Systems Biology Journal Club Talk Abstracts

Kinetic Logic

James S. Cavenaugh, Ph.D.
Department of Biostatistics and Computational Biology
University of Rochester

Feedback is a common occurrence in dynamic systems; it happens whenever the output of an element directly or indirectly affects its input. Some biological manifestations of positive feedback are differentiation and other epigenetic phenomena. Homeostasis is a common biological example of negative feedback. Naturally, the presence of feedback complicates the dynamics of a system. The most common way of handling complicated dynamics is with ordinary differential equations (ODEs), but the parameterization of systems of ODEs is usually problematic (in biology anyway) due to lack of accurate data with frequent sampling. However, while it is usually the case that we cannot obtain high quality estimates (i.e., with narrow confidence intervals) of the parameters of a living system, it is also usually the case that we can say something about it – we are not in complete ignorance. For example, genetic studies with knockout mutations give no information at all about the rate constants of enzymes which have been knocked out, but from such studies one can infer reasonable pathways in which the knocked-out enzymes play distinct parts. This results in partial, qualitative knowledge that is usually communicated verbally or with pictures (usually as some sort of an improper arrow diagram). Such a qualitative understanding is of course inferior to a detailed differential description of a dynamic system, but in reality, such qualitative models are absolutely essential towards shaping our mental picture of the phenomena at hand. Furthermore, there are some quantities which are inherently qualitative but which nevertheless have an associated dynamics (e.g., emotional states, alertness, feelings of hunger, levels of stress or pain, etc.).

Kinetic logic is one way in which the dynamics of a qualitative system can be described, or by which a continuous, quantitative system can be approximated as a qualitative one. (A related but separate formalism is that of piecewise continuous differential equations.) It is well suited towards handling biological feedback, and it was designed with that in mind. It allows one to infer the principal features of a dynamic system which can be approximated satisfactorily by step functions. In the simplest cases, these step functions are Boolean (we often speak of a gene being turned on or turned off), although it has been extended since its initial formulation to include multiple values for qualitative variables and also to include logical parameters. I will present an overview based on a mini-tutorial paper: R. Thomas, Journal of Theoretical Biology 153, 1-23 (1991). Unfortunately the .pdf for this is not available, so I will provide photocopies at tomorrow’s meeting.