Mathematical Models: A Central Organizing Tool for Integrative Biology Drew Tyre School of Natural Resources

Outline Why What Examples Strengths and Gaps at UNL?

GENOMICS Murky associations Am. J. Hum. Genet. (2009) Genome-wide association studies have been hailed for their ability to find genetic variations that may contribute to disease risk. But assigning meaning to these variations is more difficult. Just collect more data …

Doesn’t always work Data don’t say very much – Schizophrenia, height Data are “indirect” – Remote sensed spectra are not species ID or richness Or hard to get – Population size of grassland birds "The combination of some data and an aching desire for an answer does not ensure that a reasonable answer an be extracted from a given body of data." - John Tukey.

We have a theory! Evolution by Natural Selection (Darwin 1859) – And all that came in the next 150 years … Too general – Doesn’t make predictions in specific cases Theory Data Models

The preferred average dimensions for a male model are a height of 5 ft 11 in (1.80 m) to 6 ft 2 in (1.88 m), a waist of 26–33 in (66.04–83.82 cm) and a chest measurement of 32–40 in (81.28– cm).

Merriam-Webster – 12 meanings! 11 : a description or analogy used to help visualize something (as an atom) that cannot be directly observed 12 : a system of postulates, data, and inferences presented as a mathematical description of an entity or state of affairs; also : a computer simulation based on such a system

A theoretical scheme for the control of hormone balance Penfield S, King J Proc. R. Soc. B 2009;276: ©2009 by The Royal Society

M Thomson & J Gunawardena Nature 000, 1-4 (2009) doi: /nature08102 General model of multisite phosphorylation with substrate S having n sites, kinase E and phosphatase F.

Ticks on Lizards

Key Features Explicit assumptions, leading to … Specific predictions “All models are wrong; some are useful.” -George Box

…trial and error … can be costly. …developed a method to predict …

From the following article: The large-scale organization of metabolic networks H. Jeong, B. Tombor, R. Albert, Z. N. Oltvai and A.-L. Barabási Nature 407, (5 October 2000)

Simple rules yield complex food webs Richard J. Williams and Neo D. Martinez Nature 404, (9 March 2000) UK Grassland Food web “To make progress, different fields have suppressed certain complications while highlighting others.” – Steven Strogatz

Systems Biology Examples from all levels of biological hierarchy Best/most data from the lowest levels Need for improved mathematical models at all levels “Elegant mathematics does not overcome biological ignorance, but only compounds it.” -John Pastor

Math Biology at UNL Strong program in Population Biology & Individual Behavior & Life History – Math in the Middle Optimisation of oligonucleotides for DNA synthesis Others?

Gaps? Math at the extremes – Genomics – Ecosystems – Lots of data! Optimisation – Practical – Evolutionary connections

"The greatest challenge today, not just in cell biology and ecology but in all of science, is the accurate and complete description of complex systems. Scientists have broken down many kinds of systems. They think they know most of the elements and forces. The next task is to reassemble them, at least in mathematical models that capture the key properties of the entire ensembles.“ – E.O. Wilson Consilience.