Illuminating the relationship between network topology and dynamics is a critical task for systems biology. Genetic regulatory networks are known to be robust against structural and dynamic perturbations, but the design features that foster robustness remain largely hidden. Here we investigate the design and designability of cell cycle networks, with the goal of understanding how the cell robustly carries out the cell cycle.
Methods
Boolean networks are commonly used to model cell cycle networks. We employ an 11-node budding yeast cell cycle model and build a 13-node network model of the mammalian cell cycle. We compute the number of network topologies capable of performing their dynamic trajectories. Designability is defined as the base-10 logarithm of this number. Next, we compare the designability of cell cycle trajectories to random trajectories and activation cascades. Type-I random trajectories are simply random paths through state space, while type-II random trajectories preserve the rate of node flipping of the corresponding cell cycle trajectory.
To uncover the design principles of cell cycle networks, we use a bottom-up approach to find minimally functional network topologies that produce several types of activation cascades. A minimally functional topology is one that exhibits a particular dynamical phenotype with the fewest links.
Results
Networks that exhibit cell cycle behavior prove to be highly designable. The yeast cell cycle dynamical trajectory has a designability of 35.22, compared to 2.87 among type-I random trajectories and 28.79 among type-II random trajectories. The mammalian cell cycle model yields a designability of 53.99, compared to 1.53 (type-I) and 41.54 (type-II) for random trajectories. Regular activation cascades are also very designable, producing similar designability scores.
We then identify minimally functional network topologies that perform activation cascades. As the width of an activation cascade increases (more regulators are activated at the same time), designability increases. This is because there are more valid combinations of node wirings (those that produce the given dynamical phenotype).
Conclusions
Cell cycle behavior is highly designable. This high designability and robustness is not unique to the cell cycle, but rather a general feature of activation cascades. A relatively simple core topology enables cascade-like behavior without the need for fine-tuning, producing highly designable and structurally robust networks. This architectural theme likely underlies cell cycle networks and provides much of their robustness. These results can be applied to design robust synthetic systems for activation cascades. Altogether, the findings suggest that nature converges on particular network architectures because they are easily designed and stable against mutations.