jackman/biol125-lectures
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

spring2018 week1

Browse Source
This commit is contained in:
ackman678
2018-04-11 12:51:49 -07:00
parent c933bf3625
commit b3f05472d2
5 changed files with 557 additions and 593 deletions
Download Patch File Download Diff File Expand all files Collapse all files

165
neurophysiology1.md
View File

@@ -1,4 +1,4 @@
## Neuronal signaling
# Neuronal signaling
* Electrical signals of nerve cells
* Voltage-dependent membrane permeability
@@ -104,6 +104,13 @@ mole
: this number is expressed by the Avogadro constant
electricity
: movement of charged carriers through a medium in presence of electric field
: duality of electromagnetic waves as wave or particle
: AC (oscillation of electrons in place) vs DC (movment of electrons)
100 m/s == 360K m/hr == 223 mph
---
## Electrical signals
@@ -208,7 +215,7 @@ Now we already saw that we can stick an electrode into a cell, and hook it up to
Now what if do the same recordings, but also electrically stimulate the cell so that positive or negative charge is added—
---
--
## Recording passive and active electrical signals in a nerve cell
@@ -249,11 +256,24 @@ All electrical signals are the due to the flow of charge, positive or negative.
---
## Ionic movements across neuronal membranes
<figure><img src="figs/Neuroscience5e-Fig-02.04-0R_cf6b01f.png" height="400px"><figcaption>Neuroscience 5e Fig. 2.4</figcaption></figure>
Note:
there are active ion transporters like the Na-K ATPase and there are ion channels. For example you could pretend this is a Na channel that opens when the neuron is depolarized.
---
## Ion transporters and ion channels
* Ion transporters– actively move ions against their concentration gradients, therefore create ion concentration gradients
* Ion channels– proteins that allow only certain kinds of ions across the membrane
* Allow ions to diffuse across the membrane (e.g. due to concentration gradients).
* Allow ions to diffuse across the membrane (e.g. due to concentration gradients).
Note:
@@ -295,19 +315,6 @@ Ion channels span the membrane and act as pores. They can open and close, often
And they can be additionally regulated or ‘gated’ by different mechanisms including voltage or binding of ligands such as neurotransmitters. We will learn much more about the selectivity and function of ion channels a couple lectures from now.
---
## Ionic movements across neuronal membranes
<figure><img src="figs/Neuroscience5e-Fig-02.04-0R_cf6b01f.png" height="500px"><figcaption>Neuroscience 5e Fig. 2.4</figcaption></figure>
Note:
So again there are active ion transporters like the Na-K ATPase and there are ion channels. For example you could pretend this is a Na channel that opens when the neuron is depolarized.
---
## The resting potential
@@ -381,7 +388,7 @@ Note:
## Nernst equation
<div style="font-size:0.7em;">
<div style="font-size:0.6em;">
<div></div>
* Statement of the equilibrium condition for a single ion species across a membrane that is permeable only to that ionic species:
@@ -391,13 +398,13 @@ Note:
* *F* = faraday constant (9.6x10<sup>4</sup> J mol<sup>-1</sup> V<sup>-1</sup>)
* *z* = valence of the ion, including sign.
* ln = natural logarithm (base *e*)
* [*x*]<sub>out</sub> extracellular concentration of an ion extracellular; [*x*]<sub>in</sub> intracellular concentration
* [*x*]<sub>out</sub> extracellular concentration of an ion; [*x*]<sub>in</sub> intracellular concentration
* RT/F can be a constant at room temperature to give a simplified equation
</div>
<div><figcaption class="big">Nernst equation</figcaption><img src="figs/ScreenShot2016-01-12at12.35.02PM_cfc06b6.png" height="100px"><figcaption>For calculations for any temperature, E<sub>x</sub> in volts (V)</figcaption></div>
<div><figcaption class="big">Nernst equation</figcaption><img src="figs/ScreenShot2016-01-12at12.35.02PM_cfc06b6.png" height="100px"><figcaption>For calculations at any temperature, E<sub>x</sub> in volts (V)</figcaption></div>
<div><figcaption class="big">Simplified Nernst equation</figcaption><img src="figs/ScreenShot2016-01-12at12.35.07PM_dc81a98.png" height="100px"><figcaption>For calculations at room temperature (68ºF = 20ºC = 20+273 = 293ºK), E<sub>x</sub> in millivolts (mV)</figcaption></div>
@@ -426,7 +433,8 @@ z
: the valence of the ion in question
ln
: the natural logarithm which has the mathematical constant e or 2.718 as it’s base
: the natural logarithm which has the mathematical constant *e* =~2.718 as it’s base (Euler's number)
: ln(e) = 1, where e =~ 2.718
Now many of the classical experiments recording membrane potential in squid axon or other preparations were conducted at room temperature, which is 20ºC or about 68ºF.
@@ -442,9 +450,9 @@ ln(x) / log10(x) = 2.30
—> 2.30 * log10(x) = ln(x)
logarithm slope example:
x = seq(0,10,0.10)
plot(x,log(x), asp=1)
plot(x,log10(x), asp=1)
x = seq(0,10,0.10);
plot(x,log(x), asp=1);
plot(x,log10(x), asp=1);
R = 8.3 J/K*mol, T = 37ºC + 273ºC = 310 K, F = 9.6*10^4 J/mol*V
@@ -455,22 +463,60 @@ E =
log(7) / log10(7)
R = 8.3
F = 9.6 * 10^4
T = 20+273
(R*T / F) * 1000 * 2.3
==>58.26427
<figure><img src="figs/Screen_Shot_2016-09-29_at_5.15.39_AM_6d8392d.png" height="100px"><figcaption></figcaption></figure>
<figure><img src="figs/Screen_Shot_2016-09-29_at_5.15.43_AM_5c77e27.png" height="100px"><figcaption></figcaption></figure>
--
## Obtaining the simplified Nerst equation
<div style="font-size:0.7em">
<div></div>
Open up your browser's javascript console `cmd-alt-j (or View-->Developer-->). Copy/paste the following lines:
```javascript
R = 8.3 //Gas constant
F = 9.6 * Math.pow(10,4) //Faraday constant
T = 20+273 //Room temperature in Kelvins
```
Relation of the natural lograrithm (base ~2.718...) to the base 10 logarithm is always `ln(x) = 2.30 * log10(x)` or `ln(x) / log10(x) = 2.30`. ln() is `Math.log()` and log10() is `Math.log10()` in js. Copy/paste the following lines. Try varying *x* a few times and re-calculate:
```javascript
x = 5
Math.log(x) / Math.log10(x)
```
Now use our constants defined above, convert to base10 log, and adjust the voltage from V to mV. We get 58 mV for our answer:
```javascript
(R*T / F) * 2.3 * 1000
```
=>58.26427 mV
</div>
Note:
```
var a = [2,5,7,10,1000]
a.forEach(el => console.log( Math.log(el) / Math.log10(el) ))
```
---
## Examples
<div style="font-size:0.7em;">
<div></div>
* Calculate the following equilibrium potentials at room temperature:
* Outside 10 mM KCl, Inside 1 mM KCl membrane only permeable to K⁺ ?
* E<sub>K+</sub> = <span class= "fragment fade-in">(58/1)log10(10/1) ==> +58</span>
@@ -480,6 +526,8 @@ T = 20+273
* E<sub>Ca2+</sub> = <span class= "fragment fade-in">(58/2)log10(10/1) ==> +29 mV</span>
* Nernst predicts linear relationship with a slope of 58 mV (58/z) per 10 fold ion change in concentration gradient <!-- .element: class="fragment fade-in"-->
</div>
Note:
log10(10) = 1
@@ -532,9 +580,9 @@ Note:
---
## Membrane potential influences ion fluxes
## Membrane potential influences the flux of ions
<div><figcaption class="big">Simulated cell at room temperature</figcaption><img src="figs/Neuroscience5e-Fig-02.06-1R_5d1ff2f.png" height="400px"><figcaption>Neuroscience 5e Fig. 2.6</figcaption></div>
<div><figcaption class="big">Simulated cell at room temperature</figcaption><img src="figs/Neuroscience5e-Fig-02.06-1R_5d1ff2f.png" height="350px"><figcaption>Neuroscience 5e Fig. 2.6</figcaption></div>
Note:
@@ -552,7 +600,7 @@ At more negative membrane potentials than the nernst equilbrium potential we get
## Membrane potential influences ion fluxes
<figure><img src="figs/Neuroscience5e-Fig-02.06-2R_1ec257b.png" height="500px"><figcaption>Neuroscience 5e Fig. 2.6</figcaption></figure>
<figure><img src="figs/Neuroscience5e-Fig-02.06-2R_1ec257b.png" height="400px"><figcaption>Neuroscience 5e Fig. 2.6</figcaption></figure>
Note:
@@ -565,6 +613,9 @@ The results of this thought experiment are displayed here, displaying the net mo
## Both direction and magnitude of ion flux depend on the membrane potential
<div style="font-size:0.8em;">
<div></div>
* What would happen if we could add charge to one side without changing the ion distribution?
* Adding negative charge into one side (or positive charge to the other) creates a potential difference across the membrane
* This discourages K⁺ from wanting to flow down its concentration gradient
@@ -572,6 +623,8 @@ The results of this thought experiment are displayed here, displaying the net mo
* At more negative potentials K⁺ will want to flow against its concentration gradient
* Scientists can experimentally vary both ion concentrations and membrane potential
</div>
Note:
So to summarize, remember that both the direction (inward vs outward) and magnitude of charge flow or current depends on membrane potential.
@@ -585,7 +638,7 @@ And we as scientists can experimentally vary...
## Equilibrium with more than one permeant ion
<div style="font-size:0.8em;">
<div style="font-size:0.7em;">
<div></div>
* If inside solution contains 10 mM KCl and 1 mM NaCl and outside solution contains 1 mM KCl and 10 mM NaCl...
@@ -658,7 +711,24 @@ Cells are a bit like a semipermeable bag of electrolytes with different concentr
## Extracellular and intracellular ion concentrations
<figure><img src="figs/Neuroscience5e-Tab-02.01-0_88dd39c.png" height="500px"><figcaption>Neuroscience Table 2.1</figcaption></figure>
<!-- <figure><img src="figs/Neuroscience5e-Tab-02.01-0_88dd39c.png" height="350px"><figcaption>Neuroscience Table 2.1</figcaption></figure> -->
<div style="font-size:0.6em;">
<div></div>
| ion | intracellular conc. (mM) | extracellular conc. (mM) | ratio [x]<sub>out</sub>/[x]<sub>in</sub> |
| --- | --- | --- | --- |
| potassium (K<sup>+</sup>), squid | 400 | 20 | ~0.05 |
| potassium (K<sup>+</sup>), mammal | 140 | 5 | ~0.04 |
| sodium (Na<sup>+</sup>), squid | 50 | 440 | ~9 |
| sodium (Na<sup>+</sup>), mammal | 5–15 | 145 | ~9 |
| chloride (Cl<sup>-</sup>), squid | 40–150 | 560 | ~3.7 |
| chloride (Cl<sup>-</sup>), mammal | 4–30 | 110 | ~3.7 |
| calcium (Ca<sup>2+</sup>), squid | 0.0001 | 10 | 100000 |
| calcium (Ca<sup>2+</sup>), mammal | 0.0001 | 1–2 | 10000 |
<figcaption>see also Neuroscience Table 2.1</figcaption>
</div>
Note:
@@ -687,7 +757,7 @@ As I hinted at earlier today and in a previous lecture, the squid giant axon was
<div><img src="figs/Squid_Loligo_pealei_cbafe46.jpg" height="300px"><figcaption>Atlantic squid, *Loligo pealei*</figcaption></div>
<div><iframe src="https://www.youtube.com/embed/omXS1bjYLMI" width="420" height="315"></iframe><figcaption>Squid giant axon electrophysiology</figcaption></div>
<div><iframe src="https://www.youtube.com/embed/I6jxrxcLxiI" width="560" height="315"></iframe><figcaption>Squid giant axon electrophysiology</figcaption></div>
Note:
@@ -698,10 +768,9 @@ Note:
## Alan Hodgkin and Bernard Katz– 1949
* Hypothesis– if axon resting potential (-65 mV) is predominantly due to K⁺ permeability then changing the outside (K⁺) should change the resting potential in a manner predicted by the Nernst equation
* Experiment– stick an electrode inside axon, one outside axon (in bath). Change the concentration of K⁺ in the bath and measure new membrane potential
* Assumption– intracellular K⁺ is unchanged during experiment
* Nernst predicts– resting potential goes up with a slope of 58 mV per tenfold change in K⁺ gradient
* Hypothesis– if axon resting potential (-65 mV) is predominantly due to K⁺ permeability then changing [K⁺]<sub>out</sub> should change the resting potential in a manner predicted by the Nernst equation
* Experiment– stick an electrode inside axon, one outside axon (in bath). Change the concentration of K⁺ in the bath and measure new membrane potential. Assume intracellular K⁺ is unchanged during experiment.
* Nernst equation prediction– resting potential will depolarize with a slope of 58 mV per tenfold change in K⁺ gradient
Note:
@@ -711,7 +780,7 @@ Alan Hodgkin, Andrew Huxley, Bernard Katz
## K⁺ concentration gradient determines resting membrane potential
<figure><img src="figs/Neuroscience5e-Fig-02.08-0_40bc007.png" height="500px"><figcaption>Neuroscience 5e fig. 2.8</figcaption></figure>
<figure><img src="figs/Neuroscience5e-Fig-02.08-0_40bc007.png" height="400px"><figcaption>Neuroscience 5e fig. 2.8</figcaption></figure>
Note:
@@ -744,10 +813,10 @@ So they correctly concluded that…
## Hodgkin and Katz– 2
* Question– What causes the axon to depolarize during an action potential?
* Measured the membrane potential after initiating an action potential
* Found– Membrane potential during the action potential approached E<sub>Na</sub>
* Measured the membrane potential after initiating an action potential
* Found– Membrane potential during the action potential approached E<sub>Na</sub>
* Hypothesis– During an action potential the axon becomes predominantly permeable to Na⁺ and no longer to K⁺
* Experiment– What happens to the action potential when [Na⁺] is reduced in the external medium?
* Experiment– Measure action potentials after decreasing [Na⁺]<sub>out</sub>
Note:
@@ -766,7 +835,7 @@ Their experiment was to lower Na concentrations in the extracellular medium—
## The action potential as measured by Hodgkin, Huxley, and Katz
<figure><img src="figs/hodkin-huxley-nature-1939-AP_d30dfee.png" height="500px"><figcaption>Adapted from Hodgkin Huxley *Nature* 1939</figcaption></figure>
<figure><img src="figs/hodkin-huxley-nature-1939-AP_d30dfee.png" height="400px"><figcaption>Adapted from Hodgkin Huxley *Nature* 1939</figcaption></figure>
Note:
@@ -781,7 +850,7 @@ Capacitance (farads) is the ability of a body to store an electrical charge. Any
## Role of sodium in the generation of an action potential
<figure><figcaption class="big">Lowering Na⁺ decreases both the rate and the rise of an action potential</figcaption><img src="figs/Neuroscience5e-Fig-02.09-1R_2c02203.png" height="500px"><figcaption>Neuroscience 5e Fig. 2.9</figcaption></figure>
<figure><figcaption class="big">Lowering Na⁺ decreases both the rate and the rise of an action potential</figcaption><img src="figs/Neuroscience5e-Fig-02.09-1R_2c02203.png" height="400px"><figcaption>Neuroscience 5e Fig. 2.9</figcaption></figure>
Note:
@@ -862,5 +931,3 @@ Llinas Sugimori J Physiol 1980 Purkinje neurons
Note:
And this is just a overall summary of what we have been discussing
---