Measuring Time with Minimal Clocks

TL;DR

This paper explores minimal abstract clock models in biology, analyzing their dynamics and optimal configurations, revealing diverse behaviors like oscillations and decay, and examining complex clock systems such as cascades and composite clocks.

Contribution

It introduces a formal framework for minimal pure clocks, investigates their dynamics, and characterizes different optimal and complex clock configurations in biological systems.

Findings

Oscillatory behavior for local time measurement

Decay-based clocks for global time periods

Complex clock systems exhibit diverse dynamic regimes

Abstract

Being able to measure time, whether directly or indirectly, is a significant advantage for an organism. It allows for the timely reaction to regular or predicted events, reducing the pressure for fast processing of sensory input. Thus, clocks are ubiquitous in biology. In the present paper, we consider minimal abstract pure clocks in different configurations and investigate their characteristic dynamics. We are especially interested in optimally time-resolving clocks. Among these, we find fundamentally diametral clock characteristics, such as oscillatory behavior for purely local time measurement or decay-based clocks measuring time periods of a scale global to the problem. We include also sets of independent clocks ("clock bags"), sequential cascades of clocks and composite clocks with controlled dependency. Clock cascades show a "condensation effect" and the composite clock shows various regimes of markedly different dynamics.