The central dogma of molecular biology is the principal framework for understanding how nucleic acid information is propagated and used by living systems to create complex biomolecules. Here, by integrating the structural and dynamic paradigms of DNA nanotechnology, we present a rationally designed synthetic platform that functions in an analogous manner to create complex DNA nanostructures. Starting from one type of DNA nanostructure, DNA strand displacement circuits were designed to interact and pass along the information encoded in the initial structure to mediate the self-assembly of a different type of structure, the final output structure depending on the type of circuit triggered. Using this concept of a DNA structure "trans-assembling" a different DNA structure through nonlocal strand displacement circuitry, four different schemes were implemented. Specifically, 1D ladder and 2D double-crossover (DX) lattices were designed to kinetically trigger DNA circuits to activate polymerization of either ring structures or another type of DX lattice under enzyme-free, isothermal conditions. In each scheme, the desired multilayer reaction pathway was activated, among multiple possible pathways, ultimately leading to the downstream self-assembly of the correct output structure.