Systems Biology (Methods in Molecular Biology)

whereξ_f,ξ_b are the velocities of the direct and reverse reaction

passes, respectively. Substituting expressions (7) and (6)into(5)is

obtained:

S_i¼_ξf_ξb ln

ξ_f

ξ_b

 0 ð 8 Þ

Formula (8)[14] is fulfilled regardless of whether the network

of chemical reactions is close or far from equilibrium and also ends

the controversy related to the divorce between classic thermody-

namics and chemical kinetics.

Using the expression for the Gibbs equation,GHTS, the

affinityAcan be evaluated as

A¼

∂H

∂ξ



Tp

þT

∂S

∂ξ



Tp

ð 9 Þ

The term ∂∂Hξ



Tp

represents the heat of process,qTp. Some-

times, it is possible to neglect the term ∂∂Sξ



Tp

, due to

qTp

 ∂∂Sξ



Tp

[12]. Taking into account (Eq.4), we get that the

entropy production rate can be rewritten as

δSi

∂t

¼S_i¼

1

T

Aξ_

qTpξ_

T

¼

1

T

δq

dt



Tp

ð 10 Þ

Formula (10) is an approximation to the entropy production

rate of a living organism [12]. Equation (10) can be rewritten

according to Zotin [15] using the metabolic rate δdtq



Tp

q_ as

follows:

S_i¼q_

O 2 þq_Gl

T

ð 11 Þ

whereq_O 2 ,q_Glare the metabolic rates of oxygen consumptionq_O 2 ,

due to oxidative phosphorylation (OxPhos) and due also to glycol-

ysisq_Gl, respectively. Under aerobic conditionsq_Gl is negligible,

except in cancerous cells where the glycolysis is the main

process [16].

Sometimes, it is convenient [12] to use the so-called dissipation

function, ΨTS_i, introduced by Lord Rayleigh. According to

Eq. (11) the dissipation function can be rewritten as

ΨTS_i¼q_O 2 þq_Gl ð 12 Þ

In the tumor cells the glycolysis is the main process [16], thus

Eq. (12) can be written as

S_iq_Gl

T

ð 13 Þ

Parameters Estimation in Phase-Space Landscape Reconstruction of Cell Fate... 131