# Cumulative dose responses for adapting biological systems

## TL;DR

This paper introduces a new way to study biological adaptation by analyzing cumulative dose responses over time, revealing insights into how systems adapt to inputs.

## Contribution

The paper introduces the concept of cumulative dose response (cDR) and shows that only negative integral feedback motifs can produce non-monotonic cDRs.

## Key findings

- Incoherent feedforward loop motifs yield monotonic cDRs and are inconsistent with experimental data.
- Negative integral feedback motifs can produce non-monotonic cDRs, aligning with observed cytokine accumulation.
- Cumulative dose response provides a new framework for analyzing adaptation in biological systems.

## Abstract

Physiological adaptation is a fundamental property of biological systems across all levels of organization, ensuring survival and proper function. Adaptation is typically formulated as an asymptotic property of the dose response (DR), defined as the level of a response variable with respect to an input parameter. In pharmacology, the input could be a drug concentration; in immunology, it might correspond to an antigen level. In contrast to the DR, this paper develops the concept of a transient, finite-time, cumulative dose response (cDR), which is obtained by integrating the response variable over a fixed time interval and viewing that integral—area under the curve—as a function of the input parameter. This study is motivated by experimental observations of cytokine accumulation under T-cell stimulation, which exhibit a non-monotonic cDR. It is known from the systems biology literature that only two types of network motifs, incoherent feedforward loops and negative integral feedback (IFB) mechanisms, can generate adaptation. Three paradigmatic such motifs—two types of incoherent loops and one integral feedback—have been the focus of much study. Surprisingly, it is shown here that these two incoherent feedforward loop motifs—despite their capacity for non-monotonic DR—always yield a monotonic cDR, and are therefore inconsistent with these experimental data. On the other hand, this work reveals that the IFB motif is indeed capable of producing a non-monotonic cDR, and is thus consistent with these data.