#### The statistical mechanics of sloppy models: nerve growth factor signaling

Kevin S Brown

Murray Lab

Dept of Molecular and Cellular Biology

Harvard University

Models of biochemical regulation in cells, typically consisting of a set of first-order nonlinear ordinary differential equations, are increasingly being applied to growth regulation and development in higher organisms. Because of challenges in performing experiments on living systems, such mathematical descriptions of cells and pathways typically have large numbers of poorly known parameters, simplified dynamics, and uncertain connectivity: three key features of a class of problems I call *sloppy models*. There is a famous aphorism in physics: "Give me four parameters and I can fit an elephant. Give me five and I can make it wag its tail". When one considers that even simple models may have tens or hundreds of parameters and such models get more complex very quickly, an attempt to generate meaningful and useful models of biological regulation appears even more daunting. I will discuss the use of a statistical ensemble method to study the behavior of such systems, in order to extract as much useful predictive information as possible from a "sloppy model" given the available data used to constrain it. I will show the utility of spectral decompositions in understanding the behavior of the model's parameter fluctuations, including measures of robustness and sensitivity, and in extracting the five parameters that "fit the elephant.". By application of these methods to a protein network important for neuronal differentiation in a model cell line, I will show that (i) biologically relevant predictions can be extracted from complex models of cellular signaling even in the absence of measurements of all the rate constants and (ii) one can use these techniques to gain insights into the design and possible evolution of cellular signaling systems.

KS Brown, JP Sethna, "Statistical mechanical approaches to models with many poorly known parameters", Phys Rev E, 68:021904, 2003. PubMed.