which is an extension of Equation 1 to include an additional ε'-term: a one-to-one mapping was created between each colored particle i and a randomly assigned, but non-matching colored, particle m * (i). Consequently, a colored particle i can form one of three interactions (Figure ): 1) correct native interaction between particles of matching colors, ci = cj , conducive to forming the designed target structure with a strength of ε, 2) non-native interaction between most edges of different colors, with a strength of ε'', and 3) non-native interaction with only one differently colored particle, between i and j = m * (i), with a strength of ε' (mimicking the tendency of a sequence to have only a single or few ε' interactions with other sticky end sequences in the assembly of DNA-tiles).