GENERAL DISCUSSION Dr. B. L. Clarke (Alberta) said The cooperation between positive and negative feedback effects discussed by Franck shows up clearly in the linear steady state stability problem for chemical reaction networks. The necessary and sufficient conditions for the asymptotic stability of a linearized network are that the Hurwitz deter- minants are all positive. 1 have shown that each term in the Hurwizt polynomials can be interpreted as a product olfeedback loops. Negative terms are combinations of feed-back loops that cooperate to destabilize and positive terms are combinations which stabilize. The Hurwitz determinant can therefore be viewed as a mathematical algorithm for construct iiig all the combinations of feedback loops which are significant for stability and weighting them with coefficients and algebraic signs according to their importance and stabilizing or destabilizing character.Only one product of feedback loops is usually important at any one time. Franck has illustrated that the waveforms of oscillatory systems have portions which are dominated by various feedback loops. The reason for this can be under- stood from steady state stability analysis. Fast changing variables attain pseudo- steady states for given values of the slowly changing variables. The latter variables move slowly on a manifold which passes through regions of instability of the pseudo- steady state. In these regions the trajectory moves rapidly in a manner determined by the product of feedback loops which destabilize the pseudosteady state.Dr. R. Lefever (Brussels) said I must say that the necessity of two counteracting feedbacks positive and negative in order for a chemical system to produce an oscil- latory behaviour is not obvious to me or else that the definitions of negative and positive feedback are not so clear as it may seem. In the Brusselator there is indeed a step usually viewed as a positive (autocatalytic) feedback on the production of X but then no step can be associated with what would usually be called a negative feedback. Indeed what brings the concentration of X down during an oscillation is the fact that at the same time the autocatalytic step produces X and consumes Y. This consumption occurs at a rate proportional to X2 Y which cannot be matched by the linear Y production step (B +X -+ Y + D) if the concentration of X goes beyond a certain level.One thus sees that in a way the autocatalytic step is self inhibitory. On the other hand following the author’s rules since here both X and Y may have sharp breaks in the course of their oscillation both variables should be considered of the positive feedback type. As another illustration of the ambiguity between negative and positive feedback concepts I may perhaps mention the Yates-Pardee type of enzymatic chain regulation ; EO EI EZ En-1 A -+ X -+ X2 3 . . . -+ X B 3 Ot I In this chain of reaction the first enzyme of the chain Eo is inactivated by the end of chain product X,. This is generally considered as a purely negative feedback type of control.Nevertheless limit cycle behaviour can be observed in such systems. Dr. P.Rapp (Cambridge) said In his paper Franck notes the importance of time delays in allowing nonlinear feedback systems to oscillate. I would like to confirm B. L. Clarke J. Chern. Phys, 1974 60 1481. 215 21 6 GENERAL DISCUSSION the importance of this observation and also connect points raised by Auchmuty and Lefever in the discussion of this paper. Auchmuty has pointed out that if the dif- ferential equation contains terms with retarded arguments then it is possible for a system with a single variable to possess a stable periodic solution. As an example he cites the well known equation proposed by Hutchinson as a model for a fluctuating population dm --x(t)[l -Kx(t-T)].dt This equation has been investigated by Cunningham and Jones.3 1 would like to point out that the presence of time delays has an important effect on the stability properties of differential equations which describe phase shift oscillators mentioned by Lefever. Systems of this type consist of a sequence of reactions in which the first step is inhibited by the product of the last reaction. The most familiar class of differential equations describing these oscillations takes the following form (G~odwin,~ and Walter 5). = h(x,)-b,x ij= gj-lxj-l -bjxj ;j = 2 . . . n. For eqn (2) it can be shown that for an arbitrary nonlinear function h(x,) IZ is required for periodic solutions (Higgins and Rapp 7). Eqn (3) is the governing equation corresponding to eqn (2) where delays occur between each reaction.The constants Tj are positive real numbers. Pj = gj-1xj-1 -bj~j xj = yj(t-Tj) ; j = 2.. .IZ 1 Here it is possible to construct a one dimensional system which possesses a stable periodic solution. For example ; k dx --bx dt 1+ax(t-T)2 when k = 30 000 CI = 1 b = 1 T = 2 oscillates from xmin= 11.01 to xmax= 156.90 with period = 5.99. Clearly this is an extreme case which is valuable primarily as an object lesson. However such considerations are important when selecting between theoretical models of oscillatory processes. For example it can be shown * G. E. Hutchinson Ann N. Y. Acad. Sci. 1948,50,221. W. J. Cunningham Proc. Nat. Acad. Sci. 1954,40 708. G.S. Jones Interlinear Symposium on Nonlinear Differential Equationsand Nonlinear Mechanics ed. J. LaSalle and S. Lefschetz (Academic Press New York,1963). B. C. Goodwin Temporal Organization in Cells (Academic Press New York,1963). C. Walter Biochemical Regulatory Mechanisms in Eukaryotic Cells ed. E. Kun and S. Grisolia (Wiley Interscience New York 1971). J. Higgins R. Frenkel E. Hulme A. Lucas and G. Rangazas Biological and Biochemical Oscillators ed. B. Chance E. Pye A. Ghosh B. Hess (Academic Press New York 1973). 'P. Rapp FEBS (Federation European Biochemical Societies) General Meeting Budapest August 1974. GENERAL DISCUSSION that it is impossible to fiiid a set of physically realizable reactions Constants such that the following system oscillates i2 = gix1-62x2 (4) i3 = g2~2-b3~3 24 = 93~3-b4~4.However in the corresponding delayed system if c = Tl+T,+T3+T4 > 0 then it is possible to find reaction constants which give an oscillatory system. Dr. H. Tributsch (Bedin)said in his interesting review article Franck has demon-strated a remarkable similarity between artificial oscillating systems and a variety of non linear biological phenomena. In this connection it is interesting to note that there are apparently no simple model systems known which can simulate the property of biological receptors of modulating the frequency of excitable membranes according to the intensity of external physical and chemical stimuli. The transformation of continuous signals into spike patterns (pulse signals) is an important prerequisite for advanced data acquisition and processing methods.It would therefore be of considerable interest to develop technical detectors with digit a1 response . 10 N k8 light intensity 12%/ 100 'lo L 37 % 1 I I 1 I 1 0 I 0 5 10 15 20 25 30 35 40 45 time FIG.1 .-Influence of visible light on the oscillation behaviour of the system Cu2S-electrode/elec-trolyte+H202. Electrode potential -0.5 V against S.C.E. Our own experience with the development of a digital photodetector indicates that efforts in this direction might be promising. To achieve our aim it was necessary to find a suitable electrochemical oscillator with a light sensitive feedback mechanism. This condition was met by the new oscillating system Cu,S -electrode/electrode+HzOz.The light sensitive reactant (absorption between 400 and 600 nm) turned out to be an oxide bond on the electrode surface which is formed through the oxidizing action of hydrogen peroxide and which can be destroyed by a photo-electrochemical reaction. It is participating in an autocatalytical reaction which is crucial for the occurrence of the electrode current oscillations. Light can consequently be used to modulate the frequenc:y of these oscillations (fig. 1). Detectors of this type might become examples for a useful technical application of oscillating mechanism GENERAL DISCUSSION Dr. M. Blank (ONR London) said The ionic mechanism proposed by Shaslioua to account for the properties of a polycation w polyanion junction membrane can also explain the oscillations we have observed in a much thinner bilayer system.We formed the bilayers from decane solutions of cholesterol in contact with two identical aqueous phases containing NaCl and cetyltrimethylammonium bromide (CTAB). The resistance of these bilayers depended strongly upon the concentration of CTAB.l At low CTAB concentration the bilayer behaves as if it were negatively charged (probably as a result of adsorbcd anions) and as the CTAB concentration increases the bilayer becomes positively charged. The variation of the resistance with surface charge is in line with earlier experiments on mono1ayers.2 On passing current across bilayers formed in a range of CTAB concentrations around the point of zero surface charge we produced potential oscillations which we believe are due to the variations in CTA+ ion concentration that cause the bilayer to alternate between positive and negative surface charge.The concentration changes arise because of differences bet -ween the transport numbers of the aqueous phases and the bilayer. It should be possible to analyze the oscillatory behaviour of this bilayer system in terms of the physical properties of the components and the known behaviour of monolayer and interfacial systems. It may therefore serve as a model to elucidate the mechanism of oscillatory bioelectric phenomena involving ion flow in more complex biological systems. I would also like to point out that although oscillatory phenomena exist in bio- logical membrane systems excitation per se is not oscillatory.If we consider the prototype of an excitable cell a nerve axon the normal sequence is stimulus + de-polarization + potential reversal repolarization to complete the cycle. The cycle can be repeated but only with additional or continued stimuli. Oscillatory behaviour can be seen in the pacemaker cells of the cardiac muscle conduction system but these are specialized in as much as the membranes depolarize spontaneously with no externally applied stimulus. From an electrophysiological point of view these cells represent a special case where the membrane permeabilities to Naf and K+ ions do not stabilize on repolarization. Prof. P. Meares (Aberdeen) said On consideration of Shashoua’s paper it is not immediately obvious that the conformational “ shrinkage ” of a polyelectrolyte at high ionic strength would lead to an increase in the conductance or permeability of the membrane.The term shrinkage in this context refers to a decrease in the end-to- end vector of the polymer chains. Such a shrinkage does not require a decrease in the volume of the polymeric component such as would create pores. It is also un- certain whether the polyelectrolyte complex in the interaction zone of the c +a junction would respond to changes in ionic strength in the same way as a purely polycationic or purely polyanionic material. For these reasons I would like to offer for consideration an alternative mechanism of the periodic changes in conductance of the polyelectrolyte membranes.The material in the interaction zone is held together primarily by electrostatic attractions between polyanions and polycations (in this respect Ca2+ and Ba2+ can be regarded as polycations crosslinking polyanions by electrostatic forces). When during the passage of a current the salt concentration in the interaction zone is increased by the simultaneous arrival of Na+ and C1- from opposite sides the osmotic pressure in the interaction zone must increase. A point will be reached when this osmotic pressure is sufficient to overcome the electrostatic binding forces between the polyanions and G.W.Sweeney and M.Blank J. CulZoid Znterfuce Sci. 1973,42,410. I. R.Miller and M.Blank J. Colloid Interface Sci. 1968 26 34 GENERAL DISCUSSION polycations.These will then be forced apart adopting the Na-!-and Cl- ioiis respec-tively as their counterions by the incoming water i.e. the polyelectrolyte coinplex will be dissociated. The resulting conductance increase would cause the membrane to depolarize rapidly. Subsequent reformation of the polyelectrolyte complex by diffusion of NaCl away from the interaction zone would lead to a relatively slow recovery of polarization and the cycle of events would then be repeated. Dr. T. Keleti (Budapest)said 1 would like to make a comment coiicernirig one of the possible mechanisms of oscillations in biological systems. We are interested in the analysis of "three-body systems ",in which at least one substrate and two modifiers interact on the enzyme.These modifiers can be either one inhibitor and one liberator or two inhibitors. '* The liberator is a modifier which has no enect on the free enzyme but liberates the enzyme from the action of an inhibitor or a~tivator.~A peculiar effect can be shown in the case of certain types of inhibitions and liberations. One of these types is illustrated in fig. 1 as a function of liberator concentration its effect changes from partial liberation (i.e. inhibition) through complete liberation to activation. Competitive inhibitor non-competitive liberator If KSI KS,> 1 I --0s ILPIL'I -IL3=11'1 -lLl>Il!J FIG.1 .-Interaction of a non-competitive liberator with a competitive inhibitoi. Similar effects can be shown in the case of double inhibitions where different interactions between the substrate and/or inhibitors may appear (fig.2).4 One peculiar effect is the triple-faced enzyme-inhibitor relation. As a function of substrate concentration the antagonistic effect of the two inhibitors changes through the simple summation of their action to a synergetic effect (fig. 3).2 Moreover in the case of two partial inhibitors if the concentrations of the inhibitors and the substrate are higher than the "characteristic " one we obtain the inhibition paradox (fig. 4). In this case the initial rate of the enzyme in the presence of two inhibitors may be higher than in the absence of inhibit0rs.l. T. Keleti in Proc. 9th FEBS Meeting.Vol. 32. Symp. on Mechanism ofAcrion and Regulation of Enzymes (Akadtmiai Kiad6 Budapest and North-Holland Amsterdam 1975) ed.T. Keleti. Cs. Fajszi and T. Keleti in Mathematical Models of Metabolic Regulation ed. T. Krlei and S. Lakatos (Akademiai Kiado Budapest 1975). T. Keleti J. Theoret. Biol. 1967 16,337-355. T.Keleti and Cs. Fajszi Mathemat. Biosci, 1971,12,197. GENERAL DISCUSSION ESB I2 l-l(;. 3.-Schcnw of the general nicchanisni of double inhibitions. Triple-faced erlzyme inhibitor relation In the cuse of two purdy competltive lnhlbitors if f<oC<~ tihihrc of the two inhlYIIVI on the free enzyme n_ L Dc0:antagonism I/ K 0=IEIISI/ESl ~--IS]*lSoI -ISol=Ko (d-1) -ISI*ISo I-FIG.3.-The triple-faced enzyme-inhibitor relation. Assuming a linear chain of three enzymes where the substrate of the first enzyme is an inhibitor or liberator and the product of the third enzyme is the inhibitor of the second one we can obtain oscillations in the above-mentioned cases.This means that oscillations do not require the presence of an allosteric enzyme in the enzyme system. GENERAL DlSCUSSlON 22I Dr. H. Tributsch (Berlin) said As most researchers in the field are aware one must sometimes resist the temptation to interpret biological oscillations as true chemical oscillations. Periodic phenomena in complicated molecular structures such as sub- cellular and cellular systems may also be the consequence of a nonlinear energy con-version mechanism known as parametric energy coupling or variable parameter energy conversion. Parametric energy conversion proceeds through the periodical variation of an energy storing quantity (e.g.an electrical capacitance or an elastic constant) and is known to occur in all fields of physics both on the macroscopic and atomic levels (e.g. mechanism of a swing movements of a pendulum on a spring vibrating capacitor amplifiers or parametric amplifiers in electronics nonlinear (laser) optics the Raman effkct the parametric motor) (cf. N. Minorsky ref. (1)). An example of a parametric mechanism which could be operative in subcellular systems can easily be demonstrated with a physical model (fig. 1). If a pendulum is constructed with a piece of dielectric material and placed within the plates of a capacitor to which an alternating voltage is applied it will-under certain conditions- start oscillating and reach a stationary state of constant amplitude.A periodical FIG.1 .-Dielectric model of phenomenon of Bethenod. perturbation of a variable (energy storing) quantity (the capacitance) by a high fre- quency low aniplitude oscillation can thus lead to the generation of a low frequency high amplitude (capacity) oscillation. This type of parametric phenomenon which is difficult to understand in a purely intuitive way was first described by Bethenod with a model consisting of a coil carrying alternating current and a pendulum made of a piece of soft iron placed above it and has theoretically been investigated by Minorsky. By analogy with the phenomenon of Bethenod low amplitude relatively high frequency chemical oscillations (e.g.,of the type reported by Shashoua in protein membranes) could be the actual cause for the occurrence of pronounced low frequency (parametric) oscillations in subcellular (e.g.mitochondria) systems. It is suggested that a search for these faster oscillations of much lower amplitude should be made since parametric energy conversion has recently been proposed as playing a major role in membrane bound bioenergetical mechanisms. Dr. A. Boiteux (Dortmund)(communicated):Tributsch’s initial comment is perhaps based on a misunderstanding. We do not propose a sequence of simple chemical reactions as in glycolysis to cause oscillations in the mitochondria1 system. On the N. Minorsky in Nonlinear. Oscihtiortr (D. van Nostrand Inc. Princeton New York 1962) p.390 and p. 438. J. Bethenod Compr. Rend. 1338. 207. El. Tributsch J. Theor. bid. 1975 52 S47. GENERAL DISCUSSION contrary we have pointed out in our paper that the involvement of membrane per- meability and vectorial transport processes provide the necessary non-linearity for this parametrically controlled system. Compare also ref. (14) p. 354 cit. " The state of energy charge in the capacitor for the storage of chemical energy therefore is a controlling variable for the mitochondria1 oscillation. " Dr. A. Goldbeter (Rehovot)said Metabolic oscillations controlled by cyclic AMP in the slime mould Dictyostelium discoideum present a striking similarity to those observed in yeast glycolysis (see the communication of Boiteux and Hess at this Symposium for a detailed presentation of these oscillatory systems).In both cases models based on the molecular properties of the enzymes involved in the oscillatory mechanism indicate that periodic behaviour corresponds to a temporal dissipative structure i.e. to sustained oscillations of unique amplitude and frequency around a nonequilibrium unstable stationary state (see the communication of Nicolis and Pri- gogine at this Symposium). The models account for several experimental obser- vations in yeast and in the slime mould. In the following I briefly compare the predictions of the models with corresponding experiments and present evidence for a common molecular mechanism for sustained oscillations in the two systems. Glycolytic periodicities observed in yeast and muscle extracts as well as in single cells and cell populations of yeast originate from the activation of the allosteric enzyme phosphofructokinase by one of the reaction products.Recently Lefever and I analyzed a model for this reaction in the frame of the concerted transition theory of Moiiod Wyman and Changeux. The model considered is that of an open K-V system in which the product is a positive effector of the dimer enzyme. In the liomo- geneous case where diffusion is neglected this system is described by the following evolution equations for the substrate (a) and product (y) normalized concentrations (see ref. (3) and (6) for a definition of various parameters) da -= al-aM@ dt with The limit cycle behaviour of the model matches the oscillations observed in yeast extracts with a constant periodic or stochastic source of sub~trate.~ Qualitative and quantitative agreement is obtained in the model for the variation of period and ampli- tude in the oscillatory range of substrate injection rates which extends over one order of magnitude of parameter CT,,for the phase-shift exerted by the reaction product ADP and for the periodic change in enzyme acti~ity.~.' Thus in the middle of the G. Gerisch and B. Hess Proc. Nut. Acud. Sci. 1974 71,2118. B. Hess A. Boiteux and J. Kruger Adu. Enzyme Regul. 1969 7 149. A. Goldbeter and R. Lefever Bioplzys. J 1972 12 1302. J. Monod J. Wyman and J. P. Changeux J. Mol. Biol. 1965 12 88. .'I A. Boiteux A. Goldbeter and B.Eiess Proc. Nor. Acad. Sci. 1975 72 (IOj in thc press. A. Goldbeter and G. Nicolis Prugr. Tlreoret. Biol. 1975 4 in the press. GENERAL DISCUSSION unstable domain of o1 values the enzyme reaction rate v oscillates between 0.95 % and 73 % of the maximum rate V, with a mean value of 17.5 % VM(fig. 1). Experi-mentally Hess et al.' have reported a periodic variation of phosphofructokinase activity between 1 % and 80 % VM,with a mean value of 16 % V and an activation factor of 80 comparable to the factor 77 obtained theoretically. Further analysis of the model shows that the coupling between limit cycle behaviour and diffusion can give rise to propagating concentration waves at the supracellular level.2 t15 FIG.1.-Periodic variation of enzyme activity in the concerted allosteric model for the phospho- fructokinase reaction.The curve is obtained by integration of the evolution equations of a and y for u1 = 0.7/s k = O.l/s OM = 4/s L = lo6 c = E = c' = 8 = 1 (see text and ref. 6). The model for metabolic oscillations in Dictyosteliuin discoideum is based on the regulation of two membrane-bound enzymes involved in the synthesis of cyclic AMP namely ATP pyrophosphohydrolase and adenyl cyclase which transform ATP into S'AMP and CAMP,respectively (see ref. (8) and fig. 14 in the communication of Boiteux and Hess at this Symposium). The system is further coupled by a membrane-bound phosphodiesterase which transforms cyclic AMP into 5'AM P. Rossomando IIIIII 8 4E I '0 5 6 160-2 120-' ! I 1 I 1 02 0.3 0.4 05 0.6 0.7 UI Is-' FIG.2.-Variation of the period (7') and of the amplitude (A,) of noimalized cAMP concentration in the oscillatory domain of ATP injection rates ol in the model for the oscillatory synthesis of cAMP in D.discoideum (see text and ref.(8)). B. Hess. A. Boiteaux and J. Kruger Adv. Enzyme Regul. 1969 7 149. * A. Goldbeter Proc. Nat. Acad. Sci. 1973 70 3255. A. Goldbeter Nuture 1975 253 540. G. Gerisch and B. Hess Proc. Nut. Acud. Sci. 1974 71 2118. GENERAL DISCUSSION and Sussman have shown that cAMP activates ATP pyrophosphohydrolase whereas 5’AMP activates adenyl cyclase. In both cases regulatory interactions are highly cooperative pointing to the oligoineric structure of the enzymes.The variables considered in the model are the intracellular concentrations of ATP SAMP and CAMP. A stability analysis indicates that the cooperative and regul- atory properties of adenyl cyclase and ATP pyrophosphohydrolase can give rise to sustained oscillations in the synthesis of cyclic AMP around a nonequilibriuin unstable steady state.’ The oscillations have a unique amplitude and frequency and therefore correspond to a temporal dissipative structure. Simulations of the model as to the effect of continuous or discontinuous addition of CAMP match the observations of Gerisch and Hess in suspended Dictyosteliunz cells. It should be noted that sustained oscillations of intracellular cAMP may result through transport of this metabolite across the cell membrane in a periodic release of cyclic AMP into the extracellular medium.As cyclic AMP is the chemotactic factor in D.discoideum the mechanism for intracellular oscillations can also account for the periodic aggre- gation in this species of slime The pulsatory nature of cAMP oscillations in the model and the extreme stability of their period (fig. 2) correspond well to the observation that centre-founding cells in D.discoideunz aggregation release pulses of cyclic AMP with a period of 3-5 min.4 Both the pulsatory nature of the oscillations and the stability of the period with respect to a variation of enzyme parameters or environmental constraints (influx of substrate protein concentration etc.) result from the allosteric properties of the enzymes involved in the oscillatory mechanism as in the case of phosphofructokinase for glycolytic oscillations.A further similarity between these oscillatory systems becomes apparent when noting that in the absence of ATP pyrophosphohydrolase the mechanism of CAMP-controlled oscillations in the slime mould reduces to that of oscillating glycolysis of yeast and muscle.2 Thus the molecular basis of periodic behaviour is identical in the two metabolic systems both phosphofructokinase and adenyl cyclase are allosteric enzymes under positive feedback control. Dr. A. Winfree (Indiana) said Hanusse Noyes Tributsch and Goldbeter have independently used visible light or an injected reaction intermediate to test the limit- cycle stability of an oscillating reaction.In order to compare his analytic model for glycolysis with Pye’s corresponding experimental determinations Goldbeter went a step further he measured the inflicted phase shift after recovery to the limit cycle as a function of the original phase when ADP was injected. Is it too ambitious to suggest that consumable intermediates light thermal shock or even a differently-phased volume of the same oscillating reaction could be used as transient perturbations to measure new phase as a function of old phase? Particularly in the latter case this would allow us to approach chemical dynamics from a quite new perspective via some remarkably general theorems rccently proved by Guckenheimer in response to similar conjectures by Winfree. These theorems describe a variety of topologically-inescapable singularities and discontinuities which should be conspicuous in those measurements.The arrangement of these features reveals some thing about the reactions’ dynamical organization about the number of critical reactants and of stationary states about their stability properties etc. Such * E. F. Rossomando and M. Sussman Proc. Nat. Acad. Sci. 1973,70 1254. A. Goldbeter Nature 1975 253 540. G. Gerisch and B. Hess Proc. Nut. Acad. Sci. 1974 71 21 18. G. Gerisch Curr.. Top. Derd. Biol. 1968 3 157. .I. Guckenheitnct J. Mcrtli. Bid. 1975 I 259. GENERAL DISCUSSION measurements have begun to bear fruit in oscillating biological systems such as glycolysis the circadian “ clock ” * and the mitotic cell cycle.3 Why not in physical chemistry? Dr.Th. Plesser (Dortmund) said Goldbeter’s description of biochemical oscilla- tions by the concerted model of Monod Wyman and Changeux can be generalized very easily to the case of n promoters. The linear stability analysis gives the following results For all n there is only one stationary state in the positive quadrant of the phase plane. If the product is an allosteric inhibitor of the enzyme then the stationary state is always stable. If the product is an allosteric activator then the stationary state may be stable or unstable and give rise to self excited oscillations. The stationary state in the positive quadrant can never be a saddle point if the input rate of substrate is lower than the maximum velocity of the enzyme.If the number of protomers is odd there is only one stationary state. For even n there is a second one for negative and therefore unphysical con- centration. Numerical analysis shows that the oscillatory domain is not very sen-sitive to the number of protomers. A. T. Winfree Arch. Biochem. Biophys. 1972 149 388. ’A. T. Winfree Nature 1975 253 315. S. A. Kauffman private communication. S9-8