Project 2 Sloppy Systems
Gutenkunst and Sethna (2007) proposed that it is useful to consider two layers of organization in biological systems in between genotype and phenotype, the chemotype and the dynatype. The DNA sequence (genotype) determines the properties of gene products, including how they interact with each other and other substances, including modifications that alter their properties. The chemotype of a system performing a particular function consists of a network of components and the parameters characterizing the components and their interactions. The dynatype characterizes the functioning of the system for a particular set of chemotype parameters. A phenotype observed in the organism in turn results from the dynatypes (behavior) of many systems.
Sehna and his colleagues ( ) analyzed a large number of biological systems for which models have been proposed that mimic the behavior observed in organisms, cells, or in vitro extracts. They quantified how much the behavior of each model changes as its parameters are systematically varied. For each system they specified what would be considered success. For example, for a circadian rhythm model success would be to have the oscillation of the output have period within a range around 24 hours. For a metabolic pathway success might be defined as production of the product within a range of rates for a given concentration of the substrate.
For each model they determined the output while systematically vaying the n chemotype parameters (θ1..θn). When every combination of parameters which produce success was plotted as point in n-dimensional parameter space, the (success) region was found to be reasonably approximated by an n-dimensional hyper-ellipsoid. It is typically found that for some parameters varying more than a small amount prevented success, and thus their values are critical, while for other parameters they can vary considerably without affecting success.
They typically would assign the two most critical parameters as θ1and θ2. The figure at right shows what is typically observed: if the other n-2 are assigned values within successful region, all the successful points from then varying θ1and θ2 lie within an ellipse. The other lines around the ellipse represent ellipses that would be obtained if the range for success is increasingly made larger.
If we "move" in parameter space so that θ1 increases while θ2 decreases (or vice versa) the output changes rapidly with distance. This direction was called "stiff." In contrast, if θ1and θ2 change together, the output changes considerably slower. In the figure this is called a "sloppy" direction. Another way of putting this would be to say that in the stiff direction the diameter of the hyper-ellipsoid is small, while in a sloppier direction the diameter is larger. In fact, the direction called sloppy in this diagram is much stiffer than other directions involving variation of 3rd through nth parameter where the diameters of the hyper-ellipsoid can be much greater.
For all of the biological models studied, the diameters along the axis of the hyper-ellipsoid are spread out over a large range. They called this property sloppiness. This strongly suggests that sloppiness is also a property of the biological systems the models mimic.
In contrast to sloppy systems, in a precise system, movement by small distances in most directions in parameter space would move the system out of the success region. If biological systems were precise, they would be prone to failure because many of mutations occurring in genes coding for components of the system would change the parameters enough to preclude functioning successfully. Sloppiness thus confers robustness. In another section, I argue that homeothermy allows more precision in an organism's systems, and also allows increasing complexity in the interactions of those systems.