Compare the results from equations created for estimating animal populations to the actual animal populations, to see if these equations produce realistic results.

Determine how reaction rates of polyphenoloxidase, an enzyme that is responsible for the browning of damaged surfaces of fruits and vegetables, shifts under differing temperature conditions and enzyme concentrations.

Theory

• Derivative as an instantaneous rate of change (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 97)

References

• Yemenicioglu, A. et al. 1997. Heat inactivation kinetics of apple polyphenoloxidase and activation of its latent form. Journal of Food Science. 62(3): 508-510.
• Nourian, F. et al. 2003. Kinetics of quality change associated with potatoes stored at different temperatures. Lebensmittel-Wissenschaft Und-Technologie-Food Science and Technology. 36(1): 49-65.
• Chutintrasri, B. and A. Noomhorm 2006. Thermal inactivation of polyphenoloxidase in pineapple puree. Lwt-Food Science and Technology. 39(5): 492-495.

Determine the dispersal rates for pines, in order to calculate the rate of repopulation of a burned area following a fire.

Theory

• Derivative as an instantaneous rate of change (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 97)

References

• Daskalakou, E. N. and C. A. Thanos 1996. Aleppo pine (Pinus halepensis) postfire regeneration: The role of canopy and soil seed banks. International Journal of Wildland Fire. 6(2): 59-66.
• Reilly, M. J. et al. 2006. Wildfire effects on plant species richness at multiple spatial scales in forest communities of the southern Appalachians. Journal of Ecology. 94(1): 118-130.

In order to produce viable young, organisms need to provide their offspring with energy. As that energy is divided among more and more offspring, the fitness of the individual offspring is reduced. In order to get the best return for their offspring investment, organisms can adjust their clutch/brood size, either by producing many small or a few large offspring. The clutch size where organisms can rear their young without significantly reducing their own or their offspring’s fitness and survival is referred to as the optimal clutch size. Choose an organism for which you wish to determine the optimal clutch size and then create a model in order to calculate what that clutch size will be.

Theory

• Optimization (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 195)

References

On a stretch of DNA the operator (the “on” sequence for a group of functionally related genes), promoter (the “on” sequence for a gene), and genes that they control is called an operon. Operons are switched on and off by repressor proteins, which in turn are activated or inactivated by a corepressor, which is usually one of the proteins coded for in the operon. As the concentration of the corepressor increases the more and more repressors are activated, which in turn switches off the operon and ceases the production of the corepressor. Create a model/equation that describes the operon feedback loop. How would the model/equation change if the corepressor inactivated instead of activated the repressor protein?

Theory

• Cellular dynamics: pathways of gene expression (Stephen P. and John Guckenheimer. Dynamic Models in Biology. New Jersey: Princeton University Press, 2006. 107)
• A mathematical model for enzyme reactions (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 624; DMB pg.

References