[Frontiers in Bioscience 10, 844-852, January 1, 2005] |
IDENTIFICATION OF CRITICAL HETERODIMER PROTEIN INTERFACE PARAMETERS BY MULTI-DIMENSIONAL SCALING IN EUCLIDIAN SPACE Cui Zhanhua, Jacob Gah-Kok Gan, Li Lei, Venkatarajan Subramanian Mathura, Meena Kishore Sakharkar, and Pandjassarame Kangueane ^{} 1Nanyang Centre for Supercomputing and Visualization, School of Mechanical & Production Engineering, Nanyang Technological University, Singapore, ^{2}Roskamp Institute, 2040 Whitfield Ave, Sarasota FL 34243, USA TABLE OF CONTENTS
1. ABSTRACT Protein subunit dimers are either homodimers (consisting of identical polypeptides) or heterodimers (consisting of different polypeptides). Protein dimers are involved in several cellular processes and an understanding of their molecular principle in complexations (subunit - subunit interaction) is essential. This is generally studied using 3D structures of homodimers and heterodimers determined by X-ray crystallography. However, the current knowledge on subunit interaction is limited due to lack of sufficient 3D dimer structures. It is our interest to study heterodimers using 3D structures to identify interaction parameters that would help in the development of a model to predict heterodimer interaction sites just from protein sequences. The efficiency of such models depends on the weighted contribution of numerous parameters characterizing heterodimer interfaces. Therefore, we studied the salient features of 111 interface parameters in 65 heterodimer structures. In this study, we applied multi-dimensional scaling for dimensionality reduction on these parameters to select the most critical ones that best characterize heterodimer interfaces. The significance of these parameters in subunit interaction is discussed. 2. INTRODUCTION Protein-protein interactions play a key role in many biological processes such as signal transduction, gene regulation and antibody-antigen recognition (1-2). Therefore, a study on the principles of protein-protein interaction is critical for developing reliable prediction models from sequence data. Current models largely depend on the available knowledge of protein-protein interaction sites (3-5). However, many model parameters have not been fully captured due to limited structural data and lack of rigorous mathematical formulations. Studies indicate the presence of charge and electrostatic complementation at the protein-protein interfaces (6-7). Formation of hydrogen bonds between subunits plays an important role in the association and stability of protein subunits (8-9). Residue propensity between interior, exterior and interface regions of oligomeric proteins has been examined (10-12). This showed the selective occurrence of non-polar residues in the interior and at interface regions of proteins, while polar (or charged) residues prefer solvent exposed exterior regions. Thus, a number of parameters have been known to characterize protein-protein interfaces. Nonetheless, it is extremely difficult to capture all the non-linear dependencies of such parameters. A number of methods have been used to identify interface parameters in oligomeric complexes. These methods utilize conserved residues at interface (13), surface patches (14), sequence features (15-17), atomic contact vectors (ACV) (18), topological entities (19), neural network trained sets (20), interface energy landscapes (21), and support vector machines (SVM) (22). However, these methods lack sufficient parameters for model development and are often less conclusive in prediction. Here, we analyze 111 interface parameters in 65 heterodimer structures to select the most critical ones in subunit interactions using a multidimensional procedure described elsewhere (35). 3. MATERIALS AND METHODS 3.1. Creation of a heterodimer structural dataset We created a dataset of 65 high resolution (≤ 3Å) heterodimer structures determined by X-ray crystallography for this analysis (Table 1). These structural data were obtained from the protein databank (PDB). The dataset was selected such that each polypeptide in these heterodimers is at least 50 residues long. 3.2. Interface parameters Each of the 65 heterodimer interfaces was studied using 111 parameters and the corresponding values were determined. The parameter list is given in Table 2. Consequently, a 65 X 111 matrix was generated for the 65 heterodimers. 3.3. Parameter normalization Each parameter value was normalized such that standard deviation is equal to one and the average is equal to zero. The standard deviation was calculated using STDEVP function in Microsoft Excel. The normalization ensures that all parameters are expressed as dimensionless numbers. The normalized parameter value is represented by S using α (parameter index whose range is from 1 to 111), i (heterodimer interface index whose range is from 1 to 65), P (parameter value), n (number of heterodimers i.e. 65 in number), (parameter mean) and (standard deviation). By definition, S is given as (1) where, (2) This procedure generated a 65 x 111 matrix containing normalized parameter values. 3.4. Representation of parameters There are 65 heterodimer structures used in this analysis and each dimer interface (i) is represented as a vector in 111 dimensional 'continuous space', where the components are the normalized parameter values. The scalar product between two vectors and, where j is another index for a heterodimer interface, is given by (3) The 65 x 65 matrix Q is positive symmetric consisting of the scalar products of the parameter vectors S(i) and S(j) , where i = 1 to 65 and j = 1 to 65. 3.5. Calculation of eigenvectors and eigenvalues The symbolic eigenvectors (E) of a square matrix Q and eigenvalues (λ) of Q are computed, respectively, using the MATLAB command E = eig(Q). The eigenvalues of Q are the zeros of the characteristic polynomial of Q. As Q is of order 65, we will have 65 eigenvectors and eigenvalues λ and the smallest eigenvalue λ_{65} is near zero due to normalization of the parameters. The eigenvalues and their corresponding eigenvectors are indexed in decreasing order of eigenvalues. 3.6. Selection of interface descriptors The distribution of the eigenvalues of the Q matrix (Figure 1), containing the scalar products between all pairs of the 111 dimensional heterodimer vectors, rapidly decreases from the largest value l _{1} to l _{65}. The rapid decrease of the eigenvalues derived from the 111 physical - chemical parameters shows a large anisotropy of the distribution of the parameter values. This anisotropy is a consequence of the large redundancy in the sets of parameter values. This suggests that the number of parameters can be reduced while retaining approximately the same distribution of heterodimers in the property space. We found that the eigenvalues rapidly decrease within the first six largest eigenvalues. 3.7. Calculation of distances in the parameter space If μ represents the index of eigenvalue and eigenvector, each heterodimer can be represented as a vector in a six-dimensional Euclidean space with each dimension perpendicular to each other. The co-ordinates of the i^{th} heterodimer can be written as: (4) where μ varies from 1 to 6. The distance between the i^{th} and j^{th} heterodimer interface is given by (5) where n is 6. Distances computed between heterodimers in the six dimensional Eigen sub-space constitute the parameter distance matrix (PDM). Small distances values between two heterodimers indicate that they are similar in all of the 111 physical and chemical parameters. 3.8. Calculation of correlation coefficient Pearson's correlation coefficient between pairs of parameter values (x_{i},y_{i}) is calculated using the correlation function (CORRCOEF) in MATLAB. 4. RESULTS 4.1. Quantitative descriptors for heterodimer interface parameters in six dimensions We used 65 high resolution heterodimer structures (Table 1) to derive a comprehensive list of 111 physical/chemical parameters for heterodimer interfaces (Table 2). Each heterodimer was represented as a vector in the 111-dimensional space of normalized parameters with mean value of zero and standard deviation 1. Our multi-dimensional scaling approach reveals the high redundancy of the parameter values. The computational approach and justification for reduction to a lower dimensional space follows closely the practice of embedding in distance geometry and it is easy to eliminate redundant variables when describing complex phenomenon in molecular recognition. The distribution of eigenvalues decreases rapidly (Figure 1). This is due to large redundancy in the parameter set. This suggests that the number of parameters can be reduced while retaining approximately the same distribution of heterodimers in the parameter space. The eigenvalues rapidly decrease within the first six largest eigenvalues. We compared distances in the original parameter space with those regenerated from a subset of n eigenvectors, varying n systematically from 2 to 65 (Figure 2). The correlation coefficient between the original and regenerated distances was more than 95% for n = 6, and approaches 1 very rapidly. We therefore chose the first six eigenvalues and eigenvectors to calculate the six dimensional descriptors of the heterodimer interfaces. The individual distances in the original parameter space and in the sub-space using the first six eigenvectors were highly correlated (Figure 3). The correlation coefficient between the distances was 0.96. 4.2. Selection of critical interface parameters from highly correlated descriptors We used the first six highly correlated descriptors (dimension 65 X 65) and normalized parameter values (dimension 65 X 111) to calculate the correlation coefficients between the selected descriptors (E_{1} to E_{6}) and the original normalized parameter values. This operation generated a matrix (dimension 6 X 111) containing correlations between the six highly correlated descriptors and the normalized parameter values. We then used this matrix to select the most significant interface parameters using the calculated correlation coefficients (Table 3). This further enabled us to select the most significant parameters that best describe a heterodimer protein interface (Table 3). We then used the parameter values for these six parameters to calculate its distances from the rest of 111 original parameter values. The distances were then used to calculate the correlation coefficients. These values suggest that these six parameters have different weights in heterodimer subunit interactions. Data shows that the H-bonds have the highest weight among the six parameters listed in Table 3. We also calculated the individual distances between the original parameter values and the six selected parameter values (Figure 4). The correlation coefficient between these distances was found to be 0.7. 5. DISCUSSION Heterodimer protein interaction is a common phenomenon in cellular regulation and signaling. This occurs by a huge combination of physical-chemical parameters that characterize their interacting surfaces. The multi dimensional scaling method applied in this study helps to reduce a large pool of interface parameters to a small set of six quantitative descriptors of heterodimer interfaces. Here, we show that the six parameters (Figure 3) were sufficient to reproduce the distances in the complete parameter space (Figure 4). The most significant parameters that are found to reproduce the original parameter set are given in Table 3. They are dominated by (1) interface H-bonds, (2) interface tryptophan, (3) interface residues, (4) interface hydrophobicity, (5) interface coils and (6) interface methionine. It should be noted that several linear combinations of parameter values represent a descriptors and it is often difficult to further refine or simplify such non-linearity. The goal here is to identify the most critical parameters that represent hetero dimer interfaces. In general it is difficult to decide a priori which of the many parameters dominate at the interface. Our quantitative descriptors represent a precise spatial relation of all hetero dimers with respect to the 111 physical-chemical parameters. This enabled us to identify the most critical parameters and these parameters are further discussed below. 5.1. Interface H-bonds Intermolecular hydrogen bonds between subunits are important in the association and stability of hetero-dimers (26). This analysis suggests that interface H-bonds have a good correlation co-efficient of r = 0.61 with the distances of other interface parameters. 5.2. Interface tryptophan and methionine Aromatic and aliphatic residues have greater propensity at the protein-protein interfaces (27-28). As given in Table 3, the correlation coefficients of interface tryptophan and methionine with the numerical descriptors (E_{2} and E_{6}) are 0.51 and -0.36. This relation is weak. In fact, E_{2} is a descriptor that describes a combination of aliphatic residues and E_{6} is a descriptor that describes a combination of aromatic residues. In this study, tryptophan and methionine residues were chosen as prominent parameters because of their high correlation coefficients compared to other members of aliphatic or aromatic residue groups. 5.3. Interface residues and interface hydrophobicity Hydrophobicity plays an important role in protein association (23-24). Thus, interface hydrophobicity was among the prominent parameters for heterodimer interaction. The number of interface residues relates to interface area. Stronger protein subunit associations were generally associated with larger interface areas (12). These parameters are shown to be used in the prediction of heterodimer interaction sites by surface patch analysis (14). The method detects the most possible interaction sites by the incorporation of this parameter. 5.4. Interface loop residues It has been shown that secondary structural elements at the interface play an important role in heterodimer protein assembly (12). Studies also suggest that protein active sites might appear in coiled regions (25). Thus, interface loop residues have critical role in heterodimer interaction. 6. CONCLUSIONS A large number of structurally important physical - chemical parameters characterize heterodimer interfaces and each of these parameters contributes differently to the stability of a heterodimer interface. A weighted value was assigned to each parameter to indicate the differential contribution. 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Venkatarajan, M. S. & Braun W: New quantitative descriptors of amino acids based on multidimensional scaling of a large number of physical-chemical properties. J Mol Model 7, 445-453 (2001) Key Words: Euclidean distance, Hetero-Dimer Interface, Eigenvector, Linear Correlation Coefficient, Protein-Protein Interaction, Send correspondence to: Pandjassarame Kangueane Ph.D, N3-2c-113b, School of Mechanical and Production Engineering, Nanyang Technological University, Singapore - 639798, Tel: +65 6790 5836, Fax: +65 6774 4340, E-mail: MPandjassarame@ntu.edu.sg |