Dynamics of Cellular Networks
Networks of cells form tissues and organs, where aggregations of cells operate as systems. It is similar to how single cells function as systems of protein networks, where, for example, ion channel currents of a single cell are integrated to produce a whole cell membrane potential. A cell in a network may behave differently from what it does alone. Dynamics of a single cell affect to those of others and vice versa, that is, cells interact with each other. Interactions are made by different mechanisms. Cardiac cells forming a cardiac tissues and heart interact electro-chemically through cell-to-cell connections called gap junctions, by which an action potential generated at the sino-atrial node conducts through the heart, allowing coordinated muscle contractions from the atrium to the ventricle. They interact also mechanically because every cell contracts mechanically to produce heart beats. Neuronal cells in the nervous system interact via chemical synapses, by which neuronal networks exhibit spatio-temporal spiking dynamics, representing neural information. In a neuronal network in charge of movement control of a musculo-skeletal system, such spatio-temporal dynamics directly correspond to coordinated contractions of a number of skeletal muscles so that a desired motion of limbs can be performed. This chapter illustrates several mathematical techniques through examples from modeling of cellular networks.