X-Ray Crystallography and Free Energy Calculations Reveal the Binding Mechanism of A2A Adenosine Receptor Antagonists

We present a robust protocol based on iterations of free energy perturbation (FEP) calculations, chemical synthesis, biophysical mapping and X-ray crystallography to reveal the binding mode of an antagonist series to the A_2A adenosine receptor (AR). Eight A_2AAR binding site mutations from biophysical mapping experiments were initially analyzed with sidechain FEP simulations, performed on alternate binding modes. The results distinctively supported one binding mode, which was subsequently used to design new chromone derivatives. Their affinities for the A_2AAR were experimentally determined and investigated through a cycle of ligand-FEP calculations, validating the binding orientation of the different chemical substituents proposed. Subsequent X-ray crystallography of the A_2AAR with a low and a high affinity chromone derivative confirmed the predicted binding orientation. The new molecules and structures here reported were driven by free energy calculations, and provide new insights on antagonist binding to the A_2AAR, an emerging target in immuno-oncology.     

Computing the extended centroid of abelian—group graded rings

We compute the extended centroid of a prime ring graded by an abelian group.     

Semigroup graded algebras and graded PI-exponent

Let S be a semigroup. We study the structure of graded-simple S-graded algebras A and the exponential rate PIexp ^S-gr(A):= lim_n→∞ \(\sqrt[n]{{c_n^{S - gr}\left( A \right)}}\) of growth of codimensions c _n ^S-gr (A) of their graded polynomial identities. This is of great interest since such algebras can have non-integer PIexp ^S-gr(A) despite being finite dimensional and associative. In addition, such algebras can have a non-trivial Jacobson radical J(A). All this is in strong contrast with the case when S is a group since in the group case J(A) is trivial, PIexp ^S-gr(A) is always integer and, if the base field is algebraically closed, then PIexp ^S-gr(A) equals dimA. Without any restrictions on the base field F, we classify graded-simple S-graded algebras A for a class of semigroups S which is complementary to the class of groups. We explicitly describe the structure of J(A) showing that J(A) is built up of pieces of a maximal S-graded semisimple subalgebra of A which turns out to be simple. When F is algebraically closed, we get an upper bound for \({\overline {\lim } _{n \to \infty }}\sqrt[n]{{c_n^{S - gr}\left( A \right)}}\). If A/J(A) ≈ M ₂(F) and S is a right zero band, we show that this upper bound is sharp and PIexp ^S-gr(A) indeed exists. In particular, we present an infinite family of graded-simple algebras A with arbitrarily large non-integer PIexp ^S-gr(A).     

Jacobson rings and rings strongly graded by an abelian group

LetR be ring strongly graded by an abelian groupG of finite torsion-free rank. Lete be the identity ofG, andR _e the component of degreee ofR. AssumeR _e is a Jacobson ring. We prove that graded subrings ofR are again Jacobson rings if eitherR _e is a left Noetherian ring orR is a group ring. In particular we generalise Goldie and Michlers’s result on Jacobson polycyclic group rings, and Gilmer’s result on Jacobson commutative semigroup rings of finite torsion-free rank.