Proc. Nadl. Acad. Sci. USAVol. 85, pp. 8355-8359, November 1988Physiological Sciences

Dynamic determination of kinetic parameters for the interactionbetween polypeptide hormones and cell-surface receptors in theperfused rat liver by the multiple-indicator dilution method

(hepatic transport of peptide hormones/receptor-mediated endocytosis/epidermal growth factor/receptor dynamics/insulin)

H. SATO*, Y. SUGIYAMA*, Y. SAWADA*, T. IGA*t, S. SAKAMOTO*, T. FUWAt, AND M. HANANO**Faculty of Pharmaceutical Science, University of Tokyo, Tokyo 113, Japan; and tCentral Research Laboratories, Wakunaga Pharmaceutical Co., Ltd.,Hiroshima 729-64, Japan

Communicated by Susumu Ohno, June 10, 1988

ABSTRACT Hepatic elimination of epidermal growth fac-tor (EGF) via receptor-mediated endocytosis was studied by amultiple-indicator dilution method in the isolated perfused ratliver, in which cell polarity and spatial organization are main-tained. In this method EGF was given with inulin, an extracellu-lar reference, as a bolus into the portal vein, and dilution curvesof both compounds in the hepatic vein effluent were analyzed.Analysis of the dilution curve for EGF, compared with that forsomatostatin, which showed no specific binding to isolated liverplasma membranes, resulted as follows: (i) both extraction ratioand distribution volume of '2MI-labeled EGF decreased as theinjected amount of unlabeled EGF increased; (ii) the ratio plot [In(inulin/EGF) versus time] ofthe dilution curve for EGF exhibitedan upward straight line initially for a short period of time (-10sec), whereas the ratio plot [In (inulin/somatostatin) versus time]of somatostatin gradually decreased. The multiple-indicator di-lution method was used for other peptides also. Insulin andglucagon, known to have hepatocyte receptors, behaved similarlyto EGF in shape of their ratio plots. Thus, analysis of dilutioncurves can reveal whether or not the cell surface has receptors forcertain peptides. In addition, the dilution curves for EGF atvarious doses (tracer 30 jag) were analyzed simultaneouslybased on a kinetic model incorporating the perfusion rate, theassociation rate constant of EGF to surface receptors (kon), thedissociation rate constant of EGF from the EGF-receptor com-plex (ko)9 and the sequestration rate constant ofthe complex. Thekinetic parameters [the dissociation constant (Kd = kl/k,) andthe number of surface receptors] calculated by this analysis werecomparable with reported values obtained by in vitro directbinding measurements at equilibrium using liver homogenates.We conclude that the multiple-indicator dilution method is a goodtool for analyzing the dynamics of peptide hormones-cell-surfacereceptor interaction under a condition in which spatial architec-ture of the liver is maintained.

Many peptide hormones in the circulating blood are elimi-nated by the liver. Above all, for hormones taken up viareceptor-mediated endocytosis, the liver is a major homeo-static regulator in controlling the concentration of peptidehormones in circulating blood (1-3).The interaction between peptide hormones and their spe-

cific receptors has been analyzed principally by in vitrostudies with isolated or cultured hepatocytes (4) and liverplasma membranes (5). These systems, however, neithermaintain cell polarity nor include ligand delivery by the bloodflow, thus creating difficulty when the physiological signifi-cance ofthe peptide-receptor interaction is being experimen-tally evaluated. Use of the liver-perfusion method mayeffectively resolve this problem, because cell polarity and

spatial architecture between hepatocytes and the capillarybed are maintained in this system. However, determinationof the microscopic kinetic constants for the ligand-receptorinteraction, such as the association rate constant, the disso-ciation rate constant, and the receptor density, has beendifficult to determine in the liver-perfusion system.Our experimental goal was to resolve this dilemma by ap-

plying a method to measure the interaction between peptidehormones and their specific receptors in terms of kinetic con-stants in the perfused-liver system. Therefore, we applied themultiple-indicator dilution (MID) method, previously used chief-ly for analyzing hepatic transport of low-M, substances (6-9).Epidermal growth factor (EGF: Mr, 6045) was mainly

studied as a model peptide, because it is taken up by the livervia receptor-mediated endocytosis and acts as a mitogen inthe liver (10). Insulin and glucagon were also used, as thesepeptides are well known to have specific receptors on theliver-cell surface (11, 12). We selected somatostatin as areference peptide, because its specific binding to the liver cellsurface has not been detected in in vitro binding experiments.

MATERIALS AND METHODSLiver Perfusion Study (MID Method). The procedures are

basically as reported (8). Wistar male rats (250-270 g)anesthetized with ether were used. The liver was perfused ina temperature-controlled cabinet at 370C; the perfusate con-sisted of 20% (vol/vol) washed bovine erythrocytes inKrebs-Ringer bicarbonate buffer, pH 7.4, containing glucoseat 100 mg/dl and 2% (wt/vol) bovine serum albumin. Theperfusate flow rate was maintained at 12-14 ml/min.

After a 10-min stabilization period, 250 p.l of [14C]inulin (2.0p.Ci; 1 Ci = 37 GBq) as an extracellular reference and 125I_labeled EGF (125I-EGF) (3.0 p.Ci) prepared by the chloramine-T method (13) were injected rapidly (=0.5 sec) as a 250-1.lbolus into the portal vein. Subsequently, the total hepatic veineffluent was collected at 1-sec intervals for 30 sec. After a10-min stabilization period, the second run was performed,during which unlabeled EGF (human; Wakunaga Pharmaceu-tical) at 0.1 to 30 ,ug [injection concentration (labeled plusunlabeled), 20 nM-20 A.M] was added to the injectant.The 1251 radioactivities in the collected samples and the

aliquot of injection solution were determined with the Cl3-CCOOH precipitation method (3). 14C radioactivity wasdetermined in a Tri-Carb liquid scintillation spectrometer andcorrected for 1251 radioactivity.The Cl3CCOOH-precipitable radioactivities correlated

well with those of intact 125I-EGF that appeared in the voidvolume after gel filtration on a Sephadex G-25 column.

Abbreviations: EGF, epidermal growth factor; MID, multiple-indicator dilution; 125I-EGF, 125I-labeled EGF.tTo whom reprint requests should be addressed.

The publication costs of this article were defrayed in part by page chargepayment. This article must therefore be hereby marked "advertisement"in accordance with 18 U.S.C. §1734 solely to indicate this fact.

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We also performed the MID experiments similarly with"25I-labeled insulin (2 p.Ci) with or without unlabeled insulinand with 1251I-labeled glucagon (1.7 uCi) with or withoutunlabeled glucagon. The 1251 radioactivities were determinedby the C13CCOOH precipitation method. As for somato-statin, we performed the MID experiment using 1251I-labeled[Tyr"]somatostatin (2.0 uCi) and [Tyr"1]somatostatin. The1251I radioactivities in the samples were determined with thetalc adsorption method (14).

Analysis of Dilution Curve. To compare inulin and EGF, theoutflow radioactivity of each sample was normalized bydividing it by the injected radioactivity. Concentrations in theeffluent were thus expressed as the outflow fractions of thedose per ml. The obtained data were analyzed in both amodel-dependent and independent fashion.

In the model-independent analysis, we calculated theextraction ratio (E) and the distribution volume (Vd) from thezero moment (AUC) and the first moment (AUMC) of thedilution curve (15, 16).When first-order kinetics hold true, the dilution curve of a

tracer dose of the test substance was also analyzed accordingto the flow-limited distributed model proposed by Goresky etal. (9, 16, 17). This analysis gave three rate constants, k1, k2,and k3, corresponding to influx, efflux, and sequestration rateconstant, respectively.When the receptor-mediated endocytosis system plays a

major role in hepatic removal of peptide hormones, the threeparameters thus obtained may be related to the parametersrepresenting the kinetic processes in the receptor-mediatedendocytosis system as shown in Eqs. 1-3:

k, = kon * PT/Vdref [1]

k2= kff [2]

k3 = ks, [3]

where kon is the association rate constant of a peptide fromthe extracellular space to the cell-surface receptor, koff is thedissociation rate constant from the cell-surface receptor tothe extracellular space, k. is the sequestration rate constantfrom the cell-surface receptor to the interior of the cell, andPT is the density of the available receptor on the cell surface.A ratio plot [ln Cref(t)/CpT(t) versus time] obtained from

the dilution curves has been often used to estimate theapparent k1 value (7). Initially (=10 sec) the "throughout"component dominates the output, and a ratio plot gives astraight upward line with a slope of k1. Therefore, the initialslope of the ratio plot yields the hybrid parameter consistingof ko PT, and Vd ref

1.0

2 0.84J1

cr-

0.60

t 0.40

4L0xi 0.2-

0 10 20Dose of EGF (ig)

FIG. 2. Relationship betweenthe extraction ratio and the dose ofEGF injected into the portal vein.Details of the calculation of the

30 extraction ratio (E) are describedin Analysis of Dilution Curve.

Determination of Kinetic Parameters for the InteractionBetween EGF and Its Cell-Surface Receptor. The modelequations to determine kon, koff, ks, and PT were derivedbased on the venous-equilibrium model (18), and the appli-cability ofthe venous-equilibrium model was examined underthe linear condition by comparing the parameters with thoseobtained by the distributed model. In the venous-equilibriummodel, the extracellular space and the cell surface wereconsidered as well-stirred compartments, respectively. Themass-balance equations for EGF in each compartment aregiven by:

Vdref dt= - kon-(PT - X2)'C1 - Q.C1 + koffX2 [4]

dX2= ko -(PT - X2)-C1 - (koff + ks)'X2, [5]dt

where Vdref iS the volume of the extracellular space, C1 is theconcentration of the peptide in the extracellular space, Q isthe perfusion rate, and X2 is the amount of the peptide boundto the receptors. The plasma flow rate at each dose was in therange of 0.85-1.13 ml of plasma per min per g of liver.Similarly, the mass-balance equation of an extracellularreference, inulin, is given by:

Vdref dCl ref = _Q.C [6]

where C1,ref is the concentration of inulin in the extracellularspace. The concentration ratio of inulin to EGF, designatedas R, is given by:

R = C1 ref/Cl. [7]

The value of Vdref was calculated by a model-independentanalysis of the dilution curve of [14C]inulin.Each ratio plot with =18 data points was experimentally

obtained at six doses (0.01, 0.1, 1.0, 2.5, 9.3, and 30 ,ug). Six0.8

0.6-E

0.4

(l 0.2o

<D Cot_ 0.8

U-

:r 0.640.2

a m 14C-inul in

* 125e1-EGF| tracer dose )

IA

10 20

b ° 14C-Inul in

30

2. 5r

2.04.LU-

-1

0.5.E

* 1251-EGF( tracer * cold 30 jig )

0 10 20Time (sec)

30

FIG. 1. Representative dilution curves for ['4C]inulin and 125I-EGF without (a) and with (b) 30 ,ug of unlabeled-(cold) EGF in theinjectant. Abscissas, time in sec (actual time including large vesseland catheter transit time); ordinates, outflow fraction per ml.

0 0

tracer onlY >

00.0 .

0/ + cold 2.5 ,jg00 *

/ A cold 9.3 pg+ cold 30pg

a-a

10 20Time (sec)

30

FIG. 3. Plots of ln (["4C]inulin outflow fraction per ml)/(125I-EGFoutflow fraction per ml) versus time (designated as a ratio plot).Representative ratio plots at four doses of EGF are illustrated. Lineswere calculated by simultaneous fitting of the ratio plots at six doses(0.01, 0.1, 1.0, 2.5, 9.3, and 30 ,ug) with the SALS method (statisticalanalysis with nonlinear least-squares fitting) using a digital computer.

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=l.54-00

l01.04-

0

-0

.E

0.k Tracer Dose (0)000

O

O*oil Tracer + Cold (0)

60

0..808so

0 10 20Time (sec)

3u

FIG. 4. Representative ratio plots of "25I-labeled [Tyrllsomato-statin with and without excess unlabeled [Tyrll]somatostatin (18 ,ug)in the injectant. ['4C]Inulin was used as an extracellular reference.

sets of simultaneous differential equations (Eqs. 4 and 5) werewritten and were numerically solved by the Runge-Kutta-Marson method (19). Eqs. 4 and 5 together with Eqs. 6 and7 were simultaneously fitted to the 110 experimental datapoints of ratio plots at six doses to obtain the values of ko.,koff, ks, and PT by iterative nonlinear least-squares method(program, SALS) (20). The input data were weighted as thereciprocal of the square of the observed values.The model equations in the linear condition based on the

venous-equilibrium model were obtained by solving Eqs. 4and 5 under the condition PT >> X2. Then, considering Eq.7, the equation representing the ratio plot is given by:

R =

C1 ref -

C, (13 - a) exp(- Q/Vdref-t)(k2 + k3 - a) exp(- a-t) + (,8 - k2 - k3)-exp(- 83t)where

2 Vd,ref

2 [(Vdref

+ ki + k2 + k3) + q]

+ k, + k2 + k3) - q]

[(Vdref )k+ k2 + 13

-V

(k2 + k3) + ki k3 [10]

Statistical analysis was performed using Student's t testwith P = 0.05 as the minimal level of significance.

RESULTS AND DISCUSSIONDose Dependence of the Dilution Curve of 12'I-EGF. Fig. 1

shows the time courses ofthe concentrations of 1251-EGF and[14C]inulin emerging into the outflow after simultaneousbolus injection with and without excess (30 1Lg) unlabeledEGF. The increase in the amount of unlabeled EGF in theinjectant made the dilution curve of 1251-EGF resemble thatof [14C]inulin, indicating the dose dependence of EGF ex-traction by the liver. The E value ofEGF was =0.8 at a tracer

C 1.0~

5' 0.8-

!0.6

s 0,6L

0.2

E-

-E 0.2

1.0

0.8

,0,6

014; 06,2

0.2

0

-0.2

Tracer only

Tracer +cold 25jug

an d.~~~~~~4 An

, Tracer only

|Tracer t cold 30 jig

m -

Au 10 20

Time (sec)30

FIG. 5. Representative ratio plots of 125I-labeled insulin (Upper)and '25I-labeled glucagon (Lower) with and without excess unlabeledinsulin (25 gg) and unlabeled glucagon (30 ,ug) in the injectant,respectively. ['4C]Inulin was used as the extracellular reference.

dose, whereas E decreased with the dose increase andbecame close to zero in 30 gg of unlabeled EGF (Fig. 2). TheVd of EGF also decreased in a dose-dependent manner;namely, 0.8-1.2 ml/g of liver at a tracer dose and 0.15 ml/gof liver in the presence of 30 ,ug of EGF, which approximatesthat of inulin, an extracellular reference substance. Thesedose-dependent decreases in the values ofE and Vd may beeasily explained when we recall that EGF has specific bindingsites (receptor) on the liver cell surface (2-5, 21).

Fig. 3 shows representative ratio plots of 1251I-EGF withvaried amounts of unlabeled EGF in the injectant. At thetracer dose, the ratio plot exhibited an upward straight lineinitially (=10 sec) and plateaued for the next 20-30 sec. Theinitial upslope decreased clearly with the increase in unla-beled EGF. This decrease may reflect a decrease in availablereceptors on the cell surface due to their occupation, becausethe slope is proportional to the value of koflPT (Eq. 1).

Dilution Curves of Somatostatin, Insulin, and Glucagon.Fig. 4 shows the ratio plots of somatostatin. In contrast tothat of 125I-EGF, the ratio plot of 1251I-labeled [Tyr1l]somato-statin gradually decreased. Also, the ratio plot did not changesignificantly with excess unlabeled peptide, contrary to thatofEGF. Calculated values ofEand Vd for the tracer dose andvalues with excess unlabeled peptide are shown (Table 1); Eor Vd did not differ significantly between the two doses. Sucha great difference in shape of the ratio plots between EGF andsomatostatin may be explained as follows, considering theinitial upslope to represent kOnfPT (Eq. 1). That is, somato-statin may nonspecifically bind to the cell surface and thatdistribution of somatostatin to the cell surface occurs almostinstantaneously; hence, ratio plots of somatostatin may showonly the downslope influenced by the sequestration rateconstant. On the other hand, EGF specifically binds to thecell-surface receptor at a relatively slow rate, which can bedetected from the slope of the ratio plot.

Table 1. The extraction ratio (E), distribution volume (Vd), and the shape of ratio plots of the peptide hormones in the liver

Experiments, Extraction ratio Vd (peptide)/Vd (inulin) Initial upslope of ratio plotPeptide n Low dose High dose Low dose High dose at a tracer dose

Somatostatin 4 0.247 ± 0.041 0.151 ± 0.037 1.74 ± 0.22 1.40 ± 0.07 NoneEGF 5-8 0.826 ± 0.022 0.232 ± 0.068* 5.01 ± 0.80 1.26 ± 0.09* PresentInsulin 3-5 0.502 ± 0.020 0.203 ± 0.099* 1.88 ± 0.07 1.32 ± 0.16* PresentGlucagon 3-4 0.572 ± 0.009 0.441 ± 0.070 2.33 ± 0.06 2.09 ± 0.22 Present

Data are expressed as mean ± SE.*Significantly different (P < 0.05) from that at a low (tracer) dose.

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Table 2. Classification of peptide hormones in terms of the properties of the distribution and elimination in the liver

Vd (peptide)* Extraction

Type Distribution Elimination Vd (inulin) ratio*1 Extracellular space None 1 -02 Extracellular space Degradation 1 >03 Nonspecific and rapid binding to cell surface None >1 -04 Nonspecific and rapid binding to cell surface Degradation >1 >05 Specific and slow binding to cell surface None (receptor-peptide complex is not internalized) >1 -O6 Specific and slow binding to cell surface Degradation and/or receptor-mediated endocytosis >1 >0

*Values at a tracer dose.

We previously reported that somatostatin has no specificbinding site on the liver cell surface by use of rat liver plasmamembranes (22, 23). In that experiment no displacementof 1251I-labeled [Tyr11]somatostatin bound to the plasmamembrane (protein concentration, 0.8 mg/ml) by unlabeled[Tyr11]somatostatin was seen, even when its concentrationwas varied over a wide range (z150 nM). The average bindingpercentage was 9.8 + 2.8% (mean + SE; n = 3). Meanwhile,EGF showed a high (=60%o)'and saturable binding to the samemembrane preparations (24).To confirm the above-mentioned hypothesis, we did the

MID experiments using insulin, taken up via receptor-medi-ated endocytosis (11) as well as EGF, and glucagon, whichalso has its specific receptor on the cell surface (12) (Fig. 5).The ratio plot of insulin was similar to that ofEGF. At a tracerdose, an upward straight line for the first 4-5 sec and aplateau for the following 20 sec were seen. On the other hand,the decrease in the initial slope with excess amount (25 ,ug)of unlabeled insulin was obvious. Further, the dose depen-dency of E and Vd was seen (Table 1). The ratio plot ofglucagon at a tracer dose also showed a positive slope for theinitial period but decreased at a constant slope with excessamount of unlabeled glucagon (Fig. 5). Values of E and Vdboth decreased slightly with the increase of dose, but notsignificantly (Table 1). This minimal saturability in glucagonkinetics may suggest a relatively dominant contribution of anonspecific mechanism.From these considerations, we can classify the peptide

hormones in terms of their properties of distribution andelimination in the liver as shown in Table 2. Values ofE andVd and the dose dependencies of these parameters reflect thecorresponding properties shown in Table 2. In addition, thepatterns of the ratio plots may be classified according to therate of peptide-receptor interaction as shown in Fig. 6. In thisway we can estimate the mechanisms of hepatic handling ofpeptide hormones when the model-independent parameters (Eand Vd), the patterns of the ratio plots, and their dosedependencies are measured.'In fact, we can infer from our

4-,a)

CL

Qa_CL

.-4

-1Ca0-

u

Type652

\4

3

TimeFIG. 6. Ratio plots expected from the properties of the distribu-

tion and the elimination of peptide hormones in the liver (see Table1). Abscissas, time scale corrected for the large-vessel transit timeand the catheter delays; ordinates, the logarithmic ratio (inulinoutflow fraction per ml)/(peptide outflow fraction per ml). Eachpattern of the ratio plot is predicted from Eq. 8, by considering theextents and the rates of distribution and elimination of peptides.Numbers correspond to the types described in Table 2.

present data that somatostatin belongs to type 4, whereas EGFand insulin belong to type 6.Time Course of the Recovery of the Free EGF Receptors on

the Liver Cell Surface. The following experiment was done toascertain that the analysis based on the MID experiment forEGF actually gave information about the interaction betweenEGF and its receptor. First, the MID experiment of _251-EGFat a tracer dose was done as control. Then, after 15-minperfusion, 20 pug of unlabeled EGF was injected as a bolus,and at 1, 3, 10, and 30 min the MID experiments of 1251I-EGFat a tracer dose were done to chase the recovery of availablereceptors on the cell surface. As shown in these ratio plots(Fig. 7), the initial slopes, which correspond to kO -PT (Eq. 2),decreased greatly at 1 min after injection of excess (20 tig)unlabeled EGF and then gradually recovered to near controlvalue. Representative recoveries of the E and Vd values of1251I-EGF are shown in Fig. 8. The E value, which decreasedto -0.5 of control recovered with time (recovery half-life, -5min) and so did the Vd. Kinetic analysis of the dilution curveshowed that this recovery is mainly associated with that of k1.Therefore, these recoveries may be explained by two possi-ble mechanisms; (i) EGF molecules bound to their cell-surface receptors are dissociated during the perfusion andremoved by the perfusate flow, resulting in an increase inavailable receptors, or (it) EGF-receptor complexes are inter-nalized, and free receptors return to the cell surface from theintracellular pool by recycling. This mechanism is related tothe phenomenon of so-called down-regulation (25). Discrim-ination between the two mechanisms has not been made inthe present studies. However, this recovery experiment con-firmed that the MID experiment could yield quantitativeinformation about available receptors on the liver cell surface.

Determination of Kinetic Parameters for Interaction Be-tween EGF and Its Cell-Surface Receptor. We determined the

Time (sec)

FIG. 7. Recovery of available EGF receptors on the liver cellsurface after injection of an excess amount of unlabeled EGF. Afterpreperfusion for 10 min, the MID experiment at a tracer dose of1251I-EGF was done (control). After 15-min perfusion, 20 ,ug of EGFdissolved in 200 pA of the perfusate was injected as a bolus into theportal vein; then the MID experiment at a tracer dose of 1251I-EGFfollowed at 1, 3, 10, and 30 min. The logarithmic ratio ([14C]-inulin/125I-EGF) was calculated from the dilution curve obtained ateach time (expressed as T) after the injection. All results are thusexpressed in terms of the ratio plot.

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Table 3. Comparison of the kinetic parameters of 1251-EGF in the distributed and the venous-equilibrium model at the tracer dose

k, (= kon.PT/Vdref), sec - 1 k2, sec'- k3, sec'-Distributed model (n = 8) 0.416 ± 0.030 0.045 ± 0.008 0.141 ± 0.010Venous-equilibrium* model (n = 8) 0.498 ± 0.047 0.052 ± 0.007 0.138 ± 0.015Data are expressed as mean ± SE.

*Calculated according to Eqs. 8-10.

three kinetic parameters, kon, koff, and PT, by simultaneousfitting of the ratio plots of EGF at six doses. Fitting curves atfour representative doses are shown (Fig. 3). The parameterswere calculated as follows (mean + SE): k0n = 2.0 ± 0.67gM'- sec1, koff = 0.035 ± 0.013 sec, k, = 0.069 + 0.017sec1, and PT = 35.6 + 3.5 pmol/g of liver. The dissociationconstant (Kd = koff/k0d) was calculated to be 17.5 nM. Kdvalues determined from the in vitro binding studies atequilibrium are 3-15 nM at 4TC using rat liver homogenates(2, 26) or isolated rat liver cells (2) and 1.5-3 nM at 24-370Cwith rat liver plasma membranes (5, 24). Densities of EGFreceptors on the liver cell surface are reported to be 17.5-33.0pmol/g of liver, which was obtained from the binding studyat 40C with rat liver homogenates (2, 26) or isolated rat livercells (2). Binding parameters (Kd and PT) obtained from theMID analysis thus fell within the values obtained previouslyfrom the direct in vitro binding experiments.

It is not so clear which kinetic process the parameter ksrepresents; this parameter may be related either to theinternalization process of EGF-receptor complex or to itsclustering process (1). We directly determined the internal-ization rate constant in isolated rat hepatocytes by anacid-washing technique (26). The preliminarily obtained rateconstant (0.001-0.002 sec1) was smaller by a factor of -100than the ks value from the present study (unpublished ob-servation). Therefore, the ks value obtained by the MIDanalysis may represent more rapid kinetic processes, such asthe clustering or the conformational change of the EGF-receptor complex. For analyzing slower kinetic processes,including internalization and recycling of the receptors, simul-taneous use of a conventional liver-perfusion method, such asthe recirculating method (26), would be necessary.The fitting analysis to obtain the binding parameters was

done with derived equations based on the venous-equilibriummodel. Use of the distributed model is ideal, but due tomathematical difficulty in handling the nonlinear kinetics, wecould not avoid use of the simple venous-equilibrium model inthis analysis. Therefore, to check the feasibility ofthe venous-equilibrium model' the two models were compared using thedata at a tracer dose of EGF, where linear kinetics holds true.The obtained parameters were comparable between the two

b

aa -Control1.0 Eil 0 o, EGF

-20. Control 20.8 Inuilin-0.86

0 6 ,0.40.420

4-10.2~ ~ ~ 0.

0o 10 20 30 00 10 20 30Time After Injection (min)

FIG. 8. Recoveries ofextraction ratio (a) and distribution volume(b) of 125I-EGF after injection of excess (20 ug) unlabeled EGF.Extraction ratio and distribution volume were calculated from thedata of Fig. 7. Arrow, EGF (20 jug) injected into the portal vein.

models (Table 3). The parameter k, gave the greatest model-dependent difference among these parameters, but the differ-ence was still within 30%. Such comparisons suggest that theparameters obtained based on the venous-equilibrium modelmay give reasonable values also for the nonlinear condition.Although the venous-equilibrium model does not predict theappropriate shape of the dilution curves (27), it can thuspredict the ratio plot properly and may be used in analyzing theindicator dilution data for nonlinear conditions.

In conclusion, the present studies revealed that the MIDmethod can be a good tool for analyzing the dynamics ofinteraction between peptide hormones and cell-surface re-ceptors. This method may be applied to analysis of theinteraction of peptide hormones with the hepatic receptors indisease states, in the regenerating period after a partialhepatectomy, and in conditions under hormonal regulations.

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