The missing timepiece: Optimal time allocation in the work-constraint cycle of autonomous agents

Area of Science:

• Systems Biology
• Theoretical Biology
• Cell Biology

Background:

• Kauffman's work-constraint (W-C) cycle describes interdependence in living systems.
• The optimal timing and duration of W-C cycle phases remain underexplored.
• Autonomous agents must satisfy temporal constraints for survival and proliferation.

Purpose of the Study:

• To determine the optimal relative duration of work and constraint phases in autonomous agents.
• To apply an optimal stopping problem framework to biological cycles.
• To investigate the role of temporal allocation in autonomous agency.

Main Methods:

• Framing the work-constraint cycle as an optimal stopping problem.
• Analyzing the eukaryotic cell cycle (G1 as work, S/G2/M as constraint).
• Comparing theoretical predictions with empirical data from yeast and human cancer cells.

Main Results:

• The optimal duration for the work phase is predicted to be 1/e (approximately 37%) of the total cycle.
• Empirical data from proliferating cells show G1 phase durations (work phase) of 35-40%, aligning with the 1/e prediction.
• Stochastic gene expression fluctuations are proposed as a potential implicit time-tracking mechanism in cells.

Conclusions:

• Temporal allocation is a critical dimension of autonomous agency, alongside structural and thermodynamic factors.
• The 1/e proportion represents an optimal balance between energy extraction and constraint reconstruction.
• Further research is needed to validate stochastic gene expression as a cell cycle timing mechanism.