Control of pattern formation in excitable systems

Pattern formation embodies the beauty and complexity of nature. Some patterns like traveling and rotating waves are dynamic, while others such as dots and stripes are static. Both dynamic and static patterns have been observed in a variety of physiological and biological processes such as rotating action potential waves in the brain during sleep, traveling calcium waves in the cardiac muscle, static patterns on the skins of animals, and self-regulated patterns in the animal embryo. Excitable systems represent a class of ultrasensitive systems that are capable of generating different kinds of patterns depending on the interplay between activator and inhibitor dynamics. Through manipulation of different excitable parameters, a diverse array of traveling wave and standing wave patterns can be obtained. In this thesis, I use pattern formation theory to control the excitable systems involved in cell migration and neuroscience to alter the observed phenotype, in an attempt to affect the underlying biological process. Cell migration is critical in many processes such as cancer metastasis and wound healing. Cells move by extending periodic protrusions of their cortex, and recent years have shown that the cellular cortex is an excitable medium where waves of biochemical species organize the cellular protrusion. Altering the protrusive phenotype can drastically alter cell migration — that can potentially affect critical physiological processes. In the first part of this thesis, I use excitable wave theory to model and predict wave pattern changes in amoeboid cells. Using theories of pattern formation, key nodes of the underlying excitable network governing cell migration are altered — to drastically change the cellular migratory phenotype, moving from amoeboid cells to oscillatory cells and from cells that extend long finger-like protrusions to cells that sustain stable rings on the cortex, potentially uncovering a novel method of pattern formation. Excitable systems originated in neuroscience, where different patterns of activity reflect different brain states. Sleep is associated with slow waves, while repeated high-frequency waves are associated with epileptic seizures. These patterns arise from the interplay between the cerebral cortex and the thalamus, which form a closed-loop architecture. In the second part of this thesis, I use a three-layer two-dimensional thalamocortical model, to explore the different parameters that may influence different spatio-temporal dynamics on the cortex. This study reveals that inter- and intra-cortical connectivity, excitation-inhibition balance and synaptic strengths can influence the wave activity patterns, to recreate different dynamic patterns observed in different brain states