Systems Biology (Methods in Molecular Biology)

the mechanism rate [158]. These processes have also been identi-

fied as main targets for cancer treatment [134, 159].

We developed our model (seeFig. 12) as a representation of the

dynamics of the glycolysis for HeLa cell lines on the basis of the

above-discussed experimental evidence. From the biochemical net-

work model (Fig.12), using the classic chemical kinetics method

that applies the law of mass action, the following system of ordinary

differential equations (ODEs) was obtained:

d½ŠATP

dt

¼VPFKþ 4 VPYKVATPasess

d½ŠADP

dt

¼VHKþVPFKVPYKþVATPases

d½ŠNAD

dt

¼VGAPDHþVLDH

d½ŠNADH

dt

¼VGAPDHVLDH

d½ŠPyr

dt

¼VPYKVLDH

ð 39 Þ

Where Viare the reaction rate and the numerical values of the

constants are obtained [160]. Fixed points, stability analysis, and

bifurcation were performed using the standard procedure [161]

and using as control parameters the concentration of Glucose (Glu)

and Inorganic phosphate (Pi).The LZ complexity [54] was calcu-

lated using the proposed algorithm by Lempel and Ziv. Figures 13

and14 show how the LZ complexity varies for different Glucose

(Glu) and Inorganic phosphate (Pi) concentrations.

For modeling chemical network model (Fig.12), COPASI

v. 4.6.32 software was used.

Fig. 12Biochemical network for a mechanism for glycolysis for HeLa cell lines

160 Sheyla Montero et al.