Bio-Rad Gene Pulser Xcell™ Electroporation Systems - Manual (Page 51)

4.1 Exponential Decay Pulses
The exponential decay circuit of the Gene Pulser Xcell generates an electrical pulse by discharging a capacitor.
When a capacitor is discharged into the sample, the voltage across the electrodes rises rapidly to the peak
voltage then declines over time, t, with an exponential decay waveform (Figure 4.1A) according to the
following equation:
V
t
= V
0
[e -(t/RC) ],
where V
0
is the initial voltage in the capacitor, V
t
is the voltage at time = t (msec) after the pulse, e is the base
of the natural logarithm, R is the resistance of the circuit (expressed in ohms), and C is the capacitance
(expressed in microfarads). The time required for the initial voltage to drop to V
0
/e is referred to as the time
constant, τ, a convenient expression of the pulse length (expressed in msec). When t = τ = R x C, the
voltage has declined to 1/e (~37%) of the initial value, V
0
(V
τ
= V
0
/ e).
By changing the capacitor of the instrument or by changing the resistance of the circuit, the time
constant may be readily changed. When high-resistance media is used (e.g., low ionic-strength media
used for most bacteria and yeast), the resistance of the circuit may be controlled using the PC Module
which places a resistor in parallel with the sample. For resistors connected in parallel, the total resistance
of the circuit is given by the equation:
R
T
= (R
sample
* R
PC
) / (R
sample
+ R
PC
).
When the sample resistance is much greater than the resistor in the PC Module (R
sample
>> R
PC
), the
latter is the primary determinant of the resistance of the circuit and R
T
~ R
PC
. Therefore, the PC Module
reduces the resistance of the circuit thereby reducing the time constant of the circuit.
When low-resistance media is used (e.g., high ionic-strength media such as PBS or growth media
used for most mammalian cells), the time constant is most easily manipulated by selecting the proper
capacitor for the circuit using the CE Module. Additionally, changing the volume of low -resistance
media in the cuvette will alter the resistance of the circuit (resistance is inversely proportional to volume).
4.2 Square Wave Pulses
Truncating the pulse from a capacitor after discharging it into the sample generates square wave pulses.
The ideal square wave pulse has the same voltage at the end as at the beginning of the pulse (Figure
4.1B). However, using a charged capacitor to produce this waveform (as is done in all commercially
available electroporation instruments), the voltage at the end of the pulse, V
t
, is always less than the
voltage at the beginning of the pulse, V
0
. This is because when the switch is closed across a charged
capacitor, maximum current instantaneously flows through the circuit and gradually falls to zero. To
produce a square wave, the pulse is terminated at some time, t, following discharge of the capacitor.
This time (t) is termed the pulse length. The longer the pulse length, the greater is the difference in voltage
between the beginning and the end of the pulse. This voltage decay may be determined from the
following equation:
ln (V
0
/ V
t
) = t / (R C).
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