NBIO 140: Lecture 2-4 (Resting Membrane Potential)
K+ equilibrium potential
** in resting potential diagram overall concentration gradient favors K+ OUT but membrane potential (which gets created by K+ absence) drives K+ to get back in - once K+ diffusion has preceeed to a certain point the electrical driving force of K+ exactly balances the chemical one - outward movement of K+ (driven by concentration gradient) is equal to the inward movement of K+ (driven by the electrical gradient)
Driving force
- An ion is not at equilibrium it has a potential to move. The total driving force equal to the difference between the membrane potential and the equilibrium potential for that ion - Driving force = Vm-Eion - We can figure out whether current inward/outward (direction) by knowing where the membrane potential is and reverse potential is. - When we are at equilibrium potential, the current is 0 because there is no net flow of ions across the membrane. When we have a membrane potential different from the equlibrium direction we willl have it going one direction or the other.
Hodgkin and Huxley voltage-clamp experiment - voltage-dependent changes of Na+ and K+ conductances
- Huxley invented the voltage clamp, steps to go from one membrnae potential to another and then measure the current at those instances in time. - They did the following experiment in a squid axon. The cell was @ -60mV. They set the command voltage @ 0mV. They recorded what happened. They saw a biiphasic current - Early after depolarization they saw an early inward current Late they saw a late outward current At -60, there is no NET current When we take the command voltage to -40, small inward current that we are measuring @ .5ms -20 larger inward + outward current At 0 very large inward + large outward At +20 inward smaller + outward bigger At +50 no early current+ outward bigger At +50 early outward current followed by a late outward current
Q: Permeability vs. conductance
- Permeabilitiy and coductance deal with the same issues, the ease of ions going though the same channel. - However, there are two different things Permeability (E) • intrinsic property of the membrane • physical-chemical property, deals with energy of ions through ion channel • independent of the concentration of permeant ions; (i.e. does NOT vary whether ions to be conducted are are present or not) Conductance (Siemens) = • depends on not only permeability but also concentration of ions • how much current is flowing through the channel • we will only be talking about conductance - We semi-derived the equivalent circuit form of the Goldman equation - In this equation, what appears is conductance, easy to measure, 1/R. - Our book also gives us the permeability form of the GHK
Q: Why is a peak of an AP near the equilibrium potential of sodium (EnA)?
- Sodium channels open, conductance gets high, so GDK membrane potential gets near the equilibrium potential of sodium. - Only holds if number of sodium channels is very large
Q: We want to understand why different cells have different resting potentials?
- Some cells do nothing and some fire lots of APs. - Action potentials can have many different properties and different shapes. Some neurons have true resting potentials others are SPONT ACTIVE and generate APs or other wave forms as well. - In silent neurons it is easy to ask What gives rise to the resting potential we record?
Q: If a small cell and a large cell had the same conductance density (same number of channels) which would you expect to have the highest resistance?
- The smaller cell since R is inversely proportional to area - In general very small neurons might have Input resistance = total resistance of the cell measured by one of the experiments. EX) 500-100 Mega Ohms Large neurons Ex) 5-20 Mega ohms Muscle fibers Ex) 200 Kohms
Q: What is the difference between resting membrane potential (Vm) and equilibrium potential (Eion)?
- Vm is the resting potential for the membrane - Takes into account all of the ions involved, as well as their relative permeabilities (since there is some leakage of ions, even when the membrane isn't depolarizing). - E(ion) is the equilibrium potential - it refers to a single ion, and it's the potential at which electrical and diffusional forces cancel each other out. - It's the voltage at which there will be no more net flow for a particular ion, when the membrane is permeable to that ion.
Ex) Analogy of an electrical circuit to a water pumpt
- Water flowing out of a tank from a pump. It pump forces water out in one direction than it comes back to the pump (circular). - we can measure voltage/potential difference between the two (where it pumps and where it comes back) - current ~ how much water is flowing - resistor ~ would be making a pipe smaller, harder for current to flow - capacitor ~ dam; as current flows we build up potential energy filled with water into another tank at a lower height. Each molecule of water is analogous to a charge particle. The potential difference is the difference in water pressure between your input and output (or the height of the water column). And the current analog is the flow of water out of the tank. This also makes it easier to visualize other analogs like resistance and series and parallel connections.
Resting potential Cell Diagram
- We all started in the sea! - High K+ ions inside; there the membrane is more permeable to K; it readily crosses/diffuses the membrane more than Na+ or Cl-) along its concentration gradient - there is an efflux of K+ - this results of an electrical potential difference - outside getting more positive and the inside getting more negative (due to the absence of K+) ** overall concentration gradient favors K+ OUT but membrane potential (which gets created by K+ absence) drives K+ to get back in
current clamp
- We change the current and see what happens to the voltage - x-axis = current - y-axis = voltage - slope = resistance y = mx+b V = IR + E
***Q: GRAPH In this R-C circuit: Ic = Cm dv/dt, therefore when dv/dt is 0, there is no capacitve current and all the positive current is going through the resistor
- What we see early in the pulse is a lot of the current is capacitive current - charging the capacitor, later in the current it goes to 0. - Early in the puslse, the resistive current is a small amount and then it builds up until we reach a steady state. - Voltage rises exponentially, some of it charging plamam membrane - Other is going through the ion channels - Less capacitor more to ion channels (resistor) - Voltages reach steady state (V infinity) - This is the condition we want if we want to measure the resistance.
insulator
- a type of resistor - a resistor with infinite resistance; does not allow current to go through - i.e. plasma membrane is not perfect insulator since ions can leak through channels
Conductance (g)
- any object which electrical charges flow is called a conductor (ion channels) - unit of electrical conductance = siemens (S) - Ohm's Law: - Current (A) = Potential difference (V) x Conductance (S) I = v•g
Q: Why was the discovery of the voltage clamp so important?
- by holding the membrane potential at a constant value, eliminated the capacitative current - (current that charges the membrane in response to voltage across the membrnae) - It charges the membrane capacitance really quickly.
R-C circuit
- circuit that has both resistors and capacitors - the current that flows through resistor and capacitor changes over time after the switch is turned on - it is important to understand how RC circuits function because they behave in the same way in which the membrane potential changes in response to sudden changes in current and the way membrane current changes in voltage changes - much of what we learn about neurons is through the use of voltage or current clamp, so we have to be able how either voltage or current changes in response to the other - also these properties are very critical in understanding how neurons integrate inputs and how effort is needed to change the membrane potential
Hodgkin and Huxley determined that ________________ of ions is voltage-sensitive
- conductance - Varying the potential across a membrane makes it possible to deduce the equilibrium potential for the ionic fluxes through the membrane, and thus to identify the ions that are flowing
Current (I)
- defined as the net movement of charge per time (rate) - in neurons the current is carried by both + and - ions - units = ampere (A) = 1C/s - represented as arrows Ohm's Law: - Current (A) = Potential difference (V) x Conductance (S) I = v•g
∆V max
- dependent I and R - R is solely dependent on number and type of channels - to change a membrane's charge you can change two main variable's, the ∆V in response to some current pulse I ir you can change tao, thus how long it takes to reach ∆Vmax or return to resting
Conductor/conductivity (σ)
- each type of material has an intrinisc conducitivity (σ) which is determined by molecular structure - metal - highest conductivity - aq. sln - high conductivity - lipids - low conductivity; poor conductors - symbol for a conductor is a squiggly line in circuits - infinit econductivity is a straight line g = (σ) x area/length Length is defined as the direction which one measures conductance. Conductance is measured along the cytoplasmic core of an axon.
Membrane potential (Vm)
- electrical potential difference/voltage difference between the inside and outside the cell (Vm = Vin - Vout) - measured by glass electrodes via intracellular recording - relative to a reference point. For a cell's membrane potential, the reference point is the outside of the cell
time constant (τ)
- has to do with the R-C circuit - the product of resistance and capacitance unit of time - defines how quickly capacitors (plasma membrane) charge or discharge overtime in response to external signals, such as a sudden current of ion flow (as would result from the opening of ions channels - the larger the time constant, the longer it takes to charge a capacitor and the more electrical signal is spread over time - τ is solely dpepdent on R and C • C is solely dependent on surface area • R is dependent on surface area, since number of channels usually increase with surface area (though not always)
Goldman-Hodgkin Katz Eqaution
- in reality most neurons are a bit less negative than the K+ equilibrium potential since the membrane is permeable to other ions, so we use the GHK equation - substitute terms from each of the individual ion current equations Vm = Ik/gk + Ek Vm = Icl/gcl + Ecl Vm = Ina/gna + Ena Vm = InCa/gCa + Eca Vm (gk+gcl+gna+gCa) = Ekgk + Eclgcl + EnagNa + Eca + Ik + Icl + Na + Ica At rest, the net current that flows through themembrane should be 0: Ik + I cl + Ina + I - Whats going to happen to the membrane potential every time we open/close a set of channels - At every instant in time we can reason what will happen to the membrane potential what will happen to ion channels just by looking at this equation
capacitor
- insulator which accumulates charge of either face - consists of two parallel conductors separated by a layer in between - charge storing device; does not allow current to pass through the insulating layer - i.e. lipid bilayer of plasma membrane 2-13B: when switch is turned on, the current flows from battery to capacitor until the capacitor is charged to the same voltage as the battery. + charge accumulates in one conductor, - in the other
electrical circuit
- interconnection of electrical elements that contain at least one closed circuit path - simplest electrical circuit consists of a battery and resistor - across any wire (line) current can flow freely, potential is the same, voltage is the same (no voltage drop) - charge flowing in one element must equal charge flowing out
parallel R-C circuit is more widely used in neurobiology
- ion channels function as resistors - lipid bilyar together with the intra and extra cellular enviroment act as capacitors, storing electrical charge in the form of ions accumulating near the surface of the membrane
pump
- maintain resting potential by maintaining the assymetric distribution of charges - use energy to concentrate or change the distribution of ions - so we end up with a different distribution of concentrion on the outside than the end EX) Na+ K+ ATPase pump = Takes 3+ Na out for 2 K+ in. There are also pumps that move calcium into intracellular space so that it is sequestered
battery (E)
- maintains a constant voltage/electrical potential difference across two terminals - provides energy - electromototive force E = battery; maintains the potential difference R (Squiggly line) = Resistance V = Voltage For figures A: Current (I, arrow) = flows from positive terminal to the negative terminal Middle two resistors (with resistance R1 and R2) are connected in a series. The current that flows in them is the same. The sum of the voltages across each resistor (V1 + V2) equals the voltage across the battery. Right, two resistors are connected in parallel. The voltage across each is the same across the battery. The currentl equals the sum of the currents passing through it. B E = battery C = capicitor S = switch, a transient current (dashed arrows) charges the capicitor until it equals the voltage across the battery
K+ Cl- cotransporter
- maintains the Cl- gradient
voltage clamp
- meas allows the membrane potential (voltage) to be changed while ionic currents are being measured - conductance changes as a function of membrane potential/voltage - start at a baseline current, its already depolarized and steady state. - Steady state is having build enough sustained current along the membrane to bring it to a certain voltage and leave it there. Vm is held constant. - x-axis = voltage - y-axis = current (depends on X) - slope = conductance EX) -60, command to -60, nothing EX) -70, command to -60 we will pass current into the cell, to bring the cell up to the command voltage - units: nanoamps/mV - It was a straightforward matter for Hodgkin and Huxley to determine ionic permeability by examining how the properties of the early inward and late outward currents changed as the membrane potential was varied (Figure 3.2). As already noted, no appreciable ionic currents flow at membrane potentials more negative than the resting potential.
Potential difference (V or M)
- measure of work that must be done to move a unit of positive charge (one coulumb) from one point to the other - potential diff exists within a system whever positive and negative charges are seperated (via battery, ion channels, or pumps) - Electrical charges exert forces on each other, like charges repel, opp charges attract - force decreases as the distance between the two decreases - work is done when the two charges are brought together - 1 Volt = Energy required to move one Coulmb a distance of one meter against a force of one newton
Resting Membrane potential (Vr)
- membrane potential for a neuron at "rest" - ranges usually between -50 to -80 mV depending on cell type - thus, electrically polarized - results from: 1. Asymmetric distribution of charges/ions - we are began in the sea - LOT of K+ in the cell but little K+ out - LOT of Na+Cl- out but little Na+Cl-in - Ca2+ out but very little Ca2+ in *mainted by active PUMPS like Na+ K+ ATPase (3Na+ out for 2K+ in) 2. Ion channels specificity/permeability • passive flow individual ions species through several classes of specific resting channels • some ion channels are highly selective for one type of ion. Sodium channels allow only Na+ to pass through and not K+, not Ca2+ not Cl-) • In neurons, the resting membrane potential depends mainly on movement of K+ in potassium channels
inward (negative) current
- positive ions flow INTO cell; negative ions flowing OUT - gaining positive charge in the membrane - plotted going DOWN i < 0 EX) Na+ negative current during depolarization entering the cell would be considered an inward current
Ion channels
- proteins that open/close and allow charge to cross the membrane. - We can see changes in membrane potential or voltage changes depending on which ions pass (Na+, K+, Cl-, Ca2+)
Equilibrium Potential (Eion)
- refers to a single ion, and it's the potential at which electrical and diffusional forces cancel each other out. - It's the voltage at which there will be no more net flow for a particular ion, when the membrane is permeable to that ion. - Vm is the resting potential for the membrane - Takes into account all of the ions involved, as well as their relative permeabilities (since there is some leakage of ions, even when the membrane isn't depolarizing). - no net current flow, despite the fact that channels are open - it doesn't mean no ions are flowing just that there is no NET current flow - if the cell goes higher or lower than the equilibrium potential, it becomes dependent on charge - follows the Nerst Equation (just for one ion) - when there are multiple ions it follows the Goldman-Hodgkin-Katz equation E Na+ = +50 mV E Cl = -60 mV E Ca2+ = 150 mV
resistor
- resists the flow of current (of electrons, ions), like narrowing of a pipe - implements electrical resistance (opposes the passage of the electrical current) - produces a voltage across two terminals when current flows through it
resistor what makes a good resistor?
- restricts the flow of current in a a circuit - proportional to length. (i.e. Longer then higher R) - inversely proportional to area (i.e. Wider then lower R) - use ohm's law to figure out how much voltage goes through resistor I = V/R
Capacitor
- stores charge in a circuit - two plates seperated by an insulating later; fundamental property is the ability to separate charges (i.e. membrane) - we measure charge by Q = C * V
Negative Feedback
- the output value (i.e. Vm in voltage clamp) is fed back as an input to a system and compared to a reference signal (the command signal). - System that is designed to maintain a stable output (regardless of pertubation whether the pertubation is in positive or negative direction) EX) Sensor connected to amplifier and effector. Thermometer measures the temperature of the room is going to a device that is comparing the temperature that the room is at with a desired temperature. If there is a difference. The amplifier is supposed to keep A-B to 0. The effector changes - All loops have internal sensors and internal physiological regulators *negative more common than positive feedback
threshold
- the voltage @ which we get an AP - occurs after we start opening Na+ channels - depolarization exceeds threshold; magnitude is no longer proportional to injected current - the size of AP does not change when threshold is reached sub-threshold stimulus - cannot generate AP supra threshold stimulus - stimulus that can cause neuron to generate AP
Na+ K+ ATPase pump
- uses energy from ATP hydrolysis to pump Na+ outward and K+ inward against therir electrochemical gradients - maintains the assymetric distribution of charges in the resting potential as well - Takes 3+ Na out for 2 K+ in.
resistance (R)
- voltage across the resistor - as electrical wires that connect the battery are assumed to have zero resistance the voltage across the resistance is the same as the voltage across the battery - units are ohms (Ω) - opposite of conductance 1Ω = 1/1S - dependent on three things: 1. Material 2. Length (proportional) 3. Area (inversely proportional)
When a channel is open, we characterize its ability to transfer charge by _____________.
-Conductance (g,S) - g is its symbol in the equation - S or Siemens are the units - Things that have high conductance - carry charge really well. Thing that have low - carry charge badly R = I/g R=Resistance I = Current g= conductance
Outward (positive) current
-positive ions going OUT of the cell; negative ions going IN - losing positive charge (+) - plotted going UP i > 0 EX) K+ exiting; EX) Cl- entering
Q: Relating circuits to cell biology
1. Apply a current pulse 2. Builds up across membrane (capacitor) 3. Voltage gets so depolarized that as some point ion channels (resistors) open 4. Discharging of capacitor to charging of the resistor. 5. As charge builds up to the maximum in the resistor, reaches equilibrium, ion channels (resistors) start to close. 6. Charging the capacitor discharging the resistor.
Q: Resting potentials exist because of which two things?
1. Assymetric distribution of charges (due to pumps) 2. ION CHANNEL specificity (Na+ exclusive)
What are two driving forces that drive them across a membrane?
1. Chemical Driving force - a a function of the concentration gradient 2. electrical driving force - function of the electrical potential difference
Q: How does the time constant change in these circumstances 1. If you INCREASE surface area WITHOUT increasing the number of channels? 2. If you increase the surface area, but also increase the number of channels proportionally 3. Increase the number of channels
1. Increases; since C increases and R stays the same 2. Unchanged 3. Decreases R so that ∆V max will decrease, meaning that it owuld take more ccurrent to equilivanetly change the membrane potential
2.5: Neurons are electrically polarized because of which three things?
1. Ion concentrations between the two compartments sep by membrne; intracellular and extracell environment 2. Permeability of the plasma membrane to each of the 3 major ions is diff - determined by # of open ion channels that conduct specific ions - [Na+] and [Cl-] are MUCH higher on the outside - [K+] much higher on the inside - Thus, since K+ ions are present at a much higher concentration; the membrane is more permeable to K; it readily crosses/diffuses the membrane more than Na+ or Cl-) - ionic concentrations are maintained by the Na+ K+ ATPase
Q: If you wanna know what R or G is, how do you do it? And what are the experiments you would do?
1. Perturb V and measure I (Voltage clamp) 2. Perturb I and measure V (current clamp) - In both cases we are trying to measure some feature of R or some feature of G. Some things can only be measured in voltage clamp.
Ion channels are SELECTIVE because of _______ and _____
1. Specific chemical interactions 2. Molecular sieving based on pore diameter
Q: What are three important properties of ion channels?
1. Specific to ions 2. Open/Close to either electrical (voltage-gated) or chemical (ligand-gated) signals 3. They conduct ions across the membrane
Q: Many ion channels open and close in respond to a specific event. What events/stimuli regulate the opening and closing of ion channels?
1. Voltage-dependent = regulated by changes in membrane potential 2. Ligand-gated = changes due to ligand/chemical binding to receptor 3. Mechanically gated = regulated by pressure or stretch *These are usually closed when the cell is at rest* However some channels are normally open in the cell at rest. The ion flux to these "resting"/leaking channels contributes significantly to the resting potential.
Q: 1. A small neuron has _______ R, _______ C 2. The same neuron with a large density of ion channels 3. If neurons are the same size, but another has 3X channels open
1. large R; small C 2. small R, large C; time constant might be the same because both scale with surface area 3. the one with more channels will have a lower time constant
Resting Potential Diagram
A. Micro electrode - fine tip filled with K+ Cl- so that it makes electrical contact with the cell. The other end connects to the amplifier B. Amplifier - connects to the microelectrode and ground. Measures voltage (mV)/membrane potential difference between difference between ground and the tip of the electrode C. Ground wire/reference electrode - connects from ground to the water bath • Prior to insertion in the cell: V = 0 mV • After insertion drops to V = -75 mV the resting potential of the model neuron, but it varies anywhere from -50 to -80 mV
Q: What happens to voltage in these scenarios in response to an input current pulse A. A circuit with just a resistor B. A circuit with just a capacitor C. An RC circuit
A. Voltage across resistor changes instantaneously B. Voltage across the capicitor increases linearly as the capacitor charges C. The voltage will decrease exponentially The rate at which it charges and discharges is determined by τ = RC. The larger τ the longer both processes take
Q: K+ concentration cell. A. We have a membrane down the middle of a K+ concentration cell. - When K+ channels are closed initially: Side A = 1L; KCl; 1M Side B = 1L; KCl; 0.1M - Which side will K+ flow? When we open the channels what will the equilibrium potential be? B. What if we make side A -40 mV (less negative, depolarized)? C. What happens if we make side B -80 (more negative, hyperpolarized)? D. Make side A -40 K (more positive?)
Answer for A: • K+ will flow from high to low concentration so from A-->B • According to the simplified Nerst equation Ek = -58 log [K+]a/[K+]b, side A will be -58 mV RELATIVE to side B Answer for B: • Then more K+ Ions will flow from A --> B and vice versa Answer C: B--->A Answer D A---> B
Q: Plotting the outward current
At -6
Q: Plotting the PEAK INWARD CURRENT /Na+ Channels from experiment @.5ms
At -60, 0. (No NET current) At -40, small inward. At -20, large inward. At 0, very large inward At +20 smaller inward At +50 no net current but channels open At +70 close As we start getting closer to Ena, the driving force it decreases. At 0, if all the sodium channels that are open, open. At +20 if those sodium channels are still open, there will be less sodium current. Conductance will be the same, but the current will be different Current = g * (Driving force)
Q: Capacitor vs. Battery
Capacitor - build up and store charge - plasma membrnae Battery - build up and start moving it
Q: How do they Na+/K+ open/close with a function of voltage and time?
Change in the membrane potential in the cell causes the Na+ channels to open or close.
Neurons are named according to their _________.
Features 1. Shape 2. Size 3. Protein receptor 4. Who they make synapses 5. Neurotransmitter they contain **6. Electrophysiological characteristics/Intrinsic excitability
Nerst Equation
If we say 20°C at r.t. Then the equation would be The only thing that is in the Nerst equation is the concentration of the ions on two sides of the membrane Ek = -58/z log ([K+]in/[K+]out) Z = charge of ion
Q: Why are ion pumps important?
It is essential to maintain the concentration gradients to keep electrical forces. K continues to leak out and Na in, until conc.s across membrane are equal. The membrane compensates by pumping these ions against their conc. gradient. Requires ATP. Three Na ions bind to protein on the inside of the membrane, and when ATP binds, the protein changes conformation to release Na on the outside. K binds and that cause the protein to change back. This causes a positive current out of the cell. Ca2+ is used differently, generally herded elsewhere. Ca has low intracellular conc.
In neurons, the resting membrane potential depends mainly on movement of ____ through ____ leak channels
K+
Amplifier
Measures voltage (mV)/membrane potential difference between difference between ground and the tip of the electrode
Depolarization is a __________ inward current
NEGATIVE
Q: What determines intrinsic excitability?
Number and distribution of ion channels
Q: How do we find the total number of ions channels in two cells of different sizes?
Since the ion channels are PARALLEL in the membrane - Gt = gK + gna + gcl + gca + ...
***Q: Tao (T) = R x C Answer the following question. What is T equal to the product of the resistor and the capcitor? To understand this, we have to figure out how charge is coming on and off the cirucit. Why T=RC? Why does Tao have units of a time and how does that arise as a function of resistor and capcitor?
Tao is how long charge takes to move In terms capacitor - how long charge to build up Resistor - how long it takes to take to go through R*C Capcitance (Farads) * Restance (Ohms) Units involve seconds that when you multiply them they cancel out.
The brain is ALWAYS awake unless you are dead
The nervous system always has activity. If you put an electrode in anywhere in awake brain you will see activity, in a sleeping brain - activity, in an anaestasized animal - activity. It will be different, but always activity. The challenge is to understand how sensory inputs influence that activity
Plotting outward current from experiment. Plot @ 7 ms.
The outward current is now in the opposite direction, we go beyond Ena. Ek = -80 mV At -60 mV, if we had an open potassium channel, it would be small (20 mV) - We should get a small current At +60 mV, its 140 mV (very large) - we should get a BIG current - Many channels open and a big driving force As we depolarize. Different than the ones that are open @ rest. They start opening, right when we see this deflection, the channels start opening. At 0mV, we have an 80mv df. As channels open and the cell depolarizes, we will have more of a df, the current will get bigger and bigger
Q: Diagram of Action Potential in current clamp We start @ -60mV and depolarize the cell a bit Then going have a larger depolariizing current Larger Larger Then an AP Label threshold, ENa, overshoot, and undershoot
The voltage at which we get an AP is called the threshold. - Occurs start opening enough Na+ channels We often called the peak of the AP the overshoot - The peak is around the Ena - sodium's equilibrium potential - Sodium channels open, conductance gets high, so GDK membrane potential gets near the equilibrium potential of sodium. - Only holds if number of sodium channels is very large We call the refractory period dip part the undershoot - The undershoot is Ek - around potassium's equilibrium potential
Ohm's Law
V=Voltage I=Current R= Resistance
positive feedback
When there is a diff between set point and measured point, at some time there will be a threshold, which will give us a positive result, which makes the system increase increase and increase or decrease decrease Ex) If the temp goes above 75, turn on the heat and make it explode Ex) Oxytocin in childbirth, Action potentials Positive feedback is rare in biology but negative feedback is common
Q: GHK Equation Theoretical Questions What is the membrane potential at all of these instances in time? a. If only k+ channels are open? b. If we have both K+ channel and Cl- channels open? c. If only K+ channels are open but we open up 100X Na+ channels? d. Then we open up 1000X more K+?
a. Vm = Ekgk/gk, gks cancel out; Vm = Ek = -80 mV b. Vm = Ekgk+Eclgl/gk+gcl; gcl=gK; 1/2 in between since conductance is equal c. Vm = Ena = +50mv d. Vm = Ek = -80 mv, goes back down; a simple aP
Q: At equilibrium potential (Eion): a. membrane potential (Vm) b. driving force = c. current flow
a. Vm=Eion b. 0; since driving force = (Vm-Eion) and Vm=Eion, there is no difference c. 0; no driving force; no NET current flow of ions even though channels are open
Intrinsic excitability
characteristic properties of a neuron; come from nature determined by the number and distribution of ion channels
in theory when a circuit has no resistance the capacitor is ________________
charged instantaneously in reality though, circuits always have resistance
resistor is the same as a ___________
conductor; - used interchangeably depending on the context - a resistor with high resistance is a poor conductor - a resistor with low resistance is a good conductor
Q: How do we prove that it is indeed sodium and not any other ion?
e best evidence that we can find is by using GHK. They did sodium replacement equations. They found that sodium concentrations changed. Na channels are opening/closing as a function of membrane potential. The function of current is independent. Current as a function of voltage.
Q: GHK Equation Theoretical Questions What is the membrane potential at all of these instances in time? For g-h: Will it depolarize or hyper-polarize the membrane? e. If we only have K+, what is the exact voltage? f. If we only have Cl- what is the exact voltage? g. If we are @ -50mV, we polarize with -60mV? h. If we are @ -70mV and open up -60mV Cl- channels? i. If we are @ -60 mV and open up 3X more -60mV Cl- channels
e. -80 mV f. -60 mV g. Hyperpolarize h. Depolarize i. Stay the same *Here we see that opening up the same Cl- channels will depolarize or hypolarize the cell depending on the starting point.
you may always figure out the direction of ion flow
i(ion) = g(ion)• (Vm-eion) Current of ion = potassium conductance X (Membrane potential - equilibrium potential) At equilibrium current is 0
capicitor: plasma membrane conductor/resistor: ______________; current flow: ___________
ion channel ions
Capcitance (C)
measured in farads (F); the greater density, greater force Q ( charge, coulumbs) = C (farads) x V (volts)
Remember to convert units!
nA => A mV => V MΩ => Ω
Ligand-gated ion channel
open/close depends on the binding of ligand to receptor
Voltage dependent/Voltage-gated ion channel
opening and closing depends on the membrane potential with the voltage across the membrane
Ligand
small molecule which binds to protein receptor (receptor of ion channel)
More channels make Rm ______-
smaller
Q: What is the recording electrode going to read when we move its tip inside of a cell?
• If we move the tip of the electrode to the tip of the cell, we see a resting potential which might be -50mv. • In cell 1 it might be -50mv • In cell 2 it might be -80mv • In cell 3 I might be -65 mv.
Q: What is recording electrode going to read when its tip is in the saline bath (which is filled with Na+ Cl- ions)?
• Since it is in the bath and NOT in the cell, it is going to read 0 mV • Amplifier measures ground - ground = 0
capicitance (C)
• ability of a capicitor to store charge • C = Q/V • units = farads (F) • addition in a series: 1/C1 + 1/C2 = 1/C • addition in parallel: C1 + C2 = C
