Thermodynamic Constraints Drive Hierarchical Preemption in Cellular Decision-Making: A Hybrid Petri Net Framework with Application to Bacillus subtilis Sporulation

TL;DR

This paper introduces a hybrid Petri net framework incorporating thermodynamic constraints to model cellular decision-making, demonstrating how energy-efficient sporulation in Bacillus subtilis is driven by dynamic energy management under stress.

Contribution

The study develops a novel hybrid Petri net model that integrates thermodynamic constraints with stochastic regulatory transitions and continuous energy sources, revealing mechanisms of energy-efficient cellular decision-making.

Findings

Achieved 16-fold ATP efficiency gain during sporulation under stress

Rescued sporulation yield despite 99.7% ATP depletion through continuous regeneration

Identified GTP as an energy buffer facilitating robustness

Abstract

Cellular decision-making under stress involves rapid pathway selection despite energy scarcity. Here we demonstrate that thermodynamic constraints actively drive energy-efficient sporulation, where continuous metabolic sources enable system robustness through dynamic energy management. Using hybrid Petri nets (stochastic transitions with continuous sources) to model Bacillus subtilis sporulation, we show that stress conditions (ATP = 300 mM, 94% depletion) enable sporulation completion with extreme energy efficiency: 0.73 mM ATP per mature spore versus 11.6 mM ATP under normal conditions--a 16-fold efficiency gain. Despite ATP dropping to 1 mM (99.7% depletion) during the crisis, continuous ATP regeneration rescues the system, producing 67 mM mature spores (89% of normal yield) with only 49 mM total ATP consumption. This efficiency emerges from the interplay between stochastic regulatory transitions and continuous metabolic sources, where GTP accumulation (+4974 mM, 166% increase) provides an energy buffer while ATP regeneration (+240 mM) prevents complete depletion. The hybrid Petri net formalism--combining stochastic transitions for regulatory events with continuous sources for metabolic flux--extended with thermodynamic constraints through inhibitor arcs and energy-coupled rate functions, provides the mathematical foundation enabling this discovery by integrating discrete regulatory logic with continuous energy dynamics in a resource-aware concurrency model.