Systems and methods for making two dimensional graphs of complex molecules

A computer system for visualizing physical properties of a molecule in two dimensions, wherein the molecule comprises the set of {p1, . . . , pN} particles, each particle pi in the set of particles representing a different plurality of covalently bound atoms in the molecule, the computer system comprising at least one processor and memory storing at least one program for execution by the at least one processor, the memory further comprising instructions for:

• (A) obtaining a set of N three-dimensional coordinates {x1, . . . , xN} wherein each respective xi in {x1, . . . , xN} corresponds to a pi in {p1, . . . , pN} and represents the position of pi in three-dimensional space;
• (B) minimizing a cost function containing an error in a set of two-dimensional coordinates corresponding to the set of N three-dimensional coordinates using a minimization function:
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• using the set of N three-dimensional coordinates, wherein N is a positive integer of greater than 30 and wherein,
• i and j are integers greater than zero,
• δij is a distance between a pair of three-dimensional coordinates xi and xj in {x1, . . . , xN},
• E(c1,c2, . . . , cN) is an error in the set of two-dimensional coordinates (c1, . . . , cN), wherein each two-dimensional coordinate ci in (c1, . . . , cN) uniquely corresponds to a three-dimensional coordinate xi in {x1, . . . , xN} so that each respective pi in {p1, . . . , pN} is represented by a three-dimensional coordinate xi in {x1, . . . , xN} and a corresponding two-dimensional coordinate ci in (c1,. . . , cN),
• D(ci, cj) is a distance between the two-dimensional coordinates ci and cj in (c1, . . . , cN), and
• wij is a weight for the two-dimensional pair (pi, pj) in a matrix of weights, wherein the matrix of weights has a weight for each two-dimensional pair (pi, pj) in (p1, . . . , pN),
• wherein the minimizing alters the values of coordinates of the set of two-dimensional coordinates (c1, . . . , cN) using a refinement algorithm until an exit condition is achieved;
• (C) obtaining a first set of physical properties SM from a non-transitory computer readable storage medium, each physical property sij in SM representing a respective physical property shared by a pair of particles (pi, pj) in {p1, . . . , pN} in the molecule;
• (D) plotting (c1, . . . , cN), after the exit condition is achieved, as a plurality of nodes of a two-dimensional graph;
• and
• (E) plotting-a first plurality of edges for the two-dimensional graph, wherein
• each respective edge in the first plurality of edges connects a two-dimensional coordinate pair (ci, cj) in the graph that corresponds to a pair of particles (pi, pj) in {p1, . . . , pN}, and
• a first characteristic of each respective edge in the first plurality of edges is determined by a respective physical property sij in SM for the pair of particles (pi, pj) in {p1, . . . , pN} corresponding to the two-dimensional coordinate pair (ci, cj) that is connected by the respective edge.

A non-transitory computer readable storage medium storing a visualization module for visualizing physical properties of a molecule in two dimensions, wherein the molecule comprises the set of {p1, . . . , pN} particles, each particle pi in the set of particles representing a different plurality of covalently bound atoms in the molecule, the visualization module comprising instructions for:

• (A) obtaining a set of N three-dimensional coordinates {x1, . . . , xN} wherein each respective xi in {x1, . . . , xN} corresponds to a pi in {p1, . . . , pN} and represents the position of pi in three-dimensional space;
• (B) minimizing a cost function containing an error in a set of two-dimensional coordinates corresponding to the set of N three-dimensional coordinates using a minimization function:
• E
• ⁡
• (
• c
• 1
• ,
• c
• 2
• ,
• …
• ⁢
• ,
• c
• N
• )
• =
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• i
• <
• j
• N
• ⁢
• w
• ij
• ⁢
• 
• δ
• ij
• -
• D
• ⁡
• (
• c
• i
• ,
• c
• j
• )
• 
• 2
• using the set of N three-dimensional coordinates, wherein N is a positive integer of greater than 30 and wherein,
• i and j are integers greater than zero,
• δij is a distance between a pair of three-dimensional coordinates xi and xj in{x1, . . . , xN},
• E(c1, c2, . . . , cN) is an error in the set of two-dimensional coordinates (c1, . . . , cN), wherein each two-dimensional coordinate ci in (c1, . . . , cN) uniquely corresponds to a three-dimensional coordinate xi in {x1, . . . , xN} so that each respective pi in {p1, . . . , pN} is represented by a three-dimensional coordinate xi in {x1, . . . , xN} and a corresponding two-dimensional coordinate ci in (c1, . . . , cN),
• D(ci, cj) is a distance between the two-dimensional coordinates ci and cj in (c1, . . . , cN), and
• wij is a weight for the two-dimensional pair (pi, pj) in a matrix of weights, wherein the matrix of weights has a weight for each two-dimensional pair (pi, pj) in (p1, . . . , pN),
• wherein the minimizing alters the values of coordinates of the set of two-dimensional coordinates (c1, . . . , cN) using a refinement algorithm until an exit condition is achieved;
• (C) obtaining a first set of physical properties SM from a non-transitory computer readable storage medium, each physical property sij in SM representing a respective physical property k shared by a pair of particles (pi, pj) in {p1, . . . , pN} in the molecule;
• (D) plotting (c1, . . . , cN), after the exit condition is achieved, as a plurality of nodes of a two-dimensional graph;
• and
• (E) plotting a first plurality of edges for the two-dimensional graph, wherein
• each respective edge in the first plurality of edges connects a two-dimensional coordinate pair (ci, cj) in the graph that corresponds to a pair of particles (pi, pj) in {p1, . . . , pN}, and
• a first characteristic of each respective edge in the first plurality of edges is determined by a respective physical property sij in SM for the pair of particles (pi, pj) in {p1, . . . , pN} corresponding to the two-dimensional coordinate pair (ci, cj) that is connected by the respective edge.