<p>The author has just chosen to draw the battery "backward" in the diagram to go along with the negative sign. In the equations, the direction of the battery should just be oriented by convention according to outward vs. inward.</p>

<p>Note that <span class="math-container">$E_{K} = -75 mV$</span>. If you were to use instead your equation:</p>

<p><span class="math-container">$$V_m = -E_{K} + I_{K} / g_{K}$$</span> </p>

<p>you would need to take <span class="math-container">$E_{K} = 75 mV$</span> and you'd arrive at the same answer.</p>

<p>I'd say there is a bit of a physics vs. biology clash here; in physics, it's more typical to go with certain explicit/literal conventions which then fit nicely into particular equations, and that's how you're thinking about it. In biology, we tend to take some shortcuts.</p>

CC BY-SA 4.0
2020-06-08T22:09:56.550Z
2020-06-08T22:09:56.550Z
Bryan Krause
<p>From chapter <span class="math-container">$7$</span> of Kandel et all's Principles of Neural Science:, <a href="https://www.google.com/url?sa=t&amp;rct=j&amp;q=&amp;esrc=s&amp;source=web&amp;cd=&amp;ved=2ahUKEwiegpi-_PLpAhVWG80KHYPbA40QFjAAegQIBxAB&amp;url=http%3A%2F%2Fwww.columbia.edu%2Fcu%2Fbiology%2Fcourses%2Fw3008%2F2004%2FWeek_03_22%2Fchapter_7_KS.pdf&amp;usg=AOvVaw3G0xCQgu_D3ylJE0UEVIzC" rel="nofollow noreferrer">Go to page 12, Box 7-2</a> (particular image attached below)</p>

<p>The author claims that <span class="math-container">$$V_m = E_{Na} + I_{Na} / g_{Na}$$</span> on one side of the equation and then says <span class="math-container">$$V_m = E_{K} + I_{K} / g_{K}$$</span> by looking at the other side of the circuit.</p>

<p>But how can this be?  Since the battery is showing a negative side facing <span class="math-container">$V_{in}$</span> doesn't it have to be</p>

<p><span class="math-container">$$V_m = -E_{K} + I_{K} / g_{K}$$</span> </p>

<p>Am I misunderstanding something or did the author make a mistake in calculation?</p>

<p><a href="https://i.sstatic.net/mcmUA.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/mcmUA.png" alt="enter image description here"></a></p>

<theoretical-neuroscience>
Equivalent Circuit of cell membrane potential
Oliver G
# Equivalent Circuit of cell membrane potential

(Asked by: username_0 on 2020-06-08)

From chapter $7$ of Kandel et all's Principles of Neural Science:, [Go to page 12, Box 7-2](https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwiegpi-_PLpAhVWG80KHYPbA40QFjAAegQIBxAB&url=http%3A%2F%2Fwww.columbia.edu%2Fcu%2Fbiology%2Fcourses%2Fw3008%2F2004%2FWeek_03_22%2Fchapter_7_KS.pdf&usg=AOvVaw3G0xCQgu_D3ylJE0UEVIzC) (particular image attached below)

The author claims that $$V\_m = E\_{Na} + I\_{Na} / g\_{Na}$$ on one side of the equation and then says $$V\_m = E\_{K} + I\_{K} / g\_{K}$$ by looking at the other side of the circuit.

But how can this be? Since the battery is showing a negative side facing $V\_{in}$ doesn't it have to be

$$V\_m = -E\_{K} + I\_{K} / g\_{K}$$

Am I misunderstanding something or did the author make a mistake in calculation?

[![enter image description here](https://i.sstatic.net/mcmUA.png)](https://i.sstatic.net/mcmUA.png)

**Tags:** theoretical-neuroscience


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## 1 answers

### Answer by username_1 on 2020-06-08. Score: 1

The author has just chosen to draw the battery "backward" in the diagram to go along with the negative sign. In the equations, the direction of the battery should just be oriented by convention according to outward vs. inward.

Note that $E\_{K} = -75 mV$. If you were to use instead your equation:

$$V\_m = -E\_{K} + I\_{K} / g\_{K}$$

you would need to take $E\_{K} = 75 mV$ and you'd arrive at the same answer.

I'd say there is a bit of a physics vs. biology clash here; in physics, it's more typical to go with certain explicit/literal conventions which then fit nicely into particular equations, and that's how you're thinking about it. In biology, we tend to take some shortcuts.


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