Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
Is the age of this very old man statistically believable?
bioNRICH is the area of the stemNRICH site devoted to the
mathematics underlying the study of the biological sciences,
designed to help develop the mathematics required to get the most
from your study of biology at A-level and university.
Published December 2011,February 2011.
Gregor Mendel was one of the early pioneers in the field of
genetic inheritance. Mendel used true breeding garden pea plants
(Pisum sativum) to
investigate how seven different phenotypes were represented in the
offspring of parent plants across generations. These experiments
led Mendel to propose that:
As discussed previously, Mendel's principles have needed slight
modifications to still be valid in light of new experimental
evidence. This is the case for the situation of genetic
Mendel stated that genes segregated independently of one another
and this can be seen to be true if individual genes are on
different chromosomes. However, if there is more than one gene per
chromosome then can the inheritance of these two genes be linked?
i.e. is it more likely that certain allelic combinations segregate
Experimental evidence suggested that this could be the case.
Bateson and Punnet for example found that pollen shape and flower
colour showed an inheritance pattern where parental genotypes are
more likely. Thomas Hunt Morgan's Drosphila melanogaster studies
of the inheritance of purple eyes (pr) and vestigial wings (vg) also indicated that linkage
was a real phenomenon. Morgan suggested that the two genes were
carried on the same pair of homologous chromosomes and pairing
during meiosis lead to new genetic combinations, a process known as
recombination. It was
eventually conjectured that chiasmata formation between
homologous chromosomes and crossing over lead to the
exchange of genetic material.
Of course the human genome is a highly complex assemblage of
genetic code. Genes can interact with both the external environment
and each other in terms of their expression. The effect of gene
interaction may be seen by considering the relationship between the
genotype of an individual
and its phenotype.
An interesting genetic interaction is epistasy. This is when the effect
of one gene is masked by the effect of another meaning it does not
find expression in the phenotype of an individual. An example of
this is the eyegone gene
in Drosphila which is
clearly epistatic to any eye colour gene as eye formation itself
does not occur! Another interesting genetic phenomenon is the
"viability effect". Certain mutations may actually slow the growth
of certain species in such a way that they become under-represented
in the population. These effects are quite common in mutated genes
in fungi such as Aspergillus
Previously we met a situation where the mapping of a chromosome
could be conducted by considering the recombination frequency of
certain genetic markers in
a cross. Now we consider a method where enzyme catalysed digestion
of DNA can give a cruical insight into its structure.
A wide variety of bacteria produce restriction endonucleases in
order to cleave foreign DNA and so destroy its coding capacity.
This is a useful strategy against infecting bacteriophages. The
cuts that a restriction endonuclease makes to a molecule of DNA may
be flush or staggered, giving protruding sticky ends.
Why do you think that restriction
enzymes don't digest the bacterium's own DNA?
Examples of restriction enzymes include EcoR I, Hind III and
BamHI. Most recognize a specific DNA sequence that is 4-6 bases
long and palindromic. For
example the recognition sequence of EcoR I (produced by the
bacterium E. coli) is 5'
Many fungi and bacteria can be grown on synthetic media of a
known chemical composition. This means single gene mutations
introduced into organisms which affect a certain metabolic pathway
can be characterised. This is because mutation can cause the
requirement for a specific
chemical for growth depending on which step in the pathway if
Mutants which require a specific supplement are produced and can
be genetically analysed to see how many genes are involved.
Furthermore, the mutants are grown on media containing various
intermediates in the metabolic pathway to investigate where in the
pathway the mutation is acting. This approach is often sufficient
to identify the intermediates and their order of formation.
In an experiment, a 1st year scientist replicates a master plate
containing 26 colonies of the fungus Aspergillus to 5 plates
containing different media. The plates have a nitrogen source that
is an intermediate in the metabolic pathway that degrades
hypoxanthine to NH$_4^+$.
The scientist wants to establish:
1) The growth responses of each of the strains
2) The order of intermediates in the pathway
3) The strains which are blocked in each step giving an idea of
the genetics underlying the growth patterns
The table above shows the process by which the growth of the
fungus is classified, where the "+" indicates growth of the strain
on this medium and a "-" scoring means no growth.
Can you think what the purpose of
the colony number 26 is, given it grows on all the media?
The order of intermediates a $\rightarrow$ can be
If a mutation occurs affecting a step of a metabolic pathway
close to the initial
susbstrate, then if the species is plated onto media
containing nutrients occuring downstream as intermediates in the
pathway, then growth is still possible.
If mutation occurs affecting a step of the metabolic pathway
close to the final product,
then if a species is plated onto media containing nutrients
occuring upstream as intermediates in the pathway, growth still
won't be possible because of the mutation!
As all of the strains are capable of growth on media containing
e, it must occur closest to NH$_4^+$ in the pathway. Using a
similar analysis the order can be established as:
Hypoxanthine $\rightarrow$ d
$\rightarrow$ a $\rightarrow$ c $\rightarrow$ b $\rightarrow$ e
Can you determine which strains are
blocked in which steps of the pathway? For example the step d
$\rightarrow$ a is blocked by the mutants 1,3,6,9,15,17,18,20 and
25. What does this imply about the species genetically?
Such analysis is highly useful in the
early investigation into the genetics behind metabolic
In this article, we've covered
topics ranging from Mendelian inheritance, chromosome mapping,
genetic interactions, the genetic analysis of metabolic pathways
and restriction mapping. Hopefully over the course of this article
you have gained an appreciation of some useful genetic concepts you
will frequently encounter in your future studies.