Beta Structure Definitions

Kabsch and Sander define all beta structure in terms of `bridges' which are either parallel or antiparallel. Where two or more bridges of the same type are consecutive, the structure is termed a ladder. Finally, overlapping ladders are amalgamated into sheets. Additional complications arise because ladders may have discontinuities in them, and ladders may consists of just a single bridge. These aspects of protein structure make the coding of beta-structure in Prolog a little less straightforward than for helix.

In finding the sheets in a protein, the following steps are performed:

• Define the parallel and antiparallel bridges.

• Define start and end points of ladders.

• Build ladders of that consist of two or more consecutive bridges.

• Identify ladders that consist of a single bridge (bridge_ladder).

• Locate ladder pairs that are linked by a - bulge.

• Identify - sheets in terms of the ladders that make them up.

• Identify - strands by examining the sheets.

The general Prolog rules developed for - structure are:

bridge(I-J,CID1,CID2,Btype)
ladder_start(A-B,CID1,CID2,Btype)
ladder_end(A-B,CID1,CID2,Btype)
ladder(BridgeList,CID1,CID2,Ltype)
bridge_ladder(ladder([A-B],CID1,CID2,Type))
bulge_linked_ladders(Ladder1,Ladder2)
l_sheet(PID,LadderList,Type)
strand(NumberList,CID)
s_sheet(PID,StrandList,Type)

Where I-J is a pair of residue identifiers from chains CID1, CID2 respectively. Btype is the bridge type, either parallel or antiparallel. BridgeList is a Prolog List containing bridge/4 facts. Similarly, LadderList is a list of ladder/4 definitions, whilst NumberList is a list of residue numbers. The bulge_linked_ladders/2 rule identifies two ladders that are linked by a - bulge.

Examples of these facts specific to the protein 1fb4 are shown here:

bridge(200-205,1fb4l,1fb4l,antiparallel)
bridge(228-340,1fb4h,1fb4h,parallel)

ladder([4-101,4-102,4-103],1fb4l,1fb4l,parallel)
ladder([35-90,36-89,37-88,38-87,39-86],1fb4l,1fb4l,antiparallel)

l_sheet(1fb4,
       [ladder([4-101,4-102,4-103],1fb4l,1fb4l,parallel),
        ladder([8-106,9-106,10-107,11-108,12-109,12-110],1fb4l,1fb4l,parallel),
        ladder([35-90,36-89,37-88,38-87,39-86],1fb4l,1fb4l,antiparallel),
        ladder([36-49,37-47,38-46],1fb4l,1fb4l,antiparallel),
        ladder([85-107,86-106,87-105],1fb4l,1fb4l,antiparallel),
        ladder([89-102,90-101,91-100,92-99,93-98],1fb4l,1fb4l,antiparallel)
       ],mixed)

s_sheet(1fb4,
       [strand([4],1fb4l),
        strand([8,9,10,11,12],1fb4l),
        strand([35,36,37,38,39],1fb4l),
        strand([46,47,48,49],1fb4l),
        strand([85,86,87,88,89,90,91,92,93],1fb4l),
        strand([98,99,100,101,102,103],1fb4l),
        strand([105,106,107,108,109,110],1fb4l)
       ],mixed)

Two alternative representations of a - sheet are shown. The first consists of the list of ladder clauses that are used in the definition of the sheet. This representation immediately shows which residues are involved in the sheet and what their hydrogen bonding partners are. The sheet type is also defined as one of pure parallel, pure antiparallel, or mixed, depending upon the type of ladders in the sheet. Having established the sheet definition, it is possible to define the - strands that make up the sheet and consequently to define the second alternative sheet fact. This shows a list of strand definitions in place of the ladder definitions.

The time required to calculate all secondary structure definitions for a protein is dependent upon the number of residues present, and the total secondary structure content. Some typical examples are: 1fb4 (Immunoglobulin) a protein of 445 residues in total takes 50 seconds (including consultation time); 1mbn (Myoglobin) an all protein of 153 residues takes 25 seconds on a SPARCstation 1.