Techniques for Controlling Spatial Structure of Nucleic Acid Structures Based on Lattice-free, Three Dimensional Junction Coordinates

A non-transitory computer-readable medium carrying one or more sequences of instructions, wherein execution of the one or more sequences of instructions by one or more processors causes the one or more processors to perform the steps of:

• determining, for each junction type of one or more nucleic acid junction types, a plurality of values corresponding to a plurality of fixed parameters that indicate a ground-state geometry and translational and rotational junction stiffness coefficients for perturbations from the ground-state geometry;
• determining design data that indicates, for a nucleic acid structure, a number of nucleic acid bases in each helix of a set of two or more helices, wherein the set of helices are joined at a corresponding junction, for a plurality of sets of helices in the nucleic acid structure, wherein the plurality of sets of helices are connected by a plurality of junctions;
• determining initial positions of each base in the nucleic acid structure by connecting helices at junctions using the ground-state geometry of each junction, wherein the initial positions are in arbitrary three dimensional coordinates that are not confined to lattice coordinates;
• determining a set of one or more misalignment vectors, wherein each misalignment vector indicates a difference in three dimensional coordinates between initial positions of a pair of bases that are not adjacent or coincident in the initial positions but are adjacent or coincident, respectively, in the design data;
• determining one or more forces or moments or both at the plurality of junctions to reduce magnitudes corresponding to the set of misalignment vectors based on the set of misalignment vectors and the translational and rotational junction stiffness coefficients at each junction of the plurality of junctions;
• determining a three dimensional structure comprising position and orientation in three dimensional coordinates of each base in the nucleic acid structure, by reducing the magnitudes corresponding to the set of misalignment vectors and balancing forces and moments across the nucleic acid structure;
• and
• causing output data based on the three dimensional structure to be presented on a display device.

A system comprising:

• a display device;
• at least one processor;
• and
• at least one memory including one or more sequences of instructions,
• the at least one memory and the one or more sequences of instructions configured to, with the at least one processor, cause an apparatus to perform at least the following,
• determine, for each junction type of one or more nucleic acid junction types, a plurality of values corresponding to a plurality of fixed parameters that indicate a ground-state geometry and translational and rotational junction stiffness coefficients for perturbations from the ground-state geometry;
• determine design data that indicates, for a nucleic acid structure, a number of nucleic acid bases in each helix of a set of two or more helices, wherein the set of helices are joined at a corresponding junction, for a plurality of sets of helices in the nucleic acid structure, wherein the plurality of sets of helices are connected by a plurality of junctions;
• determine initial positions of each base in the nucleic acid structure by connecting helices at junctions using the ground-state geometry of each junction, wherein the initial positions are in arbitrary three dimensional coordinates that are not confined to lattice coordinates;
• determine a set of one or more misalignment vectors, wherein each misalignment vector indicates a difference in three dimensional coordinates and orientations between initial positions of a pair of bases that are not adjacent or coincident in the initial positions but are adjacent or coincident, respectively, in the design data;
• determine forces at the plurality of junctions to reduce magnitudes corresponding to the set of misalignment vectors based on the set of misalignment vectors and the translational and rotational junction stiffness coefficients at each junction of the plurality of junctions;
• determine a three dimensional structure comprising position and orientation in three dimensional coordinates of each base in the nucleic acid structure, by reducing the magnitudes corresponding to the set of misalignment vectors and balancing forces and moments across the nucleic acid structure;
• and
• causing output data based on the three dimensional structure to be presented on the display device.