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Capacitance measurements

In order to measure exocytosis, we take advantage of the fact that during the fusion of the neurotransmitter containing vesicle with the plasma membrane the cells surface area increases,  at least transiently:

 

 

This increase in cell surface area can be measured by determining the cell membrane capacitance C_m since the value of a capacitor is directly proportional to its surface area. All biological membranes seem to have the same specific capacitance (i.e. capacitance per unit area) of 1mF/cm². The current that flows across a capacitor is given by:

                                   I_c= C*dV/dt

                                                            Thus, if the voltage does not change there is no capacitative current flow. Membranes do not only behave as capacitors, but also have resistive properties. The current that flows across a resistor is given by Ohm"s law:

                                     I_R = V/R  

                                                            In other words, there is only a current if there is a voltage and the two are directly proportional. So if we know the voltage command and measure the current that flows across a cell, we can separate the capacitative current and the resistive current.

 

 

Imagine applying a sine wave command (V_Command, top) to the cell and measuring the resulting membrane current (I_m, bottom, dashed black curve). This overall current contains a resistive and a capacitative component. When the voltage does not change, i.e. at the peaks of the sine wave (vertical blue dashed lines), there is no no capacitative current and thus all the current is resistive. At this point we can determine the magnitude of R_m since we know the voltage and just measured the current. At the point where the voltage changes the most, i.e. at the inflection points of the sine wave (vertical red dashed lines), there is no net applied voltage and thus no resistive current. All the current we are measuring is thus capacitative. Again, since we know the voltage and the current we can calculate the membrane capacitance.

For this method to work, it is best to deal with a release site that is electrically compact (sphere like). Most nerve terminals are too small to be impaled with microelectrodes or to be patched. We are thus using hair cells from the frog vestibular system for these experiments. These cells have interesting release properties in that they seem to release over tens of milliseconds and release is thought to be triggered by graded potentials rather than action potentials. The release site is structurally distinct by the presence of a "synaptic body". This is a structure of unknown function that can be easily seen under the electron microscope as having synaptic vesicles attached to it. One goal of our studies is to investigate whether vesicles that are tethered to the synaptic body constitute a special subset or pool of synaptic vesicles.

 

 

 

 

This picture illustrates the two recording conditions that we use. The perforated patch recording technique has the advantage of not disturbing the intracellular milieu, while whole-cell recording allows for the introduction of macromolecules into the intracellular compartment.

The red circle indicates the synaptic body while the yellow filled circles are synaptic vesicles. In reality, these hair cells do not contain one but on average about 20 active zones with synaptic bodies.

 

 

In this experiment a hair cell was depolarized from a holding potential of -75mV to -20mV for 25ms at the arrow. The capacitance before the depolarization was about 14pF and increased by about 400fF in response to the depolarization. Since all membranes have the same capacitance per unit area and since we know the diameter of the synaptic vesicles, we can calculate that about 500 vesicles fused at each synaptic body in response to this stimulus.