A common goal in the domain of systems and synthetic biology is to understand the relationship between design and function of gene regulatory networks. This is a significant challenge for several reasons. Typically understanding the behavior of a gene regulatory network means understanding the associated dynamics. Traditionally this requires having an acceptable nonlinear model, knowledge of parameter values, and knowledge of initial conditions, all of which are difficult to obtain in the setting of complex multi-scale problems. To circumvent these challenges we have developed a novel approach to nonlinear dynamics based on order theory and algebraic topology. This method allows for efficient computations of rigorous combinatorial/algebraic topological descriptions of the global dynamics over large ranges of parameter space. As a consequence, given a regulatory network, we are able to construct a database describing all the associated dynamics. I will discuss the theory behind this tool and demonstrate how it can be applied to specific examples.