Background: Mathematical models are widely regarded as a means to gain quantitative understanding of chemical and biochemical systems. Models of these systems are generally formulated based on available knowledge and their analysis typically involves the following series of steps: (1) establishing a nominal parameter set on the basis of experimental data or estimated values, (2) performing local analyses of the model at the nominal parameter set, and (3) exploring the global behaviors of the model through sampling of parameter space. However, mechanistic models of biochemical systems typically involve a large number of parameters with values that are generally poorly defined or unknown altogether. Therefore, it is a fundamental challenge to explore the full repertoire of behaviors latent in any particular system design.
Recent developments within the framework of the power-law formalism have lead to an alternative approach, known as the system design space methodology. This methodology inverts the order of many of the steps typically taken to analyze biochemical systems; it (1) decomposes a system into a finite set of qualitatively-distinct phenotypes to provide a global-perspective of system behavior; (2) performs local analyses of model phenotypes; and (3) focuses computational efforts at localized regions of parameter space for in-depth analysis using conventional methods. The most recent developments of this methodology can be used to positively discriminate between hypotheses based on their global repertoire of potential behaviors, independent of specific values for the parameters.
The system design space toolbox is a collection of software tools that facilitate analysis using the design space methodology by automating the difficult steps of the process. The design space toolbox automatically calculates critical system properties both analytically and numerically. Examples of analyses automated by the design space toolbox include calculation of steady-state solutions; log-gain factors for signal amplification; parameter sensitivities to small quantitative changes; global tolerances to large qualitative changes; local stability of the fixed points for local bifurcations; and identification of global topological structures for global bifurcations.
Objective: The goal of this workshop is to provide an introduction to the design space toolbox. This workshop will emphasize the capabilities of the toolbox as a means to elucidate the link between genotype and phenotype of biochemical systems from a global perspective. Participants of this workshop will have a working version of the toolbox and will learn the basic steps required for analysis of a biochemical system. Specifically, the workshop will focus on the following steps: (1) formulation of problems using the design space toolbox, (2) enumeration of the complete repertoire of qualitatively-distinct phenotypes; (3) determination of parameter values for any phenotype of a given system; (4) identification of ensembles of phenotypes that can be simultaneously realized to achieve a specific sequence of functions, i.e. for the rational design of synthetic constructs.
Requirements: Participants are highly encouraged to bring a laptop with the design space toolbox installed. In addition, participants should have a simple mathematical model involving mass action kinetics and rational function kinetics that will be used for the last segment of the workshop. The laptop will need a POSIX compliant operating system, such as GNU/Linux (preferably Ubuntu) or Mac OS X (preferably Mavericks or later), together with a collection of open-source libraries. A virtual machine running GNU/Linux on Windows is perfectly acceptable. Registered participants will be given access to the design space toolbox software prior to the workshop, together with installation scripts and/or instructions on how to install it. Examples of simple systems for the last segment of the workshop and papers for background information on the design space method will also be provided.
Jason G. Lomnitz
Savageau Lab
Department of Biomedical Engineering
University of California
Davis, CA 95616
jlomn@ucdavis.edu