## Costa et al (2014). An extended dynamic model of Lactococcus lactis metabolism for mannitol and 2,3-butanediol production.

May 2018, model of the month by *Matthew Roberts*

Original model: BIOMD0000000572

### Overview

Mannitol has several therapeutic effects such as reducing intercranial pressure and preserving renal function [1]. The FI9630 strain of *Lactococcus lactis* with lactate dehydrogenase deficiency (derived from MG1363 strain) was further genetically modified in 2004 to increase the yield of mannitol [2]. This was achieved by deletion of the mtlA or mtlF genes that are involved in the phosphotransferase system. This double mutant strain additionally resulted in increased yield of 2,3-butanediol which is an industrial chemical used in the production of rubber and antifreeze [3]. In 2014, a mathematical model of *Lactococcus lactis* metabolism was formulated to include the mannitol and butanediol pathways [4]. Time series data of metabolite concentrations obtained through *in vivo* Nuclear Magnetic Resonance (NMR) was used to parametrise the mathematical model and the subsequent model analysis produced results that were consistent with the experimental observations from a decade earlier.

Figure 1 Metabolic pathways of *Lactococcus lactis*. The authors expanded an existing model [5] to incorporate the mannitol metabolic pathway and extended pyruvate metabolism to include 2,3-butanediol. Figure taken from [4].

Figure 2 Simulation of ATP, NAD, NADH and PEP using parameter values to reproduce the red line in figure 2 of the publication [4]. The simulation was performed in COPASI 4.22 (Build 170).

### Model

A previous model [5] incorporating glycolysis, pyruvate metabolism, ATPase pathway and phosphate exchange was extended to include the mannitol and butanediol pathways (Figure 1). The model used 'convenience' kinetic laws. 'Convenience kinetics' is a term introduced in 2006 [6] to describe a generalised Michaelis-Menten kinetic law that can accommodate reversible reactions, enzyme saturation, random binding, various stoichiometries and regulation by activators and inhibitors. The model consists of two compartments (intra- and extracellular), 26 species (15 intracellular), 21 reactions (20 convenience kinetics, 1 Hill function) and 112 parameters. Since the parameters in the previous model were obtained from in vitro experimental data, the model was then reparametrized *de novo* by fitting the time series *in vivo* data of eight metabloites of the central carbon metabolism. Unmeasured metabolites initial concentration and parameters are estimated from the model. The Michaelis Menten parameters were estimated using COPASI's [7] evolutionary programming method with the Michaelis Menten constants (Km) range-constrained between 0.01 and 100 mM and maximal velocity constants range-constrained between 0.001 and 1000 mM s^{-1}. The results were then used for 10 additional optimisation simulations using the Hookes and Jeeves algorithm to reduce the probability of missing the global optimum solution. The final model could simulate the time series data reflecting metabolite concentrations after addition of a glucose pulse.

### Results

The *in vivo* model simulation results are shown in figure 2. Although each simulation provided a general good fit to the data, the parameter sets were quite different, highlighting the issue of identifiability [8 - 10]. Model validation was performed by comparing predicted metabolite concentrations against different data sets relating to independent experimental runs with varied glucose pulses (publication figures 3 and 4 [4]). In addition to accurate predicted simulations, sensitivity analysis revealed interesting results. To consider changes in the integrated response a global sensitivity analysis was performed in contrast to a local sensitivity analysis that only investigates changes in the steady state values. The maximal velocity (Vmax) parameters that relate to gene expression were perturbed. In the wild-type strain, perturbation of the Vmax relating to lactate dehydrogenase resulted in a large change in mannitol and 2,3 butanediol yield. Additionally, perturbations in the parameter relating to the phosphotransferase system (mtl) that regulates mannitol transport was found to significantly influence mannitol yield. This is consistent with the 2004 experiment that used the lactate dehydrogenase deficient FI9630 *Lactococcus lactis* strain with deletion of mtlA or mtlF genes to optimise mannitol yield. Sensitivity analysis also revealed both known optimisation targets for mannitol and 2,3-butanediol from experimental evidence and new targets that had not yet been investigated. A summary of these targets is listed in table 1 of the publication [4].

### Conclusion

Costa et al. (2014) [4] proposed a mathematical model of *Lactococcus lactis* metabolism with kinetic laws and parameter value references that provided accurate fits to experimental data. Additionally, sensitivity analysis provided results that were consistent with previous research findings, such as mannitol yield being highly sensitive to lactate dehydrogenase activity, as well as presenting novel optimisation targets for improved metabolite yields. This analysis illustrates the predictive power of mathematical models of appropriately detailed biological system using suitable kinetic laws.

### References

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