Math Tools for Life

Jimena Davis

(page 2 of 3)

“I’d never heard of a mosquitofish,” laughs Davis, who’s now contributed as much to understanding their population biology as almost anyone on Earth.

In rice fields in the United States and other major rice-growing countries, including India, mosquitofish are used as a natural mosquito control tool, reducing the need for pesticides. The challenge for biologists is to understand the mechanisms behind the growth of mosquitofish populations as a way to maximize the fishes’ impact on mosquitoes.  For example, when seeding a field with fish, what’s the optimum fish-size distribution to use?

“What we know is that there isn’t a single growth rate to describe the entire mosquitofish population but, rather, a distribution of growth rates. Individuals, and individuals at different sizes, grow at different rates, just as with humans,” Davis says.  “Estimating the distribution of the growth rates is impossible without computationally efficient approximation methods.”

This problem, she notes, is an example of her specialty: inverse mathematical questions.  These are ones in which the final solution is known and the challenge is to determine the parameters, or factors, that led to it — in this case the distribution of growth rates among the fish.

With the mosquitofish population model, she’s not only improved the approximation methods for the growth rate distribution but also tested their reliability.

“We’ve been able to go a step further and compute confidence bands for these probability distributions,” she says.  “This is exciting because these techniques aren’t just applicable to this problem, but to a whole range of probability estimation problems.”

Bacterium Biology

At Sandia, Davis teamed with her practicum advisor, Elebeoba May, to tackle a more complex inverse biological computation problem — one that took her from fish populations to bacterium biochemistry.

May is leading an ambitious project to develop a large-scale systems biology simulation platform that can computationally model whole-cell, multi-cellular and host-pathogen systems at the molecular level.  Called the BioXyce Project, it’s based on modeling the flow of proteins and genetic molecules as if they were current flowing through an electrical circuit.  This large-scale, parallel computing biocircuit simulation is one of the holy grails of computational biology — to mathematically model the hundreds of interacting genetic and protein pathways that constitute an organism’s metabolism.

Davis’ task was to improve a component of the system dedicated to computationally modeling the E. coli bacterium’s central metabolic system.  Once again, as with the mosquitofish work, Davis was thrown into deep waters.

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