hw02 first attempt

5 files changed, 216 insertions, 0 deletions

diff --git a/assignments/hw02/answers.txt b/assignments/hw02/answers.txt
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+
+Q1: The concentrations of ATP and Glucose never reach a stable steady-state.
+Q2: 20.98, 18.66
+Q3: no, no, yes, no
+Q4: second choice is the fastest
+Q5: first is fastest
+Q6: no, no, yes, no
+Q7: the last is the damped one (spiral)
+Q8: true, false, false, false ("When  is higher than 1 no sustained
+    oscillations will be observed.")
+Q9: false, false (decaying), true, false
+Q10: true, false, false, false
+Q11: false, false, true, false
+
+
+got 2x wrong:   Q7 (forgot to select?)
+                Q4 (typo? forgot to select?)
+
diff --git a/assignments/hw02/euler.jl b/assignments/hw02/euler.jl
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+

+# Use Euler's method to integrate simple one variable ODE

+# Use program as template for more interesting models

+

+# Note:  produces slightly different output compared with 

+# example shown in class.  Different values of b, dt, tlast

+

+using Winston

+

+a = 20

+b = 0.5

+c = 5

+ 

+dt    = 0.2

+tlast = 20

+ 

+iterations = integer(round(tlast/dt))

+xall = zeros(Float64, (iterations, 1))

+

+x = c

+for i = 1:iterations

+  xall[i] = x

+  dxdt = a - b*x

+  x = x + dxdt*dt

+end

+

+time = dt*(0:iterations-1)'

+figure

+plot(time,xall)

diff --git a/assignments/hw02/euler.m b/assignments/hw02/euler.m
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+% % Use Euler's method to integrate simple one variable ODE

+% % Use program as template for more interesting models

+

+% % Note:  produces slightly different output compared with 

+% % example shown in class.  Different values of b, dt, tlast

+

+a = 20 ;

+b = 0.5 ;

+c = 5 ;

+ 

+dt    = 0.2 ;  

+tlast = 20 ; % s

+ 

+iterations = round(tlast/dt) ; 

+xall = zeros(iterations,1) ;

+

+x = c ;

+for i = 1:iterations 

+  xall(i) = x ;

+  dxdt = a - b*x ;

+  x = x + dxdt*dt ;    

+end % of this time step

+

+time = dt*(0:iterations-1)' ;

+figure

+plot(time,xall)

diff --git a/assignments/hw02/euler_mod.jl b/assignments/hw02/euler_mod.jl
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+++ b/assignments/hw02/euler_mod.jl
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+

+using Winston

+

+function doPlot(V_in, k_l, k_p, K_m)

+    

+    dt    = 0.2

+    tlast = 1000

+    

+    iterations = integer(round(tlast/dt))

+    ATPall = zeros(Float64, (iterations, 1))

+    Gall = zeros(Float64, (iterations, 1))

+

+    ATP = 4

+    G = 3

+    for i = 1:iterations

+        ATPall[i] = ATP

+        Gall[i] = G

+

+        dATPdt = 2 * k_l * G * ATP - (k_p * ATP) / (ATP + K_m)

+        dGdt = V_in - k_l * G * ATP

+

+        ATP = ATP + dATPdt * dt

+        G = G + dGdt * dt

+    end

+

+    tall = dt*(0:iterations-1)'

+    figure()

+    hold(true)

+    plot(tall, ATPall, color="red")

+    plot(tall, Gall, color="blue")

+    hold(false)

+    xlabel("Time")

+

+    println("max(G) = ", maximum(Gall))

+    println("max(ATP) = ", maximum(ATPall))

+    # max(G) = 20.97673324771467

+    # max(ATP) = 18.65978074314273

+    title("")

+end

+

+doPlot(0.36, 0.02, 6, 12.0)

+

+function doXY(V_in, k_l, k_p, K_m)

+    

+    dt    = 0.2

+    tlast = 1000

+    

+    iterations = integer(round(tlast/dt))

+    ATPall = zeros(Float64, (iterations, 1))

+    Gall = zeros(Float64, (iterations, 1))

+

+    ATP = 4

+    G = 3

+    for i = 1:iterations

+        ATPall[i] = ATP

+        Gall[i] = G

+

+        dATPdt = 2 * k_l * G * ATP - (k_p * ATP) / (ATP + K_m)

+        dGdt = V_in - k_l * G * ATP

+

+        ATP = ATP + dATPdt * dt

+        G = G + dGdt * dt

+    end

+

+    tall = dt*(0:iterations-1)'

+    figure()

+    hold(true)

+    plot(Gall, ATPall, color="red")

+    hold(false)

+    xlabel("G")

+    ylabel("ATP")

+end

+

+function testStability(V_in, k_l, k_p, K_m)

+    

+    dt    = 0.05

+    tlast = 2000

+    

+    iterations = integer(round(tlast/dt))

+    ATPall = zeros(Float64, (iterations, 1))

+    Gall = zeros(Float64, (iterations, 1))

+

+    ATP = 4

+    G = 3

+    for i = 1:iterations

+        ATPall[i] = ATP

+        Gall[i] = G

+

+        dATPdt = 2 * k_l * G * ATP - (k_p * ATP) / (ATP + K_m)

+        dGdt = V_in - k_l * G * ATP

+

+        ATP = ATP + dATPdt * dt

+        G = G + dGdt * dt

+    end

+

+    #deltaATP = maximum(ATPall[length(ATPall)/2:end]) - minimum(ATPall[length(ATPall)/2:end])

+    #deltaG = maximum(Gall[length(Gall)/2:end]) - minimum(Gall[length(Gall)/2:end])

+    #return (deltaATP, deltaG)

+    return (maximum(ATPall[length(ATPall)/2:end]),

+            minimum(ATPall[length(ATPall)/2:end]),

+            maximum(Gall[length(Gall)/2:end]),

+            minimum(Gall[length(Gall)/2:end]), )

+end

+

+function doBistable()

+    x = 0.1:0.05:1.6

+    varATP = zeros(length(x))

+    varG = zeros(length(x))

+    ATP_h = zeros(length(x))

+    ATP_l = zeros(length(x))

+    G_h = zeros(length(x))

+    G_l = zeros(length(x))

+    for i=1:length(x)

+        (a_h, a_l, g_h, g_l) = testStability(x[i], 0.02, 6, 12.0)

+        varATP[i] = a_h - a_l

+        varG[i] = g_h - g_l

+        ATP_h[i] = a_h

+        ATP_l[i] = a_l

+        G_h[i] = g_h

+        G_l[i] = g_l

+        println((a_h, g_h))

+    end

+    figure()

+    hold(true)

+    plot(x, varG, color="blue")

+    plot(x, varATP, color="red")

+    xlabel("V_in")

+    ylabel("Stability")

+    hold(false)

+    title("Stability plot")

+

+    figure()

+    hold(true)

+    plot(x, G_h, color="blue")

+    plot(x, G_l, color="blue")

+    plot(x, ATP_h, color="red")

+    plot(x, ATP_l, color="red")

+    xlabel("V_in")

+    ylabel("Value")

+    hold(false)

+    title("Values plot")

+end

+

diff --git a/assignments/hw02/quiz2.pdf b/assignments/hw02/quiz2.pdf
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+++ b/assignments/hw02/quiz2.pdf