Although my fascination with mathematical/systems biology did not kick in until relatively late in my education, I was encouraged by Professor Michael Brenner to pursue additional research beyond my limited coursework in the field. The project that we worked on involved using the technique of dominant balances to simplify the mathematical model built by the Macara group to probe the role of the Ran gradient in nuclear import. Although this research was never completed, it afforded me a rare opportunity to apply some simple Applied Mathematics reasoning to a very “traditional” biological problem and to arrive at some interesting conclusions.

### Applying Dominant Balances to a Model of Nuclear Import

**Abstract:**

Mathematical models of complex biological systems are oftentimes exceedingly complex despite relatively simple system dynamics. This report investigates one complex model of protein nuclear import, a process which has been experimentally shown to depend on the large concentration gradient of Ran-GTP between the nucleus and cytoplasm. It shows that the method of dominant balances can be used to selectively study the system’s behavior, including determining a simple, yet accurate relationship which yields the numerical value of the Ran-GTP gradient.

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