Surface potential determination in planar lipid bilayers: a simplification of the conductance-ratio method

One of the methods available for the measurement of surface potentials of planar lipid bilayers uses the conductance ratio between a charged and a neutral bilayer doped with ionophores to calculate the surface potential of the charged bilayer. We have devised a simplification of that method which does not require the use of an electrically neutral bilayer as control. The conductance of the charged bilayer is measured before and after the addition of divalent cations (Ba(2+)) to the bathing solution. Ba(2+) ions screen fixed surface charges, decreasing the surface potential. If the membrane is negatively charged the screening has the effect of decreasing the membrane conductance to cations. The resulting conductance ratio is used to calculate the surface potential change, which is fed into an iterative computer program. The program generates pairs of surface potential values and calculates the surface charge density for the two conditions. Since the surface charge density remains constant during this procedure, there is only one pair of surface potentials that satisfies the condition of constant charge density. Applying this method to experimental data from McLaughlin et al. [McLaughlin, S.G.A., Szabo, G. and Eisenman, G., Divalent ions and the surface potential of charged phospholipid membranes, J. Gen. Physiol., 58 (1971) 667-687.] we have found very similar results. We have also successfully used this method to determine the effect of palmitic acid on the surface potential of asolectin membranes.     

Role of incidence function in vaccine-induced backward bifurcation in some HIV models

The phenomenon of backward bifurcation in disease models, where a stable endemic equilibrium co-exists with a stable disease-free equilibrium when the associated reproduction number is less than unity, has important implications for disease control. In such a scenario, the classical requirement of the reproduction number being less than unity becomes only a necessary, but not sufficient, condition for disease elimination. This paper addresses the role of the choice of incidence function in a vaccine-induced backward bifurcation in HIV models. Several examples are given where backward bifurcations occur using standard incidence, but not with their equivalents that employ mass action incidence. Furthermore, this result is independent of the type of vaccination program adopted. These results emphasize the need for further work on the incidence functions used in HIV models.     

Effects of density-dependent migrations on stability of a two-patch predator-prey model

We consider a predator-prey model in a two-patch environment and assume that migration between patches is faster than prey growth, predator mortality and predator-prey interactions. Prey (resp. predator) migration rates are considered to be predator (resp. prey) density-dependent. Prey leave a patch at a migration rate proportional to the local predator density. Predators leave a patch at a migration rate inversely proportional to local prey population density. Taking advantage of the two different time scales, we use aggregation methods to obtain a reduced (aggregated) model governing the total prey and predator densities. First, we show that for a large class of density-dependent migration rules for predators and prey there exists a unique and stable equilibrium for migration. Second, a numerical bifurcation analysis is presented. We show that bifurcation diagrams obtained from the complete and aggregated models are consistent with each other for reasonable values of the ratio between the two time scales, fast for migration and slow for local demography. Our results show that, under some particular conditions, the density dependence of migrations can generate a limit cycle. Also a co-dim two Bautin bifurcation point is observed in some range of migration parameters and this implies that bistability of an equilibrium and limit cycle is possible.     

How predator functional responses and Allee effects in prey affect the paradox of enrichment and population collapses

In Rosenzweig-MacArthur models of predator-prey dynamics, Allee effects in prey usually destabilize interior equilibria and can suppress or enhance limit cycles typical of the paradox of enrichment. We re-evaluate these conclusions through a complete classification of a wide range of Allee effects in prey and predator's functional response shapes. We show that abrupt and deterministic system collapses not preceded by fluctuating predator-prey dynamics occur for sufficiently steep type III functional responses and strong Allee effects (with unstable lower equilibrium in prey dynamics). This phenomenon arises as type III functional responses greatly reduce cyclic dynamics and strong Allee effects promote deterministic collapses. These collapses occur with decreasing predator mortality and/or increasing susceptibility of the prey to fall below the threshold Allee density (e.g. due to increased carrying capacity or the Allee threshold itself). On the other hand, weak Allee effects (without unstable equilibrium in prey dynamics) enlarge the range of carrying capacities for which the cycles occur if predators exhibit decelerating functional responses. We discuss the results in the light of conservation strategies, eradication of alien species, and successful introduction of biocontrol agents.     

Solution structure of inhibitor-free human metalloelastase (MMP-12) indicates an internal conformational adjustment

Macrophage metalloelastase or matrix metalloproteinase-12 (MMP-12) appears to exacerbate atherosclerosis, emphysema, aortic aneurysm, rheumatoid arthritis, and inflammatory bowel disease. An inactivating E219A mutation, validated by crystallography and NMR spectra, prevents autolysis of MMP-12 and allows us to determine its NMR structure without an inhibitor. The structural ensemble of the catalytic domain without an inhibitor is based on 2813 nuclear Overhauser effects (NOEs) and has an average RMSD to the mean structure of 0.25 Å for the backbone and 0.61 Å for all heavy atoms for residues Trp109-Gly263. Compared to crystal structures of MMP-12, helix B (hB) at the active site is unexpectedly more deeply recessed under the β-sheet. This opens a pocket between hB and β-strand IV in the active-site cleft. Both hB and an internal cavity are shifted toward β-strand I, β-strand III, and helix A on the back side of the protease. About 25 internal NOE contacts distinguish the inhibitor-free solution structure and indicate hB's greater depth and proximity to the sheet and helix A. Line broadening and multiplicity of amide proton NMR peaks from hB are consistent with hB undergoing a slow conformational exchange among subtly different environments. Inhibitor-binding-induced perturbations of the NMR spectra of MMP-1 and MMP-3 map to similar locations across MMP-12 and encompass the internal conformational adjustments. Evolutionary trace analysis suggests a functionally important network of residues that encompasses most of the locations adjusting in conformation, including 18 residues with NOE contacts unique to inhibitor-free MMP-12. The conformational change, sequence analysis, and inhibitor perturbations of NMR spectra agree on the network they identify between structural scaffold and the active site of MMPs.     

Critical role of mac-1 sialyl lewis x moieties in regulating neutrophil degranulation and transmigration

Leukocyte cell surface sialyl Lewis x (sLe^x) and related epitopes play an important role in cell rolling and adhesion during diapedesis via interaction with E-selectin. Here, we present evidence that Mac-1 (CD11b/CD18, CR-3) is a major neutrophil glycoprotein decorated with sLe^x and ligation of these carbohydrate moieties by anti-sLe^x antibody significantly impairs neutrophil functions. First, Western blot analysis shows that both CD11b and CD18 subunit of purified Mac-1 are decorated with sLe^x moieties. A significant co-localization of CD11b and sLe^x moieties is observed at neutrophil secondary granules. With stimulation of formyl-Met-Leu-Phe (fMLP), neutrophil surface labeling with anti-sLe^x antibody follows an identical up-regulation pattern of Mac-1. Second, protein-binding assays indicate that sLe^x moieties on Mac-1 are critical for binding interaction of Mac-1 to E-selectin. Removal of sLe^x moieties completely abolishes Mac-1-E-selectin binding. Finally, ligation of Mac-1 sLe^x by anti-sLe^x antibody induces a significant degranulation of neutrophil secondary granules at the absence of chemoattractant stimulation. This “dysregulated” degranulation induced by anti-sLe^x antibody strongly inhibits neutrophil transmigration in response to fMLP. In summary, Mac-1 sLe^x moieties play a critical role in regulating β₂ integrin functions during neutrophil transmigration and degranulation.     

Evidence that human histidine triad nucleotide binding protein 3 (Hint3) is a distinct branch of the histidine triad (HIT) superfamily

Human Hint3 (hHint3) has been classified as a member of the histidine triad nucleotide (Hint) binding protein subfamily. While Hint1 is ubiquitously expressed by both eukaryotes and prokaryotes, Hint3 is found only in eukaryotes. Previously, our laboratory has characterized and compared the aminoacyl-adenylate and nucleoside phosphoramidate hydrolase activity of hHint1 and Escherichia coli hinT. In this study, hHint3-1(Ala36) and its single nucleotide polymorphism, hHint3-2 (A36G variant), were cloned, overexpressed, and purified. Steady-state kinetic studies with a synthetic fluorogenic indolepropinoic acyl-adenylate (AIPA) and with a series of fluorogenic tryptamine nucleoside phosphoramidates revealed that hHint3-1 and hHint3-2 are adenylate and phosphoramidate hydrolases with apparent second-order rate constants (kcat/Km) ranging from 10(2) to 10(6) s(-1) M(-1). Unlike hHint1, hHint3-1 and hHint3-2 prefer AIPA over tryptamine adenosine phosphoramidate by factors of 33- and 16-fold, respectively. In general, hHint3s hydrolyze phosphoramidate 370- to 2000-fold less efficiently than hHint1. Substitution of the potential active-site nucleophile, His145, by Ala was shown to abolish the adenylate and phosphoramidate hydrolase activity for hHint3-1. However, 0.2-0.4% residual activity was observed for the H145A mutant of hHint3-2. Both hHint3-1 and hHint3-2 were found to hydrolyze lysyl-adenylate generated by human lysyl-tRNA synthetase (hLysRS) by proceeding through an adenylated protein intermediate. hLysRS-dependent labeling of hHint3-1 and hHint3-2 was found to depend on His145, which aligns with the His112 of the Hint1 active site. The extent of active-site His145-AMP labeling was shown to be similar to His112-AMP labeling of hHint1. In contrast to all previously characterized members of the histidine triad superfamily, which have been shown to exist exclusively as homodimers, wild type and the H145A of hHint3-1 were found to exist across a range of multimeric states, from dimers to octamers and even larger oligomers, while wild type and the H145A of hHint3-2 exist predominantly in a monomeric state. The differences in oligomeric state may be important in vivo, because unlike tetracysteine-tagged Hint1, which was found along linear arrays exclusively in the cytoplasm in transfected HeLa cells, tagged Hint3-1 and Hint3-2 were found as aggregates both in the cytosol and in the nucleus. Taken together, these results imply that while Hint3 and Hint1 prefer aminoacyl-adenylates as substrates and catalytically interact with aminoacyl-tRNA synthetases, the significant differences in phosphoramidase activity, oligomeric state, and cellular localization suggest that Hint3s should be placed in a distinct branch of the histidine triad superfamily.     

Zigzagging: theoretical insights on climbing strategies

Human and animal trails on steep hillsides often exhibit dramatic switchbacks and shortcuts. Helbing et al. have recently examined the emergence of human trail systems on flat terrains while Minetti and Margaria established the effect of gradients on human metabolic efficiency. In this paper we use these ideas to develop a semi-quantitative theoretical model of the behaviour of humans moving on a terrain with relief. The model determines the direction of movement by minimising metabolic cost per unit of distance in a desired direction. The structure of the theory resembles the Landau Theory of Phase Transitions, much used in theoretical physics. We find that both hairpin bends (switchbacks) and shortcuts appear as efficient strategies for downhill walkers, while uphill walkers retain switchbacks. For weakly inclined slopes, the best strategy involves walking directly uphill or downhill. For sufficiently steep slopes, however, we find that the best strategy should undergo a transition to a broken symmetry solution corresponding to the switchback trail patterns typical of rugged environments. The critical slope at which this transition takes place should be less steep for uphill and downhill walkers. The theory should be amenable to empirical investigation. Amongst other applications, this model will enable us to generalize the work of previous authors to real landscapes, eventually permitting the reconstruction of ancient patterns of movement in archaeological landscapes.     

Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations

We investigate the emergence of spatio-temporal patterns in ecological systems. In particular, we study a generalized predator-prey system on a spatial domain. On this domain diffusion is considered as the principal process of motion. We derive the conditions for Hopf and Turing instabilities without specifying the predator-prey functional responses and discuss their biological implications. Furthermore, we identify the codimension-2 Turing-Hopf bifurcation and the codimension-3 Turing-Takens-Bogdanov bifurcation. These bifurcations give rise to complex pattern formation processes in their neighborhood. Our theoretical findings are illustrated with a specific model. In simulations a large variety of different types of long-term behavior, including homogenous distributions, stationary spatial patterns and complex spatio-temporal patterns, are observed.