Oscillating Reactions

1
Oscillating Reactions Composite reactions whose
mechanisms contain autocatalytic steps may result
in oscillating reactions which have chemical
concentrations that oscillate in time or
space. Chemical examples of these oscillating
reactions are known and they are suspected of
playing a role in rythmic biochemical cycles,
e.g. beating hearts, respiration, etc.
2
One of the simplest examples of a mechanism
capable of exhibiting chemical oscillations is
the Lotka mechanism (developed originally to
model ecological dynamics in oscillating
interdependent animal populations, e.g., foxes,
rabbits, and cabbage)
k1 A X -----gt 2 X k2
X Y -----gt 2 Y k3 Y
-----gt 2 Z The 1st two steps in this mechanism
represent coupled autocatalytic reactions. What
makes them coupled? What makes them
autocatalytic? A is a reactant that is present in
essentially unlimited amount (a feedstock or
infinite food source) and so its concentration is
taken to be large and approximately constant at
its initial concentration of Ao.
3
The coupled differential equations describing the
time dependence of concentrations in the Lotka
mechanism are d X / dt k1
Ao X - k2 X Y Why is the 1st
term in this expression positive?
d Y / dt k2 X Y - k3 Y
d Z / dt k3 Y These equations can
be solved numerically.
4
Using a numerical technique (e.g. the method of
finite differences) to solve the coupled
differential equations model the Lotka
mechanism k1 A X -----gt 2 X k2
X Y -----gt 2 Y k3 Y
-----gt 2 Z on a spreadsheet. Once the model is
working determine the value of the variables, k1,
k2, k3, Ao, and Xo that will cause this model
to exhibit oscillations in the concentrations of
X and Y. Be careful not to confuse artifacts
of the modeling process for oscillations. Hand
in a copy of your spreadsheet program and a plot
of the oscillations as a function of time. The
plot should contain the values of the variables
that gave rise to the oscillations.