The causal mapping technique has the potential to be an effective tool for studying complex biological systems. On the one hand, CMAP is a semi-quantitative method similar to Boolean networks and its extensions 
. On the other hand, CMAP provides a more detailed description than other graphical approaches with similarities to the difference equation approach. Thus, in terms of modeling techniques, the CMAP technology occupies an intermediate position between purely graphical methods and more quantitative models based on either ordinary or partial differential equations or stochastic formulations and it puts some limitations on possible mechanisms. For example, both mechano-chemical models of cortical oscillations that have been developed recently (
) include a negative feedback from contractility to a mechano-sensitive source of calcium such as stretch activated calcium channels (SAC). This feature was predicted by CMAP modeling 
and suggests that application of the coarse-grained CMAP technology can illuminate key qualitative requirements of mechanisms put forward to account for system behavior.
In this paper, we have added hypotheses generation to the CMAP toolbox. This methodology enables investigators to rank hypotheses according to a fitness index. Hypotheses with high fitness indices represent operating mechanisms that are robust to variations in parameter values, and, therefore, in theory represent good design principles for operating in the fluctuating environments found at the cellular and molecular levels. Thus, one interpretation of a high fitness index is that these systems represent architectures most likely to survive natural selection.
We applied the hypothesis generation tool to a simple test case of a three-element signaling module and to the more complex phenomenon of cortical oscillations 
. For the former case, we demonstrated that the CMAP protocol can be used to generate pathway architectures capable of adaptation to persistent signal. Intriguingly, our analysis found a configuration that produced adaptation for all parameter values (F
1). It would be interesting to determine if this pathway architecture exists in real signaling or regulatory systems. For the case of cortical oscillations, the two main conclusions are that i) a negative feedback from cell contractility to mechanochemically-activated calcium release is required to qualitatively reproduce experimental observations for this system 
and ii) that there are possible connections between the Rho pathway and contractility 
that should be explored experimentally and in future modeling. Our methodology also provides a mechanism for generating experimentally testable predictions to discriminate competing high-fitness hypotheses. An important feature of our approach is that the predictions are not based on perturbations to a single parameter set, but represent trends in the behavior of the hypotheses when all the parameter sets that generate results consistent with experimental data are considered. Because we are able to exhaustively sample the parameter space, a consistency between new experimental results and model predictions is more likely to be indicative of the design architecture of the biological system rather than reflect a particular choice parameter values. While a single experiment may not definitively prove a mechanism, it would reduce the regions of parameter space for various hypotheses that produce behavior consistent with all the experimental results. It may then be possible to find experimental perturbations for which valid hypotheses produce qualitatively different behavior for all parameter values within this restricted space.
Coarse-grained approaches such as this will have some limitations. Of course, as the complexity of biological networks increases, the number of possible configurations increases in an exponential fashion. However, this is limited in a practical sense by the prior knowledge we have about this system derived from laboratory experiments and the biological literature. It could also be argued that the weight interval we employ [−1, 1] is unduly restrictive in limiting the range of variation of weights that we employ. In this regard, it should be noted this is already an improvement in terms of modeling dynamics when compared to the frequently employed Boolean networks which are binary in nature. Moreover, this range of weights employed already produces a rich repertoire of parameter combinations that qualitatively reproduce the observed behavior.
As biologists continue to move toward studying cellular and molecular systems as a whole, there will be an increased need for mathematical approaches to interpret and codify experimental results. We believe the CMAP provides the appropriate level of description within an intuitive framework to make sense of these complex biological systems.