S- EQUATIONS:

S- EQUATIONS:
Ss equations are statistical equations.these are of two types

1.steady state equations
2.unsteady state equations or non steady state equations

Steady state equations:

The state model where the variables are unchanging in time but where there is a net flow of mass across its boundaries is called as steady state
And steady state cannot be affected by any external effects i.e cannot be affected by harmones.

Unsteady state equations:
The state models where the variables are changing with time and unsteady state cannot be affected by any harmones


Methods to determine statistical equations:
For Steady state:
PBN metod is use to determine steady state equations
PBN is probability Boolean network
PBN is a binary type of method where binary digits like 0 and 1 are use to determine,for every mismatch 0 is given and for every match 1 is given

For unsteady state equations:
There are three methods to determine unsteady type of S equations
1.ordinary differential equations
2.partial differential equations
3.baysein equations

Ordinary differential equqtions:
Derived formula for ordinary differential equations for cancerous cells
For single cancerous cells

dx=γx(1-x/k)
Where: γ=rate of growth
K=constant
X=concentration of cells
For more than one cancerous cells:
We use xi,xi+1

dxi=γixi(1-xi/k)

partial differential equations:
let us explain partial differential equations using nutrient concentrations
here ‘n’ and ‘c’ depends on kd and km values
where kd denotes rate of death of cells
km value denotes mass of cells
and here we can notice when nutrient concentration
decreases death of cells occurs.

Dn=kd
For concentration of cells:dc=km+kd

Theorem for PBN type:
Given PBN value of G(v,f) with an existing state distribution,let пy be a limiting probanility of state y. here p=0 and пy(if 0
(пy- пy )/пy <=(1-(1-p)n)


If the above equation satisfies then we can say that it is in steady state