Biomedical subjects

M Randić

Publications and source records attributed to M Randić.

84 records · Page 5Linked to original sources

PubMedDate not supplied

Retro-regression--another important multivariate regression improvement.

We review the serious problem associated with instabilities of the coefficients of regression equations, referred to as the MRA (multivariate regression analysis) "nightmare of the first kind". This is manifested when in a stepwise regression a descriptor is included or excluded from a regression. The consequence is an unpredictable change of the coefficients of the descriptors that remain in the regression equation. We follow with consideration of an even more serious problem, referred to as the MRA "nightmare of the second kind", arising when optimal descriptors are selected from a large pool of descriptors. This process typically causes at different steps of the stepwise regression a replacement of several previously used descriptors by new ones. We describe a procedure that resolves these difficulties. The approach is illustrated on boiling points of nonanes which are considered (1) by using an ordered connectivity basis; (2) by using an ordering resulting from application of greedy algorithm; and (3) by using an ordering derived from an exhaustive search for optimal descriptors. A novel variant of multiple regression analysis, called retro-regression (RR), is outlined showing how it resolves the ambiguities associated with both "nightmares" of the first and the second kind of MRA.

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On use of the variable connectivity index 1chi(f) in QSAR: toxicity of aliphatic ethers.

The number of non-hydrogen atoms in a molecule, N, appears as a very good molecular descriptor for the toxicity of aliphatic ethers, despite the fact that it does not differentiate among isomers. The regression based on N as a descriptor for the toxicity in mice of 21 alkyl ethers was reported to yield the regression coefficient r = 0.9751. The simple connectivity index 1chi produced for the same data a less satisfactory regression: r = 0.9548. To see if variable connectivity index 1chi(f) can improve the regression characterized by N we examined the same data using the variable connectivity index 1chi(f) as a molecular descriptor. By varying x, y, the variables that discriminate between carbon and oxygen atoms, we obtained regression which approaches in quality the best reported regression using weighted paths as descriptor and which is marginally better than the regression based on N.

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Graph theoretical descriptors of two-dimensional chirality with possible extension to three-dimensional chirality.

We report on construction of a graph theoretical descriptor of chirality for two-dimensional benzenoid hydrocarbons. For achiral molecules the index is zero, while for chiral molecules it takes a positive or negative value for a molecule and one for its mirror image. Hence, we also have obtained a descriptor that measures chirality on an absolute scale, i.e., it assigns to a molecule a positive (or a negative) value without ever requiring information on the enantiomer of the molecule considered or any other pair of standards. In addition, we have briefly outlined how this is the 2-D approach extended to characterization of chiral objects in 3-D space, at least in the case of n-alkane rotamers.

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PubMedDate not supplied

A new descriptor for structure-property and structure-activity correlations.

We consider an improvement of a multiple regression analysis (MRA) for the correlation of boiling points of alcohols using descriptors that involve a variable part. In the search for the best descriptors based on weighted paths we came upon a novel molecular descriptor, the use of which was apparently overlooked in the past. The novel descriptor counts paths of length three; however, only those associated with an oxygen atom are counted.

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Variable connectivity index for cycle-containing structures.

In the early applications of the connectivity index the index was empirically modified for some properties of cyclic structures by subtracting 1/2 from the computed value based solely on valence of vertices in the molecular graph. In this article we looked into the origin of this heuristic adjustment of the connectivity indices for cyclic structures. We have examined the relative role of carbon atoms in cycle-containing structures by differentiating carbon atoms making up a ring and carbon atoms in exocyclic bonds. We found in the case of the boiling points of cycloalkanes and alkylcycloalkanes that contributions of "cyclic" and "acyclic" atoms to molecular additivities differ somewhat.

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The variable connectivity index 1chi(f) versus the traditional molecular descriptors: a comparative study of 1chi(f) against descriptors of CODESSA.

In this study we compared the prediction abilities of the variable connectivity index 1chi(f) (not included in CODESSA) with topological indices available from CODESSA. We selected the boiling points of n = 100 alcohols as the property and examined the pool of 56 topological indices. Prediction capabilities of the developed models were evaluated by classical training/test set approach. RMS errors calculated from the prediction set for the MLR models obtained from CODESSA software with 1, 2, 3, 4, and 5 parameters were 9.06, 5.69, 5.40, 4.9, and 3.37 degrees C, respectively. Using the variable connectivity index with weights x = 0.10 and y = -0.92 for carbon and oxygen atom respectively, we obtain regression BP = 38.12 1chi(f) - 37.56 with the correlation coefficient r = 0.9915, RMS error 4.21 degrees C calculated from the test set, and Fisher ratio F = 5691. Prediction capability of the variable connectivity index was better than for MLR regression model with up to four parameters.

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On the characterization of DNA primary sequences by triplet of nucleic acid bases.

We consider construction of a set of smaller 4 x 4 matrices to represent DNA primary sequences which are based on enumeration of all 64 triplets of nucleic acids bases. The leading eigenvalue from the constructed matrices has been selected as an invariant for construction of a vector to characterize DNA. Additional invariants considered of the derived condensed matrices of DNA include a 64-component vector, the components of which consist of ordered triplets XYZ, with X, Y, Z = A, C, G, T. Construction of similarity/dissimilarity tables based on different invariants for a set of sequences of DNA belonging to the first exon of the beta-globin gene of eight species illustrates the utility of newly formulated invariants for DNA.

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PubMedDate not supplied

Graph valence shells as molecular descriptors.

We have introduced a new simple structural descriptor for molecules that is based on the count of the valence shells for vertices in molecular graphs. The construction of the new descriptor is illustrated on 2,3-dimethylhexane and is reported for the 18 octane isomers. The relationship of the new descriptor to the path numbers of a graph is discussed. It can be seen that the path counts and the count of valence of neighbor shells are related for paths of length two (and shells of range two). There is no appreciable correlation between the count of the longer paths and the count of the corresponding neighbor valence shells at larger separations. Use of the neighbor valence shells as molecular descriptors is illustrated on the boiling point, the entropy, and the density of octanes. An intriguing situation is observed for regressions involving considered properties of n-octane isomers C8H18 in that the paths of length two, three, and four and the shells of the range two, three, and four give identical multivariate regression statistics. An explanation for this somewhat unusual aspect of MRA (multiple regression analysis) is offered.

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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.

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PubMedDate not supplied

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.

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PubMedDate not supplied

Condensed representation of DNA primary sequences.

With rapid reporting of DNA sequences derived from automated DNA sequencing techniques, the problem of reviewing and ordering such information has become acute. We have introduced a condensed representation of primary sequences of DNA that offers an alternative method of registering DNA. The advantage of the condensed codes for DNA is that it not only offers fast, qualitative comparisons of DNA but also allows quantitative comparisons of DNA from different sources. The approach is outlined for a particular human beta globin sequence extract. Using the condensed representation of the primary DNA sequences, comparisons are made between primary sequences for Exon 1 of human beta globin and seven other beta globins.

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PubMedDate not supplied

On the similarity of DNA primary sequences.

We consider numerical characterization of graphical representations of DNA primary sequences. In particular we consider graphical representation of DNA of beta-globins of several species, including human, on the basis of the approach of A. Nandy in which nucleic bases are associated with a walk over integral points of a Cartesian x, y-coordinate system. With a so-generated graphical representation of DNA, we associate a distance/distance matrix, the elements of which are given by the quotient of the Euclidean and the graph theoretical distances, that is, through the space and through the bond distances for pairs of bases of graphical representation of DNA. We use eigenvalues of so-constructed matrices to characterize individual DNA sequences. The eigenvalues are used to construct numerical sequences, which are subsequently used for similarity/dissimilarity analysis. The results of such analysis have been compared and combined with similarity tables based on the frequency of occurrence of pairs of bases.

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