Modularity, criticality, and evolvability of a developmental gene regulatory network

The existence of discrete phenotypic traits suggests that the complex regulatory processes which produce them are functionally modular. These processes are usually represented by networks. Only modular networks can be partitioned into intelligible subcircuits able to evolve relatively independently. Traditionally, functional modularity is approximated by detection of modularity in network structure. However, the correlation between structure and function is loose. Many regulatory networks exhibit modular behaviour without structural modularity. Here we partition an experimentally tractable regulatory network—the gap gene system of dipteran insects—using an alternative approach. We show that this system, although not structurally modular, is composed of dynamical modules driving different aspects of whole-network behaviour. All these subcircuits share the same regulatory structure, but differ in components and sensitivity to regulatory interactions. Some subcircuits are in a state of criticality, while others are not, which explains the observed differential evolvability of the various expression features in the system

A theoretical analysis of how plant growth is limited by carbon allocation strategies and respiration

Improving crop yield is essential to meet increasing global food demands. Boosting crop yield requires the coordination of carbon acquisition by leaves and carbon utilization by roots and seeds. Simple modelling approaches may be used to explain how this coordination is achieved within plant growth. Here, the limits to allocation strategies and the influence of maintenance costs are explored by analysing the sensitivity of a simple root–shoot carbon allocation model for vegetative and reproductive growth. The model is formulated based on fundamental constraints on plant growth and therefore can be applied to all plants. This general but quantitative approach shows that the relative costs of root and leaf respiration alter the relationship between carbon allocation and final plant size, enabling a range of allocation strategies to produce a similar total amount of plant material during vegetative growth. This plasticity is enhanced by increasing assimilation rate within the model. Results show that high leaf allocation during vegetative growth promotes early reproduction with respect to yield. Having higher respiration in leaves than roots delays the optimal age to reproduce for plants with high leaf allocation during vegetative growth and increases the restrictions on flowering time for plants with high root allocation during vegetative growth. It is shown that, when leaf respiration is higher than root respiration, reallocating carbon towards the roots can increase the total amount of plant material. This analysis indicates that crop improvement strategies should consider the effects of maintenance costs on growth, a previously under-appreciated mechanism for yield enhancement

Anteroposterior patterning of the zebrafish ear through Fgf- and Hh-dependent regulation of hmx3a expression

In the zebrafish, Fgf and Hh signalling assign anterior and posterior identity, respectively, to the poles of the developing ear. Mis-expression of fgf3 or inhibition of Hh signalling results in double-anterior ears, including ectopic expression of hmx3a. To understand how this double-anterior pattern is established, we characterised transcriptional responses in Fgf gain-of-signalling or Hh loss-of-signalling backgrounds. Mis-expression of fgf3 resulted in rapid expansion of anterior otic markers, refining over time to give the duplicated pattern. Response to Hh inhibition was very different: initial anteroposterior asymmetry was retained, with de novo duplicate expression domains appearing later. We show that Hmx3a is required for normal anterior otic patterning, and that otic patterning defects in hmx3a-/- mutants are a close phenocopy to those seen in fgf3-/- mutants. However, neither loss nor gain of hmx3a function was sufficient to generate full ear duplications. Using our data to infer a transcriptional regulatory network required for acquisition of otic anterior identity, we can recapitulate both the wild-type and the double-anterior pattern in a mathematical model

Gene expression time delays & Turing pattern formation systems

The incorporation of time delays can greatly affect the behaviour of partial differential equations and dynamical systems. In addition, there is evidence that time delays in gene expression due to transcription and translation play an important role in the dynamics of cellular systems. In this paper, we investigate the effects of incorporating gene expression time delays into a one-dimensional putative reaction diffusion pattern formation mechanism on both stationary domains and domains with spatially uniform exponential growth. While oscillatory behaviour is rare, we find that the time taken to initiate and stabilise patterns increases dramatically as the time delay is increased. In addition, we observe that on rapidly growing domains the time delay can induce a failure of the Turing instability which cannot be predicted by a naive linear analysis of the underlying equations about the homogeneous steady state. The dramatic lag in the induction of patterning, or even its complete absence on occasions, highlights the importance of considering explicit gene expression time delays in models for cellular reaction diffusion patterning

Algebraic structures in the light of the implicate order

SIGLEAvailable from British Library Document Supply Centre-DSC:DX207662 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

A Mutual Support Mechanism through Intercellular Movement of CAPRICE and GLABRA3 Can Pattern the Arabidopsis Root Epidermis

The patterning of the Arabidopsis root epidermis depends on a genetic regulatory network that operates both within and between cells. Genetic studies have identified a number of key components of this network, but a clear picture of the functional logic of the network is lacking. Here, we integrate existing genetic and biochemical data in a mathematical model that allows us to explore both the sufficiency of known network interactions and the extent to which additional assumptions about the model can account for wild-type and mutant data. Our model shows that an existing hypothesis concerning the autoregulation of WEREWOLF does not account fully for the expression patterns of components of the network. We confirm the lack of WEREWOLF autoregulation experimentally in transgenic plants. Rather, our modelling suggests that patterning depends on the movement of the CAPRICE and GLABRA3 transcriptional regulators between epidermal cells. Our combined modelling and experimental studies show that WEREWOLF autoregulation does not contribute to the initial patterning of epidermal cell fates in the Arabidopsis seedling root. In contrast to a patterning mechanism relying on local activation, we propose a mechanism based on lateral inhibition with feedback. The active intercellular movements of proteins that are central to our model underlie a mechanism for pattern formation in planar groups of cells that is centred on the mutual support of two cell fates rather than on local activation and lateral inhibition