Title: Interplay of synergy and redundancy in diamond motif,
Abstract: The formalism of partial information decomposition provides independent or
non-overlapping components constituting total information content provided by a
set of source variables about the target variable. These components are
recognised as unique information, synergistic information and, redundant
information. The metric of net synergy, conceived as the difference between
synergistic and redundant information, is capable of detecting synergy,
redundancy and, information independence among stochastic variables. And it can
be quantified, as it is done here, using appropriate combinations of different
Shannon mutual information terms. Utilisation of such a metric in network
motifs with the nodes representing different biochemical species, involved in
information sharing, uncovers rich store for interesting results. In the
current study, we make use of this formalism to obtain a comprehensive
understanding of the relative information processing mechanism in a diamond
motif and two of its sub-motifs namely bifurcation and integration motif
embedded within the diamond motif. The emerging patterns of synergy and
redundancy and their effective contribution towards ensuring high fidelity
information transmission are duly compared in the sub-motifs and independent
motifs (bifurcation and integration). In this context, the crucial roles played
by various time scales and activation coefficients in the network topologies
are especially emphasised. We show that the origin of synergy and redundancy in
information transmission can be physically justified by decomposing diamond
motif into bifurcation and integration motif.