Gating compliance measurements

I used electrostatic actuation to apply force steps onto the antennal sound receiver.

Jörg Albert described this method first for flies [24] and I improved and adapted it. Together with Dr. Albert I improved the technique by introducing two instead of one electrostatic probe, to equally push

and pull the antennal receiver. In addition, we kept the animal on a static potential of -100 V over ground to compensate for polarization effects. Thus, we improved the linearity of applied forces. I used bipolar tungsten stereotrodes (WE3ST31.0A5 and WE3ST31.0A10, Micro Probe, Inc.) as actuator probes. The probes were aligned in the optical axis of the LDV anterior and posterior of the arista (Figure 29). The probes could be charged up to ± 400 V. This increased the possible forces acting on the antennal sound receiver and allowed to

Figure 29 gating compliance setup One bipolar electrode was positioned anterior (aE) and a second posterior (pE) of the arista. The fly was held at a static potential of -100V over ground via a charging/indifferent electrode (cE). The LDV recorded the antennal displacement and a recording electrode (rE) allowed for a simultaneous recording of the CAP response. Modified from [24]

Mechanical Measurements

position the probes further away from the antenna, to compensate for the quadratic relation between stimulus voltage and force (previous measurements used only ± 40 V).

The antennal displacement was monitored with the LDV and the CAP response was simultaneously recorded (Figure 30). We distinguished two different stiffnesses:

and . is contributed by the combined stiffness of the a2/a3 joint and of structures that suspend JO but are not contributing to the mechanical stimulus coupling [25] from the sound receiver to the mechanotransduction channel, as such

is linear. is contributed by the gating spring and the dynamic stiffness changes based on the opening and closing of transduction channels. Thus is nonlinear and depends on the acting force, the number of channels, their open probability, the gating swing, and the energy needed to gate a single channel.

2.4.3.1 Force estimation & stiffness calculation

Stiffness is the ratio between external force and displacement = . The displacement was measured with the LDV. The external force, however, could not be directly measured. Hence, we deduced the external force from the receiver’s initial acceleration ( ) upon stimulus onset and its apparent mass ( ). At a given mass of 5 ng [54] this equation provides an estimate for the external force acting on the antennal sound receiver. For we assume that the displacement at the end of the step only depends on this external, onset force.

Thus, can be written as = and should be linear over the

Figure 30 typical displacement response to a force step

To calculate the dynamic stiffness and the linear stiffness the external forces and the peak-respectively steady-displacement had to be measured. The force relates to the acceleration of the sound receiver by its apparent mass. With a mass of 5 ng the acceleration provided the external force.

By subtracting the acceleration at the displacement peak from the onset acceleration, we corrected for inertia.

complete range of forces. Previous work had shown that was ca. 50 µN/m [24]. Whereas was linear and only depended on the onset acceleration, the dynamic stiffness, , depended on the external force but also on the mass of the sound receiver. Hence, I had to correct the external force derived from the onset acceleration for the inertia of the sound receiver. This was done by subtracting the acceleration at the displacement peak [24]) from the onset acceleration = − . was thus calculated based on the peak displacement, the acceleration at the onset of the step, and corrected for inertia by subtracting the sound receivers acceleration at the peak. Accordingly it read

= ^{( )}.

2.4.3.2 Scaling of individual sound receivers based on their apparent mass

To compare the gating compliance of individual sound receivers they had to be normalized. Previously this had been done by dividing by . This however resulted in the loss of absolute amplitudes. I chose instead to use the apparent mass to scale and normalize the stiffness responses of individual sound receivers of one genotype. I corrected the apparent mass for each individual sound receiver such that the average of the genotype was reached. To facilitate comparison, I shifted and until an average of 50 µN/m was achieved and plotted the gating compliance relative to the peak antennal displacement. Thus, I retained absolute stiffness amplitudes and was able to compare between different flies of the same genotype and between genotypes. To check for the legitimacy of this method I conducted several experiments on anesthetized animals and deduced their apparent mass by fitting a simple harmonic oscillator to the free fluctuations of their sound receivers. The resulting apparent masses were in the range needed to scale the flies of one genotype. The maximal difference in apparent mass needed to scale an individual sound receiver was 15%.

Mechanical Measurements

2.4.3.3 Gating compliance

I used a simplified version of the gating spring model without adaptation motors ( ) = − ∗ (1 − ). is the asymptotic stiffness adopted by the system at infinite displacements. It comprises the linear, passive stiffness and the gating spring stiffness ( ). is the number of channels, the single channel gating force, and the channel open probability: = 1 (1 + e⁄ ^{(( )⁄ )∗} ). The relation between and is given by = , where γ is the scaling factor between neurons and sound receiver and the gating swing. can also be written as = , where is the single channel gating spring and relates to by = . The parameters , , and were fitted.

This equation describes the stiffness changes (gating compliance) of one channel type. Based on the assumption that NompC is a mechanotransduction channel and remnant CAP responses in nompC mutants remained I assumed that a second mechanotransduction channel type must be present in JO-neurons. Accordingly, I introduced the term ∗ (1 − ), which represented the gating spring equation for a second channel type. The equation than reads ( ) = −

∗ _{_} 1 − _{_} − ∗ _{_} 1 − _{_} (Figure 31)This leads to a set of five free parameters: , , , , and . The initial parameter values for , were taken from [24]. Sigmaplot 10 was used for fitting. The fit of the sound receiver mechanics provides the open probability of the mechanosensitive channels. The given parameters and were used to calculate a for all

mechanotransduction channels.

= 1 1 +⁄ ^∗ + 1 1 +⁄ ^∗ ∗ .

Figure 31 equations describing the single channel population situation and the two channel situation

The single channel equation comprises the parallel stiffness and the dynamic stiffness changes of a single type of mechanotransduction channel. These channels are arranged symmetrically around the a2/a3 joint. In the two channel equation system a second term describing a second type of mechanotransduction channel is added. Altered after Nadrowski unpublished.

Mechanical Measurements