标题： 计算和界定非热化学系统的平衡浓度 显示英文标题

标题： Computing and Bounding Equilibrium Concentrations in Athermic Chemical Systems

摘要： 计算分子复合物的平衡浓度通常在分析上不可行，需要数值方法。 在这项工作中，我们关注聚合物-单体层次，其中不可分割的分子（单体）结合形成复合物（聚合物）。 我们不采用每个聚合物的自由能参数，而是关注所有相互作用保持焓不变的非热力学条件。 这种设置与DNA纳米技术中的强结合（基于域的）区域一致，当链可以以不同方式结合，但总是具有最大总体结合——并且与热力学结合网络（TBNs）模型中的饱和配置一致。 在此背景下，我们开发了一个迭代算法，用于分配聚合物浓度以满足详细平衡，其中目标（期望的）聚合物处于高浓度，而非目标（不需要的）聚合物处于低浓度。 即使没有直接执行，我们的算法也能提供关于非目标聚合物浓度上限的有效见解，将TBN模型中的离散配置的组合论论证与实数值浓度联系起来。 我们最后将该方法应用于减少DNA逻辑和信号传播中的泄漏。 我们的结果为当配置由熵力区分时，平衡浓度的设计和验证提供了一个新框架。 显示英文摘要

摘要： 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.