Understanding the temperature response of biological systems: Part I -- Phenomenological descriptions and microscopic models

TL;DR

The paper addresses how temperature modulates biological rates across scales and why many rate–temperature relationships deviate from simple Arrhenius behavior. It systematically reviews two classes of approaches: phenomenological (three- to four-parameter) temperature-response models that describe $r(T)$ and thermal performance curves, and microscopic single-reaction theories (e.g., Eyring, Kramers, enzyme-stability models) that explain temperature dependence from physical principles. A key contribution is organizing models by description level, highlighting that three-parameter phenomenological forms can capture common curve shapes and defining operational quantities such as $r_{ ext{o}}$, $T_{ ext{o}}$, and $W$, with discussions of a universal temperature-response form $r(T)= r_{ ext{o}} \, ext{exp}ig((T-T_{ ext{o}})/W_{ ext{U}}ig)ig[1-(T-T_{ ext{o}})/W_{ ext{U}}ig]$ where $W_{ ext{U}}=T_{ ext{max}}-T_{ ext{o}}$. The review clarifies the strengths and limitations of each class and sets up Part II to connect these local, mechanistic descriptions to system-wide, network-level dynamics. Overall, it provides a cohesive framework for comparing temperature dependences across biological scales and for guiding future mechanistic and predictive modeling under environmental change.

Abstract

Virtually every biological rate depends on temperature, yet the resulting rate-temperature relationships often deviate strongly from simple Arrhenius behavior. In this first part of a two-part review, we survey empirical and phenomenological models used to describe biological temperature responses across scales, from enzymatic reactions to organismal performance. We discuss common functional forms, including symmetric and asymmetric thermal performance curves and extensions of the Arrhenius law, and we highlight how these models define operational quantities such as optimal temperatures, thermal breadths, and thermal limits. In Part II of this review, we will discuss how system-level temperature response curves emerge from the interaction of many underlying reactions.

Figures (2)

• Figure 1: Temperature influences biological systems across scales and can be described using different classes of models. (A) Temperature acts from the level of particles and biochemical reactions to organisms and ecosystems. (B) Examples of empirical rate–temperature relationships: growth rates of a M. aeruginosa cyanobacteria colony kruger1978effect and cleavage rates during early development of D. rerio zebrafish embryos rombouts2025. Both exhibit strong, nonlinear temperature dependence. (C) Conceptual illustration of Arrhenius and non-Arrhenius behavior. In an Arrhenius plot (log rate versus $1/T$), simple reactions follow a straight line, whereas biological processes typically show curvature, an optimum temperature $T_{\mathrm{o}}$, a maximal rate $r_{\mathrm{o}}$, and thermal limits ($T_{\min}, T_{\max}$). (D) Overview of modeling frameworks used to describe temperature responses, organized by level of description. Phenomenological models provide empirical fits to observed rate–temperature curves, while microscopic models derive rate–temperature relationships from reaction-level kinetics. At a higher level, network-level models—either deterministic or stochastic—capture how temperature affects coupled biochemical or regulatory systems. The phenomenological and microscopic approaches form the focus of Part I Jacobs_review_pI, whereas deterministic and stochastic network models are the focus of Part II Jacobs_review_pII. All four approaches are illustrated by fitting the same zebrafish cleavage-timing dataset rombouts2025, demonstrating how distinct model classes can reproduce the characteristic non-Arrhenius shape of biological temperature–response curves.
• Figure 2: Phenomenological and microscopic models of temperature responses.(Top) Common phenomenological approaches for fitting rate–temperature curves, including symmetric models, asymmetric models with distinct cold and warm widths, and extensions of the Arrhenius law that incorporate optimal temperatures and upper/lower limits. (Bottom) Schematic overview of key microscopic reaction–level theories: transition-state formulations such as Arrhenius and Eyring equations, Kramers’ barrier-crossing dynamics, and enzyme-catalyzed reactions with temperature-dependent active fractions.