webPSN

General Intro

The webPSN web server employs a mixed Protein Structure Network (PSN) and Elastic Network Model-Normal Mode Analysis (ENM-NMA)-based strategy to investigate allosterism in biological systems [1,2]. PSN is used to compute the interaction strengths and connectivities among nodes while ENM-NMA provides information on system’s dynamics, which serves to compute the cross-correlation of atomic motions for path filtering. The method is hereafter indicated as PSN-ENM.

In synthesis, the first step in the PSN-ENM approach consists in performing the PSN analysis on a single high resolution structure, which serves to derive the network components (e.g. nodes, links, hubs, communities). Nodes interconnectivities represent also the basis to search for all possible shortest communication paths between all nodes in the network. The shortest paths are then filtered out according to the cross-correlation of atomic motions derived from ENM-NMA resulting in a reduced pool of paths composed of highly correlated nodes. Finally, a global metapath made of the most recurrent links in the shortest path pool is computed to infer a coarse picture of the structural communication in the considered system. Single paths can be inferred as well by providing a single node pair as an input of path search.

The first version of webPSN server was designed to compute only Single-structure PSN-ENM analyses. Important novelties concern the possibility to: a) compare Protein Structure Graphs (PSGs) (e.g. nodes, hubs, and links) or metapaths computed on two structures (i.e. difference network) and b) infer links, hubs, communities, and metapaths from consensus networks computed on a set of homologous or analogous systems. Computation of consensus network allows to infer common structural communication features in proteins sharing the same functionality [1, 2, 5, 7, 9] or even sharing only the fold. On the other hand, computation of difference network is particularly useful to infer commonalties and differences in the structural communication of two functionally different states of the same protein either induced by ligand or mutation [1, 2, 6, 7].

The updated version deals not only with proteins but also with nucleic acids and protein-nucleic acid complexes.

Difference and consensus network computations rely on a unique positional labeling and the server provides different options for this task: from a fully automated approach, based on the structural and/or sequence alignment performed by external, state of the art, software [10-14], which does not require any user intervention, to a fully customizable labeling syntax for advanced users.

The webPSN server produces high quality and publication-ready plots and 3D outputs, as PyMol and VMD scripts, as well as a number of easy-to-access data files. Additionally, all these outputs are conveniently zipped for download.

Selection Syntax

Appendix A: Selection Syntax

webPSN adopts a modified version of the selection syntax used in Wordom .

This syntax employs a string structured as follows:

/chain/segment/residues

Note: a segment is the 12th field in the pdb (3rd after coordinates). It is a 4-character field, which must not be confused with the chain (single-character) field after the residue-type in the pdb (5th field).

Wild cards such as * (any number of any character), ? (any single character), [abc] (any single character among a, b and c) and [!abc] (any single character except a, b and c) are supported. Ranges can also be defined using - character.

Syntax       Meaning
/*/*/*       selects all residues in all chains and segments (can be omitted, applied by defualt)
/C/S/*       selects all residues in chain C and segment S
/C/S/135     selects only residue 135 from chain C and segment S
/C/S?/*/*    selects all residues in chain C and segment S1, SB, SC ...
/C/S[AB]/*   selects all residues in chain C and segment SA, SB
/C/S/1-326   selects all residues in the range 1-326 (terminals included) from chain C and segment S

Ranges can be concatenated using the | character

Syntax               Meaning
/C/S/1-10|15|20-30   selects the following residues from chain C and segment S:
                     from 1 to 10, 15 and from 20 t0 30

Finally, several selections can be concatenated using the ; character

Syntax                               Meaning
/A/Q/* ; /B/W/1-10|15 ; /G/E/20-30   selects all residues from chain A and segment Q
                                     residues from 1 to 10 and 15 from chain B and segment W and
                                     residues from 20 to 30 from G and segment E

External Values Files

Appendix B: External Values Files

The user can, optionally, provide numerical values to be associated with any number of residues (e.g. conservation scores, mutation effect, etc.). If provided, these values will appear in the output tables (column OutVal) and the user will be able to search and sort output tables on the basis of these values.

The user can submit external values using one of the following file formats:

1. A text file with 2 columns per line, one residue definition and one numerical value separated by at least one space or tab character, as in the following excerpt:

   ...
   C:S:Y10   7
   C:S:V11   7
   C:S:P12   5
   C:S:F13   6
   C:S:S14   4
   C:S:N15   7
   C:S:?100  5
   ...

   
   Residues are defined using the following syntax:

   Chain:Segment:ResTypeResNum

   
   

   Please use one-letter codes for standard amino acids (e.g. P for proline, Y for tyrosine, etc) and the following lower case one-letter codes for standard nucleotides:

   Base	Code
   A, DA	a
   C, DC	c
   G, DG	g
   DT	t
   U	u

   Use ? character for any other molecule present in your pdb.



2. A csv (comma-separated) file with 2 columns per line. The same rules for the residue definition listed above apply to this format.
   A csv file can be created using common spreadsheet software (e.g. LibreOffice Calc, MS Excel and Google Sheets).


3. ConSurf conservation scores. The user can directly submit the consurf.grades output file generated by the ConSurf server without any modification. Please, note that the COLOR column will be used and not the SCORE (i.e. the 5th column after the header and not the 4th one).

Note: When used in difference and consensus networks, the values refer to the selected reference structure and will be applied to all other networks using labels.

Labels Files

Appendix C: Label Files

This server provides four options for this task:

1. Label generation using the provided assisted tool (recomended)


2. User-submitted label files


3. Automatic label generation by structural/sequence alignment software


4. Label generation on the basis of a user submitted multi sequence alignment

Although the compilation of label files may require a considerable amount of time depending on the size and number of analyzed structures, label files provide the user with a full control of the labeling process.

...
C:S:Y10   Tyr10
C:S:V11   Val11
C:S:P12   Pro12
C:S:F13   Phe13
C:S:S14   Ser14
...

Chain:Segment:ResTypeResNum

Please use one-letter codes for standard amino acids (e.g. P for proline, Y for tyrosine, etc) and the following lower case one-letter codes for standard nucleotides:

Use ? character for any other molecule present in your pdb.

...
C:S:?100   Ligand
...

Summary Tables

Appendix D: Description of Summary Tables

Network Similarities
Average % Shared Neighbours (Jaccard)	Is the average of the ratio of the intersection over union of each node links. Where n is a given node in network A and B, and An and Bn are the links of node n in network A and B, respectively [20].
Average % Shared Neighbours (Otsuka version of cosine similarity)	Is the average of the ratio of the intersection over the square root of the product of the number of links made by each node in compared networks.. Where n is a given node in network A and B, and An and Bn are the links of node n in network A and B, respectively [21].
Average % Shared Neighbours (Overlap Coefficient)	Is the average of the ratio of the intersection over the smaller list of links made by each node. Also known as overlap coefficient. Where n is a given node in network A and B, and An and Bn are the links of node n in network A and B, respectively [22].
Average % Shared Cliques (k3-6)	Is the average of the ratio of the intersection over union of k=3, k=4, k=5, and k=6 cliques. Where Ak and Bk are k-cliques in in network A and B, respectively.
Graphlets Similarity	Is the Graphlet Degree Distribution Agreement calculated comparing in the two network the distribution of Graphlets small, connected, non-isomorphic subgraphs [23].

Summary Tables

Appendix E: Trajectory Statistic Plots

For each non standard aminoacids/nuclotides in your trajectory, the following statistics will also be present:

where LigName is the label of a given non standard aminoacids/nuclotides

Theory

PSN analysis is a product of graph theory applied to protein and nucleic acid structures [4, 16]. A graph is defined by a set of vertices (nodes) and connections (edges) between them. In a PSN, each amino acid residue is represented as a node and these nodes are connected by edges based on the strength of non-covalent interactions between residues. The strength of interaction between residues i and j (I_ij) is evaluated as a percentage given by equation 1:

where n_ij is the number of atom-atom pairs between the side chains of residues i and j within a distance cutoff of 4.5 Aring. N_i and N_j are normalization factors for residue types i and j, which account for the differences in size of the amino acid side chains and their propensity to make the maximum number of contacts with other amino acids in protein structures. Glycines, are now included in the PSN analysis. The webPSN server has an internal database with the normalization factors for the 20 standard amino acids and the 8 standard nucleotides (i.e. dA, dG, dC, dT, A, G, C, and U), as well as for more than 30,000 biologically relevant molecules and ions (ligands, lipids, sugars, etc) from the PDB. Additionally, the server automatically identifies un-parametrized molecules in the submitted PDB files and automatically calculates their normalization factors transparently.

I_ij are calculated for all node pairs. At a given interaction strength cutoff, I_min, any residue pair ij for which I_ij ≥ I_min is considered to be interacting and hence is connected. Node interconnectivity is used to highlight node clusters, where a cluster is a set of connected nodes in a graph. Cluster size, i.e., the number of nodes constituting a cluster, varies as a function of the Imin, and the size of the largest cluster is used to calculate the I_critic value. The latter is defined as the I_min, at which the size of the largest cluster is half the size of the largest cluster at I_min = 0.0%. Studies by Vishveshwara's [16] group found that optimal I_min corresponds to the one at which the largest cluster undergoes a transition. All resulting clusters are then iteratively connected by the link(s) with the highest sub-I_critic interaction strength to compensate, at least in part, for the lack of side chain fluctuations.

Theory - 2

Residues making four or more edges are referred to as hubs at that particular I_min. Such cutoff for hub definition relates to the intrinsic limit in the possible number of non covalent connections made by an amino acid in protein structures due to steric constraints. The cutoff 4 is close to the upper limit. The majority of amino acid hubs indeed make from 4 to 6 links, with 4 being the most frequent value.

Finally, links are then used to highlight network communities, which are sets of highly interconnected nodes such that nodes belonging to the same community are densely linked to each other and poorly connected to nodes outside the community. Communities can be considered as fairly independent compartments of a graph. They are identified using a variant of the clique percolation method, by finding all the k=3-cliques, i.e. sets of three fully interconnected nodes, and then merging all those cliques sharing at least one node.

The combination between a coarse grained representation of a protein structure (e.g. ENM) and Normal Mode Analysis (NMA) is ever increasingly used to study the collective dynamics of complex systems. ENM-NMA is a coarse grained normal mode analysis technique able to describe the vibrational dynamics of protein systems around an energy minimum. With this technique, each protein/nucleic acid structure is described by a reduced subset of atoms corresponding to the Cα-atoms, for standard amino acids, and the atom nearest to the geometric center for all other molecules.

The interactions between particle pairs are given by a single term Hookean harmonic potential. The total energy of the system is thus described by the simple Hamiltonian:

where d_ij and d_ij⁰ are the instantaneous and equilibrium distances between particle i and j, respectively, whereas k_ij is a force constant, defined as:

where C is constant (with a default value of 40 Kcal/mol ·Å²).
The cross-correlations of motions for path filtering are obtained from the covariance matrix C [17]:

where C_ij denotes the correlation between particles i and j, M is the number of modes considered for computation (the first 10 non-zero frequency modes), ν_xy and λ_y are, respectively, the x^th element and the associated eigenvalue of the y^th mode.

All ENM-NMA calculations are performed by means of the latest realease of our Wordom software [18] 

Path Search and Filtering

The search for all shortest paths relies on Dijkstra’s algorithm [19]. The method first finds all possible communication paths between all node pairs and then filters the results according to cross-correlation of atomic motions, as derived from ENM-NMA analysis.

Filtering consists in retaining only those shortest paths that contain only residues with a correlation ≥ 0.7 with at least one of the two path extremities (i.e. the first and last amino acids in the path).

Finally, filtered paths were used to build the global meta path, which is made of the most recurrent links, i.e. those links present in a number paths ≥ 10% of the number of paths in which the most recurrent link in present.

Such meta path represents a coarse/global picture of the structural communication in the considered system.

In the result page, the user can filter those paths that begin and end at a given residue pair or that pass through a residue. Such a path filtering provides a novel metapath and is particularly recommended when some information on residues involved in structural communication is available.

References

References

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