Calculating an Overall Flexibility for Amino Acid Side Chains

Enhancement of the ElMaR Scoring Function

In the previous chapters, the enhancement of rigid body docking algorithms by flexibility predictions has been described. In the following a second step to enhance protein docking is outlined. Here, the scoring of docking hypotheses is addressed.

Generally, not only for the ElMaR system, the ranking of docking hypotheses is still not solved today. The main problem is to distinguish between correct and false positive solutions (see Halperin et al., 2002). An optimal set of weights for the individual components can vary between different query proteins. During development those weights can be modified explicitly, but knowledge about the implementation details, especially about the scoring function is needed.

In this chapter a method is proposed to enhance the docking systemElMaR. This approach (Intelligent Protein Hypothesis Explorer, IPHEx) addresses the weighting scheme used in ElMaR, trying to adapt better weights by using relevance feedback techniques.

Following this introduction, the scoring scheme of ElMaR is outlined. Different methods for optimising weights used for scoring are discussed and the aim of the IPHEx system is given. In section 6.2 the principles of Query–by-Content (QbC) systems are presented and their application to protein docking is shown.

6.1 Ranking Docking Hypotheses using ElMaR

As already outlined in section 4.1 the ElMaR docking system uses the features geometry (P), hydrophobicity (H), and charge(Q) to score the hypotheses proposed by the docking algorithm. In order to combine these features to an overall score two weights (α,β) are used:

C= (1−α)(1−β)∗(P₁•P2) +α(1−β)∗(H₁•H2)−β∗(Q₁•Q2) (6.1) The cost function (C) reflects the ranking of a hypothesis of a complex¹. For testing the algo-rithm the root mean square deviation (RMSD) to a known crystallised complex is calculated as standard of truth. Plotting estimate against RMSD gives an overview about the docking algorithms performance (see Fig. 6.1). Ackermann and coworkers (Ackermann et al., 1998)

1Hypotheses with large costs are assigned a low rank whereas hypotheses with low costs receive high ranks.

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(a) Docking of 1AQ7 and 1BPI.

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(b) Docking of 1CHG and 1HPT.

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(c) Docking of 1BRA and 4PTI.

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(d) Docking of 2PTN and 5PTI.

Figure 6.1: Results of anElMaRdocking run for different test cases. Here, the parameters are chosen asα=0.5 and β=0.2. Each point in the graphics represents one docking hypothesis.

On the x-axis the estimate of the costs is plotted against the RMSD on the y-axis.²

estimated the parameters α and β by sampling. For the test set used in their work best results have been achieved forα=0.5andβ=0.2. Since the parameters are established for bound docking, they do not necessarily fit for unbound docking. Thus, the weights should be adapted.

Comparing the results of unbound docking shown in figure 6.1, in most cases, besides good hypotheses, also hypotheses with large RMSD values are placed on low ranks by the scoring function (especially in the case of Fig. 6.1(a)). In fact the parameters established on the whole test set do not fit for all test cases. A better approach might be to establish separate sets of parameters for certain subsets of the test set, e.g. protein families or proteins that have similar reaction schemes. Another example of a wrong assignment of ranks is given in figure 6.2. Here, the two docking hypotheses (blue/green) are superimposed to the

Figure 6.2: Ranking of hypotheses by the ElMaR scoring function. In yellow and red the conformation of the complex 2PTC is shown. In green the best ranked hypothesis is given.

It’s RMSD is 33 ˚A. In blue a similar hypothesis with the same RMSD (33 ˚A) is shown. This hypothesis has been assigned a rank of 37.

reference complex2PTC (yellow/red). The green coloured hypothesis has an RMSD of 33 ˚A.

Although it has been assigned the first rank, the blue coloured hypothesis is similar in its transformation and structural error (RMSD of 33 ˚A). In this caseElMaRranks the hypothesis on position 37.

In the literature, several approaches solve the parameter estimation by formulating an op-timisation problem. Rosen and coworkers (Rosen et al., 2000) e.g. propose the ENPOP algorithm that tries to find globally optimal parameters minimising energy landscapes of the problem under investigation. An iterative approach is proposed by Zien and colleagues (Zien et al., 2000), where two steps are performed: first the original application is run (here fold classification of sequences using the program 123D) to produce hypotheses and afterwards a calibration of the data is performed using an external “standard of truth”. The calibration method is based on the assumption that good solutions according to the classification score better than bad ones. Two methods called VIM and CIM are formulated that optimise the weights so that an optimal solution to a system of inequalities is found.

Comeau and coworkers (Comeau et al., 2004) proposed a clustering approach applied to a rigid body docking based on a fast Fourier transformation approach like ElMaR. Before clustering the active sites of the docking hypotheses, an energy filter (using electrostatic and desolvation potentials) is applied to cut down the number of possible solutions. Clustering is then performed on bases of pairwise RMSD calculations within the active site. Therefore, the receptor is held fix and for each ligand, all residues within 10 ˚A from its receptor are picked.

The RMSD is then calculated between the residue sets of the ligand of each hypothesis. This

approach returns in 31 out of 48 test cases at least one near native structure with an average RMSD of 5 ˚A. The processing of one complex takes up 4 hours on a 1.3GHz 16 CPU IBM pSeries690 server.

In contrast to the approaches mentioned before, the IPHEx system uses relevance feed-back techniques adapted from Query-by-Content (QbC) systems (cf. Salton & McGill, 1983;

Rui et al., 1998), especially from theINDI(Intelligent Navigation in Digital Image databases) system (K ¨ampfe et al., 2002; Bauckhage et al., 2003) which is rooted in information retrieval and was transduced to the field of image databases. Providing an easy to use interface hiding a potentially complex scoring function from the user, a set of hypotheses can be evaluated and scored easily. The 3D visualisation of the docking hypotheses enables the human expert to inspect and compare a hypothesis to other ones or to a known (homologue) complex.

The hypotheses are scored from highly relevant to highly non-relevant. The comparison and inspection of a hypothesis is not restricted to the positioning (the geometric complementar-ity) of the docked proteins. Other features like hydrophobicity and charge can be mapped onto the three–dimensional structures providing additional criteria to score the hypotheses.

After scoring a set of hypotheses, the system modifies the weights within the scoring func-tion according to the feedback. In contrast to optimisafunc-tion methods this approach also works if no “standard of truth” is available (unknown reference complex). In this case, e.g.

one hypothesis out of the predicted ones has to be chosen³.

Besides this, the approach formulated here can be used to navigate through a large set of docking results searching for hypotheses fulfilling certain criteria (defined by the user). Here, query by content retrieval can also be used. Criteria describing hypotheses to be searched for can be easily defined by picking a hypothesis as a query object. Similarity search can then be applied to find corresponding hypotheses within the set of docking results.

One goal of this work is the improvement of the scoring function and to find good weights (α,β). In a bootstrapping approach, the result of a feedback session is mapped onto all docked test sets in the database that have the same enzyme number assigned. Here, the idea is that proteins possessing the same enzyme number perform the same chemical reaction and thus, also the same biological function. This idea is derived from the definition of the enzyme numbers (c.f. NC-IUBMB, 1992). The enzyme numbers group proteins into classes according to their reaction scheme. Because of this, the docking mechanism of each enzyme class might be similar and the weights can be simply adapted.