[RASMB] 2 ligands and no equation

[Walter Stafford]

Hi Holger,

This is a fairly simple problem requiring about 10+ lines of code to solve.

We have 2 mass action equations and 3 conservation of mass equations 
which gives us 5 equations and 5 unknowns: [P], [A], [B], [PA], [PB]



substituting:



and rearranging, we have




These equations can be solved by simple straight iteration with 
initial guesses for [A] and [B] given the total molar concentration 
of protein and ligands along with Ka and Kb for ligand binding. After 
iterating until [P], [A] and [B] have converged to their final 
values, the values of [PA] and [PB] can be found by substitution. 
That should give you all you need to compute the ratios you are 
interested in.

Hope that helps,
Walter

p.s.    Just thought I'd test it out:
... in fact here's the code with sample output:
------------- output:
  enter Ka (association constant)
1.e6
   enter Kb (association constant)
1.e6
  enter p-total
1.e-6
  enter a-total
1.e-6
  enter b-total
1.e-6
  [A]=   7.071067811661710E-007
  [B]=   7.071067811661710E-007
  [P]=   4.142135624138481E-007
  [PA]=  2.928932188338290E-007
  [PB]=  2.928932188338290E-007
---------- here's another case with excess B
  enter Ka (association constant)
1.e6
   enter Kb (association constant)
1.e6
  enter p-total
1.e-5
  enter a-total
1.e-5
  enter b-total
1.e-3
  [A]=   9.901089009011984E-006
  [B]=   9.901089009011984E-004
  [P]=   9.989910291482921E-009
  [PA]=  9.891099098801730E-008
  [PB]=  9.891099098801730E-006

----------and here'e the code.

	program ligand


	implicit none


	real*8 A,B,P,PA,PB,KA,KB,ATOT,BTOT,PTOT
	real*8 delta_p,delta_a,delta_b,a_last,b_last,p_last

400	continue

	write(*,*) 'enter Ka (association constant)'
	read(*,*) ka

	write(*,*)' enter Kb (association constant)'
	read(*,*) Kb

300	continue

	write(*,*) 'enter p-total'
	read(*,*) ptot

	write(*,*) 'enter a-total'
	read(*,*) atot

	write(*,*) 'enter b-total'
	read(*,*) btot

	a=atot*0.1
	b=btot*0.1
	p=ptot


100	continue
	p_last=p
	a_last=a
	b_last=b

	p=ptot/(1.0 + ka*a + kb*b)
	a=atot/(1.0 + ka*p)
	b=btot/(1.0 + kb*p)

	delta_p=dabs((p-p_last)/p)
	delta_a=dabs((a-a_last)/a)
	delta_b=dabs((b-b_last)/b)


	if (delta_p.le.1.e-9 .and. delta_a.le.1.e-9 .and. 
delta_b.le.1.e-9)  goto 200

	! write(*,*) p,a,b

	goto 100


200	continue


	write(*,*) '[A]= ',a
	write(*,*) '[B]= ',b
	write(*,*) '[P]= ',p
	write(*,*) '[PA]=',Ka*p*a
	write(*,*) '[PB]=',Kb*p*b


	goto 400

	end




-- 
-------------------------------------------------------------------------------------------------------
Walter Stafford
mailto:stafford at bbri.org
direct dial:    617-658-7808
receptionist: 617-926-8040
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