Muscle Glycogenolysis

Transcription

1 THE JOURNAL OF BIOLOGICAL CHEMISTRY ( by The American Society for Biochemistry and Molecular Biology, Inc Vol. 266, No. 4, Issue of February 5, pp Printed in U. S. A. Muscle Glycogenolysis REGULATION OF THE CYCLIC INTERCONVERSION OF PHOSPHORYLASE a AND PHOSPHORYLASE b* (Received for publication, August 7, 1990) Marilyn H. Meinke and Ronald D. Edstroml From the Department of Biochemistry, University of Minnesota, Minneapolis, Minnesota Regulation of glycogenolysis in skeletal muscle is cently the search has been for an equivalent and complimendependent on a network of interacting enzymes and tary sequence of regulatory reactions for the inactivation of effectors that determine the relative activity of the phosphorylase by its specific phosphatase, protein phosphaenzyme phosphorylase. That enzyme is activated by tase-1 (1). An interesting development in this area has been phosphorylase kinase and inactivated by protein phos- the discovery of a glycogen-binding protein for protein phosphatase-1 in a cyclic process of covalent modification. phatase-1 which both regulates the activity and sequesters We present evidence that the cyclic interconversion is the phosphatase in the glycogen particle (2). Many investisubject to zero-order ultrasensitivity, and theffect is gations have described the kinetic and thermodynamic paramresponsible for the flash activation of phosphorylase eters of the individual enzymes or the interactions between by Ca2+ in the presence of glycogen. The zero-order adjacent pairs of the enzymes in the two sequences (1, 3). effect is observable either by varying the amounts of kinase and phosphatase or by modifying the ratio of Phosphorylase kinase-phosphorylase complexes have been their activities by a physiological effector, protein visualized by scanning tunneling and atomic force microscopy phosphatase inhibitor-2. The sensitivity of the system (4,5). It has been pointed outhat the multienzyme complexes is enhanced in the presence of the phosphorylase limit that carry out sequential metabolic reactions have properties dextrin of glycogen which lowers the K, of phospho- that are not apparent in their isolated components and that rylase kinase for phosphorylase. The in vitro experi- the kinetics of such systems are described by coupled equamental results are examined in terms of physiological tions rather than the simpler forms used for studying the conditions in muscle, and it is shown that zero-order ultrasensitivity would be more pronounced under the highly compartmentalized conditions found that in tissue. The sensitivity of this system to effector changes is much greater than that found for allosteric enzymes. Furthermore, the sensitivity enhancement increases more rapidly than energy consumption (ATP) as the phosphorylase concentration increases. Energy effectiveness is shown to be a possible evolutionary factor in favor of the development of zero-order ultrasensitivity in compartmentalized systems. Muscle glycogen metabolism is regulated by complex multienzyme signaling systems. In glycogenolysis, phosphorylase (1,4-a-D-glucan; orthophosphate a-d-ghcosyltransferase, EC ) catalyzes the phosphorolysis of the a-1,4-linked glucose residues of glycogen to form glucose 1-phosphate. Regulation of the activity of phosphorylase has been a topic of study for the several decades since its first description. Much of the emphasis of those studies has been directed toward elucidation of the steps in the signal cascade: hormone + adenylate cyclase -f CAMP + CAMP-dependent protein kinase + phosphorylase kinase + phosphorylase. More re- * This work was supported by grants from the American Diabetes Association-Minnesota Affiliate, the National Institutes of Health, and the National Science Foundation. 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 sent: Dept. of Biochemistry, Millard Hall, University of Minnesota, Minneapolis, MN Tel.: The term CAMP-dependent protein kinase is used throughout this paper to designate the catalytic subunit of that enzyme. In all cases, the purified catalytic subunit was used for the studies reported here kinetics of individual enzymes (6). We can now see that multienzyme complexes responsible for signal transmission also have properties based on systemic parameters that must be described in terms of the system (7-9). Enzyme regulation processes in which one enzyme acts to modify the activity of another have the inherent ability to modify signal strength during transmission. Substantial magnitude amplification can be achieved when several enzymes are linked in cascades. Magnitude amplification has been defined as the case in which output molecules are produced in far greater numbers than the stimulus molecules (10). This is in contrast to sensitivity amplification which occurs when a small change in the level of a stimulus produces a relatively larger, fractional change in the activity of the responding system (7). Positive allosteric regulation is an example of sensitivity amplification. A change in effector concentration produces a relatively larger change in enzyme activity. Cyclic, covalently modified interconvertible enzyme systems have been evaluated and found to provide significant advantage over those regulated simply by allosteric effector binding in terms of control pattern flexibility, potential for multiple allosteric stimuli, and magnitude amplification (7). Regulatory properties based on cyclic modification are always described by systemic parameters rather than those of the individual enzymes. A special case of regulatory enhancement in cyclic systems occurs when the regulated enzyme is present in concentrations that are high relative to the K,,, of the converter enzymes (8). The phenomenon, called zero-order ultrasensitivity, was first shown to occur in the Escherichia coli kinase-phosphatase system that regulates isocitrate dehydrogenase (11). In a preliminary report, we showed evidence that the zero-order effect could provide signal amplification for the phosphorylase activation cycle (9). Additional experimental support for zero-order ultrasensitivity was presented for the cyclic phosphorylation-dephosphorylation of a synthetic peptide by a kinase-phosphatase couple (12). Theoret-

2 2260 Cyclic Interconversion of Phosphorylase a and Phosphorylase b ical arguments have been presented showing that covalent modifications systems are capable of much higher sensitivity than allosteric enzymes (7, 13). In this paper we describe studies of the phosphorylase regulatory complex consisting of the phosphorylase a-phosphorylase b couple and their modifier proteins, phosphorylase kinase and protein phosphatase-1 phosphorylase kinase Kmk. vk phosphorylase b phosphorylase a Kmpr Vp protein phosphstasp-l We have examined effectors of phosphorylase kinase (Ca2'), phosphatase-1 (inhibitor-2), and both enzymes (soluble glycogen) on phosphorylase activation in the steady-state cycle. In addition, the effect of phosphorylase concentration on signal amplification has been determined experimentally over an extended range. Based on the results of these studies, the role and significance of zero-order ultrasensitivity in muscle glycogen metabolism are explored with regard to physiological concentrations and compartmentation of the enzymes. EXPERIMENTAL PROCEDURES Phosphorylase a (14), phosphorylase b (15), phosphorylase kinase (16), protein phosphatase-1 (17), and phosphatase inhibitor-2 (18) were prepared from rabbit skeletal muscle. CAMP-dependent protein kinase catalytic subunit, prepared from pig heart, was a gift of Susan Taylor (19). A homogeneous preparation of rabbit muscle phosphorylase phosphatase (CI) was given to us by E. Y. C. Lee (20). Creatine phosphokinase, phosphoglucomutase, and glucose-6-phosphate, all from rabbit muscle, were obtained from Sigma as were creatine phosphate, rabbit liver glycogen, ATP, and NADP. [y-32p]atp was prepared from carrier-free orthophosphate (Du Pont-New England Nuclear) (21). Phosphorylase limit dextrin was prepared from rabbit liver glycogen (22). Enzymes were assayed as described previously (23). Steady-state incubations were started by the simultaneous addition of phosphorylase kinase and protein phosphatase-1 in the desired ratio of activities. The kinase was activated with CAMP-dependent protein kinase and the phosphatase with trypsin as described previously (9). The C, phosphatase was active without further treatment. Steady-state incubation mixtures contained the following in a total volume of 100 pl: the indicated amount of phosphorylase b in 50 mm Hepes? ph 7.2,50 p~ EDTA, 2 mm dithiothreitol, 10 mm MgC12,0.2 mm CaCIZ, 1 mm MnCI2, 0.5 mm ATP, 2 mm phosphocreatine, 10 units of creatine phosphokinase, and 1 mg/ml bovine serum albumin. Reactions were at 30 'C for durations of up to 2 h. Steady state was reached within min. At that time, aliquots of the reaction mixtures were diluted 1:50 in cold buffer and assayed in triplicate for phosphorylase a by spectrophotometric measurement of glucose 1- phosphate from glycogen (9). Calculation of the mol fraction of phosphorylase a was based on a maximal value (mol fraction = 1.0) attained by incubation of the same reaction mixture without phosphatase. The average of triplicate determinations was used in a fitting routine with a second-degree steady-state expression (8, 9) in which + [(a KI - Kza)' + 4&(01 - l)(a)]" 2(a - 1) where W* is the mol fraction of phosphorylase present in the active, a, form; K, and K2 are the Michaelis constants for the kinase and phosphatase, each divided by the total phosphorylase concentration ( WT); and a = vk/v,, where V, and V, are the VmaX values for the kinase and phosphatase. In the experimental studies, the concentra- The abbreviations used are: Hepes, 4-(2-hydroxyethyl)-l-piperazineethanesulfonic acid; HPLC, high performance liquid chromatography; 1-2, inhibitor-2 of protein phosphatase-1; 1-1, inhibitor-1 of protein phosphatase-1; EGTA, [ethylenebis(oxyethylenenitrilo)]tetraacetic acid. (1) tion of phosphorylase was always much greater than that of phosphorylase kinase or protein phosphatase, and an insignificant portion of the phosphorylase was bound in E.S complexes, and the seconddegree equation could be used (9). A general curve-fitting routine (ASYST Software Technologies, Rochester, NY) was used to obtain the K, and Kz, which gave the best fit of the equation to the data. For the physiological simulations we considered cases ranging between high (10 mm) and low (1 pm) phosphorylase concentrations. In the latter case, the use of physiological concentrations of converter enzymes resulted in their concentrations being similar to that of phosphorylase. The cubic expression that had been developed for this circumstance was used to take the E. S complexes into account (8) where 6, = E~T/WT; c2 = EZT/WT; (Y = V,/V,, and the added parameters, E~T and EZT, are the total concentrations of phosphorylase kinase and protein phosphatase-1, respectively. In this case, the modified form of the enzyme W* is given by Analysis of the steady-state mixtures for adenine nucleotides was performed by HPLC (24). RESULTS Time Required to Establish a Steady-state Level of Phosphorylase a-mixtures of the kinase and phosphatase were added to phosphorylase b and MF-ATP to initiate the reaction. As phosphorylase a accumulated, the kinase rate slowed because of substrate depletion, and the phosphatase rate increased until the rates were equal. At that point a steady state was established for the concentrations of phosphorylase a and phosphorylase b. Steady-state reactions were established with phosphorylase concentrations of 1,20, and 70 PM. The phosphorylase kinase/ protein phosphatase-1 ratios (vk/vp) were varied over a range of from 0.1 to 10.0 by maintaining a constant level of phosphatase and adding increasing amounts of the kinase. Identical steady-state levels of phosphorylase a were obtained when the amount of phosphorylase kinase was held constant, and the different vk/vp ratios were established by varying the amount of phosphatase, Reaction mixtures were sampled for levels of phosphorylase a over a 90-min period. Typical results are shown in Fig. 1, in which the incubations at 1 and 70 FM phosphorylase reached steady state within 60 min. To be certain that the ATP-generating system was intact throughout the steady-state reaction, samples were analyzed for adenine nucleotide content. At all times tested, only ADP and ATP were present, with the ATP/ADP ratio varying between 10 and 20; no AMP was detected (<1 FM). This precludes the possibility of spurious results due to activation of phosphorylase b by AMP. Demonstration of the Zero-order Effect in the Glycogen Phosphorylase System-The steady-state mol fractions of phosphorylase a in the three sets of incubations containing 1, 20, and 70 NM phosphorylase are shown plotted as a function of the log vk/vp ratio in Fig. 2, A-C. Two lines are drawn for each set of data points. One is based on the parameters derived from the best fit of the data to the steady-state equation (Equation 1) and a second calculated from the kinetic constants determined by initial rate studies. At each of the three phosphorylase concentrations the two lines are nearly super- imposable, indicating that the system behaves as predicted by the steady-state equation and that the kinetic constants of the enzymes are not significantly modified by the other components of the incubation mixtures. In Fig. 20, the log vk/vp ratios have been normalized to cause all three sets of fitted

3 - 1 p t Cyclic Interconversion of Phosphorylase a and Phosphorylase b 2261 n a ' I s e A a - 0*4* Bo Bo s Incubation Time (rnin) FIG. 1. Time to establish steady-state and ATP maintenance. Steady-state levels of the mol fraction phosphorylase a were reached within 60 min for both 1 pm phosphorylase (O), vk/vp = 0.1, and 70 p~ phosphorylase (0) vk/vp = 0.5. The steady state was maintained for at least 90 min. The ATP-regenerating system kept the ATP/[ADP + ATP] ratio (A) above 0.9 throughout the course of the experiment as determined by HPLC. There was no detectable AMP at any time point. Error bars represent the S.E. and where not visible, the error was smaller than the symbol size. values for the phosphatase and kinase were identical for their respective phosphorylase substrates, which is not the case here (Table I). Fitting the steady-state data to the equation also yields K, values for each enzyme. These results are presented in Table I together with K,,, values obtained by initial rate studies. Also shown in Table I, for each of the sets of data, the response coefficients, R,, are defined as The most responsive circumstance would require the smallest change in the Vk/Vp ratio to go from 10 to 90% phosphorylase a. Thus, for a maximally responsive system, R, would approach 1.0 whereas for a system with no enhanced sensitivity, R, = 81. The sensitivity of a cooperative system to changes in effector concentration is often described by its Hill coefficient, n, where (~slo.,/[slo.l) = R.5 = (81)"" (4) and where [S]0.9 and [S]O.l are the substrate concentrations giving velocities of 0.9 V, and 0.1 V,,,,,. In an analogous fashion a number can be calculated to describe the sensitivity of the zero-order system to changes in ratios of converter enzymes (8). In this case, the ultrasensitivity index, u, is defined by R" = (8l)I'". (5) Vk 1 vp FIG. 2. Signal amplification produced by zero-order ultrasensitivity. Effect of varying the kinase/phosphatase activity ratio on the mol fraction of phosphorylase in the active a form at 1 p~ (O), 20 p~ (O), and 70 p~ (A) total phosphorylase concentrations. The points shown are the average for three or more separate incubations. The V,/V, ratio was varied by holding the phosphatase-1 activity constant and changing the amount of phosphorylase kinase added. In panels A, B, and C the solid lines result from the fitting of the data to Equation 1 whereas the dashed lines are calculated from Equation 1 for the three phosphorylaseconcentrationsusing K, values obtained by initial rate studies. The three lines in panel D are the same fitted lines from A-C normalized to cross at vk/vp = 1 and mol fraction phosphorylase a = 0.5. In D the shallow line (-) is from 1 p~ phosphorylase; the intermediate line (---) is for 20 p~ phosphorylase; and the steepest line (-----) is for the data at 70 p~ phosphorylase. S.E. for each point is indicated by the bars, which are not seen when symbol. the error was smaller than the dimensions of the lines to cross at the same point with a mol fraction of 0.5 occurring at a VklV, ratio of 1. Without normalization the lines would only be expected to cross at that point if the K, Calculation of an ultrasensitivity index allows the sensitivity amplification from zero-order ultrasensitivity to be compared with the sensitivity found cooperative in systems. In the final column in Table I are listed the values of u for the steadystate experiments. The ultrasensitivity index calculated for the data in the steady-state reactions 70 at PM phosphorylase (2.35) is comparable to Hill coefficients found for many allosteric enzymes. Regulation by Phosphatase Inhibitor-2 Exhibits Amplification Due to the Zero-order Effect-In addition to observing zero-order ultrasensitivity by varying the amounts of phosphatase or kinase added, it was important to demonstrate an effect using a more physiologically relevant method of changing the activity of one of them. For this purpose we changed the vk/vp ratio by adding inhibitor-2 (1-2), a modifier of protein phosphatase-1 activity. 1-2 is inhibitory unless it has been acted on by Mg2+-ATP and a specific kinase known as Fa kinase (17). The results of such an experiment are presented in Fig. 3, in which the effects of 1-2 are compared at 1 and 70 PM phosphorylase. Two steady-state reaction mixtures were prepared at 70 p~ phosphorylase and a Vk/Vp ratio of To one of the mixtures was added sufficient 1-2 to cause a 40% TABLE I Kinetic parameters derived from the steady-state reactions R, is the response coefficient of Equation 3 and u the ultrasensitivitv index of Eauation 5. X, Kinase Phosohatase (R") W From steady-state experiments 1 pm phosphorylase pm phosphorylase pm phosphorylase From initial rate studies U

4 2262 Cyclic ~n~erconversion of Phosphorylase a and Phosphory~ase b "2 +h 'I, +I2 4.1, twm 1 Total Phosphorylase FIG. 3. Inhibitor-2 effect. A regulatory protein of phosphatase- 1, inhibitor-2 (1-2) is able to change the steady-state levels of phosphorylase a. The V./V, ratio (left panel) was estab~ished at 0.15 by the addition of the appropriate amounts of phosphorylase kinase and phosphatase-1 (first bar from left). That ratio resulted in a mol fraction of 0.26 for phosphorylase a (third bar). The ratio was then changed to 0.25by the addition of 1-2 to lower the phosphatase activity (second barf. At 70 pm p~osphoryiase, there was a 2.7-fold ampli~cation of the signal (fifth bar), and at 1 PM phosphorylase (fourth bar), the mol fraction phosphorylase a increased by the same factor as the Vk/Vp; no amptification occurred. Error bars are S.E. inhibition of the phosphatase, thus raising the V,lV, ratio to 0.25, a 67% increase. The mol fractions of phosphorylase a in the two incubations after steady state was reached were 0.26 and 0.70, respectively, a 170% increase. At 1 p~ phosphorylase and the same change in VdV, ratio (67%), the phosphorylase a mol fraction increased only 65%. At the low phosphorylase concentration, noamplificationoccurs, and the fractional change in phospho~lase a is the same as the fractional change in phosphatase activity caused by 1-2. There is a clear enhancement of response to re~lation by 1-2 because of the zero-order effect at 70 PM phosphorylase. Effect of Glycogen on the Sensitivity Enhancement-In muscle, phosphorylase is bound to glycogen particles (25) as are phosphorylase kinase (26) and protein phosphatase-1 (2). The interaction with glycogen lowers the Km values of both phosphorylase kinase and protein phosphatase-1 (27,28).Any diminution of the Michaelis constant of either the kinase or phosphatase should enhance the zero-order effect. We measured the Km of both enzymes and found that in the presence of 1% glycogen the Km of phospho~lase kinase for phosphorylase b dropped from 30 to 18 p~ whereas for phosphatase the Km for phosphory~~e a fell from 16 to 9.4 p ~ Thus,. at 20 p~ phosphorylase, the expected enhancement calculated from Equations 3 and 5 would be an increase in the ultrasensitivity index from 1.3 to 1.5. Addition of glycogen to the steady-state reactions generated substantial amounts of glucose 1-phosphate due to phosphate produced by the cyclic interconversion of phosphorylase b and phosphorylase a. The glucose 1-phosphate thus formed invalidated the phosphorylase a assays. To avoid this, we used phosphorylase limit dextrin, glycogen that has had its outer chains removed by phosphorylase (29). The limit dextrin has many of the properties of glycogen but is not a substrate for phosphorylase. The K,,, of phospho~lase kinase for phosphorylase b was found to be 12 p~ in the presence of 1% phosphorylase limit dextrin whereas the Km of protein phosphatase-1 was unchanged. Based on these Km values found by initial rate studies of the individual enzymes, the ultrasensitivity index at 20 p~ phosphorylase in the presence of phosphorylase limit dextrin would be At 20 p~ phosphorylase, 1% dextrin increased the sensitivity significantly, with the ultrasensitivity index rising from 1.35 to Apparently the glycogen-induced K, changes resulted in the convertor enzymes approaching the zero-order region even at 20 PM phosphorylase. In contrast, the effect of the glycogen derivative on the system at 70 PM phosphorylase was insi~i~cant, with the ultrasensitivity index staying at Glycogen Enhances the Sensitivity of the Cyclic Regulatory System of Phosphorylase to Calcium Ions-The muscle glycogen particle contains phosphorylase and both the kinase and phosphatase. A "flash activation" of the phosphorylase has been shown to occur when Ca" and Mg-ATP are added to isolated glycogen particles (30). The results presented in Fig. 4 show that the cyclic system of kinase and phosphatase used in this study for interconverting phosphorylases a and b is subject to flash activation by ea2+ when glycogen is present. In the absence of glycogen, only a slow incorporation of 32P into the phosphorylase occurred when Ca2+ was.added. Reaction conditions were the same as those used in steady-state experiments detailed above except that all proteins were dialyzed against EGTA-containing buffer, 1 mm EGTA was added to the incubations, the ATP-regenerating system was omitted, and [Y-~'P]ATP at 2.4 mm was added. Reactions were begun by the addition of phosphorylase kinase (dephospho form) and protein phosphatase-1; at intervals samples were analyzed for formation of phosphorylase a as measured by the incorporation of '*P. After 10 min, Ca2+ was added to a final concentration of 2 mm, and sampling continued. At the end of the experiment, the extent of incorporation of 32P into phosphorylase had reached 0.3 mol/mol and was still increasing. In the control incubation without phosphorylase, the level of phosphorylation corresponded to 8.3 mol of 32P/ mol of phosphorylase kinase, which corresponds to fully activated phosphorylase kinase (31). Phosphorylation in the presence of phosphorylase is due to incorporation of phosphate into phospho~lase and not its activating enzyme. PREDICTED PHYSIOLOGICAL CONSEQUENCES Using the known physiological and biochemical parameters for muscle and the theoretical studies of Goldbeter and Koshland (32, 33), we have pursued the question of the possible physiological significance of zero-order ultrasensitivity in ,. 0.3 : O** t c 4: e Incubation time (min) FIG. 4. Glycogen enhancement of Cas+ sensitivity. Incubations contained in 1 mi: 50 mm Tris, 1 mm EGTA, 2.4 mm ATP, 10 mm MgC12, 1 tng/ml bovine serum albumin, 1% rabbit liver glycogen, 80 pg of phosphorylase kinase (not activated), 34 units of protein phosphatase-1, and 70 PM phosphorylase. When added, Ca'" levels were raised to 2 mm by the addition of CaC12. At the times indicated 20-pl aliquots were removed and analyzed for acid-insoluble "P (23). The blank (0) contained no phosphorylase. In the absence of glycogen (O), Ca2* only slightly increased the rate of phosphorylase a formation. With glycogen present (A) a severalfold activation in the rate of phosphorylation occurred.

5 Cyclic Interconversion of Phosphorylase a and Phosphorylase b 2263 skeletal muscle. All of the calculations shown below are based on experimental data for the system parameters as indicated for each calculation. Combined Effect of Phosphorylase Concentration and Ratio of Converter Enzymes (vk/vd on the Mol Fraction of Phosphorylase a-the determination that zero-order ultrasensitivity enhances the response of the phosphorylase system to changes in kinase or phosphatase activity leads to the question of the possible physiological significance of this effect. The phosphorylase concentration in muscle can be calculated to be 70 p~ based on the total muscle volume (34). However, if one considers the compartmentation of the phosphorylase to the 1% of muscle space occupied by glycogen particles (35), the concentration of the enzyme may be as much as 3.5 mm phosphorylase dimers. In Fig. 5 a surface is shown which describes the mol fraction of phosphorylase a as a function of both the ratio of the converter enzyme activities (log vk/vp) and the total phosphorylase concentration. The surface is calculated from Equation 2 based on K, values of 30 pm for phosphorylase kinase and 16 p~ for the phosphatase, with phosphorylase concen- trations ranging from 1 pm to 10 mm and vk/ v,, ratios between 0.1 and The concentration of phosphorylase kinase was set at 0.65 p~ (16) and at 0.5 p~ for protein phosphatase-1 (1). At the lower phosphorylase concentration (at the right of the drawing) the sensitivity of W* to changes in the vk/vp ratio is low compared with that found at high phosphorylase concentrations (left of the drawing) where the surface has a much greater slope in the w* versus vk/v, plane. Ultrasen- sitivity indices (u) are shown for each decade of phosphorylase concentration. At 3.5 mm phosphorylase, u is 51, far higher than any known Hill coefficient for a cooperative enzyme. Finite Interval Amplification Factors-Although the response coefficient, R,, and ultrasensitivity index, u, are useful for comparison between enzymes or enzyme systems, they are arbitrarily defined only for changes in signal which result in the response changing from 10 to 90% of maximal. It is - I - unlikely that any physiological process would have a signal changing exactly that amount over that range. A more flexible, alternative method of describing the sensitivity of such a system is through the use of finite interval amplification factors (32). In this case any interval may be chosen for the change in signal (vk/vp ratio) with the corresponding change in phosphorylase activation related to it through the amplification factor A, A, = [(W*,/W*$) - 11 [(a//",) - 11 where W*/ and W*i are the final and initial values of the mol fraction of phosphorylase a, and at and ai are the final and initial values of vk/v, ratios required to achieve the final and initial values of W*. This has the advantage of allowing one to measure amplification over a physiologically relevant range of activities. In Fig. 6 are presented the amplification factors as a function of the values of the vk/vp interval ratio (af/ai) for phosphorylase concentrations ranging from 1 pm to 10 mm. For these curves, ai was arbitrarily chosen to be 0.1 with af ranging from 0.1 to As might have been anticipated from an inspection of Fig. 5, there is little signal amplification in changing the vk/vp ratio from an initial value (ai) of 0.1 to a value below 0.9 (af). However as at approaches 1.0, there is an abrupt transition to a high level of sensitivity amplification which reaches 500 at 10 mm phosphorylase. Although not obvious due to the logarithmic scale used in Fig. 5, at af 2 1.0, the amplification factor is a linear function of the phosphorylase concentration. At values of af much greater than 1.0, the amplification is of course degraded since W* is already near its maximum value (1.0) and only small changes in mol fraction phosphorylase a will result from large changes in Vk/Vp ratio. Amplification due to the zero-order effect is a function of both the concentration of phosphorylase and the interval of change in the vk/vp ratio. Energy Cost of Zero-order Ultrasensitiuity-Covalent modification systems such as the one considered in this report use cellular energy supplies to maintain regulation of the level of the modified form of the enzyme (33,36). In this case ATP is converted to ADP and Pi due to the combined action of phosphorylase kinase and protein phosphatase-1 on phosphorylase. We have evaluated energy consumption and sensitivity (6) 6007 E 1W P /,,/ log [Phosphorylase1 (MI FIG. 5. A three-dimensional representation of the effect of both phosphorylase concentration and the VJV, ratio on the mol fraction of phosphorylase a. The ultrasensitivity indices u, which ranged from 1 to 108, were calculated for the five labeled phosphorylase concentrations and are shown at the front of the graph above the concentration values. Mol fractions of phosphorylase a were calculated using the cubic equation (Equation 2), (8), which includes the correction for phosphorylase forms bound in E-S complexes. The physiological concentrations of the converter enzymes used in the calculations were 0.65 PM for phosphorylase kinase (16) and 0.5 PM for protein phosphatase-1 (1). 100 tphoephorylase1 (MI FIG. 6. Finite interval amplification curves. Amplification factors (32) calculated from Equation 6 are presented as a function of the Vk/VP interval ratio (q/a,- 1) for phosphorylase concentrations between 1 PM and 10 mm in which a, and at are the initial and final values of the V,/Vp ratio for the interval chosen. The initial value, a,, was arbitrarily set at 0.1, with a/ ranging from to 10.0 (a value of exactly 0.1 for af would have resulted in a division by zero in Equation 6).

6 2264 Cyclic Interconversion of Phosphorylase a amplification and calculated the efficiency of energy use in regulation as a function of phosphorylase concentration and the vk/vp ratio. Although amplification factors increase linearly with phosphorylase concentration, the energy consumption rate (datp/dt) should increase hyperbolically since that rate follows the Michaelis-Menten equation. One would therefore predict that the energy efficiency of zero-order ultrasensitivity will increase with phosphorylase concentration. That this is so is shown in Fig. 7. The vertical axis is an arbitrary amplification cost factor: u (the ultrasensitivity index defined in Equation 5) divided by the steady-state rate of ATP hydrolysis. As expected the energy efficiency increases with increas- ing phosphorylase concentrations; it is at least 100 times greater at 10 mm than at 1 pm. The very high value at a vk/ Vp ratiof 0.1 and 10 mm phosphorylase is due to the reduced turnover rate of the steady-state cycle at low phosphorylase kinase activities. The graph in Fig. 7 was generated for a constant phosphatase activity with the vk/vp ratio modified through changes in the phosphorylase kinase activity. If the kinase were held constant and the ratio modified by varying the phosphatase activity, the shape of the surface would be reversed along the vk/vp axis with the high point occurring at a vk/vp ratio of 10 and at 10 mm phosphorylase. Since energy consumption is saturable with regard to increasing phosphorylase concentration while sensitivity amplification factors increase linearly with concentration, it may be advantageous for an organism to operate at as high a concentration of covalently modifiable enzyme as possible. DISCUSSION Glycogenolysis in skeletal muscle is regulated by a multienzyme network containing several kinases and phosphatases and regulatory components for each. Covalent modification and ligand binding play important roles in the regulation of that signaling network. Phosphorylase, phosphorylase kinase, protein phosphatase-1, and CAMP-dependent protein kinase are the central enzymes in the complex. Glycogen, Ca", Mg2+- ATP, CAMP, and inorganic phosphate are also obligatory components of the glycogenolytic regulatory process. Other proteins such as protein phosphatase-2 (37), phosphatase inhibitors (18), calmodulin (23, 38), troponin C (39), and the protein that binds phosphatase-1 to glycogen (2) may be part tphoephorylaee1 (MI FIG. 7. Energy cost of sensitivity amplification. The values on the vertical axis are the ultrasensitivity indices u (Equation 5) for each of the phosphorylase concentrations divided by the steady-state ATP utilization rate at each phosphorylase concentration and Vk/V, ratio on the horizontal axis. The rate of ATP consumption is calculated from the Michaelis-Menten equation assuming phosphatase is limiting and a VmaX for protein phosphatase-1 in the tissue of 0.93 mm/min (50) and a K, of 16 pm. The numbers near the asterisks on the graph are values of energy efficiency at each of those points. The dimensions of the numbers are min/mm. I 17 and Phosphorylase b of that system. Small metabolites such as AMP and ADP may play a regulatory role (40, 41). There is evidence that all of the components of this process are associated with glycogen particles (42-44). Glycogen synthesis is also associated with the particle but will not be considered further here. Because this multienzyme complex has a single role, regulation of glycogenolysis, it is useful to study the signaling system of this complex as a functional unit. Glycogenolysis has a number of advantages as an experimental prototype for studies of metabolic system control. The main qualitative relationships between the various components are well known; the standard kinetic parameters of the individual enzymes have been recorded, and simple techniques are available for preparation and assay of the enzymes and other components of the glycogenolytic complex. The relatively long duration that can be achieved for the steady state allows simple experimental protocols. The maintenance of a high ATP/ADP ratio by using an ATP-regenerating system precludes the production of AMP and reduces possible complications arising from the known effects of ADP on phos- phorylase kinase and AMP on phosphorylase. The sensitivity of the relative amount of phosphorylase a to changes in the kinase/phosphatase ratio is seen to be a function of the concentration of phosphorylase. At a low concentration (1 pm), the response coefficient R, of 73 indicates little amplification. At 20 p~ an R, of 26 indicates an enhancement of sensitivity at a phosphorylase concentration near the K,,, values for the converter enzymes. When phosphorylase reaches 70 p~ a marked sensitivity enhancement is seen with an R, of 6.5. We chose that value for our highest experimental concentration based on thestimation by Fischer that the bulk concentration of phosphorylase in rabbit skeletal muscle was approximately 70 p~ (34). This is a low estimate of the concentration since phosphorylase is sequestered in the glycogen particle compartment. Assuming a normal rabbit muscle glycogen content of 1% (w/v) (35) and a hydrated density of glycogen greater than 1.0, its compartment volume is less than 1% of the cell volume. This produces values in the mm range for rabbit muscle phosphorylase dimer (44). The enhanced responsiveness to changes in Vh/Vp caused by increasing phosphorylase concentration is due to zeroorder ultrasensitivity. The comparability of the Michaelis constants derived by fitting the steady-state data to Equation 1 to those obtained by initial rate measurements confirms the validity of using the steady model and equation. The definition of the ultrasensitivity index u, an analog of the Hill coefficient of cooperative systems, is based on the relationship described by Goldbeter and Koshland (45). This provides a useful comparison between the two forms of sensitivity amplification: zero-order ultrasensitivity and enzyme cooperativity. In the present case, a value of 2.35 for u at 70 pm or 51 at 3.5 mm places phosphorylase regulation among those processes subject to substantial sensitivity amplification by either process. Sensitivity enhancement was seen in a system in which the vk/vp ratio was modified by changing the activity of one of the components, phosphatase-1, rather than the amount. We chose to use 1-2 because of its inherent inhibitory activity. Phosphatase inhibitor-1 (1-1) may be more significant in glycogen metabolism (2); however, the inhibitory capacity of 1-1 is itself dependent on a cyclic phosphorylation involving CAMP-dependent protein kinase that would have complicated the experimental protocols. Phosphorylase limit dextrin significantly modifies the parameters of the cyclic interconversion of phosphorylase a and b. However, the limit dextrin may

7 Cyclic Interconversion of Phosphorylase a and Phosphorylase b 2265 not bind well to the glycogen storage site on phosphorylase skeletal muscle phosphorylase was 22% in the a form and which is responsible for the formation of the particulate after 25 s of isometric contraction had risen to 65% (47). glycogen-phosphorylase complex. That noncatalytic site has Using a steady-state equation for W* (8,9) and the K,,, values a high affinity for the nonreducing ends of the glycogen, given in Table I, one can calculate that for such a %fold which contain seven a-1,4-linked glucopyranose units. The change in phosphorylase a, a 6-fold increase in the V,/V, limit dextrin has on average only 4 glucose residues in its ratio would be needed at 1 p ~ 2.2-fold, at 70 p ~ and, at 200 outer chains (29) and might have a lower affinity for the p~ phosphorylase only a 1.45-fold increase in Vk/V, would be phosphorylase binding site. In spite of that limitation, sub- needed. The corresponding finite interval amplification facstantial sensitivity enhancement was observed. tors for the cyclic system over that range of changes in Vk/Vp The increased phosphorylase activity during muscle contraction is believed to be caused by Ca2+ activation of phosphorylase kinase. The Ca2+ activation of phosphorylase ob- served in this work simulates the flash activation first described by Heilmeyer et al. (30). Although there was an increase in the level of incorporation of 32P into phosphorylase by the addition of Ca2 to the cyclic interconversion mixture, it was only after the addition of glycogen that the marked stimulation characteristic of flash activation was observed. The graphical presentation in Fig. 5 shows that some enhancement of the response of phosphorylase to changes in the Vh/Vp ratio occurs well before the zero-order region of the substrate saturation curve is reached. The effect would be absent only in a truly first-order relationship, where v is a linear function of [SI. The hyperbolic nature of the v versus [SI relationship provides the nonlinearity of response necessary for the enhancement afforded by zero-order ultrasensi- tivity. The greatest sensitivity occurs precisely where v is least responsive to a change in [SI, the zero-order region. In evaluating the extent to which sensitivity amplification may play a role in cellular metabolism, one may wish to estimate the response in output signal over something other than the 10-90% change for which R, is defined. Most physiological studies indicate that phosphorylase a changes only from a level of 10 or 20% of the total phosphorylase to less than 80% with maximal stimulation. The finite interval amplification factor defined by Goldbeter and Koshland (32) ATP hydrolysis in rabbit muscle. The sensitivity increases provides a quantitative description of sensitivity amplification more rapidly than ATP consumption as the zero-order region over any range of input or output changes. Amplification is entered. factors A, of several hundred are found over some intervals of The results of this study show that one can work with the the phosphorylase system using the kinetic parameters found glycogenolytic system as a functional unit. It is possible to for the zero-order region. As an example, for the interval in define quantitative relationships for the systems in much the which the V,/V, ratio changes from 0.1 to 1.1, the mol fraction same way that the kinetic parameters V,,, and K, describe of phosphorylase a changes from about to 0.99, yielding catalytic properties of individual enzymes. Through such an A, of 100. In a sequence of regulatory steps such as the studies we hope to understand more clearly the way metabolic glycogenolytic cascade, it is the amplification factors that can be multiplied to obtain the overall sensitivity of the system to changes in signal. These concepts of sensitivity amplification need to be contrasted with those of magnitude amplifi- cation generally presented in conjunction with the cascade. Although one can obtain rather impressive numbers by multiplying the kcat values of individual enzymes in a regulatory sequence it should be understood that the products of such calculations have little physiological meaning. The potential for large amplifications will almost always be constrained by one or more attenuations such as dilution of effector, reversal by opposing regulatory sequences (e.g. cyclic covalent interconversion), or limited concentration of substrate enzyme. Although the k,,, for phosphorylase kinase acting on phosphorylase b may be as high as 430 s (46), the ratio of phosphorylase to phosphorylase kinase in the muscle cells is only in the range of :l. Such a high kinase kcat and phosphorylase concentration suggest that all of the muscle phosphorylase could be activated within a few ms. The amplification factors calculated for the in vitro system can be compared with those calculated to be required in physiologically intact systems. Chasiotis found that at rest, human and W* and at those three phosphorylase concentrations are 0.38, 1.63, and There is invariably a cost associated with maintenance of life. In regulation by covalent modification, the expense is readily seen; it is the hydrolysis of ATP by the cyclic phosphorylation-dephosphorylation of the regulated enzyme. Goldbeter and Koshland (33) have presented a detailed analysis of energy expenditures in covalent modification systems. They considered three mechanisms of control for a cyclic covalent system: (a) varying an effector of the modifying enzyme; (b) varying an effector of the demodifying enzyme; and (c) varying a single effector having opposite influences on the modifying and demodifying enzymes. For large changes in modification level, case c provides the smallest energy expenditure in changing from one steady-state level to another. The control of muscle glycogenolysis appears to have the elements of case c. Phosphorylase kinase is activated directly by CAMP-dependent protein kinase whereas protein phosphatase-1 is inhibited by CAMP kinase through phosphorylation of inhibitor-1 (48) or the specific glycogen binding system that maintains the phosphatase in the glycogen particles in an active state (49). In this study we have only considered the energy effectiveness when moving from the first-order region into the near and then zero-order far region. The estimates presented in Fig. 7 were obtained by dividing the ultrasensitivity index u by calculated maximal rate of processes are controlled through amplification or attenuation of signals such as hormones, second messengers, or nerve impulses. The zero-order ultrasensitivity effect, the enhancement by glycogen of the Ca2+ stimulation of phosphorylase, and the amplification of the inhibitor-2 signal are all consequences of the interactive nature of the complete subsystem. An organism that uses zero-order ultrasensitivity has a profoundly sensitive component of its regulatory system with ultrasensitivity indices orders of magnitude greater than can be found for allosteric enzymes. In addition the energy effectiveness increases as the system moves further into the zero- order region. This enhanced sensitivity coupled with reduced unit cost of sensitivity may be a selective pressure in evolution favoring compartmentalized regulatory systems. 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