Categories
Writers Solution

A modified Hodgkin-Huxley model

It is a biological modeling assignment to be written using the Xppaut software. There will need to be postscript graphs.
1) A modified Hodgkin-Huxley model
One considers a neuron model where voltage evolution is given by
C ddVt = Gl(Vl – V ) + GNam8(V )3h(ENa – V ) + GKn(EK – V ) + I
Sodium current activation is assumed to be instantaneous m
and the gating variables h and n satisfy the equations th ddht = h8(V ) – h and tn ddnt = n8(V ) – n
where th and tn are both equal to 1 ms,
h n
Other parameters are C = 0.8nF, Gl = 0.3µS, GNa = 40µS, GK = 3.5µS, Vl = – 66mV, ENa = 50mV, EK = – 90mV.
Draw the voltage response of the model to a constant injected current for several values of this current.
Draw the bifurcation parameter using the injected current as the bifurcation parameter.
Interpret the results.
2) Effect of an AHP current
One adds to the model a afterhyperpolarization (AHP) current IAHP = GAHPz(EK – V ) where GAHP = 0.3µS.
The gating variable z satisfies
tz(V ) ddzt = z8(V ) – z
where z8(V ) = 1 and tz = 0.1ms above -20 mV (spike voltage threshold) and z8(V ) = 0 and tz = 10ms below -20 mV.
Show how the discharge of the neuron is modified by this AHP current.
Show that small oscillations are observed before action potentials and characterize these oscillations. What is their typical frequency? How do they vary with the injected current? Show that these oscillations disappear if the injected current is too much increased.
Show that the firing frequency of the neuron displays a series of plateaus above the firing threshold and explain why. Explain why the firing frequency smoothly increases for higher values of the injected current.
3) Reduction to a three-dimensional model
Reduce the above four-dimensional model to a three-dimensional model in a way similar to what is done for the standard Hodgkin-Huxley model. Explain how you do that and write down the resulting equations.
What is the discharge of this three-dimensional model? How does it vary with the injected current? Does it display small oscillations between action potentials.
4) Origin of the small oscillations
Compute the bifurcation diagram of the reduced model. How does the resting state become unstable when the current is increased?
Draw the trajectory of the model in three dimensions when the injected current is just above the firing threshold. Describe this trajectory. Why does it explain the small oscillations between action potentials?
Draw the the trajectory of the model in three dimensions when the injected current is larger and one does not observe small oscillations. How does it differ for the previous case? Why are small oscillations no longer observed?
Conclude on the role of the AHP in the emergence of small oscillations between action potentials. 5) Excitability
One increases the excitability of the reduced model by adding a persistent sodium current, which does not inactivate. Its activation is instantaneous, and its activation curve is the same as the transient sodium current above but shifted downward by 5 mV.
Draw the two parameter bifurcation diagram of the model using the injected curent and the conductance GNap of the persistent sodium current as bifurcation parameters. Interpret the results. Show that the small oscillations preceding action potentials then disappear as GNap is increased

GET SOLUTION FOR THIS ASSIGNMENT, Get Impressive Scores in Your Class

CLICK HERE TO MAKE YOUR ORDER

TO BE RE-WRITTEN FROM THE SCRATCH

GET SOLUTION FOR THIS ASSIGNMENT

CLICK HERE TO MAKE YOUR ORDER

TO BE RE-WRITTEN FROM THE SCRATCH

NO PLAGIARISM

  • Original and non-plagiarized custom papers- Our writers develop their writing from scratch unless you request them to rewrite, edit or proofread your paper.
  • Timely Delivery– primewritersbay.com believes in beating the deadlines that our customers have imposed because we understand how important it is.
  • Customer satisfaction- Customer satisfaction. We have an outstanding customer care team that is always ready and willing to listen to you, collect your instructions and make sure that your custom writing needs are satisfied
  • Confidential- It’s secure to place an order at primewritersbay.com We won’t reveal your private information to anyone else.
  • Writing services provided by experts- Looking for expert essay writers, thesis and dissertation writers, personal statement writers, or writers to provide any other kind of custom writing service?
  • Enjoy Please Note-You have come to the most reliable academic writing site that will sort all assignments that that you could be having. We write essays, research papers, term papers, research proposals A modified Hodgkin-Huxley model

Get Professionally Written Papers From The Writing Experts 

Green Order Now Button PNG Image | Transparent PNG Free Download on SeekPNG