Information capacity of specific interactions

Specific interactions are a hallmark feature of self-assembly and signal-processing systems in both synthetic and biological settings. Specificity between components may arise from a wide variety of physical and chemical mechanisms in diverse contexts, from DNA hybridization to shape-sensitive depletion interactions. Despite this diversity, all systems that rely on interaction specificity operate under the constraint that increasing the number of distinct components inevitably increases off-target binding. Here we introduce "capacity," the maximal information encodable using specific interactions, to compare specificity across diverse experimental systems and to compute how specificity changes with physical parameters. Using this framework, we find that "shape" coding of interactions has higher capacity than chemical ("color") coding because the strength of off-target binding is strongly sublinear in binding-site size for shapes while being linear for colors. We also find that different specificity mechanisms, such as shape and color, can be combined in a synergistic manner, giving a capacity greater than the sum of the parts.