Team:SZMS 15 Shenzhen/Collaborations

Title

Collabotations
(With help from Shenzhen_SFLS)

    We have acknowledged that one Ab with wAg + one Ag coming into one Ab with Ag and one wAg is irreversible and the amount of this kind of changes is related to the amount of Ab with wAg(x2) , the amount of Ag (x1) and time.

According to Volterra Model,we can know that ‘dx1/dt=dx2/dt=-k*x1*x2’.

k is a regular value which is related to affinity(f) between one Ab with wAg and one Ag which is defined as p,so we can attain an another equation:’k=pf’.

According to the first equation above,we can know that ‘x2=x1+m’.

We assume that the inchoate value of x1 is x0.
‘dx1/dt=dx2/dt=-k*x1*x2’

’k=pf’

‘x2=x1+m’

‘x1(0)=x0’

And the program code of matlab is:

dsolve('Dx1=-p*f*x1*(x1+m)','x1(0)=x0','t')

ans =

m/(exp(m*(log((m + x0)/x0)/m + f*p*t)) - 1)

x1= m/(exp(m*(log((m + x0)/x0)/m + f*p*t)) - 1)

We can define the extend of combination as E.

‘E=(x0-x1)/x1’ which is simplified as ‘E=1- m/((exp(m*(log((m + x0)/x0)/m + f*p*t)) - 1)*x0)’
Collaborations Team:SZMS_15_Shenzhen