Remarks on Feedforward Circuits, Adaptation, and Pulse Memory

TL;DR

This paper analyzes feedforward circuits as models for biological adaptation, proving a convergence theorem and highlighting their inability to adapt to pulse signals due to a memory effect, with estimates of this phenomenon.

Contribution

It provides a general convergence theorem for feedforward circuits and reveals their limitation in pulse adaptation, supported by estimates of the memory effect.

Findings

Feedforward circuits achieve perfect adaptation to step signals.

They do not adapt to pulse signals due to a memory phenomenon.

The paper offers estimates of the magnitude of the memory effect.

Abstract

This note studies feedforward circuits as models for perfect adaptation to step signals in biological systems. A global convergence theorem is proved in a general framework, which includes examples from the literature as particular cases. A notable aspect of these circuits is that they do not adapt to pulse signals, because they display a memory phenomenon. Estimates are given of the magnitude of this effect.