On minimum dominating sets with minimum intersection

AbstractIn the developing theory of polynomial/linear algorithms for various problems on certain classes of graphs, most problems considered have involved either finding a single vertex set with a specified property (such as being a minimum dominating set) or finding a partition of the vertex set into such sets (for example, a partition into the maximum possible number of dominating sets). Alternatively, one might be interested in the cardinality of the set or the partition. In this paper we introduce an intermediate type of problem. Specifically, we ask for two minimum dominating sets with minimum intersection. We present a linear algorithm for finding two minimum dominating sets with minimum possible intersection in a tree T, and we show that simply determining whether or not there exist two disjoint minimum dominating sets is NP-hard for arbitrary bipartile graphs

Structural and Thermodynamic Approach to Peptide Immunogenicity

In the conventional paradigm of humoral immunity, B cells recognize their cognate antigen target in its native form. However, it is well known that relatively unstable peptides bearing only partial structural resemblance to the native protein can trigger antibodies recognizing higher-order structures found in the native protein. On the basis of sound thermodynamic principles, this work reveals that stability of immunogenic proteinlike motifs is a critical parameter rationalizing the diverse humoral immune responses induced by different linear peptide epitopes. In this paradigm, peptides with a minimal amount of stability (ΔGX<0 kcal/mol) around a proteinlike motif (X) are capable of inducing antibodies with similar affinity for both peptide and native protein, more weakly stable peptides (ΔGX>0 kcal/mol) trigger antibodies recognizing full protein but not peptide, and unstable peptides (ΔGX>8 kcal/mol) fail to generate antibodies against either peptide or protein. Immunization experiments involving peptides derived from the autoantigen histidyl-tRNA synthetase verify that selected peptides with varying relative stabilities predicted by molecular dynamics simulations induce antibody responses consistent with this theory. Collectively, these studies provide insight pertinent to the structural basis of immunogenicity and, at the same time, validate this form of thermodynamic and molecular modeling as an approach to probe the development/evolution of humoral immune responses