Great Deluge Algorithm for Protein Structure Prediction

Transcription

1 Great Deluge Algorithm for Protein Structure Prediction Edmund Burke 1, Yuri Bykov 2, Jonathan Hirst 3 1,2 School of Computer Science & IT, University of Nottingham, Jubilee Campus, Wollaton Road, Nottingham, NG8 1BB, UK {ekb,yxb}@cs.nott.ac.uk 3 School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, UK jonathan.hirst@nottingham.ac.uk 1. Introduction Proteins are the basis of organic life on the Earth. These macromolecules appear as polymer chains comprising 70 to more than 500 residues (amino acids) of 20 different monomer types. In nature such chains fold into certain 3-dimensional structures (see example in Fig.1). The distinct property of proteins (which distinguishes them from other polymers) is that all molecules with the same order of residues fold into the same structure (so-called native state conformation). There is a general hypothesis that in the native state all interatomic forces are balanced and a molecule has the minimum possible internal energy. Fig. 1: The typical structure of a real protein The synthesis of new proteins is an important direction of modern biochemistry. Understanding how proteins fold is useful for creating new drugs, including ones against fatal diseases. However, the real engineering of new proteins and the recognition of their native state is a very slow and expensive process. The expenses of new proteins design can be substantially reduced by employing of different ways of prediction of the 3-dimensional structures of proteins. Every two

2 years the most effective prediction methods are evaluated at the CASP (Critical Assessment of Structure Prediction) research competition. However, up to the present time the best results have come from semi-empirical prediction techniques, which are based partly on human experience supplemented by computational tools. Most completely automated systems (such as ab initio methods) generally achieved weaker results. Our analysis of several such systems (e.g. [1],[5]) suggested that there is scope for the application of improved optimisation techniques. Our project lies at the interface of biochemistry and computer science (operations research) and aims to apply modern and powerful metaheuristics in order to improve ab initio protein structure prediction. 2. Great Deluge Algorithm The Great Deluge algorithm was introduced by Dueck in [4], but unfortunately was not widely useful in succeeding years. This local search metaheuristic is different to its predecessors (e.g. Hill-Climbing or Simulated Annealing) in the acceptance of a candidate solution from a neighbourhood. The Great Deluge algorithm accepts all solutions, for which absolute values of the cost function are less than or equal to the current boundary value, called level. The local search starts with the initial value of level equal to an initial cost function and during the search its value is monotonically reduced. A decrement of the reduction (defined by the user) appears as a single algorithmic parameter. In [2] the authors extended the Great Deluge algorithm by accepting all downhill moves (hybridising it with Hill-Climbing). This variant was successfully applied to university exam timetabling problems and its performance was thoroughly investigated. Further multiobjective modifications of this algorithm, which drive the search through specified trajectories in the criteria space were introduced and evaluated in [3] and [6]. These investigations reveal several advantages of this technique, in particular, that it allows in advance the definition of the characteristics of a search process (such as a processing time and a region of an expected final solution) more precisely than other approaches. The proper utilisation of these properties significantly increases the performance of a local search. When

3 experimentally compared with other existing techniques, the Great Deluge algorithm produced higher quality results on most benchmark problem instances. 3. The application of the Great Deluge Algorithm to a Protein Folding Problem In the terms of optimisation, the protein structure prediction can be viewed as solving the so-called Protein Folding Problem. It considers a chain of residues, which folds into a 3-dimensional conformation. Given the energy of interactions between each pair of residues as a function of the distance between them, the goal is to find the conformation, which imposes the minimum sum energy for the whole chain. It is supposed that the resulting conformation should conform to the native state of a real protein. Due to the high complexity of this problem, several simplifications were proposed in the literature: excluding most atoms from amino-acids, leaving only one; reduction of the number of residues types according to their properties; use of several types of lattices to restrict the number of possible conformations. In the course of our research, the performance of the Great Deluge algorithm applied to the Protein Folding Problem. Different levels of simplification were investigated. In most cases the algorithm was able to produce near-optimum solutions, however these solutions did not reflect real protein structures. One of the major weaknesses of the simplified models is that their inter-residue interactions are not well-defined. 4. Results of All-Atom Off-Lattice Model The most promising performance was achieved by rejecting the proposed simplifications and using an all-atom off-lattice model. Here all (or most) atoms participate in the search procedure and their positions are not restricted by any lattice. However, it is the most complex and a highly time-consuming variant. Therefore, our initial experiments were done with fragments of real proteins, in particular with those, which in the real world would fold into a helix (see Fig. 1). The model was developed in Delphi 7 and run on a PC Intel Celeron 2.2GHz. During development of the

4 software, significant attention was paid to the optimisation of the algorithm with respect to processing time. Our experiments were carried in order to define a dependence of the final results on the number of moves from the beginning to the convergence. The Great Deluge algorithm allows setting up this number (approximately) as an input parameter and thus, to define in advance the total search time. In Fig. 2 we present results of four different runs of the algorithm with the same 12-residue chain. All algorithmic parameters were the same except the predefined processing time (number of moves). Fig.2. Conformations of the same chain produced in different processing time In this figure the conformation a) was produced in moves (processing time was around 15 minutes) and has nothing similar to the native protein conformation (helix). In the result b), produced in moves (processing time 30 min) some helical tendencies are already visible. The result c), produced in moves( 1 hour of calculations) looks even more close to a helix. Finally, when launching the algorithm for moves (it took 2 hours) it produced the regular helix (result d), the same as in a real protein. 5. Conclusions and Future Work The obtained results demonstrate that the Great Deluge algorithm could be effective for protein structure prediction. The sample fragment should be gradually enlarged with the goal to envelop complete proteins. We recognize that computational expense

5 could rise disproportionately with the length of fragments. Therefore, the significant work should be done in order further increase processing speed. 6. Acknowledgment The research described in this paper was supported by BBSRC grant (42/BIO14458). References [1] R.Bonneau, J.Tsai, I.Ruczinski, D.Chivian, C.Rohl, C.E.M.Strauss, D.Baker. Rosetta in CASP4: Progress in Ab Initio Protein Structure Prediction, PROTEINS: Structure, Function, and Genetic Suppl, 5, 2001, [2] E. K. Burke, Y. Bykov, J. P. Newall, S. Petrovic. A Time-Predefined Local Search Approach to Exam Timetabling Problems. Accepted for publication in IIE transactions on Operations Engineering, [3] Y. Bykov. Time-Predefined and Trajectory-Based Search: Single and Multiobjective Approaches to Exam Timetabling. PhD Thesis. The University of Nottingham, Nottingham, UK, [4] G. Dueck. "New Optimization Heuristics. The Great Deluge Algorithm and the Record-to-Record Travel". Journal of Computational Physics 104, 1993, [5] D.T.Jones. Predicting Novel Protein Folds by Using FRAGFOLD, PROTEINS: Structure, Function, and Genetic Suppl, 5, 2001, [6] S. Petrovic, Y. Bykov. "A Multiobjective Optimisation Technique for Exam Timetabling Based on Trajectories". E. Burke, P. De Causmaecker (eds.), The Practice and Theory of Automated Timetabling IV: Selected Papers (PATAT 2002). Lecture Notes in Computer Science, Springer-Verlag, Berlin, Heidelberg, New York, 2003,