# Biochem 721; Foster
# gnuplot script for plotting the kinetics of a series reaction
# A -> B -> C
# d[A]/dt = k1[A]; integrating, we get:
a(x) = a0*exp(-k1*x)
# d[B]/dt = k1[A] - k2[B] = k1[A0]*exp(-k1*t) - k2[B]; integrating, we get:
b(x) = ((k1*a0)/(k2-k1))*(exp(-k1*x)-exp(-k2*x))
# d[C]/dt = k2[B] = ((k1*k2*a0)/(k2-k1))(exp((k2-k1)*x)); integrating, we get:
c(x) = a0*(1 - (1/(k2-k1))*((k2*exp(-k1*x)-k1*exp(-k2*x))))
# settings:
set xlabel "Time"
set ylabel "Concentration"
a0 = 1.
k1 = 1.1; k2 = 1.
set title "k1 = k2"
plot [0:10] a(x), b(x), c(x)
print "k1 ~ k2"
pause -1 "Return to continue..."
k1 = 10.; k2 = 1.
set title "k1 >> k2"
plot [0:10] a(x), b(x), c(x)
print "k1 >> k2"
pause -1 "Return to continue..."
k1 = 1.; k2 = 10.
set title "k1 << k2"
plot [0:10] a(x), b(x), c(x)
print "k1 << k2"
pause -1 "Return to continue..."