Transitions to slow or fast diffusions provide a general property for in-phase or anti-phase polarity in a cell.

Cell polarity is an important cellular process that cells use for various cellular functions such as asymmetric division, cell migration, and directionality determination. In asymmetric cell division, a mother cell creates multiple polarities of various proteins simultaneously within her membrane and cytosol to generate two different daughter cells. The formation of multiple polarities in asymmetric cell division has been found to be controlled via the regulatory system by upstream polarity of the membrane to downstream polarity of the cytosol, which is involved in not only polarity establishment but also polarity positioning. However, the mechanism for polarity positioning remains unclear. In this study, we found a general mechanism and mathematical structure for the multiple streams of polarities to determine their relative position via conceptional models based on the biological example of the asymmetric cell division process of C. elegans embryo. Using conceptional modeling and model reductions, we show that the positional relation of polarities is determined by a contrasting role of regulation by upstream polarity proteins on the transition process of diffusion dynamics of downstream proteins. We analytically prove that our findings hold under the general mathematical conditions, suggesting that the mechanism of relative position between upstream and downstream dynamics could be understood without depending on a specific type of bio-chemical reaction, and it could be the universal mechanism in multiple streams of polarity dynamics of the cell.

Modelling Aedes aegypti mosquito control via transgenic and sterile insect techniques: endemics and emerging outbreaks.

The invasion of pest insects often changes or destroys a native ecosystem, and can result in food shortages and disease endemics. Issues such as the environmental effects of chemical control methods, the economic burden of maintaining control strategies and the risk of pest resistance still remain, and mosquito-borne diseases such as malaria and dengue fever prevail in many countries, infecting over 100 million worldwide in 2010. One environmentally friendly method for mosquito control is the Sterile Insect Technique (SIT). This species-specific method of insect control relies on the mass rearing, sterilization and release of large numbers of sterile insects. An alternative transgenic method is the Release of Insects carrying a Dominant Lethal (RIDL). Our objective is to consider contrasting control strategies for two invasive scenarios via SIT and RIDL: an endemic case and an emerging outbreak. We investigate how the release rate and size of release region influence both the potential for control success and the resources needed to achieve it, under a range of conditions and control strategies, and we discuss advantageous strategies with respect to reducing the release resources and strategy costs (in terms of control mosquito numbers) required to achieve complete eradication of wild-type mosquitoes.

The dynamics of Turing patterns for morphogen-regulated growing domains with cellular response delays.

Since its conception in 1952, the Turing paradigm for pattern formation has been the subject of numerous theoretical investigations. Experimentally, this mechanism was first demonstrated in chemical reactions over 20 years ago and, more recently, several examples of biological self-organisation have also been implicated as Turing systems. One criticism of the Turing model is its lack of robustness, not only with respect to fluctuations in the initial conditions, but also with respect to the inclusion of delays in critical feedback processes such as gene expression. In this work we investigate the possibilities for Turing patterns on growing domains where the morphogens additionally regulate domain growth, incorporating delays in the feedback between signalling and domain growth, as well as gene expression. We present results for the proto-typical Schnakenberg and Gierer-Meinhardt systems: exploring the dynamics of these systems suggests a reconsideration of the basic Turing mechanism for pattern formation on morphogen-regulated growing domains as well as highlighting when feedback delays on domain growth are important for pattern formation.

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.

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.