Neurobiology Problem Set 1: Action Potentials, Equilibrium, and Glial Cells - Prof. Nichol, Assignments of Biology

Download Neurobiology Problem Set 1: Action Potentials, Equilibrium, and Glial Cells - Prof. Nichol and more Assignments Biology in PDF only on Docsity! Problem Set 1 Cellular Neurobiology Fall 2008 1. Action potentials: a). List 5 general characteristics of action potentials. 1). The AP has a threshold (the unit is in voltage). So when the electric potential reaches threshold, the AP fires. 2). The AP is all-or-none. If potential does not reach threshold, no AP. If it reaches threshold, AP occurs or fires. 3). Information is carried in a digital code, and the strength of the stimulus is coded in the form of AP frequency. 4). The rate of change of membrane potential depends on the stimulus strength (or the speed of depolarization). The larger the stimulus the faster the rate of change in membrane potential. 5). Refractory period: time during which the cell is not excitable or difficult to excite. Absolute refractory period is 1-2 ms so during this period the neuron cannot be excited no matter what happens. The relative refractory period is 3-5 ms; during this period the neuron can be excited but it’s hard to do so. b). In section, your TA thinks that stimulating a neuron with a large stimulus will cause an action potential with a large amplitude, and stimululation with a small stimulus will generate an action potential with a small amplitude. Explain why this is not correct. The amplitude of an action potential is independent of the amount of current which produced it. In other words, a larger stimulus does not generate larger action potentials. Therefore action potentials are said to be all-or-none, since they either occur fully or they do not occur at all. Instead, the frequency of action potentials is what encodes the intensity of a stimulus. 2. Briefly explain the following terms and indicate what they are used for: a). RNA probe: b). Reduced silver stain c). Antibodies d). Voltage-sensitive dye e). Intracellular recording f). Colchicine a). RNA probes target RNA by recognizing and binding to complementary RNA sequence. These probes can be used to visualize the location of RNA. b). Reduced silver stain (Golgi stain) stains the entirety of a neuron and allows visualization of its morphology. c). Antibodies bind to specific proteins to allow visualization d). Voltage-sensitive dyes will change emission wavelength when there’s a voltage change. It can be used to study large changes in membrane potential, i.e. action potentials. e). Intracellular recording measures the transmembrane potential of a neuron. It can be used to study resting potentials, action potentials, synaptic potentials and sensory (generator) potentials.. f). Colchicine breaks down microtubules. One can use it to distinguishe the function of microtubules from the function of neurofilaments or microfilaments. 3. Glial cells: a). Name the three types of glial cells in the central nervous system (CNS); name one type of glial cell in the peripheral nervous system (PNS). The three types of cells in CNS are oligodendroglia, astrocytes, and microglia. Schwann cells are found in PNS. b). Glial cells have rapid and slow functions. Give three examples of each. Rapid functions: 1). They make up myelin which speeds up the conduction of action potentials. 2). Some glial cells take up K+ ions to prevent unwanted signaling 3). Glial cells can release neurotransmitters that can affect neurons and other glia. 4). Glial cells can take up neurotransmitters. Slow functions: 1). Astrocytes form the bloodbrain barrier around capillaries. 2). Formation of neuronal connections during development. 3). Specificity of regeneration. 4). Scavenging function of microglia 4. Equilibrium potentials and resting potentials: a). A giant axon of a squid is incubated at 22o C under the following conditions: Ion: Inside Concentration (mM) Extracellular Concentration (mM) Na+ 40 400 K+ 500 5 Cl‾ 50 500 The resting membrane potential is -100 mV. Calculate EK , ENa and ECl . (Show your calculations). Use the Nernst equation: ⎟⎟ ⎠ ⎞ ⎜⎟ ⎝ ⎛ = in out ion ion ion zF RT E ][ ][ ln . ENa = 58 log (400mM/40mM) = +58 mV EK = 58 log (5mM/500mM) = -116 mV ECl = -58 log (500mM/50mM) = -58 mV b). Which is the most permeable ion at rest? (Explain your answer). K+, because resting membrane potential is closest to EK, meaning the K+ gradient has the largest influence on the membrane potential since it is the most permeable among the three types of ions. Thus 5.3 x 107 monovalent ions have to move to establish a potential of 70 mV. Total volume = 4πaa3/3 = 4.2 X 10–9 cm3 Total number of ions inside the cell = 4.2 x 10–9 ml (0.5 moles/1000 ml) (6 x 1023 ions/mole) = 1.3 x 1011 ions Therefore the fraction of ions that have to move is 5.3 x 107/1.3 x 1011 x 100% = 0.0004% b. What is the significance of the answer from (a)? Movement of a very small amount fraction of the available ions is sufficient to establish a physiological membrane potential. 7. Suppose that a cell membrane is permeable to K+ but not to Cl– or large organic ions R+. The concentrations of the ions for the outside and the inside of the cell are: Outside R+ 150 mM K+ 193 mM Cl- 343 mM Inside R+ 150 mM K+ 257 mM Cl- 257 mM a. What is the Vm of the cell? Vm = 58 log (193/257) = -7.2 mV b. Why doesn’t K+ continue to diffuse down its concentration gradient? It DOES diffuse down its concentration gradient, but as fast as it does so it is driven back up its concentration gradient by the membrane potential. An equilibrium has been established. 8. For what purpose is the GHK equation needed? (What was the motivation for GHK’s work?) Support your reasoning with a graph. It is needed because as the graph shows, the linear relationship between membrane potential and log of outside K+ concentration fails to match the data. 9. Last year, an astute student asked in class, “Why have myelination?” Demyelination of axons occurs in a serious disease called Multiple Sclerosis (MS), in which conduction of action potentials is blocked. You have three axons with the following parameters: Axon Myelination (multiply rm by 1000) Diameter (a) 1 Yes 5 µm 2 No 5 µm 3 No 10 µm Calculate the relative membrane resistance, internal resistance, time constant, and length constant. Then explain the significance of the values you’ve calculated using the cable equation. Assume all constants are the same. rm = Rm/(2πaa) 1: 1000 Rm/10πa = 100 Rm/πa 2: Rm/10πa 3: Rm/20πa Myelination improves membrane resistance and increasing axon diameter decreases it ri = Ri/(πaa2) 1: Ri/(25 πa) 2: Ri/(25 πa) 3: Ri/(100 πa) Increasing axon diameter decreases internal resistance Time constant = rmcm Cm = cm/2πaa 1: cm = Cm x 2πaa = 10πa µF/cm2 rmcm = 1000 µF/cm2 2: cm = Cm x 2πaa = 10πa µF/cm2 rmcm = Rm uF/cm2 3: cm = Cm x 2πaa = 20πa µF/cm2 rmcm = Rm µF/cm2 Large time constant in presence of myelination Length constant = sqrt(rm/ri); (Assuming that the ro ≈ 0) 1:  = sqrt(4 Rm/Ri) 2:  = sqrt (Rm/ 250 Ri) 3:  = sqrt (Rm/ 2000 Ri) The length constant is large in the presence of myelination. Using the equation, € Vx =V0 e −x /λ , large  gives small –x/ and therefore 1/ex/ becomes smaller. This means that Vx will be greater for myelinated, small neurons. Demyelination is a disease in which action potential propagation is blocked. The depolarization generated by the action potential at one node of Ranvier does not produce a depolarization at an adjacent internode that is sufficient to generate an action potential there.