Chemical Senses Vol. 29 No. 6 © Oxford University Press 2004; all rights reserved
Dose–Response Relationships in an Olfactory Flux Detector Model Revisited
1 Max-Planck-Institut fuer Verhaltensphysiologie, Seewiesen, 82319 Starnberg, Germany and 2 Unité de Phytopharmacie et Médiateurs chimiques, INRA 78026 Versailles Cedex, France
Correspondence to be sent to: Prof. Dr. Karl-Ernst Kaissling, Max-Planck-Institut fuer Verhaltensphysiologie, Seewiesen, 82319 Starnberg, Germany. E-mail: Kaissling{at}mpi-seewiesen.mpg.de
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Abstract |
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 Top Abstract Model of a flux...Dose-response relation at...Dose-response at pulsed...AcknowledgementsReferences |
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A simple model of an odorant flux detector including odorant uptake, activation of odorant receptor molecules and enzymatic odorant deactivation can produce different types of static dose–response relationships. Depending on the binding characteristics of the odorant to the receptor molecule and to the deactivating enzyme, the receptor occupation by the odorant as related to the odorant uptake is quasi-hyperbolic, linear or, close to saturation, steeper than linear. In Rospars et al. (2003, Chem. Senses, 28: 509–522) a note contributed by both of us stated erroneously that an equation describing these relationships given previously (Kaissling, 1998, Chem. Senses, 23; 99–111; Kaissling, 2001, Chem. Senses, 26: 125–150) was incorrect. We show here that the difference in equations was due to a simplifying assumption in Rospars et al. (2003) about the deactivating enzyme, we summarize briefly the properties of the correct equation of Kaissling (1998, 2001) and we discuss the relation with the model studied in Rospars et al. (2003).
Key words: chemoreceptors, dose–response relationships, flux detectors, odorant deactivation, pulsed odorant stimulation, receptor occupation modeling
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Model of a flux detector |
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TopAbstractModel of a flux...Dose-response relation at...Dose-response at pulsed...AcknowledgementsReferences |
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Olfactory organs which adsorb from the air space but do not desorb odorant molecules need a mechanism for odorant deactivation in order to avoid accumulation of active stimulus molecules at the receptor cells. Here, we consider a network of chemical reactions including the uptake of the odorant or ligand L, its reversible binding to a receptor R, the reversible change of the complex LR to an activated state LR' (Minor and Kaissling, 2003
), a reversible binding of L to a hypothetical deactivating enzyme N, and an irreversible odorant deactivation by changing of the complex LN to P + N (Figure 1).
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This is a slightly extended version of the network considered in Kaissling (1998
, figure 7) where the activation of the complex LR was not included. In the 1998 network the deactivating enzyme was called E. The present network is a simplified version of the system of Kaissling (2001, figure 1) since the complex FBred (Kaissling, 2001) of pheromone and binding protein (PBP) is considered here as ligand L and since the pheromone degrading enzyme is neglected. This simplification is possible since in the 2001 model the pheromone adsorbed by the olfactory hairs is rapidly bound to the PBP and thereby largely protected from degradation by a pheromone degrading enzyme. It should be noted that the degrading enzyme (called E in Kaissling, 2001) is not to be confused with the above deactivating enzyme N. The latter was postulated since the deactivation process shows significant saturation at high odorant uptake. The concentration of the seven species or states considered are denoted between brackets: [L], [R], [LR], [LR'], [N], [LN], [P].
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Dose–response relation at constant stimulation |
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TopAbstractModel of a flux...Dose-response relation at...Dose-response at pulsed...AcknowledgementsReferences |
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The correct equation for static dose–response relationships is (cf. Kaissling, 1998
, equation 18; 2001, equation 4)
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with
the maximum concentration of activated receptor LR' (see Rospars et al., 2003, equation B4);
the dissociation constant of ligand and receptor;
the Michaelis constant of ligand and deactivating enzyme;
the total concentration of deactivating enzyme;
the total concentration of receptor molecules, where
(see Kaissling, 2001, equation A26; Rospars et al., 2003, equations B1 and B2); U, the odorant uptake (measured as concentration per s of odorant taken up);
the odorant uptake at which [LR] = [LR']max.
According to equation (1), the static value of [LR']/[LR']max depends on the uptake U and on the quantity
The dose–response relationships differ in three cases, K < 1 (receptors half-saturate at lower U than enzyme), K = 1 and K > 1 (enzyme half-saturates at lower U than receptors). The relationships for the three cases are shown in semilog (Figure 2a) and log–log plots (Figure 2b). For U << Usat, the relationship between [LR'] and U is linear; in all three cases it is
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The relationships differ from each other when U approaches Usat. For K < 1 the relationship saturates similarly to a hyperbolic one, for K = 1 it remains linear, and for K > 1 it becomes steeper than linear. All dose–response curves end at U = Usat where N works with maximum velocity. At U > Usat the deactivation process is overloaded by the ligand. No equilibrium between odorant uptake and deactivation can be reached, and the ligand concentration [L] increases permanently.
In Kaissling (2001) it was assumed that K = 1, i.e. that receptor molecules and deactivating enzyme half-saturate at the same ligand concentration. (The same relation holds true numerically in Rospars et al., 2003.)
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Dose–response at pulsed stimulation |
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TopAbstractModel of a flux...Dose-response relation at...Dose-response at pulsed...AcknowledgementsReferences |
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In Rospars et al. (2003
) the model of Kaissling (2001) was studied for examining its responses to pulsed stimulation. For simplicity it was assumed that the enzyme N is an ‘external species, i.e. with constant concentration despite entering in different reactions, in contrast to R, whose free amount is decreased by bound and activated states’ (Rospars et al., 2003, p. 520). A similar assumption was made in the ‘generalized flux detector’ model in Rospars et al. (2000), an intermediate between concentration and flux detectors. With this assumption (not made by Kaissling, 1998, 2001) an equation of the static dose–response relation similar to equation (1) was obtained, except that the –1 term was missing. This equation exclusively produces true hyperbolic dose–responses (Figure 3a, dashed line).
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The exact solution and the approximated one (assuming N is an ''external species'') are compared for constant stimulations in Figure 3a, and for pulsed ones in Figure 3b. These figures show, as expected, that using the simplifying assumption affects the conclusions about the responses to both constant and pulsed stimulations but only at high values of stimulus uptake, i.e. when concentration of the complex LN becomes high. With constant stimulation the exact and approximated solutions are identical for uptake values U up to 5 µM/s. With periodic pulses of 20 ms duration, they are identical for pulse heights UH up to 100 µM/s. In particular, the quantitative results given on the average concentration and amplitude of [LR'] under pulsed stimulation (50 ± 4 molecules at 2 Hz; see Rospars et al., 2003
, table 4) remain unchanged, the pulse height used being 0.1 µM/s. Therefore, whether N is considered as an external species or not, the conclusion that the network can resolve repetitive pulses at 2 Hz but not at 10 Hz still holds true. |
Acknowledgements |
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We thank Dr Alexander V. Minor, Moscow, Russia, and Dr Petr Lansky, Prague, Czech Republic, for checking the derivation of equation (1) and for useful remarks on a previous version of this paper. We also thank our referees for valuable suggestions.
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References |
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TopAbstractModel of a flux...Dose-response relation at...Dose-response at pulsed...AcknowledgementsReferences |
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Kaissling, K.-E. (1998) Flux detectors versus concentration detectors: two types of chemoreceptors. Chem. Senses, 23, 99–111.
Kaissling, K.-E. (2001) Olfactory perireceptor and receptor events in moths: a kinetic model. Chem. Senses, 26, 125–150.
Minor, A.V. and Kaissling, K.-E. (2003) Cell responses to single pheromone molecules may reflect the activation kinetics of olfactory receptor molecules. J. Comp. Physiol. A, 189, 221–230.
Rospars, J.-P., Krivan, V. and Lansky, P. (2000) Perireceptor and receptor events in olfaction. Comparison of concentration and flux detectors: a modeling study. Chem. Senses, 25, 293–311.
Rospars, J.-P., Lansky, P. and Krivan, V. (2003) Extracellular transduction events under pulsed stimulation in moth olfactory sensilla. Chem. Senses, 28, 509–522.
Accepted May 6, 2004
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