C. C. Chancey
American Journal of Undergraduate Research, University of Northern Iowa, Cedar Falls, Iowa 50614-0150 USA
Authors and Affiliations:
Gregory A. Ciccarelli
Schreyer Honors College, The Pennsylvania State University, 10 Schreyer Honors College, University Park, Pennsylvania 16802-3905 USA
Physics Department, Abington College, The Pennsylvania State University, Abington, Pennsylvania 19001 USA
Whether the car’s gas tank is filled up on Monday and the paycheck is deposited on Tuesday, or vice versa, the contribution of those two transactions to the checkbook’s final balance is the same. By the commutative property, order does not matter for the algebraic addition of a finite number of terms. However, for a super banker who conducts an infinite number of transactions, order may matter. If a series (sum of all transactions/terms) is convergent and the order of term does not matter, then the series is absolutely convergent. If a series is convergent but the order of terms does matter, then it is conditionally convergent. Georg Bernhard Riemann proved the disturbing result that the final sum of a conditionally convergent series could be any number at all or divergent. In two, three and higher dimensions, the matter is even worse, and such series with double and triple sums are not even well-defined without first giving sum interpretation to the (standard) order in which the series is to be summed, e.g., in three dimensions, summing over expanding spheres or expanding cubes, whose points represent ordered triples occurring in the summation. In this note we show using elementary notions from distribution theory that an interpretation exists for conditionally convergent series so they have a precise, invariant meaning.
Lokesh Kukreja and Shubhik DebBurman
Biology Department, Lake Forest College, 555 N. Sheridan Road, Lake Forest, Illinois 60045 USA
Parkinson’s disease is a progressive neurodegenerative disease caused by the death of midbrain dopaminergic neurons. The misfolding and aggregation of α-synuclein plays a ruinous role in this disease, but how the protein becomes toxic is unclear. Using yeasts as model organisms for studying α-synuclein properties, our study explores the hypothesis that α-synuclein toxicity depends on plasma membrane phospholipid binding. First, using a chemical approach, we induced phospholipid synthesis in both fission and budding yeast with dimethyl sulfoxide (DMSO), a known inducer . Instead of regulating α-synuclein-dependent toxicity, DMSO unexpectedly exerted its own toxicity in both yeasts, in addition to inducing a lethal morphology defect in budding yeast. Moreover, instead of inducing plasma membrane localization of α-synuclein in either yeast, DMSO altered α-synuclein localization in both yeasts into as-yet unidentified cytoplasmic structures. We speculate that some of these structures may be internal, membrane bound organelles. To test for membrane phospholipid binding specifically, α-synuclein localization was analyzed in a phosphatidylserine-deficient budding yeast strain. We observed no loss of plasma membrane localization, suggesting that other phospholipids may regulate such specificity to α-synuclein. Together, these related studies illustrate the usefulness of yeasts in evaluating genetic and environmental factors that regulate α-synuclein toxicity linked to Parkinson’s disease.
Alex Kreuzer, Jinger Walrath, Meaghan Hirsch, and Olcay Akman (Department of Mathematics)
Dori Pitynski, Jason Jannot, and Steve Juliano (School of Biological Sciences)
Illinois State University, Normal, Illinois 61790 USA
Immunity is an important biological property of organisms that protects them from parasites. Similarly, body size is one of the most important biological traits because almost all biological processes, from the cellular to the ecosystem level, scale with body size. Our goal was to determine the correlation between body size and immune function in different populations of the eastern lubber grasshopper (Romalea microptera) which differ in body size. Field data was collected on grasshopper location, size (thorax and femur lengths), and immune function (measured by melanization response). In accordance with previous work, we found a significant body size cline among populations of south Florida grasshoppers: on average, small adult grasshoppers are found in western populations whereas large grasshoppers are found in eastern populations. However, we did not find a significant relationship between body size and one measure of immune function, either within or across these populations. Future work should be directed at understanding when body size and immune function might or might not be correlated.