chronotropic effects of norepinephrine and tyramine: a system

Chronotropic Effects of Norepinephrine andTyramine: A System Response Analysis

By Edward J. Battersby, M.D., and Elliot V. Newman, M.D.

• In 1958, Burn and Rand 1 proposed thatthe drug, tyramine, had no direct sympathomi-metic effects and that its pharmacologic actionwas wholly mediated by the liberation ofnorepinephrine from endogenous stores. Thiswas based upon the observation that prepara-tions severely depleted of stored norepi-nephrine by pretreatment with reserpine re-sponded poorly, if at all, to tyramine. Largeamounts of norepinephrine infused into suchpreparations prior to tyramine administrationrestored the potency of the latter amine andthis was interpreted as the result of storagesite repletion.

Such repletion of storage site with nor-epinephrine does not seem to be a necessarycondition for the restoration of tyramine effi-cacy. Certain investigators 2-3 have concludedthat the presence of proportionately smallamounts of unbound extracellular norepi-nephrine is sufficient to enhance tyramineeffect. These authors argue that tyraminemust have an effect different from, and inaddition to, the simple release of norepi-nephrine from storage and that this super-added effect is functionally related to thepresence of unbound norepinephrine.

Direct evidence for the release of nor-epinephrine from organs responding to ty-ramine is abundant.4"0 However, the amountsof norepinephrine liberated by tyramine aresmall compared to those needed to achievethe same pharmacologic response by adminis-tration of exogenous norepinephrine.7 The

From the Department of Medicine, VanderbiltUniversity School of Medicine, Nashville, Tennessee.

Supported in part by the John A. Hartford Foun-dation, Inc., and Grant HE-08195 from the U. S.Public Health Service.

Dr. Battersby held a postdoctoral research fellow-ship from the U. S. Public Health Service.

Received for publication January 10, 1964.

112

time course of sympathomimetic response toan injectate of tyramine is protracted as com-pared to an injectate of norepinephrine atleast in its inotropic and chronotropic effectsupon the canine heart-lung preparation.8 Thissuggests a capacitative effect upon the nor-epinephrine released by tyramine; that its rateof decay of concentration in the region of thereceptors is much slower than would bepredicted by elutional processes. This mightbe explained by some mechanism of slowrelease of norepinephrine by tyramine. If thiswere the mechanism responsible one mustthen invoke the hypothesis of "strategicliberation" to explain profound pharmacologiceffects by small amounts of liberated nor-epinephrine. This type of hypothesis has led tothe proposal that local liberation of nor-epinephrine near the S-A node is a possibleexplanation for the chronotropic effects oftyramine,3 but this ignores the concomitantrate independent, inotropic effect on thewhole cardiac muscle mass. "Strategic libera-tion" theories do not explain the potentiationof tyramine effect by unbound norepinephrineunless one predicated a nonsymmetric ingress-egress pathway for norepinephrine resultingin tyramine liberating norepinephrine fromstrategic sites but not blocking its access tothose sites.

It is the purpose of this paper to propose akinetic hypothesis consistent with the ob-served interaction between the two amines inquestion. In essence, the proposal of Burn andRand concerning tyramine mechanism isaccepted. No direct effect is attributed to tyra-mine. The release of norepinephrine fromstorage site is considered to be mediated bya shift of a dynamic equilibrium betweenfree and bound norepinephrine effected bythe competition of tyramine with norepineph-rine for free storage sites. A concentrating

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NOREPINEPHRINE AND TYRAMINE 113

mechanism is proposed between intravascularspace and "receptor site space," i.e., the siteof action of norepinephrine. This is viewed asproducing a mass partition ratio greatly favor-ing receptor site space. This would allowaccumulation of tyramine liberated nor-epinephrine in receptor site space so long asthe concentrating mechanisms were highlyspecific for norepinephrine, thereby disallow-ing tyramine competitive inhibition. Receptorsite space as considered in this formulationis an operationally defined mathematical spaceand cannot be precisely delimited anatomi-cally on the basis of the present study. Whileit may be viewed as being in extracellularspace it cannot be assumed with any certaintyto be identical with that space.

In such a system injected norepinephrineeffect would be rate-limited by the availabil-ity of storage sites for uptake from receptor-site space. Tyramine would have no effect ina system devoid of norepinephxine. However,tyramine may still occupy storage sites and inthe absence of significant amounts of nor-epinephrine might partially saturate thosesites. Norepinephrine arriving subsequent tothis blockade would be removed relativelyslowly from receptor-site space and wouldhave a longer and greater response. It neednot be presumed that this space have a greatmass capacitance and thus uptake in dener-vated preparations, i.e., without storage sites,might not be significant.

MethodsIsolated heart-lung preparations were prepared

from mongrel dogs in the usual manner employ-ing ether-chloralose (1 g iv) anesthesia. Thesuperior vena cava and brachiocephalic arterywere cannulated and other major systemic vesselsligated. A Starling resistor in the arterial outflowwas set at an occlusion pressure of approximately100 mm Hg. Blood circulated through a tempera-ture regulated external reservoir initially filledwith heparinized blood removed from donor dogsunder ether anesthesia just prior to the experi-ment. When done, coronary sinus cannulationwas performed with a polyethylene cannulapassed via the right atrial appendage into theostium of the coronary sinus and secured withan encircling suture of 4-0 silk.

Experimental dogs were reserpinized by intra-CircuUtion Rtittrch, Vol. XV, August 1964

peritoneal injection of 0.5 mg reserpine U.S.P.48 hours and 0.75 mg 24 hours prior to theexperimental procedure.

Labelled amines used in this study were Id-norepinephrine-2-CJ* and p-hydroxyphenylethyl-amine-1-C'^ (tyramine). Whole blood con-centrations of these compounds were estimatedby proportional counting of P activity of air-driedwhole blood aliquots on aluminum planchettes.Standards were prepared for each set of deter-minations and calibration curves were satisfac-torily linear in the range of interest.

Cardiac rate was monitored on a digital cardio-tachometer with an output for analog recording.The "arterial" pressure pulse in the outflow tub-ing from the preparation was used as thetriggering voltage for the tachometer. Recordingswere made on a Sanbom six-channel paper striprecorder.

Electronic simulations were constructed on theproblem boards of two Donner 3400 analog com-puters employing model 3732P quarter squaremultipliers for multiplication and power functionsand a model 3750 variable base function gen-erator for the simulation of empirically determinedforcing functions.

ResultsSTEADY STATE CALIBRATION

Carbon-14 norepinephrine was infused intothe inflow tubing of heart-lung preparationsand allowed to recirculate through a small vol-ume while the heart rate was continuouslymonitored and recorded. A plateau of constantrate was established between one and twominutes after addition. During rate equilib-rium two consecutive ten-second aliquots ofblood were removed from the arterial cannulaand considered representative of blood enter-ing the coronary circulation. Norepinephrineconcentration was measured as C " activity.The criterion of steady state norepineprrrineinput was that the difference between thepaired aliquots be no greater than three timesthe standard error of the method of estimation,i.e., the samples differed by no more than13.2%. The value was omitted from considera-tion if this criterion was not fulfilled. Imme-diately after sampling additional norepi-nephrine was administered and the procedurerepeated. No more than six additions weremade in any preparation so that all valueswere obtained within twelve minutes afterthe first addition. Blood that had been re-



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114 BATTERSBY, NEWMAN

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FIGURE 1

Rate increase in beats per minute above base line rateplotted against the concentration of C'$ norepineph-rine in the aortic root. Values were obtained understeady state conditions in preparations from reserpinepretreated dogs. Dashed line represents the approxi-mating function: rate increase equals 10.24 times thesquare root of norepinephrine concentration.

moved from the reservoir prior to the addi-tions of norepinephrine and kept at the sametemperature was returned to the reservoir andsamples were taken when rate equilibriumwas established. The values obtained on de-creasing concentrations are not included inthe graphed data. There was no difference inthe range of values obtained immediately inthis manner and the rate-concentration rela-tionship obtained during the period of in-creasing concentrations. The absence of signif-icant hysteresis in the system, thus demon-strated, was important in the formulation ofthe dynamic response analysis given belowand gives reasonable assurance that the CJ J

label largely represented the originally la-belled molecular species during the time ofthe study.

Sixteen points were obtained from fourpreparations from reserpinized animals in thismanner. The coronary sinus was cannulated intwo of these preparations and the efflux ex-cluded from recirculation. The diversion of

die coronary outflow did not affect the con-centration-rate relation in any evident manner.There was approximately 50% reduction in C H

activity in the coronary sinus blood as com-pared to aortic root blood activity. Rate in-crease over base line levels was plotted againstaorta root norepinephrine concentration,yielding the array of points seen in figure 1.

Because of the distribution of the pointsand because there is no a priori theoreticreason to necessitate the use of another func-tion, the positive limb (y = A^x) of a para-bola of the form y2 = A 2 x was chosen torepresent in continuous form the functional re-lationship between rate increase and norepi-nephrine concentration. A least squares fit gavea value of 10.24 for the coefficient A; the coef-ficient of variation of the points was 18.0%,equivalent to a standard deviation of A of ±1.84. Iteration on increments to the origin ofthe point array in each dimension was per-formed on an IBM 650 digital computer with

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Rate increase plotted against C1Ji norepinephrineaortic root concentration. Solid points represent thevalues obtained from reserpine pretreated hearts as infigure 1. Open circles represent values from normalhearts with an increment of 18 beats per minute and3.6 fig/liter norepinephrine concentration on each.Arrow indicates the translated origin of the point arrayfrom normals. Dashed line is the approximating func-tion; rate increase equals 9.48 times the square rootof C'i norepinephrine concentration.

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least squares fit and variance estimate for eachiteration to determine if a portion of a para-bolic limb not containing the vertex mightgive a better approximation. No better fit wasfound. The approximating function, rate in-crease equals 10.24 times the square root ofnorepinephrine concentration, is shown infigure 1.

Nineteen points were obtained from fiveheart-lung preparations from normal dogs. Di-version of coronary sinus flow apparently didnot alter the response pattern in the two dogsin which this was done. A similar extractionratio of label between the aortic and coronarysinus blood was found in these hearts as wasfound in the reserpine pretreated hearts. Thearray of points from these preparations fellwell below the points from reserpinized dogswhen plotted in a like manner. The best fitting

FIGURE 3

Circuit A represents the analog computer configura-tion for solution of equations 1 and 2. See text. Cir-cuit B represents the computer configuration for solu-tion of equations 3, 4, and 5. QSM designates aquarter-square-nuihiplieT in square root mode whoseoutput is 10 V input. As shotcn simulation is in realtime.

CircmUaion Reitrcb, Vol. XV, A*mut 1964

parabolic limb including the vertex had avalue for the coefficient A of 6.2. The origin ofthis array was translated along the previouslydetermined approximating function until allbut two points lay within the range of twostandard deviations of the original A. Thisresulted in an initial state offset of approxi-mately 3.6 fig/liter norepinephrine concen-tration for normal values. Considering allpoints, a predicting function resulted with avalue of coefficient A of 9.48, differing by 0.4standard deviation from the original and witha coefficient of variation of 20%. Using this re-lation, the initial state offset for normal valueswas 18 beats per minute. The combined arrayof points and the approximating function, rateincrease equals 9.48 times the square root ofnorepinephrine concentration, are shown infigure 2.

RESPONSE TO TRANSIENTS

The study of the system response to tran-sient increases of norepinephrine concentra-tion was now undertaken. Injections of la-belled norepinephrine were made rapidly intothe inflow tubing of the heart-lung prepara-tions. The whole blood concentration of nor-epinephrine as a time function was estimatedat the aortic root by interrupted sampling at2.25-second intervals and appropriate count-ing. The heart rate was continuously recordedduring this time as an analog curve. Thus in-put and output (response) of the system wereavailable as time functions.

The curve of the input concentration wasapproximated by linear segments of an elec-tronic function generator and used as theforcing function of an analog computer cir-cuit (fig. 3A). The square root mode of aquarter-square multiplier with proper attenua-tion was used to generate the nonlinear cali-bration curve relationship. One /ig/liter nor-epinephrine concentration and one beat perminute rate change were each scaled to onevolt. Time scaling was done for rapidity of re-peated solution. Suitable initial state voltageswere supplied for simulation of normal(C(0)=3.6 V) and reserpine pretreated(G(0 )=0V) preparations. A single computerunit-lag circuit was found satisfactory to trans-



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form the forcing function into a good repre-sentation of the rate response displayed ac-cording to the calibration transformation. Theunit-lag circuit solves a first order differentialequation with unity gain.

Repetitive solution was performed and thebest fit chosen by visual match on an oscillo-scope face. The only variable system param-eters were the coefficient A of the calibra-tion transformation and the time constant ofthe unit-lag circuit. These could be varied bychanging potentiometer settings.

The equations describing the simulating cir-cuitry are:

G(t) = F ( f ) - ( ! / « ) (dG/dt) (1)and R(t) = A\/G(t) + G(0) - R(0) (2)where F(t) = Aortic root norepinephrine

concentration time functionR(t) = Rate increase above base line

rateG(0) = Initial displacement on cali-

bration curve in /Ag/literR(0) = Initial rate displacement =

and

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G(t) = A time function defined in thefirst equation above

I /a = The natural time constant ofthe unit-lag circuit.

The correspondence between computer pre-dicted response and experimental results isseen in figure 4. The values of time constantsthat yielded good fits were between five andthirteen seconds. A quantitative description ofthe norepinephrine input-response transfer re-lation is thus available and must be satisfiedby the general system model.

The system response to transient increaseof tyramine concentration was now estab-lished by a similar method of aortic root samp-ling and rate monitoring. Because of the"cumulative" type of tyramine response totransients, it is clear that no steady state cali-bration could be performed as was done fornorepinephrine. Assuming that tyramine effectwas norepinephrine mediated, the norepi-nephrine static calibration transform was usedas the last stage in the tyramine computersimulation.

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Dashed line represents the time course of norepineph-rine concentration at the aortic root in micrograms perliter. Dotted line is the computer predicted responseaccording to equations 1 and 2. See text. Solid linerepresents the measured rate response of the realpreparations. Curve set A is from a normal and curveset B from a reserpinized preparation.

Computer parameters for set A: a =. 0.077, A =11.7, GO = 3.8; for set B: a = 0.167, A = 9.2, Go =0.0.

A computer circuit (fig. 3B) similar to thatused for norepinephrine simulation was usedfor tyramine effect simulation. A second seriesunit-lag circuit with a long time constant wasnecessary for satisfactory simulation. An activ-ity coefficient was introduced to relate tyra-mine-effect relation to that of norepinephrine.As would be expected this coefficient wasmuch attentuated in reserpinized preparations.

The equations describing the simulating cir-cuitry are:

G(t) = (BxF(t))-(l/a) (dG/dt) (3)H(t)=G(t)-(l/p) (dH/dt) (4)

and R(t)=Ay/H(t)+G(0)-R(0) (5)where F(t) = Aortic root tyramine concentra-

tion time function (/xg/Iiter)

B = An activity coefficient of ty-ramine

H(t) = A time function defined by thefirst two equations

and 1//3 = The natural time constant ofthe second unit-lag function.

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Figure 5 shows the correspondence betweenbiologic and computer simulated responsesfor the normal and reserpinized case. Attenu-ation on B in the reserpinized case is morestriking than one might assume by simplynoting the relative rate increase compared tonormal but this is explained by the relative"suprasensitivity" of the reserpinized prepa-ration to norepinephrine.

Constraints on a System Model

An analog of the system response to nor-epinephrine and tyramine must simulate theexperimentally derived information in all itsimportant aspects. Certain hypotheses maybe introduced and their value judged by theiruniqueness or lack thereof in producing acertain transform, the likelihood of such aproposed mechanism in a biologic system andfinally their potential for suggesting discrim-inating experimental designs.

The linear* and nonlinear elements of thesystem rate response as covered in the preced-ing sections must be reasonably approximatedby the system model. The mass-response char-acteristics, in terms of norepinephrine in thecoronary sinus efflux, must be considered.Thus, approximately 50% of norepinephrineentering the coronary arteries appear in thecoronary sinus and a very small concentrationof norepinephrine appears in the efflux aftertyramine administration. The observed "inter-action" between unbound norepinephrine andtyramine must be explained preferably with-out invoking a strategic liberation hypothesis.

MATHEMATICAL CONSIDERATIONS

If the modalities and magnitudes of therates of exchange of a substance among spaces

* In terms of Laplacian transfer function notationthe general system model must approximate the fol-lowing transforms for the linear part of the system;i.e., up to but excluding the nonlinear calibrationtransform:

aFor epinephrine: . >

c ,_ . Bafltor tyrarrune: —— —y

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FIGURE 5

Comparison of the real rate response (solid line) andthe computer predicted rate response (dotted line) totyramine. The computer solution is according to equa-tions 3, 4, and 5. Set C is from a normal and set Dfrom a reserpinized preparation.

Computer parameters: For set C: B = 0.177, A =10, a = 0.163, p = 0.0089, GO = 3.8; for set D: B =0.014, A = 10, a = 0.095, (3 = 0.0089, Go = 0.0.

can be numerically expressed, the amountsof that substance in the spaces as a functionof time are solutions of the simultaneous dif-ferential equations resulting from the exchangerate expressions. As the system increases incomplexity, hand solution becomes difficult,protracted, and often impossible. In such sys-tems the use of electronic analog computercircuitry to simulate the system may makesolution rapid and facile and allow repeatdisplay of the resultant of variation on prob-lem parameters. This section will set forththe rate expressions describing the proposedexchange system.

The exchange of norepinephrine will be de-scribed among three spaces in series: 1) in-travascular space, 2) receptor site space, 3)storage space.

The rates of change of mass in the intra-vascular space (V) are attributable to threefactors:

1) Norepinephrine entering in the inflowblood equal to the concentration-time function(CTF) of the amine in blood entering the in-travascular space multiplied by the bloodflow:

dV/Vt = CTF X Flow (6)

2) Norepinephrine leaving in the outflow



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blood. This was programmed as a single mixeddilutional volume with the rate of elution di-rectly proportional to the flow and inverselyrelated to the volume

ZV/&t = V X Flow/Volume (7)

3) Norepinephrine exchanging with recep-tor site space. This is programmed as a systemwith a partition coefficient greatly in favor ofmass transfer to receptor site space. RS is themass of norepinephrine in receptor site space.

dVfdt=-K(V-PxRS) (8)

where P is a small number and K is the rateconstant.

The total derivative of V may now be ex-

the type A + B ̂ AB with equilibrium greatlyin favor of formation of AB. This is secondorder from left to right and first order in re-verse. Defining total storage site mass asSmax, those occupied by norepinephrine asSo and those unoccupied as Se; clearly Smaxequals So plus Se.

3RS/3*=-K'(SE) (RS)+K"(So) (12)

The total derivative of RS can be ex-pressed:dRS/dt = K(V-PxEC)-K'(Se) (RS) +

K" (So) (13)

and the mass of norepinephrine in the receptorsite space at time t when the mass at time zerois RS (0) is given by the expression:

RS(t)=RS(O) K(V-PxRS)-K' (Se)(RS) + K" (So) dt (14)

pressed assuming there are no other signifi-cant pathways of norepinephrine in the vas-cular space:

dV/dt = Flow (CTF - V/Volume) -K(V-PXRS) (9)

and the mass of norepinephrine in the intra-

So(t)=So(0)

vascular compartment at time t, when the massat time zero is V(0), is given by the expres-sion:

The total derivative of stored norepineph-rine, So, is given by:

dSo/dt = K'(Se) (EC)-K"(So) (15)

and the mass of norepinephrine stored at timet when the mass stored at time zero is So(0)is given by the expression:

K'(Se) (RS)-K"(So)dt (16)

The drug tyramine is considered to be incompetition with norepinephrine for freestorage sites in a manner akin to the kinetics

V( t )=V(0)+ f Flow (CTF-V/Volume)-K(V-P xRS)d*J o

(10)

The rates of change of norepinephrine massin the receptor site space (RS) are attributedto two factors:

1) Norepinephrine exchange with intravas-cular space. Except for a change in sign thisis identical with the third partial derivativediscussed in reference to intravascular space.

=K (V-PXRS) (11)

2) Norepinephrine taken up by storagesites. This is treated as a reversible reaction of

of norepinephrine storage. Designating tyra-mine activity as Ty and tyramine filled stor-age sites as St, we have for the derivative oftyramine storage:

dSt/dt=K'(Se) (Ty)-K"(St) (17)

and the integral equation is of identical formas for norepinephrine.

The storage space equality now becomes:

Smax = Se + So+St (18)Note that tyramine is considered to be in

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CTF

FIGURE 6

Analog computer circuit for simultaneous solution ofequations 6 through 18. For norepinephrine depletion(reserpinized) simulation base line rate automaticallyapproximates + 1 and for normal simulation -f 20beats per minute. Appropriately scaled RS is concen-tration in the receptor site space and is used as theinput to the calibration curve circuit. This circuit andthat describing tyramine storage kinetics are omittedfrom the diagram for simplicity. CTF represents theconcentration time curve of norepinephrine input.Diagram notation is consistent with that of the equa-tions in the text with the exception of certain gaindesignations. QSM represents a quarter-square-multi-plier in the multiplication mode. Except where notedotherwise, gain is unity.

Parameters: G = 0.0833, F/V — 0.833, K = 0.0833,P — 0.06, Se = 4O, Sm = 80 (normal), 42 (reserpine),So — 40 (normal), 2 (reserpine), c — 0.023, a — b =44, K' = 0.005, K" = 0.005.

competition for storage with norepinephrinebut not for preferential accumulation in thereceptor site space.

RESPONSE OF THE COMPUTER MODEL

A computer circuit solving the equationsfor norepinephrine transfer is shown in figure6. By proper selection of system parametersrather good approximations of the drug in-put, rate output transformation can beachieved (fig. 7). Such a system has excellentconformity to the mass input-output relation-ship in allowing the appearance of approxi-mately half of infused norepinephrine at the"coronary sinus" and yet predicting the ap-pearance of only small concentrations oftyramine released norepinephrine at that siteeven when tyramine is exerting a sizeable rateincrease in a "preparation" with a normal com-plement of norepinephrine (fig. 8). No strate-gic release pathway is necessary to explain thediscrepancy between tyramine effect and thesmall amount of norepinephrine released.Further, such a system will demonstrate an"interaction" between tyramine and unbound

norepinephrine. By decreasing the rate ofstorage of infused norepinephrine, tyraminemay be seen to have a potentiating effect; anaction that is not attributable to release of nor-epinephrine from storage sites but that is infact a corollary of the proposed mode oftyramine release of norepinephrine. A simula-tion of such interaction is seen in figure 9.

Discussion

The analysis of a system by analog simula-tion implies that a model is sought that cor-responds in certain modalities to the realsystem behavior, given similar input pulsesand/or initial states. The dynamic similarityof input-output relations of the real systemand the model is no guarantee that the simula-tion is unique or that any component opera-tional units bear a one-to-one correspondenceto mechanisms in the real system. Dependingupon a knowledge of the mechanics of thereal system, the model may formally analogcertain known operational units. Complemen-tary mechanisms may then be proposed, al-ways under the constraint that the overallmodel conform to the real system behavior inall important respects. This may lead to uni-fying hypotheses and suggest the design ofexperimental approaches to the real system.Paradoxically, a model whose components areincompletely identified with objective cor-relates in the real system is the most useful;when all the mechanisms of the real systemare delineated the model reduces to an instru-ment of pedagogy. Models of the norepi-nephrine-tyramine interaction do not seem tobe in present danger of this latter fate.

Nonlinear responses of biologic systems topharmacologic agents are common phenome-na. Many of these responses demonstrate suc-cessively decreasing increments of responsefor linear increments of drug in the range ofdrug dosage of interest to the investigator.Thus, the pharmacologic literature is repletewith instances of "logarithmic" dose-responserelationships. In certain instances the pharma-cologic agent is present normally in the bio-logic system and maintains a base line level ofresponse. In such systems, the simple depletionof endogenous drug should produce certain

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T IME IN SECONDSFIGURE 7

Comparison of the response of the system model to the experimentally derived input-outputtransfer function for norepinephrine and tyramine in simulated normal (N) and reserpinized (R)preparations. Curve pair A is generated from an idealized norepinephrine input according toequations 1 and 2. Curve pair C is generated from the identical input by the system model(fig. 5). An excellent conformity of response is evident. Curve pair B is generated from anidealized tyramine input according to equations 3, 4, and 5. Curve pair D is generated fromthe system model in accordance with the equations describing tyramine competition fornorepinephrine storage sites. The system model tends to underpredict the magnitude oftyramine effect and yield somewhat later peak effects but is generally in good conformitywith the overall duration and magnitude of tyramine effect.

Parameters of the simulating systems: a = 0.111, p = 0.0089, B(N) = 0.104, B(R) = 0.008,SJN) — 40, SJR) = 2, otherwise as in figure 5.

predictable results. The base line level of re-sponse should be lessened if depletion is ofsufficient magnitude. The response to a giveninitial increment of administered drug shouldbe increased as compared with the undepletedbecause it operates over a portion of the dose-response curve having a steeper slope. Thenormal response curve should be in close con-formation to the upper portion of the curve

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FIGURE 8

Simulated coronary sinus efflux concentrations of nor-epinephrine in a "normal" preparation responding tonorepinephrine and tyramine with approximately

equal peak responses. Solid line represents the resid-ual exogenous norepinephrine appearing in thecoronary sinus blood after an injection of that drug.Dotted line represents the slower and smaller con-centrations appearing as the result of the release ofendogenous norepinephrine by tyramine.

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60-

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Curve pair A is the rate response recorded from areserpinized heart4ung preparation. Curve NEwas the result of a 15-second constant infusionof norepinephrine into the inflow tubing (total 2£ ing).Curve NE + TY resulted from an identical infusionexcept that one milligram of tyramine was rapidlyinjected midway during the infusion. Curve pair B isthe system model analog of these responses. Lowervalues than those realized experimentally are predictedfor both curves after 40 seconds since redrculation,

Circulation Riiwcb, Vol. XV, Aug*st 1964

from the more sensitive, depleted preparations.Within the limits of biological variability, thenorepinephrine chronotropic effects in thecanine heart-lung preparation demonstratethese attributes. The response is clearly non-linear, initial rates are lower in depletedpreparations which are "suprasensitive," andfinally the normal response and the upper por-tion of the depleted response are similar. Nomechanism for the nonlinearity itself is pro-posed in the present formulation. The relationis simply approximated by a satisfactory fittingand easily generated continuous function. Itis suggested, however, that no separate mecha-nistic hypothesis need be proposed to explaindepletion suprasensitivity but that the phe-nomenon may be viewed as a corollary of thesystem response nonlinearity.

Depletion of endogenous norepinephrine isnot the only possible mechanism that mightincrease sensitivity to exogenous amine.Mechanisms that might greatly decrease therate of storage of norepinephrine would bringabout suprasensitivity, e.g., reduction of freestorage sites or interference with the unknownmechanisms that bring about this storage.Suprasensitivity might then appear without asignificant alteration in the amount of storednorepinephrine. Similar mechanisms have beenproposed as a possible explanation for supra-sensitivity without storage depletion in thedecentralized nictitating membrane of the cat.0

In the canine heart-lung preparation tyra-mine rate responses and inotropic effects areconsistently later in reaching maximal valuesand of much longer duration as compared toresponses to norepinephrine.8 Aspects of thistemporal discrimination have been noticed bymany investigators but quantitative descrip-tion of the time course of these responses hasnot heretofore been set forth. Such analysisrequires a definition of the temporal course

allowed in the real experiment, was not simulated.Curve pair C illustrates the proposed mechanism

for tyramine "interaction" with unbound norepineph-rine. Values on the abscissa represent norepinephrineentering the system. Ultimately total storage is approx-imately the same but the relatively slower rate ofstorage in the presence of tyramine would explain thegreater and more prolonged effects of the infused nor-epinephrine.



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of drug entering the system and that its pres-entation and removal be relatively rapid com-pared to the time course of response. Theseconditions are most readily fulfilled in per-fused preparations. From the nature of thetransfer function for tyramine it is clear thatthe prolonged response to this drug is notsimply attributable to the recirculation of un-metabolized drug. With the exclusion of re-circulation, tyramine still has a much longertime course of response than norepinephrine.The release of norepinephrine from the heartby tyramine is slow and the increase incoronary sinus concentration is small.4 Basedupon a bio-assay, the response of aortic spiralstrips to bath fluid in which normal atria wereexposed to tyramine, Hall concluded thateither a large amount of the catechol amineliberated by tyramine is destroyed or that amuch smaller amount of endogenous materialthan of added norepinephrine is required toproduce the same effect.7 This prolonged re-lease of relatively small amounts of nor-epinephrine by tyramine while producing asizeable biologic response of long durationsuggests that the response characteristic mightbe the result of a capacitative mechanism fornorepinephrine in the receptor site space. Thisproposal taken with the assumption thattyramine competes for storage sites withnorepinephrine forms the major hypothetica]formulation upon which the system model isbased. The latter assumption is clearly a non-unique kinetic solution; reduction in the rateof norepinephrine storage by interference withthe processes of storage (reduction of K'in the model) would be equivalent to the re-duction of available storage sites (Se). Whilethe former possibility would not have a pre-dictable rate limitation the latter mechanismwould be at least rate limited by the timecourse of tyramine available for storage com-petition. In the latter case one would predicta significant amount of tyramine to be in-corporated into storage sites. In isolatedchromaffin granules the amount of releasedcatechol amine under the influence of tyra-mine is replaced stoichiometrically by an up-take of tyramine.10 In the rat heart, perfusionwith tyramine may result in a greater concen-

tration of that amine than of norepinephrineoriginally present.11 In addition, norepi-nephrine inactivation by catechol-O-methyltransferase, the major pathway of inactivationof tyramine released norepinephrine, is notinhibited by tyramine although its ability tometabolize the excess norepinephrine liberatedappears to be limited.12'18 Thus, the assump-tion of competition between the amines forstorage sites is supported by some direct evi-dence and there appears to be no significantnorepinephrine "potentiation" by the suppres-sion of normal metabolic pathways of inactiva-tion of tyramine. Since the amounts of tyra-mine stored in the heart are of sufficient mag-nitude to be consistent with the concept ofcompetitive storage, one would predict that acertain portion of the stored tyramine wouldbe released by increasing the norepinephrinecontent of the organ perfusate. Further in-vestigation on this point is clearly indicated.In addition, the study of the alteration byother agents of the response to norepinephrineand tyramine-like drugs, with regard to tem-poral aspects, may prove more profitable indefining the mechanism of alteration than themere recording of peak responses.

A kinetic model based upon these hy-potheses will demonstrate "interaction" be-tween tyramine and unbound norepinephrine.Smith concludes that since the action of ty-ramine may be enhanced in the presence ofincreased extracellular norepinephrine, itsaction may not be explained solely by anability to release norepinephrine from tissuestores.8 Viewed in the dynamic aspects pre-sented herein which reject the connotativeconfines of the term "release" in favor of amechanistic description, what is considered tobe the "normal" mode of tyramine action andthe "interaction" of tyramine and unboundnorepinephrine are two aspects of the samephenomenon. What is apparently an evocativeeffect in the normal mode becomes a per-missive effect when tyramine decreases therate of norepinephrine storage by occupyingstorage sites. This is most readily observed inthe absence of stored norepinephrine. Simula-tion of the permissive effect is demonstratedin figure 9.

Circulation Research, Vol XV, August 1964



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NOREPINEPHRINE AND TYRAMINE

Storage space inhomogeneity as first pro-posed by Trendelenburg is not simulated inthis model.14 Different half-lives have beendemonstrated for exogenous norepinephrineentering a smaller tyramine-releasable pooland that entering a larger tyramine-resistantpool with a slow transfer from the former tothe latter.6 Since the events simulated in thepresent formulation are relatively rapid thestorage space simulated may be assumed tobe the available or tyramine releasable por-tion. The capacity of the storage space cannotbe assigned a meaningful numerical value asthe values that enter the simulation are rateconstant-storage size products and cannot beseparately evaluated.

Presently, extrapolation from the chrono-tropic effects of the amines considered hereto other modalities of their biologic responsemust be cautious. The present study does sug-gest, however, that a system response analysismight be fruitful in a system in which re-sponse modality is a simply dependent varia-ble and can be continuously quantified.

Summary

An analog simulation of the chronotropiceffects of norepinephrine and tyramine in thecanine heart-lung preparation is presented.The temporal aspects of those responses aredescribed in quantitative terms.

Reserpine produced deprivation suprasensi-tivity to norepinephrine may be considered asa corollary of the system response nonlinearityto that drug.

Discrepancies between tyramine rate re-sponses and the relatively small amounts ofnorepinephrine released are resolved by theassumption that the receptor space for nor-epinephrine has a capacitative function andis not in free dilutional equilibrium with theperfusing blood. This mechanism would al-low for a unitary explanation of tyramine ac-tion based upon competition with norepi-nephrine for available storage sites.

AcknowledgmentThe authors are deeply grateful to Professor J.

Harold Bum and Dr. John M. Walker of Oxford,England, for advice and encouragement during the

Circulation Relttrcb, Vol. XV, August 1964

123

early phases of this investigation and to Mr. GeorgeC. Gundlach, Jr., and Mr. Harold Ling for invaluabletechnical assistance.

References1. BURN, J. H., AND RAND, M. J.: Action of sym-

pathomimetic amines in animals treated withreserpine. J. Physiol. 144: 314, 1958.

2. NASMYTH, P. A.: Some observations on the ef-fects of tyramine. In Adrenergic Mechanisms.Boston, Little, Brown and Company, 1960, pp.337-344.

3. SMITH, E. R.: The effect of norepinephrine in-fusions upon some responses of reserpinetreated spinal cats to tyramine. J. Pharmacol.Exptl. Therap. 139: 321, 1963.

4. CrrmsEY, C. A., HARBISON, D. C, AND BRAUN-

WALD, E.: Release of norepinephrine from theheart by vasoactive amines. Proc. Soc. Exptl.Biol. Med. 109: 488, 1962.

5. DAVEY, M. J., AND FARMER, J. B.: The mode of

action of tyramine. J. Pharm. Pharmacol. 15:178, 1963.

6. POTTER, L. T., AND AXELROD, J.: Studies on the

storage of norepinephrine and the effect ofdrugs. J. Pharmacol. Exptl. Therap. 140: 199,1963.

7. HALL, W. J.: The action of tyramine on the dogisolated atrium. Brit. J. Pharmacol. 20: 245,1963.

8. HOLMES, J. C , AND FOWLER, N. O.: Cardiac

effects of tyramine. Circulation Res. 11: 364,1962.

9. KIRPEKAR, S. M., CERVONI, P., AND FUHCH-

GOTT, R. F.: Catecholamine content of the catnictitating membrane following proceduressensitizing it to norepinephrine. J. Pharmacol.Exptl. Therap. 135: 180, 1962.

10. SCHUMANN, H. J., AND PHHXPPU, A.: Untersu-

chungen zum Mechanismus der Freisetzungvon Brenzcatechinaminen durch Tyramin.Naunyn-Schmiedeberg's Arch. Exptl. Pathol.Pharmakol. 241: 273, 1961.

11. AXELROD, J., GORDON, E., HERTTTNG, G., KOPIN,

I. J., AND POTTER, L. T.: On the mechanismof tachyphylaxis to tyramine in the isolatedrat heart. Brit. J. Pharmacol. 19: 56, 1962.

12. KOPIN, I. J., AND GORDON, E. K.: Metabolism of

administered and drug-released norepinephrine-7-H8 in the rat. J. Pharmacol. Exptl. Therap.140: 207, 1963.

13. CHIDSEY, C. A., KAHT.KR, R. L., KELMINSON,

L. L., AND BRAUNWALD, E.: Uptake and me-tabolism of tritiated norepinephrine in theisolated canine heart. Circulation Res. 12: 220,1963.

14. TRENDELENBURC, U.: Modification of the effectof tyramine by various agents and procedures.J. Pharmacol. Exptl. Therap. 134: 8, 1961.



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EDWARD J. BATTERSBY and ELLIOT V. NEWMANChronotropic Effects of Norepinephrine and Tyramine: A System Response Analysis

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chronotropic effects of norepinephrine and tyramine: a system

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