I need corrections to be done.On hw 1 my professor said:There are still issues with Q3 and Q4.On hw 2 my professor said:Q1c. the analytical and numerical solutions do not coincide... Q1d. There...

I need corrections to be done.
On hw 1 my professor said:



There are still issues with Q3 and Q4.

On hw 2 my professor said:









1) Equilibrium Potential Ei= (R*T)/(z*F)* ln [C]out/[C]in Temp=20 C R T z F [C]out [C]in Ek= -0.086 8.314 293 1 96500 5 150 Ena= 0.058 8.314 293 1 96500 150 15 Ecl= -0.064 8.314 293 -1 96500 125 10 Eca= 0.116 8.314 293 2 96500 2 0.0002 *Temp=25 C Ek= -0.087 8.314 298 1 96500 5 150 Ena= 0.059 8.314 298 1 96500 150 15 Ecl= -0.065 8.314 298 -1 96500 125 10 Eca= 0.118 8.314 298 2 96500 2 0.0002 At Temp=20 C Ek=--0.086 Ena=0.058 Ecl=--0.064 Eca=0.116 Temp=25 C Ek=--0.087 Ena=0.059 Ecl=--0.065 Eca=0.118 All results are in J/C which is equal to volts. This is the Equilibrium potential from 10 to 40 for each component: K, Na, Cl, Ca when temperature is increasing from 10 to 40 Celsius. In part a we saw Ek and Ecl are both negative which correlates with this graph. Eca rises the fastest, then Ena, then Ecl and lstly Ek which is what the graph shows too. 2) a and b C]out/[C]in= e^(Ei*(z*F)/(R*T) 0.093 0.097 In order to find the concentration, you must separate ln(C[out]/C[in]) and take the ln of both sides. Therefore, C]out/[C]in= e^(Ei*(z*F)/(R*T) and the concentration needed when Temperate=293.15 K is 0.093 and when Temperature=298.15 K is 0.097. As temperature increases so does concentration of Cout/Cin. 2c) Here is the concentration rate vs temperature. To maintain V=-60mV, the concentration ranges from 0.85 to 0.11 from Temperature ranging from 10C to 40C. 3) R_MOhms = 100; % megaOhms C_pF = 100; % picoFarads Iapp_nA = 0.5; % nanoAmperes V_initial = -60; % mV V_final_c = -50; % mV V_final_d = -30; % mV % Convert units R = R_MOhms * 1e6; % Convert megaOhms to ohms C = C_pF * 1e-12; % Convert picoFarads to Farads Iapp = Iapp_nA * 1e-9; % Convert nanoAmperes to Amperes % Calculate τ (tau) tau = R * C; % Calculate R * Iapp RIapp = R * Iapp; % Calculate the time for V = -50 mV t_c = tau * log((V_final_c - V_initial) / (V_initial - V_final_c)); % Calculate the time for V = -30 mV t_d = tau * log((V_final_d - V_initial) / (V_initial - V_final_d)); Answers: Tau (τ): 0.010000 seconds R * Iapp: 5.000000e-02 Amperes Time for V = -50 mV: 0.000000 seconds Time for V = -30 mV: 0.000000 seconds I checked the value of Tau and R*Iapp and since Iapp=0.25 in part a and doubled here, tau does not change and R*Iapp=2.500000e-02 Amperes. I think my results makes sense here. Biol635 / Math635 / Biol432 / Math430 Fall 2023 . Assignment 3 Answer the following questions. • Justify your answers. • Explain your results. • Provide the necessary calculations in a clear way. • Provide the necessary supporting graphs and codes. • Make sure the graphs are properly labeled and include the information (title and parameter values) nec- essary to understand your explanations. • You may write your own code or adapt the template code provided in class. Consider the following passive membrane equation τ dV dt = −(V − EL) +RIapp(t) (1) with EL = −60 mV, C = 1 µF/cm2, GL = 0.1 mS/cm2, Write a Matlab code (or use the template code) to solve eq. (1). Use V (0) = −60 mV and the following units for V , t and Iapp respectively: [V ] = mV,[t] = msec, [Iapp] = µA/cm2. 1. Build a leaky integrate-and-fire (LIF) model using Vth = −50mV , Vrst = −65mV and the parameters values for the passive membrane equation above. (a) Simulate the model for the following values of Iapp and plot the solutions. i. Iapp = 0.5 ii. Iapp = 1 iii. Iapp = 1.01 iv. Iapp = 2 1 (b) Calculate (analytically) the interspike-interval (ISI) firing rate (risi), if possible, for the values of Iapp above 2. (Graduate level) Build an integrate-and-fire model with spike rate adaptation using Vth = −50mV , Vrst = −65mV and the parameters values for the passive membrane equation above. (a) Compute the numerical solutions and plot the corresponding graphs for for Iapp = 2, Ek = −85, ∆gsra = 0.1 and i. τsra = 10msec. ii. τsra = 100msec. (b) Based on the literature, speculate on what are possible roles of spike-rate adaptation? (c) Find examples of adaptation in other biological systems. Choose (b) or (c) 2 Biol635 / Math635 / Biol432 / Math430 Fall 2023 . Assignment 2 Answer the following questions. • Justify your answers. • Explain your results. • Provide the necessary calculations in a clear way. • Provide the necessary supporting graphs and codes. • Make sure the graphs are properly labeled and include the information (title and parameter values) nec- essary to understand your explanations. • You may write your own code or adapt the template code provided in class. 1. Consider the following passive membrane equation τ dV dt = −(V − EL) +RIapp(t) (1) with EL = −60 mV, C = 1 µF/cm2, GL = 0.1 mS/cm2, Write a Matlab code (or use the template code) to solve eq. (1). Use V (0) = −60 mV and the following units for V , t and Iapp respectively: [V ] = mV,[t] = msec, [Iapp] = µA/cm2. (a) Calculate the time constant τ . (b) Consider the following two time-independent applied currents Iapp = −0.5 and Iapp = 0.5. For each these values of Iapp, compare the numerical and analytical solutions to the passive membrane equation (1) by i. Plotting superimposed graphs of these solutions ii. plotting the error (absolute value of the difference between these two solutions). 1 (c) Consider a square pulse of current Iapp(t) = I0Heav(t− ti) ∗Heav(tf − t) with I0 = 0.5, ti = 100 msec and tf = 200 msec. i. Plot both the numerical and analytical solutions to the passive membrane equation (1) ii. compare them as in (b). Run your simulation for 400 msec. (d) Consider the following current Iapp(t) = I0 sin(2π ω t/1000). with I0 = 0.5. The input frequency ω is given in Hz (number of cycles per second). i. Plot the numerical solution to the passive membrane equation (1) for ω = 1, ω = 5, ω = 10, ω = 20, and ω = 100. ii. Plot a graph relating the output frequency (y-axis) vs. the input frequency (x-axis) iii. Plot a graph relating the amplitude of the output oscillations (y-axis) vs. the input frequency (x-axis) 2. (Graduate level) Find examples in the literature of both biological neuronal systems and models that behave like low-pass filters and band-pass filters. Speculate on the differences between them. 2