lecture04

2016-09-17-lecture01.md

@@ -38,11 +38,12 @@ REASON YOU CANNOT ENROLL:
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+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.
 
 ---
 
@@ -147,7 +148,7 @@ sinew
 <div></div>
 
 * We are now in a gene-centric “post-genomic” phase of neuroscience
-* Most genes are expressed in the brain, either during development or in the adult. It is the spatial and temporal regulation of these genes and an organisms interaction with the environment that builds a nervous system.
+* Many genes are expressed in the brain, either during development or in the adult. It is the spatial and temporal regulation of these genes and an organisms interaction with the environment that builds a nervous system.
 * Neuroscience therefore encompasses many fields, including genetics, cell biology, physiology, and development biology.
 
 </div>
@@ -498,7 +499,7 @@ Note:
 
 Glia  
 : greek for 'glue'  
-: outnumber neurons 10-50 fold (higher mammals)
+: outnumber neurons 10-50 fold (higher mammals)  
 : structural support for neurons  
 : remove debris and maintain a functional nervous system environment  
 

2016-09-28-lecture03.md

@@ -9,9 +9,7 @@
 
 Note:
 
-So, how do neurons convey information over long distances that results in information transfer to other neurons at synaptic connections? It through electrical signaling that neurons are able to generate and transmit information. And this electrical signaling is possible because of a combination of…
-
-
+So, how do neurons convey information over long distances that results in information transfer to other neurons at synaptic connections? It is through electrical signaling that neurons are able to generate and transmit information. And this electrical signaling is possible because of a combination of…
 
 - voltage-dependent membrane permeability
 - which in turn requires special membrane proteins called ion channels and transporters
@@ -41,9 +39,9 @@ Note:
 
 To understand the basis of electrical excitability in neurons, we first need to understand that neurons, like other excitable cells, have a difference in electrical potential across the cell membrane when it is at rest. 
 
-To learn this neuroscientists stick electrodes inside of neurons. This electrode is hooked up to a voltmeter and another electrode sits outside the cell as a ground or reference electrode to complete the circuit. The difference in voltage between the inside of the cell and the outside of the cell is monitored over time and displayed on an oscilloscope.
+To learn this physiologists stick electrodes inside of cells, including neurons. This electrode is hooked up to a voltmeter and another electrode sits outside the cell as a ground or reference electrode to complete the circuit. The difference in voltage between the inside of the cell and the outside of the cell is monitored over time and displayed on an oscilloscope.
 
-When you do this, one finds a negative resting membrane potential of the neuron with respect to the outside. You can see in this plot at the bottom right that we’ve inserted the electrode and then over time we measure a negative membrane potential of about -70 mV.  Recall that volts are a unit of electrical potential energy —>
+When you do this such as with this model neuron shown here, one finds a negative resting membrane potential of the neuron with respect to the outside of approximately -70 mV.Recall that volts are a unit of electrical potential energy, where 1 Volt is defined as the amount of energy that will drive 1 coulomb of elementary charge or 6x10^18 electrons or protons through a resistance of 1 ohm in 1 second —>
 
 ---
 
@@ -70,38 +68,54 @@ Flow rate ~ Current (amperes) = `I`
 
 Note:
 
-And voltage is related to the resistance and current in an electrical circuit as described by Ohm’s law. This analogy of a water pump/water wheel circuit helps us understand these relationships better. 
+And recall from physics that voltage is related to the resistance and current in an electrical circuit as described by Ohm’s law. This analogy of a water pump/water wheel circuit helps us understand these relationships better. 
 
-Voltage = is the potential difference, or electromotive force measured across the conductor in units of volts. Imagine a hand pump that you use to do some work and introduce pressure in a water system, that pressure or potential difference is the voltage.
+Voltage  
+: is the potential difference, or electromotive force measured across the conductor in units of volts.  
+: So imagine a hand pump that you use to do some work and introduce pressure in a water system, that pressure or potential difference is the voltage.  
 
-* - Volt is defined as the difference in electric potential between two points of a conducting wire when an electric current of one ampere dissipates one watt of power between those points
-* - voltmeter, ammeter
+*Volt is defined as the difference in electric potential between two points of a conducting wire when an electric current of one ampere dissipates one watt of power between those points*  
+*voltmeter, ammeter*
+
+Current  
+: measured in amperes is the flow of electric charge across a surface at the rate of one coulomb per second. Used to express the flow rate of electric charge.  
+: So imagine the rate of water flow in this water pump as the the flow of electric charge across a cell membrane. What is the charge that is moving for a cell? Monovalent and divalent atoms like Na⁺, K⁺, Cl⁻, and Ca²⁺.  
+
+*1A equivalent to one coulomb (roughly 6.241×10^18 times the elementary charge) per second*  
+*coulomb = charge (symbol: Q or q) transported by a constant current of one ampere in one second. 1C equivalent to a charge of approximately 6.242×10^18 protons or electrons.*  
+*elementary positive charge: This charge has a measured value of approximately 1.6021766208×10^−19 coulombs*  
+
+Resistance  
+: is the difficulty to pass a current through a conductor measured in ohms.  
+: Image the diameter of a pipe or a valve that you can regulate to be the resistance  
+: inverse of resistance is conducance *g* measured in siemens (S)  
+: for studying neuronal excitability rewriting Ohm's law as I = g(Vm-Ex) is most useful. g = conductance, no. of open channels. (Vm-Ex) = driving force causing either positive or negative current.  
 
 
-Current: measured in amperes is the flow of electric charge across a surface at the rate of one coulomb per second. Used to express the flow rate of electric charge. Imagine the rate of water flow in this water pump as the the flow of electric charge across a cell membrane. What is the charge that is moving for a cell?  Monovalent and divalent atoms like Na⁺, K⁺, Cl⁻, and Ca²⁺.
+**Ohm’s law** from physics class relates these quantities together as V = IR, and rearranging this equation and reading it as I = V/R or Current = Voltage divided by Resistance gives you a better intuitive feel for these relations. **Notice that when you have 0 voltage or potential difference you have no current.**  
 
-* - 1A equivalent to one coulomb (roughly 6.241×10^18 times the elementary charge) per second
-* - coulomb = charge (symbol: Q or q) transported by a constant current of one ampere in one second. 1C equivalent to a charge of approximately 6.242×10^18 protons or electrons.
-* - elementary positive charge: This charge has a measured value of approximately 1.6021766208×10^−19 coulombs
+Avogadro constant  
+: (symbols: L, NA)  
+: is the number of constituent particles, usually atoms or molecules, that are contained in the amount of substance given by one mole.  
+: Avogadro’s constant = 6.022×10^23 and is dimensionless.  
 
-* Resistance: is the difficulty to pass a current through a conductor measured in ohms. Image the diameter of a pipe or a valve that you can regulate to be the resistance
-* Ohm’s law from physics class relates these quantities together as V = IR, and rearranging this equation and reading it as I = V/R or Current = Voltage divided by Resistance gives you a better intuitive feel for these relations. Notice that when you have 0 voltage or potential difference you have no current. 
-* Avogadro constant (symbols: L, NA) is the number of constituent particles, usually atoms or molecules, that are contained in the amount of substance given by one mole. Avogadro’s constant = 6.022×10^23 and is dimensionless.
-* mole =  It is defined as the amount of any chemical substance that contains as many elementary entities, e.g., atoms, molecules, ions, electrons, or photons, as there are atoms in 12 grams of pure carbon-12 (12C). This number is expressed by the Avogadro constant
+mole  
+: it is defined as the amount of any chemical substance that contains as many elementary entities, e.g., atoms, molecules, ions, electrons, or photons, as there are atoms in 12 grams of pure carbon-12 (12C).  
+: this number is expressed by the Avogadro constant
 
 
 ---
 
 ## Electrical signals
 
-* Can be generated by changing the resting potential of the neuron
+* Can be generated by changing the membrane potential of the neuron
 * Receptor potentials can be generated from the activation of sensory receptors, from touch, light, sound, and heat
 * Synaptic potentials are transmitted from one neuron to another at the synapse
 * Action potentials are the booster system to propagate electrical signals a long distance
 
 Note:
 
-Signals in neurons can be generated by changing the resting membrane potential.  
+Signals in neurons can be generated by changing the membrane potential.  
 
 This includes receptor potentials inside your body’s sensory neurons for touch, heat, light, and sound. 
 
@@ -124,9 +138,9 @@ This figure shows these 3 types of neuronal signals.
 
 - Here is a synaptic potential recorded in a postsynaptic neuron.
 
-- Here is an action potential in a motor neuron. Look as the y-axes here— the action potential has a much larger amplitude change than receptor or synaptic potentials. 
-
+- Here is an action potential in a motor neuron. **Look as the y-axes here**— the action potential has a much larger amplitude change than receptor or synaptic potentials. 
 
+To understand the basis of these electrical signals we first need to learn about how this baseline membrane potential is generated, which is the neurons membrane potential while it is at rest. We will spend most of today's class learning about the neurons resting membrane potential and which will lead into how the action potential is generated that we'll continue with next class.
 
 ---
 
@@ -148,11 +162,11 @@ This figure shows these 3 types of neuronal signals.
 
 Note:
 
-I said that the resting membrane potential is more negative on the intracellularly than extracellularly– this is because of the lipid bilayer and its transmembrane proteins which together make a functional cell membrane
+I said that the resting membrane potential is more negative inside the neuron with respect to its extracellular space– this is because of the lipid bilayer and its transmembrane proteins which together make a functional cell membrane
 
-We can that the cell, a bit like American politics, is polarized with one side more negative and the other being more positive
+We can think of the cell, a bit like American politics, is polarized with one side more negative and the other being more positive
 
-This polarization results in a potential difference across the membrane (remember our water pump example) of about -70 mV
+This polarization of the cell results in a potential difference across the membrane (remember our water pump example) of about -70 mV
 
 And its there is a concentration gradient in ions (which are charged atoms like sodium, potassium, and chloride) that results in this difference in distribution of charge across the neuron’s membrane
 
@@ -212,15 +226,15 @@ Note:
 
 So we insert the microelectrode into the cell and find that this neuron is resting at -65 mV. 
 
-
 Then we inject a small amount of negative current (less than 1 nA) so that we hyperpolarize the cell and we see that the membrane responds passively, meaning that the membrane potential changes and recovers with an exponential relationship.
 
-* 1-(1/e) = 63% Vm and 1/e (37%) of Vm
+* 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. 
 
 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. 
 
+We will go over more detail each of these components later on...
 
 ---
 
@@ -231,7 +245,7 @@ Notice if we inject stronger current pulses, we get more action potentials, also
 
 Note:
 
-All electrical signals are the due to the flow of charge, positive or negative. In this case of neurons we the charge is due to the movement cations such as Na and K and anions such as Cl and neuronal membranes are selectively permeable to some of these ions giving the rise to the flow of charge or current across the cell membrane. 
+All electrical signals are the due to the flow of charge, positive or negative. In this case of neurons the charge is due to the movement cations such as Na and K and anions such as Cl and neuronal membranes are selectively permeable to some of these ions giving rise to the flow of charge or current across the cell membrane. 
 
 ---
 
@@ -243,9 +257,7 @@ All electrical signals are the due to the flow of charge, positive or negative.
 
 Note:
 
-How do ions get across the lipid cell membrane bilayer? Remember there are proteins in the cell membrane. Some of these are selective ion transporters, remember the Na-K ATPase from cell biology. These work to create concentration gradients. 
-
-
+So how do ions get across the lipid cell membrane bilayer? Remember there are proteins in the cell membrane. Some of these are selective ion transporters, remember the Na-K ATPase from cell biology. These work to create concentration gradients. 
 
 There are also ion channels that form pores in the cell membrane that are selectively permeable for certain kinds of ions to cross the membrane. These allow ions move across the membrane
 
@@ -279,9 +291,9 @@ Here is one these ion transporters— the Na-K pump that moves 3 Na out of the c
 
 Note:
 
-Ion channels span the membrane and act as pores. They can open and close, often in a voltage-dependent fashion as we will learn thursday. They show selectively such that there are different types of Na, K channels as well as others. 
+Ion channels span the membrane and act as pores. They can open and close, often in a voltage-dependent fashion as we will learn thursday. And ion channels even show selectively such that there are different types of Na, K channels as well as others. 
 
-And they can be additionally regulated or ‘gated’ by different mechanisms including voltage or binding of ligands such as neurotransmitters as we will learn in subsequent classes. 
+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.
 
 
 ---
@@ -306,7 +318,7 @@ So again there are active ion transporters like the Na-K ATPase and there are io
 
 Note:
 
-We actually can predict what the resting membrane potential by knowing the concentrations of ions inside and outside the cell and knowing the relative permeability of these ions to move across the cell membrane. 
+We actually can predict what the resting membrane potential is by knowing the concentrations of ions inside and outside the cell and knowing the relative permeability of these ions to move across the cell membrane.
 
 If a cell membrane is largely permeable to just one ion species, we can use the Nernst equation to predict the membrane potential for all kinds of cells. 
 
@@ -315,14 +327,14 @@ If a cell membrane is permeable to more than one ion, we can use the Goldman equ
 We will come back to these in a minute. 
 
 
-*Walther Nernst (1864-1941)*
+*Walther Nernst (1864-1941), West Prussia, 1920 Nobel Prize in chemistry*
 
 
 ---
 
 ## Electrochemical equilibrium
 
-<figure><figcaption class="big">orange dots K⁺, green dots Cl⁻</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 Fig. 2.5</figcaption></figure>
 
 
 
@@ -334,7 +346,7 @@ Imagine the following experiment. We have a cell and record intracellular membra
 
 If this membrane is only permeable to K⁺, and KCl concentration is the same inside and outside the cell, there is no net flux of K⁺
 
-If KCl is more concentrated inside the cell, initially there is a net flux of positively charged K⁺ from inside to outside the cell due to the chemical concentration driving force leaving the membrane hyperpolarized until the this chemical force is balanced by the electrical driving force from the positively charged K⁺ being repelled by the more positive environment now outside the cell. This is called electrochemical equilibrium, and the potential at which this occurs is called the equilibrium potential for that ion.   
+If KCl is more concentrated inside the cell, initially there is a net flux of positively charged K⁺ from inside to outside the cell due to the chemical concentration driving force which leaves the membrane hyperpolarized because of the net movement of postive charge to the outside until the this chemical force is balanced by the electrical driving force from the positively charged K⁺ being repelled by the more positive environment now outside the cell. This is called electrochemical equilibrium, and the potential at which this occurs is called the equilibrium potential for that ion.   
 
 
 ---
@@ -395,8 +407,7 @@ So I stated that the Nernst equation is how we can calculate the equilibrium pot
 
 And here is the Nernst equation is:  
 
-Where Ex is: 
-
+Where Ex is...
 
 
 Gas constant R  
@@ -453,10 +464,14 @@ T = 20+273
 ==>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>
+
 ---
 
 ## Examples
 
+* 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>
 * Outside 1 mM KCl, Inside 100 mM KCl membrane only permeable to K⁺ ? <!-- .element: class="fragment fade-in"-->
@@ -479,8 +494,6 @@ Since the Nernst equation is really just a linear equation of the form y = mx, y
 
 ## Electrochemical equilibrium
 
-
-
 <div><img src="figs/Neuroscience5e-Fig-02.05-2R_c30075c.png" height="500px"><figcaption>Neuroscience 5e Fig. 2.5</figcaption></div>
 
 
@@ -521,7 +534,7 @@ Note:
 
 ## Membrane potential influences ion fluxes
 
-<figure><img src="figs/Neuroscience5e-Fig-02.06-1R_5d1ff2f.png" height="500px"><figcaption>Neuroscience 5e Fig. 2.6</figcaption></figure>
+<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>
 
 
 Note:
@@ -535,7 +548,6 @@ If our hypothetical battery holds the membrane at -58 mV, the equilbrium potenti
 At more negative membrane potentials than the nernst equilbrium potential we get net inward flow due to the stronger electrical driving force which in the case of potassium here is causing it to move against its chemical gradient.
 
 
-
 ---
 
 ## Membrane potential influences ion fluxes
@@ -564,9 +576,9 @@ Note:
 
 So to summarize, remember that both the direction (inward vs outward) and magnitude of charge flow or current depends on membrane potential. 
 
-Just remember Ohm’s law, I = V/R
+Just remember Ohm’s law, I = V/R and rewrite it as Ix = (Vm - Ex)/R
 
-And we can experimentally vary...
+And we as scientists can experimentally vary...
 
 
 ---
@@ -624,7 +636,7 @@ For a typical neuron at rest, pK : pNa : pCl = 1 : 0.05 : 0.45. Note that becaus
 
 Note:
 
-And as we will soon learn, the resting membrane potential and action potential voltage is mostly due to changes in K permeability and Na permeability across the neuronal membrane. As you can see in this figure, the resting membrane potential for a neuron is close to the EK eq potential due to much greater permeability for K. During an action potential Na permeability initially increases, until the Vm approaches the ENa  and then Na permeability decreases until the Vm again approaches the resting membrane potential and Pk increases.
+And as we will soon lecarn, the resting membrane potential and action potential voltage is mostly due to changes in K permeability and Na permeability across the neuronal membrane. As you can see in this figure, the resting membrane potential for a neuron is close to the EK eq potential due to much greater permeability for K. During an action potential Na permeability initially increases, until the Vm approaches the ENa  and then Na permeability decreases until the Vm again approaches the resting membrane potential and Pk increases.
 
 ---
 
@@ -745,7 +757,7 @@ To answer this Hodgkin and and Katz measured the membrane potential while induci
 
 They observed that the Vm approached ENa during an AP...
 
-They reason they hypothesized is that during an AP...
+They reasoned that during an AP...
 
 Their experiment was to lower Na concentrations in the extracellular medium—
 
@@ -793,6 +805,8 @@ As you can see on the left here changing extracellular [Na] changes the action p
 * During depolarization membrane becomes super permeable to Na⁺
 * There must be Na⁺ channels that are closed during rest but become open during an action potential, and closed again at the end of an action potential
 
+<figure><img src="figs/Neuroscience5e-Fig-02.07-0_caebcb8.png" height="200px"><figcaption>Neuroscience 5e Fig. 2.7</figcaption></figure>
+
 Note:
 
 So a summary of the Hodgkin and Katz experiment conclusions...

2016-10-03-lecture04.md

@@ -0,0 +1,593 @@
+## Voltage dependent membrane permeability
+
+<div style="font-size:0.8em;">
+<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
+
+</div>
+
+<div><img src="figs/Neuroscience5e-Fig-02.07-0_2233a33.png" height="200px"><figcaption>Neuroscience 5e Fig. 2.7</figcaption></div>
+
+Note:
+
+We learned last time that the experiments of Hodgkin, Huxley, and Katz showed that the Vm during an AP approaches ENa. And they thought that this might be due to changes in permeability for Na in the cell membrane that changes during the course of an action potential. Thus Hodgkin and Huxley hypothesized that APs can be explained by ion channels that change their permeability due to voltage— that these channels are voltage-gated.
+
+Alan Hodgkin and Andrew Huxley began this work in the late 1930s, and quickly finished one paper before helping with the British war effort during WWII.  Indeed Hodgkin said that he lost all interest in neurophysiology during those dark years as one might imagine. But as things calmed down after the war they renewed their collaboration and got back to the business of neuronal excitability.
+
+So they needed to proved that ion permeability changes according to membrane potential but there was an issue— how to vary the membrane potential in a systematic way and also measure the ion permeabilities? 
+
+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
+
+<div><video height=400px controls src="figs/Animation02-03TheActionPotential.mp4"></video><figcaption>Neuroscience 5e Animation 2.3</figcaption></div> 
+
+Note:
+
+Summary of last time…
+
+--
+
+## More Vm examples
+
+<div style="font-size:0.7em;">
+<div></div>
+
+* Given a cell with intracellular: 1 mM NaCl, 10 mM KCl; extracellular: 10 mM NaCl, 1 mM KCl
+* What is the resting potential of the cell at room temperature (20ºC + 273 = 293 K) if the membrane is only permeable to K⁺?
+    * <span class= "fragment fade-in">`(58/1)*log10(1/10) = -58 mV`</span>
+* Only permeable to Na⁺? <!-- .element: class="fragment fade-in"-->
+    * <span class= "fragment fade-in">`(58/1)*log10(10/1) = +58 mV`</span>
+* Only permeable to Cl⁻? <!-- .element: class="fragment fade-in"-->
+    * <span class= "fragment fade-in">`(58/-1)*log10(11/11) = 0 mV`</span>
+* Equally permeable to K⁺ and Na⁺? <!-- .element: class="fragment fade-in"-->
+    * <span class= "fragment fade-in">`Pk = 0.5; Pna = 0.5; Pcl = 0; kOut = 1; kIn = 10; naOut = 10; naIn = 1; clIn = 11; clOut = 11`</span>
+    * <span class= "fragment fade-in">`(58)*log10( (Pk*kOut + Pna*naOut + Pcl*clIn) / (Pk*kIn + Pna*naIn + Pcl*clOut) ) = 0 mV`</span>
+
+</div> 
+
+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
+
+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
+
+* 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) )
+
+* -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)
+* 
+
+-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) )
+
+
+-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) )
+
+
+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
+
+
+---
+
+## The voltage clamp method
+
+<div><img src="figs/Neuroscience5e-Box-03A-0R_5d20ab3.png" height="400px"><figcaption>Neuroscience 5e Box 3A</figcaption></div>
+
+
+Note:
+
+This is an illustration of the voltage clamp recording method.
+
+One internal electrode measures membrane potential and is connect to the voltage clamp amplifier.
+
+voltage clamp amplifier compares membrane potential to the desired command potential
+
+When Vm is different from the command potential the clamp amplifier injects current ion the axon through a second electrode. This feedback arrangement causes the membrane potential to become the same as the command potential.
+
+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. 
+
+
+>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.
+
+>A differential amplifier is a type of electronic amplifier that amplifies the difference between two input voltages but suppresses any voltage common to the two inputs.[1]
+
+>An operational amplifier (often op-amp or opamp) is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output.[1] In this configuration, an op-amp produces an output potential (relative to circuit ground) that is typically hundreds of thousands of times larger than the potential difference between its input terminals.[2]
+
+
+---
+
+## Hodgkin and Huxley 1952
+
+* Do neuronal membranes have voltage-dependent permeability?
+* Which ions are changing their permeability?
+* Experiment– Change potential to make neuron membrane potential more negative (hyperpolarize). No currents need to be injected into cell to maintain that potential. Therefore no current is moving from inside and outside of cell
+* Change potential– Depolarize cell, now see both inward and outward currents between the inside and outside of cell
+
+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. 
+
+They asked…
+
+So the experiment was to hold the membrane potential at different voltages and measure charge flux into or out of the cell... —>
+
+
+---
+
+## 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">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:
+
+And so here are the results from this type of voltage clamp experiment.
+
+If you command that the cell membrane potential be hyperpolarized, you get very little or negligible current flowing across the membrane except for a very brief capacitive current that you always see in these voltage clamp experiments. 
+
+This is because the cell membrane essentially acts as a parallel RC circuit where a resistor and a capacitor are connected in parallel and to a constant current source. Ion channels are resistors, lipid bilayer with the extracellular and intracellular environments act as capacitor, storing charge in the form of ions accumulating near the surface of the membrane. When a switch is turned on in an RC circuit current flows from the battery to the capacitor until the capacitor is charged to a voltage that is same as the battery.
+
+However when Hodgkin and Huxley depolarized the membrane, a transient inward current occurs followed by a slow outward current.
+
+
+*A capacitor (originally known as a condenser) is a passive two-terminal electrical component used to store electrical energy temporarily in an electric field. Consists of two parallel conductors. Lipid membrane with the inner and outer cellular environment acts as this. The membrane capacitance per unit areas is mostly constant at about 1 µF/cm2.*
+
+* When the voltage is constant, the current through the capacitative pathway is zero because the capacitor has acquired the charge Q (coulombs) according to the relationship  Q=CV. C is capacitance (farads)  Ic is capacitive current.  Ic = C(dV/dt)
+* as long as V is changing with time, there will be a current flowing towards the capacitor.
+* if V is constant in time, there is no capacitive current.
+* product of resistance and capacitance has the unit of time and is called the time constant. Time constant defines how quickly capacitors charge or discharge over time. 
+
+[http://nerve.bsd.uchicago.edu/med98c.htm](http://nerve.bsd.uchicago.edu/med98c.htm)
+
+---
+
+## Current produced by different membrane depolarizations during voltage clamp
+
+<figure><img src="figs/Neuroscience5e-Fig-03.02-0_5ee332f.png" height="400px"><figcaption>Neuroscience Fig. 3.2</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. 
+
+---
+
+## 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>
+
+
+Note:
+
+This summarizes the peak magnitude of these these two currents at different Vm
+
+---
+
+## How do we prove the inward current is sodium?
+
+* Prediction– If you could change the Na⁺ concentrations in the system, for example have less sodium outside than inside (instead of the normal high outside low inside),  Nernst equation would predict an early outward current instead of an early inward current
+* Experiment– Change the Na⁺ concentration in the bath. Normally 440 mM NaCl outside & 50 mM inside for squid axon, now make it 50 mM inside & 0 mM outside
+
+Note:
+
+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><iframe src="https://www.youtube.com/embed/Wd_gKJoo25Y" width="420" height="315"></iframe><figcaption>Squid giant axon voltage clamping</figcaption></div>
+
+
+Note:
+
+>Choline is a water-soluble nutrient. It is usually grouped within the B-complex vitamins. Choline generally refers to the various quaternary ammonium salts containing the N,N,N-trimethylethanolammonium cation. (X− on the right denotes an undefined counteranion.)
+
+*The cation appears in the head groups of phosphatidylcholine and sphingomyelin, two classes of phospholipid that are abundant in cell membranes. Choline is the precursor molecule for the neurotransmitter acetylcholine, which is involved in many functions including memory and muscle control.*
+
+---
+
+## Voltage clamp method summary
+
+<div><video height=400px controls src="figs/Animation03-01TheVoltageClampMethod.mp4"></video><figcaption>Neuroscience 5e Animation 3.1</figcaption></div> 
+
+Note:
+
+---
+
+## Pathways of the two currents are distinct
+
+* Question– Do Na⁺ and K⁺ go through the same channels? Or do they have distinct channels?
+    * Experiment– Add tetrodotoxin (TTX) to block inward current but not outward current
+    * Experiment– Add tetraethylammonium (TEA) to block outward current but not inward current
+* TTX inactivates Na⁺ channels, TEA blocks K⁺ channels
+
+Note:
+
+
+--
+
+## Neurotoxins as pharmacological tools
+
+<div>
+<div></div>
+
+* Fugu (puffer fish or blow fish)
+* TTX concentrated in their livers (don’t eat it)
+* TTX blocks voltage-gated Na⁺ channels 
+
+</div>
+
+<div><img src="figs/1f421_8622cf0.png" height="300px"><figcaption>puffer fish</figcaption></div>
+<div><iframe src="https://www.youtube.com/embed/4g8KeqjSyqg" width="420" height="315"></iframe><figcaption>Simpsons poison tasty fish</figcaption></div>
+
+Note:
+
+Its mechanism of action, selective blocking of the sodium channel, was shown definitively in 1964 by Toshio Narahashi and professor John W. Moore at Duke University, using the sucrose gap voltage clamp technique (Narahashi et al, J Gen Physiol 1964)
+
+---
+
+## 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>
+
+
+Note:
+
+Tetramethylammonium chloride is one of the simplest quaternary ammonium salts. 
+
+[https://en.wikipedia.org/wiki/Tetramethylammonium_chloride](https://en.wikipedia.org/wiki/Tetramethylammonium_chloride)
+
+TTX and TEA experiments from Moore 1967 J Gen Physiol; Armstrong and Binstock, 1965 J Gen Physiol
+
+
+---
+
+## Voltage dependent membrane conductances of Na⁺ and K⁺
+
+<div style="font-size:0.6em;">
+<div></div>
+
+* Another way of describing permeability is using membrane conductance (*g*). Conductance (measured in siemens, *S*) is the reciprocal of resistance
+    * *g = 1/R*
+* Ohm’s law: 
+    * *I = V/R*
+    * *I = gV*
+    * 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<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>)*
+* *I<sub>x</sub>* determined from measurement of current changes plus or minus ion (or during pharmacological inhibition)
+* *E<sub>x</sub>* calculated from Nernst equation using concentrations of inside and outside ions
+
+</div>
+
+Note:
+
+For our purposes, we can consider conductance to be another way of describing permeability. 
+
+technically conductance is the degree to which an object conducts electricity, calculated as the ratio of the current that flows to the potential difference present. It deals with the movement of charge, whereas permeability refers to the ability of a specific ion to move across the cell membrane.
+
+* [http://www2.montana.edu/cftr/ion_channel_glossary.htm](http://www2.montana.edu/cftr/ion_channel_glossary.htm)
+
+Ohms law= Voltage = Current times resistance.
+
+Can use this to calculate the dependence of Na and K conductances vs. time and membrane potential.
+
+
+---
+
+## 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>
+
+
+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>
+
+
+Note:
+
+Determine the peak conductance of ions at different membrane potentials.  
+
+---
+
+## Description of an action potential using Na⁺ and K⁺ conductances
+
+<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
+* Depolarization also opens voltage gated K⁺ channels, which causes K⁺ to flow out, thus lowering the membrane potential
+
+</div>
+
+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>
+
+Note:
+
+
+<!-- ## Feedback cycles responsible for membrane potential changes
+
+<div><img src="figs/Neuroscience5e-Fig-03.09-0_0ffcd53.jpg" height="100px"><figcaption></figcaption></div> -->
+
+---
+
+## Properties of action potentials explained
+
+<div style="font-size:0.8em;">
+<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 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.
+
+</div>
+
+
+Note:
+
+The threshold is a point of criticality in the system like trying to balance on a knifes edge. Just imagine any self-organized phenomena in nature:  a snow field suddenly turning into an avalanche, liquid water turning into gas or solid forms, videos of cats or korean pop stars suddenly going viral.  The point at which the states of these systems veer on the edge of order or disorder is the point of criticality also known to physicists as a phase transition.
+
+---
+
+## Properties of action potentials explained
+
+* Action potential propagation and directionality?
+* Refractory periods?
+* What does myelin do?
+
+Note:
+
+Next we will look at the following properties of APs such as:  
+
+---
+
+## Action potential propagation
+
+* Charge flowing in through Na⁺ channels can diffuse inside the axon. This passive current cannot diffuse very far because of current leakage. Potentials below threshold taper out fast (like passive conduction of subthreshold depolarizations).
+* Potentials above threshold cause increased depolarization (due to more Na⁺ channels open). Now there is enough current to diffuse laterally and still be above threshold for a new set of Na⁺ channels.
+
+Note:
+
+First let’s talk about AP propagation.
+
+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>
+
+
+Note:
+
+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>
+
+Note:
+
+bottom graph shows the peak Vm
+
+---
+
+## Action potential conduction requires both active and passive current flow
+
+<div><img src="figs/Neuroscience5e-Fig-03.10-1R_070270d.png" width="500px"><figcaption>Neuroscience 5e Fig. 3.10</figcaption></div>
+
+<div><img src="figs/Neuroscience5e-Fig-03.10-2R_a528229.png" width="500px"><figcaption>Neuroscience 5e Fig. 3.10</figcaption></div>
+
+<div><img src="figs/Neuroscience5e-Fig-03.10-3R_d3311ca.png" width="500px"><figcaption>Neuroscience 5e Fig. 3.10</figcaption></div>
+
+<!-- <div><img src="figs/Neuroscience5e-Fig-03.10-4R_03ef878.png" width="200px"><figcaption>Neuroscience 5e Fig. 3.10</figcaption></div> -->
+
+
+Note:
+
+Active and Passive current flow.  
+
+* Na+ chan locally open in response to stimulus, generating an AP
+* Depolarzing current passively flows down axon
+* Local passive depolarization causes nearby Na chan to open and another AP is generated
+* Na chan upstream inactivate and K chan open. Vm repolarizes and is refractory to further AP generation upstream
+* Process repeated downstream, propagating AP along the axon
+
+---
+
+## Why is there a refractory period?
+
+<div style="font-size:0.8em;">
+<div></div>
+
+* Remember during the falling to undershoot phase of an action potential K⁺ channels are still open but Na⁺ are channels inactivated (decreased g<sub>Na</sub>), leading to temporary hyperpolarization more negative than the resting membrane potential 
+* Therefore (1) inactivation of Na⁺ channels and (2) slow K⁺ channel kinetics are responsible for the refractory period
+* This makes it harder to initiate a new AP either from a new stimulus or for an AP to propagate backwards
+* Different axons will have different refractory periods (and thus different maximal firing rates) depending on the particular subtypes of Na⁺ and K⁺ channels they express
+
+</div>
+
+<div><img src="figs/action_potential_ab5134f.png" height="150px"><figcaption></figcaption></div>
+
+Note:
+
+
+--
+
+## Voltage-gated channel states during an action potential
+
+<div><img src="figs/Neuroscience5e-Fig-04.03-0_6eef262.png" width="500px"><figcaption>Neuroscience 5e fig. 4.3</figcaption></div>
+
+
+
+Note:
+
+---
+
+## What does myelin do?
+
+* Rate of action potential formation limits the flow of information
+* How to speed up AP conduction?
+    * Increase the diameter of the axon– bigger axon diameters have less resistance (decreased resistance to passive current flow)
+    * Myelin **insulates the axon**, reducing current leak. Example AP conduction velocities for axons: unmyelinated 0.5–10 m/s, myelinated 150 m/s
+
+Note:
+
+
+---
+
+## Nodes of Ranvier
+
+* Can’t insulate the whole axon because transmembrane current flow is required to generate the action potential
+* Current from one action potential flows passively to next node where a new action potential is made
+* Action potentials have saltatory conduction– meaning from node to node
+
+Note:
+
+
+
+---
+
+## Nodes of Ranvier
+
+<div><img src="figs/Neuroscience5e-Fig-03.11-0-crop_d8af80c.jpg" height="500px"><figcaption>Neuroscience 5e Fig. 3.11</figcaption></div>
+<div><img src="figs/Neuroscience5e-Fig-03.10-4R_03ef878.png" width="300px"><figcaption>Neuroscience 5e Fig. 3.10</figcaption></div>
+
+Note:
+
+saltatory action potential condution along a myelinated axon.
+
+red indicates imaged expression of voltage gated Na channels. green indicates a protein (Caspr) associated with the nodes of Ranvier.
+
+
+---
+
+## Speed of action potential conduction in unmyelinated versus myelinated axons
+
+<div><img src="figs/Neuroscience5e-Fig-03.12-0_214d611.png" height="500px"><figcaption></figcaption></div>
+
+
+Note:
+
+figure comparing action potential propagation speed in an unmyelinated and myelinated axon.
+
+action potential genaration occurs only at specific points, the nodes of Ranvier, along the myelinated axon
+
+---
+
+## The Nobel Prize in Physiology or Medicine (1963)
+
+>"for their discoveries concerning the ionic mechanisms involved in excitation and inhibition in the peripheral and central portions of the nerve cell membrane"
+
+<div style="width:300px; float:left;"><img src="figs/q002_155484b.jpg" height="200px"><figcaption class="big">
+
+Alan Lloyd Hodgkin 
+
+</figcaption></div>
+
+<div style="width:600px; float:left;"><img src="figs/q003hux_505f8c6.jpg" height="200px"><figcaption class="big">
+
+Andrew Fielding Huxley 
+
+</figcaption></div>
+
+
+Note:
+
+
+---
+
+## Painless dentistry
+
+* Lidocaine blocks some types of Na⁺ channels
+* Blocks action potentials in sensory axons
+* Pain signals do not reach the brain
+
+<div><img src="figs/neuron_model-sensory_7bb4f48.png" height="100px"><figcaption></figcaption></div>
+
+<div><figcaption class="big">voltage-gated sodium channel</figcaption><img src="figs/Neurochem-Fig6-6_4995928.png" height="300px"><figcaption>Basic Neurochemistry 6e Fig. 6.6</figcaption></div>
+
+
+
+
+Note:
+
+
+
+---
+
+## Multiple sclerosis
+
+* Disease caused by myelination defects and loss of neurons
+* Seems like an autoimmune disease
+* 1/750 of population in US get multiple sclerosis (MS)
+* 1/40 risk if a parent has it
+* 1/3 if an identical twin gets it
+* Genetic and environmental risk factors
+
+Note:
+
+onset between ages 20-40.
+
+blindness, motor weakness, paralysis.
+
+ultimate cause of MS remains unclear. Immune system contributes to damage and is key component. Immune cells in CSF and injection of myelin in animals can cause EAE. Autoimmune disorder. Or persistent infection with a human retrovirus? 
+
+
+* women to men ratio 3/2
+* Genetic component is likely the effect of multiple genes
+
+---