Existing approaches in multiscale science and engineering have evolved from a range of ideas and solutions that are reflective of their original problem domains. As a result, research in multiscale science has followed widely diverse and disjoint paths, which presents a barrier to cross pollination of ideas and application of methods outside their application domains. The status of the research environment calls for an abstract mathematical framework that can provide a common language to formulate and analyze multiscale problems across a range of scientific and engineering disciplines. In such a framework, critical common issues arising in multiscale problems can be identified, explored and characterized in an abstract setting. This type of overarching approach would allow categorization and clarification of existing models and approximations in a landscape of seemingly disjoint, mutually exclusive and ad hoc methods. More importantly, such an approach can provide context for both the development of new techniques and their critical examination. As with any new mathematical framework, it is necessary to demonstrate its viability on problems of practical importance. At Sandia, lab-centric, prototype application problems in fluid mechanics, reacting flows, magnetohydrodynamics (MHD), shock hydrodynamics and materials science span an important subset of DOE Office of Science applications and form an ideal proving ground for new approaches in multiscale science.
Prokaryotic single-cell microbes are the simplest of all self-sufficient living organisms. Yet microbes create and use much of the molecular machinery present in more complex organisms, and the macro-molecules in microbial cells interact in regulatory, metabolic, and signaling pathways that are prototypical of the reaction networks present in all cells. We have developed a simple simulation model of a prokaryotic cell that treats proteins, protein complexes, and other organic molecules as particles which diffuse via Brownian motion and react with nearby particles in accord with chemical rate equations. The code models protein motion and chemistry within an idealized cellular geometry. It has been used to simulate several simple reaction networks and compared to more idealized models which do not include spatial effects. In this report we describe an initial version of the simulation code that was developed with FY03 funding. We discuss the motivation for the model, highlight its underlying equations, and describe simulations of a 3-stage kinase cascade and a portion of the carbon fixation pathway in the Synechococcus microbe.
We have developed a novel approach to modeling the transmembrane spanning helical bundles of integral membrane proteins using only a sparse set of distance constraints, such as those derived from MS3-D, dipolar-EPR and FRET experiments. Algorithms have been written for searching the conformational space of membrane protein folds matching the set of distance constraints, which provides initial structures for local conformational searches. Local conformation search is achieved by optimizing these candidates against a custom penalty function that incorporates both measures derived from statistical analysis of solved membrane protein structures and distance constraints obtained from experiments. This results in refined helical bundles to which the interhelical loops and amino acid side-chains are added. Using a set of only 27 distance constraints extracted from the literature, our methods successfully recover the structure of dark-adapted rhodopsin to within 3.2 {angstrom} of the crystal structure.
Our aim is to determine the network of events, or the regulatory network, that defines an immune response to a bio-toxin. As a model system, we are studying T cell regulatory network triggered through tyrosine kinase receptor activation using a combination of pathway stimulation and time-series microarray experiments. Our approach is composed of five steps (1) microarray experiments and data error analysis, (2) data clustering, (3) data smoothing and discretization, (4) network reverse engineering, and (5) network dynamics analysis and fingerprint identification. The technological outcome of this study is a suite of experimental protocols and computational tools that reverse engineer regulatory networks provided gene expression data. The practical biological outcome of this work is an immune response fingerprint in terms of gene expression levels. Inferring regulatory networks from microarray data is a new field of investigation that is no more than five years old. To the best of our knowledge, this work is the first attempt that integrates experiments, error analyses, data clustering, inference, and network analysis to solve a practical problem. Our systematic approach of counting, enumeration, and sampling networks matching experimental data is new to the field of network reverse engineering. The resulting mathematical analyses and computational tools lead to new results on their own and should be useful to others who analyze and infer networks.
We explore stability of Random Boolean Networks as a model of biological interaction networks. We introduce surface-to-volume ratio as a measure of stability of the network. Surface is defined as the set of states within a basin of attraction that maps outside the basin by a bit-flip operation. Volume is defined as the total number of states in the basin. We report development of an object-oriented Boolean network analysis code (Attract) to investigate the structure of stable vs. unstable networks. We find two distinct types of stable networks. The first type is the nearly trivial stable network with a few basins of attraction. The second type contains many basins. We conclude that second type stable networks are extremely rare.