0 1986 by The American Society of Biological Chemists, Inc. THE JOURNAL OF BIOLOGICAL CHEMISTRY Vol. 261, No. 4 , Issue of February 5, pp. 1702-1711, 1986

Printed in U. S. A.

Kinetics of Insulin Binding to Rat White Fat Cells at 15 ‘C*

(Received for publication, June 4, 1985)

Edward W. Lipkin$, David C. Teller, and Christoph de Haen8 From the Division of Metabolism, Endocrinology, and Nutrition, Department of Medicine and the Department of Biochemistry, University of Washington, Seattle, Washington 98195

The kinetics of insulin binding to isolated rat epi- didymal fat cells was investigated at 15 O C , at which temperature the system was simplified by the absence of lysosomal insulin degradation. The data were fit by maximum likelihood criteria with differential equa- tions describing a number of models for the interaction of insulin and cells. Among those models that yielded a fit, the selection criteria were minimization of the Akaike information criterion and compatibility of the overall equilibrium constant for the system calculated from rate constants with the previously obtained ex- perimental value. The results of the analysis indicated that insulin, I, first reversibly bound to cell surface receptors, R, whereupon this initial insulin-receptor complex, RI, reversibly altered its state or cellular location to R’I, according to the following equation.

R + I e RI R’I ~ I Z Itzs

kZl ksz

No evidence was found that insulin could either asso- ciate or dissociate from R’I directly. The association rate constant was k12 = 1.6 5 1.4 X 10‘liter mol” s-l, a value shown to be incompatible with diffusion con- trol. The other rate constants were: kZ1 = 3.4 ?$ 1.6 X

s-l, kZ3 = 3.2 ?$ 1.5 x s-’, and k32 = 2.0 5 1.5 X s-I. From these rate constants, an equilibrium constant of 8.4 ?$ 1.5 nM was calculated, in excellent agreement with the previously measured value of 8.8 5 1.3 nM (Lipkin, E. W., Teller, D. C., and de Haen, C. (1986) J. Biol. Chem. 260, 1694-1701). The kinetic analysis also yielded receptor numbers similar to those obtained by equilibrium binding studies. The nature of the R’I state is discussed in terms of an internalized state, in terms of insulin receptor complex in caveolae, in terms of receptor aggregates, and in terms of being a Michaelis complex between insulin bound to the re- ceptor and cell surface-bound insulin protease.

Early work on the kinetics of binding of insulin to fat cells purportedly showed that the process could be described by a

* This work was supported by research grants from the National Institutes of Health (AM 02456, AM 27767, and GM 13401) and facilitated by the Diabetes Research Center (AM 17047). This is Paper I1 of a series, “Insulin Binding to Fat Cells.” The preceding is Paper I. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

2 Recipient of a fellowship from the American Diabetes Association and a National Institutes of Health New Investigator Research Award AM 32794.

$Recipient of a United States Public Health Service Research Career Development Award AM 00682. To whom inquiries should be addressed.

simple reversible bimolecular interaction between cell surface receptors and insulin (1, 2). The analysis by Gammeltoft and Gliemann (3) supported this picture, although their kinetic and equilibrium constants were incompatible with the earlier values, a situation that could be attributed to inconsistencies in the earlier work. Subsequently, the kinetics of insulin binding to fat cells has been found to be more complex (4- 11). In some reports, this complexity was also apparent at binding equilibrium (9, 11-13). In contrast, other reports (3), including our own (14), indicated that the overwhelming majority of insulin binding sites could be characterized by a simple binding isotherm. To date, the kinetics of insulin binding has not been reconciled quantitatively with binding equilibrium. We have investigated the kinetics of insulin binding to isolated rat epididymal fat cells to achieve such a reconciliation. The present kinetic analysis was performed at 15 “C, the temperature used in the preceding equilibrium analysis (14). This temperature was chosen because insulin degradation by the lysosomal pathway is inhibited (15, 16). The system is simplified, yet some biological actions of insulin are preserved at this temperature (17).

In the present work, a model for insulin binding to fat cells is derived from a detailed kinetic analysis. In this model, insulin first binds reversibly to the receptor, whereupon the insulin-receptor complex converts reversibly into an altered state or location. Similar models have been proposed previ- ously (8,18-22), but no rigorous kinetic analysis has yet been reported for these models. The rate constants describing the model proposed here are shown to produce agreement with observations of binding equilibrium.

MATERIALS AND METHODS’

Theory-In the preceding paper (14), it was shown that insulin in the cell pellet after centrifugation through dinonylphthalate can be described by:

Pt = VI(U - a)[Blr + a[Tl) ( 1 )

where P is the amount of insulin in the cell pellet measured in moles, VI is the extracellular volume/incubation measured in liters, [ B ] , is the molar concentration of receptor-bound insulin (i.e. the number of mol of receptor-bound insulin divided by VI), [ T ] is the correspond- ing molar concentration of total added insulin, and a is the fraction of extracellular volume trapped in the cell pellet. The subscript t indicates that Equation 1 holds for any time during a kinetic experi- ment. This is based on the assumption that trapping of insulin is a process associated with pellet formation and thus not dependent on

Portions of this paper (including parts of “Materials and Meth- ods” and “Discussion”) are presented in miniprint at the end of this paper. Miniprint is easily read with the aid of a standard magnifying glass. Full size photocopies are available from the Journal of Biolog- ical Chemistry, 9650 Rockville Pike, Bethesda, MD 20814. Request Document No. 85M-1832, cite the authors, and include a check or money order for $4.40 per set of photocopies. Full size photocopies are also included in the microfilm edition of the Journal that is available from Waverly Press.

1702

Kinetics of Insulin Binding to Fat Cells 1703

the incubation time. Binding kinetics are thus described by the following equation:

where d[B] /d t depends on the kinetic model chosen. Equilibrium studies (14) have shown that binding of insulin to fat

cells at 15 "C is best described by the sum of 2 simple binding isotherms, one isotherm of which describes the binding to more than 99.7% of the receptors with a K"d of 8.8 5 1.3 nM. A very small fraction of the receptors (<0.3%) showed a higher affinity ( K ' d z 8 $ 3 PM). Any kinetic model would thus have to be compatible with the equilibrium observations. In the following, a number of models are introduced. These models have been selected for further scrutiny, in part through intuitive i n ~ ~ r e t a t i o n of data, and in part because they have been suggested in the literature.

~ o ~ e ~ - C o n s i d e r a single class of reversible binding sites (Model A) or two classes of independent and noncooperative binding sites (Model B).

Q' + I * Q'I

MODEL A

k '12

k ;I

Q" + I -+ Q"I k ';2 E

~

MODEL B

Q ' and Q" designate the first and second class of sites, respectively, and I stands for insulin. Binding equilibrium for Model B is described by:

where IF): = [ TIi - [B]; is the free and [B]i is the bound insulin a t the ith total added insulin concentration, [TI{. [Q'Ima. and [a"!,,, are the total concentrations of primed and double primed bmdtng sites, respectively, and K' = k; l /k;2 and K " = k!$l/k';2 are the corresponding dissociation equilibrium constants. Obviously for a single class of binding sites (Model A) the second term in Equation 3 is 0.

Now consider the following model (Model C):

R + I k12

c i g R 1

R'I MODEL C

I stands for insulin, R for the receptor to which insulin binds initially, and R' for the receptor in an altered state or locality. kc are the kinetic rate constants and Kl = k21/k12, K2 = k32/ks, and K s = k31/k13 are the equilibrium constants of the individua1 steps. Model C reduces to a simpler model under the special circumstances of kI3 = k31 = 0.

k12 ik23 k32

R + I ;Fzr RI R'I

MODEL D

In these cases, one has a t equilibrium

Equation 4 describes a simple binding isotherm, wherein [Blmax is the total concentration of receptor. This isotherm is characterized by the total concentration of all receptor forms, [Bjmm, and the apparent dissociation equilibrium constant:

Next, consider the model in which the receptor can be in 2 states or locations, R and R', even without bound insulin (Model E):

The equilibrium constants for the individual steps are KO = &l/klo, Kl =: kzl/kls, Kt = k32/kz3, and K3 = kso/ko,. In this case, one has a t equilibrium

Equation 6 again describes a simple binding isotherm characterized by the total concentration of all receptor forms, [Blrnax, and the apparent dissociation equilibrium constant:

Model E reduces to a simpler model under special circumstances.

& = kso = 0

MODEL F Equations 6 and 7 continue to describe the overa'fl equilibrium of

the system. However, if one assumes, in addition, that the receptors alter their state or location uninfluenced by their occupancy by insulin, one has the following:

ko:, = k30 = 0, &I = k32, klo = k23, &*pp = KI = k21/k12

MODEL G

i.e. the overall equilibrium constant corresponds directly to the step of insulin binding to the accessible empty receptor species, R. Model E can also yield Model D under the condition

&% = k3o = k+1 = kt0 = 0

MODEL D

where equilibrium is described by Equations 4 and 5.

RESULTS

Equilibrium binding experiments had shown that the great majority (>99.7%) of receptors on isolated rat fat cells be- haved at 15 "C as if they represent a single class of noncoop- erative binding sites (14). In order to explore the kinetics of insulin binding to these sites, fat cells (7.8 X IO5 cellsfml) were preincubated with labeled insulin (1.08 X lo-" M) for 4 h, at which time dissociation of labeled insulin was initiated by the addition of unlabeled insulin in large excess (1@" M). New binding of labeled free insulin thus was reduced to negligible levels. Dissociation of the labeled insulin was mon- itored. Fig. 1 shows the data presented in the form of the observation function, i.e. insulin in the cell pellet above the dinony~phthalate, P, against time. The data was fit by func- tions of the form of Equation 9 with 1 to 3 exponential terms and the statistically most appropriate fit was selected based on the Akaike information criterion (see "Materials and Methods"). The AIC' for 1, 2 and 3 exponential terms was 65.8, 62.1, and 64.1, respectively, indicating that only 2 ex- ponential terms could be statistically justified. Note that this did not preclude a more complex situation. It only said that our data would not suffice for its description. The curve in

~ ~-

The abbreviations used are: AIC, Akaike information criterion; BSA, bovine serum albumin; HEPES, N-2-hydroxyethyl-piperazine-

phate-HEPES buffer; 1, liter. N'-2-ethanesulfonic acid; mKRPH, modified Krebs-Ringer-phos-

1704 Kinetics of Insulin Binding to Fat CeuS

L"-..L-."-A '0 60 120 I80 240

T~rne (rnln!

FIG. 1. Dissociation of labeled insulin from fat cells at 15 O C

in the presence of 10" M unlabeled insulin. Fat cells (7.8 X lo6 cells/ml) were preincubated with 1.08 X M labeled insulin at 15 "C for 4 h. A time 0 min dissociation of labeled insulin was initiated by the addition of enough unlabeled insulin to reach a concentration of 1.03 X IO4 M. The graph shows the loss with time of labeled insulin from the cell pellet collected as described under "Materials and Methods." The curve remesents the best fit of Model D to the data.

Time ( min )

FIG. 2. Time course of association of insulin with fat cells at 15 OC. Packed fat ceIls (40 pl , 2.37 X IO6 cells) were added at time 0 min to aliquots (260 p l ) of labeled insulin in incubation buffer. The cells were incubated at 15 "C in the shaking incubator, and at various times insulin in the cell pellet was measured as described under "Materials and Methods." Experiments with six different 'insulin concentrations were performed on the same cell batch. Final insulin concentrations based on extracellular water space were: A, 1.24 X 10"O M; ., 3.31 X 10"O M; a, 1.05 X IO-* M; A, 3.17 X M; 0,1.04 x lo-* M; 0, 3.10 x lo-' M. Curves represent the best fit sofution for Model D fit simultaneously to this data as well as two experiments of the kinds shown in Fig. 4. The parameters were those of Table I1 (combined analysis).

Fig. 1 corresponds to the biexponential decay P' = 2.92 X lo4 (1.72 X e-O.m'llt + 0.99 X lo"* e-o.ooo962t + 0.452 X 10-"), where t is measured in seconds. The experimental control in which the large concentration of unlabeled insulin was present from the start of the experiment indicated trap- ping to account for a constant term in Equation 9 of Via[ T'J, = 0.996 X lopL6 mol. Comparison of this value with the

constant term calculated from the above equation for disso- ciation of 1.32 X mol revealed a residual nondissociable binding of 0.32 x mol. Given that 2.15 X loJ cells were present, the nondissociable binding represents 90 receptors,' cell, or 0.09% of the total receptors. This exceedingly small number indicated that insulin binding was in essence com- pletely reversible under our conditions. The small amount of irreversibly bound insulin may represent the small number of extra-high-affinity sites (<0.3% of binding sites) observed in some equilibrium binding experiments (14).

In considering the exponential terms themselves, the factor 1 - a in Equation 9 was neglected, since a << 1. The most impo~an t result was that the dissociation was biexponential in nature, directly ruling out the simplest binding model involving only the reversible and noncooperative binding of insulin to a single class of receptors (Model A). This biexpo- nentiality was compatible with Models B, C, D, and G. Models E and F would have predicted a tetraexponential decay. only if Model B were applicable would the amplitudes represent the concentrations of the two receptor species, and would the exponents represent first-order rate constants, corresponding to half-lives of 103 and 12 min, respectively. When the as- sumption was made that before the initiation of dissociation equilibrium had been achieved, it was possible to extract the rate constants b,, kZ3, and k32 for Model D from this data. They were similar to the constants obtained from experiments described below. Because we believe that the constants ob- tained from the present pure dissociation experiment were less trustworthy than those from later experiments, they are not reported in detail. For the same reason, the data were not analyzed in terms of the remaining models.

Next, association rates were examined. Six insulin concen- trations were used simultaneously yielding from 0.1 to 75% saturation of receptors a t equilibrium. While the error in experiments at these high insulin concentrations was larger than in similar experiments performed at low insulin concen- trations only, use of high concentrations was important to assure that the kinetics was describing the majority of the receptors. Fig. 2 shows typical data. Various models were fitted to these data and a repeat experiment. Analysis of earlier data had shown that Model A had a higher AIC than Model D.3 Together with the biexponential dissociation ki- netics, this led us to drop Model A from further consideration. No fit was obtainable for Models C, E, and F, because one or more of the rate constants, except those in common with Model D, tended to vanish. Among the other models, Model D had the lowest AIC for the data set shown in Fig. 2 and a repeat thereof (Table I). Table I1 shows the kinetic parameters obtained for that model, From the rate constants of Model D, the overall equilibrium constants for the two experiments were calculated by Equation 5 as K',, = 14.2 and 8.3 nM, respectively (Table I).

In order to tap the information contained in dissociation experiments without having to first reach equilibrium, asso- ciation and dissociation were measured consecutively on the same cells, Labeled insulin at three concentrations, designed to correspond to about 1, 10, and 50% of saturation of ail receptors at equilibrium, was allowed to associate with fat cells for 150 min, at which time a large excess of unlabeled insulin was added, yielding a final concentration of at least

M. The time course of association and dissociation of only the labeled insulin present during the association phase was monitored. Fig. 3 shows data from such an experiment.

de Haen, C., Teller, D. C., and Lipkin, E. W. (1983) 2nd Inter- national Symposium on Insulin Receptors, (De Pirro, R., ed) Tipo- grafia Ambrosini, Rome, August 31-September 3, 1983, P. 21.

Kinetics of Insulin Binding to Fat Cells 1705

TABLE I Test results for various models fitted to kinetic data for insulin b i ~ ~ n g to fat celk at I5 "C

The various models described in the text were fitted to the data shown in Figs. 2 and 3 and repeat experiments. For those models for which the fitting routine converged to a unique solution, the model parameters crucial for the comparative evaluation are listed. Also Iisted is the Akaike information criterion (AIC), useful for statistical model identification.

Model B "

Model D Model G Experiment

K G 10-3 QL, K" 10-3 QL AIC K~~~ 10-313- AIC 10" B,, AIC RM sites/cell RM sitesjcell

- n~ sites f cell nM sitesfcell

Fig. 2 59.6 277.0 30.05 92.2 705.7 14.20 242.9 410.9 18.10 306.0 695.8 Fig. 2 repeat 13.1 111.7 4.95 76.9 232.7 8.26 191.6 224.3 4.20 96.0 232.1 Fig. 3 32.9 100.3 3.84 35.3 289.5 6.38 82.4 301.0 6.60 73.9 315.1 Fig. 3 repeat 23.3 78.6 3.96 37.7 357.0 6.58 90.3 362.3 7.27 85.7 371.8 Joint fit

Fig. 2 1 29.1 187.7 49.9 120.7 123.9

Fig. 3 89.9 4.70 48.0 1450.6 7.08 100.2 1461.7 8.52 103.8 1506.1 Fig. 3 repeat 92.2 48.6 101.9 105.6 - ~ _ _ - _

TABLE XI Kinetic constants for insulin binding to fat ceuS at 15 "C ~ c o ~ ~ ~ to Model U

The constants were obtained by fitting the differential equations for Model D to individuaf experiments as we11 as by fitting several experiments simultaneously, but requiring common rate constants.

Experiment 10" kt2 10' k,, 10' ka3 lo-' A32 B, 104 a* KdCrnb

1 mol" s-* S" siteslcell ItM

Fig. 2 1.37 4.80 2.01 1.37 242.9 4.58 14.20 Fig. 2 repeat 2.56 5.08 4.88 3.48 191.6 2.17 8.26 Fig. 3 1.19 1.98 3.04 1.88 82.4 8.69 6.38 Fig. 3 repeat 1.38 2.60 3.29 1.76 90.3 9.11 6.58

exp (In x)' exp (S.D.)

Joint fit

- 1.6 3.4 3.2 2.0 136 5.3 8.4 5 1.4 $ 1.6 $1.5 5 1.5 5 1.7 5 1.9 5 1.5

Fig. 2 120.7 16.13 Fig. 3 1.37 2.86 3.14 1.62 100.2 6.25 7.08 Fig. 3 repeat 101.9 7.88

Fig. 4 1.65 2.07 2.27 2.47 172.9 120.90 6.52 Normalized to lo5 cells/incubation.

'This is calculated from Equation 5. Mean and standard deviations were taken on the iogarithm of the parameter values, because the error

~ s t r i b u t i ~ n s as judged by probit transformation were more normal on that scale (14, 23).

Various models were fit to the data. Again, Models C, E, and F could not be fit to the data because one or more of the rate constants, except those in common with Model D, tended to vanish. Among the other models, Model B had the lowest AIC for the data set shown in Fig. 3 and a repeat thereof (Table I). The analysis described the two classes of binding sites in these experiments as having equilibrium constants of 28 and 3.9 nM, and being present in a ratio between 21 and 3:1. The half-lives for dissociation from the two sites were -5 and -70 min, respectively. Model D had the second lowest AIC. The corresponding kinetic parameters are given in Table 11.

In order to increase the number of data poin ts / f i~d param- eter, and to obtain the best estimates for the model parame- ters, two association-dissociation experiments and one pure association experiment were fit simultaneously with various models, requiring common kinetic rate parameters but allow- ing individual values for receptor concentrations and trapping constants. In the interest of keeping computation time within practical limits, only three experiments were combined. Models C, E, and F could not be fit to this increased data base, because one or more rate constants, except those in common with Model D, still tended to vanish. Among the other models, Model B had the iowest and Model D the second lowest AIC (Table I). The kinetic parameters given in Table

11 were not s i ~ i f i c a n t l ~ different from the means calculated from indiv~dual experiments.

A satisfactory choice between Models I3 and D was not possible based solely on the AIC associated with the kinetic experiments. However, if the equilibrium binding results ob- tained previousiy (14) were considered together with the ki- netic results, a elearcut answer emerged. The equilibrium constants and ratios of capacities of the two classes of binding sites, predicted by the kinetic analysis according to Model B (Table I), were incompatible with the equil~brium observation of a simple binding isotherm with Kd,epp = 8.8 1.3 nM describing over 99.7% of the binding sites (14). In contrast, the equilibrium constant of = 8.4 5 1.5 nM predicted by the kinetic analysis according to Model D (Table 11) was in excellent agreement with equil~brium experiments. We con- cluded that Model D was a better model for insulin interaction with fat cells than Model 3. Solid lines in Figs. 2 and 3 show the best fit curves calculated with the parameters for Model D. At some time and concentration combinations in Fig. 3, there were significant discrepancies of data and best fit line, especially at the highest insulin concentration. This could mean that Model D is not yet a complete description of the system. For example, cell death sometim~s noted in prolonged incubations (14) has not been considered. The defects of the

1706 Kinetics of Insulin Binding to Fat Cells

0 IO0 200 3 00 Tlme tmm)

FIG. 3. Time course of association of labeled insulin with fat cells followed by dissociation in the presence of 10" M unlabeled insulin. Packed fat cells (40 pl, 3.06 X 106 cells) were added at time 0 min to aliquots (260 pl) of labeled insulin in incuba- tion buffer. The cells were incubated at 15 "C in the shaking incuba- tor, and insulin in the cell pellet was determined in samples being incubated for various times up to 150 min, as described under "Ma- terials and Methods." At 150 min, 30 pI of 1.1 x lod6 M unlabeled insulin was added to the remaining samples, and dissociation of labeled insulin was monitored in the same fashion for an additional 150 min. Concentration of labeled insulin: 0,0.96 X 10"' M; 0, 1.03 X lo-' M; A, 1.04 X SO-' M. Curves represent the best fit solution for Model D fit simultaneously to this data, a repeat of this experiment and the experiment in Fig. 3. The parameters were those of Table I1 (combined analysis).

model also could reflect more directly reactions missing or misrepresented. Certainly the low statistical weight that the maximum likelihood fitting procedure assigned to data at high occupancy of binding sites could have compounded any prob- lem of deviations at such occupancies.

In a novel type of experiment, fat cells were preincubated at a high (6.83 X lo-' M) and a low (2.93 X 10"' M) concen- tration of labeled insulin for 2 h, after which time the cell suspension was diluted 10-fold with incubation buffer) causing relaxation of the system to a new equilibrium level (Fig. 4). Note that the dilution in terms of extracellular water space was 13.5-fold. When the assumption was made that during preincubation a state reasonably close to equilibrium had been attained) the equation for Model D could be fit to the data as explained under "Materials and Methods." Dissociation ex- periments of this kind are able to yield all rate constants, including the association rate constant k12. Table I1 shows that the rate constants obtained are compatible with those obtained from the other types of kinetic experiments, al- though the trapping constant was higher than usual. No

FIG. 4. Time course of dissociation of labeled insulin from fat cells after 10-fold dilution of a cell suspension preasso- ciated with insulin. A batch of fat cells (7.10 X 10' eellslml) was split in two batches, and these were preincubat~ with either 6.83 X lo-@ M ( A ) or 2.93 X lo-" M ( B ) lZ5I-labeled insulin for 2 h at 15 "C. At time 0 min, the cell suspensions were diluted 10-fold with insulin- free incubation buffer. Curves represent the best fit of Model D simultaneously to data in panels A and B, as described under "Ma- terials and Methods.''

attempt was made to obtain fits for the other models, since the assumptions needed in the analysis of the data left this experimental design with less discriminatory power than the other experiments described. Nonetheless, the fact that Model D was able to describe these data with the same values of the constants as required for the other experiments, showed the range of applicability of Model D and thus added to its attractiveness.

Taking all the above experiments together, it appeared that Model D was an adequate first approximation to the descrip- tion of the kinetics of insulin binding to the majority of insulin binding sites on rat fat cells at 15 "C. Obviously, Model D did not account for the possible existence of ~ 0 . 3 % of extra-high- affinity binding sites for insulin) as suggested by binding equilibrium studies (14). However, two factors would have conspired against their detection in some of the above exper- iments. First, a t high insulin concentrations their contribu- tion to total binding is negligible. Second, the initial binding being a bimolecular reaction, their net rate of occupation would also be much slower than that of the major class of binding sites. In order to explore the issue further, association experiments at four insulin concentrations in the low concen- tration range were performed. Based on the reported equilib- rium constants and site capacities (14) at the lowest insulin concentration used, i.e. 0.48 X 10"' M, binding equilibrium would be expected to correspond to 86% saturation of the extra-high-affinity receptors and 0.5% saturation of the ma- jority of receptors. The two classes of receptors can be ex- pected to contribute to binding in the ratio 1:2 under these conditions; i.e. the extra-high-affinity receptors should make a substantial contribution. Fig. 5 shows the data. Such data had previously been found to be fit by Model D better than by Model A? The kinetic parameters from multiple experi- ments were very similar to those describing the majority of receptors alone. This suggested that if extra-high-affinity binding sites are real, their association kinetics is sufficiently similar to that of the majority of binding sites to prevent their separate kinetic characterization, or that the extra-high-affin- ity state is formed subsequent to the interaction of insulin with the major class of binding sites. Because we suspect that

Kinetics of Insulin Binding to Fat Cells 1707

Time (minl

Time course of association of insulin at low concen- trations with fat cells at 16 "C, Aliquots (100 pl) of labeled insulin were added at time 0 min to aliquots (200 pl) of fat cell suspension (1.08 x IO6 cells/ml). The cells were incubated at 15 "C with periodic gentle vortexing, and at various times insulin in the cell pellet was measured as described under "Materiais and Methods." Experiments with four different insulin concentrations were performed on the same cell batch. Final insulin concentrations based on extracellular water space were: 0 , 4 4 7 X 10"' M; A, 1.37 X 10"' M; 0,2.76 X lo-'' M; 0,5.07 X 10"o M. Curues represent the best fit solution for Model D.

the constants obtained from experiments performed only at low insulin concentrations are less accurate than those ob- tained over a wider range of saturation of binding sites, we do not report them in detail here.

DISCUSSION

A kinetic analysis of insulin binding to isolated rat fat cells was performed at 15 'C. At this temperature, we have found previously that insulin binding to the overwhelming majority of binding sites was describable by a simple binding isotherm. Moreover, insulin degradation to trichloroacetic acid-soluble products under the incubation conditions used was negligible (14), consistent with absence of lysosomal processing at this temperature (15, 16). Our study differed in a number of ways from earlier studies of insulin binding kinetics to fat cells (1, 3-11). First, the insulin concentration range included concen- trations capable of giving high fractional occupancies of re- ceptor. Second, the number of data points was made large (Le. 160) to allow the fitting of complex models and to compensate for the large experimental error associated with measurements at high insulin concentrations. Third, models were fitted to the data via their differential equations. This allowed models to be tested that defy analytical integration. Fourth, model selection was assisted by the use of AIC, a powerful means of comparison of quality of fit among non- linear models differing in the number of independently ad- justed parameters (24,25).

Model D emerged as the best of the models tested based on a joint requirement for a small AIC and for compatibility of constants among various kinetic experiments and between kinetic and equilibrium experiments. While Model B de- scribed the kinetics in some cases better than Model D, it was incompatible with the equiiibrium results. None of the models allowing direct equilibration of insulin with an R' state could be fit. In attempts to fit other models to the data, the rate constants frequently changed in a direction leading to resto- ration of Model D. It needs to be emphasized that other models, not yet tested, may be even better. However, we believe that such other models will be extensions of Model D, rather than being completely different. Areas of systematic

deviation between data and expectations based on Model D in certain kinetic experiments indeed suggest that the present model will require modification. It is not yet sure whether such modification will describe important additional steps in the mechanism of binding, or whether it will only correct for certain limitations of the experiment, such as a small amount of cell death, which has not been dealt with in the present model.

A number of authors have proposed models for insulin binding to various cell types which share similarities with the model proposed here (8,18-22,26,27). A detailed comparison of these models is outside the scope of this discussion. Note, however, that our preferred model, Model D, does not ailow association of insulin directly to the receptor in the R' state. Our model also disallows dissociation of intact insulin from that state. Whether altered insulin can dissociate from that state is currently under investigation. This lack of direct interaction of insulin with the R' state would render incorrect designation of the R' state in our model as an extra-high- affinity state or as a slowly dissociating state of the receptor. Thus our model clearly differs from any model that allows such direct interaction.

According to our Model D, insulin first binds reversib1y to a single class of binding sites. It is plausible to assume that these binding sites represent accessible receptors on the cell surface. The corresponding forward,rate constant of k , = (1.6 5 1.4) X lo6 1 mol" s" is similar to the value of 4.2 X lo6 1 mol" s" reported for fat cells at 37 "C and pH 7.4 (3). This comparison is legitimate despite differences in models under- lying the data analyses, because the latter value was estimated from initial velocities, and such velocities are affected mini- mally by the presence or absence of the receptor interconver- sion proposed here.4 The rate constants for fat cells are smaller than those reported for hepatocytes and IM9 lympho- cytes by a factor 10 at both temperatures (22). These higher values were obtained via integrated rate equations for Model A. Assumption of distinct models perhaps explains the differ- ences between our fat cell values and the higher values re- ported for other cells.

We have examined the possible role location of the recep- tors on the surface of spherical cells may play in determining the value of klz. According to Berg (291, the diffusive intrinsic rate constant for productive collision between a ligand and a circular target of radius b located on a plane under angular constraints, @A, is ka - 27rDb ~ i n ' ~ @ ~ / 2 ) [ ( ~ ~ ) ~ + (%)"j, where L) is the tr~slational diffusion coefficient of the ligand. For dimerization of the ligand under the assumption of identical angular constraint, the expression is kd = 4rDb sin'(@~/2), where D has the same meaning as above. This expression has incorporated the statistical factor one-half associated with identity of the interacting ligands and is corrected for the factor 2 error in the von Smoluchowski theory of dimerization identified by Keizer (30). Thus association to the site on the plane is slower than dimerization by the factor &/kd = 0.66. Using steric constraint factors computed by a different theory (31), this factor is even closer to 1. If N = IOs receptors are on spherical fat cells (14) of radius a = 3 X cm, and if the binding site on the receptor has a radius of r = 10 A, an additional correction factor of Nr/(ar + Nr) = 0.51 applies

* For multiple reasons, some of which were discussed in Gammeitoft and Gliemann (3), earlier fat cell data by Cuatrecasas (1, 2) cannot be accepted as valid. Sonne et at. (10) reported values for pH 7.2 and 7.8 at 37 "C and Olefsky and Kobayashi (6) reported values for pH 7.6 at 24 "C. These values were determined by model-dependent integrated rate equations, making comparison with our values prob- lematic.

1708 Kinetics of Insulin Binding to Fat Cells

(28). Now the assumption will be made that the angular constraint on productive collisions between insulin and recep- tor are similar to those for collisions leading to the formation of insulin dimers in solution. With the above correction factors and the experimental dimerization rate constant of ka = 1.14 X 10' 1 mol" s" at 23 "C (32), the diffusive forward rate constant for insulin binding to fat cells is predicted to be 3.8 X lo7 1 mol" s-'. Finally, after correction for the temper- ature dependence of water viscosity, one predicts the diffusive rate constant to be 3.0 x 10' 1 mol" s" at 15 "C. Similar values indeed have been observed for the association of nerve growth factor with glia cells (33). In contrast, the predicted diffusion controlled rate is 200-fold larger than observed here for fat cells, and 20-fold larger than reported for IM9 lympho- cytes (34). Notwithstanding the limitations of the above the- ories, we conclude two things. First, the influence of cell size on diffusive association rates is too small to explain the differences between association rates in fat cells and IM9 lymphocytes discussed above. Second, the forward rate of insulin binding to fat cells is not dominated by diffusion. The opposite conclusion has been reached by Cuatrecasas (1) and Pollet et al. (34). Our conclusion is further supported by the observation that porcine insulin monoiodinated either on TyFL6 or TyrB26 exhibit a higher association rate constant with fat cells than plain insulin or insulin monoiodinated on Ty+" (35). The existence of insulin derivatives with in- creased association rate constants suggests that only a subset of insulin conformers is reactive, and that chemical modifi- cation can change the conformational equilibrium. Lack of diffusion control could result from slow confo~a t iona~ tran- sitions in insulin. Alternatively, lack of diffusion control could originate in conformational equilibria in the binding site or the presence of a repulsive coulomb potential. Should associ- ation rates in hepatocytes and IM9 lymphocytes, when ana- lyzed in a way similar to what was presented here, still be larger than those observed for fat cells, one would be forced to attribute the lack of diffusion control to a major extent to conformational states or differences in coulombic potentials in the binding site. Conformational equilibria of fat cell bind- ing sites may be linked to the presence of an insulin-sensitive glucose transport system, a system which is missing in the other two cell types.

Dissociation of insulin from the initially formed complex with the receptor, RI, was described by kZl = (3.3 ?$ 1.6) X

s-l corresponding to a half-life of & = 3.2 ?$ 1.6 min. This shows that it would be dangerous to attempt separation of bound from free hormone in equilibrium binding studies unless the separation could be performed in a few seconds. Indeed, introduction of a quick washing step introduced cur- vature to Scatchard plots (9), although the same group pre- viously had obtained linear Scatchard plots when equil~brium was left unpe~urbed (3). The above T& cannot be compared with any literature values, because in all previous reports half- lives were directly calculated from the X values of Equation 9. This procedure corresponds to an interpretation of the data according to Model B, a model which we reject. Similarities in values are thus purely coincidental.

According to Model D, once the initial complex of insulin and cell surface receptor, RI, is formed, it can change its state or cellular location reversibly to form an insulin-r~eptor complex, R'I, which is not in direct equilibrium with free insulin. Formation of R'I and reversion to RI are described by k23 = (3.2 3 1.5) x s-', and kS2 (2.0 ?$ 1.5) X s-', corresponding to processes with half-lives of 36 31.5 min and 58 ?$ 1.5 min, respectively. Although these constants are very similar, they differ s i ~ i ~ c a n t l y by Student's two-sided, paired

t test, performed on either the values of Table I1 directly or on their logarithms. Thus, at equilibrium, the R'I state con- stitutes 63% of the occupied receptors. Despite the slight excess of R'I over RI, the roughly equimolar amounts of RI and R'I at equilibrium are compatible with a nearly zero-free energy process. Alternatively, both $3 and k32 are associated with processes requiring metabolic energy, and their similarity simply reflects a cellular balance.

The nature of R'I is currently unknown, but a number of possibilities are discussed critically in the Miniprint Supple- ment, and experiments towards elucidation of this problem are in progress.

AcknowZedgment+"he excellent technical help of James T. Champagne and Rosario F. Bowen and the secretariat assistance of Ann L. Ferguson are gratefully acknowledged. We thank Dr. Thomas L. Paquette from the Radioimmunoassay Core of the Diabetes Re- search Center at the University of Washington for 1261-lsbeled insulin, Dr. Richard A. Roth for making a manuscript available before pub- lication, and Penny E. Phillips for critical reading of the manuscript.

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605-613

S u p p l ~ n t a r y material to

KINETICS OF INSULIN BIND~NG to RAT WHITE FAT CELLS a1 wc

Edward Y. Lipkin, David C. Teller, and Christoph de Xakn

MTERIALS AN0 HETHOOS

Dawley rats (Tyler Laboratories. Bellevue, UA) according to Rodbell (36). All the materials Materipis: Epididymal fat cells were isolated f r m 150-175 g, ad libitum fed, Sprague-

were those specified in Lipkin et ai. (14) .

insulin were those described previously (14). The method of gama counting, determination of General Hethods: The preparations of fat cells. BSA and €A14-~3-~1251~iodotyrosine!1

extracellular volw~e, collection of cell-bound insulin by flotation through dinonylphthalate. and the themstated shaking water bath for microfuge tubes also Mere described previously

as that of pure lZ5I (2.17 Citwml). Also. because insulin mnoiodinated on TySil4 has the (14). For reasons given before (14). the specific radioactivity of monoiodoinsulin was taken

Same kinetic properties as insulin (37.38). labeled insulin of any desired specific radio- activity could be prepared by mixing pure monoiodinated insulin with regular insulin, Fat cells were suspended and Zn-free insulin was dissolved in a mdified Krebs-Ringer- phosphate^ HEPES buffer, pH 7.4, containing the following camponents: 10 mM Na2HW4. 30 np( HEPES,

0.7 wJ1ml (-500 uM) Zn-free bacitracin, 100 aim1 penicillin, 100 ug/ml streptomycin, and 4% 128 np( NaCl, 1.4 M CaCI2, 1.4 mH MgS04, 5.2 mM YC1. In addition. it contained 10 mM glucose,

(wlu) charcoal-treated 8% (14).

Dissociation Rate Experiwnts: 1251-insulin was bound tu DdiDOCytes by adding 1251- labeled insulin at a final cmcentration of 2.0 x 10"oM directly to 20 ml of cell suspension

at 15°C with gentle swirling. After this preincubation period, insulin binding at 0 sin 10.9-1.1 x lo6 cells/mil in a 250 sl polypropylene beaker. The cells were incubated for 4 h

of dissociation was estimated in pentuplieate samples (275 vl 5f cell suspension + 25 "1 of

of labeled insulin Mas initiated by dispensing 275 ul aliquots of the cell suspension into insulin-free incubation medium) by rapid flotation through dinonylphthalate. Dissociation

aicrofuge tubes preloaded vith 29 ul of 1.2 x 10-%4 of vnlabeled Zn-free insulin to prevent

gentle swirling on a vortex mixer. After tiw intervals ranging from 5-180 ai". the incpba- rebinding o f dissociated labeled insulin. The cell suspension was mixed every 10 mi" by

tion was terminated by flotation of the cells thmvgh dino"y1phthal~te.

with an equivalent amoun: (ca. 2 x 10-'%) o f cold insulin. This cell suspension was trans-

An experimental Control Consisted of a portion of the same celi suspension preincubated

ferred at the Start of t k preincubation to Serum tubes prelmded vith 10 u l of insulin suffi- cient to bring the final concentration to 10-6?4 and containing 2 x fl iZ51-insulin. At the end of the experiment. these samples were worked up i n the same fashion as the experi- mental group for pelletable radioactivity,

rate experiments w e ~ e performed under incubation conditions identical to those used in equi- Rrsociation Rate Experiments: All association rate and combined ~ssociat ion-disSociat ion

librium binding studies. This was to assure cmparability of the results. Thus, reactions were performed in 1.5 ml conical polypropylene centrifuge tubes with caps open [ S e c h n Micro- fuge tuber). and placed in a tempe'ature-Controlled shaking incubator at IsLC, described previously (14). Tubes were preloaded with 260 ul of labeled insulin in mXRPH . The con- centrations of insulin Were chosen so as to produce the following concentrations i n the extra- ceilslar space after addition of 40 pl of packed cells. All tubes contained a fixed initial concentration of mnoiodoinsulin (0.5 x 8 ) . The tubes f o m d 6 sets with additional unlabeled insulin to produce initial total concentrations of insulin, i.e. mon*iodoi"sulin plus regular insulin. of: 1.0 x 15-10 M. 3.0 x 10-10 n, 1.0 x 10-9 n.. 3 x H, 1.0 x

N. and 3 x IO-' M. The actual concentrations yew calculated after correcting for the

P., Sparks, H. V., Jr., and Geiger, S. R., eds) Section 2, Vol. 11, pp. 33- 67, American Physiological Society, Bethesda, MD

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R&. Cokrnuri. 74,545-552

(1979) Proc. Nutl. Acad. Sci. U. S. A. 76,635-639

. _ 68. Duckworth, W. C., Stentz, F. B., Heinemann, M., and Kitabchi, A. E.

69. Yokono, K., Roth, R. A., and Baba, S. (1982) Endocrinology 111, 1102-

70. Terris, S., Hoffmann, C., and Steiner, D. F. (19791 Can. J. Biochern. 57,

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1108

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istry 8.16-22

Proceedings of the 2nd Internutionul Research Conference (Fritz, H., Tschesche, H.,Green, L. J.,andTruscheit, E., e&) pp. 389-411, Springer-

74. Jering, H., and Tschesche, H. (1974) Angew. Chern. Int. Ed. Eng. 13,661- Verlag, New York

66x3 75. Ria< M.,P., Peavy, D. E., Frank, B. H., and Duckworth, W. C. (1984)

76. Shii, K., Baba, S., Yokono, K., and Roth, R. A. (1985) J . Biol. Chern. 260, E n d o e r L ~ ~ g y 115,591-599

6503-6506

observed extracellular volume (14). Reactions Were started in D time-staggered fashion by stopping the shaking incubator for no more than 25 I . allowing addition of 40 ul Of packed

After time intervals from 5 to 180 mi", the incubations were terminated by flotation throwh cells to 6 tubes at a time. This yielded cell concentrations Of 2-3 x IO5 ceilS/300 ul.

250 "1 of di~onyl~hth~late (3). The cell pellet was collected and counted as described previously (141. Each association experiaent was accwanied by an equilibrium experiment perfonned on the same cell batch (14).

Cmbined Association-Dissociation Experiments: The association Part Of the experiment was identical to the association experiments described above except that Only 3 insulin COR- centtations. namely 10"' M, 50-9 n and M we?e m e d . At 150 win to each tube 30 ul of

cellular volume VI changed to the new extracellular volume Vp - V i + 30 "1. which corresponded IOs5 H unlabeled insulin i n incubation buffer was added. In the process, the original extra-

to an increase of around 11%. The amount o f labeled insulin in the cell pellet was followed as it function of time as described IboYe. i n order to obtain a description Of the binding Of

just that insulin present during the association phase. called labeled insulin, obsec'ved dpm were converted to molar amunts using for both the a$saciation and the dissociation phase the specific radioactivity at 0 mi". Each experiment was accompanied by an equilibrium experiment performed on the same cell batch.

bated for 2 h at 15°C with labeled insulin at total concentrations of 6.83 x lO+ M and 2.93 x Relaxation Experiwnts: Two 1 a1 batches o f fat cells (7.10 x IO6 cellsfmli were incu-

N respectively. nOte that these total concentrations are based on the extracellular space (723 "1) of the Cell suspensions only. a space that was determined as described pre- viously (141. At time 0 min, the cell suspensions were diluted 10-fold vith incubation

concentrations of receptors and insulin. insulin remaining bound to cells was mnitored buffer. Considering extracellular space. this Corresponded to a 13.5-fold reduction in

as a function af time by taking 300 ul aliquot8 and separating cells by flotation through dino"ylphtha1ate.

EXPPesrion Of Data: All data Were expressed as molar awunts of insulin i o the cel3 pellet above the dinonylphthalate P, vs. time t. Except for cell concentrations, ali concentrations in cell suspensions, including the receptm concentration, are based on the extracellular volume. Y, determined as described previously (14).

Cwutation: Programs for data fitting Were written i n FORTRAN IY for a Digital Corp. VAX 111780 computer. Reliability of the programs was checked by comparison of results with simulations performed vith the program SPICE 2F.1 (39) and by comparing solutions based on fitting differential rate equations with those based on integrated rate ewations. where the

tlons reported required many hours Of central processor ti=. latter were available (for model 0: 40,411. As a note of caution, several of the cmputa-

D and G are Obtained simply by putting sane o f the rate constants to zero. Extension of the Kinetic analysis: The approach used will be illustrated for the case of mdel F. Rodels

approach to the other models i s Straightfomrd, and will not be illustrated.

Oisssciation experiments: Consider the Case wherein dissociation of prebound labeled

unlabeled insulin. Here the simplifying assunption is made that this procedure effectively insulin f r m a receptor preparation is initiated by the addition of a large excess of

Prevents rebinding of dissociated labeled insulin. 8y eq. I one has at all times:

Vt * VI ((l-a!fE'lt + a[T'I) ( 8 )

where primed quantities shall be used to indicate that they pertain only to the labeled insulin used in the incubation prior to initiation of the dissociation. Considering only labeled hormone, one has k12 = 0. nodel A predicts monoexponential dissociation kinetics. Uodels 8. C, 0 . an4 6 predict biexponential dissociation kinetlcs (40.41) of the form

1710 Kinetics of Insulin Binding to Fat Cells ?; = VI i(Ale-'lt i A2e-'Zt)(l-a) + a [ T ' l l (91

wherein the amplitudes, A, and exponents, A, have meanings dependent on t h e model. Hodels E and F p r e d i c t t e t r a e x p o n e n t i a l d i s s o c i a t i o n k i n e t i c s 142). Only i n models A and 8 do t h e ampl i tudes . A i . cor respond d i rec t l y to in i t ia l concent ra t ions o f occup ied receptw spec ies and t h e Ai c o r r e s p o n d d i r e c t l y t o k i n e t i c r a t e c o n s t a n t s . Y h i l e it i s p o s s i b l e t o a l g e b r a i c a l l y convert ampli tudes and exponents i n t o i n i t i a l c o n c e n t r a t i o n s and rate constants for model D (40.41). i t i s complex.

Association Experiments: Model F i s k i n e t i c a l l y d e s c r i b e d b y t h e d i f f e r e n t i a l e q u a t i o n s :

dP iTi - v1 ( ( ] -a ) + TI) (2)

igl , q l + a p ( l o a )

- - kl2[II[R1 + kZ1[RI1 ( l o b )

- kol[R'1 + klo[Rl ( l a c )

= 4kZl + kZ3)[RI1 + kj2[R'11 + kl2[RltI1 (1Od)

- kZ3[RII ~ kJ2[R'I] (IGe)

= -kl2[Il[R1 - kla[Rl + kZ1[RI1 + kol[R'l (]Of)

The equat ions fo r model D are o b t a l m d b y s e t t i n g kO1 = k10 = 0. and kG3 = k30 = 0. Model G,

Mhich makes the assumpt ions that the ra tes a t which the receptor Conver ts between i t s primed and unprimed f o n , i s independent of the presence o f bound i n s u l i n , and t h a t i n s u l i n c a n n o t b i n d d i r e c t l y t o R ' , i s ob ta ined by se t t i ng kl0 - kZ3 and k01 = k32. and k03 = k30 = 0. The i n i t i a l c o n d i t i o n s a t t4 a r e t h a t []I0 = [TI , [Rllo = 0 and [R'll,, = 0. '

Camblned a s S O C i ~ t i o n - d i S I O C 1 1 t i o n experiments: Consider an associat ion exper iment o f the

The 30 u l volume used f o r r e l i a b l e a d d i t i o n o f u n l a b e l e d i n r u l l n i n t r o d u c e d a significant

k ind descr ibed above. However, b e f o v e e q u i l i b r i u m i s a c h i e v e d . u n l a b e l e d i n s u l i n i s added.

volume change from V 1 t o Y2 . The above d i f f e r e n t l a l e q u a t i o n s and associated i n i t i a l con- d i t i ons con t inue t o desc r ibe t he assoc ia t i on phase fo r labe led insu l7n fo r the respec t ive models up t o t h e t i m e t = r -6 t I nmed ia te l y be fo re add i t i on o f un labe led i nsu l i n and associated d i l u t i o n . A t t h e t i m e o f a d d i t i o n . r , 'new i n i t i a l c o n d i t i o n s become e f fec t i ve : i .e . [1 Ix =

[R'I],=(V,/V2)[R'I],.6t. Moreover, i f J designates the newly added unlabeled insul in. then (Y1IV2)11lT.6t * [Rl, (V1/V2)[RIT-6t , [R'I, = (V1/v2)[R'lT.6t I [ ~ l I , = ( V ~ I V ~ ) [ ~ ~ l , ~ ~ t I and

vo lume t rapped by the fa t ce l l pe l le t will n o t depend an t h e t o t a l volume, t h e f l a c t i o n a l [J], = [Jltotal added a t t ime T. [RJIT = 0 and.[R'J], - 0. Sjnce t h e a b s o l u t e e x t r a c e l l u l a r

vo lume t rapped a f te r d i lu t ion will become atLr = (Vl/V21a. Equation 2 cor rec ted fo r the d i l u t i o n becomes

P i V,i(l - > a ) [ a ' ] + ' a [T'] ) > 2 t v 2

(11)

The prime i n eq. 11 i n d i c a t e s t h a t t h i s e q v a t i o n p e r t a i n s o n l y t o t h e l a b e l e d i n s u l i n , I , present dur ing the assoc ia t ion phase, and no t t o t he un labe led i nsu l i n . J, used i n t h e d i l u t l o n .

I n the absence of the s impl i fy ing assumpt ions about reb lnd ing O f l a b e l e d i n s u l i n made i n the pure d issociat ion exper iments descr ibed above, a t t imes tL7 the system i s described by

eq. 11. 10 a-e and the fo l low ing add i t iona l equat ions :

9 - -k12[JI[RJ + kZ1[RJ1

= -(kPl+ kZ3)[RJ1 + k321R'J l + klZ [RIIJI (12)

9 = kZ3[RJ] - kJ2[R'J]

= - klz([Il + [ J l ) l R l - kla[R] + kzl([R1] + [RJI) + kol[R'1

Relaxat ion exper iments: Para l le l ce l l suspensions were d i lu ted 10- fo ld a f te r p re incuba-

was fo l lowed. To determine the k inet lc parameters for these two experiments, i t had t o be t i o n w i t h " h i g h " or " low" concent ra t ions o f insu l in and the approach to the new e q u i l i b r i u m

assumed tha t the "h igh" concent ra t ion sample had reached e q u i l i b r i u m b e f o r e d i l u t i o n . The

pre incubat ion phase O f the " low" concentrat ion sample was t hen s imu la ted t o ob ta in t he va lves

c a l c u l a t i o n was i t e ra ted as t he ra te cons tan ts were found. O f [ R I ] . [ R ' I ] . and [I] b e f o r e d i l u t i o n and thus the i n i t l a l c o n d i t i o n s a f t e r d i l u t i o n . T h l s

Maxmum Likel ihood Parameter Estimation: Various models Were f i t t e d t o t h e d a t a always i n t h e f o m of the observat ion equat ion (e.g. eq. 1. 8. 9). vhlch describes the dependent observed var iable as a func t ion o f the Independent var iab le . [Bit i n eq. I and 8 was g iven as an i m p l i c i t f u n c t i o n o f [ T I b y eq. 3 , 4 or 6, depending on t h e model considered. Ye have p r e v i o u s l y shown tha t t he ma jo r source of measwement e r r o r i s t h e a l i q u a t i n g o f c e l l

Thus maximum l i k e l i h o o d estimates o f parameters were obta ined by per forming an i t e r a t i v e l y suspension, l e a d i n g t o a normal ly d i s t r i b u t e d errop i n P p r o p o r t i o n a l t o the mean (14).

reweighted non- l inear least squares regress ion analys is incorporat ing th is er ror s t ructure (14,431. Having a maximum l i ke l~hmd so lu t i on a l l owed compu ta t i on o f t he Aka ike l n fo rma t ion Cviterion (AIC) (24,25) as adapted fo r we igh ted da ta by L ipk in e t a l . (14) . A1C i s a number wh ich d i f f e rs when t h e same data are fit by various models. It i s des igned to est imate the q u a l i t y o f f i t co r rec ted f o r d i f f e rences i n number of independently adjusted parameters i n cares of nan- l inear models. The model w i t h t h e l a e s t number fo r a g i ven da ta se t i s t o be p r e f e r r e d on s t a t i s t i c a l grounds. Differences i n AIC must be a t l e a s t 2 t o c l a i m a s i g - n i f i c a n t d i f f e r e n c e between two models. Some of the erperiments were also evaluated using u n i t s t a t i s t i c a l w e i g h t s f o r reasons t o be given under Results.

I n o r d e r t o f i t a r p e c l f i c model described by a s y s t m o f d i f f e ren t i a l equa t ions t o k inet ic data. the equat ions were numer ica l ly in tegrated us ing the four th-order Runge-Kut ta method (44). Parametem t o be f i t t e d were per turbed (1%) one at a t ime, and t h e p a r t i a l dev i va t i ve o f t he f i t t ed f unc t i on w i th respec t t o t ha t pa ramete r was approximated using the f i n i t e d i f f e rences ob ta ined . The v a l u e s o f t h e p a r t i a l d e r i v a t i v e e s t i m a t e s i n t u r n were used to ad jus t the parametep es t imates i te ra t i ve ly by the method o f Newton-Gauss, w i t h or w i t h o u t the convergence improvement of Levenberg-Marquart (45). The Runge-Kutta method and t h e p ~ o -

based on known k ine t i c cons tan ts . Th i s he lped i n t he des ign o f expe r imen ts t ha t op t ima l l y gram SPICE2 F . l (39) a l s o were used to s imu la te t ime dependences of experimental outcomes

d i s t i n g u i s h between var ious models.

OISCUSSION

An obvious quest ion 1s t h a t o f t h e n a t u w o f t h e R ' I s t a t e . One p o s s i b l l i t y n e e d i n g Cons idera t ion invo lver reversible in te rna l l ra t i on o f occup ied recep to r . A t 15 - t furlon o f

endocy to t i c ves i c les w i th lysosomes appears t o be i n h i b i t e d i n a v a r i e t y o f c e l l t y p e s ( 4 6 ) ,

i n c l u d i n g f a t c e l l s (15, 16). Thus retroendocytosed l n s u l l n would remaln t r i c h l o r o a c e t i c ac id p rec ip i t ab le (14 ) , and blnding would be t o t a l l y reversible, I S requi red by model 0 and ac tua l l y observed here . I n t e r n a l l z a t l o n i n g e n e r a l can proceed a t 15Y, a l t h o u g h a t a

endocytosis has been observed ( 4 6 ) . The slowness of internalization i s supported by the r a t e d r a s t i c a l l y r e d u c e d f r o m t h a t seen a t 3 7 T (15,16,47-50) . S i rmlar ly , cont inued re t ro-

O b s e r v a t i o n s t h a t a t 1 5 T . i n s u l i n a s s o c i a t e d w i t h f a t c e l l s f o r 30 m n appears t o r e m a i n w i t h t h e plasma membrane f r a c t i o n o f f a t c e l l s a f t e r s u b c e l l u l a r fractionation (51) . p h o t o a f f l n l t y -

t i v i t y t o t r y p s i n (52). and i n s u l i n i n the presence Of tns-(hydroxymethy1)-aminomethdne

l a b e l e d i n s u l l n r e c e p t o r on f a t ce l l s over d p e r i o d o f 60 min does not appear t o l o s e sensl -

buffer doer not cause veceptor downregulation (12). Cruc la l fa r p resent purposes I S t h a t If R'I were t o be in ternal ized Insu l?n-receptor complex. our k lnet lc constants would have pre-

measurab le In te rna l i za t ion a rgues aga lns t R ' I be ing an internalized s ta te . A lso . p re l im inary d ic ted notable receptor-mediated In ternal izat ion under the condl t lons quoted. Absence o f

w h i l e endo- and re t roendacy tanr requ i re metabo l ic energy (15. 161. F i n a l l y , i n s u l i n d i r - resu l t s w i th ATP-dep le ted ce l l s sugges t t ha t ATP i s n o t i n v o l v e d I " t h e f o n a t l o n of R ' l ,

Soc lat lon f rom iso la ted ad lpocyte plasma membranes (81 as w e l l as l i v e r p l a ~ r n a membranes (21) 1s m u l t i - e x p a n e n t l a l . We therefore cons ider i t u n l i k e l y t h a t R'I represents a t r u l y I n t e r n a l i z e d s t a t e .

d i r t l n c t from the access ib le pa r t o f t h e membrane, b u t does not r e q u i r e I n t e P n a l l z a t i o n

Another p a t e n t i a l i n t e r p r e t a t I a n O f R'I does r e q u l r e sequestrat ion of R'I a t a Site

proper. Smith and J a r e t t ( 5 4 ) have shown t h a t a t 37'C, i n s u l i n r e c e p t o r s on f a t c e l l plasma rnembldne f l a t s . i . e . plasma membrane areas d e v o i d o f d l r t i n c t ? v e anatomical defomdt?ons, s a t u r a t e r a p i d l y . A t 1 much slowe? rate. accupred receptors appear i n d i s t i n c t i v e plasma mem-

used to designate such Structures ~n moscle. Caveolae are recognizable by VaIiOuP morphologic brane invaginat ions, for which we prefer the t e n caveolae, a func t i ona l l y neu t ra l t e rn w ide l y

and r t a i m n g C r i t e r i a . Whether they a r e S t a t i c i n n a t u r e ( 5 5 ) or t a k e p a r t i n i n t e r n a l i z a t i o n

processes (54) i s s t i l l debated. Thelr number I S about 8 - fo ld (56) h igher than tha t o f

d pseudo-f l r r t order react ion. Whi le est lmates of the Contributions O f Caveolae t o t h e t o t a l i n s u l i n b l n d l n g sites (14) . Thus t h e i r Occupat ion by insul in-receptor complex could appear as

plasma membrane bi layer range f rom 17: (54) to 339: (55) , coa ted p l t s cons t i t u te on l y abou t

0.3% (54). It i s bel ieved that occupat ion o f caveolae by the insu l in- receptor complex i s a

b i layer . Th is Mou ld be cons is ten t w i th the similarity O f k23 and k32 discussed above. If t h e passive process. i .e. governed only by lateral d i f fusion of receptor i n the Phospho l ip id

caveolae b y i n s u l i n r e c e p t o r complex. it i s p o s s i b l e t o c a l c u l a t e a d i f f u s i o n c o e f f i c i e n t f o r r a t e c o n s t a n t k Z 3 i s i n t e r p r e t e d as descr ib ing a pseudo-f irst order process of occupation Of

The ca lcu la ted d i f fus ion coe f f i c ien t i s 1000- fo ld h igher than exper imenta l l y observed (57). the receptor. (eq. 84 of 28). given the surface density (56) and dimensions ( 5 5 ) of caveolae.

part of the t ime. ov t h a t d i f f u s i o n i n t h e c a v e o l a r membrane i s e x t r a slow. perhaps due suggest ing that R ' I i s n o t i n s u l i n - r e c e p t o r c m p l e x i n c a v e o l a e , or that caveolae are open

exp la in t he slow occupation of caveolae a t 37°C seen by Smith and J a r e t t ( 5 4 ) . Y h i l e i n o t h e r

t o m a t e r i a l i n t h e c a v e o l a r lumen. One o f t h e l a t t e r two explanat ions has t o be invoked t o

cel l types caveolae are sometimes seen t o be covered by a diaphragm or as havlng a clogged neck (58.59). i n f a t c e l l s no such occlus ions have been v isua l i zed thus fa r f 5 5 ) . I n t e r - p r e t a t i o n o f R ' I as the occupied receptor i n caveolae also Suffevs frm t h e d i f f i c u l t y Of

exp la in ing uhy the empty receptor does no t appear to par take i n the Process. as shown by the poorer fit of model G i n comparison t o model 0.

f a l l i n t o 2 categor ies . mob i le s ing le receptors and inmob i le c lus te rs o f receptors . The e lect ron microscopic observat ions o f Smi th and Jare t t (54) a lso Suggest t h a t

It tha t on l y t he mob i l e recep to rs move subsequently into caveolae. To l e c a n c i l e t h i s ObservEi t ion wi th k inet ic Model 0. t h e f o l l o w i n g v a r i a n t model might be considered.

where the subscr ip ts m and iin designate moblle and i m b i l e r e s p e c t l v e l y , and the prime i n d i c a t e s t h a t t h e r a t e c o n s t a n t k j 3 w u l d b e s u b s t a n t i a l l y d i f f e r e n t frm k23 O f model 0. n o b i l e and i n m o b i l e r e c e p t o r s i n membrane f l a t s are assumed t o be k i n e t i c a l l y e q u i v a l e n t . However. the ra te cons tan t . ti3, describing the format ion Of GI i s now pr imed to i nd i ca te t h a t i t i s r e f e r r i n g o n l y t o t h e m o b i l e r e c e p t o r s . The va lue o f k i3 i s abv ious l y i nc reased r e l a t i v e t o k Z 3 b y t h e f a c t o r ( [ % I + [Rim?)/ [%I. but otherwise the Var iant model i s

k i n e t i c a l l y i n d i s t i n g u i s h a b l e f r o m Model 0.

I" f a t c e l l s a t e q u i l i b r i u m a t 37'c, 17% of i nsu l i n Pecep to r complex was observed I n

caveolae ( 5 4 ) . whereas OUT k ine t i c ana lys i s Sugges ts t ha t a t 15*C a much l a r g e r f r a c t i o n o f t h e complex i s i n t h e R ' I state. i .e. about 62%. It i s conce ivab le tha t the lower temperature converted some o f t he recep to rs imnob i l i zed i n c lus te rs l oca ted on membrane f l a t s ( 5 4 ) i n t o mobi le receptors capable o f d i f fus ing in to caveolae. Increased temperature has been repor ted t o f a v o r c l u s t e r i n g (57) or t o leave it unchanged (601, although it i s n o t c l e a r t h a t t h e t w o

Kinetics of Insulin Binding to Fat Cells 1711

observat ions pertain to the raw phenomenon. Nonetheless. i t appears tha t our k l n e t i c data could be conr is tent wi th the observat ions O f Smith and Jare t t (54) . bu t u l t imate iden t i f i ca- t i o n of R ' I as i n s u l i n r e c e p t o r s i n caveolae Hill requ i re k ine t ic b ind ing and electron micro- scoptc Ioca11zat ion studies at the same temperature.

plasma membrane specia l izat ions are present I" a number of c e l l types with insu l in-sensi t ive Currently. the func t ion o f caveolae I S an enigma, bu t i t i s i n t r i gu ing to note that these

glucose transport [e.g. ver tebrate ske leta l muscle ( 6 1 , 6 2 ) and heart muscle (581, smooth muscle ( 6 3 ) . cap i l la ry endothe l ia l ce l l s (64) . e tc . ] . wh i le to our kna ledge the l i te ra tu re does not report their existence in hepatocytes. Moreover, i n s k e l e t a l muscle. caveolae are

glycogen granules are found i n s t r i k i n g a s s o c a t i o n w t h m i t o c h o n d r i a (62.63). again suggesting concentrated i n t h e i n t e r f i b r i l l a r r e g i o n Of the I -band to both r ider of the 2- l ine. where

a ro le in metabo l ic regu la t ion .

Another p o s s l b i l ~ t y f o r t h e n d t w e o f R ' I needing consideration lnvolves the clusters O f

i nsu l in receptors mentioned above. I n f i b rob las ts . c l us te rs O f i nsu l in receptors form under

A t 37'C i n f a t c e l l s , 65% O f receptors are Observed i n c l u s t e r s . Ye f i n d a t 15'C a s im i la r t he i n f l uence o f i nsu l i n (57). whereas i n adipocyter clusters seem t o be preexisting (54).

percentage. i.e. 62%. of occupied receptors i n the R'1 state. R'I therefore could represent c lusters . However, it i s n o t obvious how such c lus te r ing cou ld g ive r i se to the k lne t ics observed here. Oimerization O f i n l u l i n w h i l e bound t o the receptor has been proposed (27).

interchange. Disulf ide interchange reactions can be revers ib le and therefore th is mechanism Clark and Harrison (65) dercnbed covalent b lndlng of i n s u l l n t o f a t c e l l s v i a d i s u l f i d e

I S not cont ra ind icated by our f ind ing O f esrent7al ly complete reverstbr l i ty . Nonetheless, we

do no t be l l eve t ha t t h i s mechanism i s a l i ke ly exp lananon Of the fomat lon o f R ' I .

c e l l surface. Although i n our experiments degradation O f i nsu l i n t o t r i ch lo race t i c acid- F ina l l y , we consider the p o s s i b i l i t y t h a t R'I ir re la ted to insu l in degradat ion on the

soluble products was no more than 1% O f t he t o ta l added i n w l l n (14) . l im i ted p ro teo l ys i s o f ce l l -bound insu l in has no t been excluded. Preliminary experiments using high-pressure liquid chromatographic characterization of insul in dissociated frm c e l l s at 15'C conf i rm that suspicion. Oegradation Of i n s u l i n w h i l e bound t o plasma m b r a n e r from adlpocyte (66) and l i v e r (67) has been reported. The r e c e p t o r i t s e l f does not appear to suf f ice for degradat ion (9). HoweveF, an i n s u l i n degrading protease ( E . C . 3.4.22.11: insul inase), which appears t o cleave Insulin i n i t i a l l y between TyrB16 and Leu817 (68). has been found t o e x i s t n o t o n l y i n a soluble. apparent ly cytosol ic form, bu t a lso on c e l l surfaces of multiple tissues (69). It i s

thus possible that the receptor can present i n s u l i n t o the degrading protease, leadlng t o receptor-mediated degradation distinct frm tha t l l nked t o lysosomes a t temperatures above

2 0 Y and characterized previously (7.70.71). Several featwe5 O f i n s u l i n protease acting an

mind. On dissoc iat ion of the t ryps in- t ryps in inhibitor complex. pa r t Of t he t r yps in i nh ib i t o r

i n s u l i n b r i n g t h e s i t u a t i o n i n t h e system O f t r y p r i n and pro te inac ious t ryps in inh ib i to rs to

h y d r o l y n r of the peptide bond i n t r y p s i n i n h i b i t o r o n l y s l i g h t l y favors the hydrolyzed form i s re leased in tact and pa r t possesses a hydrolysed peptide band (72-741. The equi l ibr ium for

the proteo ly t ic products are kept i n c l o s e p r o x i m t y t o each other by the three-dimensional

(86:14) (72). A similar si tuation can be expected f o r any other protease substrate i n which

pos i t ions ( 6 8 ) m y wel l constitute such a case. Thus, i f R ' I were a ternary Cmplex O f

st ructure O f the substrate. I m t i a l cleavage o f i n s u l i n by insu l jn protease in the observed

insul in, receptor and protease, one would pred ic t tha t insu l in d issoc ia t ing frm c e l l s would

have undergone l im i ted p ro teo lys is .

A s t r i k i ng f ea tu re o f t he i nsu l i n p ro tease i s i t s low apparent tUrnOveF number. i n

pa r t i cu la r when act ing On i nsu l i n . From the V,,, data of Ryan et a l . (75). and the molecular weight reported by Shii e t a l . (76). one estimates 6 x sec-'. One wonders whether the s i m i l a r i t y o f k 3 2 - 2 x IO-' s-', the rate constant for conversion of R ' I t o R I wi th the apparent turnover number of the enzyme I S a coincidence. The low turnover number can be expected to cause accumulation of the Michaelis complex that could be mistaken for an l n s u l i n receptor cmplex.

Could R ' I be the Michaelis canplex7 I n order to explore whether t h l s i d e a i s realistic. two-dimensional surface concentrations need t o be converted l n t o equivalent three-dimensional Concentrations. If the three-dimensional Concentration. c ( i o H). equivalent t o the ce l l

surface concentration of receptor. d O n cm-2). i s modeled as .one i n which receptors are separated by the same mean distance, one has c = 750n1I2 d3121U~. where NA i s Avogadro's number. From the receptor number of IO5 per cel l (14). and the mean surface area of the c e l l of 1.67 x cm2 ( 5 6 ) . one f inds d = 6 x 10' cm-' and the e f fect lve to ta l receptor

Michael is cmplex, given a '(n of 24 nM (75). a concentration of f ree pvoteasc of 4 I: M

Concentration c 3 3 x lO-'M. I n order to convert 62s Of receptor-bound insu l i n i n t o a

would be required. The t o t a l protease concentration would not have t o exceed 6 x I4 t o provide for such a free Concentration. Note that th i r represents on ly a smal l excess o f pfo- tease over receptor. The concentration requirements are not Unrealistlc, and the hypothesis thus remains v iable. Object ions to the interpretat ion of R ' I j us t g iven can be raised. Insu l in shou ld in add i t ion to b ind ing to receptor , a lso d i rec t l y b ind to mmbrme-bound pro-

p o s s i b i l i t y i n t o account. The Complete model uould be more cmpler than any of the ones tease. Neither the equi l ibr ium analysis (141 nor the present kinetic analysis has taken t h i s

investigated thus far. and i t s t e s t i n g will requi re addi t ional data. York i n t h l s d i r e c t i o n i s i n p r o g r e r r .