Systems Biology (Methods in Molecular Biology)

by Prigogine. As Prigogine states, “classical thermodynamics is an admirable but fragmentary doctrine” [6]. This fragmentary cha ...

nonlinear dynamics, network modeling, influence of biophysical constraints, operating on different scales, rather than solely fo ...

2 Thermodynamics Framework From the formalism of the classical thermodynamics [12] entropy production can be evaluated through t ...

whereξ_f,ξ_b are the velocities of the direct and reverse reaction passes, respectively. Substituting expressions (7) and (6)int ...

The appearance of new structures in nature far from thermody- namic equilibrium appears similar to a “phase transition,” generi- ...

Lyapunov function forpif for certain neighborhoodNofpthe following conditions hold: 1.V(x)>0 for everyx 6 ¼pinNandV(p)¼ 0 Th ...

angiogenesis, vascular growth. We conjectured about it, in a previ- ous work [35], where apparent fluctuations related to the jo ...

Steps 1, 2 are related to the process of mitosis and apoptosis, wherexrepresents the population of proliferating tumor cells in ...

wherexas we have said, represents the population of proliferating tumor cells in the region of characteristic sizeLanddfis the f ...

the primary site with the secondary tumors being too small to be clinically detected. The model proposed (seeFig. 3) contains as ...

dx dt ¼xðÞ 2 Nx Hxz, dy dt ¼yðÞþ 4  0 : 14 y 0 : 5 x^2 Iy 0 : 5 Hyzþ 0 : 001 z^2 , dz dt ¼Izþ 0 : 07 y^2 þ 0 : 5 Hyz 0 : 0 ...

For the modeling of the chemical network model which appears in Fig.3, COPASI v. 4.6.32 software was used. On the other side, nu ...

For the critical valueI3.71 it appears as a phase transition of the type “first-order” through a supercritical Andronov-Hopf bi ...

periodic oscillations, the maximum concentration of z cells increases, and in fact they become predominant. From the control par ...

It is important to emphasize how the homoclinicity in the Shilnikov scenario for Shilnikov condition: ℜe 3 ℜe > 0 appears. ...

The diagnosis of tumor proliferation capacity and invasion capacity is a very complex issue, because these terms include many fa ...

the fractal dimension, and the tumor growth rate. A common property of invasive cancers is their altered glucose metabolism. The ...

dΨ dt ¼ ∂Ψ ∂_ξ  df dξ_ dt þ ∂Ψ ∂df  ξ_ ddðÞf dt ð 30 Þ Taking tumor growth rateξ_ constant as in [38] and taking fractal dim ...

researchers understand the full scope of Warburg’s work [78, 84] despite its great importance. Altered energy metabolism is prov ...

tumors in nude mice. Indeed, MCF-7 are widely recognized to present only some malignant features, showing a low aggressive behav ...