Single hole dynamics in the Kondo Necklace and Bilayer Heisenberg models on a square lattice

We study single hole dynamics in the bilayer Heisenberg and Kondo Necklace models. Those models exhibit a magnetic order-disorder quantum phase transition as a function of the interlayer coupling J_perp. At strong coupling in the disordered phase, both models have a single-hole dispersion relation with band maximum at p = (\pi,\pi) and an effective mass at this p-point which scales as the hopping matrix element t. In the Kondo Necklace model, we show that the effective mass at p = (\pi,\pi) remains finite for all considered values of J_perp such that the strong coupling features of the dispersion relation are apparent down to weak coupling. In contrast, in the bilayer Heisenberg model, the effective mass diverges at a finite value of J_perp. This divergence of the effective mass is unrelated to the magnetic quantum phase transition and at weak coupling the dispersion relation maps onto that of a single hole doped in a planar antiferromagnet with band maximum at p = (\pi/2,\pi/2). We equally study the behavior of the quasiparticle residue in the vicinity of the magnetic quantum phase transition both for a mobile and static hole. In contrast to analytical approaches, our numerical results do not unambiguously support the fact that the quasiparticle residue of the static hole vanishes in the vicinity of the critical point. The above results are obtained with a generalized version of the loop algorithm to include single hole dynamics on lattice sizes up to 20 X 20.Comment: 12 pages, 13 Fig

Asymmetric spin-1/2 two-leg ladders

We consider asymmetric spin-1/2 two-leg ladders with non-equal antiferromagnetic (AF) couplings J_|| and \kappa J_|| along legs (\kappa <= 1) and ferromagnetic rung coupling, J_\perp. This model is characterized by a gap \Delta in the spectrum of spin excitations. We show that in the large J_\perp limit this gap is equivalent to the Haldane gap for the AF spin-1 chain, irrespective of the asymmetry of the ladder. The behavior of the gap at small rung coupling falls in two different universality classes. The first class, which is best understood from the case of the conventional symmetric ladder at \kappa=1, admits a linear scaling for the spin gap \Delta ~ J_\perp. The second class appears for a strong asymmetry of the coupling along legs, \kappa J_|| << J_\perp << J_|| and is characterized by two energy scales: the exponentially small spin gap \Delta ~ J_\perp \exp(-J_|| / J_\perp), and the bandwidth of the low-lying excitations induced by a Suhl-Nakamura indirect exchange ~ J_\perp^2 /J_|| . We report numerical results obtained by exact diagonalization, density matrix renormalization group and quantum Monte Carlo simulations for the spin gap and various spin correlation functions. Our data indicate that the behavior of the string order parameter, characterizing the hidden AF order in Haldane phase, is different in the limiting cases of weak and strong asymmetry. On the basis of the numerical data, we propose a low-energy theory of effective spin-1 variables, pertaining to large blocks on a decimated lattice.Comment: 18 pages, 11 figure

Spin gap and string order parameter in the ferromagnetic Spiral Staircase Heisenberg Ladder: a quantum Monte Carlo study

We consider a spin-1/2 ladder with a ferromagnetic rung coupling J_\perp and inequivalent chains. This model is obtained by a twist (\theta) deformation of the ladder and interpolates between the isotropic ladder (\theta=0) and the SU(2) ferromagnetic Kondo necklace model (\theta=\pi). We show that the ground state in the (\theta,J_\perp) plane has a finite string order parameter characterising the Haldane phase. Twisting the chain introduces a new energy scale, which we interpret in terms of a Suhl-Nakamura interaction. As a consequence we observe a crossover in the scaling of the spin gap at weak coupling from \Delta/J_\| \propto J_\perp/J_\| for \theta < \theta_c \simeq 8\pi/9 to \Delta/J_\| \propto (J_\perp/J_\|)^2 for \theta > \theta_c. Those results are obtained on the basis of large scale Quantum Monte Carlo calculations.Comment: 4 page

QMCube (QM3): An all‐purpose suite for multiscale QM/MM calculations

QMCube (QM3) is a suite written in the Python programming language, initially focused on multiscale QM/MM simulations of biological systems, but open enough to address other kinds of problems. It allows the user to combine highly efficient QM and MM programs, providing unified access to a wide range of computational methods. The suite also supplies additional modules with extra functionalities. These modules facilitate common tasks such as performing the setup of the models or process the data generated during the simulations. The design of QM3 has been carried out considering the least number of external dependencies (only an algebra library, already included in the distribution), which makes it extremely portable. Also, the modular structure of the suite should help to expand and develop new computational methods

Equilibrium Sampling From Nonequilibrium Dynamics

We present some applications of an Interacting Particle System (IPS) methodology to the field of Molecular Dynamics. This IPS method allows several simulations of a switched random process to keep closer to equilibrium at each time, thanks to a selection mechanism based on the relative virtual work induced on the system. It is therefore an efficient improvement of usual non-equilibrium simulations, which can be used to compute canonical averages, free energy differences, and typical transitions paths

Structure of Tagatose-1,6-bisphosphate Aldolase. Insight into chiral discrimination, mechanism, and specificity of class II aldolases

Tagatose-1,6-bisphosphate aldolase (TBPA) is a tetrameric class II aldolase that catalyzes the reversible condensation of dihydroxyacetone phosphate with glyceraldehyde 3-phosphate to produce tagatose 1,6-bisphosphate. The high resolution (1.45 Å) crystal structure of the Escherichia coli enzyme, encoded by the agaY gene, complexed with phosphoglycolohydroxamate (PGH) has been determined. Two subunits comprise the asymmetric unit, and a crystallographic 2-fold axis generates the functional tetramer. A complex network of hydrogen bonds position side chains in the active site that is occupied by two cations. An unusual Na(+) binding site is created using a interaction with Tyr(183) in addition to five oxygen ligands. The catalytic Zn(2+) is five-coordinate using three histidine nitrogens and two PGH oxygens. Comparisons of TBPA with the related fructose-1,6-bisphosphate aldolase (FBPA) identifies common features with implications for the mechanism. Because the major product of the condensation catalyzed by the enzymes differs in the chirality at a single position, models of FBPA and TBPA with their cognate bisphosphate products provide insight into chiral discrimination by these aldolases. The TBPA active site is more open on one side than FBPA, and this contributes to a less specific enzyme. The availability of more space and a wider range of aldehyde partners used by TBPA together with the highly specific nature of FBPA suggest that TBPA might be a preferred enzyme to modify for use in biotransformation chemistry

Thermal conductivity of the Toda lattice with conservative noise

We study the thermal conductivity of the one dimensional Toda lattice perturbed by a stochastic dynamics preserving energy and momentum. The strength of the stochastic noise is controlled by a parameter $\gamma$. We show that heat transport is anomalous, and that the thermal conductivity diverges with the length $n$ of the chain according to $\kappa(n) \sim n^\alpha$, with $0 < \alpha \leq 1/2$. In particular, the ballistic heat conduction of the unperturbed Toda chain is destroyed. Besides, the exponent $\alpha$ of the divergence depends on $\gamma$

Gene variant effects across sodium channelopathies predict function and guide precision therapy

Pathogenic variants in the voltage-gated sodium channel gene family (SCNs) lead to early onset epilepsies, neurodevelopmental disorders, skeletal muscle channelopathies, peripheral neuropathies and cardiac arrhythmias. Disease-associated variants have diverse functional effects ranging from complete loss-of-function to marked gain-of-function. Therapeutic strategy is likely to depend on functional effect. Experimental studies offer important insights into channel function, but are resource intensive and only performed in a minority of cases. Given the evolutionarily conserved nature of the sodium channel genes we investigated whether similarities in biophysical properties between different voltage-gated sodium channels can predict function and inform precision treatment across sodium channelopathies. We performed a systematic literature search identifying functionally assessed variants in any of the nine voltage-gated sodium channel genes until 28 April 2021. We included missense variants that had been electrophysiologically characterised in mammalian cells in whole-cell patch-clamp recordings. We performed an alignment of linear protein sequences of all sodium channel genes and correlated variants by their overall functional effect on biophysical properties. Of 951 identified records, 437 sodium channel-variants met our inclusion criteria and were reviewed for functional properties. Of these, 141 variants were epilepsy-associated (SCN1/2/3/8A), 79 had a neuromuscular phenotype (SCN4/9/10/11A), 149 were associated with a cardiac phenotype (SCN5/10A) and 68 (16%) were considered benign. We detected 38 missense variant pairs with an identical disease-associated variant in a different sodium channel gene. 35 out of 38 of those pairs resulted in similar functional consequences indicating up to 92% biophysical agreement between corresponding sodium channel variants (odds ratio = 11.3; 95% CI = 2.8 to 66.9; P < 0.001). Pathogenic missense variants were clustered in specific functional domains, whereas population variants were significantly more frequent across non conserved domains (odds ratio = 18.6; 95% CI = 10.9 to 34.4; P < 0.001). Pore-loop regions were frequently associated with loss-of-function (LoF) variants, whereas inactivation sites were associated with gain-of-function (GoF; odds ratio = 42.1, 95% CI = 14.5 to 122.4; P < 0.001), whilst variants occurring in voltage-sensing regions comprised a range of gain- and loss-of-function effects. Our findings suggest that biophysical characterisation of variants in one SCN-gene can predict channel function across different SCN-genes where experimental data are not available. The collected data represent the first GoF versus LoF topological map of SCN proteins indicating shared patterns of biophysical effects aiding variant analysis and guiding precision therapy. We integrated our findings into a free online webtool to facilitate functional sodium channel gene variant interpretation (http://SCN-viewer.broadinstitute.org)

Protein folding using contact maps

We present the development of the idea to use dynamics in the space of contact maps as a computational approach to the protein folding problem. We first introduce two important technical ingredients, the reconstruction of a three dimensional conformation from a contact map and the Monte Carlo dynamics in contact map space. We then discuss two approximations to the free energy of the contact maps and a method to derive energy parameters based on perceptron learning. Finally we present results, first for predictions based on threading and then for energy minimization of crambin and of a set of 6 immunoglobulins. The main result is that we proved that the two simple approximations we studied for the free energy are not suitable for protein folding. Perspectives are discussed in the last section.Comment: 29 pages, 10 figure

An initial event in insect innate immune response: structural and biological studies of interactions between β-1,3-glucan and the N-terminal domain of β-1,3-glucan recognition protein

In response to invading microorganisms, insect β-1,3-glucan recognition protein (βGRP), a soluble receptor in the hemolymph, binds to the surfaces of bacteria and fungi and activates serine protease cascades that promote destruction of pathogens by means of melanization or expression of antimicrobial peptides. Here we report on the NMR solution structure of the N-terminal domain of βGRP (N-βGRP) from Indian meal moth (Plodia interpunctella), which is sufficient to activate the prophenoloxidase (proPO) pathway resulting in melanin formation. NMR and isothermal calorimetric titrations of N-βGRP with laminarihexaose, a glucose hexamer containing β-1,3 links, suggest a weak binding of the ligand. However, addition of laminarin, a glucose polysaccharide (~ 6 kDa) containing β-1,3 and β-1,6 links that activates the proPO pathway, to N-βGRP results in the loss of NMR cross-peaks from the backbone 15N-1H groups of the protein, suggesting the formation of a large complex. Analytical ultra centrifugation (AUC) studies of formation of N-βGRP:laminarin complex show that ligand-binding induces sel-fassociation of the protein:carbohydrate complex into a macro structure, likely containing six protein and three laminarin molecules (~ 102 kDa). The macro complex is quite stable, as it does not undergo dissociation upon dilution to sub-micromolar concentrations. The structural model thus derived from the present studies for N-βGRP:laminarin complex in solution differs from the one in which a single N-βGRP molecule has been proposed to bind to a triple helical form of laminarin on the basis of an X-ray crystallographic structure of N-βGRP:laminarihexaose complex [Kanagawa, M., Satoh, T., Ikeda, A., Adachi, Y., Ohno, N., and Yamaguchi, Y. (2011) J. Biol. Chem. 286, 29158-29165]. AUC studies and phenoloxidase activation measurements carried out with the designed mutants of N-βGRP indicate that electrostatic interactions involving Asp45, Arg54, and Asp68 between the ligand-bound protein molecules contribute in part to the stability of N-βGRP:laminarin macro complex and that a decreased stability is accompanied by a reduced activation of the proPO pathway. Increased β-1,6 branching in laminarin also results in destabilization of the macro complex. These novel findings suggest that ligand-induced self-association of βGRP:β-1,3-glucan complex may form a platform on a microbial surface for recruitment of downstream proteases, as a means of amplification of the initial signal of pathogen recognition for the activation of the proPO pathway