Systems of mutually-triggering event generators: Basic properties and functions in information transmission and rhythm generation

1. Linkages of multiple distinct event generators, coupled so that the firing of any one triggers the remainder, are found in many biological settings. This paper analyzes such networks under the assumption that individual event generators emit discrete events of a fixed type in a more-orless random time series. The aspects of their behavior studied herein include the frequency of network event emissions, their regularity, and their sensitivity to stimuli impinging equally on all generators. This analysis includes rhythm-generating and information-encoding functions within its purview. 2. Under specified conditions on the “ageing” properties of interevent intervals characterizing individual generators, the output frequency of such networks depends weakly on the number of more-or-less similar generators in the network. This phenomenon, termedpseudosaturation, would promote robustness of function in the face of injury or elaborational error, and is enhanced when all generators exhibit a substantial sure silent period following event emission. 3. Given certain assumptions about the manner of encoding and decoding of a single stimulus parameter, networks whose function is to encode information improve their overall signal-to-noise ratios with increasing numbers of generators. Where the properties of the generators permit pseudosaturation in output rate, this improvement comes about at a low expense of dynamic range, so that in addition to redundancy, this type of linkage offers a potentially adaptive means of channel compression. 4. The dependence of generator output on an encoded stimulus parameter may be severely distorted under mutually-triggering linkage. Conditions guaranteeing the absence of various degrees of distortion are given, and the possible selective advantage of serious distortion in respect of reducing sensitivity to extraneous influences is discussed. 5. The mutually-triggering feature in networks functioning to produce rhythmic behavior does not necessarily enhance the regularity of a rhythm, the presence of enhancement depending both upon the detailed statistical characteristics of the constituent generators, and upon the statistic used to assess “regularity”. Larger networks generally display less variation in longterm output frequency, but their instantaneous frequencies seem to be more constant only when individual generators tend to emit a substantial number of atypically long intervals, and/or exhibit sizeable post-event silent periods. 6. Various of the ideas developed are applied to two systems which have been studied experimentally. Mutual triggering between different spikeinitiating zones in the lateral-line afferents ofXenopus laevis can not at present be shown to improve signal-to-noise ratio, sensitivity, or robustness — its function remains unknown. The published statistical properties of isolated marginal-ganglion oscillators in scyphomedusae would permit, in the absence of influences other than mutual triggering, both increases in robustness and in rhythm regularity. Experiments are suggested to determine the nature of additional influences known to exist.