151/251 MCDB - HOMEWORK #2 Due Friday 10/16/09 in Lecture 1) A cell containing only Na+ channels and K+ channels has the following intracellular and extracellular ionic composition:
Name____________________ Section_____________ Ion: K+ Na+ ClExtracellular Concentration: 10 mM 130 mM 150 mM Intracellular Concentration: 120 mM 20 mM 120 mM
a) What are the equilibrium potentials for K+, Na+, and Cl-? (3 pts)
Use the Nernst equation: Eequil. = 58 log10 [ion]out [ion]in Z ENa = 58 log (130/20) = +47 mV EK = 58 log (10/120) = -63 mV ECl = (58/-1) log (150/120) = -6 mV
b) At what potential will the Na current through open Na channels be zero? (1 pt)
When voltage = equilibrium potential for sodium = +47 mV (it would only be 0mV if the extracellular and intracellular concentrations were equal)
c) You perform voltage clamp experiments on this cell by holding the membrane potential at -90 mV, then the currents from the whole cell are recorded for voltage pulses to -20 mV, +20 mV and +60 mV (voltage pulses are indicated below). Draw the currents that you would expect from this cell. Label your currents corresponding to each of the voltage pulses (-20, +20 and +60 mV). (6 pts)
How do you do problem 1C?
First, ask which channels are present in a cell. You are told that only Na and K channels are in this cell. No blockers have been added, so you should expect both voltage-activated Na currents and voltage-activated K currents. Remember that Na currents are fast. They activate fast, then inactivate. K currents are slower: the K currents activate, but do no inactivate. You know that the Na and K currents each will be described by the equation: I = G (V-Eequil) It is easiest to separately figure out the Na and K currents, then to draw them summed together. You will need to calculate the equilibrium potential for each ion (Remember that you already did this in part 1a above). Eequil = RT log10 [ion]out ZF [ion]in
ENa = 58 log (130/20) = +47 mV EK = 58 log (10/120) = -63 mV Then you need to know the driving force (V-Eequil) to know whether the currents will be inward or outward. You will also need to estimate G, which is proportional to the probability that the channel is open. In other words, is the channel open or closed at the test voltage. It is easiest to fill in a table like the one shown below: Test voltage Na currents K currents
Driving force = (V ENa)
Channel open? Yes, fast Yes, fast Yes, fast
Driving force = (V EK)
Channel open? Yes, slow Yes, slow Yes, slow
+ 60 mV + 20 mV - 20 mV
+60 (47) = +13, outward +20 (47) = -27, inward -20 (47) = -67, inward
+60-(-63)=+123, outward +20-(-63)=+83, outward -20-(-63)= +43, outward
So, for the -20 mV test voltage, you will expect a fast inward Na current that activates, then inactivates, followed by an outward K current. For the +20 mV test voltage, you expect a fast inward Na current, followed by a slow outward K current. The outward K current amplitude will be bigger than the K current from the -20 mV test voltage because the driving force is larger. For the + 60 mV test voltage, you expect a fast outward Na current followed by a slow outward K current. The K current amplitude will be bigger than for the K current from the +20 mV test voltage because the driving force is larger.
d) The cell above is now treated with tetraethylammonium, and the experiment is repeated. For this TEAtreated cell, currents are measured for voltage pulses to -20, +20 and +60 mV. (1 pt each) i) What type of channel will carry current in this experiment? ii) Which test potential(s), if any, will give outward currents? ____ Na channel_________ _______+60 mV___________
+
3) The neuron of a flamencajaminfopper, which contains only voltage-activated I- channels (that slowly open upon depolarization), voltage-activated Cs+ (that channels rapidly open upon depolarization), and background I- channels, is studied electrophysiologically at room temperature. The neuron has the following intracellular and extracellular ionic composition: Ion: ICs+ Rb+ Extracellular concentratrion: 250 mM 10000 mM 20 mM Intracellular concentration: 10 mM 100 mM 200 mM
You place an electrode in the cell. What resting potential do you expect? What action potential peak do you expect? (2 pts)
Use the Nernst equation: Eequil. = 58 log10 [ion]out [ion]in Z EI- = (58/-1)log 250/10 = -81 mV ECs+ = 58 log 10000/100 = 116 mV ERb+ = 58 log 20/200 = -58 mV The background (resting) channels are I- channels (see description above) so you would expect the resting membrane potential to be -81 mV (based on EI-). The channels that open rapidly upon depolarization are Cs+ channels, so the action potential peak would be close to +116 mV (based on ECs+)
4) Starting with the initiation of a signal on the postsynaptic membrane, name and briefly describe the four stages of neuronal electrical signaling that result in transmitting the signal to the next neuron in the neuronal network. (2 pts)
1) Initiation of signal--receptor potential from a sensory cells or synaptic input from a presynaptic neuron; the signal is graded and local; EPSPs and IPSPs 2) Signal integration--the passive signals are carried through the dendrites and cell body, decreasing in amplitude at greater distances, then sum at the axon hillock; temporal and spatial summation 3) Action Potential--Active Signal is generated at axon hillock if the summed stimulus is more positive than threshold; action potential travels long distance due to saltatory conduction; maintains amplitude due to regeneration at the node of Ranvier. 4) Synaptic Signaling--At the synaptic terminal, calcium influx through voltage-gated Ca channels, causes release of neurotransmitter; neurotransmitter traverses the synaptic cleft and stimulates or inhibits the next neuron
5) In 1906, Camillo Golgi and Santiago Ramn y Cajal shared the Noble Prize for their pioneering work in neuroscience. Describe each scientist's theory on the organization of the nervous system. Who was eventually proven correct and what was the definitive piece of evidence in support of their theory? (3 pts)
Cajal Cell Theory / Neuron Doctrine The nervous system, like every other tissue in the body, is made up of discrete cellular units. Golgi Reticular Theory The nervous system is made up of a meshwork of cells that are connected via their cytoplasm, acting together as a single unit. Cajal was eventually proven correct, the definitive piece of evidence was the ability to see the synapse using the electron microscope, proving that individual neurons were separated from each other.
6) In their 2008 opinion piece, Jeff Lichtman and Joshua Sanes champion for developing a field of neuroscience known as connectomics. In what organism would the mapping of a connectome be considered complete? Identify and explain one major challenge to establishing the connectome of complex nervous systems. (3 pts)
The first (and thus far only) organism to have its entire connectome mapped was Caenorhabditis elegans, a nematode, by Sydney Brenner and colleagues. Lichtman and Sanes list three major challenges to mapping the connectome of complex nervous systems: 1) Dimensionality the connectome must be done in three dimensions unlike the single dimension of the genome. 2) Variablity while major features of the nervous system are found in every animal of the same species, the fine details of many neurons, and therefore their connections, can vary tremendously between different individuals, even genetically identical ones. 3) Stability The nervous system, unlike the genome, is changing throughout an individual's life.