6,535 research outputs found
Combining intracellular selection with protein-fragment complementation to derive AÂ interacting peptides
Aggregation of the β-amyloid (Aβ) peptide into toxic oligomers is considered the primary event in the pathogenesis of Alzheimer's disease. Previously generated peptides and mimetics designed to bind to amyloid fibrils have encountered problems in solubility, protease susceptibility and the population of small soluble toxic oligomers oligomers. We present a new method that opens the possibility of deriving new amyloid inhibitors. The intracellular protein-fragment complementation assay (PCA) approach uses a semi-rational design approach to generate peptides capable of binding to Aβ. Peptide libraries are based on Aβ regions responsible for instigating amyloidosis, with screening and selection occurring entirely inside Escherichia coli. Successfully selected peptides must therefore bind Aβ and recombine an essential enzyme while permitting bacterial cell survival. No assumptions are made regarding the mechanism of action for selected binders. Biophysical characterisation demonstrates that binding induces a noticeable reduction in amyloid. Therefore, this amyloid-PCA approach may offer a new pathway for the design of effective inhibitors against the formation of amyloid in general
The Grassmannian Origin Of Dual Superconformal Invariance
A dual formulation of the S Matrix for N=4 SYM has recently been presented,
where all leading singularities of n-particle N^{k-2}MHV amplitudes are given
as an integral over the Grassmannian G(k,n), with cyclic symmetry, parity and
superconformal invariance manifest. In this short note we show that the dual
superconformal invariance of this object is also manifest. The geometry
naturally suggests a partial integration and simple change of variable to an
integral over G(k-2,n). This change of variable precisely corresponds to the
mapping between usual momentum variables and the "momentum twistors" introduced
by Hodges, and yields an elementary derivation of the momentum-twistor space
formula very recently presented by Mason and Skinner, which is manifestly dual
superconformal invariant. Thus the G(k,n) Grassmannian formulation allows a
direct understanding of all the important symmetries of N=4 SYM scattering
amplitudes.Comment: 9 page
New differential equations for on-shell loop integrals
We present a novel type of differential equations for on-shell loop
integrals. The equations are second-order and importantly, they reduce the loop
level by one, so that they can be solved iteratively in the loop order. We
present several infinite series of integrals satisfying such iterative
differential equations. The differential operators we use are best written
using momentum twistor space. The use of the latter was advocated in recent
papers discussing loop integrals in N=4 super Yang-Mills. One of our
motivations is to provide a tool for deriving analytical results for scattering
amplitudes in this theory. We show that the integrals needed for planar MHV
amplitudes up to two loops can be thought of as deriving from a single master
topology. The master integral satisfies our differential equations, and so do
most of the reduced integrals. A consequence of the differential equations is
that the integrals we discuss are not arbitrarily complicated transcendental
functions. For two specific two-loop integrals we give the full analytic
solution. The simplicity of the integrals appearing in the scattering
amplitudes in planar N=4 super Yang-Mills is strongly suggestive of a relation
to the conjectured underlying integrability of the theory. We expect these
differential equations to be relevant for all planar MHV and non-MHV
amplitudes. We also discuss possible extensions of our method to more general
classes of integrals.Comment: 39 pages, 8 figures; v2: typos corrected, definition of harmonic
polylogarithms adde
Unification of Residues and Grassmannian Dualities
The conjectured duality relating all-loop leading singularities of n-particle
N^(k-2)MHV scattering amplitudes in N=4 SYM to a simple contour integral over
the Grassmannian G(k,n) makes all the symmetries of the theory manifest. Every
residue is individually Yangian invariant, but does not have a local space-time
interpretation--only a special sum over residues gives physical amplitudes. In
this paper we show that the sum over residues giving tree amplitudes can be
unified into a single algebraic variety, which we explicitly construct for all
NMHV and N^2MHV amplitudes. Remarkably, this allows the contour integral to
have a "particle interpretation" in the Grassmannian, where higher-point
amplitudes can be constructed from lower-point ones by adding one particle at a
time, with soft limits manifest. We move on to show that the connected
prescription for tree amplitudes in Witten's twistor string theory also admits
a Grassmannian particle interpretation, where the integral over the
Grassmannian localizes over the Veronese map from G(2,n) to G(k,n). These
apparently very different theories are related by a natural deformation with a
parameter t that smoothly interpolates between them. For NMHV amplitudes, we
use a simple residue theorem to prove t-independence of the result, thus
establishing a novel kind of duality between these theories.Comment: 56 pages, 11 figures; v2: typos corrected, minor improvement
On All-loop Integrands of Scattering Amplitudes in Planar N=4 SYM
We study the relationship between the momentum twistor MHV vertex expansion
of planar amplitudes in N=4 super-Yang-Mills and the all-loop generalization of
the BCFW recursion relations. We demonstrate explicitly in several examples
that the MHV vertex expressions for tree-level amplitudes and loop integrands
satisfy the recursion relations. Furthermore, we introduce a rewriting of the
MHV expansion in terms of sums over non-crossing partitions and show that this
cyclically invariant formula satisfies the recursion relations for all numbers
of legs and all loop orders.Comment: 34 pages, 17 figures; v2: Minor improvements to exposition and
discussion, updated references, typos fixe
The Yangian origin of the Grassmannian integral
In this paper we analyse formulas which reproduce different contributions to
scattering amplitudes in N=4 super Yang-Mills theory through a Grassmannian
integral. Recently their Yangian invariance has been proved directly by using
the explicit expression of the Yangian level-one generators. The specific
cyclic structure of the form integrated over the Grassmannian enters in a
crucial way in demonstrating the symmetry. Here we show that the Yangian
symmetry fixes this structure uniquely.Comment: 26 pages. v2: typos corrected, published versio
The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM
We provide an analytic formula for the (rescaled) one-loop scalar hexagon
integral with all external legs massless, in terms of classical
polylogarithms. We show that this integral is closely connected to two
integrals appearing in one- and two-loop amplitudes in planar
super-Yang-Mills theory, and . The derivative of
with respect to one of the conformal invariants yields
, while another first-order differential operator applied to
yields . We also introduce some kinematic
variables that rationalize the arguments of the polylogarithms, making it easy
to verify the latter differential equation. We also give a further example of a
six-dimensional integral relevant for amplitudes in
super-Yang-Mills.Comment: 18 pages, 2 figure
Local Spacetime Physics from the Grassmannian
A duality has recently been conjectured between all leading singularities of
n-particle N^(k-2)MHV scattering amplitudes in N=4 SYM and the residues of a
contour integral with a natural measure over the Grassmannian G(k,n). In this
note we show that a simple contour deformation converts the sum of Grassmannian
residues associated with the BCFW expansion of NMHV tree amplitudes to the CSW
expansion of the same amplitude. We propose that for general k the same
deformation yields the (k-2) parameter Risager expansion. We establish this
equivalence for all MHV-bar amplitudes and show that the Risager degrees of
freedom are non-trivially determined by the GL(k-2) "gauge" degrees of freedom
in the Grassmannian. The Risager expansion is known to recursively construct
the CSW expansion for all tree amplitudes, and given that the CSW expansion
follows directly from the (super) Yang-Mills Lagrangian in light-cone gauge,
this contour deformation allows us to directly see the emergence of local
space-time physics from the Grassmannian.Comment: 22 pages, 13 figures; v2: minor updates, typos correcte
Truncated and Helix-Constrained Peptides with High Affinity and Specificity for the cFos Coiled-Coil of AP-1
Protein-based therapeutics feature large interacting surfaces. Protein folding endows structural stability to localised surface epitopes, imparting high affinity and target specificity upon interactions with binding partners. However, short synthetic peptides with sequences corresponding to such protein epitopes are unstructured in water and promiscuously bind to proteins with low affinity and specificity. Here we combine structural stability and target specificity of proteins, with low cost and rapid synthesis of small molecules, towards meeting the significant challenge of binding coiled coil proteins in transcriptional regulation. By iteratively truncating a Jun-based peptide from 37 to 22 residues, strategically incorporating i-->i+4 helix-inducing constraints, and positioning unnatural amino acids, we have produced short, water-stable, alpha-helical peptides that bind cFos. A three-dimensional NMR-derived structure for one peptide (24) confirmed a highly stable alpha-helix which was resistant to proteolytic degradation in serum. These short structured peptides are entropically pre-organized for binding with high affinity and specificity to cFos, a key component of the oncogenic transcriptional regulator Activator Protein-1 (AP-1). They competitively antagonized the cJun–cFos coiled-coil interaction. Truncating a Jun-based peptide from 37 to 22 residues decreased the binding enthalpy for cJun by ~9 kcal/mol, but this was compensated by increased conformational entropy (TDS ≤ 7.5 kcal/mol). This study demonstrates that rational design of short peptides constrained by alpha-helical cyclic pentapeptide modules is able to retain parental high helicity, as well as high affinity and specificity for cFos. These are important steps towards small antagonists of the cJun-cFos interaction that mediates gene transcription in cancer and inflammatory diseases
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