You are a neuroengineer interested in developing better nerve stimulators for pr

Question

You are a neuroengineer interested in developing better nerve stimulators for prothetic limbs, such as arms, hands or legs. You want to understnad the flow of ions across the typical nerve cell membrane during action potentials, or spikes.

Assumptions:

a) Depolrization phase: Na+ ions flow into the cell at a rate of 8.2 X 10^15 ions/(cm^2*s)

b) Duration of the Depolarization phase: 0.15 ms.

c) Repolarization phase: K+ ions flow out of the cell at a rate of 4.4 X 10^15 ions/(cm^2*s)

d) Duration of the Repolarization phase: 0.27ms

e) Size of the nerve cell membrane patch involved the action potential: 25 micrometers^2

f) Area conversion : 1 cm^2 /10^8 micrometers^2

g) Na+ and K+ have an elementary charge of +1 , or +1.7 X 10^-19 C/ion

1) Calculate the inlet rate (ions/s ) for Na+ during the depolrization phase?

2) Calculate the outlet rate (ions/s) for K+ during the Repolarization phase?

3) Calculate the current (C/s) for Na + during the Depolarization phase?

4) Calculate the current (C/s) for K+ during the Repolarization phase?

5) Calculate the total charge increae inside the nerve cell (C) for Na+ during the Depolarization phase?

6) Calculate the total charge decrease inside the nerve cell (C) for K+ during the Repolarization phase?

7) Calculate the net change in charge inside the nerve cell (C) for both phases of the action potential?

8) This change in charge does not remain for very long. What cell membrane mechanism reduces this charge imbalance over time?

Explanation / Answer

Using the given assumptions,

1) The inlet rate for Na+ during the depolarization phase

= (Na+ ion flow rate)*(Size of the nerve cell membrane patch involved the action potential)

= (8.2 * 1015 ion s-1 cm-2)*(25 µm2) = (8.2 * 1015 * 10-4 ion s-1 m-2)*(25 * 10-12 m2)

= 8.2 * 25 * 1015-12+4 ion s-1= 205 * 107 ion s-1 = 2.05 * 109 ion s-1

2) The outlet rate for K+ during the Repolarization phase

= (K+ ion flow rate)*(Size of the nerve cell membrane patch involved the action potential)

= 4.4 * 1015 * 25 * 10-8  ion s-1(In the same way as in part 1) = 110 * 107 ion s-1 = 1.10 * 109 ion s-1

3) The current for Na + during the Depolarization phase

= (Elementary charge of Na+) * (The inlet rate for Na+ during the depolarization phase, as calculated in part 1)

= ~1.602 * 10?19 * 2.05 * 109 C s-1 = ~3.28 * 10-10 C s-1

4) The current for K+ during the Repolarization phase

= (Elementary charge of K+) * (The outlet rate for K+ during the Repolarization phase)

= ~1.602 * 10-19 * 1.10 * 109 C s-1 = ~1.76 * 10-10 C s-1

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.