The design principles of discrete turing patterning systems.

The formation of spatial structures lies at the heart of developmental processes. However, many of the underlying gene regulatory and biochemical processes remain poorly understood. Turing patterns constitute a main candidate to explain such processes, but they appear sensitive to fluctuations and variations in kinetic parameters, raising the question of how they may be adopted and realised in naturally evolved systems. The vast majority of mathematical studies of Turing patterns have used continuous models specified in terms of partial differential equations. Here, we complement this work by studying Turing patterns using discrete cellular automata models. We perform a large-scale study on all possible two-species networks and find the same Turing pattern producing networks as in the continuous framework. In contrast to continuous models, however, we find these Turing pattern topologies to be substantially more robust to changes in the parameters of the model. We also find that diffusion-driven instabilities are substantially weaker predictors for Turing patterns in our discrete modelling framework in comparison to the continuous case, in the sense that the presence of an instability does not guarantee a pattern emerging in simulations. We show that a more refined criterion constitutes a stronger predictor. The similarity of the results for the two modelling frameworks suggests a deeper underlying principle of Turing mechanisms in nature. Together with the larger robustness in the discrete case this suggests that Turing patterns may be more robust than previously thought.

Boolean analysis of lateral inhibition.

We study Boolean networks which are simple spatial models of the highly conserved Delta-Notch system. The models assume the inhibition of Delta in each cell by Notch in the same cell, and the activation of Notch in presence of Delta in surrounding cells. We consider fully asynchronous dynamics over undirected graphs representing the neighbour relation between cells. In this framework, one can show that all attractors are fixed points for the system, independently of the neighbour relation, for instance by using known properties of simplified versions of the models, where only one species per cell is defined. The fixed points correspond to the so-called fine-grained "patterns" that emerge in discrete and continuous modelling of lateral inhibition. We study the reachability of fixed points, giving a characterisation of the trap spaces and the basins of attraction for both the full and the simplified models. In addition, we use a characterisation of the trap spaces to investigate the robustness of patterns to perturbations. The results of this qualitative analysis can complement and guide simulation-based approaches, and serve as a basis for the investigation of more complex mechanisms.

Realizations of kinetic differential equations.

The induced kinetic differential equations of a reaction network endowed with mass action type kinetics is a system of polynomial differential equations. The problem studied here is: Given a system of polynomial differential equations, is it possible to find a network which induces these equations; in other words: is it possible to find a kinetic realization of this system of differential equations? If yes, can we find a network with some chemically relevant properties (implying also important dynamic consequences), such as reversibility, weak reversibility, zero deficiency, detailed balancing, complex balancing, mass conservation, etc.? The constructive answers presented to a series of questions of the above type are useful when fitting differential equations to datasets, or when trying to find out the dynamic behavior of the solutions of differential equations. It turns out that some of these results can be applied when trying to solve seemingly unrelated mathematical problems, like the existence of positive solutions to algebraic equations.

Network Translation and Steady-State Properties of Chemical Reaction Systems.

Network translation has recently been used to establish steady-state properties of mass action systems by corresponding the given system to a generalized one which is either dynamically or steady-state equivalent. In this work, we further use network translation to identify network structures which give rise to the well-studied property of absolute concentration robustness in the corresponding mass action systems. In addition to establishing the capacity for absolute concentration robustness, we show that network translation can often provide a method for deriving the steady-state value of the robust species. We furthermore present a MILP algorithm for the identification of translated chemical reaction networks that improves on previous approaches, allowing for easier application of the theory.

Structural simplification of chemical reaction networks in partial steady states.

We study the structural simplification of chemical reaction networks with partial steady state semantics assuming that the concentrations of some but not all species are constant. We present a simplification rule that can eliminate intermediate species that are in partial steady state, while preserving the dynamics of all other species. Our simplification rule can be applied to general reaction networks with some but few restrictions on the possible kinetic laws. We can also simplify reaction networks subject to conservation laws. We prove that our simplification rule is correct when applied to a module of a reaction network, as long as the partial steady state is assumed with respect to the complete network. Michaelis-Menten's simplification rule for enzymatic reactions falls out as a special case. We have implemented an algorithm that applies our simplification rules repeatedly and applied it to reaction networks from systems biology.

Radiological assessment of complications after laparoscopic suprabursal adjustable gastric banding for morbid obesity.

BACKGROUND: The purpose of this study was to investigate the clinical impact of radiological assessment on delivery of therapy in patients with laparoscopic adjustable gastric banding for morbid obesity who have developed gastroesophageal symptoms or have inadequate excess weight loss. METHODS: Institutional review board approval and informed consent were obtained from all patients. Suprabursal banding was performed in 373 patients who underwent 869 upper gastrointestinal series. The control group comprised 59 asymptomatic subjects from the study population with satisfactory weight loss at follow-up. RESULTS: There were no intra-operative deaths or gastric perforations. A small gastric pouch was found above the band in 13 (22.03%) of the 59 control subjects; the upper limit of the gastric pouch volume was 9.85 ml (mathematical formula for a sphere used). The main postoperative complications included: 21 of 373 (5.63%) gastric portions above the band with a mean volume of 137.98 ml and narrowed stoma of 0.99 mm; 15 of 373 (4.02%) gastric portions above the band with a mean volume of 33.27 ml and open stoma of 4.95 mm; and 16 of 373 (4.28%) tubing disconnection and displacement into the peritoneal cavity. Twenty-one of 21 narrowed-stoma and eight of 15 open-stoma gastric portions underwent repeat surgery, upward herniation of the stomach (from below the band) being found in all 29 cases. CONCLUSION: Our main findings following the use of the suprabursal approach for surgical band positioning suggest that repeat surgery may be worthwhile for all gastric upper portions >10 ml in patients with gastroesophageal symptoms or inadequate excess weight loss.