8 research outputs found
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, and . The
construction recipe for diamond graphs depends on a branching number and a segmenting number , for which a larger value
of the ratio 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 , 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 case.Comment: 28 pages, 1 figur
Predicting âHotâ and âWarmâ 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 âhotâ
and âwarmâ spots from the Protein Data Bank (PDB). Additionally,
we describe PLImap, a novel protocol for fragment mapping based on
the ProteinâLigand 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 âHotâ and âWarmâ 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 âhotâ
and âwarmâ spots from the Protein Data Bank (PDB). Additionally,
we describe PLImap, a novel protocol for fragment mapping based on
the ProteinâLigand 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-PLA<sub>2</sub>)
Lp-PLA<sub>2</sub> 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-PLA<sub>2</sub>. The starting fragment hit was discovered through an X-ray
fragment screen and showed no activity in the bioassay (IC<sub>50</sub> > 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-PLA<sub>2</sub> inhibitors was generated with low lipophilicity and a promising
pharmacokinetic profile
Exploitation of a Novel Binding Pocket in Human Lipoprotein-Associated Phospholipase A2 (Lp-PLA<sub>2</sub>) Discovered through Xâray Fragment Screening
Elevated levels of
human lipoprotein-associated phospholipase A2
(Lp-PLA<sub>2</sub>) are associated with cardiovascular disease and
dementia. A fragment screen was conducted against Lp-PLA<sub>2</sub> 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 Ă
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-PLA<sub>2</sub>) Discovered through Xâray Fragment Screening
Elevated levels of
human lipoprotein-associated phospholipase A2
(Lp-PLA<sub>2</sub>) are associated with cardiovascular disease and
dementia. A fragment screen was conducted against Lp-PLA<sub>2</sub> 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 Ă
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