Quantifying the relative contributions of divisive and subtractive feedback to rhythm generation.
PLoS Computational Biology
Public Library of Science
This is the final version of the article. Available from PLoS via the DOI in this record.
Biological systems are characterized by a high number of interacting components. Determining the role of each component is difficult, addressed here in the context of biological oscillations. Rhythmic behavior can result from the interplay of positive feedback that promotes bistability between high and low activity, and slow negative feedback that switches the system between the high and low activity states. Many biological oscillators include two types of negative feedback processes: divisive (decreases the gain of the positive feedback loop) and subtractive (increases the input threshold) that both contribute to slowly move the system between the high- and low-activity states. Can we determine the relative contribution of each type of negative feedback process to the rhythmic activity? Does one dominate? Do they control the active and silent phase equally? To answer these questions we use a neural network model with excitatory coupling, regulated by synaptic depression (divisive) and cellular adaptation (subtractive feedback). We first attempt to apply standard experimental methodologies: either passive observation to correlate the variations of a variable of interest to system behavior, or deletion of a component to establish whether a component is critical for the system. We find that these two strategies can lead to contradictory conclusions, and at best their interpretive power is limited. We instead develop a computational measure of the contribution of a process, by evaluating the sensitivity of the active (high activity) and silent (low activity) phase durations to the time constant of the process. The measure shows that both processes control the active phase, in proportion to their speed and relative weight. However, only the subtractive process plays a major role in setting the duration of the silent phase. This computational method can be used to analyze the role of negative feedback processes in a wide range of biological rhythms.
This work is supported by National Institutes of Health (NIH) grant DK043200 (JT, RB). JR values the hospitality and resources provided by the Laboratory of Biological Modeling, NIDDK-IR, on the NIH campus. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Research Support, N.I.H., Extramural
PLoS Computational Biology, 2011, Vol. 7 (4): e1001124
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