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2006-4-26
Highly designable phenotypes and mutational buffers emerge
from a systematic mapping between network topology and
dynamic output
Nochomovitz & Li
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The idea• Map network topologies to dynamical phenotypes
The designability of a phenotype is defined as the number of topologies mapped onto it.
Designability = 2
Designability = 1
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Dynamic phenotype
Network topology
A 5-cycle phenotype(0001 0010 1001 0111 1010)
A limit cycle passing through a specific series of states or a particular fixed point.
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Updating rules
Rule 1:
Rule 2:
The time scales of the decay process and the activating or inhibitory processes are of equal order.
The decay process occurs on a much slower time scale than the activating or inhibitory processes.
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Phenotypes that are neither excessively rare nor excessively simple
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Comparison of the two
rules
Under both rules, the strong, intermediate, and weakly designable phenotypes emerge consistently.
2
22
ˆ( )
( )
i ii
ii
y yR
y y
y
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Designing larger cycles is exponentially hard.
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Designability spectrum of 4-cycles for 4-node networks
Mean designability of 4-cycles
0001 0010 0101 0011
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Designability spectrum of 5-cycles for 4-node networks
Mean designability of 5-cycles
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Designability spectrum of 6-cycles for 4-node networks
Mean designability of 4-cycles
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What are the dynamical features of highly designable dynamical phenotypes?
Case 1: (2 3 6 11)
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
0001 0010 0101 1010
Designability = 2500
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Case 2: (2 3 5 9 10)
(0001 0010 0100 1000 1001)
Designability = 250
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Designability is independent of robustness
Robustness of a phenotype is measured by the number of transient states that flow toward the stable phenotype.
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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.
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An example of mutational buffer
Buffering strength = 11
Scaffold
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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.