The Energy Distribution Data Bank: Collecting Energy Features of Protein Molecular Structures *

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1 The Energy Distribution Data Bank: Collecting Energy Features of Protein Molecular Structures * Dariusz Mrozek 1, Bożena Małysiak-Mrozek 1, Stanisław Kozielski 1, Andrzej Świerniak 2 1 Institute of Informatics, 2 Institute of Authomatic Control Silesian University of technology, Akademicka 16, Gliwice, Poland Dariusz.Mrozek@polsl.pl, Bozena.Malysiak@polsl.pl, Stanislaw.Kozielski@polsl.pl, Andrzej.Swierniak@polsl.pl Abstract The analysis of structural and energy features of proteins can be a key to understand how proteins work and interact to each other in cellular reactions. Potential energy is a function of atomic positions in a protein structure. The distributions of energy over each atom in protein structures can be very supportive for the studies of the complex processes proteins are involved in. Energy profiles contain distributions of different potential energies in protein molecular structures. Therefore, they constitute a full descriptor of energy properties for protein structures. The Energy Distribution Data Bank (EDB, stores energy profiles for protein molecular structures retrieved from the wellknown Protein Data Bank. In the paper, we describe the purpose of the EDB, a possible use of the information stored in it, query possibilities, and plans for future development. 1. Introduction Protein conformation is a key factor deciding about protein activity and protein functions in living cells. The conformation is determined by the arrangement of atoms in a protein structure which forms the general shape of the molecule in the 3-dimensional space [1], [2], [3]. Protein biological functions are usually the result of the folding process during the protein synthesis. Appropriately folded molecules can play their biological roles correctly. Misfolded molecules can cause disease states such as Alzheimer's. These states are usually results of genetic disorders at the very early stage of the protein formation [4]. Protein functioning and activity is often regulated by the cell environment or by binding to other molecules such as ligands. This usually results in a protein conformation switching. Some proteins spontaneously switch from one conformational state to another as a part of their normal life cycle. They can be involved in many cellular processes, like cell signaling, where they switch their conformations according to incoming stimuli [5], [6], [7]. Fig. 1 shows an example of the conformation switching of the Human Cyclin-Dependent Kinase 2 (CDK2) caused by the phosphorylation on the Thr 160. Fig. 1a shows the structure of the CDK2 molecule before the phosphorylation process and Fig. 1b shows the same region of the structure after the phosphorylation process. In order to make the conformation switching more visible, only parts of molecular structures of the CDK2 are presented (8 amino acids in the neighborhood of the Thr 160 ). Modeling of protein conformations and modeling of some phenomena the proteins are involved in makes regularly use of molecular mechanics, which produces a set of energy properties for particular molecular structures [8], [9]. The molecular mechanics plays an important role here, since quantum mechanics is sometimes too computationally complex to model molecular processes for such huge molecules, like proteins. a) b) Figure 1. Parts of molecular structures of the CDK2 molecule (amino acid ): a) before phosphorylation (molecule 1B38), b) after phosphorylation on the Thr 160 (molecule 1B39). Structures were taken from the Protein Data Bank [10] * Scientific research supported by the Ministry of Science and Higher Education, Poland in years

2 For example, it is much easier to use force field methods to model protein structures in particular processes instead of quantum methods. The potential energy is one of the property or function of a protein structure. The energy is a product of 3N-6 internal coordinates or 3N Cartesian coordinates, where N is a number of atoms [9]. All computations performed during the molecular modeling processes involve calculations of potential energy, e.g. to find energy minima related to the stable points of the structure. While protein structures are stored in dedicated repositories, like Protein Data Bank (PDB) [10], their energy properties have to be calculated any time the structure is used in modeling processes. This can be troublesome in some situations and can generate additional computational costs. For these reasons, we have developed a data repository to store information associated to energy distributions, which are calculated for known protein structures using molecular mechanics methods. The repository is called Energy Distribution Data Bank (EDB) and it has several main purposes: 1. The molecular data and energy profiles stored in the EDB can be used to support various processes. In our research, they have been used in searching particular structural regions of proteins, e.g. active sites of enzymes, or energetically favorable places in protein structures. We have developed the EAST method for the searching [11], [12]. 2. The EDB gives access to energy profiles, which can be perceived as energy templates for structure prediction, just like structural templates. We use energy profiles in our work as referential templates in the structure prediction processes with the NPF algorithm [13]. 3. Energy profiles allow observation of small changes in protein conformations at the level of protein molecular structure and at the energy level in 3D space or 2D grids after the projection [14]. This can be a part of the conformational analysis, e.g. Fig. 2 presents the same parts of the CDK2 molecular structures as Fig. 1 with additional van der Waals potential surfaces around particular atoms. The conformation switch causes changes in the distribution of the potential energy in the structure, which is observable. 4. Users can use the EDB in the similarity searching carried at the level of structure and energy, simultaneously [12]. 5. Finally, we believe that energy breakdowns can be useful in protein docking, analysis of protein reactivity and modeling of cellular reactions. This paper gives a brief description of the Energy Distribution Data Bank (EDB). The idea of energy profiles and how they are calculated are presented in section 2. a) b) Figure 2. Parts of molecular structures of the CDK2 molecule (amino acid ) with the van der Waals potential surfaces: a) before phosphorylation (molecule 1B38), b) after phosphorylation on the Thr 160 (molecule 1B39). The computational process of energy profiles is described in section 3. Main features of the EDB are assembled in section How energy profiles are calculated The Energy Distribution Data Bank consists both protein structural data in the form of Cartesian coordinates of particular atoms in a protein structure and energy profiles including energy breakdown over each atom of the structure. The computations of energy profiles were done with the use of the Amber94 force field [15]. The following functional form for the force field can be used to model molecules: T N ( r ) EBS + E AB + ETA + EVDW ECC E = +, where E T (r N ) denotes the total potential energy, which is a function of the positions (r) of N atoms [9]. Atom positions are described by (x, y, z) Cartesian coordinates. There are different types of contributing energies that are calculated for the molecular structure r N : bond stretching (E BS ) bonds N ki 0 2 EBS ( r ) = ( di di ), i= 1 2 where: k i is a bond stretching force constant, d i is a distance between two atoms, d 0 i is an optimal bond length; angle bending (E AB ) angles N ki 0 2 E AB ( r ) = ( θ i θi ), i= 1 2 where: k i is a bending force constant, θ i is an actual value of the valence angle, θ 0 i is an optimal valence angle; torsional angle (E TA ) torsions N Vn ETA ( r ) = ( 1+ cos( nω γ )), 2 i= 1

3 where: V n denotes the height of the torsional barrier, n is a periodicity, ω is the torsion angle, γ is a phase factor; van der Waals (E VDW ) 12 6 N N σ ij σ N ij E ( ) VDW r = = = + 4ε, ij i 1 j i 1 rij rij where: r ij denotes the distance between atoms i and j, σ ij is a collision diameter, ε ij is a well depth; electrostatic (charge-charge, E CC ), described by the Coulomb s law N N qiq j ECC =, 4πε r i= 1 j= i+ 1 0 ij where: q i, q j are atomic charges, r ij denotes the distance between atoms i and j, ε 0 is a dielectric constant [9]. The total potential energy E T (r N ) is a sum of all contributing energies. These contributing energies summarize charges coming from all atomic interactions. In Fig. 3 we present results of the energy calculation process for a sample molecule. We used the TINKER software [16] to perform the calculations. The energy breakdown in Fig. 3 is generated for the whole molecule, grouped by energy type and summed for all atoms. In our research, we calculate not only total values of particular energies for the structure, but also distributions of energy over all atoms in the structure r N. We call these distributions as energy profiles. In Fig. 4 we can observe the breakdown of different energies over all atoms in the same sample molecular structure. Total Potential Energy : Kcal/mole Energy Component Breakdown : Kcal/mole Interactions Bond Stretching Angle Bending Improper Torsion Torsional Angle Van der Waals Charge-Charge Figure 3. Results of the potential energy calculations Total Potential Energy : Potential Energy Breakdown over Atoms : Kcal/mole Values of potential energies for particular atoms are given in appropriate records (EB, EA, ET, EV, EC). Once again we used TINKER to generate result set presented in Fig. 4. In our work, energy profiles are calculated on the basis of protein structures taken from the well-known Protein Data Bank (PDB). The Energy Distribution Data Bank consists of energy profiles for many structures from the PDB. 3. Potential Energy Computation Energy profiles are computed by the EDBLoader program. The process is presented in Fig. 5. The EDBLoader and its Molecular Mechanics Module (3M) takes a single PDB file on the input and produces Energy Breakdown File (EBF) on the output. The EBF is similar to the file presented in Fig. 4. Single EBF consists of the energy profile for the structure given in the input PDB file. The 3M makes use of the TINKER package and calls some of its procedures while computing energy distributions. Since we need to store some additional structural information (e.g. Cartesian coordinates, amino acid sequence, descriptions, etc.), data from the EBF are integrated with appropriate records of the PDB by the Integration Module (IM) and complete data are then stored in the EDB database. The computation of energy profiles for particular molecular structures needs additional set of parameters, also known as force field. There are different types of force fields proposed by many researchers. These force fields provide a possibility to compute various types of potential energies. At the moment, the EDB stores profiles generated with the Amber94 [15] force field parameter set. However, we are working to incorporate the possibility of usage other force field files, like Charmm [17] or Amoeba [18], and compute different energy profiles. Force Field (Amber) Atom EB EA EBA EUB EAA EOPD EID EIT ET EPT ETT EV EC ECD ED EP ER ES ELF EG PDB file EDBLoader Molecular Mechanics Module Integration Module EBF txt Figure 4. Calculation of the potential energy breakdown over atoms EDB Figure 5. The architecture of the EDBLoader

4 4. The Energy Distribution Data Bank The Energy Distribution Data Bank stores energy profiles of protein structures taken from the American database of molecular structures the Protein Data Bank. Apart from energy profiles, the EDB collects additional structural information, secondary structures and protein descriptions. The access to deposited information is free to the community of users ( similarly to the Protein Data Bank. Users can get the data through the EDB website, which provides a simple query mechanism to retrieve data from the EDB database. As of Tuesday there are energy profiles in the EDB Query Possibilities The EDB website (Fig. 7, see section 7, Appendix: Additional figures) makes data available to broad community of users. There are two possibilities how users can access energy profiles of concrete molecules that are stored in the EDB database (Fig. 6). In the first way, users can specify the PDB ID of the molecule they want to display at the website. The PDB ID is a unique identifier of structures stored in the Protein Data Bank. The PDB ID is also used to identify molecules and energy profiles stored in the EDB. This makes the query process easier for people who are familiar with the PDB. E.g. users can specify 4HHB in the PDB ID field, if they want to get the energy profile for the hemoglobin molecule. As a result, users get summary information of the specified molecule, a list of isomers (if any), a possibility to download the energy profile in the EDML format, and a possibility to generate energy charts for chosen types of energy. New or refined query keyword Multiple Molecules Energy Profiles Brief descriptions of molecules Select single molecule User Query PDB ID Single Molecule Energy Profile New query Summary Information Isomers Download energy profile Generate energy charts Figure 6. Query options available for the EDB In the second way, users can specify a keyword, which is used to search through descriptions of molecules in the EDB. E.g. they can type hemoglobin, if they want to find energy profiles for all hemoglobin molecules. As a result, users obtain a list of molecules that meet search criteria. In the searching, many description fields are examined, e.g. Name, Description, Protein Class, Organism, Tissue, Cell, etc. After choosing one of the molecules from the result list, users obtain a detailed description of the molecule, as in previous case (when PDB ID was specified). There is also a third way users can access energy profiles stored in the EDB. This way is related to similarity searching with the use of energy distributions, which is implemented in our EAST method [11], [12]. This method is supportive for searching structural patterns with specific energetic features, e.g. active sites of enzymes. However, currently there is no possibility to use the EAST method at the EDB website, since it has been originally developed as a stand-alone application for internal use only. This will change in the future, when we re-implement the EAST method as a web applet Aggregated Energy Characteristics Energy profiles are supportive in the analysis of molecular properties, e.g. detection of small structural changes, conformation switching, etc. Distributions of the potential energy can be visualized at the EDB website in the form of charts. However, since it is difficult to present the multidimensional information in the 3D space, charges are aggregated for each amino acid in a protein polypeptide chain producing so called energy characteristics for each of the energy types. First versions of the mentioned EAST method used these characteristics in the search process [19]. Energy characteristics are distributions of energy over amino acid chain. Aggregated electrostatic energy characteristic for molecule 2H6D (5'-AMP-Activated Protein Kinase Catalytic Subunit Alpha-2) is presented in Fig. 8 (section 7) The EDML Format to Exchange Data Energy profiles of chosen molecules can be downloaded from the EDB using EDML data sets. Single EDML file consists of different information that is grouped in appropriate XML elements. The most important are data containing: protein descriptions, secondary structure information, Cartesian coordinates of atoms, and distribution of different component energies for all atoms in the protein structure. The EDML file can be generated for the chosen and displayed molecule, in the detailed view of the molecule at the EDB website.

5 5. Concluding Remarks The Energy Distribution Data Bank is a universal purpose repository of energy profiles generated for protein structures. We have identified several processes where the information from the EDB can be used, e.g. conformational-energy analysis, investigation of protein reactivity, studies of protein-protein and protein-ligand interactions, structural changes detection, structure prediction support, similarity searching at the structure-energy level. However, we believe there are several more. At the moment, there are protein energy profiles in the EDB (Mar 10, 2009). In comparison, there are protein structures in the Protein Data Bank (Mar 10, 2009). In the future, we plan to generate and store energy profiles for other molecules from the PDB repository. Since the number of structures in the PDB rises exponentially every year, we also expect the number of energy profiles will simultaneously rise. Although there is not much description information deposited in the EDB (which is stored in the PDB), the current version of the database occupy about 90 GB of storage place and it will definitely grow. 6. References [1] J.P. Allen, Biophysical Chemistry, Wiley-Blackwell, [2] C. Branden, J. Tooze, Introduction to Protein Structure, Garland, [3] C.R. Cantor, P.R. Schimmel, Biophysical Chemistry, W.H. Freeman, [4] H. Lodish, A. Berk, S.L. Zipursky, et al., Molecular Cell Biology. Fourth Edition. W. H. Freeman and Company, NY, [5] R.E. Dickerson, I. Geis, The Structure and Action of Proteins, 2nd ed. Benjamin/Cummings, Redwood City, Calif. Concise, [6] T.E. Creighton, Proteins: Structures and molecular properties, 2 nd ed. Freeman, San Francisco, [7] M.J. Berridge, The Molecular Basis of Communication within the Cell, Scientific American, 253 (4), 1985, pp [8] U. Burkert, N.L. Allinger, Molecular Mechanics, American Chemical Society, Washington D.C., [9] A. Leach, Molecular Modelling: Principles and Applications, 2nd Edition. Pearson Education EMA, UK, [10] H.M. Berman, J. Westbrook, Z. Feng, G. Gilliland, T.N. Bhat, H. Weissig, et al., The Protein Data Bank, Nucleic Acids Res., 28, 2000, pp [11] D. Mrozek, B. Małysiak, Searching for Strong Structural Protein Similarities with EAST, Journal of Computer Assisted Mechanics and Engineering Sciences, 14, 2007, pp [12] B. Małysiak, A. Momot, S. Kozielski, D. Mrozek, On Using Energy Signatures in Protein Structure Similarity Searching, In: Rutkowski, L., et al. (eds.) Artificial Intelligence and Soft Computing, LNAI, Springer, Heidelberg, vol. 5097, 2008, pp [13] A.W. Znamirowski, L. Znamirowski, Two-Phase Simulation of Nascent Protein Folding, Proc. of the 4th IASTED Inter. Conference on Modelling, Simulation, and Optimization 2004, Kauai, Hawaii, ACTA Press, 2004, pp [14] D. Mrozek, B. Małysiak, S. Kozielski, Energy Profiles in Detection of Protein Structure Modifications, In: IEEE International Conference on Computing and Informatics, Kuala Lumpur, 2006, pp [15] W.D. Cornell, P. Cieplak, et al., A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules. J.Am. Chem. Soc., 117, 1995, pp [16] J. Ponder, TINKER Software Tools for Molecular Design, User s Guide. Dept. of Biochemistry & Molecular Biophysics, Washington University, School of Medicine, St. Louis, 2001 (June). [17] A.D. Jr. MacKerrell, et al., All-Atom Empirical Potential for Molecular Modeling and Dynamics Studies of Proteins, J. Phys. Chem. B, 102, 1998, pp [18] J.W. Ponder, D.A. Case, Force Fields for Protein Simulation, Adv. Prot. Chem., 66, 2003, pp [19] D. Mrozek, B. Małysiak, S. Kozielski, An Optimal Alignment of Protein Energy Characteristics with Crisp and Fuzzy Similarity Awards, In: IEEE Conference on Fuzzy Systems, London, UK, 2007, pp

6 7. Appendix: Additional figures Figure 7. The EDB website main page Figure 8. Electrostatic energy characteristic for 5'-AMP-Activated Protein Kinase Catalytic Subunit Alpha-2 (molecule 2H6D)