quantitative definition of biological robustness of intracellular substances.
• Constraint transcription and smoothing techniques are applied in our identification model.
• A parallel migration particle swarm algorithm is constructed to solve our model.

The bio-dissimilation of glycerol to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae (K. pneumoniae) can be characterized by a complex metabolic system of interactions among biochemical fluxes, metabolic compounds, key enzymes and genetic regulation. In this paper, in consideration of the fact that the transport ways of 1,3-PD and glycerol with different weights across cell membrane are still unclear in batch culture, we consider 121 possible metabolic pathways and establish a novel mathematical model which is represented by a complex metabolic system. Taking into account the difficulty in accurately measuring the concentration of intracellular substances and the absence of equilibrium point for the metabolic system of batch culture, the novel approach used here is to define quantitatively biological robustness of the intracellular substance concentrations for the overall process of batch culture. To determine the most possible metabolic pathway, we take the defined biological robustness as cost function and establish an identification model, in which 1452 system parameters and 484 pathway parameters are involved. Simultaneously, the identification model is subject to the metabolic system, continuous state constraints and parameter constraints. As such, solving the identification model by a serial program is a very complicated task. We propose a parallel migration particle swarm optimization algorithm (MPSO) capable of solving the identification model in conjunction with the constraint transcription and smoothing approximation techniques. Numerical results show that the most possible metabolic pathway and the corresponding metabolic system can reasonably describe the process of batch culture.