Roy equation analysis of ππ scattering

We analyse the Roy equations for the lowest partial waves of elastic ππ scattering. In the first part of the paper, we review the mathematical properties of these equations as well as their phenomenological applications. In particular, the experimental situation concerning the contributions from intermediate energies and the evaluation of the driving terms are discussed in detail. We then demonstrate that the two S-wave scattering lengths a00 and a02 are the essential parameters in the low energy region: Once these are known, the available experimental information determines the behaviour near threshold to within remarkably small uncertainties. An explicit numerical representation for the energy dependence of the S- and P-waves is given and it is shown that the threshold parameters of the D- and F-waves are also fixed very sharply in terms of a00 and a20. In agreement with earlier work, which is reviewed in some detail, we find that the Roy equations admit physically acceptable solutions only within a band of the (a00,a02) plane. We show that the data on the reactions e+e−→ππ and τ→ππν reduce the width of this band quite significantly. Furthermore, we discuss the relevance of the decay K→ππeν in restricting the allowed range of a00, preparing the grounds for an analysis of the forthcoming precision data on this decay and on pionic atoms. We expect these to reduce the uncertainties in the two basic low energy parameters very substantially, so that a meaningful test of the chiral perturbation theory predictions will become possible.

Structural analysis of dihydrofolate reductases enables rationalization of antifolate binding affinities and suggests repurposing possibilities

Antifolates are competitive inhibitors of dihydrofolate reductase ( DHFR), a conserved enzyme that is central to metabolism and widely targeted in pathogenic diseases, cancer and autoimmune disorders. Although most clinically used antifolates are known to be target specific, some display a fair degree of cross-reactivity with DHFRs from other species. A method that enables identification of determinants of affinity and specificity in target DHFRs from different species and provides guidelines for the design of antifolates is currently lacking. To address this, we first captured the potential druggable space of a DHFR in a substructure called the `supersite' and classified supersites of DHFRs from 56 species into 16 `site-types' based on pairwise structural similarity. Analysis of supersites across these site-types revealed that DHFRs exhibit varying extents of dissimilarity at structurally equivalent positions in and around the binding site. We were able to explain the pattern of affinities towards chemically diverse antifolates exhibited by DHFRs of different site-types based on these structural differences. We then generated an antifolate-DHFR network by mapping known high-affinity antifolates to their respective supersites and used this to identify antifolates that can be repurposed based on similarity between supersites or antifolates. Thus, we identified 177 human-specific and 458 pathogen-specific antifolates, a large number of which are supported by available experimental data. Thus, in the light of the clinical importance of DHFR, we present a novel approach to identifying differences in the druggable space of DHFRs that can be utilized for rational design of antifolates.