Structural impact of GTP binding on downstream KRAS signaling

Oncogenic RAS proteins, involved in ∼30% of human tumors, are molecular switches of various signal transduction pathways. Here we apply a new protocol for the NMR study of KRAS in its (inactive) GDP- and (activated) GTP-bound form, allowing a comprehensive analysis of the backbone dynamics of its WT-, G12C- and G12D variants. We found that Tyr32 shows opposite mobility with respect to the backbone of its surroundings: it is more flexible in the GDP-bound form while more rigid in GTP-complexes (especially in WT- and G12D-GTP). Using the G12C/Y32F double mutant, we showed that the presence of the hydroxyl group of Tyr32 has a marked effect on the G12C-KRAS-GTP system as well. Molecular dynamics simulations indicate that Tyr32 is linked to the γ-phosphate of GTP in the activated states – an arrangement shown, using QM/MM calculations, to support catalysis. Anchoring Tyr32 to the γ-phosphate contributes to the capture of the catalytic waters participating in the intrinsic hydrolysis of GTP and supports a simultaneous triple proton transfer step (catalytic water → assisting water → Tyr32 → O1G of the γ-phosphate) leading to straightforward product formation. The coupled flip of negatively charged residues of switch I toward the inside of the effector binding pocket potentiates ligand recognition, while positioning of Thr35 to enter the coordination sphere of the Mg²⁺ widens the pocket. Position 12 mutations do not disturb the capture of Tyr32 by the γ-phosphate, but (partially) displace Gln61, which opens up the catalytic pocket and destabilizes catalytic water molecules thus impairing intrinsic hydrolysis.

Nucleotide exchange to the physiological, activated, GTP-bound form of KRAS results in the anchoring of Tyr32 within the active site.     

Characterisation of grafted weak anion-exchange methacrylate monoliths

A weak ion-exchange grafted methacrylate monolith was prepared by grafting a methacrylate monolith with glycidyl methacrylate and subsequently modifying the epoxy groups with diethylamine. The thickness of the grafted layer was determined by measuring permeability and found to be approximately 90nm. The effects of different buffer solutions on the pressure drop were examined and indicated the influence of pH on the permeability of the grafted monolith. Protein separation and binding capacity (BC) were found to be flow-unaffected up to a linear velocity of 280cm/h. A comparison of the BC for the non-grafted and grafted monolith was performed using beta-lactoglobulin, bovine serum albumin (BSA), thyroglobulin, and plasmid DNA (pDNA). It was found that the grafted monolith exhibited 2- to 3.5-fold higher capacities (as compared to non-grafted monoliths) in all cases reaching values of 105, 80, 71, and 17mg/ml, respectively. It was determined that the maximum pDNA capacity was reached using 0.1M NaCl in the loading buffer. Recovery was comparable and no degradation of the supercoiled pDNA form was detected. Protein z-factors were equal for the non-grafted and grafted monolith indicating that the same number of binding sites are available although elution from the grafted monolith occurred at higher ionic strengths. The grafted monolith exhibited lower efficiency than the non-grafted ones. However, the baseline separation of pDNA from RNA and other impurities was achieved from a real sample.     

A Polynomial Bound for Untangling Geometric Planar Graphs

To untangle a geometric graph means to move some of the vertices so that the resulting geometric graph has no crossings. Pach and Tardos (Discrete Comput. Geom. 28(4): 585–592, 2002) asked if every n-vertex geometric planar graph can be untangled while keeping at least n ^ε vertices fixed. We answer this question in the affirmative with ε=1/4. The previous best known bound was \(\Omega(\sqrt{\log n/\log\log n})\). We also consider untangling geometric trees. It is known that every n-vertex geometric tree can be untangled while keeping at least \(\Omega(\sqrt{n})\) vertices fixed, while the best upper bound was \(\mathcal{O}((n\log n)^{2/3})\). We answer a question of Spillner and Wolff (http://arxiv.org/abs/0709.0170) by closing this gap for untangling trees. In particular, we show that for infinitely many values of n, there is an n-vertex geometric tree that cannot be untangled while keeping more than \(3(\sqrt{n}-1)\) vertices fixed.     

Curvature effect on droplet impacting onto hydrophobic and superhydrophobic spheres

Droplet impact on hydrophobic and superhydrophobic solid surfaces finds numerous applications, while the wide range of the parameters affecting its outcome necessitate a thorough study to reveal the underlying physics. Specific applications are related to the drop impact upon curved surfaces, such as micro-encapsulation in fluidized beds. Three-dimensional numerical simulations by applying Level-Set Method have been performed to investigate the water droplet impact on curved and flat hydrophobic and superhydrophobic substrates. Parameters such as the impact Weber number, the surface curvature and the equilibrium contact angle have been varied in order to assess their effects on the dynamics of the impact process. After providing a strong validation, it is found that impact on spherical surfaces generally presents a higher area of liquid to be in contact with the substrate with respect to the case of flat surfaces, when all other impact conditions are the same.     

Every Large Point Set contains Many Collinear Points or an Empty Pentagon

We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next open case of the “big line or big clique” conjecture of Kára, Pór, and Wood [Discrete Comput. Geom. 34(3):497–506, 2005].     

On the preconditioning of the block tridiagonal linear system of equations

Two algorithms for computing the inverse factors of general tridiagonal and pentadiagonal matrices are obtained. Then, these algorithms are used for computing a block ILU preconditioner for the block tridiagonal linear system of equations. Some numerical results are given to show the robustness and efficiency of the preconditioner. The performance of the proposed preconditioner is compared with a recently proposed method.     

A new relaxed HSS preconditioner for saddle point problems

We present a preconditioner for saddle point problems. The proposed preconditioner is extracted from a stationary iterative method which is convergent under a mild condition. Some properties of the preconditioner as well as the eigenvalues distribution of the preconditioned matrix are presented. The preconditioned system is solved by a Krylov subspace method like restarted GMRES. Finally, some numerical experiments on test problems arisen from finite element discretization of the Stokes problem are given to show the effectiveness of the preconditioner.