Highly designable phenotypes and mutational buffers emerge from a systematic mapping between network topology and dynami

1. Highly designable phenotypes and mutational buffers emerge from a systematic mapping between network topology and dynamic output Nochomovitz & Li

2. The idea • Map network topologies to dynamical phenotypes Designability = 2 The designability of a phenotype is defined as the number of topologies mapped onto it. Designability = 1

3. Dynamic phenotype A limit cycle passing through a specific series of states or a particular fixed point. A 5-cycle phenotype (0001 0010  1001  0111  1010) Network topology

4. Updating rules The time scales of the decay process and the activating or inhibitory processes are of equal order. Rule 1: Rule 2: The decay process occurs on a much slower time scale than the activating or inhibitory processes.

5. Phenotypes that are neither excessively rare nor excessively simple

6. Comparison of the two rules Under both rules, the strong, intermediate, and weakly designable phenotypes emerge consistently.

7. Designing larger cycles is exponentially hard.

8. Designability spectrum of 4-cycles for 4-node networks Mean designability of 4-cycles 0001  0010  0101 0011

9. Designability spectrum of 5-cycles for 4-node networks Mean designability of 5-cycles

10. Designability spectrum of 6-cycles for 4-node networks Mean designability of 4-cycles

11. What are the dynamical features of highly designable dynamical phenotypes? Case 1: (2 3 6 11) 0001  0010  0101  1010 Designability = 2500 Two classes of connections: • fully conserved connections • Correspond to a subnetwork module that is necessary to encode the disignable, stable phenotype. • variable connections • Control the transient dynamical flow. Network with fully conserved connections

12. Case 2: (2 3 5 9 10) (0001  0010  0100  1000  1001) Designability = 250

13. Designability is independent of robustness Robustness of a phenotype is measured by the number of transient states that flow toward the stable phenotype.

14. Mutational buffering: The incorporation of a fourth node bearing specific connections to a set of genetically distinct three-node networks would trigger the three-node networks to acquire the same dynamical phenotype, despite possessing differing dynamical phenotypes as isolated three-node systems. A scaffold refers to a fixed manner by which a fourth node interacts with a three-node subnetwork. Buffering strength reports the ratio of designability of a dynamical phenotype observed on three-node subnetworks attached via scaffold to a fourth node, to that phenotype’s designability on isolated three-node networks.

15. An example of mutational buffer Buffering strength = 11 Scaffold

16. Summary • A small fraction of dynamical phenotypes possesses atypically high designabilities. • Highly designable dynamical phenotypes arise via the presence of a core of fully conserved network links. • No correlation exists between the stability of a dynamical phenotype and its designability. • Identification of mutational buffers, which act to suppress phenotypic variation through specific dynamical relationships to other genes.