Action Potential with Nerve Cell and Finding Power

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SUMMARY

The discussion focuses on calculating the power required for active Na+ pumping during an action potential in nerve cells. The Na+ ions enter the cell at a rate of approximately 3 x 10^-7 mol/m²/s against a potential difference of +30 mV. The power output is estimated using the formula P = IV, resulting in a calculated power of approximately 9.09 x 10^-9 W. The calculations involve converting moles of Na+ ions to charge units and utilizing the dimensions of the axon, specifically its length of 40 cm and diameter of 30 µm.

PREREQUISITES
  • Understanding of action potentials in nerve cells
  • Familiarity with the formula P = IV for power calculations
  • Knowledge of basic electrochemistry, specifically charge of ions
  • Ability to calculate area from geometric dimensions (axon dimensions)
NEXT STEPS
  • Research the resistivity of biological fluids for accurate calculations
  • Learn about the role of ion channels in action potentials
  • Study the conversion of moles to coulombs for ion charge calculations
  • Explore the impact of axon diameter on conduction velocity and power requirements
USEFUL FOR

This discussion is beneficial for students in neuroscience, biophysics, and biomedical engineering, particularly those studying cellular physiology and electrical properties of nerve cells.

PeachBanana
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Homework Statement



During an action potential, Na + ions move into the cell at a rate of about 3 x 10^-7 mol / m^2 s. How much power must be produced by the "active Na+ pumping" system to produce this flow against a + 30 mv potential difference? Assume that the axon is 40cm long and 30 mu m in diameter.

Homework Equations



P = IV
maybe R = ρL / A

The Attempt at a Solution



I understand I need to use P=IV but I don't understand how to incorporate the measurements of the axon without knowing the resistivity of the liquid. Should I assume water?

P = (3.7 * 10^-7 mol/m^2 s)(0.03 V)
P ≈ 9.09 * 10^-9 W
 
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The diffusion rate is given in terms of moles per unit area per second. Use the axon dimensions to estimate area. You'll also have to convert the moles of charges into actual charge units (what's the unit charge of an Na+ ion in coulombs?).
 

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