On characterizing proteomics maps by using weighted Voronoi maps

In contrast to the standard construction of Voronoi regions, in which the boundaries between different regions are at equal distance from the given points, we consider the construction of modified Voronoi regions obtained by giving greater weights to spots reported to have higher abundance. Specifically we are interested in applying this approach to 2-D proteomics maps and their numerical characterization. As will be seen, the boundaries of the weighted Voronoi regions are sensitive to the relative abundances of the protein spots and thus the abundances of protein spots, the z component of the (x, y, z) triplet, are automatically incorporated in the numerical analysis of the adjacency matrix, rather than used to augment the adjacency matrix as non-zero diagonal matrix elements. The outlined approach is general and it may be of interest for numerical analyses of other maps that are defined by triplets (x, y, z) as input information.     

On 3-D graphical representation of proteomics maps and their numerical characterization

We consider numerical characterization of proteomics maps by representing a map as a three-dimensional graphical object based on x, y coordinates of the spots and using their relative abundance as the z coordinate. In our representation the protein spots are first ordered based on their relative abundance and labeled accordingly. In the next step a 3-D path is constructed connecting spots having adjacent labels. Finally a matrix is constructed by assigning to each pairs of labels (i, j) matrix element, the numerical value of which is based on the quotients of the Euclidean distance and the distance along the 3-D zigzag between the two points. The approach has been illustrated on a fragment of a proteomics map and compared with 2-D graphical representation of proteomics maps.     

On graphical and numerical characterization of proteomics maps

We outlined a mathematical approach suitable for characterization of experimental data given by 2-D densitograms. In particular we consider numerical characterization of proteomics maps. The basis of our approach is to order "spots" of a 2-D map and assign them unique labels (that in general will depend on the criteria used for ordering). In this way a map is "translated" into a sequence. In the next step one associates with the generated sequence a geometrical path and views such a path as a mathematical object that needs characterization. We have ordered spots representing proteins in 2-D gel plates according to their relative intensities which results in a zigzag path that produces a complicated "fingerprint" pattern. Mathematical characterization of zigzag pattern follows similar mathematical characterizations of embedded patterns based on matrices, the elements of which are given as quotients of Euclidean distance between spots and the distance along the zigzag path. The leading eigenvalue of constructed matrices is taken to represent characterization of the original 2-D map. Comparison of different 2-D maps (simulated by using random generator) allows one to construct partial order, which although qualitative in nature gives some insight into perturbation induced by foreign agents to the proteome of the control cell.     

On the dependence of a characterization of proteomics maps on the number of protein spots considered

We have reexamined the numerical characterization of proteomics maps based on the construction of novel distance matrices associated with the nearest neighbor graph for the protein spots. In particular we consider dependence of a characterization of proteomics map on the number of proteins considered in the analysis. We examined a collection of proteomics maps in which we approximately doubled the number of spots to be used for quantitative analysis, considering cases of maps having 30, 50, 100, 250, 500, and 1054 protein spots. For each case we have compared the similarity-dissimilarity results for five proteomics maps of rat liver cells associated with the control group and four proliferators administrated by intraperitoneal injection. We found that proteins maps based on a set of about the 250 most abundant proteins spots suffice for a satisfactory numerical characterization of such maps.     

Canonical labels for protein spots of proteomics maps

We consider the problem of canonical labeling for a class of maps, which include proteomics maps, which consist of a set of vertices or protein spots. If this problem is solved and followed, different laboratories studying proteomics maps will arrive at the same numbering of spots, which would facilitate comparisons of data from different sources. In addition, the proposed canonical numberings of protein spots would allow compiling a catalog of proteomics maps just as canonical labeling allows making catalogs graphs, or molecules, and other canonically labeled systems, which would make search for similar sets of maps very efficient. We approach the problem by modifying the algorithm of Jeffrey for graphical representation of DNA based on the chaos game. Graphical representation of DNA as a chaos game map has an important property in that this representation allows one to assign sequential labels to spots in a DNA map. We have modified the approach for sequential labeling of chaos game map representations to graphical representation of any tabular data, such as listing of (x, y) coordinates of protein spots of proteomics maps.     

Novel matrix invariants for characterization of changes of proteomics maps

Previous studies on mathematical characterization of proteomics maps by sets of map invariants were based on the construction of a set of distance-related matrices obtained by matrix multiplication of a single matrix by itself. Here we consider an alternative characterization of proteomics maps based on a set of matrices characterizing local features of an embedded zigzag curve over the map. It is shown that novel invariants can well characterize proteomics maps. Advantages of the novel approach are discussed.     

A comparative study of proteomics maps using graph theoretical biodescriptors

This paper reports the development of new methods for mathematical characterization of effects of different toxic agents on the cellular proteome. We describe numerical characterization of proteomics maps based on mathematical invariants. A graph is first associated with a proteomics map by considering partial ordering of spots on 2-D gels by ordering proteins with respect to the mass and the charge, the two properties by which proteins are separated. The graph is then embedded over the map, and several graph theoretical invariants have been constructed. In particular we consider invariants that can be extracted from the Euclidean distance-adjacency matrix of the embedded graph, in which only Euclidean distances between adjacent vertices of a graph are considered. The approach is illustrated using proteomics patterns of normal liver cells of rats and those derived from liver cells of animals exposed to four peroxisome proliferators. In contrast to direct comparison of spot abundance our approach incorporates information on spots locations. The difference between the two approaches is that in the first case only changes in abundances are considered as a measure of perturbation of the proteome map, but in the second case not only the charge but also the mass of proteins are used for ordering protein spots.     

Novel matrix invariants for characterization of changes of proteomics maps

Previous studies on mathematical characterization of proteomics maps by sets of map invariants were based on the construction of a set of distance-related matrices obtained by matrix multiplication of a single matrix by itself. Here we consider an alternative characterization of proteomics maps based on a set of matrices characterizing local features of an embedded zigzag curve over the map. It is shown that novel invariants can well characterize proteomics maps. Advantages of the novel approach are discussed.     

A new integrated statistical approach to the diagnostic use of two-dimensional maps

Two-dimensional (2-D) electrophoresis is a very useful technique for the analysis of proteins in biological tissues. The complexity of the 2-D maps obtained causes many difficulties in the comparison of different samples. A new method is proposed for comparing different 2-D maps, based on five steps: (i) the digitalisation of the image; (ii) the transformation of the digitalised map in a fuzzy entity, in order to consider the variability of the 2-D electrophoretic separation; (iii) the calculation of a similarity index for each pair of maps; (iv) the analysis by multidimensional scaling of the previously obtained similarity matrix; (v) the analysis by classification or cluster analysis techniques of the resulting map co-ordinates. The method adopted was first tested on some simulated samples in order to evaluate its sensitivity to small changes in the spots position and size. The optimal setting of the method parameters was also investigated. Finally, the method was successfully applied to a series of real samples corresponding to the electrophoretic bidimensional analysis of sera from normal and nicotine-treated rats. Multidimensional scaling allowed the separation of the two classes of samples without any misclassification.     

Novel characterization of proteomics maps by sequential neighborhoods of protein spots

We consider a characterization of proteomics maps based on an alternative kind of neighborhood graphs for the protein spots on 2-D gel. The novel approach considers for every protein spot only the nearest neighborhood consisting of protein spots of higher abundance. The approach has the simplicity and advantages of the recently introduced characterization of proteome maps based on considering the nearest neighborhoods of protein spots, but it also has important additional desirable computational features. The characterization of the nearest neighborhood graphs of 2-D gel proteomics maps is sensitive to the number of spots considered and may lead to changes in the degree of similarity of different maps when the number of points has been changed, thus imposing restrictions on the protocol used for comparison of maps. The novel approach presented in this work is less sensitive to the number of points used in the analysis because graphs are constructed in a stepwise process in which the role of more distant neighbors has been diminished by linking a new spot to the nearest spot that has been already part of the neighborhood graph. In this way a graph with N + 1 spots is obtained from the graph on N spots by adding a single new link, while in the case of the nearest neighborhood graphs adding a new spot introduces novel neighborhoods and generally results in a graph that may differ significantly from the neighborhood graph on N points.     

Spot overlapping in two-dimensional polyacrylamide gel electrophoresis separations: a statistical study of complex protein maps

A statistical approach able to extract the information contained in a two-dimenisional polyacrylamide gel electrophoresis (2-D PAGE) separation is here reported. The method is based on the quantitative theory of peak overlapping, a procedure previously developed by the authors and here extended to 2-D separations. The whole map is divided into many strips in order to obtain 1-D separations on which the statistic procedure is applied: the developed algorithms, on the basis of spot experimental data (intensity and spatial coordinates) permit to estimate the intrinsic number of components and to single out the specific order present in spot positions. The procedure was validated on computer-simulated maps. Its applicability to real samples was tested on maps obtained from literature sources. The following important information on protein mixtures can be extracted: (i) the number of proteins can be accurately estimated, on the basis of the spatial coordinates and intensities of spots detected in the 2-D PAGE map; (ii) the model describing distribution of interdistance between adjacent spots can be identified in both the separation dimensions; (iii) the presence of repeated interdistances in spot positions in the maps can be easily singled out: these regularities suggest specific protein modifications.     

The principle of exhaustiveness versus the principle of parsimony: a new approach for the identification of biomarkers from proteomic spot volume datasets based on principal component analysis

The field of biomarkers discovery is one of the leading research areas in proteomics. One of the most exploited approaches to this purpose consists of the identification of potential biomarkers from spot volume datasets produced by 2D gel electrophoresis. In this case, problems may arise due to the large number of spots present in each map and the small number of maps available for each class (control/pathological). Multivariate methods are therefore usually applied together with variable selection procedures, to provide a subset of potential candidates. The variable selection procedures available usually pursue the so-called principle of parsimony: the most parsimonious set of spots is selected, providing the best classification performances. This approach is not effective in proteomics since all potential biomarkers must be identified: not only the most discriminating spots, usually related to general responses to inflammatory events, but also the smallest differences and all redundant molecules, i.e. biomarkers showing similar behaviour. The principle of exhaustiveness should be pursued rather than parsimony. To solve this problem, a new ranking and classification method, “Ranking-PCA”, based on principal component analysis and variable selection in forward search, is proposed here for the exhaustive identification of all possible biomarkers. The method is successfully applied to three different proteomic datasets to prove its effectiveness.     

Proteomic analysis of cellular soluble proteins from human bronchial smooth muscle cells by combining nondenaturing micro 2DE and quantitative LC‐MS/MS. 2. Similarity search between protein maps for the analysis of protein complexes

Human bronchial smooth muscle cell soluble proteins were analyzed by a combined method of nondenaturing micro 2DE, grid gel‐cutting, and quantitative LC‐MS/MS and a native protein map was prepared for each of the identified 4323 proteins [1]. A method to evaluate the degree of similarity between the protein maps was developed since we expected the proteins comprising a protein complex would be separated together under nondenaturing conditions. The following procedure was employed using Excel macros; (i) maps that have three or more squares with protein quantity data were selected (2328 maps), (ii) within each map, the quantity values of the squares were normalized setting the highest value to be 1.0, (iii) in comparing a map with another map, the smaller normalized quantity in two corresponding squares was taken and summed throughout the map to give an “overlap score,” (iv) each map was compared against all the 2328 maps and the largest overlap score, obtained when a map was compared with itself, was set to be 1.0 thus providing 2328 “overlap factors,” (v) step (iv) was repeated for all maps providing 2328 × 2328 matrix of overlap factors. From the matrix, protein pairs that showed overlap factors above 0.65 from both protein sides were selected (431 protein pairs). Each protein pair was searched in a database (UniProtKB) on complex formation and 301 protein pairs, which comprise 35 protein complexes, were found to be documented. These results demonstrated that native protein maps and their similarity search would enable simultaneous analysis of multiple protein complexes in cells.     

Proteome analysis of Oncorhynchus species during embryogenesis

To understand the molecular mechanisms underlying normal and abnormal development of two salmonids, masu salmon (Oncorhynchus masou) and rainbow trout (O. mykiss), we used two-dimensional (2-D) electrophoresis to construct a series of 2-D maps during the embryonic period. We identified all visible protein spots on the 2-D map by assigning numbers for masu salmon and rainbow trout, and we determined N-terminal sequences of proteins for one hundred of the spots, that appear at very high concentrations in the whole embryos of masu salmon and rainbow trout. We also characterized embryonic stages according to the periods of appearance of spots. Most of the N-terminal sequences were identical or at least highly similar to partial sequences reported for vitellogenin (Vtg) of O. mykiss. A potential proteolytic processing of Vtg for rainbow trout is discussed in relation to the time of appearance and relative position of Vtg fragments within the complete protein sequence.     

Development of an integrated approach for evaluation of 2-D gel image analysis: impact of multiple proteins in single spots on comparative proteomics in conventional 2-D gel/MALDI workflow

With 2-D gel mapping, it is often observed that essentially identical proteins migrate to different positions in the gel, while some seemingly well-resolved protein spots consist of multiple proteins. These observations can undermine the validity of gel-based comparative proteomic studies. Through a comparison of protein identifications using direct MALDI-TOF/TOF and LC-ESI-MS/MS analyses of 2-D gel separated proteins from cauliflower florets, we have developed an integrated approach to improve the accuracy and reliability of comparative 2-D electrophoresis. From 46 spots of interest, we identified 51 proteins by MALDI-TOF/TOF analysis and 108 proteins by LC-ESI-MS/MS. The results indicate that 75% of the analyzed spots contained multiple proteins. A comparison of hit rank for protein identifications showed that 37 out of 43 spots identified by MALDI matched the top-ranked hit from the ESI-MS/MS. By using the exponentially modified protein abundance index (emPAI) to determine the abundance of the individual component proteins for the spots containing multiple proteins, we found that the top-hit proteins from 40 out of 43 spots identified by MALDI matched the most abundant proteins determined by LC-MS/MS. Furthermore, our 2-D-GeLC-MS/MS results show that the top-hit proteins in 44 identified spots contributed on average 81% of the spots' staining intensity. This is the first quantitative measurement of the average rate of false assignment for direct MALDI analysis of 2-D gel spots using a new integrated workflow (2-D gel imaging, "2-D GeLC-MS/MS", and emPAI analysis). Here, the new approach is proposed as an alternative to traditional gel-based quantitative proteomics studies.     

Decoding two-dimensional polyacrylamide gel electrophoresis complex maps by autocovariance function: a simplified approach useful for proteomics

This paper describes a mathematical approach applied for decoding the complex signal of two-dimensional polyacrylamide gel electrophoresis maps of protein mixtures. The method is helpful in extracting analytical information since separation of all the proteins present in the sample is still far from being achieved and co-migrating proteins are generally present in the same spot. The simplified method described is based on the study of the 2-D autocovariance function (2D-ACVF) computed on an experimental digitized map. The first part of the 2D-ACVF allows for the estimation of the number of proteins present in the sample (2D-ACVF computed at the origin) and of the separation performance (mean spot size). Moreover, the 2D-ACVF plot is a powerful tool in identifying order in the spot position, and singling it out from the complex separation pattern. This method was validated on synthetic maps obtained by computer simulation to describe 2-D PAGE real maps and reference maps retrieved from the SWISS-2DPAGE database. The results obtained are discussed by focusing on specific information relevant in proteomics: sample complexity, separation performance, and identification of spot trains related to post-translational modifications.     

On novel representation of proteins based on amino acid adjacency matrix

A novel characterization of proteins is presented based on selected properties of recently introduced 20 x 20 amino acid adjacency matrix of proteins in which matrix elements count the occurrence of all 400 possible pair-wise adjacencies obtained by reading protein primary sequence from the left to the right. In particular we consider the characterization based on the sum and the difference of the rows and the corresponding columns, which characterize proteins by a pair of 20-component vectors. The approach is illustrated on a set of ND6 proteins of eight species.     

On novel representation of proteins based on amino acid adjacency matrix

A novel characterization of proteins is presented based on selected properties of recently introduced 20 × 20 amino acid adjacency matrix of proteins in which matrix elements count the occurrence of all 400 possible pair-wise adjacencies obtained by reading protein primary sequence from the left to the right. In particular we consider the characterization based on the sum and the difference of the rows and the corresponding columns, which characterize proteins by a pair of 20-component vectors. The approach is illustrated on a set of ND6 proteins of eight species.     

A turning point in proteome analysis: sample prefractionation via multicompartment electrolyzers with isoelectric membranes

Sample prefractionation, as obtained via multicompartment electrolyzers with isoelectric membranes, greatly enhanced the load ability, resolution and detection sensitivity of two-dimensional (2-D) maps in proteome analysis. This was demonstrated with different samples. In an Escherichia coli total cell extract, analysis by a 2-D map run in a pH 4-5 gradient showed many more spots when prefractionated, as compared with standard maps available in databases such as SWISS-2DPAGE. Analysis of human plasma in the pH 3-6 range showed an increase in the number of highly acidic proteins in the fractionated sample compared to whole plasma. With both samples no protein precipitation or smears occurred and much larger sample amounts could be loaded upon prefractionation, so that a large number of spots could be visualized by Coomassie staining, which is fully compatible with subsequent matrix assisted laser desorption/ionization-time of flight (MALDI-TOF) analysis.     

Two-dimensional gel electrophoresis maps of the proteome and phosphoproteome of primitively cultured rat mesangial cells

Mesangial cells (MC) play an important role in maintaining the structure and function of the glomerulus. The proliferation of MC is a prominent feature of many kinds of glomerular disease. The first reference 2-DE maps of rat mesangial cells (RMC), stained with silver staining or Pro-Q Diamond dye, have been established here to describe the proteome and phosphoproteome of RMC, respectively. A total of 157 selected protein spots, corresponding to 118 unique proteins, have been identified by MALDI-TOF-MS or LC-ESI-IT-MS/MS, in which 37 protein spots representing 28 unique proteins have also been stained with Pro-Q Diamond, indicating that they are in phosphorylated forms. All the identified proteins were bioinformatically annotated in detail according to their physiochemical characteristics, subcellular location, and function. Most of the separated or identified protein spots are distributed in the area of mass 10-70 kDa and pI 5.0-8.0. The identified proteins include mainly cytoplasmic and nuclear proteins and some mitochondrial, endoplasmic reticulum, and membrane proteins. These proteins are classified into different functional groups such as structure and mobility proteins (21.2%), metabolic enzymes (16.9%), protein folding and metabolism proteins (13.6%), signaling proteins (14.4%), heat-shock proteins (7.6%), and other functional proteins (12.7%). While structure and mobility proteins are mostly represented by protein spots with high abundance, signaling proteins are mostly represented by protein spots with relatively low abundance. Such a 2-DE database for RMC, especially with many signaling proteins and phosphoproteins characterized, will provide a valuable resource for comparative proteomics analysis of normal and pathologic conditions affecting MC function or pathologic progress.