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1. WO2014138994 - SYSTEMS AND METHODS FOR IDENTIFYING THERMODYNAMIC EFFECTS OF ATOMIC CHANGES TO POLYMERS

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[ EN ]

What is claimed is:

1. A method of identifying a thermodynamic effect of an atomic replacement, insertion or deletion in a polymer, the method comprising:

at a computer system having one or more processors and memory storing one or more programs to be executed by the one of more processors:

(A) using a set of three-dimensional coordinates {y1; ... , y } for a derivation of the polymer, the derivation of the polymer formed by incorporating the atomic replacement, insertion or deletion into the polymer, to compute a first effective atomistic Hessian of a first portion of the derivation of the polymer, wherein each respective y; in {y i, ... , y } is a three dimensional coordinate for an atom in a first plurality of atoms in the derivation of the polymer;

(B) using a native set of three-dimensional coordinates {x1; .. . , X } for the native polymer to compute a second effective atomistic Hessian of a second portion of the native polymer, wherein each respective x; in {x1; ... , xM} is a three dimensional coordinate for an atom in a second plurality of atoms in the native version of the polymer;

(C) computing a thermodynamic property of the first portion of the derivation of the polymer using the derived set of three-dimensional coordinates {y1; ... , y } and the first effective atomistic Hessian; and

(D) computing a thermodynamic property of the second portion of the native polymer using the native set of three-dimensional coordinates {x1; .. . , X } and the second effective atomistic Hessian.

2. The method of claim 1 , wherein an identity of each atom in the first portion of the derived set of three-dimensional coordinates {y1; ... , y } is identical to the corresponding atom in the second portion of the native three-dimensional coordinates

{xi, XN} .

3. The method of claim 1 or 2, wherein the thermodynamic effect of the atomic replacement, insertion or deletion is quantified by taking a difference between the thermodynamic property of the first portion and the thermodynamic property of the second portion.

4. The method of any one of claims 1 -3, wherein the polymer is a protein and the atomic replacement, insertion or deletion is a mutation of one or more residues in the derivation of the polymer relative to the native polymer.

5. The method of any one of claims 1 or 3-4, wherein the polymer is a protein and wherein the derivation of the polymer differs from the native polymer by the insertion or deletion of one or more residues at a location in the polymer.

6. The method of any one of claims 1-5, wherein the thermodynamic property of the first portion of the derivation of the polymer is entropy, average energy, average enthalpy, free energy or heat capacity.

7. The method of any one of claims 1-6, wherein the first portion consists of those atoms in the first plurality of atoms within a distance threshold of the location of the atomic replacement, insertion or deletion.

8. The method of any one of claims 1-3 or 6-7, wherein the polymer is a protein, a polypeptide, a polynucleic acid, a polyribonucleic acid, a polysaccharide, or an assembly of any combination thereof.

9. The method of any one of claims 1-8, wherein

the derived set of three-dimensional coordinates {y1; ... , y } for a derivation of the polymer is prepared prior to the using (A) by structurally refining a region encompassing the first portion of the derivation of the polymer while holding the other portions of the derivation of the polymer fixed; and

the native set of three-dimensional coordinates is prepared prior to the using (B) by structurally refining a region encompassing the second portion of the native polymer while holding the other portions of the native polymer fixed.

10. The method of any one of claims 1-3 or 6-8, wherein

the derived set of three-dimensional coordinates {y1; ... , y } is obtained by structurally refining a first refinement zone of the derivation of the polymer, the first refinement zone including the atoms in the atomic replacement, insertion or deletion; the using (A) partitions atoms in the first refinement zone into a first partition and a second partition, wherein the first partition consists of the atoms in the refinement zone that are in the atomic replacement, insertion or deletion and the second partition consists of all or a subset of those atoms in the first refinement zone other than those atoms in the first partition, and wherein the second partition is deemed to be the first portion of the derivation of the polymer,

the derived native set of three-dimensional coordinates {x1; .. . , X } is obtained by structurally refining a second refinement zone of the native polymer, the second refinement zone including the atoms in the atomic replacement, insertion or deletion;

the using (B) partitions atoms in the second refinement zone into a third partition and a fourth partition, wherein the fourth partition consists of those atoms in the native set that are equivalent to those atoms in the second partition, and wherein the fourth partition is deemed to be the second portion of the native polymer.

11. The method of claim 10, wherein

an atomistic Hessian of the first refinement zone is decomposed using a vibrational subsystem analysis to produce the first effective atomistic Hessian , and the entropy of the first portion is computed from the first effective atomistic Hessian; and

a second atomistic Hessian of the second refinement zone is decomposed using a vibrational subsystem analysis to produce the second effective Hessian, and the entropy of the second portion is computed from the second effective Hessian.

12. The method of claim 10, wherein the polymer is a protein, and the atomic replacement, insertion or deletion in the polymer is a mutated residue.

13. The method of claim 10, wherein the refinement zone consists of those atoms in the first plurality of atoms within a distance threshold of the location of the atomic replacement, insertion or deletion.

14. The method of claim 1, wherein

the derived set of three-dimensional coordinates {y1; ... , y } is obtained by structurally refining a first refinement zone of the derivation of the polymer, the first refinement zone including the atoms in the atomic replacement, insertion or deletion; the using (A) partitions atoms in the first refinement zone into a first partition and a second partition, wherein

the atoms in the second partition consists of all or a subset of the atoms in the refinement zone other than those atoms in the atomic replacement, insertion or deletion,

the atoms in the first partition consists of those atoms in the first refinement zone that are not in the second partition,

the structurally refined native set of three-dimensional coordinates {x1; ... , X } is obtained by refining a second refinement zone of the native polymer, the second refinement zone corresponding to the first refinement zone but differing by those atoms participating in the atomic replacement, insertion or deletion;

the using (B) partitions atoms in the second refinement zone into a third partition and a fourth partition, wherein the identity of the atoms in the fourth partition exactly correspond to their counterparts in the second partition and wherein the second portion of the native polymer consists of the atoms in the fourth petition.

15. The method of claim 14, wherein

the atomistic Hessian of the first refinement zone is decomposed using a vibrational subsystem analysis to produce a first effective Hessian matrix, and the entropy of the first portion is computed from the first effective Hessian matrix; and the atomistic Hessian of the second refinement zone is decomposed using a vibrational subsystem analysis to produce a second effective Hessian matrix, and the entropy of the second portion is computed from the second effective Hessian matrix.

16. The method of claim 14, wherein the polymer is a protein, and the atomic replacement, insertion or deletion in the polymer is a mutated residue.

17. The method of claim 14, wherein the first partition consists of those atoms in the first plurality of atoms within a distance threshold of the location of the atomic replacement, insertion or deletion.

18. A method of identifying a thermodynamic effect of an atomic replacement, insertion or deletion in a polymer, the method comprising:

at a computer system having one or more processors and memory storing one or more programs to be executed by the one of more processors:

(A) using a derived set of three-dimensional coordinates {y1; ... , y } for a derivation of the polymer, the derivation of the polymer formed by incorporating the atomic replacement, insertion or deletion into the polymer, to compute a first effective atomistic Hessian of the derivation of the polymer, wherein each respective yi in {yi, ... , yw} is a three dimensional coordinate for an atom in a first plurality of atoms in the derivation of the polymer;

(B) using a native set of three-dimensional coordinates {x1; .. . , X } for the native polymer to compute a second effective atomistic Hessian of the native polymer, wherein each respective x; in {x1; ... , xM} is a three dimensional coordinate for an atom in a second plurality of atoms in the native polymer;

(C) computing an unnormalized thermodynamic property of the derivation of the polymer using the derived set of three-dimensional coordinates and the first effective atomistic Hessian;

(D) computing an unnormalized thermodynamic property of the native polymer using the structurally refined native set of three-dimensional coordinates and the second effective atomistic Hessian; and

(E) normalizing the unnormalized thermodynamic property of the derivation of the polymer and the unnormalized thermodynamic property of the native polymer by taking into account a difference in a number of degrees of freedom of {y i, ... , y } relative to {x1; .. . , X }, thereby identifying a thermodynamic effect of the atomic replacement, insertion or deletion in the polymer.

19. The method of claim 18, wherein the polymer is a protein and the atomic replacement, insertion or deletion is a mutation of one or more residues in the derivation of the polymer relative to the native polymer.

20. The method of claim 18, wherein the polymer is a protein and wherein the derivation of the polymer differs from the native polymer by the insertion or deletion of one or more residues at a location in the polymer.

21. The method of any one of claims 18-20, wherein

the derived set of three-dimensional coordinates is prepared prior to the using

(A) by structurally refining a first portion of the derivation of the polymer about a location of the replacement, insertion or deletion while holding the other portions of the derivation of the polymer fixed; and

the native set of three-dimensional coordinates is prepared prior to the using

(B) by structurally refining a second portion of the native polymer while holding the other portions of the native polymer fixed, the second portion being the part of the native polymer corresponding to the first portion of the derivation of the polymer.

22. The method of claim 21, wherein the first region consists of those atoms in the first plurality of atoms within a distance threshold of a location of the replacement, insertion or deletion.

23. The method of any one of claims 18, 21 or 22, wherein the polymer is a protein, a polypeptide, a polynucleic acid, a polyribonucleic acid, a polysaccharide, or an assembly of any combination thereof.

24. A computer system for identifying a thermodynamic effect of an atomic replacement, insertion or deletion in a polymer, 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) using a derived set of three-dimensional coordinates {y1; ... , y } for a derivation of the polymer, the derivation of the polymer formed by incorporating the atomic replacement, insertion or deletion into the polymer, to compute a first effective atomistic Hessian of a first portion of the derivation of the polymer, wherein each respective y; in {y i, ... , yw} is a three dimensional coordinate for an atom in a first plurality of atoms in the derivation of the polymer;

(B) using a native set of three-dimensional coordinates {x1; .. . , X } for the native polymer to compute a second effective atomistic Hessian of a second portion of the native polymer, wherein each respective x; in {x1; ... , xM} is a three dimensional coordinate for an atom in a second plurality of atoms in the native version of the polymer;

(C) computing a thermodynamic property of the first portion of the derivation of the polymer using the derived set of three-dimensional coordinates {y1; ... , y } and the first effective atomistic Hessian; and

(D) computing a thermodynamic property of the second portion of the native polymer using the native set of three-dimensional coordinates {x1; .. . , X } and the second effective atomistic Hessian.

25. The computer system of claim 24 wherein an identity of each atom in the first portion of the derived set of three-dimensional coordinates {yi, ... , y#} is identical to the corresponding atom in the second portion of the native three-dimensional coordinates {x1; ... , xjv}.

26. A non-transitory computer readable storage medium storing a computational module for identifying a thermodynamic effect of an atomic replacement, insertion or deletion in a polymer, the computational module comprising instructions for:

(A) using a derived set of three-dimensional coordinates {y1; ... , y } for a derivation of the polymer, the derivation of the polymer formed by incorporating the atomic replacement, insertion or deletion into the polymer, to compute a first effective atomistic Hessian of a first portion of the derivation of the polymer, wherein each respective y; in {y i, ... , yw} is a three dimensional coordinate for an atom in a first plurality of atoms in the derivation of the polymer;

(B) using a native set of three-dimensional coordinates {x1; .. . , X } for the native polymer to compute a second effective atomistic Hessian of a second portion of the native polymer, wherein each respective x; in {x1; ... , xM} is a three dimensional coordinate for an atom in a second plurality of atoms in the native version of the polymer and wherein

an identity of each atom in the first portion of the derived set of three-dimensional coordinates {y1; ... , y } is identical to the corresponding atom in the second portion of the native three-dimensional coordinates {x1; ... , x };

(C) computing a thermodynamic property of the first portion of the derivation of the polymer using the derived set of three-dimensional coordinates {y1; ... , y } and the first effective atomistic Hessian; and

(D) computing a thermodynamic property of the second portion of the native polymer using the native set of three-dimensional coordinates {xi, .. . , X } and the second effective atomistic Hessian.

27. The non-transitory computer readable storage medium of claim 26 wherein an identity of each atom in the first portion of the derived set of three-dimensional coordinates {y1; ... , y } is identical to the corresponding atom in the second portion of the native three-dimensional coordinates {x1; ... , x }.