Systems and methods for making two dimensional graphs of complex molecules

1. A computer-implemented method for visualizing physical properties of a molecule in two dimensions, wherein the molecule comprises a set of {p 1 , . . . , p N } particles, each particle p i in the set of particles representing a different plurality of covalently bound atoms in the molecule, the method performed on a first computer system having at least one processor and memory storing at least one program for execution by the at least one processor to perform the method, comprising:

(A) obtaining a set of N three-dimensional coordinates {x 1 , . . . , x N } by x-ray crystallography, nuclear magnetic resonance spectroscopic techniques, electron microscopy, modeling or from a non-transitory computer readable storage medium, wherein each respective x i in {x 1 , . . . , x N } corresponds to a p i in {p 1 , . . . , p N } and represents the position of p i in three-dimensional space, wherein N is a positive integer of greater than 30;

(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 module:

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using the set of N three-dimensional coordinates wherein,

i and j are integers greater than zero,

δ ij is a distance between a pair of three-dimensional coordinates x i and x j in {x 1 , . . . , x N },

E(c 1 , c 2 , . . . , c N ) is an error in the set of two-dimensional coordinates (c 1 , c N ), wherein each two-dimensional coordinate c i in (c 1 , c N ) uniquely corresponds to a three-dimensional coordinate x i in {x 1 , . . . , x N } so that each respective p i in {p 1 , . . . , p N } is represented by a three-dimensional coordinate x i in {x 1 , . . . , x N } and a corresponding two-dimensional coordinate c i in (c 1 , . . . , c N ),

D(c i , c j ) is a distance between the two-dimensional coordinates c i and c j in (c 1 , . . . , c N ), and

w ij is a weight for the two-dimensional pair (p i , p j ) in a matrix of weights, wherein the matrix of weights has a weight for each two-dimensional pair (p i , p j ) in (p 1 , . . . , p N ),

wherein the minimizing alters the values of coordinates of the set of two-dimensional coordinates (c 1 , . . . , c N ) using a refinement algorithm until an exit condition is achieved;

(C) obtaining a plurality of sets of physical properties S Mk from a non-transitory computer readable storage medium, each physical property s i,j in S Mk representing a respective physical property k shared by a pair of particles (p i , p j ) in {p 1 , . . . , p N } in the molecule;

(D) plotting (c 1 , . . . , c N ), with a graphical user interface, after the exit condition is achieved, as a plurality of nodes of a two-dimensional graph; and

(E) plotting, with the graphical user interface, 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 (c i , c j ) in the graph that corresponds to a pair of particles (p i , p j ) in {p 1 , . . . , p N }, and

a first characteristic of each respective edge in the first plurality of edges is determined by a respective physical property s i,j in S M1 for the pair of particles (p i , p j ) in {p 1 , . . . , p N } corresponding to the two-dimensional coordinate pair (c i , c j ) that is connected by the respective edge.

2. The computer-implemented method of claim 1 wherein k is a positive integer of 2 or greater.

3. The computer-implemented method of claim 1 wherein the plotting (E) is done on a conditional basis in which each respective edge in the first plurality of edges is conditionally plotted as a function of the respective physical property s i,j in S M1 for the pair of particles (p i , p j ) in {p 1 , . . . , p N } corresponding to the two-dimensional coordinate pair (c i , c j ) that is connected by the respective edge.

4. The computer-implemented method of claim 3 , wherein:

a first edge in the first plurality of edges is not plotted by the plotting (E) when the physical property s i,j does not satisfy a first threshold condition, and

the first edge is plotted by the plotting (E) when the physical property s i,j satisfies the first threshold condition.

5. The computer-implemented method of claim 4 , wherein a histogram of values for the physical property s i,j of S M1 are displayed and the first threshold condition is determined by a selection of a subset of the histogram of values.

6. The computer-implemented method of claim 5 , wherein the first threshold condition is satisfied when a value of the physical property s i,j is outside the subset of the histogram values.

7. The computer-implemented method of claim 5 , wherein the first threshold condition is satisfied when a value of the physical property s i,j is within the subset of the histogram of values.

8. The computer-implemented method of claim 5 , wherein the subset of the histogram values is user adjustable using mouse cursor functions.

9. The computer-implemented method of claim 1 , wherein the plotting (E) further comprises:

plotting a second plurality of edges for the two-dimensional graph, wherein

each respective edge in the second plurality of edges connects a two-dimensional coordinate pair (c i , c j ) in the graph that corresponds to a pair of particles (p i , p j ) in {p 1 , . . . , p N }, and

a first characteristic of each respective edge in the second plurality of edges is determined by a respective physical property s i,j in S M2 for the pair of particles (p i , p j ) in {p 1 , . . . , p N } corresponding to the two-dimensional coordinate pair (c i , c j ) that is connected by the respective edge.

10. The computer-implemented method of claim 9 , wherein the plotting (E) further comprises:

plotting a third plurality of edges for the two-dimensional graph, wherein

each respective edge in the third plurality of edges connects a two-dimensional coordinate pair (c i , c j ) in the graph that corresponds to a pair of particles (p i , p j ) in {p 1 , . . . , p N }, and

a first characteristic of each respective edge in the third plurality of edges is determined by a respective physical property s i,j in S M3 for the pair of particles (p i , p j ) in {p 1 , . . . , p N } corresponding to the two-dimensional coordinate pair (c i , c j ) that is connected by the respective edge.

11. The computer-implemented method of claim 10 , wherein the user is able to individually toggle on or off the display of the first plurality of edges, the second plurality of edges, and the third plurality of edges.

12. The computer-implemented method of claim 10 , wherein

each edge in the first plurality of edges is plotted with a first edge style,

each edge in the second plurality of edges is plotted with a second edge style, and

each edge in the third plurality of edges is plotted with a third edge style.

13. The computer-implemented method of claim 1 , wherein each respective node in the plurality of nodes is associated with one or more properties associated with the respective particle p i in {p 1 , . . . , p N } represented by the respective node and wherein the plotting (D) conditionally, graphically highlights a subset of the plurality of nodes as a function of the one or more properties associated with the respective particles p i in {p 1 , . . . , p N } corresponding to the plurality of nodes.

14. The computer-implemented method of claim 1 , wherein

each particle in a first subset of the particles p i in {p 1 , . . . , p N } has a first property and each particle in second subset of the particles p i in {p 1 , . . . , p N } does not have the first property, and

the plotting (D) comprises plotting the nodes in the plurality of nodes corresponding to the first subset of the particles and not plotting the nodes in the plurality of nodes corresponding to the second subset of the particles.

15. The computer-implemented method of claim 14 , wherein the user is able to individually toggle on or off the display of (i) the nodes in the plurality of nodes corresponding to the first subset of the particles and (ii) the nodes in the plurality of nodes corresponding to the second subset of the particles.

16. The computer-implemented method of claim 1 , wherein

each particle in a first subset of the particles p i in {p 1 , . . . , p N } has a first property and each particle in a second subset of the particles p i in {p 1 , . . . , p N } does not have the first property and

the plotting (D) comprises plotting the nodes in the plurality of nodes corresponding to the first subset of the particles with a first graphic attribute and plotting the nodes in the plurality of nodes corresponding to the second subset of the particles with a second graphic attribute.

17. The computer-implemented method of claim 16 , wherein the first graphic attribute is a first color and the second graphic attribute is a second color.

18. The computer-implemented method of claim 1 , wherein the method further comprises providing a graphical user interface that performs the plotting (D) and the plotting (E), wherein

each respective node in the plurality of nodes is associated with one or more properties associated with the respective particle p i in {p 1 , . . . , p N } represented by the respective node,

the plotting (D) conditionally, graphically highlights a subset of the plurality of nodes as a function of the one or more properties associated with the respective particles p i in {p 1 , . . . , p N } corresponding to the plurality of nodes, and

a property of one or more of the nodes in the plurality of nodes is determined by launching a computational module directly inline within the graphical user interface.

19. The computer-implemented method of claim 1 , wherein

each respective node in the plurality of nodes has a value for a property associated with the corresponding particle p i in {p 1 , . . . , p N } represented by the respective node, and

the plotting (D) conditionally graphically highlights a subset of the plurality of nodes as a function of the value of property associated with the respective particles p i in {p 1 , . . . , p N } corresponding to the plurality of nodes.

20. The computer-implemented method of claim 19 , wherein

a node is not graphically highlighted by the plotting (D) when the property does not satisfy a first threshold condition, and

a node is graphically highlighted by the plotting (D) when the property does satisfy a first threshold condition.

21. The computer-implemented method of claim 20 , wherein a histogram of values for the property is displayed and the first threshold condition is determined by a selection of a subset of the histogram of values.

22. The computer-implemented method of claim 21 , wherein the first threshold condition is satisfied when a value of the property is outside the subset of the histogram values.

23. The computer-implemented method of claim 21 , wherein the first threshold condition is satisfied when a value of the property is within the subset of the histogram of values.

24. The computer-implemented method of claim 21 , wherein the subset of the histogram values is user adjustable using mouse cursor functions.

25. The computer-implemented method of claim 1 the obtaining (C) is performed by launching a computational module directly inline within the graphical user interface that computes a set of physical properties in the one or more sets of physical properties SM.

26. The computer-implemented method of claim 1 , wherein the plurality of nodes can be zoomed by user action so that a subset of the plurality of nodes is displayed, and wherein, the method further comprises receiving instructions to display all or a subset of the N three-dimensional coordinates {x 1 , . . . , x N } in a side by side fashion to all or a portion of the plurality of nodes.

27. The computer-implemented method of claim 26 , wherein the plurality of nodes and the N three-dimensional coordinates {x 1 , . . . , x N } can be rotated, translated and zoomed in three dimensional space in a concerted fashion.

28. The computer-implemented method of claim 26 , wherein the plurality of nodes and the N three-dimensional coordinates {x 1 , . . . , x N } can be rotated, translated and zoomed in three dimensional space independently of each other.

29. A computer system for visualizing physical properties of a molecule in two dimensions, wherein the molecule comprises the set of {p 1 , . . . , p N } particles, each particle p i 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 {x 1 , . . . , x N } by x-ray crystallography, nuclear magnetic resonance spectroscopic techniques, electron microscopy, modeling or from a non-transitory computer readable storage medium, wherein each respective x i in {x 1 , . . . , x N } corresponds to a p i in {p 1 , . . . , p N } and represents the position of p i in three-dimensional space, wherein N is a positive integer of greater than 30;

(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 module:

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using the set of N three-dimensional coordinates wherein,

i and j are integers greater than zero,

δ ij is a distance between a pair of three-dimensional coordinates x i and x j in {x 1 , . . . , x N },

E(c 1 , c 2 , . . . , C N ) is an error in the set of two-dimensional coordinates (c 1 , . . . , c N ), wherein each two-dimensional coordinate c i in (c 1 , . . . , c N ) uniquely corresponds to a three-dimensional coordinate x i in {x 1 , . . . , x N } so that each respective p i in {p 1 , . . . , p N } is represented by a three-dimensional coordinate x i in {x 1 , . . . , x N } and a corresponding two-dimensional coordinate c i in (c 1 , . . . , c N ),

D(c i , c j ) is a distance between the two-dimensional coordinates c i and c j in (c 1 , . . . , c N ), and

w ij is a weight for the two-dimensional pair (p i , p j ) in a matrix of weights, wherein the matrix of weights has a weight for each two-dimensional pair (p i , p j ) in (p 1 , . . . , p N ),

wherein the minimizing alters the values of coordinates of the set of two-dimensional coordinates (c 1 , . . . , c N ) using a refinement algorithm until an exit condition is achieved;

(C) obtaining a plurality of sets of physical properties S Mk from a non-transitory computer readable storage medium, each physical property s i,j in S Mk representing a respective physical property k shared by a pair of particles (p i , p j ) in {p 1 , . . . , p N } in the molecule;

(D) plotting (c 1 , . . . , c N ), with a graphical user interface, after the exit condition is achieved, as a plurality of nodes of a two-dimensional graph; and

(E) plotting, with the graphical user interface, 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 (c i , c j ) in the graph that corresponds to a pair of particles (p i , p j ) in {p 1 , . . . , p N }, and

a first characteristic of each respective edge in the first plurality of edges is determined by a respective physical property s i,j in S M1 for the pair of particles (p i , p j ) in {p 1 , . . . , p N } corresponding to the two-dimensional coordinate pair (c i , c j ) that is connected by the respective edge.

30. 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 {p 1 , . . . , p N } particles, each particle p i 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 {x 1 , . . . , x N } by x-ray crystallography, nuclear magnetic resonance spectroscopic techniques, electron microscopy, modeling or from a non-transitory computer readable storage medium, wherein each respective x i in {x 1 , . . . , x N } corresponds to a p i in {p 1 , . . . , p N } and represents the position of p i in three-dimensional space, wherein N is a positive integer of greater than 30;

(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 module:

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using the set of N three-dimensional coordinates wherein,

i and j are integers greater than zero,

δ ij is a distance between a pair of three-dimensional coordinates x i and x j in {x 1 , . . . , x N },

E(c 1 , c 2 , . . . , C N ) is an error in the set of two-dimensional coordinates (c 1 , . . . , c N ), wherein each two-dimensional coordinate c i in (c 1 , . . . , c N ) uniquely corresponds to a three-dimensional coordinate x i in {x 1 , . . . , x N } so that each respective p i in {p 1 , . . . , p N } is represented by a three-dimensional coordinate x i in {x 1 , . . . , x N } and a corresponding two-dimensional coordinate c i in (c 1 , . . . , c N ),

D(c i , c j ) is a distance between the two-dimensional coordinates c i and c j in (c 1 , . . . , c N ), and

w ij is a weight for the two-dimensional pair (p i , p j ) in a matrix of weights, wherein the matrix of weights has a weight for each two-dimensional pair (p i , p j ) in (p 1 , . . . , p N ),

wherein the minimizing alters the values of coordinates of the set of two-dimensional coordinates (c 1 , . . . , c N ) using a refinement algorithm until an exit condition is achieved;

(C) obtaining a plurality of sets of physical properties S Mk from a non-transitory computer readable storage medium, each physical property s i,j in S Mk representing a respective physical property k shared by a pair of particles (p i , p j ) in {p 1 , . . . , p N } in the molecule;

(D) plotting (c 1 , . . . , c N ), with a graphical user interface, after the exit condition is achieved, as a plurality of nodes of a two-dimensional graph; and

(E) plotting, with the graphical user interface, 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 (c i , c j ) in the graph that corresponds to a pair of particles (p i , p j ) in {p 1 , . . . , p N }, and

a first characteristic of each respective edge in the first plurality of edges is determined by a respective physical property s i,j in S M1 for the pair of particles (p i , p j ) in {p 1 , . . . , p N } corresponding to the two-dimensional coordinate pair (c i , c j ) that is connected by the respective edge.