Speakers are named first.
8:45-9:10 Edward Gatzke, Department of Chemical Engineering, University of South Carolina, Pradeep K. Polisetty and Eberhard Voit.
Model Identification and Yield Optimization for Metabolic Pathway Systems Using Global Optimization Methods and GMA Models [new title]
Metabolic engineering involves the optimization and modeling of biochemical systems. Branched pathway models such as Generalized Mass Action (GMA) capture realistic reaction information in relatively simple nonlinear dynamic model form. The goals of this work are 1) to identify reaction rate parameters in a GMA model given measurement information and 2) optimally manipulate fluxes within a metabolic pathway model in GMA form. These problems require the solution to a difficult nonconvex nonlinear optimization problem.
9:15-9:40 Lincoln Lu, University of South Carolina,
Fan Chung Graham (UCSD), T. Gregory Dewey (KGI), and David J. Galas (KGI).
Duplication Models for Biological Networks
Are biological networks different from other large complex networks? Both large biological and nonbiological networks exhibit power-law graphs (the number of vertices with degree x proportional to 1/xb), yet the exponents, b, fall into different ranges. This may be because duplication of the information in the genome is a dominant evolutionary force in shaping biological networks (like gene regulatory networks and protein protein interaction networks) and is fundamentally different from the mechanisms thought to dominate the growth of most nonbiological networks (such as the Internet). The preferential choice models used for nonbiological networks like web graphs can only produce power-law graphs with exponents greater than 2. We use combinatorial probabilistic methods to examine the evolution of graphs by node duplication processes and derive exact analytical relationships between the exponent of the power law and the parameters of the model. Partial duplications with vertex-deletions are also analyzed. We demonstrate that partial duplication with vertex-deletion can produce power-law graphs with exponents less than 2, consistent with current data on biological networks. The power-law exponent for large graphs depends only on the growth process, not on the starting graph.
9:45-10:10 John Schwacke, Medical University of South Carolina,
Eberhard O. Voit
Insights in the design and operation of the MAP Kinase cascade
The Mitogen Activated Protein Kinase (MAPK) cascade is an important, highly conserved, module common in eukaryotic cellular signal processing and is responsible for transducing signals from cell surface receptors to various cytosolic and nuclear targets. Existing models have treated the MAPK cascade as a mechanism for propagating a single signal from a receptor to an intended set of targets. However, evidence of crosstalk and synergistic activation suggests that this module offers design variations that allow it to function as a signal processor, integrating signals from various sources. Our research aims to determine the potential for signal integration and processing in interacting MAP kinase cascades.
Using computational models of the MAPK cascade we have characterized the effects of MAPK and MAPKK component concentrations on the system's response to stimulation. The distributive nature of kinase activation was found to produce complex relationships between the component concentrations and the speed and efficiency of the response, and the observed kinetics appears to facilitate a rapid and efficient response. Using a mathematical model of interacting cascades and a genetic algorithm to select appropriate kinetic parameters, we have shown that useful logic functions and amplitude-dependent signal processing can be implemented with limited crosstalk. A network implementing the `exclusive or' function and a network capable of responding only in a prescribed band of signal strengths (in-band detector) were identified and characterized. Analysis of the in-band detector revealed remarkable similarities with the MKK4/MKK7/JNK pathway including non-monotonic responses, transient responses, and phosphorylation-site preference. An overview of the cascade, the associated mathematical model, and a characterization of the `exclusive or' and in-band detector networks will be presented.
2:00-2:25 May Wang, Department of Biomedical Engineering, Georgia Tech., and Emory University,
Jin-Young Hong and Alfred H. Merrill
Visualization of metabolic networks
Biological information in systems biology research is often represented as large and complex hierarchies. The hierarchical data usually are generated in large quantities that are hard for interpretation. To improve human understanding of these large data and complex hierarchies, we have researched and developed a novel visualization system BioHViz to represent hierarchies. Specifically, we have been researching this tool to study metabolic pathways, with a focus on sphingolipid pathway. Sphingolipids are one of the major components of membranes. Their intermediates and products regulate diverse cell functions. The metabolic pathway of sphingolipids has thousands of individual components. Using current mass spectrometry methods, these components studies produce very complicated datasets that are mind-boggling for scientists to interpret directly. Our novel pathway visualization system, BioHViz, allows the biological and experimental scientists to visualize complex biological hierarchies interactively. It is configured to input data from mass spectrometric analyses of cellular sphingolipids, In addition, it allows the display of interactive context such as changes in the compounds with time, comparisons among groups, etc. These tools have been used to study human and mouse sphingolipids.
This work has been supported by Georgia Cancer Coalition Distinguish Cancer Scholar Award and Georgia Research Alliance Innovation Award.
2:30-2:55 James Peterson, Clemson
Mathematical models of cognitive function
A multiscale model of cognition is presented which involves dynamic interactions between cortex, the limbic system and the midbrain. The evidence for temporally and spatially constrained ensembles of neuronal activity in the cortex and its implications for cognition is reviewed. It is then shown that the brain architecture and physiology that subserve neural information transfer give powerful clues to appropriate mathematical and software models. The models are inherently multiscale and hence computations on the second/ hour/ day time scales must be integrated in some fashion. Agent based modeling is therefore appropriate for the longer time scales. There are many parameters that need to be set in these models and a roadmap for how one can glean information about their magnitudes from brain architecture/ chemistry studies of patients with psychiatric disorders such as schizophrenia is presented.
3:00-3:25 Songhui Zhu,
Department of Mathematics and Computer Science, Benedict College, Columbia, SC.
A Method to Study the Chaotic Domain in Parameter Space
A nonlinear dynamics is chaotic when the system is sensitive to initial conditions. Usually, Lyapunov exponent and phrase portraits are calculated to determine whether a dynamical system is chaotic or not. The key step of this approach is to calculate the Lypunov exponent when the value of the control parameter is given, using Wolf's algorithm. However, this algorithm is inefficient. This presentation uses another approach to determine if a system is chaotic, based on the definition of sensitivity to initial conditions. This approach is more efficient and makes possible to find and visualize the chaotic domain in the control parameter space. Furthermore, various cases of sensitivity of trajectories of a n-dimensional system are discussed. It is proved that for a n-dimensional nonlinear system, some of the n variables may be sensitive to initial conditions while the other variables are not sensitive to intial conditions.