On Poincare and logarithmic Sobolev inequalities for a class of singular Gibbs measures

This note, mostly expository, is devoted to Poincar{\'e} and log-Sobolev inequalities for a class of Boltzmann-Gibbs measures with singular interaction. Such measures allow to model one-dimensional particles with confinement and singular pair interaction. The functional inequalities come from convexity. We prove and characterize optimality in the case of quadratic confinement via a factorization of the measure. This optimality phenomenon holds for all beta Hermite ensembles including the Gaussian unitary ensemble, a famous exactly solvable model of random matrix theory. We further explore exact solvability by reviewing the relation to Dyson-Ornstein-Uhlenbeck diffusion dynamics admitting the Hermite-Lassalle orthogonal polynomials as a complete set of eigenfunctions. We also discuss the consequence of the log-Sobolev inequality in terms of concentration of measure for Lipschitz functions such as maxima and linear statistics.Comment: Minor improvements. To appear in Geometric Aspects of Functional Analysis -- Israel Seminar (GAFA) 2017-2019", Lecture Notes in Mathematics 225

The N-terminal intrinsically disordered domain of mgm101p is localized to the mitochondrial nucleoid.

The mitochondrial genome maintenance gene, MGM101, is essential for yeasts that depend on mitochondrial DNA replication. Previously, in Saccharomyces cerevisiae, it has been found that the carboxy-terminal two-thirds of Mgm101p has a functional core. Furthermore, there is a high level of amino acid sequence conservation in this region from widely diverse species. By contrast, the amino-terminal region, that is also essential for function, does not have recognizable conservation. Using a bioinformatic approach we find that the functional core from yeast and a corresponding region of Mgm101p from the coral Acropora millepora have an ordered structure, while the N-terminal domains of sequences from yeast and coral are predicted to be disordered. To examine whether ordered and disordered domains of Mgm101p have specific or general functions we made chimeric proteins from yeast and coral by swapping the two regions. We find, by an in vivo assay in S.cerevisiae, that the ordered domain of A.millepora can functionally replace the yeast core region but the disordered domain of the coral protein cannot substitute for its yeast counterpart. Mgm101p is found in the mitochondrial nucleoid along with enzymes and proteins involved in mtDNA replication. By attaching green fluorescent protein to the N-terminal disordered domain of yeast Mgm101p we find that GFP is still directed to the mitochondrial nucleoid where full-length Mgm101p-GFP is targeted

High dimensional and high resolution pulse sequences for backbone resonance assignment of intrinsically disordered proteins

Four novel 5D (HACA(N)CONH, HNCOCACB, (HACA)CON(CA)CONH, (H)NCO(NCA)CONH), and one 6D ((H)NCO(N)CACONH) NMR pulse sequences are proposed. The new experiments employ non-uniform sampling that enables achieving high resolution in indirectly detected dimensions. The experiments facilitate resonance assignment of intrinsically disordered proteins. The novel pulse sequences were successfully tested using δ subunit (20 kDa) of Bacillus subtilis RNA polymerase that has an 81-amino acid disordered part containing various repetitive sequences

Liberal intervention in the foreign policy thinking of Tony Blair and David Cameron

David Cameron was a critic of Tony Blair’s doctrine of the international community, which was used to justify war in Kosovo and more controversially in Iraq, suggesting caution in projecting military force abroad while in opposition. However, and in spite of making severe cuts to the defence budget, the Cameron-led Coalition government signed Britain up to a military intervention in Libya within a year of coming into office. What does this say about the place liberal interventionism occupies in contemporary British foreign policy? To answer this question, this article studies the nature of what we describe as the ‘bounded liberal’ tradition that has informed British foreign policy thinking since 1945, suggesting that it puts a distinctly UK national twist on conventional conservative thought about international affairs. Its components are: scepticism of grand schemes to remake the world; instinctive Atlanticism; security through collective endeavour; and anti-appeasement. We then compare and contrast the conditions for intervention set out by Tony Blair and David Cameron. We explain the similarities but crucially also the vital differences between the two leaders’ thinking on intervention, with particular reference to Cameron’s perception that Downing Street needed to loosen its control over foreign policy-making after Iraq. Our argument is that policy substance, policy style and party political dilemmas prompted Blair and Cameron to reconnect British foreign policy with its ethical roots, ingraining a bounded liberal posture to British foreign policy after the moral bankruptcy of the John Major years. This return to a patient, pragmatic and ethically informed foreign policy meant that military operations in Kosovo and Libya were undertaken in quite different circumstances, yet came to be justified by similar arguments from the two leaders

Disorder Predictors Also Predict Backbone Dynamics for a Family of Disordered Proteins

Several algorithms have been developed that use amino acid sequences to predict whether or not a protein or a region of a protein is disordered. These algorithms make accurate predictions for disordered regions that are 30 amino acids or longer, but it is unclear whether the predictions can be directly related to the backbone dynamics of individual amino acid residues. The nuclear Overhauser effect between the amide nitrogen and hydrogen (NHNOE) provides an unambiguous measure of backbone dynamics at single residue resolution and is an excellent tool for characterizing the dynamic behavior of disordered proteins. In this report, we show that the NHNOE values for several members of a family of disordered proteins are highly correlated with the output from three popular algorithms used to predict disordered regions from amino acid sequence. This is the first test between an experimental measure of residue specific backbone dynamics and disorder predictions. The results suggest that some disorder predictors can accurately estimate the backbone dynamics of individual amino acids in a long disordered region

Influence of Sequence Changes and Environment on Intrinsically Disordered Proteins

Many large-scale studies on intrinsically disordered proteins are implicitly based on the structural models deposited in the Protein Data Bank. Yet, the static nature of deposited models supplies little insight into variation of protein structure and function under diverse cellular and environmental conditions. While the computational predictability of disordered regions provides practical evidence that disorder is an intrinsic property of proteins, the robustness of disordered regions to changes in sequence or environmental conditions has not been systematically studied. We analyzed intrinsically disordered regions in the same or similar proteins crystallized independently and studied their sensitivity to changes in protein sequence and parameters of crystallographic experiments. The observed changes in the existence, position, and length of disordered regions indicate that their appearance in X-ray structures dramatically depends on changes in amino acid sequence and peculiarities of the crystallographic experiment. Our study also raises general questions regarding protein evolution and the regulation of protein structure, dynamics, and function via variations in cellular and environmental conditions

Modeling Disordered Regions in Proteins Using Rosetta

Protein structure prediction methods such as Rosetta search for the lowest energy conformation of the polypeptide chain. However, the experimentally observed native state is at a minimum of the free energy, rather than the energy. The neglect of the missing configurational entropy contribution to the free energy can be partially justified by the assumption that the entropies of alternative folded states, while very much less than unfolded states, are not too different from one another, and hence can be to a first approximation neglected when searching for the lowest free energy state. The shortcomings of current structure prediction methods may be due in part to the breakdown of this assumption. Particularly problematic are proteins with significant disordered regions which do not populate single low energy conformations even in the native state. We describe two approaches within the Rosetta structure modeling methodology for treating such regions. The first does not require advance knowledge of the regions likely to be disordered; instead these are identified by minimizing a simple free energy function used previously to model protein folding landscapes and transition states. In this model, residues can be either completely ordered or completely disordered; they are considered disordered if the gain in entropy outweighs the loss of favorable energetic interactions with the rest of the protein chain. The second approach requires identification in advance of the disordered regions either from sequence alone using for example the DISOPRED server or from experimental data such as NMR chemical shifts. During Rosetta structure prediction calculations the disordered regions make only unfavorable repulsive contributions to the total energy. We find that the second approach has greater practical utility and illustrate this with examples from de novo structure prediction, NMR structure calculation, and comparative modeling