Planar lattice gases with nearest-neighbour exclusion

We discuss the hard-hexagon and hard-square problems, as well as the corresponding problem on the honeycomb lattice. The case when the activity is unity is of interest to combinatorialists, being the problem of counting binary matrices with no two adjacent 1's. For this case we use the powerful corner transfer matrix method to numerically evaluate the partition function per site, density and some near-neighbour correlations to high accuracy. In particular for the square lattice we obtain the partition function per site to 43 decimal places.Comment: 16 pages, 2 built-in Latex figures, 4 table

Conformational exchange in the potassium channel blocker ShK

ShK is a 35-residue disulfide-linked polypeptide produced by the sea anemone Stichodactyla helianthus, which blocks the potassium channels Kv1.1 and Kv1.3 with pM affinity. An analogue of ShK has been developed that blocks Kv1.3 > 100 times more potently than Kv1.1, and has completed Phase 1b clinical trials for the treatment of autoimmune diseases such as psoriasis and rheumatoid arthritis. Previous studies have indicated that ShK undergoes a conformational exchange that is critical to its function, but this has proved difficult to characterise. Here, we have used high hydrostatic pressure as a tool to increase the population of the alternative state, which is likely to resemble the active form that binds to the Kv1.3 channel. By following changes in chemical shift with pressure, we have derived the chemical shift values of the low- and high-pressure states, and thus characterised the locations of structural changes. The main difference is in the conformation of the Cys17-Cys32 disulfide, which is likely to affect the positions of the critical Lys22-Tyr23 pair by twisting the 21–24 helix and increasing the solvent exposure of the Lys22 sidechain, as indicated by molecular dynamics simulations

Molecular Mechanism for the Hofmeister Effect Derived from NMR and DSC Measurements on Barnase

The effects of sodium thiocyanate, sodium chloride, and sodium sulfate on the ribonuclease barnase were studied using differential scanning calorimetry (DSC) and NMR. Both measurements reveal specific and saturable binding at low anion concentrations (up to 250 mM), which produces localized conformational and energetic effects that are unrelated to the Hofmeister series. The binding of sulfate slows intramolecular motions, as revealed by peak broadening in 13 C heteronuclear single quantum coherence spectroscopy. None of the anions shows significant binding to hydrophobic groups. Above 250 mM, the DSC results are consistent with the expected Hofmeister effects in that the chaotropic anion thiocyanate destabilizes barnase. In this higher concentration range, the anions have approximately linear effects on protein NMR chemical shifts, with no evidence for direct interaction of the anions with the protein surface. We conclude that the effects of the anions on barnase are mediated by solvent interactions. The results are not consistent with the predictions of the preferential interaction, preferential hydration, and excluded volume models commonly used to describe Hofmeister effects. Instead, they suggest that the Hofmeister anion effects on both stability and solubility of barnase are due to the way in which the protein interacts with water molecules, and in particular with water dipoles, which are more ordered around sulfate anions and less ordered around thiocyanate anions

1H, 13C, and 15N resonance assignments of a conserved putative cell wall binding domain from Enterococcus faecalis

Enterococcus faecalis is a major causative agent of hospital acquired infections. The ability of E. faecalis to evade the host immune system is essential during pathogenesis, which has been shown to be dependent on the complete separation of daughter cells by peptidoglycan hydrolases. AtlE is a peptidoglycan hydrolase which is predicted to bind to the cell wall of E. faecalis, via six C-terminal repeat sequences. Here, we report the near complete assignment of one of these six repeats, as well as the predicted backbone structure and dynamics. This data will provide a platform for future NMR studies to explore the ligand recognition motif of AtlE and help to uncover its potential role in E. faecalis virulence

Regional Conformational Flexibility Couples Substrate Specificity and Scissile Phosphate Diester Selectivity in Human Flap Endonuclease 1

Human flap endonuclease-1 (hFEN1) catalyzes the divalent metal ion-dependent removal of single-stranded DNA protrusions known as flaps during DNA replication and repair. Substrate selectivity involves passage of the 5′-terminus/flap through the arch and recognition of a single nucleotide 3′-flap by the α2–α3 loop. Using NMR spectroscopy, we show that the solution conformation of free and DNA-bound hFEN1 are consistent with crystal structures; however, parts of the arch region and α2–α3 loop are disordered without substrate. Disorder within the arch explains how 5′-flaps can pass under it. NMR and single-molecule FRET data show a shift in the conformational ensemble in the arch and loop region upon addition of DNA. Furthermore, the addition of divalent metal ions to the active site of the hFEN1–DNA substrate complex demonstrates that active site changes are propagated via DNA-mediated allostery to regions key to substrate differentiation. The hFEN1–DNA complex also shows evidence of millisecond timescale motions in the arch region that may be required for DNA to enter the active site. Thus, hFEN1 regional conformational flexibility spanning a range of dynamic timescales is crucial to reach the catalytically relevant ensemble

Molecular basis for bacterial peptidoglycan recognition by LysM domains.

Carbohydrate recognition is essential for growth, cell adhesion and signalling in all living organisms. A highly conserved carbohydrate binding module, LysM, is found in proteins from viruses, bacteria, fungi, plants and mammals. LysM modules recognize polysaccharides containing N-acetylglucosamine (GlcNAc) residues including peptidoglycan, an essential component of the bacterial cell wall. However, the molecular mechanism underpinning LysM-peptidoglycan interactions remains unclear. Here we describe the molecular basis for peptidoglycan recognition by a multimodular LysM domain from AtlA, an autolysin involved in cell division in the opportunistic bacterial pathogen Enterococcus faecalis. We explore the contribution of individual modules to the binding, identify the peptidoglycan motif recognized, determine the structures of free and bound modules and reveal the residues involved in binding. Our results suggest that peptide stems modulate LysM binding to peptidoglycan. Using these results, we reveal how the LysM module recognizes the GlcNAc-X-GlcNAc motif present in polysaccharides across kingdoms

Enzymatic production of β-glucose 1,6-bisphosphate through manipulation of catalytic magnesium coordination

Manipulation of enzyme behaviour represents a sustainable technology that can be harnessed to enhance the production of valuable metabolites and chemical precursors. β-Glucose 1,6-bisphosphate (βG16BP) is a native reaction intermediate in the catalytic cycle of β-phosphoglucomutase (βPGM) that has been proposed as a treatment for human congenital disorder of glycosylation involving phosphomannomutase 2. Strategies to date for the synthesis of βG16BP suffer from low yields or use chemicals and procedures with significant environmental impacts. Herein, we report the efficient enzymatic synthesis of anomer-specific βG16BP using the D170N variant of βPGM (βPGMD170N), where the aspartate to asparagine substitution at residue 170 perturbs the coordination of a catalytic magnesium ion. Through combined use of NMR spectroscopy and kinetic assays, it is shown that the weakened affinity and reactivity of βPGMD170N towards βG16BP contributes to the pronounced retardation of the second step in the two-step catalytic cycle, which causes a marked accumulation of βG16BP, especially at elevated MgCl2 concentrations. Purification, employing a simple environmentally considerate precipitation procedure requiring only a standard biochemical toolset, results in a βG16BP product with high purity and yield. Overall, this synthesis strategy illustrates how manipulation of the catalytic magnesium coordination of an enzyme can be utilised to generate large quantities of a valuable metabolite

Nonequivalence of second sphere "noncatalytic" residues in pentaerythritol tetranitrate reductase in relation to local dynamics linked to H-transfer in reactions with NADH and NADPH coenzymes

Many enzymes that catalyze hydride transfer reactions work via a mechanism dominated by quantum mechanical tunneling. The involvement of fast vibrational modes of the reactive complex is often inferred in these reactions, as in the case of the NAD(P)H-dependent pentaerythritol tetranitrate reductase (PETNR). Herein, we interrogated the H-transfer mechanism in PETNR by designing conservative (L25I and I107L) and side chain shortening (L25A and I107A) PETNR variants and using a combination of experimental approaches (stopped-flow rapid kinetics, X-ray crystallography, isotope/temperature dependence studies of H-transfer and NMR spectroscopy). X-ray data show subtle changes in the local environment of the targeted side chains but no major structural perturbation caused by mutagenesis of these two second sphere active site residues. However, temperature dependence studies of H-transfer revealed a coenzyme-specific and complex thermodynamic equilibrium between different reactive configurations in PETNR–coenzyme complexes. We find that mutagenesis of these second sphere “noncatalytic” residues affects differently the reactivity of PETNR with NADPH and NADH coenzymes. We attribute this to subtle, dynamic structural changes in the PETNR active site, the effects of which impact differently in the nonequivalent reactive geometries of PETNR−NADH and PETNR−NADPH complexes. This inference is confirmed through changes observed in the NMR chemical shift data for PETNR complexes with unreactive 1,4,5,6-tetrahydro-NAD(P) analogues. We show that H-transfer rates can (to some extent) be buffered through entropy–enthalpy compensation, but that use of integrated experimental tools reveals hidden complexities that implicate a role for dynamics in this relatively simple H-transfer reaction. Similar approaches are likely to be informative in other enzymes to understand the relative importance of (distal) hydrophobic side chains and dynamics in controlling the rates of enzymatic H-transfer

Sequential cavity method for computing free energy and surface pressure

We propose a new method for the problems of computing free energy and surface pressure for various statistical mechanics models on a lattice $\Z^d$. Our method is based on representing the free energy and surface pressure in terms of certain marginal probabilities in a suitably modified sublattice of $\Z^d$. Then recent deterministic algorithms for computing marginal probabilities are used to obtain numerical estimates of the quantities of interest. The method works under the assumption of Strong Spatial Mixing (SSP), which is a form of a correlation decay. We illustrate our method for the hard-core and monomer-dimer models, and improve several earlier estimates. For example we show that the exponent of the monomer-dimer coverings of $\Z^3$ belongs to the interval $[0.78595,0.78599]$, improving best previously known estimate of (approximately) $[0.7850,0.7862]$ obtained in \cite{FriedlandPeled},\cite{FriedlandKropLundowMarkstrom}. Moreover, we show that given a target additive error $\epsilon>0$, the computational effort of our method for these two models is $(1/\epsilon)^{O(1)}$ \emph{both} for free energy and surface pressure. In contrast, prior methods, such as transfer matrix method, require $\exp\big((1/\epsilon)^{O(1)}\big)$ computation effort.Comment: 33 pages, 4 figure

Spectral Duality Between Heisenberg Chain and Gaudin Model

In our recent paper we described relationships between integrable systems inspired by the AGT conjecture. On the gauge theory side an integrable spin chain naturally emerges while on the conformal field theory side one obtains some special reduced Gaudin model. Two types of integrable systems were shown to be related by the spectral duality. In this paper we extend the spectral duality to the case of higher spin chains. It is proved that the N-site GL(k) Heisenberg chain is dual to the special reduced k+2-points gl(N) Gaudin model. Moreover, we construct an explicit Poisson map between the models at the classical level by performing the Dirac reduction procedure and applying the AHH duality transformation.Comment: 36 page