Living systems employ both covalent chemistry and physical assembly to achieve complex behaviors. The emerging field of systems chemistry, inspired by these biological systems, attempts to construct and analyze systems that are simpler than biology, while still embodying biological design principles. Due to the multiple phenomena at play, it can be difficult to predict which phenomena will dominate and when. Conversely, there may be no single rate-limiting step, but rather a reaction network that is difficult to intuit from a purely experimental approach. Mathematical modeling can help to sort out these issues, although it can be challenging to build such models, especially for assembly kinetics. Numerical and statistical methods can play an important role to facilitate the synergistic and iterative use of modeling and experiment, and should be part of a systems chemistry curriculum. Three case studies are presented here, from our work in peptide-based systems, to illustrate some of the tools available for model construction, model simulation, and experimental design. Examples are provided in which these tools help to evaluate hypotheses, uncover design principles, and design new experiments.
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