54 research outputs found
Quiver Bundles and Wall Crossing for Chains
Holomorphic chains on a Riemann surface arise naturally as fixed points of
the natural C*-action on the moduli space of Higgs bundles. In this paper we
associate a new quiver bundle to the Hom-complex of two chains, and prove that
stability of the chains implies stability of this new quiver bundle. Our
approach uses the Hitchin-Kobayashi correspondence for quiver bundles.
Moreover, we use our result to give a new proof of a key lemma on chains (due
to \'Alvarez-C\'onsul, Garc\'ia-Prada and Schmitt), which has been important in
the study of Higgs bundle moduli; this proof relies on stability and thus
avoids the direct use of the chain vortex equations
Using Pseudocontact Shifts and Residual Dipolar Couplings as Exact NMR Restraints for the Determination of Protein Structural Ensembles
Nuclear
magnetic resonance (NMR) spectroscopy provides detailed
information about the structure and dynamics of proteins by exploiting
the conformational dependence of the magnetic properties of certain
atomic nuclei. The mapping between NMR measurements and molecular
structures, however, often requires approximated descriptions based
on the fitting of a number of parameters, thus reducing the quality
of the information available from the experiments. To improve on this
limitation, we show here that it is possible to use pseudocontact
shifts and residual dipolar couplings as “exact” NMR
restraints. We implement this strategy by using a replica-averaging
method and illustrate its application by calculating an ensemble of
structures representing the dynamics of the two-domain protein calmodulin
Statistical Mechanics of the Denatured State of a Protein Using Replica-Averaged Metadynamics
The characterization of denatured
states of proteins is challenging
because the lack of permanent structure in these states makes it difficult
to apply to them standard methods of structural biology. In this work
we use all-atom replica-averaged metadynamics (RAM) simulations with
NMR chemical shift restraints to determine an ensemble of structures
representing an acid-denatured state of the 86-residue protein ACBP.
This approach has enabled us to reach convergence in the free energy
landscape calculations, obtaining an ensemble of structures in relatively
accurate agreement with independent experimental data used for validation.
By observing at atomistic resolution the transient formation of native
and non-native structures in this acid-denatured state of ACBP, we
rationalize the effects of single-point mutations on the folding rate,
stability, and transition-state structures of this protein, thus characterizing
the role of the unfolded state in determining the folding process
Analysis of the Contributions of Ring Current and Electric Field Effects to the Chemical Shifts of RNA Bases
Ring current and electric field effects can considerably
influence
NMR chemical shifts in biomolecules. Understanding such effects is
particularly important for the development of accurate mappings between
chemical shifts and the structures of nucleic acids. In this work,
we first analyzed the Pople and the Haigh–Mallion models in
terms of their ability to describe nitrogen base conjugated ring effects.
We then created a database (DiBaseRNA) of three-dimensional arrangements
of RNA base pairs from X-ray structures, calculated the corresponding
chemical shifts via a hybrid density functional theory approach and
used the results to parametrize the ring current and electric field
effects in RNA bases. Next, we studied the coupling of the electric
field and ring current effects for different inter-ring arrangements
found in RNA bases using linear model fitting, with joint electric
field and ring current, as well as only electric field and only ring
current approximations. Taken together, our results provide a characterization
of the interdependence of ring current and electric field geometric
factors, which is shown to be especially important for the chemical
shifts of non-hydrogen atoms in RNA bases
A Rational Design Strategy for the Selective Activity Enhancement of a Molecular Chaperone toward a Target Substrate
Molecular
chaperones facilitate the folding and assembly of proteins and inhibit their aberrant aggregation. They thus offer several opportunities
for biomedical and biotechnological applications, as for example
they can often prevent protein aggregation more effectively than other
therapeutic molecules, including small molecules and antibodies. Here
we present a method of designing molecular chaperones with enhanced
activity against specific amyloidogenic substrates while leaving
unaltered their functions toward other substrates. The method consists
of grafting onto a molecular
chaperone a peptide designed to bind specifically an epitope in
the target substrate. We illustrate this strategy by describing Hsp70
variants with increased affinities for α-synuclein and Aβ42
but otherwise unaltered affinities for other substrates. These designed
variants inhibit protein aggregation and disaggregate preformed fibrils
significantly more effectively than wild-type Hsp70 indicating that the strategy presented here provides a possible
route for tailoring rationally molecular chaperones for specific purposes
Determination of Conformational Equilibria in Proteins Using Residual Dipolar Couplings
In order to carry out their functions, proteins often undergo significant conformational fluctuations that enable them to interact with their partners. The accurate characterization of these motions is key in order to understand the mechanisms by which macromolecular recognition events take place. Nuclear magnetic resonance spectroscopy offers a variety of powerful methods to achieve this result. We discuss a method of using residual dipolar couplings as replica-averaged restraints in molecular dynamics simulations to determine large amplitude motions of proteins, including those involved in the conformational equilibria that are established through interconversions between different states. By applying this method to ribonuclease A, we show that it enables one to characterize the ample fluctuations in interdomain orientations expected to play an important functional role
Analysis of the evolution of the structure of the oligomers over 11 independent simulations.
<p>(A) Development of the fraction of polypeptide chains in a oligomer (black), fraction of polypeptide chains in a oligomer that form a <i>β</i>-sheet conformation (blue), fraction of hydrogen bonds in a oligomer in a <i>α</i>-helical conformation (orange), and in a <i>β</i>-sheet conformation (red), or otherwise (green). (B) Development of the distribution function of the average number of <i>β</i>-sheets 〈<i>N<sub>n</sub></i>〉 of size <i>n</i> at <i>t</i> = 1000 (black), <i>t</i> = 5000 (red), <i>t</i> = 30 000 (blue). (C) Distribution function 〈<i>N<sub>l</sub></i>〉 of the number of protofilaments composed of <i>l</i> layers at <i>t</i> = 1000 (black), <i>t</i> = 15 000 (red), <i>t</i> = 30 000 (blue).</p
Hydrogen bonds formed between two strands.
<p>The black lines represent hydrogen bonds; residues in green are in the <i>strand</i> state. Hydrogen bonds are allowed to form when neighbouring residues are in a <i>strand</i> state and the side chains are oriented in the same parallel direction.</p
Folding chacteristics and specificity.
<p>Folding characteristics are shown for a protein sequence that is designed to fold in a specific structure, and a random protein sequence; both sequences contain 35 residues and have a similar amino acid composition (see Methods). (a) Heat capacity versus temperature. A peak in the heat capacity curve can be observed at the folding transition. (b) Number of native contacts versus temperature. (c) Number of hydrogen bonds versus temperature. From the statistics it is clear that the sequence designed to fold shows a much sharper transitions than a random sequence of the same length. Moreover, the number of hydrogen bonds formed is strongly dependent on the sequence. Please refer to the Methods and Supplement for the sequences and structures used.</p
Fibrils with a cross-beta architecture.
<p>Top and side view of fibrils formed by a grand canonical simulation with a starting configuration of s small fibrillar structure. The peptides have an alternating hydrophobic (yellow) and hydrophilic (grey) sequence composition. The <i>strand</i> and <i>coil</i> states are indicated by green and grey respectively.</p
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