A wealth of phenomena, spanning over many orders of magnitude, arise from non-equilibrium conditions. Calcium oscillation in fertilized mammalian egg cells, wave patterns during the aggregation of slime mould, electrical vortices in a fibrillating heart, ripples on sand dunes, and the stripped patterns on Jupiter are just a few examples. In chemistry, periodic temporal and/or spatial variations in concentration may develop far from thermodynamic equilibrium leading to oscillations, stationary patterns, waves and standing waves, or even chaotic behaviour. Networks of biochemical reactions coupled with transport enable dynamic responses and self-organisation in biology. My research takes a systems approach for the design of complex chemical systems displaying such behaviours.
Enzymes catalysing metabolic processes are essential to life. Their specificity and ability to operate at benign conditions make them ideal for a wide range of applications. The non-linear pH-dependence of enzyme activity allows enzymes to be utilized in designing systems exhibiting periodic spatio-temporal concentration variations, bistable switching behaviour or supporting fronts. Such systems can serve as basis for building drug delivery devices, cure-on-demand tissue scaffolding, biocompatible self-organizing active materials, etc.
Propagating pH front in the urea–urease system (left half). The sharp increase in pH triggers hydrogel formation (visualized as circular dark bands in shadowgraphs, right half).
Studying reactions in 3D requires imaging the distribution of key species in space. One way of achieving this is by optical tomography, a technique similar to the medical imaging procedure X-ray computed tomography. As opposed to X-rays, optical tomography uses visible light to scan the sample by taking photographs of a rotating reaction vessel. The 3D distribution of the key species is then reconstructed by computing the inverse Radon transform on the snapshots gathered within a full rotation.
Stationary patterns emerging in the Belousov–Zhabotinsky reaction. Imaging the spatio–temporal dynamics of the BZ reaction requires monitoring only the concentration of the catalyst, often ferroin.
Optical tomography has been successfully utilised to study the complex behaviour of propagating waves and their organizing centres [3-8], stationary patterns  as well as standing waves .
Alan M. Turing – mathematician, pioneer of computer science, war hero code-breaker – in the early 1950’s proposed a mechanism for pattern formation in living systems (Philos. T. Roy. Soc. B 237, 37). During the early stage of embryonic development - he argued - interacting chemicals diffusing through a tissue may be adequate to generate non-uniform spatial distributions of the chemicals which serve as a template for subsequent development (pigmentation in animal skin, for instance). The first evidence to support his theory came from chemistry in 1990 (Phys. Rev. Lett., 64, 2953) when self-sustained, spatially periodic, stationary patterns were observed in a gel membrane.
Schematic design of a Continuously Fed Unstirred Reactor and stationary patterns formed in the gel membrane in the Chlorite Dioxide-Iodide-Malonic acid reaction.
A great deal of the features of these striking patterns have been studied in the biological and chemical context over the years. Experiments have successfully linked the Turing mechanism to the growth of feathers and hair follicles, branching pattern of lungs and digit formation in developing mouse paw (Science, 338, 1406); and proved in the BZ reaction  that it can even create complex three dimensional stationary patterns. Yet there is still more to be discovered and understood: interactions between the Turing and other types of instabilities, Turing patterns exploited as templates to create materials, and applying the principle to other dynamic systems like dry-lands are just a few among the possible directions.
3D stationary patterns in the BZ-AOT reaction: spots, cylinders, zig-zagging cylinders, lamellae, pipe, half-pipe, and labyrinthine. Similar concentration profiles of signaling molecules that control cell differentiation may be present during early embryonic development.