Methods of Applied Mathematics II

Consider white noise levels within some range determined by the values of the variance (D)

Compute the interspike-intervals (ISIs) and the corresponding spiking frequencies (measured in Hz).

Plot the corresponding histograms (you may use the "hist" function in matlab).

Compute the coefficient of variation of the ISIs.

Using this information explain how noise affects the dynamics of the IF model and what are the fundamental differences between the two cases considered .

Part B. The following data sets were generated using the integrate-and-fire (IF) model using the same parameter values except for Iapp that was increased from Data Set 1 to 7. (The value of the membrane capacitance is C=1). Units are as discussed in class. Use these data sets to estimate the parameter values used to generate them.

Each file has 2 columns. Column 1 is time. Column 2 is voltage. .

Data Set 1 (Iapp=0.375)

Data Set 2 (Iapp=0.4)

Data Set 3 (Iapp=0.425)

Data Set 4 (Iapp=0.45)

Data Set 5 (Iapp=0.475)

Data Set 6 (Iapp=0.5)

Data Set 7 (Iapp=0.525)    

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Project III:

The goals of this project are (i) to quantify the effects of noise on the dynamics of the Hodgkin-Huxley (HH) model, (ii) to estimate parameters using the HH model, and (iii) to compare the dynamics of the HH and IF models.

Part A. Build a stochastic HH model by adding a white noise term (zero correlation and variance D) to the deterministic HH model used in Modeling Assignment III. (See Course Material for explanations on stochastic Runge-Kutta algorithms.) Run your simulations for at least 25000 msec.

Consider to representative cases (choose the appropriate values of the applied current)

(1) Spiking activity exists in the absence of noise (i.e., spiking activity is generated by the deterministic HH model).

(2) Spiking activity is generated by the added noise (i.e., the deterministic HH model is silent).