(124c) Using Multicellular Pathway Modeling to Guage the Stability of Tissue Differentiation

Using a multi-cellular, pathway model approach, we investigate the Drosophila sp. segmental differentiation network's stability as a function of initial and systemic noise. While this network's functionality has been investigated in the absence of noise, this is the first work to specifically investigate how natural systems respond to random errors or noise.

Genetic expression and control pathways can be successfully modeled as electrical circuits. Given the vast quantity of genomic data, very large and complex genetic circuits can be constructed. To tackle such problems, the massively-parallel, electronic circuit simulator, Xyce(TM), is being adapted to address biological problems. Unique to this bio-circuit simulator is the ability to simulate not just one or a set of genetic circuits in a cell, but many cells and their internal circuits interacting through a common environment. Additionally, the circuit simulator Xyce can couple to the optimization and uncertainty analysis framework Dakota allowing one to find viable parameter spaces for normal cell functionality and required parameter ranges for unknown or difficult to measure biological constants.

For this work, the differentiation control network suggested by Dassaw et. al (Nature, 406, pp 188-192, 2000) is implemented as a circuit within a cell. Though complex, this network typically forces a cell into expressing one of the genes en or wg which locks the cell into becoming one type of tissue verses another. A two-dimensional collection of 500 cells, each containing a copy of this control network, is constructed and each cell feels the presence of neighboring cells through a diffusion limited environment. This collection of cells can then be simulated within the circuit modeler. However, the control network contains 51 unknown parameters (reaction rates, enzymatic turnover rates, diffusion constants, etc.) and it is computationally infeasible to study variations all combinations of these parameters. Thus, a parameter sensitivity analysis is first performed to reduce this set to 26 parameters. Finally the optimization engine controls these cellular pathway parameters and system noise levels so that simulations can be run in a logical way to explore parameter space. Approximately 300,000 time evolving, simulations were conducted in parallel to speed computation time.

Our findings agree with earlier results that the overall network is robust in the absence of noise. However, when one includes random initial perturbations in the cellular signals that initiate differentiation, the robustness of the system decreases dramatically. The effect of noise on the system is not linear, and appears to level out at high noise levels.

Due to its scalability and connectivity to optimization software, this biological circuit simulator has the potential to handle large and complex problems. Depending on the type of data available, one can cast problems as digital or analog circuits and easily simulate many replica of a single circuit interacting with a collection of other circuits. Through the coupling to an optimization framework, one can explore the dynamics of multiple cellular networks or of entire cell cultures elucidating governing parameters as well.

Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC04-94AL85000.