• You are studying a disease in which muscle becomes weak due to difficulty in generating action potentials.

image-20250217182418491

  • Shown on the left are the responses of a control muscle fiber and a diseased muscle fiber to various levels of depolarizing ( positive ) current injection.

  • On the right are shown the responses of the same two fibers to a 10 nA ( 10-9A ) injection of hyperpolarizing ( negative ) current.

Data

https://docs.google.com/spreadsheets/d/1BXYugUqxdMbJOzF7KYZInowUu9bOUavi2shYJFBz6p4/edit?usp=sharing

  1. Determine the resting membrane potential of each fiber. Also graph the current versus voltage plot for each fiber

    • Control RMP = 70 mV

    • Disease RMP = 90 mV

    image-20250220164726226

  2. Calculate the input resistance of each fiber.

    • Let Control Vmax=130 mV

    V=IR
    ΔVcontrol=( 130 mV )( 70 mV )=60 mV
    Rcontrol=60103 V10109 A=6.01021.0108=6.010( ( 2 )( 8 ) )=6.0106 Ω
    • Let Disease Vmax=120 mV

    ΔVdisease=( 120 mV )( 90 mV )=30 mV
    Rdisease=30103 V10109 A=3.01021.0108=3.010( ( 2 )( 8 ) )=3.0106 Ω

    • Then from the graphs , the slope is the same thing as conductance

    • conductance = opposite of resistance

    Rcontrol=11.67107=5.988023952095808383233532934106 Ω
    Rdisease=13.33107=3.003003003003003003003003003106 Ω
  3. Measure the time constant of each fiber.

    60 mV( 11e )37.927 mV
    ( 70 )+( 37.927 )=107.927 mV
    τcontrol48 milli seconds

    30 mV( 11e )18.9636 mV
    ( 90 )+( 18.9636 )=108.9636 mV
    τcontrol25 milli seconds
  4. Given the difference in resting potential and the response to hyperpolarizing ( negative ) current injection , predict what functional change might account for the reduced excitability of the disease cell.

    • the disease state has an increased amount of potassium conductance at the resting state

    • it has a shorter time constant , so it charges and discharges the membrane faster

    • they probably have upregulated potassium channels somehow