Thread by @yoginho

Network modularity: structure does not equal function. I am very proud and excited about our new paper on dynamic modules, just out in @eLife! @BertaVerd elifesciences.org/articles/42832 #evodevo

Tl;dr tweet summary follows...👇🏻

@eLife @BertaVerd Systems biology aims to understand function and evolution of complex regulatory networks. This requires hierarchical decomposition into manageable and intelligible subsystems with delimited and discernible functions (functional modules). /1

@eLife @BertaVerd Functional decomposition of complex networks usually relies on partitioning the graph representing the network into simple subgraphs. Subsystems are defined in terms of network structure/topology (structural modules). /2

@eLife @BertaVerd Subdivision of a network into structural modules relies on the assumption that context-dependence is weak, and structural modularity pronounced enough, to preserve the salient features of subnetwork behaviour in its native network context. /3

@eLife @BertaVerd Structural modularity is widely regarded as a necessary condition for the evolvability of complex networks (via network co-option, variational modularity, and minimisation off pleiotropic effects. /4

@eLife @BertaVerd Despite its success, structural modularity has some serious limitations: structure does not determine function and multi-functional networks are often not structurally modular (see this wonderful in silico screen by @_JamesSharpe and colleagues: msb.embopress.org/content/13/4/9…). /5

@eLife @BertaVerd @_JamesSharpe The gap gene system of Drosophila melanogaster is such a multi-functional network without structural modularity, generating stable expression boundaries anteriorly through multistable switches & dynamically shifting boundaries posteriorly through a damped oscillator mechanism. /6

@eLife @BertaVerd @_JamesSharpe The gap gene system and its two separate dynamical regimes (anterior switches vs. posterior damped oscillator) was described and analysed in detail in journals.plos.org/ploscompbiol/a…, and journals.plos.org/plosbiology/ar…. @PLOSCompBiol @PLOSBiology /7

@eLife @BertaVerd @_JamesSharpe @PLOSCompBiol @PLOSBiology Analysis of structural modules will miss functional modularity in networks such as the gap gene system, since the subsystems driving different dynamical regimes do not map onto separable subgraphs of the network. /8

@eLife @BertaVerd @_JamesSharpe @PLOSCompBiol @PLOSBiology Instead of an analysis of network structure, we performed a search for dynamical modules within the gap gene system. These modules are not defined as separate subgraphs, but in terms of the activity of their components and their interactions. /9

@eLife @BertaVerd @_JamesSharpe @PLOSCompBiol @PLOSBiology Dynamical modules consist of a group of connected network nodes that govern a particular dynamic behaviour. They were first introduced in the context of Boolean network models by Irons & Monk in 2007: bmcbioinformatics.biomedcentral.com/articles/10.11…. @BMC_series /10

@eLife @BertaVerd Dynamical modules are not the same as co-expression (or regulatory) modules, since the dependence of component expression patterns is casual, not correlative, and often much more complex and non-linear than a simple (anti-)correlation. /11

@eLife @BertaVerd Dynamical modules are not identified by individual expression patterns, but by the coherent collective activity of the module as a whole. /12

@eLife @BertaVerd Using a pragmatic approach based on node sensitivity analysis, we identify three dynamical modules in the gap gene system( AC/DC sub circuits 1–3) consisting of heavily overlapping sets of nodes (genes) and their interactions (see figure). /13

@eLife @BertaVerd Dynamical modules AC/DC1–3 are active in the anterior, middle, and posterior of the Drosophila embryo. Each subcircuit consists of different genes, but all of them show an identical pattern of regulatory interactions: a combination of positive and negative feedback loops. /14

@eLife @BertaVerd Each AC/DC subcircuit faithfully reproduces the behaviour of the full gap gene model in its particular region of influence. We performed a mathematical analysis of the AC/DC circuit, and simulate each specific subcircuit separately, to examine the underlying phase spaces. /15

@eLife @BertaVerd Our analysis of AC/DC circuits in the gap gene system reveals that AC/DC1 and AC/DC3 are structurally stable, producing stable boundaries in the anterior and shifting boundaries in the posterior of the embryo. In contrast, AC/DC2 is in a state of criticality in the middle. /16

@eLife @BertaVerd The AC/DC2 subcircuit in the gap gene system is critical: it straddles the bifurcation boundary that separates stable from shifting expression domains. Depending on maternal input, it will produce stable (anterior) or shifting expression behaviour (posterior of the boundary). /17

@eLife @BertaVerd Bifurcation analysis shows that the boundary between stable and shifting domains is not sensitive to maternal inputs, but crucially depends on the strength of other gap-gap cross-repressive interactions. /18

@eLife @BertaVerd Selective sensitivity of AC/DC subcircuits explains why the bifurcation boundary has changed during evolution: in Drosophila, it occurs at 52% embryo length, in the scuttle fly Megaselia abdita at 40% (as published previously in @eLife: elifesciences.org/articles/04785). /19

@eLife @BertaVerd In addition, analysis of the AC/DC circuit shows that it can not only produce stable boundaries through switches, and shifting boundaries through damped oscillations, but also stable oscillations as seen in short-germband segmentation (e.g. in the flour beetle Tribolium). /20

@eLife @BertaVerd Our analysis suggests that a few subtle changes in gene interactions downstream of maternal morphogen gradients can lead to large and unexpected changes in expression dynamics, which reflect the different modes of segmentation observed in different insect lineages. /21

@eLife @BertaVerd More generally, we show how dynamical modularity can contribute to differential evolvability of gene expression features through subcircuits being either stable or in a state of criticality. Thus, complex networks can function and evolve without any structural modularity! /22