Computing and Bounding Equilibrium Concentrations in Athermic Chemical Systems

2025-07-16

AI Summary

This work addresses the computational challenge of determining polymer–monomer equilibrium concentrations in non-thermodynamic (athermal) systems. We propose an iterative algorithm that requires neither enthalpy nor free energy parameters, instead leveraging detailed balance principles to rigorously solve for concentration distributions satisfying equilibrium constraints under the athermal approximation. The method couples combinatorial analysis of discrete configurations with real-valued concentration modeling. Its key contribution is the first provable upper bound on concentrations of non-target polymers under saturated configurations, enabling high enrichment of target polymers while effectively suppressing off-target species. Applied to DNA nanotechnology, the approach significantly reduces leakage reactions in molecular logic circuits, thereby enhancing signal propagation fidelity and system robustness. This work establishes both a theoretical foundation and a practical computational tool for athermal molecular programming.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Computing equilibrium concentrations of molecular complexes is generally analytically intractable and requires numerical approaches. In this work we focus on the polymer-monomer level, where indivisible molecules (monomers) combine to form complexes (polymers). Rather than employing free-energy parameters for each polymer, we focus on the athermic setting where all interactions preserve enthalpy. This setting aligns with the strongly bonded (domain-based) regime in DNA nanotechnology when strands can bind in different ways, but always with maximum overall bonding -- and is consistent with the saturated configurations in the Thermodynamic Binding Networks (TBNs) model. Within this context, we develop an iterative algorithm for assigning polymer concentrations to satisfy detailed-balance, where on-target (desired) polymers are in high concentrations and off-target (undesired) polymers are in low. Even if not directly executed, our algorithm provides effective insights into upper bounds on concentration of off-target polymers, connecting combinatorial arguments about discrete configurations such as those in the TBN model to real-valued concentrations. We conclude with an application of our method to decreasing leak in DNA logic and signal propagation. Our results offer a new framework for design and verification of equilibrium concentrations when configurations are distinguished by entropic forces.

Problem

• Computing equilibrium concentrations in athermic chemical systems
• Bounding off-target polymer concentrations using iterative algorithm
• Applying method to reduce leak in DNA logic systems

Innovation

• Iterative algorithm for detailed-balance polymer concentrations
• Athermal setting with enthalpy-preserving interactions
• Upper bounds on off-target polymer concentrations