A Quantitative Model for the Kinetics of CAMP-dependent Protein Kinase (Type 11) Activity LONG-TERM ACTIVATION OF THE KINASE AND ITS POSSIBLE RELEVANCE TO LEARNING AND MEMORY*

Using computer simulation we have modeled the ki- netics of CAMP-dependent protein kinase, type 11, following transient pulses of CAMP. We show that under the appropriate physiological conditions, the kinase can remain activated 20 min or longer after the ces-sation of adenylate cyclase activation, in a process we term long-term activation. Long-term activation depends in part on the state of phosphorylation of the regulatory subunit, because phosphorylation of the regulatory subunit regulates the affinity of this subunit for the catalytic subunit. We have used our model to simulate experiments that have been performed on the kinetic and steady state activities of CAMP-dependent protein kinase and have found good agreement be- tween the simulations and the experimental data. The effects of the activity of phosphodiesterase, adenylate cyclase, and protein phosphatase on the kinetics of CAMP-dependent protein kinase have been modeled, as have the effects of different ratios of regulatory subunit to catalytic subunit. We have also simulated the activation of the CAMP-dependent protein kinase in Drosophila learning and memory mutants having primary or secondary defects in the cAMP cascade. We make predictions regarding the behavior of different mutants, which are in line with the experimental data. The model corroborates the assumption that the cAMP cascade may play a role in learning and short-term memory.

Using computer simulation we have modeled the kinetics of CAMP-dependent protein kinase, type 11, following transient pulses of CAMP. We show that under the appropriate physiological conditions, the kinase can remain activated 20 min or longer after the cessation of adenylate cyclase activation, in a process we term long-term activation. Long-term activation depends in part on the state of phosphorylation of the regulatory subunit, because phosphorylation of the regulatory subunit regulates the affinity of this subunit for the catalytic subunit. We have used our model to simulate experiments that have been performed on the kinetic and steady state activities of CAMP-dependent protein kinase and have found good agreement between the simulations and the experimental data. The effects of the activity of phosphodiesterase, adenylate cyclase, and protein phosphatase on the kinetics of CAMP-dependent protein kinase have been modeled, as have the effects of different ratios of regulatory subunit to catalytic subunit. We have also simulated the activation of the CAMP-dependent protein kinase in Drosophila learning and memory mutants having primary or secondary defects in the cAMP cascade. We make predictions regarding the behavior of different mutants, which are in line with the experimental data. The model corroborates the assumption that the cAMP cascade may play a role in learning and short-term memory.
Substantial evidence indicates that the cAMP cascade does not merely mediate information transfer in cellular systems but can also retain information, encoded in altered activity of the cascade, for seconds to minutes. This is probably a ubiquitous property of second messenger cascades but has attracted special attention in the context of neuronal systems, due to its potential relevance to cellular mechanisms of learning and memory (reviewed in Byrne, 1987;Dudai, 1987;Goelet et al., 1986;Schwartz and Greenberg, 1987). A most studied example in which the cAMP cascade has been implicated in elementary learning is the gill withdrawal reflex in the sea * This work was supported by the United States-Israel Binational Science Foundation, Jerusalem, the United States-Israel Binational Agricultural Research and Development Fund (BARD), and the Hermann and Lilly Schilling-Stiftung fur Medizinische Forschun im Stifterverband fur die Deutsche Wissenschaft. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "aduertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
$ To whom correspondence should be addressed. hare, Aplysia. Here, both electrophysiological and biochemical evidence suggest that short-term memory of sensitization and classical conditioning are at least partially due to sustained activation of the cAMP cascade (reviewed in Kandel and Schwartz, 1982;Byrne, 1987). In another system, namely Drosophila, mutations affecting the cAMP cascade were found to disrupt, in a relatively specific manner, acquisition and retention of both nonassociative and associative memory (reviewed in Dudai, 1988).
Different processes along the cAMP cascade may contribute to persistent activation of its activity. For example, in the case of Aplysia, adenylate cyclase was suggested to be persistently activated following transient stimulation by a neurotransmitter (Schwartz et al., 1983); this, however, was later questioned (Yovell et al., 1987). An appealing possibility, suggested by several authors, is that CAMP-dependent protein kinase (PKA)' can be persistently activated (reviewed by Schwartz and Greenberg, 1987). In PKA, in the absence of CAMP, the regulatory subunit is coupled to the catalytic subunit, inhibiting its kinase activity. Upon binding of CAMP, the regulatory subunit dissociates from the catalytic subunit, hence activating it (reviewed in Nestler and Greengard, 1986;Beebe and Corbin, 1986;Bramson et al., 1983;Flockhardt and Corbin, 1982). Various processes can lead to enduring changes in the interaction between the two subunits, for example, autophosphorylation (Rangel-Aldao and Rosen, 1976a) or proteolysis . These processes can, therefore, encode molecular memory .
In this paper we postulate that, indeed, sustained dissociation of the catalytic subunit from the regulatory subunit is a molecular memory that can be regulated by the phosphorylation state of the regulatory subunit. We present a detailed quantitative model for the interactions between the two PKA subunits and demonstrate, by computer simulation, how pulses of CAMP, generated by an intracellular signal, can persistently alter the levels of free, hence active, catalytic subunit in the cell. Our model bears upon possible cellular effects of the cAMP cascade in general and molecular mechanism of learning and memory in particular. It also predicts the effects of pharmacological and genetic alterations in cAMP level on the magnitude and time course of the activation of the cAMP cascade.
FIG. 1. Model for CAMP-dependent protein kinase, type 11. The model for the activation of PKA is shown. Phosphorylated regulatory subunit is denoted by RY, and the unphosphorylated noted by C and cyclic AMP by CAMP. By using this notation, R". C regulatory subunit is indicated by R". The catalytic subunit is deand R ' : . C are unphosphorylated and phosphorylated forms of the holoenzyme, R".cAMP and R' : .CAMP represent cAMP bound to the unphosphorylated or phosphorylated regulatory subunit, and R". C .CAMP and R' : . C .CAMP represent cAMP bound to R". C and R: ' . C, respectively. The eight principal states are numbered 1-8, as shown. Transitions from state i to state j are associated with rate constant k,,. A double arrow indicates a reversible reaction, whereas a single arrow represents an irreversible reaction. The dephosphorylation reaction (R' : + R" or R' : .CAMP + R".cAMP) progresses via an intermediate complex between the phosphatase and the phosphorylated substrate. This intermediate complex is not shown; however it is identified as state 4' or 3' in the text. Furthermore, two molecules of cAMP bind per molecule of regulatory subunit; however, that has not been shown in this scheme. For the purposes of this model, k15, k~, , and k73s are assumed to be zero (see text) and therefore have only a single arrow associated with them. Furthermore, we assume that phosphatases do not act on the species R: ' . C and R: ' . C . cAMP because the C protects the phosphorylated site on R:' .

FORMULATION OF THE KINETIC MODEL'
Mechanistic Model for the Activation of CAMP-dependent Protein Kinase-The model for the activation of CAMPdependent protein kinase, type I1 (PKA), was developed as follows: the four states (5-8; see Fig. 1) of dephosphorylated regulatory subunit, R", have been described previously (Builder et al., 1980(Builder et al., , 1981. States 1-4 for phosphorylated regulatory subunit (R2) have been defined similarly on the following experimental evidence. The catalytic subunit is known to phosphorylate R" by an intramolecular mechanism, both in vitro and in vivo (Erlichman et al., 1974). This phosphorylated regulatory subunit can bind the catalytic subunit and can bind cAMP (Rangel-Aldao and Rosen, 1976a;Hofman et al., 1975;Nestrova et al., 1981). The phosphorylated regulatory subunit can be dephosphorylated by protein phosphatases (Erlichman et al., 1974;Vereb et al., 1986). The existence of states 1-3 and 5-7 and their interconversions have also been suggested by magnetic resonance studies 'Portions of the paper (including part of "Formulation of the Kinetic Model," part of "Results," Figs. 2-5, and Table I) 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 included in the microfilm edition of the Journal that is available from Waverly Press. (Granot et al., 1980). On the basis of these data, the model for CAMP-dependent protein kinase was developed involving two isomorphic "cycles": one cycle describes processes involving R", the dephosphorylated form of the regulatory subunit, type 11, and the other cycle describes processes involving R:' , the phosphorylated form of the type I1 regulatory subunit. By the complementary processes of phosphorylation/dephosphorylation, given molecules of regulatory subunit could "switch" cycles.
Within each cycle, in the absence of CAMP, the protein kinase is found as a holoenzyme (R" . C or R: ' . C) at steady state. Upon the addition of CAMP, the holoenzyme dissociates by a two step process involving an intermediate state (R". C .CAMP or Ry . C .CAMP) involving cAMP bound to the holoenzyme, as has been demonstrated (Builder et al., 1980(Builder et al., , 1981. Although the holoenzyme exists as a dimer (i.e. C2), we have simplified the model on the assumption that the two regulatory subunits act independently (see Tsuzuki and Kiger, 1978;Smith et al., 1981;Beebe and Corbin, 1986). Furthermore, two molecules of cAMP can be bound per molecule of R" monomer; however, we assume that the binding of cAMP is first order with respect to CAMP. We make this assumption: (a) because of a lack of kinetic constants for reactions relating to the different intermediates and ( b ) because it can be assumed that the fastest on-constant and the slowest off-constant characterize the binding of both molecules of CAMP, indicating that two constants are sufficient to approximately describe the binding and dissociation of both molecules of cAMP (Smith et al., 1981; see also Corbin, 1982, 1983). We assume that both molecules of cAMP must bind to the regulatory subunit before C is released (Smith et al., 1981). With these constraints, the model is described by a series of 12 simultaneous differential equations (see Miniprint).

RESULTS
Properties of PKA-The predictions we have made regarding the mechanisms of activation of PKA, which arise from our model (Figs. 2 and 3), can be summarized as follows: (a) R:'.cAMP associates with C at a slower rate than does R" .CAMP, ( b ) R: ' .CAMP is the physiologically relevant substrate of phosphatase action, and (c) the slower rate of reassociation of R: ' and R: ' . cAMP with C, as compared to R" and R".cAMP, is what produces the experimentally observed decrease in apparent Kd of the binding of cAMP to the phosphorylated holoenzyme.
Basing ourselves on the above findings as well as on published experimental data, we were able to define the complete parameter list for PKA (Table I) and were able to simulate PKA activation under conditions expected to be found in cells. It could be seen that under these conditions, it is possible for the cAMP cascade to convert a short stimulus (i.e. a 1-s activation of adenylate cyclase) into a persistent molecular memory (i.e. activation of PKA for 20 min or longer; Figs. 3 and 4). We call this process long-term activation of PKA. Long-term activation is most pronounced when the regulatory subunit is autophosphorylated; the addition of an active RY-cAMP phosphatase will markedly reduce this phenomenon, thereby allowing the cell to modulate the time course of long-term activation (Fig. 3).
Effect of Chronic Alterations in the CAMP Cascade-If PKA can act as a molecular memory, then disruption of the cAMP cascade could lead to a failure of retention of information microscopically and perhaps macroscopically. Such alterations in the cAMP cascade might arise from pharmacological of CAMP-dependent Protein Kinase agents or genetic aberrations. Of special interest to our model is the observation that, in Drosophila, mutations affecting the cAMP cascade have relatively specific defects in learning and memory. To date, four learning and memory mutants of Drosophila have been characterized to some extent for the underlying biochemical alteration. These mutants all implicate the cAMP cascade in learning and memory in a variety of nonassociative and associative tasks. Thus, Ddchas a defect in the enyzme 3,4-dihydroxyphenylalanine decarboxylase leading to decreased levels of CAMP; rutabaga has a defect in adenylate cyclase, again leading to decreased cAMP levels; dunce has a defect in phosphodiesterase with resultant increased cAMP levels; and finally turnip has been shown to have decreased monoamine binding, decreased cAMP synthesis and requires higher cAMP levels to half-maximally activate PKA (Ka; reviewed in Quinn and Greenspan, 1984;Dudai, 1988; see also Buxbaum and Dudai, 1988). Furthermore, in adult Drosophila, the type I1 form of PKA is the dominant form of the regulatory subunit, making our model particularly relevant to this species (Foster et al., 1984). We, therefore, modeled activation of PKA under conditions simulating the in vivo condition in some of these mutants, in order to study the effects of their respective defects on the activation of PKA.
To model the kinetics of long-term activation in Drosophila learning and memory mutants, we altered k A c and k p~~ in a manner consistent with known alterations in cAMP levels in these mutants in vivo (reviewed in Dudai, 1988). Assuming, at steady state, that [CAMP] = k A c / k p D E , the appropriate values were assigned to the different mutants. For example, the mutant dunce was assumed to have altered kpDE: dunceM14 and dunceM" have 600% higher cAMP concentrations as compared with wild type; therefore, k p D E for dunce was taken to be 0.17 (100/600) times the k p D E for the wild type fly, CS. In rutabaga, which has about half the activity of adenylate cyclase as CS, k A c was taken as 0.5-fold of that of cs. By using these values, the kinetic curves produced following a simulation of a 1-s maximal activation of adenylate cyclase are shown in Fig. 6. Ddc-, having a defect in monoamine concentrations, was assumed to have a deficiency in activating adenylate cyclase in vivo and was therefore assumed to act like rutabaga in the model.
One sees changes in PKA activation in all of the mutants under these conditions (Fig. 6). rutabaga, having lower adenylate cyclase activity, is unable to activate PKA to the same degree as the wild type (CS) fly, whereas conversely, dunce, which has lower phosphodiesterase activity cannot differentially activate PKA (above base line PKA activity) to the same degree as CS because the activity of PKA is nearing saturation. turnip, when modeled for an alteration in PKA activity as described below, has lower activation of PKA, as well as faster decay kinetics as compared to CS. The decay kinetics of rutabaga are similar to CS, whereas under appropriate conditions in dunce, the decay kinetics are slower because of the persistence of CAMP. Note that it has been shown experimentally that in dunceM1' the concentration of cAMP bound to the regulatory subunit is 2.7 times that of normal (Freidrich et al., 1984): in our simulation this ratio can be estimated as 3.3 (see Table 11), suggesting that the model of PKA activation we describe reflects the condition in vivo.
The mutants Ddc-, rutabaga, and dunce have clear biochemical defects; however, the multiple defects in turnip warrant further investigation. We have shown previously that in turnip the K, of PKA is higher than in the wild type (Buxbaum and Dudai, 1988). Using our model we can show that changes , long-term activation was simulated using case 2 conditions, except that krs, klz, k66, and k,,7 in turnip were assumed to be '/IO of CS (see text). The synthesis and degradation of cAMP followed the relevant constants as described in the text: compared with CS, turnip was assumed to have the same rates of synthesis and degradation, dunce was assumed to have slower rate of degradation, and rutabaga was assumed to have a slower rate of synthesis. in the rates involving R" and C do not produce a change in KO and, conversely, that changes in the rates involving in R" and cAMP do produce a change in K, (not shown). We, therefore, have simulated turnip assuming that the rates k13, klz, ka7, and k56 have changed to %o of the value of wild type (Fig. 6). These changes in rate change the simulated K, from 160 nM in the wild type phospho-PKA to 280 nM: this change is consistent with the experimentally observed 2-fold shift in K , observed in turnip (Buxbaum and Dudai, 1988).
We show that long-term activation depends dramatically Simulation of PKA activation in Drosophila learning and memory mutants in the absence of autophosphorylation. Even in the absence of autophosphorylation, i.e. even when long-term activation does not occur, the activation of PKA in these mutants differ from that of CS. The lines and the constants are as in Fig. 6, except no autophosphorylation/dephosphorylation occurs. on the activity of phosphatases and that in the presence of potent phosphatase activity PKA acts as if it were dephosphorylated (see Fig. 3B). Therefore, activation may not last long in vivo in cells with high R: ' .CAMP phosphatase activity.
Nonetheless, in all the Drosophila mutants modeled, even if PKA is not assumed to undergo autophosphorylation, when the kinetics of the dephospho-PKA are modeled, these mutants still demonstrate alterations in the kinetics of PKA activation (Fig. 7).

DISCUSSION
The qualitative behavior of the model described here depends on the relative rates of the processes for R" and R:', and based on the experimental evidence, the qualitative aspects of long-term activation which we demonstrate could occur in vivo. The quantitative behavior of the model depends on the constants for the rates. The constants we chose came from different sources, and we tried to ensure that all the constants applied to R". Note that k56, k76, k78, and k87 have been determined in a t least two different laboratories and that the rates generally agree within a factor of three, and generally better (Table I; where the on and off rates for both molecules of cAMP were determined the fastest on constants and slowest off constant were compared for k78 and kS7; see Smith et al., 1981). The rates taken from Tsuzuki and Kiger (1978) were the more problematic ones, because it is not clear whether these rates were measured for R" (larval Drosophila contains both types of PKA; Foster et al., 1984). However, kss, &, and k87 are in close agreement with rates estimated for mammalian R". With these rates being so similar to those measured in mammalian R", we assume that k67 is very similar as well.
Regarding the qualitative and quantitative conclusions of the model, we can divide the results into three groups, concerning: ( a ) the mechanism of activation of PKA, (b) the process of long-term activation, and (c) chronic alterations in the cAMP cascade, induced either pharmacologically or genetically, for example in learning and memory mutants in Drosophila.
(a) Mechanism of Activation of PKA-All the predictions have been summarized at the beginning of the "Results" section and are detailed in the Miniprint. The predictions we made produce results that agree well with experimental data and are testable. Significantly, the three mechanistic predictions described there are based on simulations which did not depend on a shift from a phosphorylated to a dephosphorylated regulatory subunit (or vice versa); they are also still valid even if the binding of the two molecules of cAMP to R" proceed at different rates, because we are comparing relative rates between the phosphorylated and dephosphorylated regulatory subunit. Therefore, these predictions of the model are likely to be correct.
(b) Long-term Activation of PKA-The evidence seems to indicate that PKA can undergo long-term activation. In a given cell the degree of this activation would be under the control of phosphatases as well as adenylate cyclase and phosphodiesterase. It is important to note that both formulations of the model (case 1 and case 2; see Fig. 2) demonstrate significant long-term activation, and the qualitative aspects of long-term activation are similar in both cases. Furthermore, the half-life of cAMP in Aplysia (Cedar and Schwartz, 1972) closely parallels the slow phase of cAMP decay in our model. This decay rate reflects the complex interactions of phosphorylated and dephosphorylated PKA and CAMP, and the significant agreement between these two values suggests that the model as a whole reflects the in vivo situation. Comparison between experimental values and predicted values for different processes are presented in Table 11. In all cases a high degree of agreement is found.
(c) Chronic Alterations of the CAMP Cascade-The model makes predictions about the behavior of certain mutants defective in the cAMP cascade, which are in accord with experimental results. Regarding dunce and rutabaga, it has been puzzling that the increased cAMP levels observed in dunce and the decreased cAMP levels observed in rutabaga both lead to similar learning defects. Our model suggests that what is important is the kinetics of PKA activation (over the background activity) following a stimulus: by this criteria, both dunce and rutabaga demonstrate very similar altered PKA kinetics, especially when one examines the change of PKA activity over base-line activity (Fig. 6).
Based on the results presented above combined with previous studies (reviewed in Quinn and Greenspan, 1984;Schwartz and Greenberg, 1987;Tully, 1987;Dudai, 1988), we suggest the following hypotheses regarding learning and memory in Drosophila: 1) PKA is basic to learning in Drosophila; 2) PKA is basic to diverse learning skills; 3) long-term activation may be a persistent step of short-term memory; and 4) phosphatase activity regulates long-term activation and thereby may also regulate short-term memory. We suggest that possibly an intrinsic property of PKA, i.e. that it can, when autophosphorylated, undergo long-term activation, forms the basis of the persistence of information in this cascade (see Schwartz and Greenberg, 1987). If this is the case, then a phosphatase directed at R: ' .CAMP will alter the kinetics of long-term activation, and modulation of this phosphatase may effectively modulate the persistence of information. In our simulations we have assumed that the cellular phosphatase was relatively weak to emphasize the potential of long-term activation; however, in the cell, it is possible that phosphatase activity is initially highly active and is subsequently modulated to allow for long-term activation of PKA. It might, therefore, be of interest to study the effects of phosphatase mutants on memory.
Our hypothesis regarding the direct involvement of PKA in learning and memory is supported from the work carried out in Aplysia (Castelucci et al., 1982). It is further corroborated by the following experimental evidence from Drosophila. PKA activity in dunce and rutabaga are the same as wild type flies when characterized in defined steady state conditions against defined exogenous substrates (Buxbaum and Dudai, 1988). In these mutants, in vitro phosphorylation of endogenous substrate proteins is not significantly different from wild-type (Buxbaum and Dudai, 1987). In turnip PKA activity is altered, as is i n vitro phosphorylation of endogenous substrates (Buxbaum and Dudai, 1988;Smith et al., 1986). All this suggests that in dunce, rutabaga, and turn& the dynamics of PKA activity i n vivo are what cause the observed learning defect; in turnip steady state defects may also be implicated. The model suggests that the rate of loss of memory in rutabaga and dunce should parallel that of a weakly trained wild type fly. Exact decay curves have been determined for rutabaga as compared to a weakly trained CS, and indeed, the decay of memory in rutabaga closely parallels weakly trained CS . The decay of memory in dunce flies also parallels rutabaga and weakly trained CS (not shown).
In conclusion, we suggest that CAMP-dependent protein kinase can potentially undergo a process of long-term activation, which far outlives the intercellular signal which initiated it. This molecular process may subserve neuronal mechanisms of short-term memory. The model we present here is quantitative and predictive and can be used to simulate the activity of this cascade in uiuo under different physiological conditions.

FORMULATION OF THE KINETIC MODEL
Choice o/ kmrtsr ronalonte.
The choice of d l kinetic conrtanta lor R" was from vduea in the lilerslure (Table  I), with the constraint of the principle of exact balance (which states thal around B cycle. the produet of the rate constants in o m direction around the cycle is equal La the product of the rate constants in the reverse direction: Hill, 1877). For Rn. sufficient data was available to eompletely define the model in kinetic terms. The one constant which was lacking. k7B. could be estimated using the condition or erael balance around the cycle 5-57-8. f o r k56, k78 and ks7 the data of Tsuzuki and Kiger (1978) were used because many of the other constants were from that lab. Using the condition of exact balance. and kS6. k78 and kR7 from this group.
k76 was ealeulsted as 1.452XIOB M -l d l . We have found that simply modifying lhe rate of reassociation of R'! (and R ' ! . c M ) with c is sufficient to cause B change in the appareot tid roc R'!C with ~M P ( Fig. 2A). So we Suggest that the only difference belween RII end R'! is the change i n the rate of re-ciation of R'! or R'!.eAMP with C although the tid of R1!-c with CAMP differs from that of R~-c . w e predict that R' ! may not have a higher dfinity for rAMP. a fact that can be tested experimPntally.

S,mdot,ane.
The Simulations were I U~ on an IBM 1311 computer wing II simple program we developed. Simulation was carried out by integrating difference equalions using B variable At such that the curve would remain smooth under dl eondilions. At never r m above 1/10 of the relevant time units, and vas uiuaily significantly lower. As an example. the difference equations for R" (Fig. I ) (Fig. 2C). Here we see that wilh dephosphoholoenzyme (dotted line), As a matter of interat we also pram1 the r e l e e of C from the holoenzyme at different c does not undergo mmpleta dissoehlion. Long-fcvm oclivotwn o/ PhX by aulophosphorylolion, and ilb tonlrol by phoaphaloar oclion.

moeentraiions of C A M P
Because P K 4 undergoes autophosphoryiation. with resuitanl changes in the m e of reassociation of the RI! with c, c can remain free for longer periods, and therefore the enzyme can undergo the prmess we e d i long-term aclivalim. What characterizes the maximal and minimal time eourae of long-term activation are the rate ons st ants within lhe two cycles (1-2-3-4 and 6 6 7 -8 ) ; lhe actual time m u m of long-term activation under given physiological condition3 is defined by the rates of autophosphorylation and dcphmphorylation (i.e.. the P I O C~S S~S by wilh the regulatory subunit swilehes cycles). These latter rates. as they dfeet long-term activation. have been characterized in depth and are described below. The kinetic of PKA ~etivalion under conditions of either 103% phmphorylation of the regulatory subunit (solid line, case 1; dashed line. C G~C 2) and no phmphoryiation (dolled line) of the regulatory subunit are shown in Fig. 3A. These curves represent the longest and shortest activation of PKA d t e r L stimulus.
signifieanl pmeess. and furthermore note that not only the time m u m changes, but dso the Note thal regardless of how the model i . formulated, long-term aetivPion is a very mmimal release of c is dramatically dfeeted by phosphorylation.
Io order to terminate the C A M P pulse. d l / w e C A M P wm modeled as being instantaneously hydrolyzed at d l subsequent times. CAMP, therefore, decayed in lhc w t e m entirely as B result of the rate of dissoeialion of lhe &P fmm the regdatory subunit (depending on the rate constants kT8 and kE5 for Rn. and the rate, k34 and kZ1 for R?).
This diswrialion is slow (Tsuzuki and Kiger,

18781,
sod therefore il contributes to long term activation (see Friedrich., cl GI., 1084). In the presence of i esl active PDE, iong-term aelivstion will persist for longer periods (x. Fig. 4). In the presence of highly aetive phosphstwes. the behwior of lhe PKA is indistinguishable from the case of no phosphorylation, because as m n w the subunits disxiate. they are dephosphorylated ntoehiometriealiy (see Fig. 3B).