protein binding model

Hi, I am trying to include the protein binding in my model and to estimate the unbound plasma concentration, using the total plasma concentration. The drug was taken orally. It seems that I can write the differential equations as below. A(2) and A(3) represent the unbound and bound amount, respectively. DADT(1)= -KA*A(1) DADT(2)= KA*A(1) – k23*A(2)*(Bmax-A(3))+k32*A(3)-k*A(2) DADT(3)= k23*A(2)*(Bmax-A(3))-k32*A(3) My question is how could I transfer the amount in compartment 3 [A(3)] into concentration since my observation is the sum of the concentration in compartment 2 and 3. Many thanks in advance. Kehua

Kehua, For the usual sort of plasma protein binding case the time to equilibrium is very fast (seconds) so you will not be able to estimate K23 and K32 by trying to solve the kinetic binding equations because the usual time course of absorption and elimination is much slower (measured in minutes and hours). If this is the case then just assume equilibrium binding conditions: $PK ; unbound CL and V CL=THETA(1) V=THETA(2) Bmax=THETA(3) ; concentration of binding protein in central compartment Kd=THETA(4) ; equilibrium dissociation constant NS=THETA(5) ; non-saturable binding constant $ERROR Cu=F Cb=Bmax*Cu/(Kd+Cu) + NS*Cu Ct=Cu+Cb Y = Cb * (1+eps(1)) + eps(2) ; predict total conc with residual error On the other hand if you really have very slow binding to plasma proteins then you can get the sum of unbound and bound in $ERROR from your $DES solutions: $ERROR Cu=A(2) Cb=A(3) Ct=Cu+Cb+NS*Cu Y = Cb * (1+eps(1)) + eps(2) ; predict total conc with residual error