5 files changed, 216 insertions, 0 deletions
diff --git a/assignments/hw02/answers.txt b/assignments/hw02/answers.txt
new file mode 100644
index 0000000..f7a287e
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+++ 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
new file mode 100644
index 0000000..a9513bf
--- /dev/null
+++ b/assignments/hw02/euler.jl
@@ -0,0 +1,29 @@
+
+# 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
new file mode 100644
index 0000000..1773e6c
--- /dev/null
+++ b/assignments/hw02/euler.m
@@ -0,0 +1,26 @@
+% % 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
new file mode 100644
index 0000000..65446d1
--- /dev/null
+++ b/assignments/hw02/euler_mod.jl
@@ -0,0 +1,143 @@
+
+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
new file mode 100644
index 0000000..d35f763
--- /dev/null
+++ b/assignments/hw02/quiz2.pdf