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 [1] -[3] . Several key examples demonstrate this. A powerful tool for explaining the properties of the metabolic engineering system can be found in the experiments of the Metabolic Network Model [4] . Kinetic Metabolic Network modelling requires a large number of kinetic parameters. These parameters have been studied and analyzed to detect the concentration of changes in the metabolites and reactions, using a differential algebraic equation [5] . Every physiological system has a set of parameters such as temperature, reaction rates, and kinetic constants. So, to extract the parameters from experimental data in parameter optimization is generally difficult. Hence, the parameters tend to be estimated or measured in different conditions. Therefore, the Least Squares technique and Real-Coded Genetic Algorithm are used to fit the model output to the corresponding experimental measurements applied by [5] . This study focuses on large- scale kinetic parameters, which use a non-linear ODE to estimate kinetic parameters [6] . Since 2002, Sensitivity Analysis and Parameter Optimization have used less than three pathways in their kinetics modeling. In [7] , the model of glycolysis and pentose phosphate pathways was investigated by applying a Stepwise Internalization method for the Sensitivity Analysis, and Simulating Annealing was used to optimize 85 kinetics that represent his model. In [8] , twelve kinetic parameters were identified as effective parameters for the Embden-Meyerhof pathway, pentose phosphate pathway, and phosphortransferase system; they used the Monte Carlo simulation and Sobol method for calculating the times profiles. Nine of the most sensitive kinetic parameters were optimized through the Control Vector Parameterization Approach to formulate Dynamic Parameter Estimation problems [8] . They also apply Sensitivity Analysis to 100 kinetics by scaling each kinetic parameter individually. Seven kinetic parameters were identified as the most significant ones, considering V^max as a kinetic target. Real- Coded Genetic Algorithm was used for optimization [5] . Particle swarm optimization (PSO) is a relatively new family of algorithms which may be used to find out the optimal solutions to the high complexity or multi- dimensional functions [9] . The algorithm of PSO emulates the behavior of animal societies that don’t have any leader in their group or swarm, such as bird flocking and fish schooling [10] . Moreover, the PSO algorithm contains many different mechanisms that improve global and local exploration abilities [11] . It was also reported that PSO algorithm was sufficient to reduce the steady-state errors [12] .

In this work, the model in [6] is used as a study case. The model consists of glycolysis, pentose phosphate, TCA cycle, gluconeogenesis, glycoxylate pathways, phosphotransferase system and acetate formation. The Sensitivity Analysis in large-scale kinetic parameters was used to select the effective parameters that reveal significant changes among metabolites and fluxes on the model output. On the other hand, PSO was used to optimize the identification of the most effective parameters of the model. The simulation result proved that only seven kinetics were highly affected in the model. Also, it proved that the proposed optimizing method―the PSO algorithm―was highly effective in estimating the unknown parameters.

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.

Normally, estimation of the unknown parameters techniques is based on the difference between the simulated model and behavior in the actual system model [13] . The function, that used to identify the large-scale metabolic network of E. coli system model, and the transfer, is as follows:

where, has the model reaction rate resulted for kinetics and is the simulation reaction rate result for kinetics.

In order to identify the kinetic parameters sensitivity of the model employed by [6] we apply the PSO algorithm to the seven kinetics to fit both the simulation (Sensitivity Analysis) and the real values of the model [6] by using experimental metabolites data taken from [17] . The concentration of metabolites used in the optimization execution needs to fit the result of our metabolites simulation model closely. To achieve this the concentration is as follows: fructose 1,6-bisphosphate (0.67 mM), phosphoenol-pyruvate (1.04 mM), isocitrate (0.21 mM), 2-keto-D-gluconate (0.134 mM). PSO was introduced by Eberhart and Kennedy as a new heuristic method [18] . During the PSO execution, the maximum number of generations is set as 100 (bird-steps); the dimension’s problem is 7 kinetic parameters; the population size (iterations) repeats 100 times; linear inertia weight is 0.9; PSO parameter C₁ = 1.5 and C₂ = 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 [18] :

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, is an inertia weight parameter to exploration search space. c₁, c₂ are acceleration coefficients toward P and G respectively, and r₁, r₂ are random number between 0 and 1. In each iteration, the particles will use Equations (3) and (4) to update their position and velocity, the algorithm used in this work will be described in Figure 2.

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 [6] . Further investigations, particularly the inclusion of Kinetic Parameter Optimization, are needed to give a precise result regarding the relation between the Sensitivity Analysis methods and the system dynamic properties. Finally, the validation of numerical results shows that the large-scale kinetic parameters optimization procedure has provided effective estimation.

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.

PTS: 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.