The Connection of the Generalized Robinson-Foulds Metric with Partial Wiener Indices.

In this work we propose the partial Wiener index as one possible measure of branching in phylogenetic evolutionary trees. We establish the connection between the generalized Robinson-Foulds (RF) metric for measuring the similarity of phylogenetic trees and partial Wiener indices by expressing the number of conflicting pairs of edges in the generalized RF metric in terms of partial Wiener indices. To do so we compute the minimum and maximum value of the partial Wiener index [Formula: see text], where [Formula: see text] is a binary rooted tree with root [Formula: see text] and [Formula: see text] leaves. Moreover, under the Yule probabilistic model, we show how to compute the expected value of [Formula: see text]. As a direct consequence, we give exact formulas for the upper bound and the expected number of conflicting pairs. By doing so we provide a better theoretical understanding of the computational complexity of the generalized RF metric.

Optimizing the diagnostic capacity for COVID-19 PCR testing for low resource and high demand settings: The development of information-dependent pooling protocol.

AIM: To compare different pooling methods in an attempt to improve the COVID-19 PCR diagnostic capacities. METHOD: We developed a novel information-dependent pooling protocol (indept), based on transmission of less informative sequential pools on to the next pooling cycle to maximize savings. We then compared it to the halving, generalized halving, splitting and hypercube protocols in a simulation study, across variety of scenarios. RESULTS: All five methods yielded various amount of test savings, which mostly depended on the virus prevalence in the population. In situations of low prevalence (up to 5%), indept had the best performance, requiring on average 20% of tests needed for singular testing across scenarios that were analyzed. Nevertheless, this comes at the expense of speed, with the worst-case scenario of indept protocol requiring up to twice the time needed to test the same number of samples in comparison to the hypercube protocol. In order to offset this, we developed a faster version of the protocol (indeptSp), which minimizes the number of terminal pools and manages to retain savings compared to other protocols, despite marginally longer processing times. CONCLUSION: The increasing demand for more testing globally can benefit from application of pooling, especially in resource-restrained situations of the low- and middle-income countries or situations of high testing demand. Singular testing in situations of low prevalence should be systematically discouraged.

Selection and redesign for high selectivity of membrane-active antimicrobial peptides from a dedicated sequence/function database.

Antimicrobial peptides (AMPs) are plausible candidates for the development of novel classes of antibiotics with a low tendency to elicit resistance. They often form lesions in the bacterial membrane making it hard for bacteria to develop permanent resistance. However, a potent antibacterial activity is often accompanied by excessive cytotoxicity towards host cells. Modifying known natural sequences, based on desirable biophysical properties, is expensive and time-consuming and often with limited success. 'Mutator' is a freely available web-based computational tool for suggesting residue variations that potentially increase a peptide's selectivity, based on the use of quantitative structure activity relationship (QSAR) criteria. Although proven to be successful, it has never been used to analyze multiple sequences simultaneously. Modifying the Mutator algorithm allowed screening of many sequences in the dedicated Database of Anuran Defense Peptides (DADP) and by implementing limited amino acid substitutions on appropriate candidates, propose 8 potentially selective AMPs called Dadapins. Two were chosen for testing, confirming the prediction and validating this approach. They were shown to efficiently inactivate bacteria by disrupting their membranes but to be non-toxic for host cells, as determined by flow cytometry and confirmed by atomic force microscopy (AFM).

Antibacterial Activity Affected by the Conformational Flexibility in Glycine-Lysine Based α-Helical Antimicrobial Peptides.

Antimicrobial peptides often show broad-spectrum activity due to a mechanism based on bacterial membrane disruption, which also reduces development of permanent resistance, a desirable characteristic in view of the escalating multidrug resistance problem. Host cell toxicity however requires design of artificial variants of natural AMPs to increase selectivity and reduce side effects. Kiadins were designed using rules obtained from natural peptides active against E. coli and a validated computational algorithm based on a training set of such peptides, followed by rational conformational alterations. In vitro activity, tested against ESKAPE strains (ATCC and clinical isolates), revealed a varied activity spectrum and cytotoxicity that only in part correlated with conformational flexibility. Peptides with a higher proportion of Gly were generally less potent and caused less bacterial membrane alteration, as observed by flow cytometry and AFM, which correlate to structural characteristics as observed by circular dichroism spectroscopy and predicted by molecular dynamics calculations.

Tools for Designing Amphipathic Helical Antimicrobial Peptides.

Methods are described for the design of amphipathic helical AMPs, to improve potency and/or increase selectivity with respect to host cells. One method is based on the statistical analysis of known helical AMPs to derive a sequence template and ranges of charge, hydrophobicity, and amphipathicity (hydrophobic moment) values that lead to broad-spectrum activity, but leaves optimization for selectivity to subsequent rounds of SAR determinations. A second method uses a small database of anuran AMPs with known potency (MIC values vs. E. coli) and selectivity (HC50 values vs. human erythrocytes), as well as the concept of longitudinal moment, to suggest sequences or sequence variations that can improve selectivity. These methods can assist in the initial design of novel AMPs with useful properties in vitro, but further development requires knowledge-based decisions and a sound prior understanding of how structural and physical attributes of this class of peptides affect their mechanism of action against bacteria and host cells.

Predicting the Minimal Inhibitory Concentration for Antimicrobial Peptides with Rana-Box Domain.

The global spreading of multidrug resistance has motivated the search for new antibiotic classes including different types of antimicrobial peptides (AMPs). Computational methods for predicting activity in terms of the minimal inhibitory concentration (MIC) of AMPs can facilitate "in silico" design and reduce the cost of synthesis and testing. We have used an original method for separating training and test data sets, both of which contain the sequences and measured MIC values of non-homologous anuran peptides having the Rana-box disulfide motif at their C-terminus. Using a more flexible profiling methodology (sideways asymmetry moment, SAM) than the standard hydrophobic moment, we have developed a two-descriptor model to predict the bacteriostatic activity of Rana-box peptides against Gram-negative bacteria--the first multilinear quantitative structure-activity relationship model capable of predicting MIC values for AMPs of widely different lengths and low identity using such a small number of descriptors. Maximal values for SAMs, as defined and calculated in our method, furthermore offer new structural insight into how different segments of a peptide contribute to its bacteriostatic activity, and this work lays the foundations for the design of active artificial AMPs with this type of disulfide bridge.

Improving the selectivity of antimicrobial peptides from anuran skin.

Anuran skin is known to be a rich source of antimicrobial peptides although their therapeutic potential is often limited due to their toxicity against mammalian cells. The analysis of structure-activity relationships among anuran antimicrobial peptides provided the parameters to construct the "Mutator" tool for improving their selectivity for bacterial cells, by suggesting appropriate point substitutions. Double substitution analogues [K2, K16] of the Xenopus tropicalis peptide XT-7 and [I2, K19] of the Ascaphus truei peptide ascaphin-8 were predicted by this tool to have an increased 'therapeutic index' (TI = HC(50)/MIC for erythrocytes with respect to bacteria) > 80. The mutated peptides were synthesized and respectively found to have experimental TI values > 130 for S. aureus or E. coli, a considerable improvement with respect to TI < 37 for the parent compounds. Circular dichroism studies of the mutated peptides suggested this may in part be due to variations in the α-helical structure. For P. aeruginosa, which is more resistant to XT-7, the TI increased in the mutated peptide from 5 to >270, also due to a significant improvement in minimal inhibitory concentration. We have shown that the Mutator tool is capable of suggesting limited variations in natural anuran peptides capable of increasing peptide selectivity, by decreasing toxicity against mammalian erythrocytes, in general without compromising antibacterial activity. The tool is freely available on the Mutator Web server at http://split4.pmfst.hr/mutator/.

Conjugated circuits currents in hexabenzocoronene and its derivatives formed by joining proximal carbons.

We report on calculated CC bond currents for a dozen derivatives of hexabenzocoroenene in which one or more proximal carbon atoms at the molecular periphery have been bridged. The approach that we use is graph-theoretical in nature, following our outline of this method in 2003, which is based on finding all conjugated circuits in all Kekulé valence structures of these molecules. To the π-electrons having 4n + 2 π-electrons are assigned anticlockwise π-electron currents and to conjugated circuits having 4n π-electrons are assigned π-electron currents. One may summarize the results reported in this work by stating that CC bond currents in the compounds considered decrease on going from peripheral rings to the central ring of the molecule, and also that CC bond currents decrease by insertion of bridges to proximal peripheral benzenoid rings.

Knowledge-based computational methods for identifying or designing novel, non-homologous antimicrobial peptides.

We describe computational approaches for identifying promising lead candidates for the development of peptide antibiotics, in the context of quantitative structure-activity relationships (QSAR) studies for this type of molecule. A first approach deals with predicting the selectivity properties of generated antimicrobial peptide sequences in terms of measured therapeutic indices (TI) for known antimicrobial peptides (AMPs). Based on a training set of anuran AMPs, the concept of sequence moments was used to construct algorithms that could predict TIs for a second test set of natural AMPs and could also predict the effect of point mutations on TI values. This approach was then used to design peptide antibiotics (adepantins) not homologous to known natural or synthetic AMPs. In a second approach, many novel putative AMPs were identified from DNA sequences in EST databases, using the observation that, as a rule, specific subclasses of highly conserved signal peptides are associated exclusively with AMPs. Both anuran and teleost sequences were used to elucidate this observation and its implications. The predicted therapeutic indices of identified sequences could then be used to identify new types of selective putative AMPs for future experimental verification.

Master connectivity index and master connectivity polynomial.

We give the standard expressions of the Zagreb indices, Randic indices and their variants. Then we present the master connectivity index and show how this index can generate all connectivity indices of both varieties. We also present the master connectivity polynomial and show the relationship between this polynomial and the master connectivity index. Because of this relationship, the master connectivity polynomial can also be used to generate connectivity indices.

Note on the comparison of the first and second normalized zagreb eccentricity indices.

The conjecture Σuv V(G) dG(u)2 / n(G) ≤ Σuvv E(G) dG(u)dG(v) / m(G) that compares normalized Zagreb indices attracted recently a lot of attention1-9. In this paper we analyze analogous statement in which degree dG(u) of vertex u is replaced by its eccentricity δG(u) in which way we define novel first and second Zagreb eccentricity indices. We show that Σuv V(G) εG(u)2 / n(G) ≥ Σuvv E(G) εG(u)εG(v) / m(G) holds for all acyclic and unicyclic graphs and that neither this nor the opposite inequality holds for all bicyclic graphs.

Computational design of highly selective antimicrobial peptides.

We have created a structure-selectivity database (AMPad) of frog-derived, helical antimicrobial peptides (AMPs), in which the selectivity was determined as a therapeutic index (TI), and then used the novel concept of sequence moments to study the lengthwise asymmetry of physicochemical peptide properties. We found that the cosine of the angle between two sequence moments obtained with different hydrophobicity scales, defined as the D-descriptor, identifies highly selective peptide antibiotics. We could then use this descriptor to predict TI changes after point mutations in known AMPs, and to aid the prediction of TI for de novo designed AMPs. In combination with an amino acid selectivity index, a motif regularity index and other statistical rules extracted from AMPad, the D-descriptor enabled construction of the AMP-Designer algorithm. A 23 residue, glycine-rich, peptide suggested by the algorithm was synthesized and the activity and selectivity tested. This peptide, adepantin 1, is less than 50% identical to any other AMP, has a potent antibacterial activity against the reference organism, E. coli, and has a significantly greater selectivity (TI > 200) than the best AMP present in the AMPad database (TI = 125).

Graphical representation of proteins as four-color maps and their numerical characterization.

We put forward a novel compact 2-D graphical representation of proteins based on the concept of virtual genetic code and a four-color map. The novel graphical representation uniquely represents proteins and allows one to easily and quickly visually observe and inspect similarity/dissimilarity between them. It also leads to a novel protein descriptor, a 10-dimensional vector derived from a novel structure matrix S associated with the map. The introduced numerical characterization of proteins is not only useful for their comparative study, but also for cataloguing information on a single protein. The approach is illustrated with the A chain of human insulin and the A chain of human insulin analogue glargine.

Numerical Kekulé structures of fullerenes and partitioning of pi-electrons to pentagonal and hexagonal rings.

We calculated the partitioning of pi-electrons within individual pentagonal and hexagonal rings of fullerenes for a collection of fullerenes from C20 to C72 by constructing their Kekulé valence structures and averaging the pi-electron content of individual rings over all Kekulé valence structures. The resulting information is collected in Table 2, which when combined with the Schlegel diagram of fullerenes (illustrated in Figure 7) uniquely characterizes each of the 19 fullerenes considered. The results are interpreted as the basic information on the distributions (variation) of the local (ring) pi-electron density.

Kekulé structure count in corazulenic fullerenes.

Tiling modification in fullerene modeling can be achieved by some map operations. In this respect, sequences of classical operations, or single generalized operations, were used to obtain corannulene-like azulenic patterns. The aromaticity of such cages tessellated by "corazulenic" supra-faces is discussed in terms of several criteria. Particularly, the number of Kekulé valence structures, was considered as a rough measure of the fullerene aromaticity and implicitely of their stability. The covering was given as a pi-electron partition within some Kekulé valence structures. The well-known geometric index of aromaticity HOMA (harmonic oscillator model of aromaticity) enabled the evaluation of local aromaticity of the discussed supra-faces and brought evidence for several dominant Kekulé valence structures.

Linear regression model of DNA sequences and its application.

We constructed six new models to analyze the DNA sequences. First, we regarded a DNA primary sequence as a random process in t and gave three ways to define nucleotides' random distribution functions. We extracted some parameters from the linear model and analyzed the changes of the nucleotides' distributions. In order to facilitate the comparison of DNA sequences, we proposed two ways to measure their similarities. Finally, we compared the six models by analyzing the similarities of the DNA primary sequences presented in Table 1 and selected the optimal one.

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.

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.