Process for identifying similar 3D substructures onto 3D atomic structures and its applications

US 20050182570A1
Filed: 12/06/2004
Published: 08/18/2005
Est. Priority Date: 06/06/2002
Status: Abandoned Application

First Claim

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1. ) A process for identifying similar 3D substructures onto 3D atomic structures having a plurality of individual atoms comprising:

a) attributing to each individual atom of the 3D atomic structure a structural parameter combining atomic local density D, local center of mass C and orientation in relation with position P;

b) constructing chemical groups by setting individual atoms having similar structural parameters;

c) constructing clusters of at least three chemical groups by setting the chemical groups whose reciprocal distances are constrained; and

d) comparing clusters constructed in step (c) and identifying the clusters sharing similar 3D structures.

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Abstract

The invention pertains to the field of structural biology and relates to a process to compare various three-dimensional (3D) structures and to identify functional similarities among them. The process of comparison of 3D atomic structures of the invention is based on the comparisons of defined chemical groups onto the 3D atomic structures and allows the detection of local similarities even when neither the fold nor sequence for example aminoacid sequences for polypeptides sequences or nucleotide sequences for nucleic acid sequences are conserved. This process requires the attribution of selected physico-chemical parameters to each atom of a 3D atomic structure, then the representation of each 3D atomic structure by a graph of chemical groups.

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28 Claims

1. ) A process for identifying similar 3D substructures onto 3D atomic structures having a plurality of individual atoms comprising:
- a) attributing to each individual atom of the 3D atomic structure a structural parameter combining atomic local density D, local center of mass C and orientation in relation with position P;
  
  b) constructing chemical groups by setting individual atoms having similar structural parameters;
  
  c) constructing clusters of at least three chemical groups by setting the chemical groups whose reciprocal distances are constrained; and
  
  d) comparing clusters constructed in step (c) and identifying the clusters sharing similar 3D structures.
- View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28)
- - 2. ) The process according to claim 1, wherein the atomic local density D is calculated for each atom A on basis to position P defined by coordinates (x_p, y_p, z_p) as a function of density m, modulated by a weight function w, according to:
    - $D (x_{P}, y_{P}, z_{P}) = \frac{\begin{matrix} \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} w (x - x_{P}, y - y_{P}, z - z_{P}) \cdot \\ m (x, y, z) \cdot ⅆ x \cdot ⅆ y \cdot ⅆ z \end{matrix}}{\int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} w (x, y, z) \cdot ⅆ x \cdot ⅆ y \cdot ⅆ z}$
  - 3. ) The process according to claim 2, wherein the weight function w is a spherical function $w$
    - ( x , y , z ) = 1 4 ⁢
      
      ( 1 - r r c ) if r≦
      
      r, 0 otherwise where r is {square root}{square root over (x²+y²+z²)}, r_ca critical radius and the factor [¼
      
      ] allows to make r independent from r_cif m is constant.
  - 4. ) The process according to claim 1, wherein a local center of mass C(P) for a given atom A occupying a position P is calculated as a point which cartesian coordinates (x_c, y_c, z_c) match the following:
    - ${\begin{matrix} x_{C} (x_{P}, y_{P}, z_{P}) = \frac{\begin{matrix} \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} w (x - x_{P}, y - y_{P}, z - z_{P}) \cdot \\ m (x, y, z) \cdot x \cdot ⅆ x \cdot ⅆ y \cdot ⅆ z \end{matrix}}{\begin{matrix} \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} w (x - x_{P}, y - y_{P}, z - z_{P}) \cdot \\ m (x, y, z) \cdot ⅆ x \cdot ⅆ y \cdot ⅆ z \end{matrix}} \\ y_{C} (x_{P}, y_{P}, z_{P}) = \frac{\begin{matrix} \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} w (x - x_{P}, y - y_{P}, z - z_{P}) \cdot \\ m (x, y, z) \cdot y \cdot ⅆ x \cdot ⅆ y \cdot ⅆ z \end{matrix}}{\begin{matrix} \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} w (x - x_{P}, y - y_{P}, z - z_{P}) \cdot \\ m (x, y, z) \cdot ⅆ x \cdot ⅆ y \cdot ⅆ z \end{matrix}} \\ z_{C} (x_{P}, y_{P}, z_{P}) = \frac{\begin{matrix} \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} w (x - x_{P}, y - y_{P}, z - z_{P}) \cdot \\ m (x, y, z) \cdot z \cdot ⅆ x \cdot ⅆ y \cdot ⅆ z \end{matrix}}{\begin{matrix} \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} w (x - x_{P}, y - y_{P}, z - z_{P}) \cdot \\ m (x, y, z) \cdot ⅆ x \cdot ⅆ y \cdot ⅆ z \end{matrix}} \end{matrix}$ where x, y and z are spatial coordinates, m is the density function and w is a weight function.
  - 5. ) The process according to claim 4, wherein the weight function w is a spherical function:
    - $w (x, y, z) = \frac{1}{4} (1 - \frac{r}{r_{c}})$ if r≦
      
      r_c, 0 otherwise where r is {square root}{square root over (x²+y²+z²)}, r_ca critical radius and the factor [¼
      
      ] allows to make r independent from r_c, if m is constant.
  - 6. ) The process according to claim 1, wherein in step (a), orientation of each atom A occupying a position P and having a local center of mass C(P) is calculated by a density gradient represented by a vector {right arrow over (CP)}.
  - 7. ) The process according to claim 1, wherein reciprocal distances between chemical groups in step (c) are 2 to 20 Å
    - .
  - 8. ) The process according to claim 1, wherein constructing clusters in step (c) comprises orientation of the clusters against the 3D atomic structure.
  - 9. ) The process according to claim 8, wherein orientation of the constructed cluster against the 3D atomic structure is operated by a scalar triple product of three vectors {right arrow over (CP)}_i, {right arrow over (CP)}_j, {right arrow over (CP)}_k, wherein C is the center of the local centers of mass of each chemical group and P_i, P_j, P_kare three distinct points in the cluster.
  - 10. ) The process according to claim 1, wherein clusters of chemical groups are further stored in a database.
  - 11. ) The process according to claim 1, wherein comparison of a given pair of clusters in step (d) comprises identification of at least one structural similarity selected from the group consisting of:
    - same chemical groups and similar orientation, similar length of reciprocal distances between chemical groups, similar local density of the chemical groups, similar orientation of the constructed clusters, and capability of binding flexible ligands using the same kind of weak chemical bonds.
  - 12. ) The process according to claim 11, wherein after identification of at least two structural similarities, a global score is calculated as a function combining several parameters indicating similarity of the clusters, the parameters being selected from the group consisting of:
    - volume of chemical groups, scarcity of the chemical groups, quality of the superposition with respect to the standard deviation, quality of the superposition with respect to the orientation of the chemical groups, and resemblance of the atomic environment.
  - 13. ) The process according to claim 12, applied to the capability of binding flexible ligands using the same kind of weak chemical bonds.
  - 14. ) The process according to claim 13, wherein the capability may be estimated by analysis of deviation of short range distances between chemical groups.
  - 15. ) The process according to claim 12, wherein the resemblance between atomic environment comprises calculation of a score by comparing volumes of atoms around each converted pair of chemical groups.
  - 16. ) The process according to claim 15, wherein the score is calculated by the function:
    - $s (v_{1}, v_{2}, v) = 1 - \frac{2 v - (v_{1} + v_{2})}{v}$ wherein;
      
      V₁is the volume of atoms surrounding chemical groups in cluster (3D atomic substructure) extracted from atomic structure M₁;
      
      V₂is the volume of atoms surrounding chemical groups in cluster (3D atomic substructure) extracted from atomic structure M₂; and
      
      V is the volume of atoms surrounding chemical groups in both clusters after superposition of the the clusters.
  - 17. ) The process according to claim 1, wherein before step (c) a further step (f) comprising the restriction of constructed chemical groups is performed by selection of chemical groups at locations where the local atomic density is below a definite threshold.
  - 18. The process according to claim 1, wherein before step (c), a further step (g) comprising restriction of constructed chemical groups is performed from at least one step of:
    - automatic selection of most exposed chemical groups using a local density function and a selected threshold, semi-automatic selection of chemical groups that are interacting with a given set of chemical groups, and manual selection of subsets of chemical groups.
  - 19. ) The process according to claim 1, further comprising a refinement step comprising:
    - i) converting the pairs of clusters identified in step (d) to pairs of chemical groups, and ii) minimizing reciprocal distances between converted pairs of chemical groups by a distance function.
  - 20. ) The process according to claim 19, wherein steps (i) and (ii) are iteratively repeated using variable selection thresholds.
  - 21. ) The process according to claim 19, wherein the reciprocal distances between converted pairs of chemical groups are calculated by the function:
    - dist(g₁,g₂)=α
      
      ·
      
      ∥
      
      pos(g₁)−
      
      pos(g₂)∥
      
      +β
      
      ·
      
      |D(g₁)−
      
      D(g₂)|+γ
      
      ·
      
      orient(g₁,g₂) wherein pos(g) is the position of chemical group g after optimal superimposition of a given set of converted pairs, D(g) local density, orient(g₁,g₂) is the difference of orientation between chemical groups g₁and g₂after optimal superimposition, and α
      
      , β and
      
      γ
      
      are normalizing coefficients calculated such that the average value of each term is ⅓
      
      , on the basis of a statistical set of pairs of similar chemical groups.
  - 22. ) The process according to claim 1, further comprising a step (e) of clustering pairs of clusters identified in step (d) into a larger pair of clusters sharing similar 3D structures.
  - 23. ) The process according to claim 1, wherein the 3D atomic structure having a plurality of individual atoms is a covalent or weak assembly of at least one molecule selected from the group consisting of natural and artificial proteins, oligopeptides, polypeptides, nucleic acids, natural and artificial oligonucleotides, natural and artificial oligosaccharides and polysaccharides, glycoproteins, lipoproteins, lipids, ions, water, natural and synthetic polymers, non polymeric structures, and natural and artificial inorganic molecules.
  - 24. ) The process according to claim 1, wherein the 3D atomic substructure is a functional site.
  - 25. ) The process according to claim 24, wherein the functional site is selected from the group consisting of enzymatic active sites, sites of reversible or irreversible binding of specific classes of molecules, sites sensitive to physico-chemical changes in the environment, chemical groups involved in energy conversion, self modification locations, antigenic parts of a molecule, mimetic sites, consensus sites, highly variable sites, sites necessary for initiating or interrupting a biological pathway, sites with particular physico-chemical properties, sites with particular chemical composition, protein taxons, immunoglobulin domains, DNA consensus sequences, gene expression signals, promoter elements, RNA processing signals, translational initiation sites, recognition motifs of a large variety of sequence-specific DNA-binding proteins, protein and nucleic acid compositional domains, glutamine-rich activation domains, CpG island, interaction site between a protein and a ligand, and functional sugar binding site.
  - 26. ) The process according to claim 1, wherein the 3D atomic substructures are 3D structural sites obtained from combinatorial, or conventional screening.
  - 27. ) A process to predict functional sites onto 3D atomic structures comprising identifying 3D atomic substructures by a process according to claim 1, comprising correlation of the identified 3D atomic substructures with a known biological or chemical function.
  - 28. ) The process according to claim 1, further comprising calculation of average orientation of 3D atomic substructures A and B with respect to orientation of their individual atoms and a visual representation of A and B 3D atomic substructures, wherein the visual representation is operated by graphs projections matching the following conditions:
    - a) the average orientation of the 3D A atomic structure is orthogonal to the projection plane; and
      
      b) thee substructure B is optimally superimposed on the substructure A.

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Current Assignee
Centre National De La Recherche Scientifique, Université Claude Bernard Lyon 1
Original Assignee
Centre National De La Recherche Scientifique, Université Claude Bernard Lyon 1
Inventors
Deleage, Gilbert, Geourjon, Christophe, Jambon, Martin

Application Number

US11/005,346
Publication Number

US 20050182570A1
Time in Patent Office

Days
Field of Search
US Class Current

702/19
CPC Class Codes

G16B 15/00 ICT specially adapted for a...

Process for identifying similar 3D substructures onto 3D atomic structures and its applications

First Claim

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Abstract

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28 Claims

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Process for identifying similar 3D substructures onto 3D atomic structures and its applications

First Claim

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Abstract

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