Rotating spiral waves belong to the most prominent structures emerging in nonequilibrium systems by spatio-temporal selforganization. We present an overview of the properties of such waves m several biological excitable media and their chemical models, focusing on the dynamical behavior of the spiral tip with and without eternally imposed constraints.

Wave patterns in the Belousov-Zhabotinsky reaction exhibit many generic features of structure formation m excitable media. In this chemical system detailed investigations of rigidly rotating spirals as well as compound (meandering) and more complex spiral tip motions were carried out. Different types of motion, which are normally determined by the intrinsic properties of the system, were studied also in a photosensitive preparation of this reaction under the influence of an external forcing signal By using a thin laser beam, meandering spirals can be anchored to rigid rotation around an artificial core, or multi-armed spirals can be readily produced. Under global illumination of the whole sample dish, the effect of a sequence of short light impulses on a meandering spiral was studied by following the trajectory of the spiral tip with computerized video techniques. Each stimulus is applied at the moment that corresponds to the passage of the wave front through an arbitrarily chosen measuring point of the excitable medium. We show that the introduction of such a feedback results in the occurrence of spatial attractors in the vicinity of the measuring point, towards which the spiral tips move asymptotically. This offers a convenient method to preselect the spiral location.

Recent investigations of rotating spirals in biological media include the following: (1) Spiral waves of the signal transmitter cyclic AMP induce chemotactic motion of amoebae in the slime mold Dictyostelium discoideum that finally leads to an aggregation of cells m the spiral core. The circular wave motion and its chemotactic response are maintained m the anterior portion of the slug that grows out of the aggregation center. (2) Spiral wave dynamics m the phenomenon of Spreading Depuresssion was analyzed in the retina of chicken. The tip moves on a remarkably complex trajectory consisting of many "Z-type" loops, apparently a characteristic feature for excitable neuronal tissue. (3) Proton and NADH waves have been discovered in the extracted cytoplasm of yeast cells. All these spiral examples are discussed in terms of their common properties and specific differences.