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'Graphic Biology' printed from https://nrich.maths.org/
There are many possible processes that display plots matching the
graphs given. This part of the question was designed in order to
get you to think about a wide variety of biological examples. Here
we will mention a few that satisfy each of the plotted
relationships. There is much potential in terms of the possible
units that could be used for the axes.
Red- this relationship
could be followed if the rate of reaction for an enzyme catalysed
reaction was plotted against the pH as certain groups may require
deprotonation, changing the structure of the protein to make a
functional active site. Too high a pH may cause deprontonation at
other residues, altering protein structure in a way that reduces
the rate of reaction.
Green- plotting the amount
of DNA produced against time for a PCR would give a plot similar to
this. Exponential increase in the number of DNA strands occurs with
every cycle as the amount of DNA is doubled through replication.
The amount of DNA doubles with each cycle, so x in the case of this
plot would be the time take for a single cycle of PCR to
complete.
Blue- plotting the initial
rate of an enzyme catalysed reaction against substrate
concentration would yield the following relationship. A maximum is
reached when the active sites of all enzymes in solution become
saturated with substrate meaning that there is no additional
increase in rate of reaction on addition of more substrate. A plot
of something like concentration of CO$_2$ against the rate of
photosynthesis, possibly measured by evolution of O$_2$ over time,
would yield a similar plot where a maximum rate is reached as the
concentration of CO$_2$ is no longer a limiting factor to the rate
of photosynthesis (for example light intensity may be too low a
level for any additional CO$_2$ to be processed above a certain
level.
Purple-a pH curve for a
titration follows a similar shape to one of these graphs as an
interesting point. The activity of lysozyme against pH (in a large
excess of substrate) is a interesting biological example that
follows this trend as the deprotonation of a certain residue is all
that is required to cause the activation of lysozyme. If we plot
the percentage saturation of haemoglobin against the partial
pressure of oxygen also produces a similar sigmoidal curve due to
the binding affinity of oxygen being co-operative i.e. binding of
an oxygen molecule causes the affinity of the haemoglobin molecule
for further oxygen diatoms to increase until steric effects and
tendency for dissociation hinder the binding of a potential
4$$^{\text{th}}$ molecule.
Brown- a
traditional linear plot is of course very common. An example could
be volume of blood flow past a point against time at a major vessel
in a circulatory system. Rate of reaction against concentration of
a reactant may be linear if all other reactants are in excess. A
common experiment involving the placement of a potato cylinder in
solutions of varying concentration follows a linear trend if
percentage change in mass is plotted against the degree of dilution
of the surrounding solution, around the isotonic
point.
Pink- this plot is again
highly common. If we plot something like log (distance migrated) on
the y axis against the molecular weight of a fragment of DNA placed
under gel electrophoresis, we get this type of curve.
Black- an exponential
decay relationship could be, for example, a plot of concentration
of ibuprofen in the blood over time after the peak dose has been
recorded. The concentration of adrenalin over time could operate in
a similar way over defined time scales.
In order of intercept with the y-axis, the curves may be
represented by the following functions:
Red- an alteration of the
equation for the probability density function of a normal
distribution
$$f(x) = \frac{a}{\sqrt{2\pi}}e^{-\frac{(x + b)^2}{c}}$$
Green- exponential
increase
$$f(x) = a(2)^{\frac{x}{b}}$$
Blue- diminishing gradient and
reaching a maximum
$$f(x) = \frac{ax}{x + b}$$
Purple- S-shaped profile with a
rapid increase in gradient which diminishes to reach a
maximum
$$f(x) = a tanh(bx + c) + d$$
Brown- linear plot showing a
proportional increase in f(x) with an increase in x
$$f(x) = ax + b$$
Pink- linear plot showing a
proportional decrease in f(x) with an increase in x
$$f(x) = -ax + b$$
Black- exponential
decay
$$f(x) = a{(\frac{1}{2})}^{\frac{x}{b}}$$
Consider what effect changing the
values of the constants would have on the form and placement of the
graphs given.