Chemical richness from abstract physical parts

Every living cell is a tiny, intricate chemical computer. But what aspects of chemistry can create that richness? This thesis explores and expands two abstract models of chemistry, binding networks and chemical linkages, and shows that despite their simplicity, they can exhibit complex behavior. A binding network is a minimal model driven by thermodynamics that treats a molecule as simply a bag of binding sites. We prove that natural questions about binding networks at thermodynamic equilibrium are computationally hard. To answer them quickly in practice, we develop algorithms and software that translate to boolean satisfiability. By introducing a kinetic framework, we then prove that binding networks allow catalysis, a powerful, inherently kinetic behavior. Chemical linkages add minimal geometric structure to binding networks using rods and joints. Out of chemical linkages, we construct ATP-like catalyzed splitting, a fueled motor, and chemo-mechanical coupling. We show that surprisingly, graph structure alone can explain the behavior of these machines. This provides a theoretical foundation toward understanding and mimicking the complexity of living systems.