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_n</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_l</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

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

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

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