TY - CONF
AB - A constrained pseudorandom function (CPRF) F: K×X → Y for a family T of subsets of χ is a function where for any key k ∈ K and set S ∈ T one can efficiently compute a short constrained key kS, which allows to evaluate F(k, ·) on all inputs x ∈ S, while the outputs on all inputs x /∈ S look random even given kS. Abusalah et al. recently constructed the first constrained PRF for inputs of arbitrary length whose sets S are decided by Turing machines. They use their CPRF to build broadcast encryption and the first ID-based non-interactive key exchange for an unbounded number of users. Their constrained keys are obfuscated circuits and are therefore large. In this work we drastically reduce the key size and define a constrained key for a Turing machine M as a short signature on M. For this, we introduce a new signature primitive with constrained signing keys that let one only sign certain messages, while forging a signature on others is hard even when knowing the coins for key generation.
AU - Abusalah, Hamza M
AU - Fuchsbauer, Georg
ID - 1235
TI - Constrained PRFs for unbounded inputs with short keys
VL - 9696
ER -
TY - JOUR
AB - During spore formation in Bacillus subtilis a transenvelope complex is assembled across the double membrane that separates the mother cell and forespore. This complex (called the “A–Q complex”) is required to maintain forespore development and is composed of proteins with remote homology to components of type II, III, and IV secretion systems found in Gram-negative bacteria. Here, we show that one of these proteins, SpoIIIAG, which has remote homology to ring-forming proteins found in type III secretion systems, assembles into an oligomeric ring in the periplasmic-like space between the two membranes. Three-dimensional reconstruction of images generated by cryo-electron microscopy indicates that the SpoIIIAG ring has a cup-and-saucer architecture with a 6-nm central pore. Structural modeling of SpoIIIAG generated a 24-member ring with dimensions similar to those of the EM-derived saucer. Point mutations in the predicted oligomeric interface disrupted ring formation in vitro and impaired forespore gene expression and efficient spore formation in vivo. Taken together, our data provide strong support for the model in which the A–Q transenvelope complex contains a conduit that connects the mother cell and forespore. We propose that a set of stacked rings spans the intermembrane space, as has been found for type III secretion systems.
AU - Rodrigues, Christopher D. A.
AU - Henry, Xavier
AU - Neumann, Emmanuelle
AU - Kurauskas, Vilius
AU - Bellard, Laure
AU - Fichou, Yann
AU - Schanda, Paul
AU - Schoehn, Guy
AU - Rudner, David Z.
AU - Morlot, Cecile
ID - 8452
IS - 41
JF - Proceedings of the National Academy of Sciences
SN - 0027-8424
TI - A ring-shaped conduit connects the mother cell and forespore during sporulation in Bacillus subtilis
VL - 113
ER -
TY - JOUR
AB - Transverse relaxation rate measurements in magic-angle spinning solid-state nuclear magnetic resonance provide information about molecular motions occurring on nanosecond-to-millisecond (ns–ms) time scales. The measurement of heteronuclear (13C, 15N) relaxation rate constants in the presence of a spin-lock radiofrequency field (R1ρ relaxation) provides access to such motions, and an increasing number of studies involving R1ρ relaxation in proteins have been reported. However, two factors that influence the observed relaxation rate constants have so far been neglected, namely, (1) the role of CSA/dipolar cross-correlated relaxation (CCR) and (2) the impact of fast proton spin flips (i.e., proton spin diffusion and relaxation). We show that CSA/D CCR in R1ρ experiments is measurable and that the CCR rate constant depends on ns–ms motions; it can thus provide insight into dynamics. We find that proton spin diffusion attenuates this CCR due to its decoupling effect on the doublet components. For measurements of dynamics, the use of R1ρ rate constants has practical advantages over the use of CCR rates, and this article reveals factors that have so far been disregarded and which are important for accurate measurements and interpretation.
AU - Kurauskas, Vilius
AU - Weber, Emmanuelle
AU - Hessel, Audrey
AU - Ayala, Isabel
AU - Marion, Dominique
AU - Schanda, Paul
ID - 8453
IS - 34
JF - The Journal of Physical Chemistry B
KW - Physical and Theoretical Chemistry
KW - Materials Chemistry
KW - Surfaces
KW - Coatings and Films
SN - 1520-6106
TI - Cross-correlated relaxation of dipolar coupling and chemical-shift anisotropy in magic-angle spinning R1ρ NMR measurements: Application to protein backbone dynamics measurements
VL - 120
ER -
TY - JOUR
AB - Magic-angle spinning solid-state NMR spectroscopy is an important technique to study molecular structure, dynamics and interactions, and is rapidly gaining importance in biomolecular sciences. Here we provide an overview of experimental approaches to study molecular dynamics by MAS solid-state NMR, with an emphasis on the underlying theoretical concepts and differences of MAS solid-state NMR compared to solution-state NMR. The theoretical foundations of nuclear spin relaxation are revisited, focusing on the particularities of spin relaxation in solid samples under magic-angle spinning. We discuss the range of validity of Redfield theory, as well as the inherent multi-exponential behavior of relaxation in solids. Experimental challenges for measuring relaxation parameters in MAS solid-state NMR and a few recently proposed relaxation approaches are discussed, which provide information about time scales and amplitudes of motions ranging from picoseconds to milliseconds. We also discuss the theoretical basis and experimental measurements of anisotropic interactions (chemical-shift anisotropies, dipolar and quadrupolar couplings), which give direct information about the amplitude of motions. The potential of combining relaxation data with such measurements of dynamically-averaged anisotropic interactions is discussed. Although the focus of this review is on the theoretical foundations of dynamics studies rather than their application, we close by discussing a small number of recent dynamics studies, where the dynamic properties of proteins in crystals are compared to those in solution.
AU - Schanda, Paul
AU - Ernst, Matthias
ID - 8454
IS - 8
JF - Progress in Nuclear Magnetic Resonance Spectroscopy
SN - 0079-6565
TI - Studying dynamics by magic-angle spinning solid-state NMR spectroscopy: Principles and applications to biomolecules
VL - 96
ER -
TY - JOUR
AB - Solid-state NMR spectroscopy allows the characterization of the structure, interactions and dynamics of insoluble and/or very large proteins. Sensitivity and resolution are often major challenges for obtaining atomic-resolution information, in particular for very large protein complexes. Here we show that the use of deuterated, specifically CH3-labelled proteins result in significant sensitivity gains compared to previously employed CHD2 labelling, while line widths increase only marginally. We apply this labelling strategy to a 468 kDa-large dodecameric aminopeptidase, TET2, and the 1.6 MDa-large 50S ribosome subunit of Thermus thermophilus.
AU - Kurauskas, Vilius
AU - Crublet, Elodie
AU - Macek, Pavel
AU - Kerfah, Rime
AU - Gauto, Diego F.
AU - Boisbouvier, Jérôme
AU - Schanda, Paul
ID - 8455
IS - 61
JF - Chemical Communications
KW - Materials Chemistry
KW - Electronic
KW - Optical and Magnetic Materials
KW - General Chemistry
KW - Surfaces
KW - Coatings and Films
KW - Metals and Alloys
KW - Ceramics and Composites
KW - Catalysis
SN - 1359-7345
TI - Sensitive proton-detected solid-state NMR spectroscopy of large proteins with selective CH3labelling: Application to the 50S ribosome subunit
VL - 52
ER -
TY - JOUR
AB - Understanding the principles that led to the current complexity of the genetic code is a central question in evolution. Expansion of the genetic code required the selection of new transfer RNAs (tRNAs) with specific recognition signals that allowed them to be matured, modified, aminoacylated, and processed by the ribosome without compromising the fidelity or efficiency of protein synthesis. We show that saturation of recognition signals blocks the emergence of new tRNA identities and that the rate of nucleotide substitutions in tRNAs is higher in species with fewer tRNA genes. We propose that the growth of the genetic code stalled because a limit was reached in the number of identity elements that can be effectively used in the tRNA structure.
AU - Saint-Léger, Adélaïde
AU - Bello, Carla
AU - Dans, Pablo D
AU - Torres, Adrian G
AU - Novoa, Eva M
AU - Camacho, Noelia
AU - Orozco, Modesto
AU - Fyodor Kondrashov
AU - Ribas De Pouplana, Lluís
ID - 849
IS - 4
JF - Science advances
TI - Saturation of recognition elements blocks evolution of new tRNA identities
VL - 2
ER -
TY - JOUR
AB - In this paper we study a so-called separatrix map introduced by Zaslavskii–Filonenko (Sov Phys JETP 27:851–857, 1968) and studied by Treschev (Physica D 116(1–2):21–43, 1998; J Nonlinear Sci 12(1):27–58, 2002), Piftankin (Nonlinearity (19):2617–2644, 2006) Piftankin and Treshchëv (Uspekhi Mat Nauk 62(2(374)):3–108, 2007). We derive a second order expansion of this map for trigonometric perturbations. In Castejon et al. (Random iteration of maps of a cylinder and diffusive behavior. Preprint available at arXiv:1501.03319, 2015), Guardia and Kaloshin (Stochastic diffusive behavior through big gaps in a priori unstable systems (in preparation), 2015), and Kaloshin et al. (Normally Hyperbolic Invariant Laminations and diffusive behavior for the generalized Arnold example away from resonances. Preprint available at http://www.terpconnect.umd.edu/vkaloshi/, 2015), applying the results of the present paper, we describe a class of nearly integrable deterministic systems with stochastic diffusive behavior.
AU - Guardia, M.
AU - Kaloshin, Vadim
AU - Zhang, J.
ID - 8493
JF - Communications in Mathematical Physics
SN - 0010-3616
TI - A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems
VL - 348
ER -
TY - JOUR
AB - We prove a form of Arnold diffusion in the a-priori stable case. Let
H0(p)+ϵH1(θ,p,t),θ∈Tn,p∈Bn,t∈T=R/T,
be a nearly integrable system of arbitrary degrees of freedom n⩾2 with a strictly convex H0. We show that for a “generic” ϵH1, there exists an orbit (θ,p) satisfying
∥p(t)−p(0)∥>l(H1)>0,
where l(H1) is independent of ϵ. The diffusion orbit travels along a codimension-1 resonance, and the only obstruction to our construction is a finite set of additional resonances.
For the proof we use a combination of geometric and variational methods, and manage to adapt tools which have recently been developed in the a-priori unstable case.
AU - Bernard, Patrick
AU - Kaloshin, Vadim
AU - Zhang, Ke
ID - 8494
IS - 1
JF - Acta Mathematica
SN - 0001-5962
TI - Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders
VL - 217
ER -
TY - JOUR
AU - Avila, Artur
AU - De Simoi, Jacopo
AU - Kaloshin, Vadim
ID - 8496
IS - 2
JF - Annals of Mathematics
SN - 0003-486X
TI - An integrable deformation of an ellipse of small eccentricity is an ellipse
VL - 184
ER -
TY - JOUR
AB - We study the dynamics of the restricted planar three-body problem near mean motion resonances, i.e. a resonance involving the Keplerian periods of the two lighter bodies revolving around the most massive one. This problem is often used to model Sun–Jupiter–asteroid systems. For the primaries (Sun and Jupiter), we pick a realistic mass ratio μ=10−3 and a small eccentricity e0>0. The main result is a construction of a variety of non local diffusing orbits which show a drastic change of the osculating (instant) eccentricity of the asteroid, while the osculating semi major axis is kept almost constant. The proof relies on the careful analysis of the circular problem, which has a hyperbolic structure, but for which diffusion is prevented by KAM tori. In the proof we verify certain non-degeneracy conditions numerically.
Based on the work of Treschev, it is natural to conjecture that the time of diffusion for this problem is ∼−ln(μe0)μ3/2e0. We expect our instability mechanism to apply to realistic values of e0 and we give heuristic arguments in its favor. If so, the applicability of Nekhoroshev theory to the three-body problem as well as the long time stability become questionable.
It is well known that, in the Asteroid Belt, located between the orbits of Mars and Jupiter, the distribution of asteroids has the so-called Kirkwood gaps exactly at mean motion resonances of low order. Our mechanism gives a possible explanation of their existence. To relate the existence of Kirkwood gaps with Arnol'd diffusion, we also state a conjecture on its existence for a typical ϵ-perturbation of the product of the pendulum and the rotator. Namely, we predict that a positive conditional measure of initial conditions concentrated in the main resonance exhibits Arnol’d diffusion on time scales −lnϵϵ2.
AU - Féjoz, Jacques
AU - Guàrdia, Marcel
AU - Kaloshin, Vadim
AU - Roldán, Pablo
ID - 8497
IS - 10
JF - Journal of the European Mathematical Society
SN - 1435-9855
TI - Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem
VL - 18
ER -