• A :

  • current electrode $\left(I_M\right)$$\left(\ I_M \ \right)$ :

    • delivers current

    • needs a ground to complete the circuit

  • voltage electrode $\left(E_M\right)$$\left(\ E_M \ \right)$

    • measures / records the membrane potential

    • connected to amplifier ( triangle )

  • circuit diagram : electrical model of the paramecium's membrane

    • $C_M$$C_M$ : membrane capacitance ( ability to store charge )

    • $R_M$$R_M$ : membrane resistance ( ion channels / leakage )

    • Connected in parallel between inside / outside

• B :

  • Membrane Potential Recordings ( $E_m$$E_m$ ) generated by 3 different current pulses with increasing amplitude

  • Three current pulses with progressively larger current steps

    • 0.023 nA , 0.115 nA , 0.23 nA

  • Resting Membrane Potentail = $-30mV$$-30\ mV$

  • Also in the voltage traces $\left(E_m\right)$$\left(\ E_m \ \right)$ ,

    • they are both depolarizing and hyperpolarizing

    • potassium channels ?

For I/V Plots

• let 1.7 cm = 10 mV

  • $\frac{1.7cm}{10mV}$$\frac{1.7\ cm}{10\ mV}$

• https://docs.google.com/spreadsheets/d/1wifR-23MPgIjohKm3V95hU6fXJVN2OItsUKGZBsq34o/edit?usp=sharing

Calculate Input Resistance

Construct a Current-Voltage Plot

Measure the Time Constants

• Measure initial , and peak y-values

  • initial = $-30mV$$-30\ mV$

  • final = $-27mV$$-27\ mV$

• Calculate $\tau$$\tau$ graphically :

  • find difference in y-values :

    $$((-27)-(-30))=3mV$$

  • take approximately 63% of the value :

    $$3mV\ast (1-\frac{1}{e})=1.896361676485673mV$$

  • add this number to initial y-value :

    $$(-30.0)+(1.896361676485673)=-28.10363832351433mV$$

  • find corresponding x-value to this calculated y-value :

    • i got roughly 4 centimeters between initial x value of pulse and then over to where -28 would be

    • 200 milliseconds = 17.5 cm

    • so 4 centimeters :

Calculate the Capacitance

Calculate Input Resistance

Construct a Current-Voltage Plot

Measure the Time Constants

• Measure initial , and peak y-values

  • initial = $-30mV$$-30\ mV$

  • final = $-17mV$$-17\ mV$

• Calculate $\tau$$\tau$ graphically :

  • find difference in y-values :

    $$((-17)-(-30))=13mV$$

  • take approximately 63% of the value :

    $$13mV\ast (1-\frac{1}{e})=8.21756726477125mV$$

  • add this number to initial y-value :

    $$(-30.0)+(8.21756726477125)=-21.782432735228753mV$$

  • find corresponding x-value to this calculated y-value :

    • i got roughly 4 centimeters between initial x value of pulse and then over to where -21 would be

    • 200 milliseconds = 17.5 cm

    • so 4 centimeters :

Calculate Capacitance

Calculate Input Resistance

Construct a Current-Voltage Plot

Measure the Time Constants

• Measure initial , and peak y-values

  • initial = $-30mV$$-30\ mV$

  • final = $-10mV$$-10\ mV$

• Calculate $\tau$$\tau$ graphically :

  • find difference in y-values :

    $$((-10)-(-30))=20mV$$

  • take approximately 63% of the value :

    $$20mV\ast (1-\frac{1}{e})=12.642411176571153mV$$

  • add this number to initial y-value :

    $$(-30.0)+(12.642411176571153)=-17.35758882342885mV$$

  • find corresponding x-value to this calculated y-value :

    • i got roughly 4 centimeters between initial x value of pulse and then over to where -17 would be

    • 200 milliseconds = 17.5 cm

    • so 4 centimeters :

Calculate the Capacitance of this Paramecium

Comment on the Electrical and Structural Properties of this Paramecium

• human neurons have around 10-50 ? pico Farads

  • https://pmc.ncbi.nlm.nih.gov/articles/PMC1300935

• these Paramecium have much much higher capacitance of around 350-500 pico Farads

• they all have virtually the same time constant

• Capacitance is directly proportional to total surface area