We present electrical, physiological and molecular evidence for substantial electrical coupling of epithelial cells in Malpighian tubules via gap junctions. Current was injected into one principal cell of the isolated Malpighian tubule and membrane voltage deflections were measured in that cell and in two neighboring principal cells. By short-circuiting the transepithelial voltage with the diuretic peptide leucokinin-VIII we largely eliminated electrical coupling of principal cells through the tubule lumen,thereby allowing coupling through gap junctions to be analyzed. The analysis of an equivalent electrical circuit of the tubule yielded an average gap-junction resistance (Rgj) of 431 kΩ between two cells. This resistance would stem from 6190 open gap-junctional channels,assuming the high single gap-junction conductance of 375 pS found in vertebrate tissues. The addition of the calcium ionophore A23187 (2 μmol l–1) to the peritubular Ringer bath containing 1.7 mmol l–1 Ca2+ did not affect the gap-junction resistance, but metabolic inhibition of the tubule with dinitrophenol (0.5 mmol l–1) increased the gap-junction resistance 66-fold,suggesting the regulation of gap junctions by ATP. Lucifer Yellow injected into a principal cell did not appear in neighboring principal cells. Thus, gap junctions allow the passage of current but not Lucifer Yellow. Using RT-PCR we found evidence for the expression of innexins 1, 2, 3 and 7 (named after their homologues in Drosophila) in Malpighian tubules. The physiological demonstration of gap junctions and the molecular evidence for innexin in Malpighian tubules of Aedes aegypti call for the double cable model of the tubule, which will improve the measurement and the interpretation of electrophysiological data collected from Malpighian tubules.

Malpighian tubules of insects initiate the formation of urine by secreting fluid into the blind-ended (distal) segment of the tubule. The distal segment of the Malpighian tubule in the yellow fever mosquito, Aedes aegypti,consists of two types of epithelial cells: principal cells and stellate cells,with a relative distribution of 5:1(Satmary and Bradley, 1984; Yu and Beyenbach, 2004). Nevertheless, principal cells make up more than 90% of the tubule mass owing to their large size (Beyenbach,2001; Wu and Beyenbach,2003; Yu and Beyenbach,2004). Principal cells mediate transepithelial secretion of K+ and Na+ from the hemolymph to the tubule lumen by active transport (Beyenbach,1995; Beyenbach,2001; Beyenbach,2003b). Current–voltage plots of a single principal cell in the intact Malpighian tubule indicate rather low cell input resistances which,compared to the transepithelial resistance, suggest the electrical coupling of 5–6 principal cells (Masia et al.,2000). Moreover, voltage recordings from two or more adjacent principal cells of the same tubule are strikingly similar in amplitude and frequency under control and experimental conditions, which is consistent with electrical coupling.

There are two pathways for the electrical coupling of principal cells. One pathway leads through gap junctions; the other passes through the apical membrane of one cell into the tubule lumen and then across the apical membrane into the neighboring cell. Thus, gap junctions couple neighboring cells directly, whereas the tubule lumen couples them indirectly. Although insects do have gap junctions (Phelan,2005; Phelan et al.,1998), their presence in Malpighian tubules has not been established to this date.

In the present study we ascertain the functional presence of gap junctions between principal cells of Malpighian tubules of the yellow fever mosquito. The gap junctions permit the passage of current from one cell to the next, but they prohibit the passage of the dye Lucifer Yellow. Metabolic inhibition of the tubule, which is known to reduce intracellular ATP concentrations(Wu and Beyenbach, 2003) and to halt transepithelial electrolyte and fluid secretion(Beyenbach and Masia, 2002; Beyenbach et al., 2000b; Pannabecker et al., 1992),increases the gap-junction resistance 66-fold, consistent with gap-junction gating by ATP. Furthermore, PCR studies on cDNA derived from AedesMalpighian tubules reveal the expression of four innexin-like transcripts.

### Mosquitoes and Malpighian tubules

The colony of mosquitoes Aedes aegypti L. was maintained as described previously (Pannabecker et al.,1993) except for feeding larvae with TetraMin™ Tropical Flakes ground manually with mortar and piston. On the day of the experiment a female mosquito (3–7 days post-eclosion) was cold-anesthetized and decapitated. A Malpighian tubule was removed under Ringer solution from its attachment to the gut and transferred to a Lucite™ perfusion chamber containing 1.0 ml Ringer solution. The bottom of the chamber was covered with thinly stretched ParafilmM' (American National Can, Greenwich, CT, USA), to which Malpighian tubules adhere and stabilize for the impalement of principal cells with microelectrodes. The tubules were viewed from above at ×50 magnification using a stereomicroscope (Wild, Heerbrugg, Switzerland).

### Ringer solution and drugs

Ringer solution contained the following in mmol l–1: 150.0 NaCl, 25.0 Hepes, 3.4 KCl, 1.8 NaHCO3, 1.0 MgCl2, 1.7 CaCl2 and 5.0 glucose. The pH was adjusted to 7.1 with NaOH. The osmolality of the Ringer solution was approximately 320 mosmol kg–1 H2O. Synthetic leucokinin-VIII was a gift from Ron Nachman (USDA, Texas A&M University).

### Electrophysiological studies

As shown in Fig. 1, three adjacent principal cells of a Malpighian tubule were selected for impalement with conventional microelectrodes. Principal cell 1 typically was 5–10 cells away from the blind (distal) end of the tubule, and principal cells 2 and 3 were downstream towards the open-end of the tubule. Principal cell 1 was impaled with both current and voltage microelectrodes. The latter measured the basolateral membrane voltage (Vbl1) as well asΔ Vbl1 when cell 1 was voltage clamped to a hyperpolarizing voltage of 40 mV for 50 ms. Principal cells 2 and 3 were each impaled with a voltage microelectrode for the measurement of Vbl2 and Vbl3, respectively, and theirΔ Vbl when cell 1 was voltage clamped.

Stellate cells are too small for impalement with microelectrodes. Accordingly, electrical coupling could be studied only between principal cells. Moreover, we selected for study principal cells that made direct physical contact with no obvious signs of stellate cells between them. Nevertheless, we cannot entirely rule out coupling to stellate cells. As will be shown in the Results, the contributions of stellate cells to the axial coupling of principal cells can be considered minor.

Fig. 1.

Block diagram for investigating electrical coupling of principal cells through gap junctions in isolated Malpighian tubules. Cell 1 was voltage clamped at a desired command voltage and the voltage deflections in cells 1, 2 and 3 were recorded. The input resistance Rinput of cell 1 was calculated from the values of (1) current injected into cell 1 to hold it at the desired command voltage, and (2) the change in the basolateral membrane voltage of cell 1 (ΔVbl1).

Fig. 1.

Block diagram for investigating electrical coupling of principal cells through gap junctions in isolated Malpighian tubules. Cell 1 was voltage clamped at a desired command voltage and the voltage deflections in cells 1, 2 and 3 were recorded. The input resistance Rinput of cell 1 was calculated from the values of (1) current injected into cell 1 to hold it at the desired command voltage, and (2) the change in the basolateral membrane voltage of cell 1 (ΔVbl1).

Microelectrodes (Omega dot borosilicate glass capillaries, 30-30-1;Frederick Haer & Co., St Bowdoinham, ME, USA) were pulled on a programmable puller (Model P-97; Sutter Instruments, Novato, CA, USA) to yield resistances of 20–30 MΩ when filled with 3 mol l–1 KCl. The microelectrodes were bridged to the measuring hardware using Ag/AgCl junctions that were prepared by first degreasing the silver wire with alcohol, and then by Cl-plating it in 0.1 mol l–1 HCl for 20 min at a current of 50 μA. The bath was grounded with the Ag/AgCl junction lodged in a 4% agar bridge of Ringer solution.

The electronic hardware consisted of (1) the Gene Clamp model 500B voltage and patch clamp amplifier, (2) head stage HS-2A gain 10MGU for current injection, and (3) head stage HS-2A gain 1LU for voltage recording (all from Axon Instruments, Sunnyvale, CA, USA). Voltage deflections in principal cells 2 and 3 were recorded using custom-made high-impedance amplifiers (Burr-Brown,1011 Ω). We used Clampfit (pClamp 9) for data analysis (Axon Instruments).

All current and voltage data were digitized with the aid of a computer and the A/D converter DigiData1332x (Axon Instruments). Current and voltage data from principal cell 1 were also displayed on an oscilloscope (Iwatsu, Tokyo,Japan) and on a strip chart recorder (model BD 41; Kipp and Zonen, Crown Graphic, Totnes, Devon, UK).

### Circuit analysis

The transepithelial secretion of electrolytes in Malpighian tubules of Aedes aegypti can be modeled using an electrical circuit consisting of two major transepithelial transport pathways; one is active, and the other is passive (Fig. 2). Na+ and K+ must take the active transport pathway through principal cells that provide the energy for moving the two cations against their electrochemical potentials into the tubule lumen. The active transport pathway consists of the electromotive forces (E) and the membrane resistances (R) at apical (a) and basolateral (bl)membranes. The passive pathway is located outside principal cells and is represented by the single shunt resistance Rsh(Fig. 2B).

In the past we have modeled the Malpighian tubule as a simple electrical cable with only one axial resistance, i.e. the core resistance Rco as shown in Fig. 3A (Beyenbach,2003b; Beyenbach and Masia,2002; Pannabecker et al.,1992; Pannabecker et al.,1993; Scott et al.,2004; Wu and Beyenbach,2003; Yu and Beyenbach,2002). In the present study, we model the Malpighian tubule as a cable with two parallel axial resistances, the resistance of the tubule lumen(Rlu) and the gap-junction resistance(Rgj) as shown in Fig. 3B.

To obtain values of Rgj, we simplified the equivalent electrical circuit of Fig. 3Bby taking advantage of the known effects of the diuretic hormone leucokinin-VIII on the tubule. Leucokinin-VIII is known to nearly short circuit the transepithelial voltage by decreasing the paracellular shunt resistance (Rsh) from 57.8 Ωcm2 to 9.9Ωcm2, thereby decreasing the transepithelial voltage(Vt) from 59 mV to 6 mV(Pannabecker et al., 1993). If we assume that both Rsh and Vtcollapse to zero in the presence of leucokinin-VIII, then the short-circuit assumption' eliminates Rsh from the circuit, thereby placing the tubule lumen at the same ground potential as the peritubular bath. The tubule lumen is thus eliminated as a current path to adjacent principal cells, leaving the gap-junction resistance (Rgj) as the only axial resistance. The value of Rgj is determined as follows.

Fig. 2.

Transepithelial secretion of NaCl and KCl by Malpighian tubules of the yellow fever mosquito. (A) Minimal molecular transport model. Electroneutral Na/H exchange and a cAMP-activated Na+ conductance allow the entry of Na+ from the hemolymph into principal cells. K+enters via K+ channels. Na+ and K+are moved across the apical membrane via a hypothetical cation/H exchanger that in turn is driven by the transmembrane H+electrochemical potential generated by the vacuolar type H+-ATPase located in the apical membrane. The lumen-positive transepithelial voltage generated by transcellular Na+ and K+ secretion drives the transepithelial secretion of Cl through the paracellular pathway. (B) Minimal electrical transport model that illustrates the active transport pathway through the cell and the passive transport pathway between the cells. Basolateral (bl) and apical (a) membranes are represented by an electromotive force (E) and a resistance (R). The paracellular resistance is represented by the shunt resistance Rsh.

Fig. 2.

Transepithelial secretion of NaCl and KCl by Malpighian tubules of the yellow fever mosquito. (A) Minimal molecular transport model. Electroneutral Na/H exchange and a cAMP-activated Na+ conductance allow the entry of Na+ from the hemolymph into principal cells. K+enters via K+ channels. Na+ and K+are moved across the apical membrane via a hypothetical cation/H exchanger that in turn is driven by the transmembrane H+electrochemical potential generated by the vacuolar type H+-ATPase located in the apical membrane. The lumen-positive transepithelial voltage generated by transcellular Na+ and K+ secretion drives the transepithelial secretion of Cl through the paracellular pathway. (B) Minimal electrical transport model that illustrates the active transport pathway through the cell and the passive transport pathway between the cells. Basolateral (bl) and apical (a) membranes are represented by an electromotive force (E) and a resistance (R). The paracellular resistance is represented by the shunt resistance Rsh.

We begin with the tubule modeled as the double cable in Fig. 4A, where gap junctions and the tubule lumen present two parallel axial resistances along the length of the tubule. The transepithelial short circuit induced by leucokinin eliminates the paracellular shunt resistance (Rsh) and places the resistances of the apical membrane (Ra) and the tubule lumen (Rlu) in parallel to the resistance of the basolateral membrane Rbl(Fig. 4B). Representing these two parallel resistances as the single non-junctional resistance(Rnj) yields a circuit consisting of Rnj and the gap-junction resistance(Rgj) alone. The two resistances Rnjand Rgj are determined as follows.

Fig. 3.

The Malpighian tubule modeled as a single electrical cable (A) and as a double cable (B). In the single cable model, the single core resistance(Rco) is the axial resistance along the length of the tubule. It includes the tubule lumen and epithelial cells. In the double cable model, there are two axial resistances: the gap-junction resistance(Rgj) and the lumen resistance (Rlu). E, electromotive force; R, resistance; a, apical membrane;bl, basolateral membrane; sh, paracellular shunt pathway.

Fig. 3.

The Malpighian tubule modeled as a single electrical cable (A) and as a double cable (B). In the single cable model, the single core resistance(Rco) is the axial resistance along the length of the tubule. It includes the tubule lumen and epithelial cells. In the double cable model, there are two axial resistances: the gap-junction resistance(Rgj) and the lumen resistance (Rlu). E, electromotive force; R, resistance; a, apical membrane;bl, basolateral membrane; sh, paracellular shunt pathway.

As shown in Fig. 4C, the current injected into principal cell 1 (to voltage-clamp Vbl1) can take three routes. One route is through Rnj1 to ground; the second route is from cell 1 to the upstream principal cell Rgj1′; and the third route is downstream to principal cells through Rgj1. If the characteristics of all the cells are assumed to be the same, then the gap-junction current passing into upstream and downstream cells will be the same (Fig. 4C), and the current injected into principal cell 1 (Iinject) is the sum of three currents (Eqn 1):
$\ I_{\mathrm{inject}}=2I_{\mathrm{gj}1}+I_{\mathrm{nj}1},$
(1)
where Igj1 is the gap-junction current passing into cell 2 and Inj1 is the non-junctional current passing out of cell 1. Fig. 4C illustrates further that Igj1 is the sum of the gap-junction current Igj2 and the non-junctional current Inj2 passing out of principal cell 2(Eqn 2):
$\ I_{\mathrm{gj}1}=I_{\mathrm{gj}2}+I_{\mathrm{nj}2}.$
(2)
Igj1 is also the current passing through gap junction 1 according to the difference between the voltage deflections in cell 1 and 2 consequent to the current injected into cell 1(Eqn 3):
$\ I_{\mathrm{gj}1}=\frac{{\Delta}V_{\mathrm{bl}1}-{\Delta}V_{\mathrm{bl}2}}{R_{\mathrm{gj}1}}.$
(3)
A similar statement can be written for the current Igj2passing from cell 2 to cell 3 (Eqn 4):
$\ I_{\mathrm{gj}2}=\frac{{\Delta}V_{\mathrm{bl}2}-{\Delta}V_{\mathrm{bl}3}}{R_{\mathrm{gj}2}}.$
(4)
Currents passing through non-junctional resistances obey Ohm's law as follows:
$\ I_{\mathrm{nj}1}=\frac{{\Delta}V_{\mathrm{bl}1}}{R_{\mathrm{nj}1}},$
(5)
$\ I_{\mathrm{nj}2}=\frac{{\Delta}V_{\mathrm{bl}2}}{R_{\mathrm{nj}2}}.$
(6)
Since it can be assumed that Rgj1=Rgj2and that Rnj1=Rnj2, then dividing Eqn 5 by Eqn 6 yields:
$\ \frac{I_{\mathrm{nj}1}}{I_{\mathrm{nj}2}}=\frac{{\Delta}V_{\mathrm{bl}1}}{R_{\mathrm{bl}2}}.$
(7)
Combining Eqn 2 and Eqn 7 and solving for Inj1 yields:
$\ I_{\mathrm{nj}1}=(I_{\mathrm{gj}1}-I_{\mathrm{gj}2})\frac{{\Delta}V_{\mathrm{bl}1}}{{\Delta}V_{\mathrm{bl}2}}.$
(8)
Substitution of Eqn 3 and Eqn 4 in Eqn 8 yields:
$\ I_{\mathrm{nj}1}=\left(\frac{{\Delta}V_{\mathrm{bl}1}-2{\Delta}V_{\mathrm{bl}2}+{\Delta}V_{\mathrm{bl}3}}{R_{\mathrm{gj}}}\right)\frac{{\Delta}V_{\mathrm{bl}1}}{{\Delta}V_{\mathrm{bl}2}}.$
(9)
Substitution of Eqn 3 and Eqn 9 in Eqn 1 yields:
$\ I_{\mathrm{inject}}=2\left(\frac{{\Delta}V_{\mathrm{bl}1}-{\Delta}V_{\mathrm{bl}2}}{R_{\mathrm{gj}}}\right)+\left(\frac{{\Delta}V_{\mathrm{bl}1}-2{\Delta}V_{\mathrm{bl}2}+{\Delta}V_{\mathrm{bl}3}}{R_{\mathrm{gj}}}\right){\times}\frac{{\Delta}V_{\mathrm{bl}1}}{{\Delta}V_{\mathrm{bl}2}}.$
(10)
Solving for the gap-junction resistance Rgj yields:
$\ R_{\mathrm{gj}}=\frac{\frac{{\Delta}V_{\mathrm{bl}1}}{{\Delta}V_{\mathrm{bl}2}}{\times}({\Delta}V_{\mathrm{bl}1}-2{\Delta}V_{\mathrm{bl}2}+{\Delta}V_{\mathrm{bl}3})+2({\Delta}V_{\mathrm{bl}1}-{\Delta}V_{\mathrm{bl}2})}{I_{\mathrm{inject}}},$
(11)
and solving for the non-junctional resistance Rnj yields:
$\ R_{\mathrm{nj}}=\frac{R_{\mathrm{gj}}{\times}{\Delta}V_{\mathrm{bl}2}}{{\Delta}V_{\mathrm{bl}1}-2{\Delta}V_{\mathrm{bl}2}+{\Delta}V_{\mathrm{bl}3}}.$
(12)
In the typical experiment we first treated the Malpighian tubule with 1μmol l–1 leucokinin-VIII for 5 min, and then voltage-clamped cell 1 to a hyperpolarizing voltage of 40 mV for 50 ms. We then recorded the steady state current injected into cell 1(Iinject) and the steady state basolateral membrane voltage deflections (ΔVbl) in cells 1, 2 and 3(Fig. 4).
Fig. 4.

Measurement of the gap-junction resistance between principal cells of isolated Malpighian tubules of the yellow fever mosquito Aedes aegypti. (A) The measuring circuit in the tubule modeled as a double cable; (B) reduction of the circuit by eliminating Rshvia the short-circuiting effects of leucokinin-VIII; (C) further reduction of the circuit by combining the parallel resistances in circuit in B. The electromotive forces (E) are neglected in C as they should not be affected by voltage-clamping cell 1. V, R and I have their usual meaning; a, apical membrane; bl, basolateral membrane; lu, tubule lumen; gj, gap junction; nj, non-junction. The non-junctional resistance Rnj includes Ra, Rbl and Rlu.

Fig. 4.

Measurement of the gap-junction resistance between principal cells of isolated Malpighian tubules of the yellow fever mosquito Aedes aegypti. (A) The measuring circuit in the tubule modeled as a double cable; (B) reduction of the circuit by eliminating Rshvia the short-circuiting effects of leucokinin-VIII; (C) further reduction of the circuit by combining the parallel resistances in circuit in B. The electromotive forces (E) are neglected in C as they should not be affected by voltage-clamping cell 1. V, R and I have their usual meaning; a, apical membrane; bl, basolateral membrane; lu, tubule lumen; gj, gap junction; nj, non-junction. The non-junctional resistance Rnj includes Ra, Rbl and Rlu.

### The input resistance

Voltage-clamping cell 1 yields the input resistance(Rinput) as the ratio ofΔ Vbl1Iinject (Figs 1, 4). The input resistance includes cell 1 and all other cells coupled to it, as illustrated in Fig. 4B. The input resistance can also be predicted from the values of Rgj and Rnj determined in the circuit analysis above(Eqn 11, Eqn 12). Good agreement between values of Rinput measured directly and values predicted from the circuit analysis would validate the short-circuit assumption needed for reducing the double cable in Fig. 4A to a manageable level for circuit analysis. To predict values of Rinput from values of Rgj and Rnj in circuit Fig. 4C, the experimental preparation illustrated in Fig. 4A is redrawn in Fig. 5 from the perspective of current injected into cell 1 flowing symmetrically into cells upstream and downstream from cell 1. The parallel symmetry of all resistances in Fig. 5 allows the reduction of all resistances to a single resistance, which is the predicted input resistance. We have limited the number of coupled cells to 7 in this data reduction because previous studies suggested that 5–6 principal cells are coupled electrically (Masia et al.,2000).

### Cable analysis

As current is injected into cell 1, the voltage deflections(ΔV) decay exponentially from cell to cell along the length of the tubule according to Eqn 13where x is the distance from cell 1 and λ is the cell length constant:
$\ {\Delta}V_{\mathrm{x}}={\Delta}V_{\mathrm{bl}1}{\times}\mathrm{e}^{-(x{/}{\lambda})}.$
(13)
According to cable analysis, the length constant λ(ΔVx at 37% of ΔVbl1) is:
$\ {\lambda}=\sqrt{\frac{r_{\mathrm{r}}}{r_{\mathrm{a}}}},$
(14)
where rr is the length-specific resistance of epithelial cells in the radial direction, and ra is the length-specific resistance of the cells in the axial direction. Specifically,
$\ r_{\mathrm{a}}=\frac{2{\Delta}V_{\mathrm{bl}1}}{({\Delta}I_{\mathrm{inject}}){\lambda}},$
(15)
$\ r_{\mathrm{r}}=\frac{2({\Delta}V_{\mathrm{bl}1}){\lambda}}{{\Delta}I_{\mathrm{inj}}},$
(16)
where ΔIinject is the current injected into cell 1(Fig. 4B, Fig. 5), but one half of the injected current passes upstream and the other downstream the tubule.
Since rr and ra are normalized to tubule length, the gap-junction resistance Rgj and the non-junctional resistance Rnj can be estimated. Since two sets of gap junctions are expected to couple cell 1 to cell 3, Rgj is:
$\ R_{\mathrm{gj}}=\frac{(r_{\mathrm{a}})l}{2}$
(17)
and Rnj is:
$\ R_{\mathrm{nj}}=\frac{(r_{\mathrm{r}})2}{l},$
(18)
where l is the distance between the voltage electrodes in cell 1 and 3. On average this distance was 247.9±7.5 μm in 14 experiments.
Fig. 5.

Estimate of the input resistance (Rinput) from the non-junctional (nj) and gap-junctional (gj) resistances (R) of principal cells. Rinput can also be measured directly as the ratio ΔVbl1Iinject. The comparison of estimated values and values measured directly tests the short-circuit assumption needed to obtain measurements of the gap-junction resistance. In previous studies we have used Rpc to refer to Rinput (Masia et al., 2000). The non-junctional resistance Rnjincludes Ra, Rbl and Rlu.

Fig. 5.

Estimate of the input resistance (Rinput) from the non-junctional (nj) and gap-junctional (gj) resistances (R) of principal cells. Rinput can also be measured directly as the ratio ΔVbl1Iinject. The comparison of estimated values and values measured directly tests the short-circuit assumption needed to obtain measurements of the gap-junction resistance. In previous studies we have used Rpc to refer to Rinput (Masia et al., 2000). The non-junctional resistance Rnjincludes Ra, Rbl and Rlu.

### Lucifer Yellow injections of principal cells

To visualize the coupling of principal cells via gap junctions,one principal cell was injected with Lucifer Yellow to observe whether the dye appears in neighboring principal cells. Microinjecting pipettes were made from borosilicate glass (TW100F-4, WPI, Sarasota, FL, USA) using a horizontal puller (P87, Sutter Instrument Co., Novato, CA, USA) and a two-step pulling protocol. Injection pipettes had an average resistance of 4.33±0.37 MΩ (N=9) when filled with 3 mol l–1 KCl. For injections of Lucifer Yellow, the pipette was back-filled by capillary action with a 2.5 mmol l–1 Lucifer Yellow CH dilithium salt (Sigma,St Louis, MO, USA) dissolved in water.

After isolation, the Malpighian tubule was transferred to a perfusion bath pre-coated with 0.125 mg ml–1 poly-l-lysine(Sigma), which prevents the movement of tubules when a single principal cell is injected with dye. After impaling a principal cell, a hydrostatic pressure of approximately 5200 mmHg was applied to the pipette for 250 ms with the aid of a pneumatic picopump (PV830, WPI). The pressure pulse injected a volume of approximately 0.7 pl, as determined in pre-experiment pipette calibrations. The cytoplasmic volume of a principal cell is about 200 pl. The intracellular Lucifer Yellow was immediately visible when viewed with an inverted microscope(Diaphot, Nikon, Kawasaki, Japan) equipped with a B-3A filter (Chroma Technology, Brattleboro, VT, USA) and a mercury lamp light source (Chiu Technical Corp., Kings Park, NY, USA). Typically, we observed the tubule for more than 1 h for signs of Lucifer Yellow diffusing from the injected principal cells to the adjacent principal cells or stellate cells. To prevent photo bleaching of the dye, we turned on the light source briefly every 10 min.

### Computational simulation of the electrical properties of a Malpighian tubule

After finding the evidence for gap junctions in Aedes Malpighian tubules and determining the gap-junction resistance, it was clear that the tubule should be modeled as a double cable. In previous studies we have treated the tubule as a single cable in order to determine electromotive forces (E) and the resistances (R) of transcellular and paracellular transport pathways shown in Fig. 2B(Beyenbach and Masia, 2002; Pannabecker et al., 1992; Pannabecker et al., 1993). It was therefore important to determine values of E and R for the double cable model of the tubule. In brief, we modeled the tubule as a linear series of ten principal cells where each cell was represented by the electrical circuit shown in Fig. 3B. Analysis of this tubule model with the software of Electronics Workbench® 5.12 (National Instruments, Austin, TX, USA) allows current to be injected at any position in the circuit to observe voltage deflections across any two points of the circuit. By simulating our previous in vitro microperfusion experiments, where a known current was injected into the tubule lumen at one end of the tubule(Pannabecker et al., 1992), we fitted data collected from the single cable to the double cable, to obtain new values of E and R (Fig. 3).

### Generation of Malpighian tubule cDNA

To prepare Malpighian tubule cDNA, 175 Malpighian tubules were isolated from 35 female mosquitoes. The tubules were immersed in ice-cold Trizol reagent (Invitrogen, Carlsbad, CA, USA) and then stored at –80°C. Total RNA from the tubules was isolated by homogenization in Trizol reagent(Invitrogen), followed by a phenol:chloroform phase separation and an isopropyl alcohol precipitation(Chomczynski and Sacchi,1987). The resulting RNA was used as a template to synthesize a pool of single-stranded cDNA using Superscript III Reverse Transcriptase(Invitrogen) and a GeneRacer oligo dT primer (Invitrogen). Before use in PCR,the cDNA was diluted tenfold with nuclease-free H2O (Integrated DNA Technologies, Coralville, IA, USA).

### PCR of innexin-like transcripts

The genome of Drosophila lists eight genes encoding innexins(Stebbings et al., 2002). Using the predicted amino-acid sequences encoded by these genes, we searched the genomic database of Aedes(http://aaegypti.vectorbase.org)with a Basic Local Alignment Search Tool (BLAST). The search yielded six innexin-like genes in Aedes (see Results). We designed oligonucleotide-primer pairs (Table 1) to amplify fragments of the open-reading frames (ORF) for each Aedes innexin using PCR. All of the PCRs were conducted on 0.5 μl of Malpighian tubule cDNA in Platinum PCR Supermix HF (Invitrogen) using the following cycling parameters: one cycle of 94°C for 2 min; 35 cycles of 94°C for 30 s, 50°C for 30 s, and 68°C for 1 min; one cycle of 68°C for 10 min. As a negative control, each PCR was conducted on 0.5μl of Malpighian tubule RNA that was not reverse transcribed, but was diluted to the same degree as the cDNA. To verify PCR results, we also performed all PCRs on 3 μl of a double-stranded cDNA library derived from adult Aedes Malpighian tubules (generously provided by Dr Dimitri Boudko, The Whitney Laboratory, St Augustine, FL, USA). All PCR products were separated via electrophoresis on a 1%-agarose gel and stained with ethidium bromide.

Table 1.

Oligonucleotide primer pairs used in PCR reactions, and expected size of respective PCR products for cDNA and genomic DNA templates

GeneForward primer (5′ → 3′)Reverse primer (5′ → 3′)Expected product size for cDNA template (bp)Expected product size for genomic DNA template (bp)
Inx1 CGGGATCCCAACACATGTCGTCAATACA GGCGAGTTCCGCTACAACATCCTTGAAA 880 33300
Passover GACTGCGTTCACACGAAAGACATACCAG TCACCTTTCATACCAGGTACACGATGG 947 30300
Inx2 CCGGGAGTATCGAGTCACGTCGACGGCCATGATGA TCTTTGCCCTCAAATTTGAGAGAGA 800 800
Inx3 CGTGTTCAGATTCGACGGACAAGAGTAG CAGGATGAACCAGAACCACAGGAAGATG 920 1182
Inx4 TGACTTCTATCCTTTCACCTGGTGC TACAACAATATGTCGCTTGGATTGG 916 916
Inx7 ATGGAAGGAGGAAAAATTAAACGTCTTG ATAAGTTCAGTTTCGTCAGCCTCAT 800 861
GeneForward primer (5′ → 3′)Reverse primer (5′ → 3′)Expected product size for cDNA template (bp)Expected product size for genomic DNA template (bp)
Inx1 CGGGATCCCAACACATGTCGTCAATACA GGCGAGTTCCGCTACAACATCCTTGAAA 880 33300
Passover GACTGCGTTCACACGAAAGACATACCAG TCACCTTTCATACCAGGTACACGATGG 947 30300
Inx2 CCGGGAGTATCGAGTCACGTCGACGGCCATGATGA TCTTTGCCCTCAAATTTGAGAGAGA 800 800
Inx3 CGTGTTCAGATTCGACGGACAAGAGTAG CAGGATGAACCAGAACCACAGGAAGATG 920 1182
Inx4 TGACTTCTATCCTTTCACCTGGTGC TACAACAATATGTCGCTTGGATTGG 916 916
Inx7 ATGGAAGGAGGAAAAATTAAACGTCTTG ATAAGTTCAGTTTCGTCAGCCTCAT 800 861

All primers were ordered from Integrated DNA Technologies (Coralville, IA,USA)

### DNA sequencing of PCR products

PCR products were either ligated into a pCR 4-TOPO vector (Invitrogen) or purified using a QIAquick PCR purification kit (Qiagen, Valencia, CA, USA). The ligated PCR products were transformed into TOP 10 Chemically Competent E. coli (Invitrogen) according to the manufacturer's protocol. Plasmid DNA from four resulting colonies was purified using a QIAprep Spin Miniprep kit (Qiagen). DNA sequencing of plasmid DNA and purified PCR products was performed in both the 5′ and 3′ directions by the Cornell DNA Sequencing Center (Cornell University, Ithaca, NY, USA).

### Statistical evaluation of data

Each tubule/cell was used as its own control so that the data could be analyzed for the difference between paired samples, control vsexperimental (paired Student's t-test).

### Electrical coupling of principal cells

We often observe spontaneous voltage oscillations in Malpighian tubules of Aedes aegypti (Beyenbach et al.,2000a; Sawyer and Beyenbach,1985; Williams and Beyenbach,1984; Yu and Beyenbach,2002). The oscillations stem from spontaneous changes in the paracellular shunt Cl conductance(Beyenbach et al., 2000a) and have a frequency not unlike those of spontaneous cyclical changes in cytoplasmic Ca2+ concentration(Fig. 6). Leucokinin-VIII increases the paracellular Cl conductance via the activation of a Ca2+ channel in the basolateral membrane of principal cells, thereby increasing the cytoplasmic Ca2+concentration (Yu and Beyenbach,2002). Elevated cytoplasmic Ca2+ levels obliterate the spontaneous changes in cytoplasmic [Ca2+], eliminate spontaneous voltage oscillations, and maintain an increased paracellular Cl conductance as long as leucokinin-VIII is present(Beyenbach, 2003a; Yu and Beyenbach, 2001).

Fig. 6 illustrates spontaneous oscillations of the basolateral membrane in three principal cells of a single Malpighian tubule. The three cells shared a base membrane voltage between –55 and –65 mV, and as one cell hyperpolarized spontaneously, the other cells followed with virtually no time delay(Fig. 6). The magnitude of the oscillations was smallest in cell 1 (Fig. 6, red trace) and largest in cell 4(Fig. 6, green trace),suggesting that the pacemaker must be located in cell 4 or beyond. The perfect temporal superimposition of voltage oscillations from different principal cells demonstrates tight electrical coupling among them, which is consistent with the presence of gap junctions.

Fig. 6.

Spontaneous oscillations of the basolateral membrane voltage(Vbl) in an isolated Malpighian tubule of Aedes aegypti. Three principal cells were impaled with conventional microelectrodes. The remaining epithelial cells (more than 120) are not shown in the tubule diagram. Note that cell 2 separates cell 1 (red trace) from cells 3 (blue trace) and 4 (green trace) from which voltages are recorded.

Fig. 6.

Spontaneous oscillations of the basolateral membrane voltage(Vbl) in an isolated Malpighian tubule of Aedes aegypti. Three principal cells were impaled with conventional microelectrodes. The remaining epithelial cells (more than 120) are not shown in the tubule diagram. Note that cell 2 separates cell 1 (red trace) from cells 3 (blue trace) and 4 (green trace) from which voltages are recorded.

### Estimate of the gap-junction resistance by circuit analysis

Principal cells 1, 2 and 3 were impaled with current and voltage electrodes as shown in Figs 1 and 4. Principal cell 1 was then voltage-clamped at a hyperpolarizing voltage of 40 mV for 50 ms and the voltage deflections were recorded in cells 2 and 3(Fig. 7). After obtaining control data, the tubule was treated with 1 μmol l–1leucokinin-VIII. In the presence of this diuretic peptide, the voltage deflections in principal cells 2 and 3 were less than those under control conditions, in view of (1) the increase in the Clconductance of the paracellular shunt pathway(Yu and Beyenbach, 2001), and(2) the increase in the Ca2+ conductance of the basolateral membrane of principal cells (Yu and Beyenbach, 2002).

Table 2 summarizes the results of 14 experiments. Under control conditions the basolateral membrane voltage (Vbl) was –82.2 mV in principal cell 1 (and similar in cells 2 and 3, data not shown). Clamping Vbl1to a hyperpolarizing voltage 40 mV above the resting membrane voltage required the intracellular injection of 168.8 nA. Consequent to the current injection,the ΔVbl in principal cell 2(ΔVbl2) hyperpolarized by 20.7 mV, and theΔ Vbl in principal cell 3(ΔVbl3) hyperpolarized by 11.9 mV(Table 2).

Table 2.

Measurement of the gap junction resistance Rgj in Malpighian tubules of Aedes aegypti by circuit analysis

ControlLeucokinin-VIII
Vbl1 (mV) –82.2±2.5 –100.4±2.7*
Iinject (nA) 168.8±13.5 211.5±16.1*
Δ Vbl1 (mV) 40 40
Δ Vbl2 (mV) 20.7±1.2 17.0±1.0*
Δ Vbl3 (mV) 11.9±1.0 8.3±0.6*
Rgj (kΩ)  431.0±56.5
Rnj (kΩ)  546.7±59.3
ControlLeucokinin-VIII
Vbl1 (mV) –82.2±2.5 –100.4±2.7*
Iinject (nA) 168.8±13.5 211.5±16.1*
Δ Vbl1 (mV) 40 40
Δ Vbl2 (mV) 20.7±1.2 17.0±1.0*
Δ Vbl3 (mV) 11.9±1.0 8.3±0.6*
Rgj (kΩ)  431.0±56.5
Rnj (kΩ)  546.7±59.3

Values are means ± s.e.m. of 14 experiments; *significantly different (P<0.05) from control by the paired Student's t-test

Vbl, basolateral membrane voltage in principal cells 1,2 and 3; Rgj, gap junction resistance; Rnj, non-junctional resistance

Leucokinin-VIII is used to eliminate electrical coupling of principal cells through the tubule lumen

In the presence of leucokinin-VIII, Vbl hyperpolarized significantly from –82.2 mV to –100.4 mV(Table 2). The hyperpolarization is due to the increased coupling of Vblto the apical membrane voltage as the shunt resistance drops to 12% of control values, nearly short-circuiting the transepithelial voltage(Pannabecker et al., 1993). In the presence of leucokinin-VIII, cells 1, 2 and 3 are electrically coupled by primarily gap junctions, which allows measurement of the gap-junction resistance (Rgj, Table 2) and the non-junctional resistance (Rnj, Table 2). Importantly, Rgj was derived from the circuit analysis of voltage deflections described in Eqn 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

Fig. 7.

Profiles of the basolateral membrane voltage deflections(ΔVbl) along the length of Malpighian tubules of Aedes aegypti. Cell 1 was voltage-clamped at a hyperpolarizing voltage of 40 mV, and the voltage deflections across the basolateral membranes of cells 2 and 3 recorded in the absence (control) and presence of leucokinin-VIII. Values are mean ± s.e.m. of 14 experiments.

Fig. 7.

Profiles of the basolateral membrane voltage deflections(ΔVbl) along the length of Malpighian tubules of Aedes aegypti. Cell 1 was voltage-clamped at a hyperpolarizing voltage of 40 mV, and the voltage deflections across the basolateral membranes of cells 2 and 3 recorded in the absence (control) and presence of leucokinin-VIII. Values are mean ± s.e.m. of 14 experiments.

### Measured and predicted input resistances

The input resistance of principal cell 1 (Rinput) can be measured directly as the ratio ofΔ Vbl1Iinject. Rinput was 246.5±17.8 kΩ under control conditions and fell significantly (P<0.05) to 194.8±14.3 kΩ in the presence of leucokinin-VIII in the 14 experiments summarized in Table 2. The decrease reflects in part the increased transcellular secretion of Na+ and K+ in the presence of leucokinin-VIII(Beyenbach, 2003a; Hayes et al., 1989; Pannabecker et al., 1993), and also the activation of Ca2+ channels in the basolateral membrane(Yu and Beyenbach, 2002).

The input resistance Rinput can be predicted from values of Rgj and Rnj determined by circuit analysis (Eqn 11, Eqn 12; Fig. 5). The predicted Rinput is 209.6±15.4 kΩ, which comes close to the measured Rinput of 194.8 kΩ in the same tubules. Good agreement between the Rinput measured directly and the Rinput predicted from the circuit analysis validates the short-circuit assumption' needed to obtain measures of Rgj.

### Cable analysis of Rgj

Keeping track of the distances that separated the microelectrodes impaling cells 1, 2 and 3 (see Fig. 7)allowed us to re-evaluate Rgj, but by cable analysis. A two-parameter exponential decay curve was fitted to the mean voltage deflections of Fig. 7. The equation of this curve for tubules treated with leucokinin was:
$\ {\Delta}V_{\mathrm{x}}=(-38.5mV)\mathrm{e}^{-(x{/}0.016)},$
(19)
where x is the distance from cell 1, and where 0.016 cm is the length constant λ (regression correlation coefficient of 0.99). Using Eqn 15 and Eqn 16 yields 26.7 MΩcm–1 as ra and 6.5 kΩcm as rr, both normalized to tubule length in the presence of leucokinin-VIII (Table 3). Use of Eqn 17 and Eqn 18 yields 327.3 kΩ as Rgj and 524.9 kΩ as Rnj in the same 14 tubule experiments shown in Fig. 7 and Table 2.
Table 3.

Measurement of the gap junction resistance Rgj in Malpighian tubules of Aedes aegypti by cable analysis

ControlLeucokinin-VIII
Δ Vbl1 (mV) 40 40
Iinject (nA) 168.8±13.5 211.5±16.1*
Length constant λ (cm)  0.016±0.001
Axial resistance ra (MΩcm–1 26.7±2.6
Rgj (kΩ)  327.3±32.7
Rnj (kΩ)  524.9±42.6
ControlLeucokinin-VIII
Δ Vbl1 (mV) 40 40
Iinject (nA) 168.8±13.5 211.5±16.1*
Length constant λ (cm)  0.016±0.001
Axial resistance ra (MΩcm–1 26.7±2.6
Rgj (kΩ)  327.3±32.7
Rnj (kΩ)  524.9±42.6

Values are means ± s.e.m. of the same 14 experiments of Table 1; *significantly different (P<0.05) from control by the paired Student's t-test

Vbl1, basolateral membrane voltage of principal cell 1; Iinject, current injected into principal cell 1; Rnj, non-junctional resistance

### Coupling of principal cells tested with Lucifer Yellow

One principal cell of the Malpighian tubule was microinjected with Lucifer Yellow at time zero (Fig. 8). At the time of injection, the fluorescence of Lucifer Yellow was confined to the injected principal cell. About 5 s after the injection, the fluorescence of Lucifer Yellow started to appear in the tubule lumen and 1 min later the dye exited the tubule lumen at its open end, indicating the secretion of Lucifer Yellow across the apical membrane of the injected principal cell.

Although the fluorescent intensity of Lucifer Yellow faded with time in the injected cell (Fig. 8), no fluorescence was observed in neighboring principal cells or in the stellate cells, not even after 60 min. We made these observations consistently in eight additional tubules.

### Physiological regulation of gap junctions

Since it is known that intracellular calcium and metabolic inhibition can close gap junctions, we tested the effects of the calcium ionophore A23187 and dinitrophenol on the gap-junction resistance (Rgj) and the non-junctional resistance (Rnj). In these experiments we first treated the isolated Malpighian tubule with 1 μmol l–1 leucokinin-VIII to measure Rgj and Rnj by the circuit analysis shown in Figs 1, 4 and Table 2. After 5 min in the presence of leucokinin-VIII we added 2 μmol l–1 A23187 to the peritubular medium and took measurements of Rgj and Rnj 5 min later. We then added 0.5 mmol l–1 dinitrophenol (DNP) to the peritubular Ringer bath (in the presence of leucokinin-VIII and A23187) and measured Rgj and Rnj 2 min later. Table 4 summarizes the results.

Table 4.

The effects of the Ca2+ ionophore A23187 and dinitrophenol on the gap junction resistance (Rgi) and the non-junctional resistance (Rnj)

Control (8)Leucokinin-VIII (8)Leucokinin-VIII (8) A23187Leucokinin-VIII (6) A23187 Dinitrophenol
Vbl1 (mV) –83.5±3.3 –103.3±2.1* –99.3±3.6 –13.5±4.3*
Rinput (kΩ) 273.7±22.1 214.9±9.3* 193.7±5.8* 1474.3±191.3*
Rgj (kΩ)  468.0±72.2 526.1±76.6 30 762.1±6594.6*
Rnj (kΩ)  578.5±60.9 504.0±63.1* 1483.8±109.2*
Control (8)Leucokinin-VIII (8)Leucokinin-VIII (8) A23187Leucokinin-VIII (6) A23187 Dinitrophenol
Vbl1 (mV) –83.5±3.3 –103.3±2.1* –99.3±3.6 –13.5±4.3*
Rinput (kΩ) 273.7±22.1 214.9±9.3* 193.7±5.8* 1474.3±191.3*
Rgj (kΩ)  468.0±72.2 526.1±76.6 30 762.1±6594.6*
Rnj (kΩ)  578.5±60.9 504.0±63.1* 1483.8±109.2*

Values are means ± s.e.m. (number of tubule experiments); *significantly different (P<0.05) from the previous treatment by the paired Student's t-test

Vbl1, basolateral membrane voltage of principal cell 1; Rinput, input resistance of cell 1; Rnj, non-junctional resistance

Tubules were first treated with 1 μmol l–1leucokinin-VIII, then with 2 μmol l–1 A23187 in the presence of leucokinin-VIII, and finally with 0.5 mmol l–1dinitrophenol in the presence of leucokinin-VIII and A23187

The addition of leucokinin-VIII to the peritubular bath significantly(P<0.05) hyperpolarized Vbl1 from –83.5 to –103.3 mV (Table 4). The circuit analysis of voltage deflections in neighboring cells yielded a mean Rgj of 468.0 kΩ and a mean Rnj of 578.5 kΩ in this series of experiments(Table 4). After 5 min in the presence of A23187, neither Vbl1 nor Rgj changed significantly. In contrast, Rnj decreased significantly which is further reflected by the significant decrease in Rinput(Table 4).

Upon the addition of 0.5 mmol l–1 DNP to the peritubular medium, Vbl1 significantly depolarized from –99 mV to –13 mV while Rgj significantly increased from 526 kΩ to 30 762 kΩ (Table 4). In the presence of DNP, Rnj significantly increased from 504 kΩ to 1483 kΩ, and Rinputsignificantly increased from 194 kΩ to 1474 kΩ(Table 4). In summary,significant effects of Ca2+ ionophore A23187 were limited to a small reduction in the non-junctional resistance that may reflect the pore-forming action of the ionophore at the basolateral membrane. The effect of metabolic inhibition was profound on every measured variable. It increased Rnj threefold, it dropped Vblsevenfold, increased Rinput eightfold, and increased Rgj 60-fold (Table 4).

### Identification of putative innexins in Aedes

A BLAST-search for homologues of the known eight Drosophilainnexins in the genome of Aedes identified six innexin-like genes(Table 5). We refer to the innexins in Aedes after their most similar homologues in Drosophila. Among the Aedes innexins, AeInx1, AePassover, AeInx2, and AeInx3 shared over 50%amino-acid identity to their Drosophila homologues, whereas AeInx4 and AeInx7 were less than 50% identical to their Drosophila homologues (Table 5). Homologues of Inx5 and Inx6 from Drosophila were not apparent from BLAST-searches in the Aedes genome.

Table 5.

Aedes homologues of Drosophila innexins and their %amino-acid identities

Drosophila innexinAedeshomologue*% Amino-acid identity
AAEL014846 71
Passover AAEL014227 86
AAEL014847 81
AAEL011248 68
AAEL006726 34
AAEL008588 45
Drosophila innexinAedeshomologue*% Amino-acid identity
AAEL014846 71
Passover AAEL014227 86
AAEL014847 81
AAEL011248 68
AAEL006726 34
AAEL008588 45
*

Vectorbase accession number

To better resolve the relationships between Aedes and Drosophila innexins, we constructed a neighbor-joining phylogenetic tree (Fig. 9) using the predicted amino-acid sequences encoded by the genes. For Inx1, Passover, Inx2 and Inx3, the tree demonstrates that: (1) the Aedes genes cluster into discrete branches with their respective Drosophila homologues and (2) the branch length from a node (e.g. arrow in Fig. 9) to each homologue is short (see legend of Fig. 9 for explanation). For Inx7, the tree demonstrates that the Aedes gene clusters with its Drosophila homologue, but that the length between the node of the branch and the two homologues is long. For Inx4, the tree demonstrates that the Aedes gene does not cluster discretely with its Drosophila homologue, but it appears within a larger branch that includes Inx4, Inx5 and Inx6 of Drosophila. Among these three Drosophila innexins, the cumulative branch length between AeInx4 and DrInx4 is the shortest. The insights gained in the phylogenetic tree are consistent with the results of the BLAST search(Table 5). The implications of these results are analyzed further in the Discussion.

Fig. 8.

Inability of Lucifer Yellow to pass through gap junctions into neighboring epithelial cells. Green fluorescence identifies the principal cell injected with Lucifer Yellow at time 0 min. The image at 10 min is supplemented to outline the Malpighian tubule; bar, 100 μm.

Fig. 8.

Inability of Lucifer Yellow to pass through gap junctions into neighboring epithelial cells. Green fluorescence identifies the principal cell injected with Lucifer Yellow at time 0 min. The image at 10 min is supplemented to outline the Malpighian tubule; bar, 100 μm.

### Expression of innexin transcripts in Aedes Malpighian tubules

In Aedes Malpighian tubule cDNA we detected partial PCR products near the expected sizes for AeInx1, AeInx2, AeInx3 and AeInx7 cDNAs (Fig. 10, lanes a). In contrast, we did not detect a PCR product for AePassover, and the PCR product for AeInx4 was extremely weak (Fig. 10, lanes a). DNA sequencing verified that (1) the identities of the amplified transcripts were as expected and (2) the PCR products from primers that bracketed introns were not derived from genomic DNA contamination. When total RNA was used as a template for PCR in lieu of cDNA, no products were amplified for any of the innexins (Fig. 10,lanes b). Both the positive and negative results for each gene were verified using (1) a combination of at least two additional, independent primer pairs(data not shown) and (2) cDNA from adult Aedes Malpighian tubules generated by the Boudko laboratory (data not shown). The above results indicate that Aedes Malpighian tubules primarily express mRNA transcripts for four innexins.

Fig. 9.

Neighbor-joining tree showing phylogenetic relationships between innexins in Drosophila and Aedes. Innexin1 from Caenorhabditis elegans (CeInx1) is the outgroup. The tree was constructed using MEGA 3 software (Kumar et al.,2004), based on the Poisson-corrected distance estimates. In this analysis, the cumulative branch length between the node of a branch (e.g. arrow) and two genes represents the proportion of amino acids that differ between them per residue (scale bar=0.1). For example, if two genes are separated by a cumulative branch length of 0.1', then one amino-acid residue differs between them for every ten amino acids. The number at each node indicates the bootstrap score (i.e. reliability) over 1000 replicates for that node. For example, a score of 94' indicates that the node occurred in 94% of the 1000 replicates. Accession numbers for Aedes innexins are listed in Table 5. Accession numbers(GenBank) for other innexins are as follows: DrInx1, NP_524824; DrPassover, NP_728361; DrInx3, NP_524730; DrInx4,NP_648049; DrInx5, NP_573353; DrInx6, NP_572374; DrInx7, NP_788872; CeInx1, NP_741826.

Fig. 9.

Neighbor-joining tree showing phylogenetic relationships between innexins in Drosophila and Aedes. Innexin1 from Caenorhabditis elegans (CeInx1) is the outgroup. The tree was constructed using MEGA 3 software (Kumar et al.,2004), based on the Poisson-corrected distance estimates. In this analysis, the cumulative branch length between the node of a branch (e.g. arrow) and two genes represents the proportion of amino acids that differ between them per residue (scale bar=0.1). For example, if two genes are separated by a cumulative branch length of 0.1', then one amino-acid residue differs between them for every ten amino acids. The number at each node indicates the bootstrap score (i.e. reliability) over 1000 replicates for that node. For example, a score of 94' indicates that the node occurred in 94% of the 1000 replicates. Accession numbers for Aedes innexins are listed in Table 5. Accession numbers(GenBank) for other innexins are as follows: DrInx1, NP_524824; DrPassover, NP_728361; DrInx3, NP_524730; DrInx4,NP_648049; DrInx5, NP_573353; DrInx6, NP_572374; DrInx7, NP_788872; CeInx1, NP_741826.

### The electrophysiological evidence for gap junctions in Malpighian tubules of Aedes aegypti

We have used two independent electrical approaches to measure the gap-junction resistance between principal cells of Malpighian tubules of the yellow fever mosquito. In the first method we modeled the Malpighian tubule as a double electrical cable (Fig. 3B, Fig. 4) and used circuit analysis to determine the gap-junction resistance. In the second method we used cable analysis of the voltage deflections along principal cells when one principal cell was voltage clamped. Importantly, circuit analysis and cable analysis were performed in the same tubule experiments. The circuit analysis yielded an average gap-junction resistance of 431 kΩ(Table 2), and the cable analysis yielded a gap-junction resistance of 327 kΩ(Table 3). Although the two measurements are significantly different, they both document electrical coupling between principal cells.

A short-coming of the cable analysis is the reliance on the length constant, which is very sensitive to curve-fitting the data. Accordingly, we consider the circuit analysis to deliver the more accurate measurement of the gap-junction resistance, because this analysis yields values of both gap-junctional and non-junctional resistances from which the input resistance can be predicted, i.e. 210 kΩ. The input resistance measured directly as the ratio of ΔVbl1/Iinject, is 195 kΩ (Table 2). The good agreement between the predicted and measured values confirms the validity of the circuit analysis.

Fig. 10.

RT-PCR analysis of Aedes Malpighian tubules for innexin transcripts. The image shows PCR products separated on a 1% agarose gel and stained with ethidium bromide. On the gel are results for PCRs designed to amplify each Aedes innexin using the primer pairs indicated in Table 1. For each innexin, the Malpighian tubule cDNA was used as a template in lane a', and Malpighian tubule RNA was used as a template in lane b'. The lane mw' is a 1 Kb Plus DNA Ladder (Invitrogen), in which the first seven bands (starting from the bottom of gel) correspond to 100, 200, 300, 400, 500, 650 and 850 bp,respectively.

Fig. 10.

RT-PCR analysis of Aedes Malpighian tubules for innexin transcripts. The image shows PCR products separated on a 1% agarose gel and stained with ethidium bromide. On the gel are results for PCRs designed to amplify each Aedes innexin using the primer pairs indicated in Table 1. For each innexin, the Malpighian tubule cDNA was used as a template in lane a', and Malpighian tubule RNA was used as a template in lane b'. The lane mw' is a 1 Kb Plus DNA Ladder (Invitrogen), in which the first seven bands (starting from the bottom of gel) correspond to 100, 200, 300, 400, 500, 650 and 850 bp,respectively.

### Critical assumptions

Our measurement of the gap-junction resistance by circuit analysis depends on two assumptions: the current distribution assumption and the short-circuit assumption.

The current distribution assumption states that the current injected into principal cell 1 for voltage clamping splits equally in both directions along the tubule (Figs 4, 5). Indeed, in the course of our study we have found that the decay of ΔVbl from cell to cell was quantitatively similar in both directions (data not shown). Furthermore, the good agreement between the measured and predicted input resistances supports the symmetrical distribution of injected current, since the predicted value depends on the symmetrical circuit shown in Fig. 5, where no more than seven principal cells are needed for predicting the input resistance. In our experiments we have at least ten cells with at least five cells on either side of principal cell 1.

The short-circuit assumption states that the Malpighian tubule is analyzed at true short circuit. Specifically, we assume that leucokinin completely reduces the paracellular shunt resistance to zero, thereby short-circuiting the epithelium and leaving gap junctions as the major if not exclusive pathway for significant electrical coupling between cells. However, in reality,leucokinin reduces the paracellular shunt resistance nearly sixfold and causes the transepithelial voltage to drop from 59 mV to 6 mV(Pannabecker et al., 1993),which falls short of ideal short-circuit conditions. Thus it is relevant to evaluate the effect of the paracellular shunt resistance on the gap-junctional resistance using circuit analysis (Table 6).

Table 6.

The effect of the shunt resistance Rsh on the gap junction resistance Rgj and the non-junctional resistance Rnj

 Shunt resistance Rsh (kΩ) 0.1 3.87 10 23.2 50 Gap junction resistance Rgj (kΩ) 430.7 427.2 424.6 422.7 422.5 Non-junctional resistance Rnj (kΩ) 1261.6 1362.9 1464.8 1592.2 1710.9
 Shunt resistance Rsh (kΩ) 0.1 3.87 10 23.2 50 Gap junction resistance Rgj (kΩ) 430.7 427.2 424.6 422.7 422.5 Non-junctional resistance Rnj (kΩ) 1261.6 1362.9 1464.8 1592.2 1710.9

The Malpighian tubule was modeled as a double cable consisting of ten principal cells in series. Current was injected into principal cell 5 in the center of the virtual tubule. The effect of Rsh on Rgj and Rnj was evaluated using software of the Electronics Workbench®, keeping constant the values of the apical membrane resistance (2.25 MΩ), the basolateral membrane resistance (2.75 MΩ) and the lumen resistance (262 kΩ), all per unit cell

The analysis shows that as the shunt resistance changes 500-fold, the gap-junction resistance changes by only 2%(Table 6). Thus, the effect of the shunt resistance on the gap-junction resistance is negligible, and our assumption, that leucokinin completely short circuits the epithelium,introduces negligible error to our gap-junction resistance measurements.

### Revised electrical circuit model of the Aedes Malpighian tubule

In previous studies we have modeled the Malpighian tubule as a single cable that consists of a single axial resistance, i.e. the core resistance(Rco) and a radial resistance, the transepithelial resistance (Rt) as shown in Fig. 11A. Our finding of gap junctions in the present study calls for a double cable model of the tubule with two axial resistances, the lumen resistance and the gap-junction resistance (Fig. 11B). Accordingly, the electrical parameters determined in the single cable model should be corrected for the double cable model. The new set of electrical parameters were determined by fitting previous data of voltage and resistances(Pannabecker et al., 1992) to the new equivalent circuit model that includes the gap-junction resistance.

The first revision decreases the resistance of the basolateral membrane(Rbl) from 24.1 kΩcm in the single cable to 22.0 kΩcm in the double cable, and it increases the resistance of the apical membrane (Ra) from 11.4 kΩcm to 18.0 kΩcm(Fig. 11). Since the fractional membrane resistance of the basolateral membrane(fRbl) is the ratio of the basolateral membrane resistance and the transcellular resistance, Rbl/(Rbl+Ra), we now find that 55% of the transcellular resistance resides at the basolateral membrane, instead of 68% as determined previously in the single cable model. It follows that 45% of the transcellular resistance resides at the apical membrane, instead of 32% as determined by the previous model.

The second revision concerns the value of the paracellular shunt resistance Rsh, which increases from 16.8 kΩcm in the single cable model to 23.2 kΩcm in the double cable model(Fig. 11). Among other revisions of the equivalent circuit are the change of the electromotive force of the basolateral membrane (Ebl) from 17.5 mV to–8.1 mV, and the increase of the electromotive force of the apical membrane (Ea) from 146.1 mV to 151.4 mV(Fig. 11). Ebl and Ea summarize all electromotive forces operating, respectively, at the basolateral and apical membrane of principal cells. Ebl includes primarily the electrochemical potentials of ions, Na+, K+,Mg2+, Ca2+, Cl and HCO3 across the basolateral membrane. Therefore,the reversal of Ebl from 17.5 mV to –8.1 mV is an improved estimate of Ebl without identifying the more dominant electrochemical potential. In contrast to the basolateral membrane, Ea derives largely from the V-type H+ ATPase inhabiting the apical membrane. Here the revised value of Ea (151.4 mV) suggests a stronger electromotive force of the V-type H+ ATPase than previously assumed.

### Splitting the core resistance

The double cable model also resolves the discrepancy between the diameter of the tubule lumen measured optically and the electrical diameter of the core when the tubule is modeled as a single cable. Measured through a microscope,the lumen of the Aedes Malpighian tubule has a diameter between 10 and 15 μm. However, the diameter calculated from the core resistance (22.9 MΩcm–1) of the single cable model is considerably larger, 22 μm (Fig. 11A). In the presence of dinitrophenol, which shuts down ionic traffic through apical and basolateral membranes (Wu and Beyenbach, 2003), the core resistance increases to 32.8 MΩcm–1, reducing the core diameter to 17 μm. Thus,blocking ion transport across the apical membrane reduces the core diameter to values near the optical diameter of the tubule lumen. The double cable confirms this conclusion as follows.

Fig. 11.

Estimates of electrophysiological variables in the Malpighian tubule of the yellow fever mosquito. All values are normalized to cm tubule length. (A) The tubule modeled as a single cable (data from Pannabecker et al., 1992). The radial resistance is the transepithelial resistance consisting of the resistances of the apical membrane Ra, basolateral membrane Rbl and the shunt Rsh. The axial resistance of the tubule is the core resistance Rco.(B) The tubule modeled as a double cable. Here the axial resistance consists of the lumen resistance Rlu and the gap-junction resistance Rgap. In both models the transepithelial voltage Vt and the basolateral (Vbl)and apical (Va) membrane voltages are the same. E, electromotive force; De is the electrical diameter of the tubule lumen calculated from the lumen resistance Rlu (Pannabecker et al., 1992).

Fig. 11.

Estimates of electrophysiological variables in the Malpighian tubule of the yellow fever mosquito. All values are normalized to cm tubule length. (A) The tubule modeled as a single cable (data from Pannabecker et al., 1992). The radial resistance is the transepithelial resistance consisting of the resistances of the apical membrane Ra, basolateral membrane Rbl and the shunt Rsh. The axial resistance of the tubule is the core resistance Rco.(B) The tubule modeled as a double cable. Here the axial resistance consists of the lumen resistance Rlu and the gap-junction resistance Rgap. In both models the transepithelial voltage Vt and the basolateral (Vbl)and apical (Va) membrane voltages are the same. E, electromotive force; De is the electrical diameter of the tubule lumen calculated from the lumen resistance Rlu (Pannabecker et al., 1992).

The product of the single cell-to-cell gap-junction resistance (431 kΩ; Table 2) and the average number of principal cells per cm tubule (125 cells cm–1) yields 53.9 MΩcm–1 as the gap-junction resistance normalized to a Malpighian tubule of 1 cm length(Fig. 11B). The core resistance in the presence of dinitrophenol yields the resistance of the tubule lumen, 32.8 MΩcm–1. Combining these two axial resistances yields a core resistance of 20.4 MΩcm–1that approximates the core resistance of 22.9 MΩcm–1measured in the single cable model. The good agreement of these axial resistances not only confirms the validity of the short-circuit assumption,but it also confirms the electrical diameter of the core calculated in the presence of dinitrophenol as the actual lumen diameter. Moreover, the electrical diameter represents an average diameter of the tubule lumen, which is more accurate than the optical diameter, especially in view of the elaborate luminal brush border.

The good agreement between the calculated (20.4 MΩcm–1) and measured (22.9 MΩcm–1) core resistances suggests that gap junctions of stellate cells contribute little to 53.9 MΩcm–1, the gap-junction resistance of a tubule 1 cm long. Unfortunately, stellate cells are too thin and spongy for intracellular electrical recordings. The sponginess derives from deep invaginations of the basolateral membrane that leaves only 2–3 μm of cytoplasm before the microelectrode penetrates the apical membrane to arrive in the tubule lumen.

### Magnitude of the lumen and gap-junction resistances

Comparison of the gap-junction resistance of 53.9 MΩcm–1 and the lumen resistance of 32.8 MΩcm–1 is instructive. The lumen resistance stems from the saline occupying a 1 cm length of tubule lumen, without any barrier(Fig. 11B). Since the gap-junction resistance is only 1.6 times greater than the lumen resistance,there must be a substantial number of gap-junction channels coupling one cell to the next.

The gap-junction resistance between one principal cell and the next is 431 kΩ, which is equivalent to a gap-junction conductance of 2.3 μS(Table 2). The single channel conductances of invertebrate gap junctions range from 100 pS in earthworm giant axons (Brink and Fan,1989) to 248 pS in epidermal cells of the flour beetle(Churchill and Caveney, 1993)and to 375 pS in a mosquito cell line derived from Aedes albopictus(Bukauskas and Weingart,1994). If the single channel conductance in the mosquito cell line is similar to that in Malpighian tubules of Aedes aegypti, then there must be approximately 6190 gap junctions present in a single principal cell. The estimate is not unreasonable in view of as many as 10 000, the number of gap junctions per μm2 in a single gap junction plaque of the heart or liver (Unwin and Zampighi,1980).

### Permeable to current but not to Lucifer Yellow

The failure of Lucifer Yellow to move from the injected principal cell into neighboring cells (Fig. 8)calls for an explanation since these cells display substantial electrical coupling (Tables 2, 3, 4). Lucifer Yellow has a molecular mass of 457 Da. Since insect gap junctions are thought to permit the passage of hydrophilic molecules up to 1200 Da(Simpson et al., 1977), the dye would be expected to pass freely from one principal cell to another. However, permeation through gap junctions is also influenced by charge. Lucifer Yellow is a divalent anion. Hence, negative fixed charges in the gap junction pore may thwart its passage through the gap junction in Aedes Malpighian tubules (Brink and Dewey, 1980; Veenstra,1996).

In both vertebrate and invertebrate cells, reports of electrical coupling,but not dye coupling, are not uncommon. Micromeres of the starfish(Tupper and Saunders, 1972),early embryonic cells of the amphibian(Slack and Palmer, 1969),embryonic cells of the killifish (Bennett et al., 1972), cells in the developing insect epidermis(Warner and Lawrence, 1982)and cells of mouse blastocysts (Lo and Gilula, 1979), all exhibit electrical coupling but do not allow the passage of Lucifer Yellow. The permeability of gap junctions to Lucifer Yellow depends upon the proteins that compose the gap junctions. Vertebrate gap junctions composed of connexin 43 (Cx43) permit the passage of both Lucifer Yellow and current, whereas those composed of Cx45 only allow the passage of current (Martinez et al.,2002; Steinberg et al.,1994). Developmental changes involving the downregulation of Cx43 and Cx26 and the upregulation of Cx31 and Cx31.1 result in a dramatic reduction of the transfer of Lucifer Yellow between cells without affecting their electrical coupling (Brissette et al., 1994).

The permeability of gap junctions to Lucifer Yellow may also be regulated by heteromerization and/or post-translational modification of connexins. Coexpression of Cx45 with Cx43 in vertebrate HeLa cells reduces the permeability of the gap junctions to Lucifer Yellow and results in a unique electrical conductance not seen before the coexpression(Martinez et al., 2002). When gap junctions composed of Cx40 are exposed to cAMP their permeability to Lucifer Yellow is enhanced (van Rijen et al., 2000). In contrast, the permeability of gap junctions made of Cx43 to Lucifer Yellow is decreased by exposure to protein kinase C(Bao et al., 2004).

Although the above examples are from vertebrate gap junctions composed of connexins, similar functional and regulatory properties may also apply to invertebrate gap junctions made of innexins. For example, disruption of the gene encoding the innexin passover' prevents dye coupling in the giant fiber system of Drosophila (Phelan et al., 1996). Since the transcript for passover' is not expressed in Aedes Malpighian tubules (Fig. 10), the absence of this innexin may explain the failure of Lucifer Yellow to pass between principal cells in our study.

In addition to the above explanations, previous investigators have suggested that a failure to observe dye coupling between insect cells can be attributed to (1) the use of an unphysiological saline(Bohrmann and Haas-Assenbaum,1993), and (2) impalement damage that allows Ca2+ to leak into the injected cell and close dye-permeable gap junctions(Lang and Walz, 1999). The first artifact can be ruled out in the present study, because isolated Malpighian tubules of Aedes aegypti bathed in the saline that we used in the present study secrete fluid for hours(Beyenbach and Dantzler, 1990),which would not be expected with use of an unphysiological solution. The second artifact can also be ruled out, because after impaling a principal cell for the injection of Lucifer Yellow, the dye arrives first in the tubule lumen and later in the fluid exiting the open end of the tubule, which confirms that the cell was not damaged to the point of stopping secretory transport(Fig. 8).

### A glimpse at the regulation of gap junctions in AedesMalpighian tubules

Although it is known that cytoplasmic Ca2+ can close gap junctions, the Ca2+ concentration required to do so ranges from nanomolar to millimolar (Peracchia,2004). If the gap junctions in Aedes Malpighian tubules are closed by a rise in intracellular Ca2+, then a cytoplasmic Ca2+ concentration higher than that achieved in the presence of the Ca2+ ionophore A23187 and a peritubular Ca2+concentration of 1.7 mmol l–1 is necessary. A23187 significantly decreased the input resistance from 215 kΩ to 194 kΩ(Table 4), which importantly stems from the decrease in the non-junctional resistance but not from the gap-junctional resistance. Accordingly, the ionophore induced changes at the level of basolateral and/or apical cell membranes of principal cells but not gap junctions. These observations indicate that gap junctions in Aedes Malpighian tubules are relatively insensitive to changes in cytoplasmic Ca2+ concentrations.

In contrast, the metabolic inhibition of the tubule with dinitrophenol had profound effects on all measured electrophysiological variables(Table 4). What stands out is the dramatic effect on the gap-junction resistance, which increased from 0.526 MΩ to 30.7 MΩ. The 60-fold increase reflects complete uncoupling,i.e. the complete closure of gap junctions. Supporting this conclusion is the increase of the non-junctional resistance to 1483 kΩ, which is strikingly close to the input resistance of 1474 kΩ in the presence of dinitrophenol (Table 4). The non-junctional resistance reflects largely the resistances of the basolateral and apical membranes of the principal cell. When that resistance equals the input resistance of the cell, there may be no other conductive pathways out of the cell, which documents the complete closure of gap junctions during metabolic inhibition. Thus, dinitrophenol closes gap junctions in insect Malpighian tubules. It also closes gap junctions in vertebrate tissues(Deleze and Herve, 1986).

From previous studies we know that dinitrophenol or cyanide completely inhibits transepithelial electrolyte and fluid secretion in AedesMalpighian tubules (Pannabecker et al.,1992). Specifically, dinitrophenol causes (1) intracellular ATP concentrations to drop from 0.9 mmol l–1 to 0.08 mmol l–1 within 2 min, (2) membrane and transepithelial voltages to decrease towards zero, and (3) the transepithelial electrical resistance and the cell input resistance to rise to maximum values as pathways for electrolytes across the basolateral and apical membranes shut down(Beyenbach and Masia, 2002; Pannabecker et al., 1992; Wu and Beyenbach, 2003). The present study shows that next to the shutdown of traffic across cell membranes, traffic through gap junctions also shuts down. Whether this shut-down reflects the regulation of gap junctions by intracellular ATP concentration remains to be determined, but ATP regulation is known for vertebrate gap junctions (Sugiura et al.,1990). The direct effect of dinitrophenol on gap junctions is unlikely because the large increase in the input resistance in the presence of dinitrophenol (Table 4) can be duplicated with cyanide, another inhibitor of ATP synthesis(Wu and Beyenbach, 2003).

### Molecular evidence of gap junctions in insect Malpighian tubules

The molecular basis of gap junctions in invertebrates has been a mystery for decades. Connexin proteins were first identified in the 1970s as the structural components of gap junctions in vertebrates(Goodenough, 1974). For more than 20 years, the term connexin' became synonymous with gap junctions,whereas efforts to find the homologous connexin in invertebrates were unsuccessful (Phelan et al.,1998). It was only in 1998 that the gene family encoding invertebrate gap-junction proteins, innexins, was first confirmed in Drosophila (Phelan et al.,1998). To date, eight innexin genes have been found in the fruit fly, and 25 innexin genes in C. elegans(Phelan, 2005).

In the present study we identify six innexin-like genes in Aedes(Table 5). The neighbor-joining tree (Fig. 9) shows that most of the innexins in Aedes are still closely related to their Drosophila homologues despite the 250 million years of evolution that separate the mosquito from the fruit fly(Severson et al., 2004). The strong evolutionary conservation of innexins confirms the critical roles that gap junctions are now known to play in diverse functions of cells and tissues.

The neighbor-joining tree (Fig. 9) also shows that AeInx7 and AeInx4 are the least conserved with their Drosophila homologues. In particular, AeInx4 is the most divergent as it only loosely clusters with DrInx4, as well as DrInx5 and DrInx6. Two interpretations from this branching pattern are that: (1) the Inx4gene has evolved the fastest since the last common ancestor of both Aedes and Drosophila; and (2) Inx5 and Inx6 are unique to Drosophila, possibly evolving from gene duplications of Inx4. The latter interpretation is consistent with that of Stebbings et al. (Stebbings et al., 2002) who proposed that certain topological features of DrInx5 and DrInx6 are likely to have evolved recently.

Our RT-PCR studies indicate that transcripts for four of the Aedesinnexins are expressed in Malpighian tubules: AeInx1, AeInx2, AeInx3 and AeInx7(Fig. 10). Thus, one or more of these innexins may mediate the electrical coupling we observe between principal cells. Based on previous findings in Drosophila, we hypothesize that AeInx7 may be the dominant gap-junction transcript expressed in Aedes Malpighian tubules. For example, a tissue-specific`transcriptome' analysis of adult Drosophila found detectable expression of Inx2 in Malpighian tubules, but Inx7 was enriched 11-fold in Malpighian tubules compared to expression levels in the whole fly(Chintapalli et al., 2007). Furthermore, developmental studies on the expression of innexins in Drosophila indicate that Inx7 is exclusively expressed in the Malpighian tubules and midgut-progenitor cells from stage 11 onwards(Stebbings et al., 2002). Future studies aimed at quantifying the relative abundance of transcripts for AeInx1, AeInx2, AeInx3 and AeInx7 in Aedes Malpighian tubules are of obvious importance.

Our finding that Aedes Malpighian tubules express more than one innexin provides the possibility that principal cells form heteromeric gap junctions in which a single hemi-channel consists of different innexins. Such heteromerization occurs when Inx2 and Inx3 from Drosophila are coexpressed heterologously in paired Xenopus oocytes(Stebbings et al., 2000). Heteromeric gap junctions may provide a spectrum of permselectivity from ions to second messengers and increase the potential for regulating communications through gap junctions (Cottrell and Burt,2005; Zampighi et al.,2005).

To verify heteromerization of innexins in Malpighian tubules it will be necessary to localize each innexin isoform in the tubule using in situ hybridization and immunohistochemistry. The localizations would also determine if the four innexins that we have identified indeed localize in Malpighian tubules proper, and not in the tracheal tubes associated with Malpighian tubules, as was recently shown for an aquaporin channel in Aedes (Duchesne et al.,2003; Pietrantonio et al.,2000). The localization of innexins would also settle the question about the presence of gap junctions in stellate cells and identify the innexins that form them.

In conclusion, our study establishes the presence of gap junctions in Malpighian tubules of insects that may underlie the nearly perfect electrical coupling of membrane voltages and their oscillations. The inability of Lucifer Yellow to pass through gap junctions may reflect geometric and/or electrical barriers in the gap channel pore. Compared to known single gap-junction conductances, our measurement of the gap-junction resistance suggests that several thousand gap junctions join one principal cell of the tubule to the next. Calcium does not appear to regulate gap junctions in Malpighian tubules of the yellow fever mosquito, but metabolic inhibition with dinitrophenol uncouples gap junctions completely. Whether the shutdown of gap junctions is due to decreased intracellular ATP concentrations and/or reduced membrane voltages is unknown. Our initial molecular studies identified six innexins in the genome of Aedes aegypti, of which four are expressed in Malpighian tubule cDNA. Our measurement of the gap-junction resistance is the first in an intact Malpighian tubule under physiological conditions. The measurement advances the electrical model from a single cable to a double cable with the promise of increased refinement in the measurement and interpretation of electrophysiological data from the tubule.

LIST OF SYMBOLS AND ABBREVIATIONS

• DNP

dinitrophenol

•
• E

electromotive force

•
• Igj

gap-junction current

•
• Iinject

current injected

•
• Inj

non-junctional current

•
• l

distance

•
• ORF

•
• Ra

apical resistance

•
• ra

length-specific axial cell resistance

•
• Rbl

basolateral resistance

•
• Rco

core resistance

•
• Rgj

gap-junction resistance

•
• Rinput

input resistance

•
• Rlu

tubule lumen resistance

•
• Rnj

non-junctional resistance

•
• rr

•
• Rsh

single shunt resistance

•
• Vbl

basolateral membrane voltage

•
• Vt

transepithelial voltage

•
• λ

cell length constant

This work was part of a doctoral dissertation submitted by XingHe Weng to the Graduate School of Cornell University. The research would not have been possible without the support from the National Science Foundation(IOB-0542797). We thank Richard Veenstra (SUNY Upstate Medical University,Syracuse, NY, USA) for generous counsel during the years of this study, and we acknowledge Isabel Rodriguez-Barraquer for her exploratory electrophysiological work on gap junctions in mosquito Malpighian tubules. We are grateful to Dimitri Boudko (Whitney Laboratory, St. Augustine, FL, USA)for providing the adult Aedes Malpighian tubule cDNA library that we used as an independent control in our molecular studies.

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