Qualitative methods, biological network

The flux balance approach is an elegant technique for analyzing biological pathways in that the approach allows metabolic networks to be quantitatively and qualitatively studied without knowledge of specific enzyme kinetic parameters. A combination of FBA and bioinformatics provides a rapid, economical, and predictive in silico screening method for potential strategies to produce a desired compound. 

We repeat these simple examples from earlier work since they form a major justification for the elaborations we report below, and if they are understood well, then much of what follows should be clear. The dynamics in the differential equations are in qualitative agreement with the dynamics in the synthetic genetic networks in E. coU. One important aspect of biology is to understand the ways in which the organization and structure of the control networks can be used to predict the dynamics. Thus, we would like to develop methods that could be used to predict the dynamic behaviors just demonstrated without integrating or carrying out the stability analysis of the differential equations. 

Since there are many important qualitative differences between real biological systems and our model networks, it is possible that the methods described above will be applicable to only a small range of model systems. Yet, there are reasons to believe that the methods will be applicable to a broad class of systems. In the remainder of this section, we discuss several different ways in which our model equation does not capture the properties of real biological systems, and then we give arguments why the methods may stiU apply. 

Our initial studies of dynamics in biochemical networks included spatially localized components [32]. As a consequence, there will be delays involved in the transport between the nuclear and cytoplasmic compartments. Depending on the spatial structure, different dynamical behaviors could be faciliated, but the theoretical methods are useful to help understand the qualitative features. In other (unpublished) work, computations were carried out in feedback loops with cyclic attractors in which a delay was introduced in one of the interactions. Although the delay led to an increase of the period, the patterns of oscillation remained the same. However, delays in differential equations that model neural networks and biological control systems can introduce novel dynamics that are not present without a delay (for example, see Refs. 57 and 58). 

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