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Maths maximises the immune response

At most times of the day, metropolitan train stations swarm with busy people coming and going.  What if you stopped in the middle of the station and waited?  What would be the likelihood that you would see someone you know, and how long would you have to wait for that chance encounter to happen?

This is a complex probability problem and its framework can be applied to many different challenges. One problem being investigated is human immunity against disease.

Vaccines work by providing the immune system with a harmless replica of a bacteria or virus in order to prime dendritic and T cells for a potential infection. Currently, we have no real sense of how many activated T cells are needed to mount an effective immune response.  Possibly some vaccines are too strong while some many not activate enough cells. By understanding the interaction between the dendritic and T cells, vaccine development may become more effective.

A basic compartment model was initially developed and matched to experimental data generated in Dr Michael de Veer’s lab by Dr Melanie Neeland during her doctoral candidature. This model was designed to capture the essential feature of the dendritic cell-Tcell interaction. That is, how efficiently can dendritic cells (DCs) find cognate Tcells (TCs) in a lymph node and how this efficiency is affected by DC concentration, life span, scanning rate etc. This study provides a mathematical framework to assess the efficacy of a vaccination without the need for trial and error testing.

Since Melanie Neeland had her PhD conferred, Mr Dominic Maderazo completed an honors degree under the supervision of Dr Mark Flegg and Dr Jennifer Flegg. In collaboration with Dr de Veer, Mr Maderazo constructed a model of a lymph node and studied the DC-TC interaction with a particular emphasis on spatial effects. That is, how the internal structure of the lymph node affects the efficacy of DC-TC interactions. In Mr Maderazo’s studies, a particular emphasis was placed on lymph node size since lymph nodes are known to vary substantially between model organisms and during lymph node shut down (swelling).

These studies are intended to be a tool to improve scientific understanding of vaccination efficacy so that optimal doses and techniques may be found.

MAXIMA’s role as a gateway between mathematics and other disciplines has been of key importance to this research.  Working with MAXIMA has exposed Monash physiologists to the opportunities that collaboration with mathematicians can offer to support better modelling of complex physiological processes.

Furthermore, collaboration with MAXIMA has provided critical input into the successful completion of a PhD for Dr Melanie Neeland and honors degree for Mr Dominic Maderazo. A paper is currently being prepared which outlines the model and its results.