Abstract
BackgroundNetwork motifs are recurrent interaction patterns, which are significantly more often encountered in biological interaction graphs than expected from random nets. Their existence raises questions concerning their emergence and functional capacities. In this context, it has been shown that feed forward loops (FFL) composed of three genes are capable of processing external signals by responding in a very specific, robust manner, either accelerating or delaying responses. Early studies suggested a one-to-one mapping between topology and dynamics but such view has been repeatedly questioned. The FFL's function has been attributed to this specific response. A general response analysis is difficult, because one is dealing with the dynamical trajectory of a system towards a new regime in response to external signals.ResultsWe have developed an analytical method that allows us to systematically explore the patterns and probabilities of the emergence for a specific dynamical response. The method is based on a rather simple, but powerful geometrical analysis of the system's nullclines complemented by an appropriate formalization of the response probability.ConclusionOur analysis allows to determine unambiguously the relationship between motif topology and the set of potentially implementable functions. The distribution probability distributions are linked to the degree of specialization or flexibility of the given network topology. The implications for the emergence of different motif topologies in complex networks are outlined.
Highlights
Network motifs are recurrent interaction patterns, which are significantly more often encountered in biological interaction graphs than expected from random nets
The distribution probability distributions are linked to the degree of specialization or flexibility of the given network topology
In figure (1) we show an schematic representation of the feed forward loops (FFL), depicting three genes GX, GY and GZ, with regulatory interactions among each other via their corresponding proteins X, Y and Z
Summary
Network motifs are recurrent interaction patterns, which are significantly more often encountered in biological interaction graphs than expected from random nets. Their existence raises questions concerning their emergence and functional capacities. In this context, it has been shown that feed forward loops (FFL) composed of three genes are capable of processing external signals by responding in a very specific, robust manner, either accelerating or delaying responses. Simple switches and oscillators have been shown to map to the core processes of biological decision-making, implemented by two- or three-gene network motifs and characterized by their behaviour around the systems' fixed points [17,18,19,20,21,22]. It is reasonable to think that the system's steady state is of interest, and the (page number not for citation purposes)
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