IC₅₀ values obtained for Fasudil, TPCA-1 and Y-27632 <i>in vitro</i>.

<p>IC₅₀ values obtained for Fasudil, TPCA-1 and Y-27632 <i>in vitro</i>.</p

Detailed views of intramolecular interations.

<p>(<b>A</b>) Interactions involved in the small antiparallel β-sheet formed from a part of the activation loop (red) and a part of the αEF/αF loop (yellow). (<b>B</b>) Hydrogen bonding interactions involved in the stabilization of the hydrophobic motif within the dimerization domain.</p

Inhibitors of MRCKβ <i>in vitro</i>.

<p>Inhibitors of MRCKβ <i>in vitro</i>.</p

Positions of Fasudil and TPCA-1 in MRCKβ active site.

<p>(<b>A</b>) Structure of Fasudil bound to the active site of MRCKβ. Hydrogen bonds are marked with yellow dashed lines. The Fo–Fc omit map is shown contoured at 2σ, with the inhibitor modeled in the density. In the topology diagram, surface contour is shown with a gray dashed line and hydrogen bonds with blue dashed lines. Hydrophobic residues lining the cavity are shown in light green circles, and polar residues with light magenta. Blue shading indicates solvent exposed ligand groups. (<b>B</b>) Structure of TPCA-1 bound to the active site of MRCKβ. (<b>C</b>) Overlay of the structures of Fasudil and TPCA-1 bound to the active site of MRCKβ.</p

Inhibition of MRCK activity by kinase inhibitors.

<p>A collection of 159 kinase inhibitors were tested for their ability to inhibit MRCKβ activity in vitro at (<b>A</b>) 30 µM and (<b>B</b>) 3 µM. Pie charts represent the proportion inhibiting >80% at each concentration. Inhibition of (<b>C</b>) MRCKα or (<b>D</b>) MRCKβ activity by Y-27632, TPCA-1 and Fasudil. Both kinases were inhibited by these compounds, although some differences in sensitivity were apparent.</p

Structure of dimeric MRCKβ.

<p>(<b>A</b>) Overall structure of the dimeric MRCKβ shows the interactions of the two monomers at the dimerization domain. The four Fasudil molecules observed per asymmetric unit are also shown, two bound to the surface of the protein (central) and one bound to each of the ATP-binding sites (lateral). (<b>B</b>) A close-up of one monomer reveals a typical two-lobed kinase structure, with both the N-terminus (orange) and the C-terminus (purple; disorganized loop shown as a dashed line) forming the dimerization domain. The glycine-rich loop (blue) and activation loop (red) are fully ordered, and the αEF/αF-loop is also indicated (yellow). Fasudil is shown bound in the ATP-binding site.</p

An overlay of MRCKβ (green) with ROCK2 (A; cyan) and ROCK1 (B; magenta) highlights the very subtle structural differences that could be exploited in developing specific inhibitors.

<p>The surface shown is the nucleotide binding cavity of MRCKβ, with Fasudil bound at the ATP binding site. Apart from the highlighted residues, the ATP binding sites of the three kinases are identical at sequence level.</p

Sequence alignment of MRCKβ and the most closely related AGC kinases.

<p>Sequences have been truncated after the C-terminal lobe. The conserved HRD and DFG motifs have been highlighted with red arrows, and the conserved salt bridge at the active site with green arrows. Predicted phosphorylation sites have been indicated with magenta arrows, and the residues involved in hydrogen bonds between the C- and N-termini at the dimerization domain are indicated by orange arrows.</p

Inhibition of 3-D matrigel invasion by MDA MB 231 cells following MRCK and ROCK inhibition.

<p>(<b>A</b>) Knock-down of MRCKα and MRCKβ individually or in combination. Double knockdown was achieved either by combining separate siRNAs (MRCKα+β) or single siRNA duplexes that target both kinases (MRCKα/β). NTC = non-targeting control. (<b>B</b>) Optical slices were obtained every 10 µm by confocal imaging. (<b>C</b>) Invasion 40 µm above the transwell filter surface was normalized to non-targeting control (NTC) siRNA transfected cells. Significant differences between groups of columns indicated. (Average ± SEM, n = 3). MRCKα/β knockdown or ROCK inhibition with Y-27632 (Y) significantly decreased invasion, with the combination of MRCKα/β knockdown and ROCK inhibition resulting in significantly more inhibition. (<b>D</b>) Effectiveness and specificity of ROCK1, ROCK2 and MRCKαβ knockdowns. (<b>E</b>) The combination of MRCKα/β with ROCK1 and ROCK2 knockdown individually or in combinations were tested for their effects on 3-D matrigel invasion. ROCK1, ROCK2 or ROCK1+ROCK2 combination were able to significantly inhibit invasion. However, additional MRCKα/β knockdown significantly increased the inhibition of invasion in each instance. (Average ± SEM, n = 3).</p

On multiplicative structure in Quasi-Newton methods for nonlinear equations

We address the problem how additive and multiplicative structure in the derivatives can be exploited for the construction of Quasi-Newton approximations in smooth nonlinear equations. We derive a model algorithm and show its convergence properties based on a Broyden-like update rule. As a consequence of the use of exact multiplicative parts the convergence factor of the q-linear convergence rate is monotonically decreasing with the norm of the multiplicative part at the solution. Moreover, q-superlinear convergence can be shown, if certain compactness properties are valid, and q-quadratic convergence is obtained, if the multiplicative part vanishes at the solutionAvailable from TIB Hannover: RR 1843(92-22) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman