The influence of gene expression time delays on Gierer-Meinhardt pattern formation systems

There are numerous examples of morphogen gradients controlling long range signalling in developmental and cellular systems. The prospect of two such interacting morphogens instigating long range self-organisation in biological systems via a Turing bifurcation has been explored, postulated, or implicated in the context of numerous developmental processes. However, modelling investigations of cellular systems typically neglect the influence of gene expression on such dynamics, even though transcription and translation are observed to be important in morphogenetic systems. In particular, the influence of gene expression on a large class of Turing bifurcation models, namely those with pure kinetics such as the Gierer–Meinhardt system, is unexplored. Our investigations demonstrate that the behaviour of the Gierer–Meinhardt model profoundly changes on the inclusion of gene expression dynamics and is sensitive to the sub-cellular details of gene expression. Features such as concentration blow up, morphogen oscillations and radical sensitivities to the duration of gene expression are observed and, at best, severely restrict the possible parameter spaces for feasible biological behaviour. These results also indicate that the behaviour of Turing pattern formation systems on the inclusion of gene expression time delays may provide a means of distinguishing between possible forms of interaction kinetics. Finally, this study also emphasises that sub-cellular and gene expression dynamics should not be simply neglected in models of long range biological pattern formation via morphogens

Aberrant behaviours of reaction diffusion self-organisation models on growing domains in the presence of gene expression time delays

Turing’s pattern formation mechanism exhibits sensitivity to the details of the initial conditions suggesting that, in isolation, it cannot robustly generate pattern within noisy biological environments. Nonetheless, secondary aspects of developmental self-organisation, such as a growing domain, have been shown to ameliorate this aberrant model behaviour. Furthermore, while in-situ hybridisation reveals the presence of gene expression in developmental processes, the influence of such dynamics on Turing’s model has received limited attention. Here, we novelly focus on the Gierer–Meinhardt reaction diffusion system considering delays due the time taken for gene expression, while incorporating a number of different domain growth profiles to further explore the influence and interplay of domain growth and gene expression on Turing’s mechanism. We find extensive pathological model behaviour, exhibiting one or more of the following: temporal oscillations with no spatial structure, a failure of the Turing instability and an extreme sensitivity to the initial conditions, the growth profile and the duration of gene expression. This deviant behaviour is even more severe than observed in previous studies of Schnakenberg kinetics on exponentially growing domains in the presence of gene expression (Gaffney and Monk in Bull. Math. Biol. 68:99–130, 2006). Our results emphasise that gene expression dynamics induce unrealistic behaviour in Turing’s model for multiple choices of kinetics and thus such aberrant modelling predictions are likely to be generic. They also highlight that domain growth can no longer ameliorate the excessive sensitivity of Turing’s mechanism in the presence of gene expression time delays. The above, extensive, pathologies suggest that, in the presence of gene expression, Turing’s mechanism would generally require a novel and extensive secondary mechanism to control reaction diffusion patterning

A Novel Transforming Growth Factor-β Receptor-interacting Protein That Is Also a Light Chain of the Motor Protein Dynein

The phosphorylated, activated cytoplasmic domains of the transforming growth factor-β (TGFβ) receptors were used as probes to screen an expression library that was prepared from a highly TGFβ-responsive intestinal epithelial cell line. One of the TGFβ receptor-interacting proteins isolated was identified to be the mammalian homologue of the LC7 family (mLC7) of dynein light chains (DLCs). This 11-kDa cytoplasmic protein interacts with the TGFβ receptor complex intracellularly and is phosphorylated on serine residues after ligand-receptor engagement. Forced expression of mLC7-1 induces specific TGFβ responses, including an activation of Jun N-terminal kinase (JNK), a phosphorylation of c-Jun, and an inhibition of cell growth. Furthermore, TGFβ induces the recruitment of mLC7-1 to the intermediate chain of dynein. A kinase-deficient form of TGFβ RII prevents both mLC7-1 phosphorylation and interaction with the dynein intermediate chain (DIC). This is the first demonstration of a link between cytoplasmic dynein and a natural growth inhibitory cytokine. Furthermore, our results suggest that TGFβ pathway components may use a motor protein light chain as a receptor for the recruitment and transport of specific cargo along microtublules