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In metabolic network modelling, the accuracy of kinetic parameters has become more important over the last two decades. Even a small perturbation in kinetic parameters may cause major changes in a model’s response. The focus of this study is to identify the kinetic parameters, using two distinct approaches: firstly, a One-at-a-Time Sensitivity Measure, performed on 185 kinetic parameters, which represent glycolysis, pentose phosphate, TCA cycle, gluconeogenesis, glycoxylate pathways, and acetate formation. Time profiles for sensitivity indices were calculated for each parameter. Seven kinetic parameters were found to be highly affected in the model response; secondly, particle swarm optimization was applied for kinetic parameter identification of a metabolic network model. The simulation results proved the effectiveness of the proposed method.

A major advance in metabolic engineering is possible by understanding the dynamic behavior of a living cell and decreasing or increasing the production of metabolites [^{max} as a kinetic target. Real- Coded Genetic Algorithm was used for optimization [

In this work, the model in [

This paper comprises three parts. The first part presents a brief description of the model structure; the second part shows the application of the local Sensitivity Analysis technique; and the last part covers the application of the Global Optimization Algorithm.

The main metabolic pathway of E. coli formulated by reference [

The metabolite concentration rate of the changes in this metabolic network is given by the following equation:

where

Large-scale kinetic parameters of experimental data may require to be corrected through the Sensitivity Analysis to identify the parameters which are the most affected in the model output. Sensitivity Analysis is a set of

analytics and simulation used as a tool to understand the effectiveness of the parameters of the model response [

Normally, estimation of the unknown parameters techniques is based on the difference between the simulated model and behavior in the actual system model [

where,

In order to identify the kinetic parameters sensitivity of the model employed by [_{1} = 1.5 and C_{2} = 0.8, with lower and upper values for each kinetics. PSO was inspired by the food-searching behaviors of fish and their activities or a flock of birds in D-dimensional search space. The best individual position of particle i and the best position of the entire swarm are represented by [

where P_{i} is the best position already found by particle i until time t and G is the best position already found by a neighbor until t, _{1}, c_{2} are acceleration coefficients toward P and G respectively, and r_{1}, r_{2} are random number between 0 and 1. In each iteration, the particles will use Equations (3) and (4) to update their position

The One-at-a-Time Sensitivity Measures identify 7 kinetic parameters from 185 kinetic parameters of [

The changes in the V_PYKmax result show that the metabolites of FDP and ICIT are highly increased, while ACE is highly decreased. The increase in the enzyme of ALDO is due to the decrease in GLcex, which in turn is regulated by its effectors ATP, ADP and PEP (as described in

All the kinetic parameters executed on the particle swarm optimization algorithm, whose lower and upper values are started by ±1 in order to reach the best lower and upper boundaries, achieved the best optimum values. The optimized parameters are tested in the same model to reduce the errors between the experimental data and actual model data. This will be the focus of the next section. The optimal values are shown in

In oreder to prove that, the one-at-a-time sensitivity analysis measure and PSO algorithm methods has great impact in optimizing large-scale kinetic parameters, the original kinetic parameters in the model formulated by Kadir [

Kinetics | Nominal value | Optimal values |
---|---|---|

V_PYKmax | 1.085 | 0.921 |

n_PK | 3 | 3.32 |

ICDH | 24.421 | 24.62 |

Kf_ICDH | 289,800 | 2,829,800 |

Kd_ICDHnadp | 0.006 | 0.012 |

Km_ICDHnadp | 0.017 | 0.013 |

V_ICLmax | 3.8315 | 3.942 |

This study has applied One-at-a-Time Sensitivity Measures to assess the effectiveness of large-scale kinetic parameters in a dynamic metabolic network into the steady-state condition of E. coli. By programming to measure how much they affect the model response, the analysis has identified seven particular kinetic parameters as being the most effective in their allowable range. Particle swarm optimization algorithm has been applied to the kinetics result of the sensitivity analysis, based on continuous culture with a dilution rate of 0.1 to fit our result in the model output of [

The authors gratefully acknowledge financial support from the Universiti Malaysia Pahang, Faculty of computer system and software engineering. The authors thank Dr. Tuty Asmawaty Abdul Kadir, who provided the model under study and Dr. Md. Aminul Hoquea for providing the experimental data set.

MohammedAdam Kunna,Tuty AsmawatyAbdul Kadir,Aqeel S.Jaber,Julius B.Odili, (2015) Large-Scale Kinetic Parameter Identification of Metabolic Network Model of E. coli Using PSO. Advances in Bioscience and Biotechnology,06,120-130. doi: 10.4236/abb.2015.62012

Glc^{ex}: Glucose;

G6P: Glucose-6-phosphate;

F6P: Fructose-6-phosphate;

FDP: Fructose 1,6-bisphosphate;

GAP: Glyceraldehyde 3-phosphate;

DHAP: Dihydroxyacetone phosphate;

PEP: Phosphoenolpyruvate,

PYR: Pyruvate;

AcCOA: Acetyl-CoA;

AcP: Acetyl phosphate;

ACE: Acetate;

ICIT: Isocitrate;

2KG: 2-Keto-D-gluconate;

SUC: Succinate;

FUM: Fumarate;

MAL: Malate;

OAA: Oxaloacetate;

6PG: 6-Phosphogluconolactone;

Ru5P: Ribose 5-phosphate;

Xu5P: Xylulose 5-phosphate;

R5P: Ribulose 5-phosphate;

S7P: Sedoheptulose 7-phosphate;

E4P: Erythrose 4-phosphate.

EnzymesPTS: Phosphotransferase system;

PGI: Phosphoglucose isomerase/glucosephosphate isomerase;

PFK: Phosphofructokinase-1;

ALDO: Aldolase;

GAPDH: Glyceraldehyde 3-phosphate dehydrogenase;

Pyk: Pyruvate kinase;

PDH: Pyruvate dehydrogenase;

Acs: Acetyl coenzyme A synthetase;

Pta: Phosphotransacetylase;

Ack: Acetate kinase;

CS: Citrate synthase;

ICDH: Isocitrate dehydrogenase;

2KGDH: 2-Keto-D-gluconate dehydrogenase;

SDH: Succinate dehydrogenase;

Fum: Fumarase;

MDH: Malate dehydrogenase;

Mez: Malic enzyme;

Pck: Phosphoenolpyruvate carboxykinase;

Ppc: PEP carboxylase;

ICL: Isocitratelyase;

Ms: Malate synthase;

G6PDH: Glucose-6-phosphate dehydrogenase;

6PGDH: 6-Phsophogluconate dehydrogenase;

Rpi: Ribulose 5-phosphate 3-isomerase;

Rpe: Ribulose phosphate 3-epimerase;

Tkta: Transketolase I;

Tktb: Transketolase II;

Tal: Transaldolase.