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Milan Randić

Publications and source records attributed to Milan Randić.

At least 19 recordsLinked to original sources
PubMed2006

Quantitative characterizations of proteome: dependence on the number of proteins considered.

We consider the sensitivity of numerical characterizations of proteome on the number of proteins considered in the analysis. We examined data on proteomics maps belonging to the liver cells of mice subject to four proliferators. We varied the number of proteins considered for quantitative analysis from 25 up to 1000 proteins. For each case, we have compared the similarity/dissimilarity results when different number of proteins has been considered. We found that proteins maps based on a set of about 300 most abundant proteins spots suffice for satisfactory numerical characterization of corresponding proteome.

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PubMed2003

Novel map descriptors for characterization of toxic effects in proteomics maps.

We consider a novel numerical characterization of proteomics maps based on the construction of a graph obtained by connecting all protein spots in a proteomics map that are at distance equal to, or smaller than, a critical distance D(c). We refer to the so constructed graph as a cluster graph and we calculate four associated characteristic matrices, previously considered in the literature: (1) the Euclidean-distance matrix ED; (2) the neighborhood-distance matrix ND; (3) the path-distance matrix based on the shortest paths between connected spots PD; and (4) the quotient matrix Q, the elements of which are given as the quotient of the corresponding elements of ED and ND matrices. Numerical descriptors for proteomics maps include in particular the leading eigenvalue of the Q matrix and the family of associated "higher order" matrices defined as powers of Q. These map descriptors show considerable sensitivity to perturbations of proteomics maps by toxicants.

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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.

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On a four-dimensional representation of DNA primary sequences.

We consider a four-dimensional representation of DNA primary sequences by assigning to each of the four basic amino acids A, T, G, C directions along the four orthogonal coordinate axes. Advantages and limitations of the novel representation of DNA primary sequences are discussed, and the use of the 4-D representation is illustrated by constructing novel sequence invariants. Comparisons with the similarity/dissimilarity results based on 2-D and 3-D representations for a set of eight short DNA sequences corresponding to the first exon of beta globin in eight species, including human, are considered to illustrate the use of our novel sequence invariants based on the entries in derived sequence matrices restricted to a selected width of a band along the main diagonal.

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Algebraic Kekulé formulas for benzenoid hydrocarbons.

By assigning two pi-electrons of CC double bonds in a Kekulé valence structure to a benzene ring if not shared by adjacent rings and one pi-electron if CC double bond is shared by two rings we arrived at numerical valence formulas for benzenoid hydrocarbons. We refer to numerical Kekulé formulas as algebraic Kekulé valence formulas to contrast them to the traditional geometrical Kekulé valences formulas. The average over all numerical Kekulé valence structures results in a single numerical structure when a benzenoid hydrocarbon molecule is considered. By ignoring numerical values the novel quantitative formula transforms into a qualitative one which can replace incorrectly used notation of pi-electron sextets to indicate aromatic benzenoids by placing inscribed circles in adjacent rings-which contradicts Clar's characterization of benzenoid hydrocarbons.

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Algebraic Kekulé structures of benzenoid hydrocarbons.

An algebraic Kekulé structure of a benzenoid hydrocarbon is obtained from an ordinary Kekulé structure by inscribing into each hexagon the number of pi-electrons which (according to this Kekulé structure) belong to this hexagon. We show that in the case of catafusenes, there is a one-to-one correspondence between ordinary and algebraic Kekulé structures. On the other hand, in the case of perifusenes, one algebraic Kekulé structure may correspond to several ordinary Kekulé structures.

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Wiener-Hosoya index--a novel graph theoretical molecular descriptor.

We describe the construction of a novel molecular descriptor, called the Wiener-Hosoya index, in view of its structural relationship to both the Wiener number W and the Hosoya topological index Z. It is shown that this index has a smaller degeneracy than many simple topological indices, including W, Z, and the connectivity index chi. In a way the index can be viewed as a particular generalization of the Wiener number.

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Partitioning of pi-electrons in rings of polycyclic benzenoid hydrocarbons. 2.1. Catacondensed coronoids.

Various types of coronoids are examined for finding the partitioning of pi-electrons in individual benzenoid rings of polycyclic aromatic hydrocarbons. A class of catacondensed coronoids, namely fibonacenes, has four pi-electrons in every ring. Most other catacondensed coronoids have more than one type of benzenoid ring, each type with a different partition, but the average per ring is always four pi-electrons. For the class of catacondensed coronoids that have an acenic hole, simple quadratic equations in terms of their number R of rings exist for the partitions of pi-electrons in the three possible ring types.

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Random walks and chemical graph theory.

Simple random walks probabilistically grown step by step on a graph are distinguished from walk enumerations and associated equipoise random walks. Substructure characteristics and graph invariants correspondingly defined for the two types of random walks are then also distinct, though there often are analogous relations. It is noted that the connectivity index as well as some resistance-distance-related invariants make natural appearances among the invariants defined from the simple random walks.

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Algorithm for coding DNA sequences into "spectrum-like" and "zigzag" representations.

An algorithm for encoding long strings of building blocks, like 4 DNA bases (adenine-A, cytosine-C, thymine-T, and guanidine-G), 20 natural amino acids (from Alanine Ala to Valine-Val, plus the stop triplet), or all 64 possible base triplets (from AAA to TTT), into "zigzag" or "spectrum-like" representations is suggested. The new encoding scheme can be derived in the 3-, 2-, or 1-dimensional form depending on the user's wishes. The only information, besides the string for which the "spectrum-like" representation is sought, is the initial positioning of the complete set of units from which the string is composed, i.e., four positions for A, C, G, and T, or 20 positions for natural amino acids plus stop, etc. This initial positioning can be initialized in either the 3-, 2-, or 1-D form. As an illustration of the suggested encoding scheme of the visual and chemometric comparison of the first 10 exon strings of the beta globin gene of 10 different species, each string consisting of about 100 basic amino acids long is shown.

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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.

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Partitioning of pi-electrons in rings of polycyclic conjugated hydrocarbons. 5. Nonalternant compounds.

All possible nonalternant hydrocarbons with a total of two, three, or four 5-, 6-, and 7-membered rings have been examined for the partition of their pi-electrons by averaging over all Kekulé structures (considered to contribute equally to the electron distribution) the pi-electrons in each ring in accordance to the rules introduced earlier: for each double bond shared with another ring one pi-electron is taken into account, and for double bonds that are not shared two pi-electrons are added. The trends observed for the partitions are discussed, and a comprehensive bibliography is provided as Supporting Information for all such systems, including both experimental and theoretical published data.

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"Anticonnectivity": a challenge for structure-property-activity studies.

The higher-order variable connectivity indices were introduced to account for the combination of positive and negative relative contributions of atoms and bonds in the construction of the quantitative structure-property relationships or quantitative structure-activity relationships models. The coding capabilities of modified descriptors were presented on the modeling of the atmospheric reaction rate constants of selected organic compounds with OH radicals. The optimization of diagonal weights of the augmented adjacency matrix pointed out the significant enhancing effect of oxygen and the suppressive effect of chlorine on the overall molecular atmospheric reactivity of organic compounds with OH radicals. The linear regression model, using a single structural descriptor, that is, a variable connectivity index of order one, produced a root-mean-square error of 0.343 log units. Although the obtained calculation error was higher than in previously reported multiple linear regression models, the new model offered important insight into the role of the individual structural components that are influencing the reactivity of organic compounds.

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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.

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Partitioning of pi-electrons in rings for Clar structures of benzenoid hydrocarbons.

Resonance structures of polycyclic aromatic hydrocarbons can be associated with numerical formulas by assigning pi-electrons of C=C double bonds to individual benzenoid rings. Each C=C double bond in a resonance structure assigns two pi-electrons to a ring in a fused-benzenoid system if it is not shared by adjacent rings and one pi-electron when it is common to two rings, obtaining thus a "local" characterization of rings in polycyclic conjugated hydrocarbons. In the present contribution we extend this approach to the aromatic pi-sextet model of Clar, which offers an alternative description of benzenoid hydrocarbons. In this model local characteristics of individual benzenoid rings are based on partitioning of pi-electrons but only for those resonance structures (fewer in number) that contribute to Clar's formula of benzenoid hydrocarbons.

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On invariants of a 2-D proteome map derived from neighborhood graphs.

We consider the problem of the construction of invariants for characterization of 2-D maps, such as 2-D proteome maps, 2-D NMR spectral maps, etc., that in addition to facilitating cataloguing such maps, can be used for comparison of maps and numerical evaluation of their degree of similarity. A novel approach, based on the concept that the nearest neighborhood of points (spots) on a map are sufficiently flexible to allow one not only to vary the number of points used for characterization of the map but also the density of information on their relative positions, is put forward. The method is illustrated with the Coomassie brilliant blue stained 2-D gel electrophoresis patterns of the proteomes from liver cells of healthy male Fisher F344 rats and the rats treated with four peroxisome proliferators.

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Canonical labeling of proteome maps.

We propose a canonical labeling of proteome maps, which enables one to sort and catalog the maps in a simple way. The canonical label of a proteome map is based on the canonical labeling of vertexes of Hasse diagram embedded in the map resulting in the adjacency matrix, the rows of which when viewed as binary numbers are the smallest possible such numbers. The use of the approach in documentation is illustrated with the proteome maps of liver cells of healthy male Fisher F344 rats and the rats treated with different peroxisome proliferators.

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