- Email: [email protected]
Perifused fat cells—Kinetic analysis of epinephrine-stimulated lipolysis
103
Short communications Table 3. Effects of intraperitoneal administration of the liver mixed-function
of r-terpineol and isobornyl acetate oxidase system in male rats*
on the induction
* Each group of four male rats was Injected with various concentrations of r-terpincol or isobornyl acetate for 3 days. A and B 40 and 80 mg r-terpincol,‘lOO g of body weight respectively; C and D. 50 and 100 mg isobornyl acetate’100 g of body weight. Values rcprcscnt mean + S. E. i- nmoles per mg of microsomal protein. : P < 0.01. $P < 0.001. ‘1nmoles formaldehyde formed per mg of microsomal protein per min. 7 nmoles cvtochrome c reduced .ner me of microsomal protein per min. P < 0.0:5. L
**
pyrinc. p-nitroanisol and aniline in vitro. Although. x-terpineol does not induct the mixed-function oxidase system. it interacts with the latter. as evidenced bv the intense type I spectral change and the competitive inhibition of aminopyrine N-dcmethylation. Based on these results and others. once again. one cannot over-emphasize the importance of the controlled chemical-free environment in which experimental animals are housed. Without such controls, data obtained from studies concernmg kinetics of drug metabolism. induction of the enzyme sqstcm hq various xenohiotics, the mechanism of Induction. and the purification and rcconstitution of the drug-metabolizing enzyme system would be meaningless.
10. Il. 12. 13. 14. 15. 16.
and J. F. Fouts, Proc. Sot. rsp. Bid. Med. 114. 388 (1963). L. G. Hart. R. W. Schultice and J. R. Fouts, To?tic. u/$. Phumcic. 5. 371 (1963). H. C. Ferguson, J. pharn~. Sci. 55. 1142 (1966). E. S. Vesell. Scie~cr. N. Y. 157. 1057 (1967). A. E. Wade. J. E. Hall. C. C. Hillard. E. Molton and F. E. Grccnc. Phurmucolog!: I. 3I7 (I 96X).
I. L. G. Hart
17.
2.
18.
3. 4. 5.
Perifused fat cells-Kinetic
19. 20.
A. Jori, A. Bianchetti and P. E. Prestini. Biochw. Phur,nuc. 18. 2081 (1969). D. L. Cinti and J. B. Schenkman. M&c. Phurmac. 8. 327 (1972). D. L. Cinti. P. Moldeus and J. B. Schenkman. Biochml. Pharrm~. 21. 3249 (1972). H. Rcmmer. J. B. Schenkman. R. W. Estabrook. H. &same. J. Gillette. S. Narasimhula, D. Y. Cooper and 0. Rosenthal, M&c. Pkurrnuc. 2. 187 (1966). J. B. Schenkman. H. Remmer and R. W. Estabrook. Mole<. Phurrnuc. 3. I I3 (1967). T. Omura and R. Sato, J. hid. Chew. 239. 2370 (1964). A. H. Phillips and R. G. Langdon, J. hiol. Chr~tn, 237. 2652 (1962). J. B. Schenkman and D. L. Cinti, Biochm Pharn~ac. 19. 2396 (1970). 0. H. Lowry. N. J. Rosebrough. A. L. Farr and R. J. Randall. J. hiol. Chrm. 193. 265 (1951). H. Lineweaver and D. Burk. J. A~II. chon. Sec. 56. 658 (1934). J. R. Bend. G. E. R. Hook. R. E. Estcrling. T. E. Gram and J. R. Fouts. J. Phmrnuc. ezp. Tlwr. 183. 206 (1972). J. R. Gillette and T. E. Gram, Microsonles ad Dwy 0ridutior1.s. p. 133. Academic Press. New York (1969). J. L. Holtzman. T. E. Gram. P. L. Gigon and J. R. Gillette. Biochm. J. 110. 407 (196X). I. C. Gunsalus. Hoppe-S~,~lcr’.s 2. ph~sio[. Churn. 349. 1610 (196X). M. Katagiri. B. N. Ganguli and I. C. Gunsalus. J. hid. Chcn~. 243. 3543 (1968).
analysis of epinephrine-stimulated
Many reports have appeared demonstrating that epinephrine incrcascs the rate of hydrolysis of triglyceride in adipose tissue. presumably by activation of triglyceride lipasc [I. 21. Recently, a perifused fat cell system has been described which allows for continuous monitoring of the changes in lipolytic activity in isolated fat cells and provides a technique by which the kinetics of these changes can he observed 131. Based on results from this system, a kinetic model has been constructed which describes the
lipolysis
incl-case in lipolytic rates after the addition of epinephrine (IO--” M final concentration) and the decrease in lipolytic rates after cessation of the hormone. It was assumed that sufficient triglyceride exists within the cell to completely saturate the lipase enzymes. Based on this assumption. the rate of glycerol production was taken to be proportional to the amount of activated lipase present in the fat cells. One unit of lipase enzyme was defined as that amount which produced I nmole glycerol,!
Short communications
104
325300T275-;250225200-
tn [Al,=tn[Al
,‘kd
i 75\I I I I I I I 6 8 IO 12 14 I6 Time, min
I 50 0
5
IO
15
20 25 30 Time, min
35
40
45
I 0
50
Fig. I. Amount of “active lipasc” in fat cells after the initiation and cessation of cpinephritlc-stimulated tipolysis in the perihtscd fat cclt. Two ml of packed fat cells RX pa-ifused as described previously. Cells WWI‘ pcrifuscd f
(7 /Imoles!mg
of protein’min)
has
been
suhtractcd
I 2
I 4
Fig. 7. Plot of the natural log of the amount of “active lipwe” in fat c&s at various timcs tiftcr cessation of cpi~iephrine infUsion. At time KTO. the infusion of cpinephrinc was stopped. The natural log of the amount of “active lipax” was plotted \\ time. Substituting
equation Z and 1:
from
min under the conditions of these experiments. FOI- calculations of kinetic data. amounts of active lipase wcrc cxprcssed as units,‘mg of protein.
In the perifuscd fat cells preparation. cpincphrinc caused a rapid increase in the glycerol release from the fat cells (Fig. 1). The rate of lipolysis was clcwted in the lirst 2 min and ~ontintleli to incrcasc for about 20 min. after which a plateau was I-cached. The maximum lipoiytic rate was 38 nmoles glyccrol,imin,‘mg of protein. When the ina
fused epinephrinc was stopped. lipolysis rapidly rcturncd to basal rate. For all calculations of kin&x data. it was assumed that no active lipasc wisted in the ahscncc of hormone stimulation. For this rcason. the h~rs;11 lipolytic rate (7 nmoles~min~mg of prntcin) x~iis suhtractcd from uil SuhseqLmt It has
values.
been shown that. after the rcmo\-al of the hormone
where I = time nftcr addition of cpinephrinc and [A] is the concentration of lipax A xt that point in time. As cxn hc seen from this squation. the c(~n~~lit~~tioll of lipasc 11 could be Increased by cithcr increasing L, or decrclrsmg 1,:. Epinephrine. via increased cyclic AMP and activation of protein kinasc. incwascs X,. Whether or not cpinephrine also has an effect on k? is considered below. Equation h prcdlcts that the [A] would approach ;t rnarimum wluc in an asymptotic manna. Fxpcrimcntallq. it 1, found that marimum c~~neentr~~ti(~n of lipasc A ([A],,,,) aas obtained in 10 311min after cpitlephrinc addition. After this time (ri[A];rit)S,,, = 0 = h, + k2(.A],,,,. thus
stimulant. lipolytic rates return rapidly to IXKII values 131. It is logical to assume that this is accomplished b> XI inactivation of the active lipasc and a reduction in its ~IWIC
'I,,'
[Al,,,.,,= - i ,
‘L
concentration. If the inuctivc fol-m of the lipase is I-cpracntcd hi iipasc B and the active form by lipasc A. then the rcactmn for the activation and ~li~icti\l~~ti~~nczn hc dsscrihed 21s:
Llpasc
/\/ H t_’
Lipase A
(71
I
II)
where k,
is the reaction velocity for the activation and k, is the rate constant for the inactivation rcaction. It was assumed that. under ;tlI conditions. cxccss amounts of Iipnsc B uerc p”scnt. thus the activation rattion would follow zero-order kinetics. It was also assumed that under basal conditions that the amount of lipasc A was ,wo and after stimulation incrcascd to an amount insufficient to saturate the inactivation process. Thus. the inactivation reaction would follow tirst-order kinetic\. The activation reaction (I’,) m:1>hc dcscribcd as:
r; = rf[A]Aff and the mactivatton
= h,
(71
reaction I I :I as:
i; = -t/[A],‘dr
= kJA]
0,
,
02468 (3)
Because both the activation and inactivation reaction occur simultaneously. the observed velocity (I;,,,) would hc the \unl of the two and can he rc’prcscntcd:
,
,‘,
,
,
)
1
IO 12 14 I6 Time, min
,
I8
Fig. 3. Changes in apparent k, after the infusion of epinephrinc. Using the experimental data fix [A] from Fig. I. and a value of k2 of -&14/min. apparent li, values wcrc cnlculatcd for various times after the start of cninenh-
Short
105
communications
Equation 7 shows that the maximum concentration of lipase A is defined by the ratio of the activation reaction velocity and the inactivation rate constant. If it is assumed that in the absence of epinephrine stimulation k, equals zero. and if C/2 is a first-order reaction. then the fall in [A] after epinephrine removal should follow the equation for a first-order reaction: In[AII = In[A](, + kzr and a plot of In[A], vs time should result in a straight line with a slope equal to kZ. Such a plot is shown in Fig. 2. A linear relationship does exist between times 4 and I6 min. The deviation from linearity during the first 4 min probably represents incomplete washout of epinephrine. Previous work has demonstrated a 2- to 4-mm washout period for epinephrine [3]. These data are compatible with the assumptions that k, is zero in the absence of stimulation and CL is a first-order reaction. Calculation of kz using the data between 4 and 16 min gives a value of -O.l4/min. Rearranging equation 6 to: k, = [A]kZ/(&’ - I) and using a kz of -014/min. the apparent k, can be calculated from all experimental values of [A] in Fig. 1. This is plotted in Fig. 3. The apparent k, increases during the first 6 min after which it remains constant. These results can be explained in either of two ways: (I) time was required for epinephrine to elevate k, to its maximum value. that is. the step leading to activation of lipase A required time to produce maximum activation, or (2) epinephrine decreased kz as well as instantaneously increasing k,. This means that cpinephrine produced a decrease in the rate of inactivation of active lipase as well as an increase in the rate of activation. Kinetic models can be constructed for these two possibilities. If it is assumed that epinephrine had no effect on kz and. therefore. k2 in the presence of epinephrine was the same as that in its absence, then using equation 7 and the [A],,, from Fig. I (38 units/mg of protein). a value of 5.32 units/mg/min can be calculated for k,. This value would be valid at any time after 6 min. Using equation 6. kz = -0,14/min. and this value for k,. the theoretical curve shown in Fig. 4. was constructed. In the kinetic model in which there is a change in both k, and k2. it was assumed that at time zero [A] = 0. then VZ would also equal zero. Substituting in equation 5. it can be shown that for initial conditions. V,, = k,. Using the experimental value for [A] at 2 min (5.5 units/ mg of protein). an initial value of k, of 2.25 units/mg of protein/min was calculated. If this initial k, was constant during the presence of epinephrine, it can be calculated from equation 7 that kz must have been changed by epinephrine to -O.Oh/min. Using these values and cquation 6. another thcoreticdl curve was constructed (Fig. 4). Theoretical curves constructed for the two different models differ substantially. When the experimental values for [A] were plotted vs time (Fig. 4). there was a good correlation between these values and the theoretical values for the model which assumes that cpinephrine has no effect on kZ. This mathematical model does not take into account that time was required for the elevation of k, to a maximum value. This explains the less exact correlation between experimental and theoretical values at the 2-min time. No correlation exists between the experimental values and the theoretical values for the model which assumes a change in kL. Thus. the experimental data from the perifused fat cell system are consistent with a model system in which epincphrine produces a time-dependent increase in the rate * Recipient of Career Development Award (I-K04-AM50316) from the United States Public Health Service,
0 0
I 5
I I I IO 15 20 Time, min
I 25
I 30
Fig. 4. Theoretical curves for amount of “active lipasc” at various times after cpinephrine infusion. The solid lint represents conditions of X, = 5.32 and kz = -0.14. The broken line represents conditions of fi, = 2.25 and kz = -0.06. The open circles are the experimental values from Fig. I. of activation of a lipasc without any clrcct on Ihc rate of inactivation. Based on current concepts of hormonestimulated lipolysis [4 61. the effect on activation would be through the cyclic AMP-dependent protein kinase secondary to stimulation of adenylate cyclase and an elevation in cyclic AMP levels. The 6 min required to reach maximum value for k, (Fig. 3) is similar to the time nccessary to achieve peak cyclic AMP levels after the addition of epinephrine [7]. The remaining time lag to peak glycerol output conceivably represents the time necessary for the activated protein kinase to convert the lipase B to lipase A. --This work was supported bq Llnited Health Service Grants AM 15788 and AM
Acknowlrdgrrn~r1r.s
States Public 14070.
Dcpurtwnt 01 Phamucology. Indianu L’lliL’ersity. School of Mvdicinc,. I,ldirrrltrpo/i.s. III~. 46202, U.S.A.
DONALII0. Au N* ANDKLW S. KATWS. JR. ELWOOI~ F. LARWS JAWS ASHhlORt
1. M. Vaughan and D. Steinbert. in Hmdhook of Ph)xioloyy (Eds. A. E. Reynold and G. F. Cahill. Jr.). Sect’ion 5. pp. 239-51. American Physiological Society. Washington. D.C. (1965). 2. B. B. Brodie. J. I. Davies, S. Hynie. G. Krishna and B. Weiss, Phtrrnluc. Rw. 18. 273 (1966). 3. D. 0. Allen. E. E. Largis. E. A. Miller and J. Ashmorc. J. uppl. Physiol. 34. 125 (1973). 4. J. K. Huttunen. D. Steinberg and S. E. Mayer. Pm. 11orn. Acud. Sci. U.S.A. 67, 290 (1970). 5. J. D. Corbin, E. M. Reimann. D. A. Walsh and E. G. Krcbs. J. hiol. C/XVII. 245. 4849 (1970). 6. R. W. Butcher. G. A. Robison. J. G. Hardman and E. W. Sutherland, Adr. E~ym Rq~lur. 6. 357 (1968). 7. R. W. Butcher. C. E. Baird and E. W. Sutherland. J. hiol. Chm. 243. 1705 (1968).
Short communications Table 3. Effects of intraperitoneal administration of the liver mixed-function
of r-terpineol and isobornyl acetate oxidase system in male rats*
on the induction
* Each group of four male rats was Injected with various concentrations of r-terpincol or isobornyl acetate for 3 days. A and B 40 and 80 mg r-terpincol,‘lOO g of body weight respectively; C and D. 50 and 100 mg isobornyl acetate’100 g of body weight. Values rcprcscnt mean + S. E. i- nmoles per mg of microsomal protein. : P < 0.01. $P < 0.001. ‘1nmoles formaldehyde formed per mg of microsomal protein per min. 7 nmoles cvtochrome c reduced .ner me of microsomal protein per min. P < 0.0:5. L
**
pyrinc. p-nitroanisol and aniline in vitro. Although. x-terpineol does not induct the mixed-function oxidase system. it interacts with the latter. as evidenced bv the intense type I spectral change and the competitive inhibition of aminopyrine N-dcmethylation. Based on these results and others. once again. one cannot over-emphasize the importance of the controlled chemical-free environment in which experimental animals are housed. Without such controls, data obtained from studies concernmg kinetics of drug metabolism. induction of the enzyme sqstcm hq various xenohiotics, the mechanism of Induction. and the purification and rcconstitution of the drug-metabolizing enzyme system would be meaningless.
10. Il. 12. 13. 14. 15. 16.
and J. F. Fouts, Proc. Sot. rsp. Bid. Med. 114. 388 (1963). L. G. Hart. R. W. Schultice and J. R. Fouts, To?tic. u/$. Phumcic. 5. 371 (1963). H. C. Ferguson, J. pharn~. Sci. 55. 1142 (1966). E. S. Vesell. Scie~cr. N. Y. 157. 1057 (1967). A. E. Wade. J. E. Hall. C. C. Hillard. E. Molton and F. E. Grccnc. Phurmucolog!: I. 3I7 (I 96X).
I. L. G. Hart
17.
2.
18.
3. 4. 5.
Perifused fat cells-Kinetic
19. 20.
A. Jori, A. Bianchetti and P. E. Prestini. Biochw. Phur,nuc. 18. 2081 (1969). D. L. Cinti and J. B. Schenkman. M&c. Phurmac. 8. 327 (1972). D. L. Cinti. P. Moldeus and J. B. Schenkman. Biochml. Pharrm~. 21. 3249 (1972). H. Rcmmer. J. B. Schenkman. R. W. Estabrook. H. &same. J. Gillette. S. Narasimhula, D. Y. Cooper and 0. Rosenthal, M&c. Pkurrnuc. 2. 187 (1966). J. B. Schenkman. H. Remmer and R. W. Estabrook. Mole<. Phurrnuc. 3. I I3 (1967). T. Omura and R. Sato, J. hid. Chew. 239. 2370 (1964). A. H. Phillips and R. G. Langdon, J. hiol. Chr~tn, 237. 2652 (1962). J. B. Schenkman and D. L. Cinti, Biochm Pharn~ac. 19. 2396 (1970). 0. H. Lowry. N. J. Rosebrough. A. L. Farr and R. J. Randall. J. hiol. Chrm. 193. 265 (1951). H. Lineweaver and D. Burk. J. A~II. chon. Sec. 56. 658 (1934). J. R. Bend. G. E. R. Hook. R. E. Estcrling. T. E. Gram and J. R. Fouts. J. Phmrnuc. ezp. Tlwr. 183. 206 (1972). J. R. Gillette and T. E. Gram, Microsonles ad Dwy 0ridutior1.s. p. 133. Academic Press. New York (1969). J. L. Holtzman. T. E. Gram. P. L. Gigon and J. R. Gillette. Biochm. J. 110. 407 (196X). I. C. Gunsalus. Hoppe-S~,~lcr’.s 2. ph~sio[. Churn. 349. 1610 (196X). M. Katagiri. B. N. Ganguli and I. C. Gunsalus. J. hid. Chcn~. 243. 3543 (1968).
analysis of epinephrine-stimulated
Many reports have appeared demonstrating that epinephrine incrcascs the rate of hydrolysis of triglyceride in adipose tissue. presumably by activation of triglyceride lipasc [I. 21. Recently, a perifused fat cell system has been described which allows for continuous monitoring of the changes in lipolytic activity in isolated fat cells and provides a technique by which the kinetics of these changes can he observed 131. Based on results from this system, a kinetic model has been constructed which describes the
lipolysis
incl-case in lipolytic rates after the addition of epinephrine (IO--” M final concentration) and the decrease in lipolytic rates after cessation of the hormone. It was assumed that sufficient triglyceride exists within the cell to completely saturate the lipase enzymes. Based on this assumption. the rate of glycerol production was taken to be proportional to the amount of activated lipase present in the fat cells. One unit of lipase enzyme was defined as that amount which produced I nmole glycerol,!
Short communications
104
325300T275-;250225200-
tn [Al,=tn[Al
,‘kd
i 75\I I I I I I I 6 8 IO 12 14 I6 Time, min
I 50 0
5
IO
15
20 25 30 Time, min
35
40
45
I 0
50
Fig. I. Amount of “active lipasc” in fat cells after the initiation and cessation of cpinephritlc-stimulated tipolysis in the perihtscd fat cclt. Two ml of packed fat cells RX pa-ifused as described previously. Cells WWI‘ pcrifuscd f
(7 /Imoles!mg
of protein’min)
has
been
suhtractcd
I 2
I 4
Fig. 7. Plot of the natural log of the amount of “active lipwe” in fat c&s at various timcs tiftcr cessation of cpi~iephrine infUsion. At time KTO. the infusion of cpinephrinc was stopped. The natural log of the amount of “active lipax” was plotted \\ time. Substituting
equation Z and 1:
from
min under the conditions of these experiments. FOI- calculations of kinetic data. amounts of active lipase wcrc cxprcssed as units,‘mg of protein.
In the perifuscd fat cells preparation. cpincphrinc caused a rapid increase in the glycerol release from the fat cells (Fig. 1). The rate of lipolysis was clcwted in the lirst 2 min and ~ontintleli to incrcasc for about 20 min. after which a plateau was I-cached. The maximum lipoiytic rate was 38 nmoles glyccrol,imin,‘mg of protein. When the ina
fused epinephrinc was stopped. lipolysis rapidly rcturncd to basal rate. For all calculations of kin&x data. it was assumed that no active lipasc wisted in the ahscncc of hormone stimulation. For this rcason. the h~rs;11 lipolytic rate (7 nmoles~min~mg of prntcin) x~iis suhtractcd from uil SuhseqLmt It has
values.
been shown that. after the rcmo\-al of the hormone
where I = time nftcr addition of cpinephrinc and [A] is the concentration of lipax A xt that point in time. As cxn hc seen from this squation. the c(~n~~lit~~tioll of lipasc 11 could be Increased by cithcr increasing L, or decrclrsmg 1,:. Epinephrine. via increased cyclic AMP and activation of protein kinasc. incwascs X,. Whether or not cpinephrine also has an effect on k? is considered below. Equation h prcdlcts that the [A] would approach ;t rnarimum wluc in an asymptotic manna. Fxpcrimcntallq. it 1, found that marimum c~~neentr~~ti(~n of lipasc A ([A],,,,) aas obtained in 10 311min after cpitlephrinc addition. After this time (ri[A];rit)S,,, = 0 = h, + k2(.A],,,,. thus
stimulant. lipolytic rates return rapidly to IXKII values 131. It is logical to assume that this is accomplished b> XI inactivation of the active lipasc and a reduction in its ~IWIC
'I,,'
[Al,,,.,,= - i ,
‘L
concentration. If the inuctivc fol-m of the lipase is I-cpracntcd hi iipasc B and the active form by lipasc A. then the rcactmn for the activation and ~li~icti\l~~ti~~nczn hc dsscrihed 21s:
Llpasc
/\/ H t_’
Lipase A
(71
I
II)
where k,
is the reaction velocity for the activation and k, is the rate constant for the inactivation rcaction. It was assumed that. under ;tlI conditions. cxccss amounts of Iipnsc B uerc p”scnt. thus the activation rattion would follow zero-order kinetics. It was also assumed that under basal conditions that the amount of lipasc A was ,wo and after stimulation incrcascd to an amount insufficient to saturate the inactivation process. Thus. the inactivation reaction would follow tirst-order kinetic\. The activation reaction (I’,) m:1>hc dcscribcd as:
r; = rf[A]Aff and the mactivatton
= h,
(71
reaction I I :I as:
i; = -t/[A],‘dr
= kJA]
0,
,
02468 (3)
Because both the activation and inactivation reaction occur simultaneously. the observed velocity (I;,,,) would hc the \unl of the two and can he rc’prcscntcd:
,
,‘,
,
,
)
1
IO 12 14 I6 Time, min
,
I8
Fig. 3. Changes in apparent k, after the infusion of epinephrinc. Using the experimental data fix [A] from Fig. I. and a value of k2 of -&14/min. apparent li, values wcrc cnlculatcd for various times after the start of cninenh-
Short
105
communications
Equation 7 shows that the maximum concentration of lipase A is defined by the ratio of the activation reaction velocity and the inactivation rate constant. If it is assumed that in the absence of epinephrine stimulation k, equals zero. and if C/2 is a first-order reaction. then the fall in [A] after epinephrine removal should follow the equation for a first-order reaction: In[AII = In[A](, + kzr and a plot of In[A], vs time should result in a straight line with a slope equal to kZ. Such a plot is shown in Fig. 2. A linear relationship does exist between times 4 and I6 min. The deviation from linearity during the first 4 min probably represents incomplete washout of epinephrine. Previous work has demonstrated a 2- to 4-mm washout period for epinephrine [3]. These data are compatible with the assumptions that k, is zero in the absence of stimulation and CL is a first-order reaction. Calculation of kz using the data between 4 and 16 min gives a value of -O.l4/min. Rearranging equation 6 to: k, = [A]kZ/(&’ - I) and using a kz of -014/min. the apparent k, can be calculated from all experimental values of [A] in Fig. 1. This is plotted in Fig. 3. The apparent k, increases during the first 6 min after which it remains constant. These results can be explained in either of two ways: (I) time was required for epinephrine to elevate k, to its maximum value. that is. the step leading to activation of lipase A required time to produce maximum activation, or (2) epinephrine decreased kz as well as instantaneously increasing k,. This means that cpinephrine produced a decrease in the rate of inactivation of active lipase as well as an increase in the rate of activation. Kinetic models can be constructed for these two possibilities. If it is assumed that epinephrine had no effect on kz and. therefore. k2 in the presence of epinephrine was the same as that in its absence, then using equation 7 and the [A],,, from Fig. I (38 units/mg of protein). a value of 5.32 units/mg/min can be calculated for k,. This value would be valid at any time after 6 min. Using equation 6. kz = -0,14/min. and this value for k,. the theoretical curve shown in Fig. 4. was constructed. In the kinetic model in which there is a change in both k, and k2. it was assumed that at time zero [A] = 0. then VZ would also equal zero. Substituting in equation 5. it can be shown that for initial conditions. V,, = k,. Using the experimental value for [A] at 2 min (5.5 units/ mg of protein). an initial value of k, of 2.25 units/mg of protein/min was calculated. If this initial k, was constant during the presence of epinephrine, it can be calculated from equation 7 that kz must have been changed by epinephrine to -O.Oh/min. Using these values and cquation 6. another thcoreticdl curve was constructed (Fig. 4). Theoretical curves constructed for the two different models differ substantially. When the experimental values for [A] were plotted vs time (Fig. 4). there was a good correlation between these values and the theoretical values for the model which assumes that cpinephrine has no effect on kZ. This mathematical model does not take into account that time was required for the elevation of k, to a maximum value. This explains the less exact correlation between experimental and theoretical values at the 2-min time. No correlation exists between the experimental values and the theoretical values for the model which assumes a change in kL. Thus. the experimental data from the perifused fat cell system are consistent with a model system in which epincphrine produces a time-dependent increase in the rate * Recipient of Career Development Award (I-K04-AM50316) from the United States Public Health Service,
0 0
I 5
I I I IO 15 20 Time, min
I 25
I 30
Fig. 4. Theoretical curves for amount of “active lipasc” at various times after cpinephrine infusion. The solid lint represents conditions of X, = 5.32 and kz = -0.14. The broken line represents conditions of fi, = 2.25 and kz = -0.06. The open circles are the experimental values from Fig. I. of activation of a lipasc without any clrcct on Ihc rate of inactivation. Based on current concepts of hormonestimulated lipolysis [4 61. the effect on activation would be through the cyclic AMP-dependent protein kinase secondary to stimulation of adenylate cyclase and an elevation in cyclic AMP levels. The 6 min required to reach maximum value for k, (Fig. 3) is similar to the time nccessary to achieve peak cyclic AMP levels after the addition of epinephrine [7]. The remaining time lag to peak glycerol output conceivably represents the time necessary for the activated protein kinase to convert the lipase B to lipase A. --This work was supported bq Llnited Health Service Grants AM 15788 and AM
Acknowlrdgrrn~r1r.s
States Public 14070.
Dcpurtwnt 01 Phamucology. Indianu L’lliL’ersity. School of Mvdicinc,. I,ldirrrltrpo/i.s. III~. 46202, U.S.A.
DONALII0. Au N* ANDKLW S. KATWS. JR. ELWOOI~ F. LARWS JAWS ASHhlORt
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