the number of 3d protein structures determined by methods of nuclear magnetic resonance and x - ray crystallography is increasing rapidly . currently , over 54 000 structures are deposited in the protein data base ( pdb ) ( 1 ) .
results can be used for protein structure prediction and for the exploration of evolutionary studies .
protein topologies are also important for the study of protein folding processes , in particular of folding pathways ( 2,3 ) .
many proteins share similar geometric features in the conformation of the protein backbone ( 4 ) . with a few exceptions ,
the 3d structure of proteins can be characterized by patterns of secondary structure elements ( sses ) ( 5 ) .
structural protein topology can be defined as the relationship between the sequential ordering of sses and their spatial organization .
protein topology is one of the principal properties by which protein structures can be classified , categorized and compared .
the main protein structure classifications based on sses are provided by scop ( 6 ) , cath ( 7 ) and tops ( 8,9 ) .
super - secondary structure motifs , such as greek - key or  motifs , describe the interaction and position of sses .
the arrangements of sse motifs open the possibility for a topological description of protein structures .
the first theoretical work on protein topologies refer to  structure topologies ( 10,11 ) or  topologies ( 12 ) .
later , koch and co - workers ( 13,14 ) defined a protein graph incorporating helices as well as strands .
the simplest representations of protein topologies are schematic diagrams of protein folds illustrating the sses and their spatial neighborhoods .
richardson ( 4 ) derived the first protein topology diagrams as a cartoon representation of a biological point of view .
also several -motifs of sses were described , such as the greek - key or jelly roll motif ( 15 ) .
this cartoon representation is widely used , so , for example , in the protein classification databases , cath and scop .
another , but more complicated , representation is the hydrogen bond diagram that provides a graphical representation based on the hydrogen bonds between spatially neighbored sses ( 11 ) .
the protein structure databases cath , scop and pdbsum ( 16,17 ) do not provide a direct comparison of protein topologies .
cath and scop use knowledge on sequence similarity and protein function within their classification workflow , whereas protein topology graph library ( ptgl ) only relies on the underlying graph representation and does not explicitly consider the order of sses . the pdb sum database provides for every cath domain a single topological diagram generated using the promotif tool ( 11 ) , but again no global topology comparison is possible . the database tops ( 8,9 ) generates topology diagrams automatically and provides the possibility to search for secondary structure motifs .
tops uses a graph - based description of protein topologies , which is similar to ours .
they also provide a linear notation , which is restricted to only one description type . due to the underlying graph definition , which explicitly preserves the sequential order of sses , similar topologies with different sequential order of sses can not be found .
we developed a web - based database application , ptgl ( 18 ) , for representation and retrieval of protein topologies and additional protein data combined with online search tools for data interrogation by sequence similarity and keyword queries .
we provide unique linear notations of four descriptions for protein structures on different abstraction levels based on graph theory .
this enables us to represent complex information such as protein structures by relatively simple , but unique schematic descriptions .
protein topologies , i.e. the relationship between the ordering and connectedness of sses , can generally be expressed in terms of graph theory . a 
protein graph is defined as a labeled undirected graph for a single pdb chain , where the vertices correspond to sses ( helices , h and strands , e ) , and the edges represent spatial adjacencies of sses .
the sses are defined according to the assignment of the dssp algorithm ( 19 ) .
the edges are defined through contacts between sses using van der waals contacts ( 20 ) .
vertices of the protein graph are enumerated from the n- to the c - terminus . according to this direction , two spatially
neighbored sses can occur in a parallel ( p ) , antiparallel ( a ) , or mixed ( m ) neighborhood .
a protein graph consists of one or more connected components , which we call  folding graphs , because they often represent single folding units or domains . according to the considered sse type we distinguish between  ,  and  graphs .
folding graphs , containing vertices with a degree greater than two , are called  bifurcated. to explore topological aspects of sses in proteins , we provide four types of diagrams for every type of notation , key , adj , red and seq .
the arcs describe sequential neighborhoods between sses ( figure 1 ) . in the adj , red and seq diagrams
, sses are arranged according to their sequential order from the n- to c - terminus .
edges in the adj and red diagrams are colored according to their labels , red for  parallel , green for  mixed and blue for  antiparallel neighborhoods . in the adj diagrams , also
sses of other folding graphs are considered , whereas in red diagrams only sses of the folding graph under consideration are involved .
edges in the seq diagrams are drawn in black and indicate sequential neighborhoods . in dependence of the diagram type
, four linear notations can be derived , which can be used for searching and classification .
an example for a protein graph and the corresponding folding graphs in key notation is given in figure 1 . 

figure 1.the  topology browser for protein 1g3e chain a. on the left side , the  protein graph is shown together with additional information for the sses .
on the right side , the  folding graph a in key notation is shown .
topology browser for protein 1g3e chain a. on the left side , the  protein graph is shown together with additional information for the sses .
on the right side , the  folding graph a in key notation is shown .
ptgl is stored locally in an object - relational postgresql database running on a linux server .
programs for export , import and visualization have been implemented in perl and c. ptgl input data are acquired from the pdb .
additional data as header , title , molecule and information about ligands , cofactors and hetero atoms are derived from the associated pdb file .
the online search tool has five query browsers : ( i ) the simple keyword query searches for keywords , which can be connected by boolean operators ; ( ii ) the more customizable query searches in selected fields and tables , e.g. for sub - topologies in all  graphs or all graphs representing a certain cath classification ; ( iii ) a third batch query form accepts lists of proteins ; and ( iv ) a sequence search based on local blast ( 21 ) searches against the sequences stored in the ptgl main table .
the blast outputs are stored for 3 days , and the user has access via a request i d ( 5 ) .
the recent search type is the motif browser that allows the user to search for pre - defined common structural motifs , such as tim - barrel and jelly roll motifs ( figure 2 ) . 

figure 2.the tim barrel motif as 3d image ( upper left ) , the corresponding key notation ( middle left ) and two search patterns ( bottom left ) , both described in red as  graphs . for visualization purposes of the tim barrel motif ,
on the right site , the different occurrences of the motif in cath , scop and ptgl are depicted .
the differences between the ptgl and cath or scop mainly rely on applying a stronger , but more precisely definition for the motif , which limits the risk for false positives .
the tim barrel motif as 3d image ( upper left ) , the corresponding key notation ( middle left ) and two search patterns ( bottom left ) , both described in red as  graphs . for visualization purposes of the tim barrel motif ,
on the right site , the different occurrences of the motif in cath , scop and ptgl are depicted .
the differences between the ptgl and cath or scop mainly rely on applying a stronger , but more precisely definition for the motif , which limits the risk for false positives .
the clustering of the polypeptide chain sequences is done according to pre - calculated pdb cluster tables based on the cd - hit algorithm ( 22 ) .
then , the user can select the proteins of interest together with the graph type (  ,  or  ) and notation type .
links are provided to cath , scop and pdbsum . in the  topology browser , for every selected pdb chain
the topology diagrams of the protein graph and all folding graphs , consisting of more than one sse , are represented according to the selected notation together with a table compiling all sses ( figure 1 ) .
all diagrams of protein and folding graphs are generated automatically on the fly as postscript files that are converted to the portable network graphics format for representation on the web .
the topologies are also represented as 3d images which can be animated , using jmol ( http://jmol.sourceforge.net ) .
additionally , users can upload their custom pdb files to generate the different linear notations and diagrams .
all available graphs are compiled and searchable via the  content page , where general statistics is provided for every graph and notation type , including the numbers of current entries with their links to the  query browser. the  help and  user guide pages in ptgl ( http://ptgl.zib.de/ptglhelp.html ) give an exhaustive introduction with examples how to use and how to link to ptgl .
ptgl currently holds topology information of 54 859 proteins and 2 094 546 sses . only proteins with at least one defined sse according to dssp a protein structure resolution < 3.5  , and a sequence length of at least 20 amino acids
the number of unique  graphs is less than the sum of unique  and unique  graphs , because in  graphs , per definition , additional contacts between helices and strands are considered . 

1.ptgl contentgraph typetotaldifferentnon - bifurcatedbarrels606 81677 1272432666636 82029 984680191199 12213 4182246696the first column indicates the type of the folding graph .
 total gives the total amount of folding graphs of the particular graph type ; 
different the amount of different graphs among the total number ;  non - bifurcated the number of different non - bifurcated graphs including barrels ; and  barrels the number of different barrel structures .
different the amount of different graphs among the total number ;  non - bifurcated the number of different non - bifurcated graphs including barrels ; and  barrels the number of different barrel structures .
ptgl is an online database tool for retrieval and search of specific protein topologies using four linear notations , which are based on a unique graph - theoretical description of protein topology .
protein topologies are represented in four different types of schematic diagrams and as 3d images .
the database is useful for any kind of theoretical protein structure analysis , protein structure prediction and protein function prediction .
our database , ptgl , represents a useful extension to the existing protein structure topology databases .
ptgl was originally introduced in 2004 ( 18 ) ; the graph representations and corresponding topology diagrams were proposed in koch and co - workers ( 13,14 ) .
now , we added several new search functionalities as the pre - defined consensus notations for the most common structural motifs , the possibility to upload and to analyze custom protein structures , and additional functional annotation , such as enzyme commission numbers and links to the pdbsum database .
furthermore , we updated the database to the recent pdb , scop and cath releases , and moved to a new web location ( http://ptgl.zib.de ) .
german federal ministry of education and research by the forsys bmbf grant ( goforsys grant no . 0313924 to p.m. ) . funding for open access charge : max planck society .
 with growing amount of experimental data , the number of known protein structures also increases continuously . 
 classification of protein structures helps to understand relationships between protein structure and function . 
 the main classification methods based on secondary structures are scop , cath and tops , which all classify under different aspects , and therefore can lead to different results . 
 we developed a mathematically unique representation of protein structure topologies at a higher abstraction level providing new aspects of classification and enabling for a fast search through the data . 
 protein topology graph library ( ptgl ; http://ptgl.zib.de ) aims at providing a database on protein secondary structure topologies , including search facilities , the visualization as intuitive topology diagrams as well as in the 3d structure , and additional information . 
 secondary structure - based protein topologies are represented uniquely as undirected labeled graphs in four different ways allowing for exploration under different aspects . 
 the linear notations , and the 2d and 3d diagrams of each notation facilitate a deeper understanding of protein topologies . 
 several search functions for topologies and sub - topologies , blast search possibility , and links to scop , cath and pdbsum support individual and large - scale investigation of protein structures . 
 currently , ptgl comprises topologies of 54 859 protein structures . 
 main structural patterns for common structural motifs like tim - barrel or jelly roll are pre - implemented , and can easily be searched . 
INTRODUCTION
GRAPH NOTATIONS
CONTENT AND USAGE
CONCLUSIONS
FUNDING