Figure 1.
Moth pheromone-sensitive sensillum trichodeum.
The sensillum is typically composed of two ORNs and three auxiliary cells (thecogen Th, trichogen Tr and tormogen To). The tight junctions between cells separate the ORN extracellular environment in two parts with different ionic compositions, the sensillar lymph bathing the outer dendritic segment (housing the transduction machinery) and the hemolymph bathing the inner dendrite and soma. Pheromone molecules enter the sensillar lymph through pores in the hair shaft. The sensillar potential SP (ORN electrical response to pheromone stimulation) is recorded between the active electrode, slipped on the cut hair tip in contact with the sensillar lymph, and the indifferent electrode in contact with the hemolymph. Fig. 2 gives an overview of the global electrical organization of the sensillum. Fig. 3 shows part of ORN membrane processes at the molecular level. Modified from [66].
Figure 2.
Compartmental model diagram of the moth pheromone-sensitive sensillum.
The outer dendrite of the ORN is divided into N compartments, the inner dendrite and soma are lumped into a single compartment and the three auxiliary cells are also lumped into one compartment. The equivalent circuit of each outer-dendritic compartment includes the conductances of the external (gec) and internal (gic) media and six transmembrane branches for the membrane capacitance (Cd), the leak current and four types of pheromone-dependent currents. Each current is described by a conductance and a constant battery figuring the reversal potential of the permeating ion. The leak current with its constant conductance (gld) and battery (Eld) is responsible for the resting potential. The four pheromone-dependent channels are the IP3-gated Ca2+ permeable channel (gCa, ECa), DAG-gated cationic channel (gcat, Ecat), Ca2+-gated chloride channel (gCl, ECl) and Na+/Ca2+ exchanger (gx, Ex). The equivalent circuit of the inner dendrite and soma includes three branches representing the membrane capacitance (Cs), the leak current (Gls, Els) and one pheromone-dependent Ca2+-gated K+ current (GK, EK). The equivalent circuit of the auxiliary cells includes two branches for the membrane capacitance (Ca) and the current (Ga, Ea) responsible for the transepithelial resting potential. The sensillar potential SP is measured between the recording electrode and the reference electrode.
Figure 3.
Pheromone transduction cascade.
Pheromone molecules in the air (Lair) are translocated through the sensillum lymph by pheromone binding proteins (PBP) and deactivated (from L to inactive product P) by enzymes (N). These extracellular processes were taken into account in the model as previously described in [45] and [18]. Activation by L of receptors (R*) activates in turn G-proteins (G*) then effector enzymes (E*) that cleave PIP2 in IP3 and DAG. These second messengers gate Ca2+ (ICa) and cationic (Icat) currents. The resulting increase in intracellular Ca2+ concentration triggers feedback control of E*, ICa and Icat via CaCaM and PKC* and feedforward gating of a Cl− current (ICl). Ca2+ concentration is regulated by the Na+-Ca2+ exchanger (NCX). The membrane is depolarized by currents Icat and ICl in the ORN outer dendrite (cylindrical compartment on left). It is repolarized by K+ (IK) and leakage (Ild, Ils) currents in the inner dendrite and soma (spherical compartment on the right).
Table 1.
Basic geometrical and electrical parameters of the sensillum model.
Table 2.
Geometrical and electrical parameters derived from Table 1.
Table 3.
Parameters of second messengers and ionic currents.a
Figure 4.
Simulation results of the complete 42-compartment sensillum model shown in Figs. 2and 3.
(A) Kinetics of the receptor potential at the ORN soma RPs. (B) Kinetics of the sensillar potential SP1 at the tip of the outer dendrite. (C) Height of RP along the ORN (from dendrite tip to soma). Compartment 41 is the inner dendrite and soma. In all plots, kinetics and heights of the potentials are shown at three pheromone uptakes: 10−4, 0.032 and 5.6 µM/s. Heights in C are taken at the maximum of the kinetics in A and B. The bars from 0 to 2 second along the time axis in A and B indicate the pheromone stimulation period.
Figure 5.
Dose-response characteristics of the receptor potential RP and sensillar potential SP of the complete 42-compartment model.
RP and SP in response to 2-s square pulses of pheromone at various uptakes from 10−4.75 to 101.5 µM/s. (A) Heights in mV. (B) Relative heights. (C) Half-maximum rising times (τrise). (D) Half-maximum falling times (τfall). RP is shown at three compartments located at the tip (RP1), mid-length (RP20) and base (RPb) of the outer dendrite, at the inner dendrite and soma (RPs). Predicted SP (−SP1) is compared to experimentally measured data SPexp provided by K.-E. Kaissling ([45], [56]).
Figure 6.
Effects of maximum conductance GMK on the response characteristics of RP at soma (RPs) and SP.
The repolarizing conductance GMK is the Ca2+- and voltage-dependent potassium conductance located at the inner dendrite and soma (the corresponding current IK is shown in Fig. 3). (A) The height of SP (solid lines) increases, while that of RPs (dashed lines) decreases with GMK respectively. (B) The ratio of amplitudes SP/RPs increases linearly with GMK at all uptakes. (C) The ratio of half-rising times of SP and RPs increases with GMK at low uptakes and becomes close to 1 at intermediate and high uptakes. (D) The ratio of the half-falling time of SP and RPs decreases with GMK at low uptakes and becomes close to 1 at intermediate and high uptakes. The vertical dotted lines indicate the reference value GMK = 1.6 nS given in Table 3.
Figure 7.
Dose-response characteristics of the major steps in the pheromone transduction cascade.
(A) Relative heights of activated pheromone receptor R* (green), effector enzyme E* (magenta), conductance of cationic and chloride channel at the dendrite gcat (dash-dotted blue) and gCl (solid blue), and receptor potential at the dendrite base RPb (red) as a function of stimulus uptake. The EC50's of R* (11.75), E*(2.0), gcat (0.0871), gCl (1.175) and RPb (0.069) are indicated (in µM/s). (B) Half-maximum rising times; at EC50's they are 0.70 s (R*), 0.68 s (E*), 0.08 s (gcat), 1.15 s (gCl) and 0.16 s (RPb). (C) Half-maximum falling times; at EC50's they are 1.40 s (R*), 1.35 s (E*), −1.6 s (gcat), 7.9 s (gCl) and 3.70 s (RPb). It becomes negative for gcat when it declines before the end of the 2-s stimulation (falling times are determined from the end of stimulation). The curves for RPb are the same as in Fig. 5. The differential equations and data for R* and E* are the same as in [18], the corresponding parameter values are given in [46] for R* and [49] for E*.
Figure 8.
Outer-dendritic compartment and equivalent lumped conductance of the simplified model.
(A) Replacement of the original six-branch circuit including four pheromone-dependent conductances (gCa, gcat, gCl and gx as described in Fig. 1) with an equivalent three-branch circuit with a single pheromone-dependent conductance gpj given by eq. (21). (B) Kinetics of gpj in the first compartment (gp1) located at the tip of the outer dendrite in response to 2-s square pulses yielding different uptakes regularly spaces by 0.5 log units from 10−4.75 to 101.5 µM/s. (C) Idem in the 40th compartment at the base of the outer dendrite (gp40). Heights of the kinetics were taken at their maximum (indicated with double arrow in next to last uptake).
Figure 9.
Dose-response characteristics of the simplified model with a single conductance gpj shown in Fig. 8.
Characteristics of gpj shown for three compartments located at tip (j = 1), mid-length (j = 20) and base (j = 40) of the outer dendrite. (A) Heights (log10 gpj) as a function of log10 U; can be fitted by line log10 gpj = 0.32 log10 U − 1.28 for U≤1. The mean values of gpj at minimum (U = 10−4.5 µM/s), end of the linear growth (U = 1) and maximum (U = 10−1.5) uptakes are 1.8×10−3, 5.6×10−2 and 9.6×10−2 nS respectively, as indicated by the dotted lines. (B) Relative heights, gpj/max(gpj) as a function of log U at the same locations as in A. (C) Half-rising times. (D) Half-falling times.
Figure 10.
Relative error on steady-state RP and SP depending on number N of outer-dendritic compartments.
RP at base of the outer dendrite (RPb) and SP determined in the simplified single-conductance model of Fig. 8. Relative error determined with respect to exact analytical values given by eqs (27) and (34) in Methods section. (A) At low total pheromone-dependent conductance Gp = 0.01 nS. (B) At high conductance Gp = 5 nS. The relative error increases with the amplitude of Gp and decreases with N. At high conductance Gp = 5 nS, it is greater than 22% for RPb with one compartment and becomes less than 1% for both RPb and SP with 40 compartments.
Figure 11.
Steady state and kinetics of RP in the single-conductance model.
(A) Steady-state RP along the outer dendrite for various values of the total pheromone-dependent conductance Gp. Comparison of simulated values for N = 40 compartments (solid lines) with analytical results given by eqs. (27) to (33) (dashed lines). (B) Kinetics of the transient state RP(t) close to tip of outer dendrite (X = 5.5 µm, tip is taken as X = 0) in response to step pulses of conductance Gp of various strengths. Comparison of simulated values with N = 40 compartments (solid lines) with analytical results (dashed lines) given by eqs. (38) to (41) based on an approximation correct only for small RP values. (C) Same at mid-length (X = 110 µm). (D) Same at the base (X = 220 µm).
Figure 12.
Conductance-response characteristic of RP and SP in the simplified multicompartmental model.
Characteristics along the outer dendrite (RP1, RP20 and RP40), at soma (RPs) and SP in response to 2-s square pulses of conductance Gp. (A) Heights. (B) Relative heights. (C) Half-rising times. (D) Half-falling times. The vertical dotted lines indicate the range of Gp from 6.4×10−2 to 4 nS corresponding to the pheromone uptake rang from 10−4.75 to 101.5 µM/s.
Figure 13.
Effects of geometric parameters on the steady-state RP at the base of the outer dendrite.
RPb shown in response to different values of the pheromone-dependent conductivity σp (in µScm−2). (A) Length of outer dendrite Ld. (B) Diameter of outer dendrite Di. (C) Diameter of hair lumen De. (D) Area of inner dendrite and soma Ss. (E) Area of apical membrane of auxiliary cells Sapi. (F) Area of basal membrane of auxiliary cells Sbas. The vertical dotted lines indicate the biologically realistic parameter values given in Tables 1 and 2.
Table 4.
Main time-dependent variables from stimulus to responses.a