HW1.pdf - Biological Neural Computation Homework problem set1 Spring 2013 General Guidelines The homework solutions should include figures that clearly

HW1.pdf - Biological Neural Computation Homework problem...

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1 Biological Neural Computation Homework problem set1 Spring 2013 General Guidelines: The homework solutions should include figures that clearly capture the result. The figures have to be labeled, well explained and the results must be clearly discussed. The first sheet of the homework must certify that this is completely your work and list the students/people you have consulted or received help from (with your signature and date of submission). All online references used must be listed in the reference section at the end of the homework. Good luck, Barani Raman
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2 Problem1 . (a) Determine the reversal potential for the following ions at 37 degree Celcius. Ions Extracellular Concentration (in mM) Intracellular Concentration (in mM) K + 5 100 Na + 150 15 Ca 2+ 2 0.0002 Cl - 150 13 [5 pts] (b) If the membrane is permeable only to K + ions, then the resting potential would be equal to the reversal potential of the K + ions. However, this is not the case. Given that the resting potential of a hypothetical neuron with only Na + and K + ions to be -65mV, calculate the relative permeability of K + ions with respect to Na + ions at 37 degree Celsius? [5 pts]
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3 Problem 2. (a) Implement the HH model in Matlab. The equations describing the model are: Note: V in these equations represents displacement voltage with respect to the resting membrane potential and not the actual membrane potential. Hence you will have to substitute -65-V in your implementation. Implement using Euler’s integration technique. Use the following values for the constants: C = 1 microF/cm 2 , Leak reversal potential = -61 mV, K reversal potential = -77mV, Na reversal potential = 55 mv, Leakage conductance (g L = 0.3 mS/cm 2 ), K conductance (gK = 36 mS/cm 2 , N conductance (gNa) = 120 mS/cm 2 . Initial conditions V = -65 mV. Plot the following figures to validate your model: (i) Evolution of the HH variables m,n,h following an action potential.
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  • Spring '14
  • Raman

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