diff --git a/2016-09-28-lecture03.md b/2016-09-28-lecture03.md index 1b3ba3f..157c703 100644 --- a/2016-09-28-lecture03.md +++ b/2016-09-28-lecture03.md @@ -26,9 +26,14 @@ as well as general molecular signaling within neurons as any living cell might h ## Neurons have a negative membrane potential at rest. +
+
+ * For intracellular recordings, an electrode is placed inside a cell such that the inside of the pipette is contiguous with the inside of the cell. If this electrode is connected to a voltmeter, which records transmembrane voltage across the cell membrane, one can determine the difference in voltage between the inside and outside of the cell. * When one does this in neurons, the microelectrode reports a negative potential called the resting potential. Always a fraction of a volt (-40 to -90 mV). -* Volts are a unit of electrochemical potential energy. 1 Volt will drive 1 coulomb of charge (6.24X1018 electrons) through a resistance of 1 ohm in 1 second. +* Volts are a unit of electrochemical potential energy. 1 Volt will drive 1 coulomb of charge (6.24X1018 electrons) through a resistance of 1 ohm in 1 second. + +
@@ -36,98 +41,68 @@ 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. - - 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 —> --- ## Electrical current -Pump pressure ≈ Voltage (volts) = V +
+
-Pipe diameter ≈ Resistance (ohms) = R +Pump pressure ~ Voltage (volts) = `V` -Flow rate ≈ Current (amperes) = I +Pipe diameter ~ Resistance (ohms) = `R` -V = IR Ohm’s law +Flow rate ~ Current (amperes) = `I` -I = V/R +`V = IR` Ohm’s law + +`I = V/R` + +
+ +
M. Banzi Fig. 4-4, *Getting Started with Arduino* isbn:9781449363338
- - - - -
- 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. - - 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. * - 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. 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+. +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⁺. * - 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 - - - -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 - - - +* 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 --- ## Electrical signals -* Can be generated by changing the resting 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. +* Can be generated by changing the resting 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. - - This includes receptor potentials inside your body’s sensory neurons for touch, heat, light, and sound. And synaptic potentials are the changes in membrane potential at synapses that underly the transfer of information from neuron to neuron. @@ -138,25 +113,18 @@ Action potentials are the large electrical spikes or impulses that allow neurona ## Types of electrical signals in neurons -
+
Neuroscience 5e Fig. 2.1
+ Note: This figure shows these 3 types of neuronal signals. +- Here is a receptor potential in a pacinian corpuscle, which is a type of mechanosensory receptor on sensory nerve endings near the surface of your skin. +- Here is a synaptic potential recorded in a postsynaptic neuron. -Here is a receptor potential in a pacinian corpuscle, which is a type of mechanosensory receptor on sensory nerve endings near the surface of your skin. - - - -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. @@ -165,119 +133,89 @@ Here is an action potential in a motor neuron. Look as the y-axes here— the ac ## Resting Potentials of Neurons * The membrane of a nerve cell maintains an electrical polarization - - outside (+) - -The cell is polarized: at rest, an electrical gradient is maintained across the plasma membrane (negative charge is greater inside the cell) - - - - - -The cell has a resting potential: difference in voltage across the membrane of a cell (~ -70 mV) - - - - - -The cell has a concentration gradient: difference in distribution of ions between the inside and outside of a membrane - - inside (-) +* The cell is polarized: at rest, an electrical gradient is maintained across the plasma membrane (negative charge is greater inside the cell) +* The cell has a resting potential: difference in voltage across the membrane of a cell (~ -70 mV) +* The cell has a concentration gradient: difference in distribution of ions between the inside and outside of a membrane
+ 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 on the intracellularly than extracellularly– 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 +This polarization results in a potential difference across the membrane (remember our water pump example) of about -70 mV -We can that 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. - - - -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. - +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 --- ## Important terms -* Resting membrane potential– voltage across the cell membrane when it is at rest. Typically -40 to -90 mV. -* Hyperpolarization– making the membrane potential more negative. -* Depolarization– making the membrane potential more positive. -* Threshold potential– membrane potential at which an action potential is initiated. +* Resting membrane potential– voltage across the cell membrane when it is at rest. Typically –40 to –90 mV +* Hyperpolarization– making the membrane potential more negative +* Depolarization– making the membrane potential more positive +* Threshold potential– membrane potential at which an action potential is initiated Note: Some important terms to know - - - - -Just remember that a neuron not eliciting any electrical signals is ‘resting’ at around -70 mV. If electrical current makes the membrane voltage more positive than it is depolarizing. If it is making the membrane more negative than it is hyperpolarizing. - +Just remember that a neuron not eliciting any electrical signals is ‘resting’ at around -70 mV. If electrical current makes the membrane voltage more positive than it is depolarizing. If it is making the membrane more negative than it is hyperpolarizing. Depolarized is less polarized. Hyperpolarized is less polarized. --- ## Recording passive and active electrical signals in a nerve cell -* Can inject current into the cell. -* This current will add either positive charge or negative charge. This will change the resting potential accordingly. +
+
+ +* Can inject current into the cell +* This current will add either positive charge or negative charge. This will change the resting potential accordingly + +
+ +
Neuroscience 5e Fig. 2.2
-
Note: Now we already saw that we can stick an electrode into a cell, and hook it up to an oscilloscope and passively record its resting membrane potential on the slide from earlier. - - 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 -* Action potentials all have basically the same amplitude. Stronger stimuli gives more action potentials not higher amplitude ones +
+
-inject negative current +**Action potentials all have basically the same amplitude.** Stronger stimuli gives more action potentials not higher amplitude ones. +
+
Neuroscience 5e Fig. 2.2
- -inject positive current - -
- 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 - - 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. - --- ## Ionic movements produce electrical signals @@ -307,14 +245,15 @@ There are also ion channels that form pores in the cell membrane that are select --- -## Na+–K+ pump +## Na⁺–K⁺ pump -* 3 Na+ out for every 2 K+ in. +* 3 Na⁺ out for every 2 K⁺ in * Pumps against concentration gradient * Requires ATP -* Helps set up the ion concentration gradients and resting membrane potential. +* Helps set up the ion concentration gradients and resting membrane potential + +
Alberts *Mol Biol of the Cell* Fig. 11-10
-
Note: @@ -335,174 +274,159 @@ 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. - - 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. - - - --- ## Ionic movements across neuronal membranes -
+
Neuroscience 5e Fig. 2.4
+ 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 -* Can be calculated from knowing the concentrations of ions inside and outside the cell, and the relative permeability of these ions across the cell membrane. -* Nernst equation– simple formula to determine cell potentials. -* Goldman equation– formula to determine resting potential when the cell membrane is permeable to more than one ion. +* Can be calculated from knowing the concentrations of ions inside and outside the cell, and the relative permeability of these ions across the cell membrane +* Nernst equation– simple formula to determine cell potentials +* Goldman equation– formula to determine resting potential when the cell membrane is permeable to more than one ion 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. - - 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. - - If a cell membrane is permeable to more than one ion, we can use the Goldman equation. - - We will come back to these in a minute. - -Walther Nernst (1864-1941) - +*Walther Nernst (1864-1941)* --- -## Electrochemical Equilibrium +## Electrochemical equilibrium -green dots Cl- +
orange dots K⁺, green dots Cl⁻
Neuroscience 5e Fig. 2.5
-orange dots K+ -
Note: -First let’s discuss electrochemical equilibrium, which is the balance of two driving forces— electrical AND chemical diffusion– across a cell membrane. - - +First let’s discuss **electrochemical** equilibrium, which is the balance of two driving forces— electrical AND chemical diffusion– across a cell membrane. Imagine the following experiment. We have a cell and record intracellular membrane potential with electrodes and a voltmeter. +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 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. - ---- - -## What’s going on? - -* Initially each side of the container is neutral for charge– Every K+ has a Cl- partner. -* K+ however wants to diffuse down its concentration gradient. Cl- might want to but is not permeable. This creates a rush of K+ to the other side. -* After a while the positive charge builds up and the ions start to repel each other because of their like charge. This discourages more K+ to come in, even though their concentration difference wants them to. -* An equilibrium will be reached which creates a net positive charge outside the cell relative to the inside. The inside (intracellular) space of the cell relative to the outside (extracellular) space is then -58mV (for this example). -* The resting potential can be calculated using the Nernst equation. - -Note: - +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. --- -## Title Text +## Electrochemical equilibrium explained -[http://courses.pbsci.ucsc.edu/mcdb/bio125/Animation02-01TheRestingMembranePotential.mov](http://courses.pbsci.ucsc.edu/mcdb/bio125/Animation02-01TheRestingMembranePotential.mov) +
+
-
+* Initially each side of the container is neutral for charge– Every K⁺ has a Cl⁻ partner +* K⁺ diffuses down its concentration gradient since this membrane is permeable only to K⁺. Cl⁻ might want to but is not permeable. This creates a rush of K⁺ towards the other side (outside). +* After a while the positive charge builds up and the ions start to repel each other because of their like charge. This discourages more K⁺ from going out, even though its concentration difference is trying to drive it that way. +* An equilibrium will be reached which creates a net positive charge outside the cell relative to the inside. The inside (intracellular) space of the cell relative to the outside (extracellular) space is then -58 mV (for this example) +* The resting potential can be calculated using the **Nernst equation** + +
Note: +--- + +## Resting membrane potential video + +
Neuroscience 5e Animation 2.1
+ + +Note: + --- ## Nernst equation +
+
+ * Statement of the equilibrium condition for a single ion species across a membrane that is permeable only to that ionic species: -* + * *Ex* = equilibrium potential (V) for ion *x* + * *R* = the gas constant (8.3 J mol-1 K-1) + * *T* = absolute temperature (K) + * *F* = faraday constant (9.6x104 J mol-1 V-1) + * *z* = valence of the ion, including sign. + * ln = natural logarithm (base *e*) + * [*x*]out extracellular concentration of an ion extracellular; [*x*]in intracellular concentration -* -* Ex = equilibrium potential in mV -* R = the gas constant (8.3 J mol-1 K-1) -* T = absolute temperature (K) -* F = faraday constant (9.6x104 J mol-1 V-1) -* z = valence of the ion, including sign. -* ln = natural log (base e) -* [x]out concentration of an ion outside; [x]in inside -* +* RT/F can be a constant at room temperature to give a simplified equation -* RT/F can be a constant at room temperature to give a simplified equation: -* +
-
+
Nernst equation
For calculations for any temperature, Ex in volts (V)
-
+
Simplified Nernst equation
For calculations at room temperature (68ºF = 20ºC = 20+273 = 293ºK), Ex in millivolts (mV)
Note: So I stated that the Nernst equation is how we can calculate the equilibrium potential for a cell membrane permeable to one type of ion. - - And here is the Nernst equation is: Where Ex is: -Gas constant R equivalent to the Boltzmann constant but expressed in units of energy. The physical significance of R is work per degree per mole. R = 8.3144598 J mol−1 K−1 == R = work / amount x temperature. Relates the energy scale in physics to the temperature scale, when a mole of particles at the stated temperature is being considered. Joules/mol/K +Gas constant R +: equivalent to the Boltzmann constant but expressed in units of energy. +: The physical significance of R is work per degree per mole. +: R = 8.3144598 J mol−1 K−1 == R = work / amount x temperature. +: Relates the energy scale in physics to the temperature scale, when a mole of particles at the stated temperature is being considered. Joules/mol/K +Temperature +: absolute temperature expressed in degrees Kelvin +Faraday constant +: magnitude of electric charge per mole of electrons = 96485.33289 C/mol. Expressed in C/mol or J/mol/V -Faraday constant = magnitude of electric charge per mole of electrons = 96485.33289 C/mol. Expressed in C/mol or J/mol/V - - - -Temperature is: - -z is the valence of the ion in question - -ln is the natural logarithm which has the mathematical constant e or 2.718 as it’s base. +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 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. - - -Thus to make calculations simpler in the classic scientific papers (often from the 1930s and 1940s before computers) this equation for experiments carried out at room temperature is often simplified to the following of: - +Thus to make calculations simpler in the classic scientific papers (often from the 1930s and 1940s before computers) this equation for experiments carried out at room temperature (20ºC = 68ºF = 20ºC+273ºK = 293ºK) is often simplified to the following of: which uses the base10 logarithm. Since —> - 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) R = 8.3 J/K*mol, T = 37ºC + 273ºC = 310 K, F = 9.6*10^4 J/mol*V @@ -514,9 +438,7 @@ E = log(7) / log10(7) R = 8.3 - F = 9.6 * 10^4 - T = 20+273 (R*T / F) * 1000 * 2.3 @@ -524,16 +446,12 @@ T = 20+273 ==>58.26427 - - - --- -## Title Text +## Electrochemical equilibrium video -[http://courses.pbsci.ucsc.edu/mcdb/bio125/Animation02-02ElectrochemicalEquilibrium.mov](http://courses.pbsci.ucsc.edu/mcdb/bio125/Animation02-02ElectrochemicalEquilibrium.mov) +
Neuroscience 5e Animation 2.2
-
Note: @@ -543,38 +461,32 @@ Note: ## Examples -* Outside: 10 mM KCl, Inside: 1mM KCl– membrane only permeable to K+ ? -* Ek = (58/1)log10(10/1) == +58 -* Outside 1 mM KCl, Inside: 100 mM KCl ? -* Ek = (58/1)log10(1/100) == -116 -* Outside: 10 mM CaCl2, Inside: 1mM CaCl2– membrane only permeable to Ca2+ ? -* Nernst predicts linear relationship with a slope of 58 mV (58/z) per 10 fold ion change in concentration gradient +* Outside 10 mM KCl, Inside 1 mM KCl membrane only permeable to K⁺ ? + * EK+ = (58/1)log10(10/1) ==> +58 +* Outside 1 mM KCl, Inside 100 mM KCl membrane only permeable to K⁺ ? + * EK+ = (58/1)log10(1/100) ==> -116 +* Outside 10 mM CaCl₂, Inside 1 mM CaCl₂ membrane only permeable to Ca²⁺ ? + * ECa2+ = (58/2)log10(10/1) ==> +29 mV +* Nernst predicts linear relationship with a slope of 58 mV (58/z) per 10 fold ion change in concentration gradient Note: - - log10(10) = 1 - - log10(1/100) = log10(0.01) = -2 +For CaCl₂: (58/2)log10(10/1) = +29 mV - -For CaCl2: (58/2)log10(10/1) = +29 mV - - - -Since the Nernst equation is really just a linear equation of the form y = mx, you can think of this first term at the slope and the equilibrium potential for an ion varies linearly with the log of the concentration gradient. In other words there is 58 mV per tenfold change in the concentration gradient when we are talking about our potassium examples above. +Since the Nernst equation is really just a linear equation of the form y = mx, you can think of this first term at the slope and the equilibrium potential for an ion varies linearly with the log of the concentration gradient. In other words there is 58 mV per tenfold change in the concentration gradient when we are talking about our potassium examples above, which is depicted here --> --- -## Electrochemical Equilibrium +## Electrochemical equilibrium -in-out -
+ +
Neuroscience 5e Fig. 2.5
+ Note: @@ -582,51 +494,36 @@ This plot depicts this equilibrium relationship for a hypothetical cell permeabl --- -## Electrochemical equilibrium +## Electrochemical equilibrium summary * Exact balance between two opposing forces -* Initial concentration gradient causes K+ to move from compartment inside to outside. -* An opposing electrical gradient develops that tends to stop K+ from moving across the membrane. -* Therefore changing the concentrations of ions changes the chemical driving force and can induce ion flux. -* In addition changing the membrane potential changes the electrical driving force and can induce ion flux. +* Initial concentration gradient causes K⁺ to move from compartment inside to outside +* An opposing electrical gradient develops that tends to stop K⁺ from moving across the membrane +* Therefore changing the concentrations of ions changes the chemical driving force and can induce ion flux +* In addition changing the membrane potential changes the electrical driving force and can induce ion flux Note: Remember that electrochemical equilibrium is the: - - I = g(Vm-Ex). g = conductance, no. of open channels. (Vm-Ex) = driving force causing either positive or negative current. - - --- ## Membrane potential influences ion fluxes -flow from in to out +
Neuroscience 5e Fig. 2.6
-no net flow - -flow from out to in - -
Note: -So lets imagine the following experiment we have a cell membrane, at room temperature and it is permeable only to potassium shown by the orange dots going through K+ ion channels. From the Nernst eqn we can calculate that the equilibrium potential for K+ to achieve electrochemical equilbrium in this situation is -58 mV. - - - -That means that the chemical or concentration dependent driving force is predominant at more depolarized or more positive membrane potentials than -58mV as shown on the left here causing a net outward K+ flux. - - - -If our hypothetical battery holds the membrane at -58 mV, the equilbrium potential, there is no net K+ flow. +So lets imagine the following experiment we have a cell membrane, at room temperature and it is permeable only to potassium shown by the orange dots going through K⁺ ion channels. From the Nernst eqn we can calculate that the equilibrium potential for K⁺ to achieve electrochemical equilbrium in this situation is -58 mV. +That means that the chemical or concentration dependent driving force is predominant at more depolarized or more positive membrane potentials than -58mV as shown on the left here causing a net outward K⁺ flux. +If our hypothetical battery holds the membrane at -58 mV, the equilbrium potential, there is no net K⁺ flow. 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. @@ -636,11 +533,12 @@ At more negative membrane potentials than the nernst equilbrium potential we get ## Membrane potential influences ion fluxes -
+
Neuroscience 5e Fig. 2.6
+ Note: -The results of this thought experiment are displayed here, displaying the net movement of K+ ions into the cell when the membrane potential more negative or hyperpolarized than the K+ equilibrium potential, and net movement outward when the membrane potential is more positive or depolarized. +The results of this thought experiment are displayed here, displaying the net movement of K⁺ ions into the cell when the membrane potential more negative or hyperpolarized than the K⁺ equilibrium potential, and net movement outward when the membrane potential is more positive or depolarized. @@ -649,97 +547,73 @@ 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 * 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. -* At -58 mV no net flow will occur. -* At more negative potentials K+ will want to flow against its concentration gradient. -* Scientists can experimentally vary both ion concentrations and membrane potential. +* 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 +* At -58 mV no net flow will occur +* At more negative potentials K⁺ will want to flow against its concentration gradient +* Scientists can experimentally vary both ion concentrations and membrane potential 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 +And we can experimentally vary... -And we can experi - --- ## Equilibrium with more than one permeant ion -* If inside solution contains 10mM KCl and 1mM NaCl and outside solution contains 1mM KCl and 10mM NaCl… -* …then if only permeable to K+, equilibrium potential is -58 mV. If only permeable to Na+, than potential is +58. Nernst eqn. -* …if membrane is permeable to both K+ and Na+ (but not necessarily equally permeable) then equilibrium potential will be an intermediate value in between. Nernst cannot do this calculation. -* Requires Goldman equation: -* -* The relevant ions in neurons are K+, Na+, and Cl- -* No sign for valence, that is why Cl- is flipped +
+
+ +* If inside solution contains 10 mM KCl and 1 mM NaCl and outside solution contains 1 mM KCl and 10 mM NaCl... +* ...and the cell is only permeable to K⁺, equilibrium potential is -58 mV. Or if only permeable to Na⁺, than potential is +58. **Nernst eqn.** +* ...but if membrane is permeable to both K⁺ and Na⁺ (but not necessarily equally permeable) then equilibrium potential will be an intermediate value in between. Nernst cannot do this calculation. +* Requires **Goldman equation** + * The relevant ions in neurons are K⁺, Na⁺, and Cl⁻ + * No sign for valence, that is why Cl⁻ is flipped + +
+ +
Simplified Goldman equation
For calculations at room temperature
+ -
Note: This is all great but real cells have to deal with permeability of more than one ion species. - - So imagine we have 10 mM KCl and 1mM NaCl inside the cell and 1 mM KCl and 10mM NaCl outside the cell. - - If we have a simplified situation like earlier where the membrane is permeable to just K we can use Nernst eqn to show that the Veq will be -58mV at room temp. If just permeable to Na we can use Nernst to show the Veq will be +58mV - - Now imagine the cell membrane is permeable to both K and Na and that these permeabilities or ability of ions to pass across the membrane are not equal for K and Na, then we have to use the Goldman eqn. - - Which looks like a more complex version of the Nernst equation but with added terms that take into account the concentrations and relative membrane permeabilities of multiple ion species. There is no valence term, thus since choride is an anion, its concentration terms are flipped. - - For a typical neuron at rest, pK : pNa : pCl = 1 : 0.05 : 0.45. Note that because relative permeability values are reported, permeability values are unitless. +[http://www.nernstgoldman.physiology.arizona.edu/](http://www.nernstgoldman.physiology.arizona.edu/) +[http://www.physiologyweb.com/calculators/ghk_equation_calculator.html](http://www.physiologyweb.com/calculators/ghk_equation_calculator.html) +[http://jgp.rupress.org/content/27/1/37.full.pdf+html](http://jgp.rupress.org/content/27/1/37.full.pdf+html) - - - - -[http://www.nernstgoldman.physiology.arizona.edu/](http://www.nernstgoldman.physiology.arizona.edu/) - - - -[http://www.physiologyweb.com/calculators/ghk_equation_calculator.html](http://www.physiologyweb.com/calculators/ghk_equation_calculator.html) - - - -[http://jgp.rupress.org/content/27/1/37.full.pdf+html](http://jgp.rupress.org/content/27/1/37.full.pdf+html) - - - -calcium permeability is essentiall zero for cells at rest. But during active dynamics permeability changes many thousand fold - -calcium is more complicated, requires a derived goldman eqn. - -“Expansion of the constant field equation to include both divalent and monovalent ions.” (Spangler, S.G., Ala J Med Sci, 9: 218-223, 1972) - -[http://www.nernstgoldman.physiology.arizona.edu/using/](http://www.nernstgoldman.physiology.arizona.edu/using/) - - +- *calcium permeability is essentially zero for cells at rest. But during active dynamics permeability changes many thousand fold* +- *calcium is more complicated, requires a derived goldman eqn.* +- *"Expansion of the constant field equation to include both divalent and monovalent ions." (Spangler, S.G., Ala J Med Sci, 9: 218-223, 1972)* +- [http://www.nernstgoldman.physiology.arizona.edu/using/](http://www.nernstgoldman.physiology.arizona.edu/using/) --- ## Resting membrane and action potentials entail permeabilities to different ions -
+
Neuroscience 5e Fig. 2.7
+ Note: @@ -751,31 +625,12 @@ And as we will soon learn, the resting membrane potential and action potential v * Semi permeable membranes * Concentration gradients of ions across membranes -* Concentration of Na+ and Cl- higher outside than inside, while K+ is higher inside. -* The resting membrane potential is close to the equilibrium potential for K+, suggesting that at rest a cell is permeable mostly to K+. +* Concentration of Na⁺ and Cl⁻ higher outside than inside, while K⁺ is higher inside +* The resting membrane potential is close to the equilibrium potential for K⁺, suggesting that at rest a cell is permeable mostly to K⁺ +
-140 mM K+ - -10 mM Na+ - -30 mM Cl- - -0.0001 mM Ca2+ - -5 mM K+ - -145 mM Na+ - -110 mM Cl- - -1 mM Ca2+ - -inside - -outside - Note: Cells are a bit like a semipermeable bag of electrolytes with different concentrations of ionic species inside and outside. @@ -784,22 +639,22 @@ Cells are a bit like a semipermeable bag of electrolytes with different concentr ## Extracellular and intracellular ion concentrations -
+
Neuroscience Table 2.1
+ Note: -Table of physiological relevant intracellular and extracellular ion concentrations in squid neurons and mammalian neurons. Though the values are scaled about 4 times higher in squid, note that K is more concentrated inside, and sodium and chloride are more concentrated outside for both invertebrate and vertebrate neurons. - +Table of physiological relevant intracellular and extracellular ion concentrations in squid neurons and mammalian neurons. Though the values are scaled about 4 times higher in squid, note that K is more concentrated inside, and sodium and chloride are more concentrated outside for both invertebrate and vertebrate neurons. The relevant ratios of different ion species inside and outside are similar. --- -## How to test if a neuron is only permeable to K+ at rest +## How to test if a neuron is only permeable to K⁺ at rest -* Need to measure concentrations of ions extracellularly and in the cytoplasm. -* Would like to manipulate concentrations of ions outside as well as inside the cell. +* Need to measure concentrations of ions extracellularly and in the cytoplasm +* Would like to manipulate concentrations of ions outside as well as inside the cell * Be able to make reliable electrical measurements -* Need an axon big enough to get your electrode in. Initially used the squid giant axon for experiments because they are large (400x larger than a typical mammalian axon). +* Need an axon big enough to get your electrode in. Initially used the squid giant axon for experiments because they are large (400x larger than a typical mammalian axon). Note: @@ -811,9 +666,10 @@ As I hinted at earlier today and in a previous lecture, the squid giant axon was ## Squid giant axon -[https://www.youtube.com/watch?v=omXS1bjYLMI](https://www.youtube.com/watch?v=omXS1bjYLMI) +
Atlantic squid, *Loligo pealei*
+ +
Squid giant axon electrophysiology
-
Note: @@ -823,10 +679,10 @@ 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 58mV/ tenfold change in K+ gradient +* 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 Note: @@ -834,45 +690,31 @@ Alan Hodgkin, Andrew Huxley, Bernard Katz --- -## Title Text +## K⁺ concentration gradient determines resting membrane potential -K+ concentration gradient determines resting membrane potential +
Neuroscience 5e fig. 2.8
-why does it deviate from the line at low K+ concentrations? - -increasing extracellular K+ increases resting potential - -
Note: -So Hodgkin and Katz did this experiment, varying the extracellular K+ concentration while recording the squid axon membrane potential and found that increasing the Kout incr the resting membrane potential. +So Hodgkin and Katz did this experiment, varying the extracellular K⁺ concentration while recording the squid axon membrane potential and found that increasing the Kout incr the resting membrane potential. +They plotted resting membrane potential against the extracellular K⁺ concentration, shown in this red curve. +If internal K⁺ is unchanged, a plot of membrane potential against the log of external K⁺ concentration would yield a straight line with slope of 58mV per tenfold change in external K⁺ concentration at RT. -They plotted resting membrane potential against the extracellular K+ concentration, shown in this red curve. - - - -If internal K+ is unchanged, a plot of membrane potential against the log of external K+ concentration would yield a straight line with slope of 58mV per tenfold change in external K+ concentration at RT. - - - -However it deviates from this expected relationship (shown by the black line), especially at lower K+ concentrations. Why is this? - - - -Because other ions, particularly Cl- and Na+, are also slightly permeable and the contribution of these other ions is more evident at low K+ concentrations. +However it deviates from this expected relationship (shown by the black line), especially at lower K⁺ concentrations. Why is this? +**Because other ions, particularly Cl⁻ and Na⁺, are also slightly permeable and the contribution of these other ions is more evident at low K⁺ concentrations.** --- ## Hodgkin and Katz– 1949 conclusions 1 -* Inside negative resting potential is due to the axon membrane being permeable to K+ more than any other ion. -* More K+ inside than outside cell -* At rest K+ ion channels are open and allow the flow of K+ down its concentration gradient, this creates extra (+) ions on the outside relative to the inside and therefore a (-) resting potential. +* Inside negative resting potential is due to the axon membrane being permeable to K⁺ more than any other ion +* More K⁺ inside than outside cell +* At rest K⁺ ion channels are open and allow the flow of K⁺ down its concentration gradient, this creates extra (+) ions on the outside relative to the inside and therefore a (-) resting potential Note: @@ -883,68 +725,45 @@ 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 ENa -* 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? +* Measured the membrane potential after initiating an action potential +* Found– Membrane potential during the action potential approached ENa +* 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? Note: But they also wondered what is happening in the cell membrane when neurons are firing an action potential or ‘spike’ or ‘impulse’? - - To answer this Hodgkin and and Katz measured the membrane potential while inducing action potentials in the squid axon. +They observed that the Vm approached ENa during an AP... - -They observed that the Vm approached ENa during an AP… - -The reason they hypothesized is that during an AP… +They reason they hypothesized is that during an AP... Their experiment was to lower Na concentrations in the extracellular medium— - --- ## The action potential as measured by Hodgkin, Huxley, and Katz -ENa +
Adapted from Hodgkin Huxley *Nature* 1939
-EK - - - - - -
Note: Hodgkin and Huxley, Nature 1939 squid giant axon - - Image adapted from Principles of Neurobiology, L. Luo Garland Fig 2-19 which in turn adapted from Nature 1939. - - -Capacitance (farads) is the ability of a body to store an electrical charge. Any object that can be electrically charged exhibits capacitance. Dielectric materials. Storage of electrical energy temporarily in an electric field. Unlike a resistor, an ideal capacitor does not dissipate energy. Instead, a capacitor stores energy in the form of an electrostatic field between its plates. - - - - - - +Capacitance (farads) is the ability of a body to store an electrical charge. Any object that can be electrically charged exhibits capacitance. Dielectric materials. Storage of electrical energy temporarily in an electric field. **Unlike a resistor, an ideal capacitor does not dissipate energy. Instead, a capacitor stores energy in the form of an electrostatic field between its plates.** --- ## Role of sodium in the generation of an action potential -* Lowering Na+ decreases both the rate and the rise of an action potential +
Lowering Na⁺ decreases both the rate and the rise of an action potential
Neuroscience 5e Fig. 2.9
-
Note: @@ -954,7 +773,7 @@ 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 -
+
Neuroscience 5e Fig. 2.9
Note: @@ -964,24 +783,19 @@ As you can see on the left here changing extracellular [Na] changes the action p ## Hodgkin and Katz– conclusions -* 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. +* 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 Note: -So a summary of the Hodgkin and Katz experiment conclusions… +So a summary of the Hodgkin and Katz experiment conclusions... --- ## Action potential form and nomenclature -squid giant axon +
(1) Squid giant axon, (2) frog motor neuron axon
Neuroscience 5e Box 2C
-frog motor neuron axon - -Time (ms) - -
Note: @@ -989,79 +803,43 @@ The membrane potential rapidly depolarizes during the rising phase of an AP. Act -AHP due to voltage-gated K+ channels, including Ca2+ activated potassium channels— incr K+ permeability, and inactivation of Na+ permeability. +AHP due to voltage-gated K⁺ channels, including Ca²⁺ activated potassium channels— incr K⁺ permeability, and inactivation of Na⁺ permeability. --- ## Action potential forms -frog motor neuron cell body +
(1) Frog motor neuron cell body, (2) guinea pig inferior olive neuron cell body, (3) cell body of purkinje neuron
Neuroscience 5e Box 2C
-guinea pig inferior olive neuron cell body - -cell body of a purkinje neuron - -40 - -mV - --80 - -0 - --40 Note: - - - - Summation of many spikelets cause unlike most neurons, purkinje cells in cerebellum have dendrites that can initiate action potentials. The dendrites aren’t myelinated. Llinas Sugimori J Physiol 1980 Purkinje neurons ---- - -## Action potential forms + --- ## The action potential– summary +
-Rising phase - -Overshoot phase - -Falling phase - -Undershoot phase - -
- Note: And this is just a overall summary of what we have been discussing --- - ---- -