High-temperature scaling limit for directed polymers on a hierarchical lattice with bond disorder

Diamond "lattices" are sequences of recursively-defined graphs that provide a network of directed pathways between two fixed root nodes, $A$ and $B$. The construction recipe for diamond graphs depends on a branching number $b\in \mathbb{N}$ and a segmenting number $s\in \mathbb{N}$, for which a larger value of the ratio $s/b$ intuitively corresponds to more opportunities for intersections between two randomly chosen paths. By attaching i.i.d. random variables to the bonds of the graphs, I construct a random Gibbs measure on the set of directed paths by assigning each path an "energy" given by summing the random variables along the path. For the case $b=s$, I propose a scaling regime in which the temperature grows along with the number of hierarchical layers of the graphs, and the partition function (the normalization factor of the Gibbs measure) appears to converge in law. I prove that all of the positive integer moments of the partition function converge in this limiting regime. The motivation of this work is to prove a functional limit theorem that is analogous to a previous result obtained in the $b<s$ case.Comment: 28 pages, 1 figur

Predicting “Hot” and “Warm” Spots for Fragment Binding

Computational fragment mapping methods aim to predict hotspots on protein surfaces where small fragments will bind. Such methods are popular for druggability assessment as well as structure-based design. However, to date researchers developing or using such tools have had no clear way of assessing the performance of these methods. Here, we introduce the first diverse, high quality validation set for computational fragment mapping. The set contains 52 diverse examples of fragment binding “hot” and “warm” spots from the Protein Data Bank (PDB). Additionally, we describe PLImap, a novel protocol for fragment mapping based on the Protein–Ligand Informatics force field (PLIff). We evaluate PLImap against the new fragment mapping test set, and compare its performance to that of simple shape-based algorithms and fragment docking using GOLD. PLImap is made publicly available from https://bitbucket.org/AstexUK/pli

Predicting “Hot” and “Warm” Spots for Fragment Binding

Computational fragment mapping methods aim to predict hotspots on protein surfaces where small fragments will bind. Such methods are popular for druggability assessment as well as structure-based design. However, to date researchers developing or using such tools have had no clear way of assessing the performance of these methods. Here, we introduce the first diverse, high quality validation set for computational fragment mapping. The set contains 52 diverse examples of fragment binding “hot” and “warm” spots from the Protein Data Bank (PDB). Additionally, we describe PLImap, a novel protocol for fragment mapping based on the Protein–Ligand Informatics force field (PLIff). We evaluate PLImap against the new fragment mapping test set, and compare its performance to that of simple shape-based algorithms and fragment docking using GOLD. PLImap is made publicly available from https://bitbucket.org/AstexUK/pli

Fragment-Based Approach to the Development of an Orally Bioavailable Lactam Inhibitor of Lipoprotein-Associated Phospholipase A2 (Lp-PLA₂)

Lp-PLA₂ has been explored as a target for a number of inflammation associated diseases, including cardiovascular disease and dementia. This article describes the discovery of a new fragment derived chemotype that interacts with the active site of Lp-PLA₂. The starting fragment hit was discovered through an X-ray fragment screen and showed no activity in the bioassay (IC₅₀ > 1 mM). The fragment hit was optimized using a variety of structure-based drug design techniques, including virtual screening, fragment merging, and improvement of shape complementarity. A novel series of Lp-PLA₂ inhibitors was generated with low lipophilicity and a promising pharmacokinetic profile

Exploitation of a Novel Binding Pocket in Human Lipoprotein-Associated Phospholipase A2 (Lp-PLA₂) Discovered through X‑ray Fragment Screening

Elevated levels of human lipoprotein-associated phospholipase A2 (Lp-PLA₂) are associated with cardiovascular disease and dementia. A fragment screen was conducted against Lp-PLA₂ in order to identify novel inhibitors. Multiple fragment hits were observed in different regions of the active site, including some hits that bound in a pocket created by movement of a protein side chain (approximately 13 Å from the catalytic residue Ser273). Using structure guided design, we optimized a fragment that bound in this pocket to generate a novel low nanomolar chemotype, which did not interact with the catalytic residues

Exploitation of a Novel Binding Pocket in Human Lipoprotein-Associated Phospholipase A2 (Lp-PLA₂) Discovered through X‑ray Fragment Screening

Elevated levels of human lipoprotein-associated phospholipase A2 (Lp-PLA₂) are associated with cardiovascular disease and dementia. A fragment screen was conducted against Lp-PLA₂ in order to identify novel inhibitors. Multiple fragment hits were observed in different regions of the active site, including some hits that bound in a pocket created by movement of a protein side chain (approximately 13 Å from the catalytic residue Ser273). Using structure guided design, we optimized a fragment that bound in this pocket to generate a novel low nanomolar chemotype, which did not interact with the catalytic residues

Fragment-Based Discovery of a Potent, Orally Bioavailable Inhibitor That Modulates the Phosphorylation and Catalytic Activity of ERK1/2

Aberrant activation of the MAPK pathway drives cell proliferation in multiple cancers. Inhibitors of BRAF and MEK kinases are approved for the treatment of BRAF mutant melanoma, but resistance frequently emerges, often mediated by increased signaling through ERK1/2. Here, we describe the fragment-based generation of ERK1/2 inhibitors that block catalytic phosphorylation of downstream substrates such as RSK but also modulate phosphorylation of ERK1/2 by MEK without directly inhibiting MEK. X-ray crystallographic and biophysical fragment screening followed by structure-guided optimization and growth from the hinge into a pocket proximal to the C-α helix afforded highly potent ERK1/2 inhibitors with excellent kinome selectivity. In BRAF mutant cells, the lead compound suppresses pRSK and pERK levels and inhibits proliferation at low nanomolar concentrations. The lead exhibits tumor regression upon oral dosing in BRAF mutant xenograft models, providing a promising basis for further optimization toward clinical pERK1/2 modulating ERK1/2 inhibitors

Fragment-Based Discovery of a Potent, Orally Bioavailable Inhibitor That Modulates the Phosphorylation and Catalytic Activity of ERK1/2

Aberrant activation of the MAPK pathway drives cell proliferation in multiple cancers. Inhibitors of BRAF and MEK kinases are approved for the treatment of BRAF mutant melanoma, but resistance frequently emerges, often mediated by increased signaling through ERK1/2. Here, we describe the fragment-based generation of ERK1/2 inhibitors that block catalytic phosphorylation of downstream substrates such as RSK but also modulate phosphorylation of ERK1/2 by MEK without directly inhibiting MEK. X-ray crystallographic and biophysical fragment screening followed by structure-guided optimization and growth from the hinge into a pocket proximal to the C-α helix afforded highly potent ERK1/2 inhibitors with excellent kinome selectivity. In BRAF mutant cells, the lead compound suppresses pRSK and pERK levels and inhibits proliferation at low nanomolar concentrations. The lead exhibits tumor regression upon oral dosing in BRAF mutant xenograft models, providing a promising basis for further optimization toward clinical pERK1/2 modulating ERK1/2 inhibitors