Antigenic cartography has been used extensively for influenza. Influenza virus strains differ from one another by the types of molecules that they have on their surface. Likewise, antisera differ from one another by the types of such surface molecules to which they bind. The goal of antigenic cartography is to use the binding strength of each virus strain to a set of antisera as a way of quantifying the antigenic differences among viral strains.
Data on binding strength is collected through an assay called the hemaglutination inhibition (HI) assay. When an influenza virus is mixed with red blood cells, the two bind to one another and form large complexes that become visible in solution. If an antiserum is also included in the mixture, however, it will compete with the red blood cells for binding sites on the virus. If the antiserum matches the surface molecules of the virus very closely then most of the virus will bind with the antiserum rather than with red blood cells. Antiserum-virus complexes are not visible, so one can readily “see” whether the antiserum or the red blood cells have caused most of the binding. If very few complexes are visible then we know that the antiserum matches the virus very well because it has effectively inhibited the binding between the virus and the red blood cells.
In order to get a measure of the strength of the binding between an antiserum and a virus the above procedure is repeated with different concentrations of antiserum. In particular, the antiserum is sequentially diluted to obtain a sequence of decreasing concentrations. Each of these concentrations is then used, in order, in the above procedure. The lowest dilution (that is, the highest concentration of antiserum) will typically inhibit all binding between the virus and the red blood cells. As the dilution factor increases however (that is, as the concentration of the antiserum decreases) there will come a point at which the red blood cells begin to outcompete the antiserum in the binding process. When this occurs the virus-red blood cell complexes become visible. The dilution factor at which this first occurs is used as a measure of the strength of binding between the antiserum and the virus. A high dilution factor means that even very small amounts of the antiserum can outcompete red blood cells in binding, and therefore the strength of binding between the antiserum and the virus is very high.
The data set in the link on the left was obtained using the above procedure with 35 virus strains and 5 antisera (from Smith et al. 2004; click here for additional data). The rows in the data set represent the different viruses, the first column gives the year in which the virus was collected (between 1968-1976), and the remaining columns represent the five different antisera. The numerical values in the table are the dilution factors as described above. The plot below displays these data in three-dimensional antigenic space for different choices of antisera. Each point represents a particular virus.
The above data give the binding strength of the 35 viruses to each of five antisera. Binding strength can be viewed as a measure of the similarity between a virus and an antiserum. High values mean greater similarity. Often it is more convenient though to work with a measure representing the difference between a virus and an antiserum. We can do this using the above data in the following way.
Suppose xij represents the binding strength of virus i to antiserum j. We first determine the largest binding strength for a given antiserum j across all viruses and denote it by mj . In other words, mj is the maximum value of xij over all viruses i for a particular antiserum j. Then, for each binding strength xij , we calculate the quantity mj/xij. This gives a measure of the relative difference between virus i and antiserum j. This measure has a mimimum value of 1 when xij =mj (that is, when virus i is the virus in the data set that most strongly binds with antiserum j) and it increases as the binding strength between a virus and the antiserum decreases. Finally, by convention, one usually takes the base 2 logarithm of the quantity mj/xij giving log2(mj/xij). This quantity also increases as the binding strength between a virus and the antiserum decreases and it has the advantage of having a minimum value of 0. Thus it is a more natural measure of the antigenic difference between a virus and the antiserum.
The plot below displays these transformed data in three-dimensional antigenic space for different choices of antisera. While the earlier plot showed the similarity or binding strength between each virus and the three chosen antisera, the plot below depicts the antigenic difference between each virus and these antisera.
References
Smith, D.J. et al. 2004. Mapping the antigenic and genetic evolution of influenza virus. Science 305: .371-376