Abstract
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.
Highlights
Biological systems involve a large number of components that interact nonlinearly to produce complex behaviors
We develop a new strategy based on the idea that if a negative feedback process contributes significantly to episode termination, increasing its time constant should significantly increase episode duration
We use a mean field model of rhythmic activity in an excitatory neural network regulated by both synaptic depression and cellular adaptation, defined by Eqs. 1–3, to generate synthetic data
Summary
Biological systems involve a large number of components that interact nonlinearly to produce complex behaviors. In the context of an excitatory network, synaptic depression (weakening of synaptic connections between neurons) is a divisive feedback (decreasing the slope of the network input/output function) while activation of a cellular adaptation process (decreasing the neurons’ excitability) can be a subtractive feedback (shifting the network input/output function) [8,9]. With both types of negative feedback in the model, we seek to determine the contribution that each makes to episode initiation and termination
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