Щодо утворення сімейств атомарних радіальних базисних функцій

Наведено схему побудови сімейств атомарних радіальних базисних функцій, які є нескінченно диференційовними фінітними розв'язками функціонально-диференціальних рівнянь, породжених операторами Лапласа та Гельмгольца.The scheme of building a family of atomic radial basis functions which are infinitely differentiable finite solutions of the functional-differential equations containing the Laplace and Helmholtz operators is introduced

Structure-Guided Design of Selective Epac1 and Epac2 Agonists

The second messenger cAMP is known to augment glucose-induced insulin secretion. However, its downstream targets in pancreatic β-cells have not been unequivocally determined. Therefore, we designed cAMP analogues by a structure-guided approach that act as Epac2-selective agonists both in vitro and in vivo. These analogues activate Epac2 about two orders of magnitude more potently than cAMP. The high potency arises from increased affinity as well as increased maximal activation. Crystallographic studies demonstrate that this is due to unique interactions. At least one of the Epac2-specific agonists, Sp-8-BnT-cAMPS (S-220), enhances glucose-induced insulin secretion in human pancreatic cells. Selective targeting of Epac2 is thus proven possible and may be an option in diabetes treatment

Chemical structures of cAMP analogues.

<p>cAMP was modified in the cyclic phosphate and at N⁶-, 2′-, and 8-positions. Modifications are labelled with the nomenclature used for the abbreviated names of the cAMP analogues as used in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002038#pbio.1002038.t001" target="_blank">Table 1</a>. Structures of analogues with two or more modifications can be constructed based on the abbreviated names given in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002038#pbio.1002038.t001" target="_blank">Table 1</a> and <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002038#pbio.1002038.s004" target="_blank">S1 Table</a>. <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002038#pbio.1002038.s004" target="_blank">S1 Table</a> gives the full names.</p

Design of an efficient Epac2 agonist.

<p>(A) The maximal activity towards Epac2^Δ280 is increased in phosphorothioates that contain the sulphur atom in the axial position. The affinity and maximal activity is further increased by the introduction of a BnT-group at the 8-positon. The effect of the BnT-group is selectively eliminated in Epac2^Δ280,K450A. Plot data can be found in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002038#pbio.1002038.s001" target="_blank">S1 Data</a>. (B) The structure of Epac2•S-280•Rap with <i>fofc</i> density calculated in the absence of S-280. The pFBnT-group (the only difference to the BnT group and therefore to S-220 is the fluorine atom (<i>F</i>) in para-position) undergoes hydrophobic stacking interaction with Lys⁴⁵⁰ in the lid (orange). <i>S</i> marks the sulphur atom of the phosphorothioate.</p

D-007 is an efficient activator of Epac1 but not of Epac2.

<p>(A) Domain organization of Epac1 and Epac2. Only the second CNB domain of Epac2 is involved in the regulation process. DEP, Dishevelled, Egl-10 and Pleckstrin; REM, Ras exchange motif; RA, Ras Association; CDC25-HD, CDC25-homology domain. (B) Chemical structure of D-007. (C) Comparison of cyclic nucleotide induced activity for Epac1, Epac1^Q270K, Epac2^Δ280, and Epac2^Δ280,K405Q. Position 270 of Epac1 corresponds to position 405 in Epac2. Plot data can be found in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002038#pbio.1002038.s001" target="_blank">S1 Data</a>. (D) Illustration of data interpretation. Epac exists in equilibrium between an inactive and active conformation (right). The AC₅₀ is a measure for the affinity of the cAMP analogue and the k_max for the extent to what the equilibrium is shifted to the active conformation. The concentration of an analogue required to reach the same activity as induced by cAMP at its AC₅₀ is defined as the activation potential (indicated by grey lines and arrows).</p

Selective activation of Epac2 results in insulin secretion.

<p>(A) Comparison of U2OS cell lines stably expressing Epac1 or Epac2 with parent cells. Cells were mock-stimulated or received 15 μM forskolin and 200 μM IBMX to elevate intracellular cAMP levels. The activation of PKA was monitored by a phosphorylation-induced band shift of VASP. Rap•GTP was precipitated from cell lysates and compared to the total Rap levels. Epac was visualized by an anti-flag antibody. (B) Stimulation of Epac1 or Epac2 cells with reagents as indicated. To visualize the low activity levels of PKA, long exposures of the VASP blots are shown next to the normal exposure time. (C) Quantification of Western blots obtained from experiments as shown in (B). Rap•GTP and P-VASP levels were determined relative to the induction obtained with forskolin and IBMX. As the response of PKA was indistinguishable in the Epac1 and Epac2 cell lines, P-VASP levels of both cell lines were averaged. Values for L-026 and S-223 are based on two and for D-007 and S-220 on four independent experiments. For statistical analysis data were compared to non-stimulated cells in a two-tailed and unpaired Student’s <i>t</i> test; *<i>p</i> < 0.01. Bar-graph data can be found in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002038#pbio.1002038.s001" target="_blank">S1 Data</a>. (D) Primary human islets isolated from donor pancreas were stimulated with reagents as indicated, and insulin secretion was determined as the ratio of insulin level before and after stimulation (insulin secretion index). A Kruskal-Wallis test was performed for statistical analysis, which is depicted as K(χ²;<i>p</i>-value) in the graphs. Bar-graph data can be found in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002038#pbio.1002038.s001" target="_blank">S1 Data</a>.</p

Structural basis for efficient activation of Epac1 by D-007.

<p>(A) Superposition of the CNB domains of Epac2 in the absence of cAMP (grey) and bound to cAMP (blue), and of Epac2^K405Q bound to cAMP (orange) and D-007 (magenta). Binding of cAMP induces conformational changes in the phosphate binding cassette (PBC) which allow the hinge to move and the lid to flip over the CNB site, where the lid it is anchored by interactions with the base of the cyclic nucleotide [<a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002038#pbio.1002038.ref010" target="_blank">10</a>]. cAMP originates from Epac2•cAMP•Rap. Arrows illustrate the transition from the inactive to the active conformation. (B) Schematic representation of the transition of Epac to the active conformation whereby the conformational change is described as a rigid body movement of the CNB domain. (C) Alternative view on the transition in which the CNB domain is kept fixed. This point of view is adapted in (A and D–F). (D–F) Stereo view of the cAMP binding site with bound cAMP or D-007 with <i>fofc</i> density calculated in the absence of the nucleotides. The interaction networks of Lys⁴⁰⁵ and Gln⁴⁰⁵, respectively, are shown. Residues from the PBC are shown in green, and those from the hinge and the lid in orange. The 2′- and the 8-position of the cyclic nucleotides are indicated in italics. Amino acids are given by single letter code; w, water. Epac2•cAMP•Rap (D) Epac2^K405Q•cAMP•Rap with elements from Epac2•cAMP•Rap in transparent grey (E) and Epac2^K405Q•D-007•Rap with elements from Epac2^K405Q•cAMP•Rap in transparent grey (F). (D–F) are in the same orientation based on a super-position of the CNB domains.</p

Selective activation of Epac proteins <i>in vitro</i>.

<p>(A, B) Comparison of cyclic nucleotide-mediated activation of Epac1 and Epac2^fl. Plot data can be found in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002038#pbio.1002038.s001" target="_blank">S1 Data</a>. (C– F) Cyclic nucleotide mediated activation of PKA-Iα, PKA-Iβ, PKA-IIα, and PKA-IIβ. Each data point represents the mean ± standard deviation (SD) of at least two measurements. Plot data can be found in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1002038#pbio.1002038.s001" target="_blank">S1 Data</a>.</p