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61
neuroanatomy1.md
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@@ -4,7 +4,7 @@ Neuroscience is a field of scientific study that seeks to understand how the ner
<img src="figs/human-brain.svg" height="300px">
https://courses.pbsci.ucsc.edu/mcdb/bio125/
https://canvas.ucsc.edu/courses/16047/assignments/syllabus
Note:
@@ -22,34 +22,19 @@ Thus it will be you, and your children, and your children’s children that will
## Syllabus and text book
<div style="width:700px; padding:25px 0; float:left;"><a href="https://courses.pbsci.ucsc.edu/mcdb/bio125/">https://courses.pbsci.ucsc.edu/mcdb/bio125/</a></div>
<div style="width:250px; float:left;"><img src="figs/ScreenShot2016-01-04at3.59.29PM_dea1077.png" height="200px"><figcaption></figcaption></div>
<div><a href="https://canvas.ucsc.edu/courses/16047/assignments/syllabus">https://canvas.ucsc.edu/courses/16047/assignments/syllabus</a></div>
--
<div style="width:200px;"><img src="figs/ScreenShot2016-01-04at3.59.29PM_dea1077.png" height="200px"><figcaption>5e 2011</figcaption></div>
## Permission code requests
Just send me an email.
**subject line:**
```txt
permission code request: #biol125
```
**body:**
```txt
Id: 1234567
Name: First Last
Email: cruzid@ucsc.edu
Reason you cannot enroll: Brief description (one line).
```
<div style="width:250px;"><img src="figs/neuroscience6e.jpg" height="200px"><figcaption>6e 2017</figcaption></div>
--
## Site keyboard bindings
<div style="font-size:0.8em">
<div></div>
* Navigate: arrow keys and `spacebar`
* Menu: `m`
* Fullscreen: `f`
@@ -61,7 +46,9 @@ Reason you cannot enroll: Brief description (one line).
<!-- * Print: `...neuroanatomy1.html?print-pdf` -->
Recommend browser is Chrome on a laptop/PC. Some features that only have keyboard bindings (e.g. fullscreen, overview) may not work or be disabled on tablet/touch screen devices.
Recommend browser is Firefox or Chrome on a laptop/PC. Some features that only have keyboard bindings (e.g. fullscreen, overview) may not work or be disabled on tablet/touch screen devices.
</div>
---
@@ -340,12 +327,8 @@ Neurons in culture have specific endings. EM methods, dye filling experiments.
Heinrich Wilhelm Gottfried von Waldeyer-Hartz (6 October 1836 – 23 January 1921) was a German anatomist and conceived the word 'neuron'.
Golgi in his nobel lecture:
>(3) The neuron is a physiological unit. This fundamental idea which Waldeyer
expressed with perfect precision has been enlarged upon both from
anatomical and functional sides with additional propositions, for example :
**The communication between neurons is only established by casual contact.
There is scarcely any nervous tissue apart from the neurons; the neurons are
also trophic units.**
>(3) The neuron is a physiological unit. This fundamental idea which Waldeyer expressed with perfect precision has been enlarged upon both from anatomical and functional sides with additional propositions, for example : **The communication between neurons is only established by casual contact. There is scarcely any nervous tissue apart from the neurons; the neurons are also trophic units.**
---
@@ -437,10 +420,21 @@ afrotheria
</div>
<!--
<div style="width:300px; margin:0 25px; float:left;"><img src="figs/Fig_6852903.png" height="500px"><figcaption></figcaption></div>
-->
<!-- <figure><img src="figs/10-01_GlialCells_1_bddb845.jpg" height="100px"><figcaption></figcaption></figure> -->
<div style="width:300px; margin:0 25px; float:left;">
<figure><img src="figs/glia-astrocyte.svg" width="300px"><figcaption>[JA, CC0](https://creativecommons.org/share-your-work/public-domain/cc0/)</figcaption></figure>
<div style="float:left;"><img src="figs/glia-oligodendrocyte.svg" width="150px"><figcaption>JA, CC0</figcaption></div>
<div><img src="figs/glia-schwann.svg" width="100px"><figcaption>JA, CC0</figcaption></div>
</div>
Note:
@@ -484,13 +478,13 @@ Paraphysis
Pineal gland
Endothelium of the choroid plexus
There is a positive relationship between lipid solubility and brain uptake of chemical compounds
There is a positive relationship between lipid solubility and brain uptake of chemical compounds:
- permeability of lipid soluble compounds is rapid (ethanol, nicotine, diazepam, THC)
- polar molecules (e.g. glycine and catecholamines) enter slowly across BBB
- gases and volatile anesthetics diffuse rapidly into the brain
blood—brain barrier permeability of CO2 greatly exceeds that of H+ thus pH of brain interstitial fluid reflect pCO2 rather than blood pH. Therefore a patient with metabolic acidosis may be brain alkalotic at teh same time.
blood—brain barrier permeability of CO2 greatly exceeds that of H+ thus pH of brain interstitial fluid reflect pCO2 rather than blood pH. Therefore a patient with metabolic acidosis may be brain alkalotic at the same time.
glucose is primary energy substrate of the brain. Nearly all oxygen consumption for the brain. GLUT-1 glucose transporters highly enriched in brain capillary endothelial cells. Since glucose is a polar substrate, this transporter facilitates its transport across the BBB.
@@ -500,6 +494,11 @@ water enters rapidly through diffusion.
<figure><img src="figs/Neurochemistry-fig32-1-BBB_5961e8a.jpg" height="100px"><figcaption></figcaption></figure>
See also review by [^Belanger:2011a] for info on energy dynamics between astrocytes-neurons.
[^Belanger:2011a]: Bélanger, M., Allaman, I., and Magistretti, P. J. (2011). Brain energy metabolism: focus on astrocyte-neuron metabolic cooperation, Cell Metab, 14(6), 724-38
--

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neuroanatomy2.md
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@@ -21,15 +21,14 @@ First of all it is a system of systems. In other words…
Note:
This illustrates the two top level systems of the nervous system, the CNS containing the brain and spinal cord and the PNS containing nerves and ganglia exiting the spinal cord.
Middle: illustrates the two top level systems of the nervous system, the CNS containing the brain and spinal cord and the PNS containing nerves and ganglia exiting the spinal cord.
This diagram outlines the functional hierarchy of different components or systems within the whole nervous system including relations between internal and external environment and sensory receptors in the PNS as well as skeletal muscle and smooth, cardiac muscles that the nervous system controls.
Right: outlines the functional hierarchy of different components or systems within the whole nervous system including relations between internal and external environment and sensory receptors in the PNS as well as skeletal muscle and smooth, cardiac muscles that the nervous system controls.
*Don't worry too much about memorizing the exact details of diagrams such as this, focus on the major concepts and their relations*
right vagus nerve primarily innervates the SA node, whereas the left vagus innervates the AV node
pns supplies smooth muscles, cardiac muscles, and glands. functions to maintain homeostasis, and is concerned with involunary functions.
* right vagus nerve primarily innervates the SA node, whereas the left vagus innervates the AV node
* pns supplies smooth muscles, cardiac muscles, and glands. functions to maintain homeostasis, and is concerned with involunary functions.
---
@@ -45,6 +44,10 @@ pns supplies smooth muscles, cardiac muscles, and glands. functions to maintain
Note:
* white matter: so named because of the bright shiny appearance to the naked eye
* gray matter: so named because it is less bright, a little more dull looking. But nothing dull about it.
--
## Common techniques to visualize brain structure
@@ -146,7 +149,7 @@ Cortex
## Cell groupings: cortex vs nuclei
<figure><figcaption class="big">Cerebral cortex and thalamic nuclei</figcaption><img src="figs/2060_cell_abf6617.jpg" height="300px"><figcaption>[Brain Biodiversity Bank MSU, NSF](https://msu.edu/~brains/brains/human/coronal/2060_cell_labelled.html)</figcaption></figure>
<figure><figcaption class="big">Cerebral cortex and thalamic nuclei</figcaption><img src="figs/2060_cell_abf6617.jpg" height="400px"><figcaption>[Brain Biodiversity Bank MSU, NSF](https://msu.edu/~brains/brains/human/coronal/2060_cell_labelled.html)</figcaption></figure>
Note:
@@ -180,21 +183,14 @@ Note:
These are the basic parts of the CNS
Forebrain
Forebrain (prosencephalon): telencephalon (cerebral hemispheres) + diencephalon (thalamus)
Brain stem includes the midbrain, pons, medulla, and a portion of the spinal cord
Brain stem: Mesencephalon (midbrain) + rhombencephalon (pons + medulla). Brain stem includes the midbrain, pons, medulla, and a portion of the spinal cord
Think about how the nerves represent incoming and outgoing info from a specific location on the body.
Spinal cord
cervical enlargement
Note the order of nerves representing incoming and outgoing info from a specific location on the body.
lumbar enlargement
: nerves which supply the lower limbs
cauda equina
: nerves that innervate the pelvic organs and lower limbs. Includes motor innervation of the hips, knees, ankles, feet, internal anal sphincter and external anal sphincter.
Spinal nerves: cervical, thoracic, lumbar, sacral, coccygeal
---
@@ -240,7 +236,16 @@ Nerve fibers…
Is thicker…
Cervical enlargement, lumbar enlargement
cervical enlargement
: refers to thickening where nerves supplying forelimbs attach. Between 5th cervical vertebrae and 1st thoracic vertebrae (C5 to T1)
lumbar enlargement
: nerves which supply the lower limbs. 11th thoracic vertebrae to second sacral vertebrae (T11 to S2)
cauda equina
: nerves that innervate the pelvic organs and lower limbs. Includes motor innervation of the hips, knees, ankles, feet, internal anal sphincter and external anal sphincter.
Spinal nerves: cervical, thoracic, lumbar, sacral, coccygeal
---
@@ -252,6 +257,10 @@ Note:
This illustrates the overall structure of the spinal cord.
sympathetic chain ganglia
: stress, flight or flight response, epinephrine
: 20–30K cell bodies
---
## Internal anatomy of the spinal cord
@@ -277,9 +286,9 @@ Note:
Note:
sympathetic chain ganglia
: stress, flight or flight response, epinephrine
: 20–30K cell bodies
ventral nerve cord: the nervous system of bilaterians like nematodes, annelids and the arthropods (insects)
neural tube/dorsal nerve cord: chordates (fish, amphibians, reptiles, birds, and mammals)
---
@@ -306,7 +315,7 @@ Ventral columns (sometimes called anterolateral column)- carry pain info up and
*Cervical enlargement: Gray matter expanded to incorporate more sensory input from limbs and more cell bodies for motor control of limbs*
*Rexed's laminae are cytoarchitectonic divisions of spinal cord gray matter, see Table A1*
*Rexed's laminae are cytoarchitectonic divisions of spinal cord gray matter, see Table A1* ...don't worry about knowing the lamina
---
@@ -340,7 +349,7 @@ And all information from higher order or more rostral brain structures that goes
</div>
<div style="margin:0 50px;"><img src="figs/Neuroscience5e-Fig-A07-2R_debbe82.png" height="300px"><figcaption>Neuroscience 5e Fig. A7</figcaption></div>
<div style="margin:0 50px;"><figcaption class="big">Ventral surface of brain stem</figcaption><img src="figs/Neuroscience5e-Fig-A07-2R_debbe82.png" height="300px"><figcaption>Neuroscience 5e Fig. A7</figcaption></div>
Note:
@@ -388,7 +397,10 @@ XII | Hypoglossal Nerve | Controls muscles of tongue
Note:
This lists these 12 cranial nerves and their relevant sensory and/or motor function they carry. Notice that many of the nerves carry mixtures of sensory and motor information, which you could see with the color coding on the previous slide. Also notice that 4 of the 12 nerves concern sensory and motor information from the eyes. In fact the cranial nerve containing the most fibers is the optic nerve which contains 1.2 million axons that carries all the information necessary to perceive the visual world around you (compare with 130 million photoreceptors and 0.7 to 1.5 million RGCs)
This lists these 12 cranial nerves and their relevant sensory and/or motor function they carry.
Notice that many of the nerves carry mixtures of sensory and motor information, which you could see with the color coding on the previous slide.
Also notice that 4 of the 12 nerves concern sensory and motor information from the eyes. In fact the cranial nerve containing the most fibers is the optic nerve which contains 1.2 million axons that carries all the information necessary to perceive the visual world around you (compare with 130 million photoreceptors and 0.7 to 1.5 million RGCs)
---
@@ -427,7 +439,6 @@ Now you’ve all heard the phrase ‘running around like a chicken with its head
<div><iframe src="https://www.youtube.com/embed/ATz3AdbjyRI" width="420" height="315"></iframe><figcaption>Mike the headless chicken</figcaption></div>
[http://www.dailymail.co.uk/news/article-5556351/Headless-chicken-survives-WEEK-decapitated.html](http://www.dailymail.co.uk/news/article-5556351/Headless-chicken-survives-WEEK-decapitated.html)
Note:
@@ -438,6 +449,8 @@ Well here is a grotesque way of convincing you that all you need to live is your
* Fed corn dropped directly into his gullet
* Mike choked to death during a sideshow tour in 1947, when the farmer was unable to clear Mike's esophagus
[dailymail 2018, headless chicken in thailand](http://www.dailymail.co.uk/news/article-5556351/Headless-chicken-survives-WEEK-decapitated.html)
---
## Cerebellum
@@ -461,6 +474,7 @@ It has two…
Neurons are form cortical sheets.
Receives…
---
@@ -544,7 +558,7 @@ The thalamus is located in the middle of the brain…
*red nucleus is part of midbrain, without a corticospinal tract it controls gait. Baby crawling controlled by red nucleus. Arm swinging while walking*
---
--
## Thalamus subdivisions
@@ -645,7 +659,8 @@ anterior commisure
## Laminar organization of neocortex
* Cortex itself has a thickness of only about 2-4mm
* Gray matter of human neocortex has a thickness of only about 2-4 mm
* Similar thickness in other mammals-- cortical gray matter in rodents is 1-2mm!
* 6 layers (neocortex)
* Layer IV is the primary input layer
* Layers II and III are cortico-cortical output layers
@@ -677,7 +692,7 @@ Note:
---
--
## Defects in cortical development
<div style="width:500px">
@@ -812,7 +827,7 @@ Note areas 4 (primary motor cortex), 1,2,3 (primary somatosensory cortex), area
Note:
---
--
## Mapping brain activity with human neuroimaging

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neurophysiology1.md
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@@ -134,7 +134,7 @@ Action potentials are the large electrical spikes or impulses that allow neurona
## Types of electrical signals in neurons
<figure><img src="figs/Neuroscience5e-Fig-02.01-0_63cc814.png" height="500px"><figcaption>Neuroscience 5e Fig. 2.1</figcaption></figure>
<figure><img src="figs/Neuroscience5e-Fig-02.01-0_63cc814.png" height="500px"><figcaption>Neuroscience 5e/6e Fig. 2.1</figcaption></figure>
Note:
@@ -206,7 +206,7 @@ Just remember that a neuron not eliciting any electrical signals is ‘resting
</div>
<div style="margin:0 15px"><img src="figs/Neuroscience5e-Fig-02.02-1R_f6f9bef_b7eea85.png" height="400px"><figcaption>Neuroscience 5e Fig. 2.2</figcaption></div>
<div style="margin:0 15px"><img src="figs/Neuroscience5e-Fig-02.02-1R_f6f9bef_b7eea85.png" height="400px"><figcaption>Neuroscience 5e/6e Fig. 2.2</figcaption></div>
Note:
@@ -226,7 +226,7 @@ Now what if do the same recordings, but also electrically stimulate the cell so
</div>
<div style="margin:0 15px"><img src="figs/Neuroscience5e-Fig-02.02-2R_3b5b1ef.png" width="500px"><figcaption>Neuroscience 5e Fig. 2.2</figcaption></div>
<div style="margin:0 15px"><img src="figs/Neuroscience5e-Fig-02.02-2R_3b5b1ef.png" width="500px"><figcaption>Neuroscience 5e/6e Fig. 2.2</figcaption></div>
Note:
@@ -237,7 +237,7 @@ Then we inject a small amount of negative current (less than 1 nA) so that we hy
* 1-(1/e) = 63% (rise) Vm and 1/e (37%) (decat) of Vm
If we depolarize the cell membrane from rest by injecting pulses of positive current we get corresponding passive responses with exponential rises and decays of membrane potential– **unless that cell is a neuron and we’ve exceeded the threshold potential (shown by the red dotted line) for generating an action potential in that neuron.
If we depolarize the cell membrane from rest by injecting pulses of positive current we get corresponding passive responses with exponential rises and decays of membrane potential– **unless that cell is a neuron and we’ve exceeded the threshold potential (shown by the red dotted line) for generating an action potential in that neuron.**
Notice if we inject stronger current pulses, we get more action potentials, also known as a higher spiking or firing rate, rather than different action potential amplitudes. If the depolarization is sufficient to generate an AP, that AP amplitude stays largely the same within each individual neuron.
@@ -258,7 +258,7 @@ 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>
<figure><img src="figs/Neuroscience5e-Fig-02.04-0R_cf6b01f.png" height="400px"><figcaption>Neuroscience 5e/6e Fig. 2.4</figcaption></figure>
Note:
@@ -341,7 +341,7 @@ We will come back to these in a minute.
## Electrochemical equilibrium
<figure><figcaption class="big">orange dots K⁺, green dots Cl⁻. This simulated membrane is only permeable to K⁺</figcaption><img src="figs/Neuroscience5e-Fig-02.05-1R-2_163131c.png" height="500px"><figcaption>Neuroscience 5e Fig. 2.5</figcaption></figure>
<figure><figcaption class="big">orange dots K⁺, green dots Cl⁻. This simulated membrane is **only permeable to K⁺**</figcaption><img src="figs/Neuroscience5e-Fig-02.05-1R-2_163131c.png" height="500px"><figcaption>Neuroscience 5e/6e Fig. 2.5</figcaption></figure>
@@ -474,15 +474,15 @@ log(7) / log10(7)
<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:
Open up your browser's web developer javascript console (shift-ctrl-k (Firefox) or cmd-alt-j (Chrome)). Copy/paste the following lines:
```javascript
R = 8.3 //Gas constant
F = 9.6 * Math.pow(10,4) //Faraday constant
F = 9.6 * 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:
Relation of the natural logarithm (base *e* 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 javascript. Copy/paste the following lines. Try varying *x* a few times and re-calculate:
```javascript
x = 5
@@ -583,7 +583,7 @@ Note:
## 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="350px"><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/6e Fig. 2.6</figcaption></div>
Note:
@@ -769,7 +769,7 @@ 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="400px"><figcaption>Neuroscience 5e fig. 2.8</figcaption></figure>
<figure><img src="figs/Neuroscience5e-Fig-02.08-0_40bc007.png" height="400px"><figcaption>Neuroscience 5e/6e fig. 2.8; Hodgkin and Katz *J. Physiol* 1949</figcaption></figure>
Note:
@@ -823,7 +823,7 @@ 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="400px"><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 and Huxley *Nature* 1939</figcaption></figure>
Note:
@@ -838,7 +838,7 @@ 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="400px"><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/6e Fig. 2.9; Hodgkin and Katz *J. Physiol* 1949</figcaption></figure>
Note:
@@ -849,7 +849,7 @@ When Hodgkin and Katz did this low extracellular Na experiment, the AP had a sma
## Role of sodium in the generation of an action potential
<figure><img src="figs/Neuroscience5e-Fig-02.09-2R_6ca6c4f.png" height="400px"><figcaption>Neuroscience 5e Fig. 2.9</figcaption></figure>
<figure><img src="figs/Neuroscience5e-Fig-02.09-2R_6ca6c4f.png" height="400px"><figcaption>Neuroscience 5e/6e Fig. 2.9; Hodgkin and Katz *J. Physiol* 1949</figcaption></figure>
Note:
@@ -875,7 +875,7 @@ So a summary of the Hodgkin and Katz experiment conclusions...
## Resting membrane and action potentials entail permeabilities to different ions
<figure><img src="figs/Neuroscience5e-Fig-02.07-0_caebcb8.png" height="400px"><figcaption>Neuroscience 5e Fig. 2.7</figcaption></figure>
<figure><img src="figs/Neuroscience5e-Fig-02.07-0_caebcb8.png" height="400px"><figcaption>Neuroscience 5e/6e Fig. 2.7</figcaption></figure>
Note:
@@ -894,9 +894,6 @@ Note:
And this is just a overall summary of what we have been discussing
<!--
## Action potential form and nomenclature
@@ -938,5 +935,3 @@ AHP due to voltage-gated K⁺ channels, including Ca²⁺ activated potassium ch
Llinas Sugimori J Physiol 1980 Purkinje neurons
-->
---

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neurophysiology2.md
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@@ -1,12 +1,12 @@
## Voltage dependent membrane permeability
<div style="font-size:0.8em;">
<div style="font-size:0.7em;">
<div></div>
* Hodgkin and Huxley hypothesis– Action potential can be explained by **voltage-gated ion channels**
* Experiment– Measure ion permeability at varying membrane potentials
* Problem– Difficult to systematically vary the cell potential and also measure ion permeability
* Solution– Voltage clamping. Fix membrane potential in a cell without triggering an action potential while measuring ion permeability
* Solution– Voltage clamping. Fix membrane potential in a cell without triggering an action potential while measuring ion permeability (~conductance)
</div>
@@ -22,9 +22,7 @@ So they needed to proved that ion permeability changes according to membrane pot
The solution was to build an electrophysiological recording apparatus with feedback circuitry such that you can fix or clamp the voltage across the cell membrane.
[http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1469-7793/homepage/celebrating_the_work_of_alan_hodgkin_and_andrew_huxley.htm](http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1469-7793/homepage/celebrating_the_work_of_alan_hodgkin_and_andrew_huxley.htm)
--
---
## Action potential summary video
@@ -36,7 +34,7 @@ Summary of last time…
--
## More Vm examples
## More V<sub>m</sub> examples
<div style="font-size:0.7em;">
<div></div>
@@ -56,35 +54,34 @@ Summary of last time…
Note:
1. (58/1)*log10(1/10) = -58 mV
2. (58/1)*log10(10/1) = +58 mV
3. (58/-1)*log10(11/11) = 0 mV
1. `(58/1)*log10(1/10) = -58 mV`
2. `(58/1)*log10(10/1) = +58 mV`
3. `(58/-1)*log10(11/11) = 0 mV`
4. 0 mV:
* Pk = 0.5; Pna = 0.5; Pcl = 0; kOut = 1; kIn = 10; naOut = 10; naIn = 1; clIn = 11; clOut = 11
* (58)*log10( (Pk*kOut + Pna*naOut + Pcl*clIn) / (Pk*kIn + Pna*naIn + Pcl*clOut) ) = 0 mV
* `Pk = 0.5; Pna = 0.5; Pcl = 0; kOut = 1; kIn = 10; naOut = 10; naIn = 1; clIn = 11; clOut = 11`
* `(58)*log10( (Pk*kOut + Pna*naOut + Pcl*clIn) / (Pk*kIn + Pna*naIn + Pcl*clOut) ) = 0 mV`
* 0 mV:
* Pk = 1; Pna = 1; Pcl = 0; kOut = 1; kIn = 10; naOut = 10; naIn = 1; clIn = 11; clOut = 11
* (58)*log10( (Pk*kOut + Pna*naOut + Pcl*clIn) / (Pk*kIn + Pna*naIn + Pcl*clOut) )
* `Pk = 1; Pna = 1; Pcl = 0; kOut = 1; kIn = 10; naOut = 10; naIn = 1; clIn = 11; clOut = 11`
* `(58)*log10( (Pk*kOut + Pna*naOut + Pcl*clIn) / (Pk*kIn + Pna*naIn + Pcl*clOut) )`
* -59 mV (room temp and low Pna):
* Pk = 1; Pna = 0.001; Pcl = 0.5; kOut = 1; kIn = 10; naOut = 10; naIn = 1; clIn = 1; clOut = 11
* (58)*log10( (Pk*kOut + Pna*naOut + Pcl*clIn) / (Pk*kIn + Pna*naIn + Pcl*clOut)
*
* `Pk = 1; Pna = 0.001; Pcl = 0.5; kOut = 1; kIn = 10; naOut = 10; naIn = 1; clIn = 1; clOut = 11`
* `(58)*log10( (Pk*kOut + Pna*naOut + Pcl*clIn) / (Pk*kIn + Pna*naIn + Pcl*clOut)`
-62 mV (body temp and low Pna):
* R = 8.3; F = 9.6e4; T = (273+37)
* Pk = 1; Pna = 0.001; Pcl = 0.5; kOut = 1; kIn = 10; naOut = 10; naIn = 1; clIn = 1; clOut = 11
* ((R*T)/F)*log( (Pk*kOut + Pna*naOut + Pcl*clIn) / (Pk*kIn + Pna*naIn + Pcl*clOut) )
* `Pk = 1; Pna = 0.001; Pcl = 0.5; kOut = 1; kIn = 10; naOut = 10; naIn = 1; clIn = 1; clOut = 11`
* `((R*T)/F)*log( (Pk*kOut + Pna*naOut + Pcl*clIn) / (Pk*kIn + Pna*naIn + Pcl*clOut) )`
-69 mV (body temp and low Pna and physiol concentrations):
* R = 8.3; F = 9.6e4; T = (273+37)
* Pk = 1; Pna = 0.05; Pcl = 0.45; kOut = 5; kIn = 140; naOut = 145; naIn = 5; clIn = 5; clOut = 110
* ((R*T)/F)*log( (Pk*kOut + Pna*naOut + Pcl*clIn) / (Pk*kIn + Pna*naIn + Pcl*clOut) )
* `R = 8.3; F = 9.6e4; T = (273+37)`
* `Pk = 1; Pna = 0.05; Pcl = 0.45; kOut = 5; kIn = 140; naOut = 145; naIn = 5; clIn = 5; clOut = 110`
* `((R*T)/F)*log( (Pk*kOut + Pna*naOut + Pcl*clIn) / (Pk*kIn + Pna*naIn + Pcl*clOut) )`
Calculate the total concentration of all ions for these solutions. For every one NaCl that dissolves, two ions are produced (one Na⁺ and one Cl¯). Thus for 10 mmol/L NaCl outside there are (10 mmol/L)x(1 total Cl ions/NaCl) = 10mM. And for 1mM KCl outside there are (1 mmol/L)x(1 total Cl ions/KCl) = 1mM. Thus the total number of Cl⁻ ions per liter is 11mmol/L = 11mM
@@ -92,9 +89,11 @@ Calculate the total concentration of all ions for these solutions. For every one
---
## The voltage clamp method
## The voltage clamp technique
<div><img src="figs/Neuroscience5e-Box-03A-0R_5d20ab3.png" height="400px"><figcaption>Neuroscience 5e Box 3A</figcaption></div>
Voltage clamping provides a method for measuring electrical current and its direction of net flow across a cell membrane.
<div><img src="figs/Neuroscience5e-Box-03A-0R_5d20ab3.png" height="400px"><figcaption>Neuroscience 5e/6e Box 3A</figcaption></div>
Note:
@@ -109,7 +108,7 @@ When Vm is different from the command potential the clamp amplifier injects curr
The current flowing back into the axon and thus across its membrane can be measured.
**This electronic feedback circuit holds the membrane pot at the desired level, even in the face of permeability changes that would normally alter the membrane potential. (such as those generated during the action potential). Most importantly, the device permits the simultaneous measure of the current needed to keep the cell at a given voltage. This current is exactly equal to the amount of current flowing across the neuronal membrane, allowing direct measurement of these membrane currents.
**This electronic feedback circuit** holds the membrane potential at the desired level, even in the face of permeability changes that would normally alter the membrane potential. (such as those generated during the action potential). Most importantly, the device permits the simultaneous measure of the current needed to keep the cell at a given voltage. This current is exactly equal to the amount of current flowing across the neuronal membrane, allowing direct measurement of these membrane currents.
>An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the power of a signal. It does this by taking energy from a power supply and controlling the output to match the input signal shape but with a larger amplitude.
@@ -121,7 +120,7 @@ The current flowing back into the axon and thus across its membrane can be measu
---
## Hodgkin and Huxley 1952
## A. Hodgkin and A. Huxley 1952
* Do neuronal membranes have voltage-dependent permeability?
* Which ions are changing their permeability?
@@ -130,7 +129,7 @@ The current flowing back into the axon and thus across its membrane can be measu
Note:
Hodgkin and Huxley published a series of seminal papers in 1952 that summarized their investigations using this voltage clamp method to examine voltage dependent ion flux.
Alan Hodgkin and Andrew Huxley from the Univ of Cambridge published a series of seminal papers in 1952 that summarized their investigations using this voltage clamp method to examine voltage dependent ion flux.
They asked…
@@ -141,9 +140,12 @@ So the experiment was to hold the membrane potential at different voltages and m
## Electric current flow across a squid axon membrane during voltage clamp
<div><figcaption class="big">negligible current (except for a capacitive transient)</figcaption><img src="figs/Neuroscience5e-Fig-03.01-1R_5455913.png" height="300px"><figcaption>Neuroscience 5e fig. 3.1</figcaption></div>
<div><figcaption class="big">negligible current (except for a capacitive transient)</figcaption><img src="figs/Neuroscience5e-Fig-03.01-1R_5455913.png" height="300px"><figcaption>Neuroscience 5e/6e fig. 3.1; from Hodgkin et al., *J. Physiol.* 1952</figcaption></div>
<div><figcaption class="big">inward and outward currents</figcaption><img src="figs/Neuroscience5e-Fig-03.01-2R_49ec352.png" height="300px"><figcaption>Neuroscience 5e/6e fig. 3.1; from Hodgkin et al., *J. Physiol.* 1952</figcaption></div>
<div style="font-size:0.7em; margin:25px 0;">Inward current is always downward deflection from zero in these traditional voltage clamp plots. Outward current is an upward deflection. </div>
<div><figcaption class="big">inward and outward currents</figcaption><img src="figs/Neuroscience5e-Fig-03.01-2R_49ec352.png" height="300px"><figcaption>Neuroscience 5e fig. 3.1</figcaption></div>
Note:
@@ -167,26 +169,34 @@ However when Hodgkin and Huxley depolarized the membrane, a transient inward cur
---
## Current produced by different membrane depolarizations during voltage clamp
## Inward & outward currents produced at a series of clamped membrane voltages
<figure><img src="figs/Neuroscience5e-Fig-03.02-0_5ee332f.png" height="400px"><figcaption>Neuroscience Fig. 3.2</figcaption></figure>
<figure><figcaption class="big">Voltage clamp recordings from squid axon. Capacitive artifact removed for clarity.</figcaption><img src="figs/Neuroscience5e-Fig-03.02-0_5ee332f.png" height="400px"><figcaption>Neuroscience 5e/6e Fig. 3.2; from Hodgkin et al., *J. Physiol.* 1952</figcaption></figure>
Note:
This show several different voltage steps (with the brief capacitive current omitted for clarity)
...Notice as we approach ENa the inward current disappears.
Notice a few phenonmena in this figure.
---
...Notice as the command voltage becomes more positive we start to approach ENa and the inward current disappears.
--
## Relationship between current amplitude and membrane potential
<figure><figcaption class="big">External Na⁺ 440 mM, internal Na⁺ 50 mM, therefore Nernst says **E<sub>Na</sub> = 55 mV**</figcaption><img src="figs/voltage_clamp_currents_summary_plot_7450e0a.png" height="400px"><figcaption>Neuroscience 5e Fig. 3.3</figcaption></figure>
<figure><figcaption class="big">External Na⁺ 440 mM, internal Na⁺ 50 mM, therefore Nernst says **E<sub>Na</sub> = 55 mV**</figcaption><img src="figs/voltage_clamp_currents_summary_plot_7450e0a.png" height="400px"><figcaption>Neuroscience 5e/6e Fig. 3.3; from Hodgkin et al., *J. Physiol.* 1952</figcaption></figure>
Note:
This summarizes the peak magnitude of these these two currents at different Vm
Don't get confused by this plot, look at the axes it is just Vm and current.
Bascially this just summarizes the peak magnitude of these these two currents at different Vm in the previous figure 3.2.
---
@@ -201,9 +211,10 @@ So it seems like this inward current may be carried by Na ions.
---
## Dependence of the early inward current on sodium
<div><img src="figs/Neuroscience5e-Fig-03.04_0d877f5.png" height="500px"><figcaption>Neuroscience 5e Fig. 3.4</figcaption></div>
<div><img src="figs/Neuroscience5e-Fig-03.04_0d877f5.png" height="500px"><figcaption>Neuroscience 5e/6e Fig. 3.4; from Hodgkin and Huxley *J. Physiol.* 1952a</figcaption></div>
<div><iframe src="https://www.youtube.com/embed/Wd_gKJoo25Y" width="420" height="315"></iframe><figcaption>Squid giant axon voltage clamping</figcaption></div>
@@ -258,7 +269,7 @@ Its mechanism of action, selective blocking of the sodium channel, was shown def
## Pharmacological separation of inward and outward currents into Na⁺ and K⁺ dependent components
<figure><img src="figs/Neuroscience5e-Fig-03.05-0_99fe22f.png" height="400px"><figcaption>Neuroscience 5e Fig. 3.5</figcaption></figure>
<figure><img src="figs/Neuroscience5e-Fig-03.05-0_99fe22f.png" height="400px"><figcaption>Neuroscience 5e/6e Fig. 3.5; from Moore et al. *J Gen Physiol* 1967 and Armstrong and Binstock *J Gen Physiol* 1965</figcaption></figure>
Note:
@@ -285,7 +296,7 @@ TTX and TEA experiments from Moore 1967 J Gen Physiol; Armstrong and Binstock, 1
* For an ion *x*,
* *I<sub>x</sub>* = ionic current flow, *E<sub>x</sub>* = equilibrium potential
* The membrane potential (*V<sub>m</sub>*) minus the equilibrium potential (*E<sub>x</sub>*) is the electrochemical driving force acting on an ion, thus *V = V<sub>m</sub> - E<sub>x</sub>*
* *I<sub>x</sub> = g<sub>x</sub>*
* *I<sub>x</sub> = g<sub>x</sub>V*
* *I<sub>x</sub> = g<sub>x</sub>(V<sub>m</sub> - E<sub>x</sub>)*
* Solve for *g*:
* *g<sub>x</sub> = I<sub>x</sub>/(V<sub>m</sub> - E<sub>x</sub>)*
@@ -311,7 +322,7 @@ Can use this to calculate the dependence of Na and K conductances vs. time and m
## Membrane conductance changes are time and voltage dependent
<div><img src="figs/Neuroscience5e-Fig-03.06-0_757dbce.png" height="400px"><figcaption>Neuroscience Fig. 3.6</figcaption></div>
<div><img src="figs/Neuroscience5e-Fig-03.06-0_757dbce.png" height="400px"><figcaption>Neuroscience 5e/6e Fig. 3.6; from Hodgkin and Huxley *J Physiol* 1952b</figcaption></div>
Note:
@@ -322,7 +333,7 @@ Note:
## Depolarization increases Na⁺ and K⁺ conductances of the squid giant axon
<div><img src="figs/Neuroscience5e-Fig-03.07-0_fdae974.png" height="400px"><figcaption>Neuroscience Fig. 3.7</figcaption></div>
<div><img src="figs/Neuroscience5e-Fig-03.07-0_fdae974.png" height="400px"><figcaption>Neuroscience 5e/6e Fig. 3.7; from Hodgkin and Huxley *J Physiol* 1952b</figcaption></div>
Note:
@@ -336,8 +347,8 @@ Determine the peak conductance of ions at different membrane potentials.
<div style="font-size:0.8em;">
<div></div>
* At rest (-70 mV), voltage-gated Na⁺ and K⁺ channels are closed. Non voltage-gated K⁺ channels are open and dictate the resting potential, together with the distribution of ions across cell membranes
* A stimulus raises the membrane potential in the cell. Depolarization causes voltage-gated Na⁺ channels to open, which allows Na⁺ to rush in the cell which increases the membrane potential, which causes more Na⁺ channels to open, which causes more Na⁺ to rush in which causes higher membrane potential (a positive feedback loop). As membrane potential is approaching E<sub>Na</sub>, the further depolarization causes Na⁺ channels to inactivate which prevents more Na⁺ from from flowing through these channels
* At rest (-70 mV), voltage-gated Na⁺ and K⁺ channels are closed. Non voltage-gated K⁺ channels (K<sub>leak</sub>) are open and dictate the resting potential, together with the distribution of ions across cell membranes
* A stimulus raises the membrane potential in the cell. Depolarization causes voltage-gated Na⁺ channels to open, which allows Na⁺ to rush in the cell which increases the membrane potential, which causes more Na⁺ channels to open, which causes more Na⁺ to rush in which causes higher membrane potential (a positive feedback loop). As membrane potential is approaching E<sub>Na</sub>, the further depolarization causes **Na⁺ channels to inactivate** which prevents more Na⁺ from from flowing through these channels
* Depolarization also opens voltage gated K⁺ channels, which causes K⁺ to flow out, thus lowering the membrane potential
</div>
@@ -349,11 +360,17 @@ Note:
## Ion conductances underlying the action potential
<figure><img src="figs/Neuroscience5e-Fig-03.08-1R_efbfb99.png" height="400px"><figcaption>Neuroscience 5e Fig. 3.8</figcaption></figure>
<figure><img src="figs/Neuroscience5e-Fig-03.08-1R_efbfb99.png" height="400px"><figcaption>Neuroscience 5e/6e Fig. 3.8</figcaption></figure>
Note:
Summary of the conductances for Na and K during an action potential.
Based on Hodgkin and Huxley's mathematical model for the action potential (1952d).
Can see that the neuronal membrane becomes much less resistant to Na flux during the rising phase of the AP.
Can also see increases in K conductance during the AP, but this K+ conductance (underlying the outward current) are slow and sustained reaching peak permeability during the falling phase of the AP. Note when the cell is back to Vrest, the gK is still moderately high before ramping down. This is important for the refractory period.
<!-- ## Feedback cycles responsible for membrane potential changes
@@ -367,9 +384,9 @@ Note:
<div></div>
* Question– Why do APs exhibit an all-or-nothing threshold?
* Answer– When membrane potential (V<sub>m</sub>) is below threshold there is not enough Na⁺ channels open to raise V<sub>m</sub> high enough to open more channels. When V<sub>m</sub> is above threshold the 'explosive' action potential cycle is activated.
* Question– Why to APs exhibit an undershoot?
* Answer– During the AP voltage-gated K⁺ conductance slowly increases (delayed activation of voltage-gated K⁺ channels) and during the falling phase these K⁺ channels are still open and active whereas voltage-gated Na⁺ channels are inactivated… as V<sub>m</sub> approaches E<sub>k</sub> there is briefly more K⁺ flowing out than at rest and the hyperpolarization inactivates voltage-gated K⁺ channels. K⁺ leak channels and ion transporters bring back cell to resting potential.
* <span>Answer– When membrane potential (V<sub>m</sub>) is below threshold there is not enough Na⁺ channels open to raise V<sub>m</sub> high enough to open more channels. When V<sub>m</sub> is above threshold the 'explosive' action potential cycle is activated.</span> <!-- .element: class="fragment fade-in"-->
* Question– Why to APs exhibit an undershoot? <!-- .element: class="fragment fade-in"-->
* <span>Answer– During the AP voltage-gated K⁺ conductance slowly increases (delayed activation of voltage-gated K⁺ channels) and during the falling phase these K⁺ channels are still open and active whereas voltage-gated Na⁺ channels are inactivated… as V<sub>m</sub> approaches E<sub>k</sub> there is briefly more K⁺ flowing out than at rest and the hyperpolarization inactivates voltage-gated K⁺ channels. K⁺ leak channels and ion transporters bring back cell to resting potential.</span> <!-- .element: class="fragment fade-in"-->
</div>
@@ -407,7 +424,7 @@ During an action potential, inward current through Na⁺ channels
## Passive current flow in an axon
<figure><figcaption class="big">subthreshold changes diffuse rapidly</figcaption><img src="figs/Neuroscience5e-Fig-02.03-1R_aac41b9.png" height="400px"><figcaption>Neuroscience 5e Fig. 2.3</figcaption></figure>
<figure><figcaption class="big">subthreshold changes decay rapidly</figcaption><img src="figs/Neuroscience5e-Fig-02.03-1R_aac41b9.png" height="400px"><figcaption>Neuroscience 5e/6e Fig. 2.3</figcaption></figure>
Note:
@@ -418,7 +435,7 @@ bottom graph shows the peak Vm
## Propagation of an action potential
<figure><figcaption class="big">suprathreshold depolarizations propagate down the axon</figcaption><img src="figs/Neuroscience5e-Fig-02.03-2R_4bea3b6.png" height="400px"><figcaption>Neuroscience 5e Fig. 2.3</figcaption></figure>
<figure><figcaption class="big">suprathreshold depolarizations propagate down the axon and don't decay</figcaption><img src="figs/Neuroscience5e-Fig-02.03-2R_4bea3b6.png" height="400px"><figcaption>Neuroscience 5e/6e Fig. 2.3</figcaption></figure>
Note: