protein binding

From: "Anthe Zandvliet" Apaza@SLZ.NL Subject: [NMusers] protein binding Date: Wed, June 23, 2004 9:40 am Dear NM users, I would like to address this question especially to those of you who have participated in the Intermediate Level Course in Population Pharmacokinetic Data Analysis using the Nonmem System. I am trying to implement the protein binding model, which was described in lecture 5 of the course: "This protein binding model comprises 1 compartment for total drug in the body, consisting of 2 subcompartments, one for free drug and another for protein-bound drug, each one in equilibrium with each other and so also with total drug. Rate of elimination of free drug is first order. Binding is saturable." [p. 18, lecture 5 of the course manual]. Using the control stream and the data below, I have performed a simple simulation of total, free and bound concentrations during 20 hours for 1 individual. This has raised 3 questions / problems: 1) Initially, I had defined the amount of protein bound drug as follows: A(3)=BMAX*A(2)/(KD+A(2)) This returned negative values for A(2). Therefore, I have changed the code into A(3)=BMAX*A(2)/(KD+(A(2)**2)**0.5) This seems to work, however.... 2) When I try to perform the simulation, I get the following error message: SIMULATION STEP PERFORMED SOURCE 1: SEED1: 1675601867 SEED2: 1049628274 0PRED EXIT CODE = 1 0INDIVIDUAL NO. 1 ID=0.10000000E+01 (WITHIN-INDIVIDUAL) DATA REC NO. 29 THETA= 5.00E-01 1.00E+00 1.00E+02 1.00E+00 ERROR IN LSODI1: CODE 204 MESSAGE ISSUED FROM TABLE STEP Only when I try to simulate concentrations for time 0-12 and 20 (while skipping time points 12.5-19-5), the simulation can be performed successfully. Does anyone know a solution for this problem? 3) I wonder whether the elimination rate of free drug in a physiological environment should indeed be assumed to be first order, given that protein binding is saturable. If one observes the amount of total drug, eliminated per unit time, given that the rate of elimination of free drug is first order, this amount will increase with time, up to the moment where protein binding is half-maximal. During this initial phase of elimination, the concentration of free drug decreases. As I would expect that only free drug will be cleared from the body, I would also expect that the amount of total drug eliminated per unit time, will decrease along with the free concentration. In conclusion, my reasoning does not correspond to the suggested protein binding model. Can anyone comment this? Please find the control stream and the dataset below. Thank you very much in advance for your suggestions! Best wishes, Anthe Zandvliet Model: "100.CTL" ;Model Desc: PROTEIN BINDING ;Project Name: e7070_phys ;Project ID: NO PROJECT DESCRIPTION $PROB RUN# 100 $INPUT DROP ID TIME AMT RATE DV $DATA TEST.CSV IGNORE=C $SUBROUTINES ADVAN9 TOL=5 $MODEL COMP=(TOT, DEFDOS, DEFOBS) COMP=(FREE,EQUIL) COMP=(BOUND,EQUIL) $PK CL=THETA(1)*EXP(ETA(1)) V=THETA(2)*EXP(ETA(2)) BMAX=THETA(3) KD=THETA(4) K10=CL/V F1=1000 R1=1000 $AESINITIAL INIT=1 A(3)=BMAX*A(2)/(KD+(A(2)**2)**0.5) A(2)=A(1)-A(3) $AES E(2)=A(2)-(A(1)-A(3)) E(3)=A(3)-BMAX*A(2)/(KD+(A(2)**2)**0.5) IF(A(2).LT.0) EXIT 1 100 $DES C1=A(1)/V C2=A(2)/V C3=A(3)/V DADT(1)=-K10*A(2)-K10*A(2)*BMAX*KD/(KD+A(2))**2 $ERROR Y=F*EXP(EPS(1)) IPRED=F W=F IRES=DV-IPRED IWRES=IRES/W $THETA (0,0.5) ; 1 CL (0,1) ; 2 V (0,100) ; 3 BMAX (0,1) ; 4 KD $OMEGA 0 FIX ; 1 CL 0 FIX ; 2 V $SIGMA 0 FIX ; 1 PROP ;$ESTIMATION MAXEVAL=2000 NOABORT METHOD=1 PRINT=5 MSFO=MSF100 $SIMULATION (325936) ONLYSIM $TABLE ID TIME AMT RATE DV C1 C2 C3 CL V K10 ETA(1) ETA(2) NOPRINT ONEHEADER FILE=100.TAB Data: "TEST.CSV" C C ID TIME AMT RATE DV 1 0 1 -1 0 1 0.25 0 0 0 1 0.5 0 0 0 1 0.75 0 0 0 1 1 0 0 0 1 1.5 0 0 0 1 2 0 0 0 1 2.5 0 0 0 1 3 0 0 0 1 3.5 0 0 0 1 4 0 0 0 1 4.5 0 0 0 1 5 0 0 0 1 5.5 0 0 0 1 6 0 0 0 1 6.5 0 0 0 1 7 0 0 0 1 7.5 0 0 0 1 8 0 0 0 1 8.5 0 0 0 1 9 0 0 0 1 9.5 0 0 0 1 10 0 0 0 1 10.5 0 0 0 1 11 0 0 0 1 11.5 0 0 0 1 12 0 0 0 C 1 12.5 0 0 0 C 1 13 0 0 0 C 1 13.5 0 0 0 C 1 14 0 0 0 C 1 14.5 0 0 0 C 1 15 0 0 0 C 1 15.5 0 0 0 C 1 16 0 0 0 C 1 16.5 0 0 0 C 1 17 0 0 0 C 1 17.5 0 0 0 C 1 18 0 0 0 C 1 18.5 0 0 0 C 1 19 0 0 0 C 1 19.5 0 0 0 1 20 0 0 0