Yakusa Overview Yakusa databases Yakusa results Yakusa text results file

YAKUSA overview

YAKUSA (Yet Another K-Uples Structure Analyser) is a program devised to rapidly scan a structural database with a query protein structure. It searches for the longest common substructures, called SHSP for "structural high scoring pairs'', between a query structure and every structure in the structural database. It makes use of protein backbone internal coordinates (α angles) in order to describe protein structures as sequences of symbols. It uses a deterministic finite automaton for pattern matching. The structural similarity is established in five steps, the three first ones being analogous to those used in BLAST:
  1. building-up of a deterministic finite automaton describing all patterns identical or similar to those in the query structure,
  2. searching for these patterns in every structure in database,
  3. selection and extension of these patterns in longer matching substructures, i.e. the SHSPs,
  4. selection of compatible SHSPs for each query/database structure pair,
  5. ranking of the query/database structure pairs with score based on SHSP probabilities and spatial compatibility of the SHSPs.Structural fragment probabilities are estimated by the mixture transition distribution model, which is an approximation of high order Markov chain models.

Structures Description

α and τ angles Yakusa is a local structural similarity searching method that works at the residue Cα level and makes use of the backbone internal angles. The advantage of internal angles is their simplicity for describing protein structure at the "local" level.
To describe protein structures, we use the α and τ internal angles. The α angle is the dihedral angle between four consecutive α carbons and τ is the angle made by three consecutive α carbons (see left). These angles can be computed from the 3D coordinates of the Cα atoms, and the Cα backbone can be completely described by α angles, τ angles and distances between successive Cα. Since τ angles are almost constant and distances between two Cα are also almost constant (around 3.8 angstrom), protein backbone structure is accurately described by only α angles. We cluster α angles into classes over a mesh. We use a 10° mesh, so there are 36 classes of α angles. We represent a class by a numerical symbol (an integer) and we describe the structure as a run of such symbols. Then 3D backbone structure can be considered as a text and we can apply any pattern matching algorithms on this "structural text". Therefore, we consider a protein structure as an internal angle linear sequence; this description tremendously speeds up similarity searches. Furthermore, as we are interested only in finding gap-free similar structural "blocks" in two proteins, we address this problem by examining contiguous internal angle stretches in them.

General Algorithm

As protein structures are viewed as texts, the general principle is first to find all fixed size common patterns (identical or similar) between the query protein and each database protein. The execution time for this step is proportional to the length of the protein databas. In a second stage, most "promising" patterns are selected and extended and they give rise to the longest similar segments, SHSP, between query and database structures. The local structural similarities between the query structure and each database structure are established in five steps. All these steps, except the first one, are repeated for each entry of the structural database. The global score of each query/database structure pair is used for ranking the results.

Scanning the database

[words in color refer to YAKUSA parameters] The automaton contains all overlapping fixed length query patterns (seed length) and all the patterns similar to each of them; they are called seeds. When seeking protein structural similarities, an α angle of 20° can be considered as similar to an angle of 30° as to an angle of 10°, because a difference (degeneracy) between angles must be taken into account to seek not only for strictly identical patterns but also for closely related ones. To generate patterns similar to the ones of the query we introduce a "local degeneracy" at the level of every pattern symbol. This "local degeneracy" is limited to a maximum local degeneracy, δmax, and it is expressed in mesh units. For example, with a 10° mesh, the symbol 2, represents the interval of α angles between [20°,30°[. When a δmax=1 is applied, this symbol 2 will be considered similar to the symbols 1 and 3, which represent respectively the intervals [10°,20°[ and [30°,40°[. However, for two protein backbone segments, succession of cumulated small angle differences can lead to noticeable structure discrepancy. In order to limit the propagation of this local degeneracy, we define a "global degeneracy" threshold, Δmax. And, for a generated pattern to be similar to a query pattern, the sum of absolute values of local degeneracies must be lower than the threshold Δmax, also expressed in mesh units.
Each database structure, encoded into α angles, is scanned linearly, as going through the automaton and common seeds are found beetween the query structure and each database structure. These seeds are gathered, filtered and extended to SHSPs, which must be longer than a threshold.
The ranking score is based on SHSP probabilities and spatial compatibility of the SHSPs. The SHSPs "spatial compatibility" is is based on their RMS. Structural fragment probabilities are estimated by the mixture transition distribution model, which is an approximation of high order Markov chain models.

YAKUSA Parameters

YAKUSA parameters and default values are: As an option, a filter can be put on canonical α helix. It hides the middle of α helices but keeps their ends. Helices are hidden during the search of seeds, but not in the extension step. Therefore, α helices are finally still found but as they would lead to the generation of many seeds in first steps, the scan is faster.

Databases available for scanning

  1. In order to get accurate results and to limit an uninteresting huge output, we use a non redundant PDB (8742 entries in February 2004), made up of protein structures which:
  2. Others filtered databases of representative PDB structures can be used: ASTRAL databases and Culling databases, at several amino acids identity rates.

see also a more detailed explanation of the databases


In protein structures, neighbouring α angles are far from independent, and correlations between neighbouring angles spread over several residues. A higher than first order Markov chain modelling of these dependancies need many more parameters than one could estimate on available PDB structures. Therefore, we used a Mixture Transition Distribution Model for high order Markov chains modelling within a finite state space.

Briefly, the MTD model approximation is a conditional probability pair approximation. Let Xt be a random variable in a finite set A1..m. In an lth order Markov chain, the probability of Ht=α0, depends on the combination of values taken by Ht=α0. In the MTD model, the contribution of each lag to the "present" is additive: Ht=α0
where αl..α0 , probabilities αqα0 are elements of a m.m transition matrix Q={qij} each of whose rows is a probability distribution, and λ=(λl,...,λ1)' is a vector of lag parameters. To ensure that the results of the model are probabilities, λ is subject to the two following constraints:
This model has only m(m-1)+l-1 independent parameters, while a Markov chain model needs m^l-1 parameters.

Here, as a finite set of states, we take the set of α angles discretized on a 10° mesh (so Q is a 36 x 36 matrix). The MTD model parameters are estimated on the non redundant PDB structures and we take a l value of 8. To a SHSP is assigned the probability of the database structural fragment composing this SHSP. The probability of a structural fragment in the database is computed from the run of its angles according to the MTD model (for the SHSP 8 first angles, we use a conditonal probability, with l=2). With this MTD model, the probabilities associated with standard secondary structures, as α helices, increase and these fragments are therefore more easily discarded. This allows to bring to the fore interesting fragments having less standard secondary structures. The ranking score is the sum of the logarithm of these SHSPs probabilities (x-1, so they are positive). However, all found SHSPs probabilities are not always used: by default, only "spatially compatible" SHSPs are used to compute ranking scores.

Key references for MTD:

Spatial compatibility

YAKUSA have found four SHSPs but only 3 of them are "spatially compatible", the purplegreen and yellow ones. If the two structures are aligned on the cyan SHSP, other SHSPs RMS ()are very high, while if they are aligned on the three others SHSPs (on this figure, they are aligned on the green one), RMSs are low execpt for the cyan SHSP. We compute RMS of all SHSPs for each spatial alignment:

for alignment
1 2 3 4
1 0.4 39.6 14.0 24.2
2 39.9 1.2 1.7 7.4
3 55.2 6.2 0.9 8.9
4 26.9 9.0 5.9 1.7
SHSPs are considered in the same group when all their RMSs are below a threshold (15 Angstrom by default).
In red, 1i1g (chain A), crystal structure of the lrp-like transcriptional regulator from the archaeon pyrococcus furiosus. In blue, 1b4a (chain F) structure of the arginine repressor from bacillus stearothermophilus.

Last modified: Tue Dec 7 18:18:43 CET 2004