On the edge degrees of trees

Let mij(G) be the number of edges of graph G, connecting vertices of degrees i and j. Necessary and sufficient conditions are established on a symmetric matrix M of type Δ × Δ such that there is a tree T for which Mij = mij(T) holds for all i, j

design of selective peptide antibiotics by using the sequence moment concept

New antibiotics against multidrug-resistant bacteria are urgently needed, but rapid acquisition of resistance limits their usefulness. Endogenous antimicrobial peptides (AMPs) with moderate selectivity, but multimodal mechanism of action, have remained effective against bacteria for millions of years. Their therapeutic application, however, requires optimizing the balance between antibacterial activity and selectivity, so that rational design methods for increasing selectivity are highly desirable. We have created training (n=36) and testing (n=37) sets from frog-derived AMPs with determined therapeutic index (TI). The 'sequence moments' concept then enabled us to find a one-parameter linear model resulting in a good correlation between measured and predicted TI (r2=0.83 and 0.64 for each set, respectively). The concept was then used in the AMP-Designer algorithm to propose primary structures for highly selective AMPs against Gram-negative bacteria. Testing the activity of one such peptide produced a TI>200 as compared to the best AMP in the data-base, with TI=125

Improving the Selectivity of Antimicrobial Peptides from Anuran Skin

International audienceAnuran 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 = HC50/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 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/