Fig. 1. Assembly pathways.

a In analyzing the assembly pathways of an object, we start with its basic building blocks, which are the shared set of objects that can construct our target object and any other object within the class of objects. The Assembly index of an object is defined as the smallest number of joining operations required to create the object using this model. b We can model the assembly process as a random walk on weighted trees where the number of outgoing edges (leaves) grows as a function of the depth of the tree, due to the addition of previously made sub-structures. By generating several million trees and calculating the likelihood of the most likely path through the tree, we can estimate the likelihood of an object forming by chance as a function of the number of joining operations required (path length). c The probability of the most likely path through the tree as a function of the path length decreases rapidly. The colors indicate different assumptions about the chemical space. For comparison, the dashed lines indicate the ratio of (I) one star in the entire milky way, 1:10¹¹, (II) one gram out of all of Earth’s biomass, 1:10¹⁷, (III) one in a mole, 1:10²³, and (IV) one gram out of Earth’s mass (1:10²⁹). Note on this plot the path probability of the formation of Taxol would vary between 1:10³⁵ to 1:10⁶⁰ with a path length of 30 and the amount of chemical predisposition is varied with alpha biasing the effective selectivity between 50–99.9% at each step respectively.