Nearest-neighbour interactions in species-rich shrublands: the roles of abundance, spatial patterns and resources

We explored pairwise nearest‐neighbour interactions in four species‐rich shrubland plant communities, asking the question: how often is an individual of species j the nearest‐neighbour of species i? In the observed data and null models, less than 35% of the maximum possible number of nearest‐neighbour species pairs was present, and at three of the four sites the number of observed nearest‐neighbour pairs were significantly less than those occurring in simulated null communities. Many of the missing pairs included woody shrubs whose absence might be interpreted as evidence of site‐specific competition between larger growth forms for soil resources or space. Less than 5% of the pairs of species that occurred did so at frequencies different from that expected under random mixing, and many of these pairs were conspecific. Of the heterospecific pairs whose frequency differed significantly from random mixing there was a weak bias towards pairs occurring at higher rather than lower frequencies than expected. There was no evidence for asymmetry (interaction of species j with species i but not the reverse) in the frequency of species pairs. Nearest‐neighbour relationships are species‐specific rather than between plant functional types. The four sites form a soil nutrient and water availability gradient, and, according to the stress gradient hypothesis, positive species interactions should be most prevalent at the most stressful sites. However, we found the opposite: the site with the highest availability of resources had both proportionally the most heterospecific pairs, and the most conspecific and heterospecific species pairs with frequencies departing significantly from that expected under random mixing.     

Stacking energies in DNA

Variations in base mono- and dipoles result in variations in stacking energies for the 10 unique neighbor pairs in DNA. Stacking energies for pair M on N, expressed as TMN, were derived by matrix decomposition of a large set of linear algebraic expressions relating the measured Tm for subtransitions emanating from large polymeric DNAs, and the fractional neighbor frequencies, fMN, for the domains responsible for the transitions, Tm = sigma fMNTMN. Tm were determined for subtransitions that dissociate in approximately all-or-none fashion in high resolution melting profiles of partially deleted and recombinant forms of pBR322 DNA. Three different analytical maneuvers were undertaken to resolve subtransitions: site-specific cleavage of domains; deletion of domains; and addition of domains. Three dozen domains of widely divergent, quasi-random neighbor frequencies were identified and assigned, resulting in a unique set of values for TMN with standard deviation, sigma = +/- 0.23 degree C. The average difference between calculated and experimental Tm for domains is only +/- 0.17 degree C, indicating that the thermodynamic properties of these domains are not in any way unusual. Assuming delta S to be constant for all pairs, the corresponding delta HMN are found to have a precision of +/- 10 calories.mol-1 and an accuracy of +/- 606 calories.mol-1. TMN used to calculate melting curves by statistical mechanical analysis of sequences of the different plasmid specimens in this study were in quantitative agreement with observed curves for most sequences. These TMN differ significantly from those determined previously and also correlate poorly with values determined by quantum chemical analysis. Stabilities of neighbor pairs, expressed as the difference in free energy between that for a given pair (MN) and that for the average of like pairs (M, N), depend on the relationship of stacked purines and pyrimidines as follows. delta delta Gpu-py(-466 cal) greater than delta delta Gpu-pu(+52 cal) greater than delta delta Gpy-pu(+335 cal) Differences between experimental Tm and Tm calculated with TMN for the isolated neighbor pairs in the B-conformation are useful in the identification of altered structures and unusual modes of dissociation of helixes. A significantly higher Tm is observed for the highly biased repeated sequence synthetic helixes dA.dT, d(AGC).d(GCT), and d(GAT).d(ATC), reflecting auxiliary sources of stability such as bifurcated hydrogen bonds and/or altered structures for these helixes.     

Forest gap dynamics and the Ising model

The vegetation height in forest ecosystems is spatially heterogeneous. Canopy gaps (sites with low vegetation) are formed by treefalls, and they recover to canopy sites (with high vegetation) either by growth of small trees or by branch extension of surrounding trees. The dynamics of canopy gaps have been studied using a spatial Markov chain with nearest neighbor interaction. (1) If the canopy recovery rate is constant and if the gap formation rate for a site increases exponentially with the number of neighboring gap sites, the equilibrium distribution is the same as the one generated by the Ising model in statistical mechanics. Here, we extend the equivalence to the situation in which both the gap formation and canopy recovery depend on the neighborhood, as shown in recent forest data. (2) We develop a statistical test of whether a given spatial pattern is a random sample from the Ising model. The test is based on the conditional probability of configurations on a partial lattice. We apply the method to vegetation height data from the Ogawa forest reserve, Japan, measured on a 5x5 m grid in 1976, 1981, 1986, and 1991. The spatial pattern of the original forest data deviates significantly from the Ising model. We examine whether a larger sampling distance or the removal of the effects of the topography can reduce this deviation.     

Denaturation and renaturation of DNA. I. Equilibrium statistics of copolymeric DNA

The one-dimensional Ising model, with nearest neighbor correlation only, suitably modified, is used to explain the observed linear dependence of melting temperature of copolymeric DNA with GC content. Transition curves are plotted for regular, random, and Markoff distribution of base pairs for various values of a correlation parameter U between nearest neighbor bonds. Exact analytic formulas are given for fraction of bonds intact at a particular temperature for various regular distributions for all U and approximate ones for random and Markoff distributions for small U. A scheme is indicated for further improvement. The model, in principle, makes it possible to estimate the statistical distribution of base pairs from the detailed shape of the transition curve.     

Application of the one- and two-dimensional Ising models to studies of cooperativity between ion channels.

The Ising model of statistical physics provides a framework for studying systems of protomers in which nearest neighbors interact with each other. In this article, the Ising model is applied to the study of cooperative phenomena between ligand-gated ion channels. Expressions for the mean open channel probability, rho o, and the variance, sigma 2, are derived from the grand partition function. In the one-dimensional Ising model, interactions between neighboring open channels give rise to a sigmoidal rho o versus concentration curve and a nonquadratic relationship between sigma 2 and rho o. Positive cooperativity increases the slope at the midpoint of the rho o versus concentration curve, shifts the apparent binding affinity to lower concentrations, and increases the variance for a given rho o. Negative cooperativity has the opposite effects. Strong negative cooperativity results in a bimodal sigma 2 versus rho o curve. The slope of the rho o versus concentration curve increases linearly with the number of binding sites on a protomer, but the sigma 2 versus rho o relationship is independent of the number of ligand binding sites. Thus, the sigma 2 versus rho o curve provides unambiguous information about channel interactions. In the two-dimensional Ising model, rho o and sigma 2 are calculated numerically from a series expansion of the grand partition function appropriate for weak interactions. Virtually all of the features exhibited by the one-dimensional model are qualitatively present in the two-dimensional model. These models are also applicable to voltage-gated ion channels.     

The thermal stability of DNA fragments with tandem mismatches at a d(CXYG).d(CY'X'G) site.

Temperature-Gradient Gel Electrophoresis (TGGE) was employed to determine the thermal stabilities of 28 DNA fragments, 373 bp long, with two adjacent mismatched base pairs, and eight DNAs with Watson-Crick base pairs at the same positions. Heteroduplex DNAs containing two adjacent mismatches were formed by melting and reannealing pairs of homologous 373 bp DNA fragments differing by two adjacent base pairs. Product DNAs were separated based on their thermal stability by parallel and perpendicular TGGE. The polyacrylamide gel contained 3.36 M urea and 19.2 % formamide to lower the DNA melting temperatures. The order of stability was determined in the sequence context d(CXYG).d(CY'X'G) where X.X' and Y.Y" represent the mismatched or Watson-Crick base pairs. The identity of the mismatched bases and their stacking interactions influence DNA stability. Mobility transition melting temperatures (T u) of the DNAs with adjacent mismatches were 1.0-3.6 degrees C (+/-0.2 degree C) lower than the homoduplex DNA with the d(CCAG).d(CTGG) sequence. Two adjacent G.A pairs, d(CGAG).d(CGAG), created a more stable DNA than DNAs with Watson-Crick A.T pairs at the same sites. The d(GA).d(GA) sequence is estimated to be 0.4 (+/-30%) kcal/mol more stable in free energy than d(AA).d(TT) base pairs. This result confirms the unusual stability of the d(GA).d(GA) sequence previously observed in DNA oligomers. All other DNAs with adjacent mismatched base pairs were less stable than Watson-Crick homoduplex DNAs. Their relative stabilities followed an order expected from previous results on single mismatches. Two homoduplex DNAs with identical nearest neighbor sequences but different next-nearest neighbor sequences had a small but reproducible difference in T u value. This result indicates that sequence dependent next neighbor stacking interactions influence DNA stability.     

Competitive cooperative bindings of a small ligand to a linear homopolymer. I. Extension of the ising model to the case of two competitive interactions.

The theoretical study of the cooperative binding of a small ligand to a linear homopolymer is extended to systems in which two different complexes can form. The binding isotherms are derived under the assumption that the cooperative interactions exist only between molecules belonging to the same type of binding mode and are limited to nearest neighbors (Ising model). The binding to a single-stranded chain is first considered and two extreme cases are studied: (1) the two complexes can form independently from each other (model of independent classes of binding sites); (2) only one class of binding site exists, each possessing two different states of complexation (three-state model). Binding to a double-helical chain is also considered. Three simple types of competition between the different modes of binding are distinguished. The corresponding models are defined as: (1) the model of independent classes of binding sites; (2) the model of monoexclusive interactions between the different kinds of complexes (the symmetric and asymmetric cases are both considered); (3) the model of biexclusive interactions. The comparative study of the different cases shows that the binding isotherms are very similar at large polymer-to-ligand concentration ratios, while they can be very different at low polymer-to-ligand ratios. This can be used to obtain information on the mechanism of dye binding to nucleic acids by equilibrium studies as shown in a subsequent paper.     

Dynamics and metal exchange properties of C4C4 RING domains from CNOT4 and the p44 subunit of TFIIH

Zinc fingers are small structured protein domains that require the coordination of zinc for a stable tertiary fold. Together with FYVE and PHD, the RING domain forms a distinct class of zinc-binding domains, where two zinc ions are ligated in a cross-braced manner, with the first and third pairs of ligands coordinating one zinc ion, while the second and fourth pairs ligate the other zinc ion. To investigate the relationship between the stability and dynamic behaviour of the domains and the stability of the metal-binding site, we studied metal exchange for the C4C4 RING domains of CNOT4 and the p44 subunit of TFIIH. We found that Zn(2+)-Cd(2+) exchange is different between the two metal-binding sites in the C4C4 RING domains of the two proteins. In order to understand the origins of these distinct exchange rates, we studied the backbone dynamics of both domains in the presence of zinc and of cadmium by NMR spectroscopy. The differential stability of the two metal-binding sites in the RING domains, as reflected by the different metal exchange rates, can be explained by a combination of accessibility and an electrostatic ion interaction model. A greater backbone flexibility for the p44 RING domain as compared to CNOT4 may be related to the distinct types of protein-protein interactions in which the two C4C4 RING domains are involved.     

The Kinetics of Cooperative Cofilin Binding Reveals Two States of the Cofilin-Actin Filament

The interaction of cofilin with actin filaments displays positive cooperativity. The equilibrium binding and associated thermodynamic properties of this interaction are well described by a simple, one-dimensional Ising model with nearest neighbor interactions. Here we evaluate the kinetic contributions to cooperative binding and the ability of this model to account for binding across a wide range of cofilin concentrations. A Monte Carlo-based simulation protocol that allows for nearest-neighbor interactions between adjacent binding sites was used to globally fit time courses of human cofilin binding to human nonmuscle (β-, γ-) actin filaments. Several extensions of the one-dimensional Ising model were tested, and a mechanism that includes isomerization of the actin filament was found to best account for time courses of association as well as irreversible dissociation from a saturated filament. This model predicts two equilibrium states of the cofilin-actin, or cofilactin, filament, and the resulting set of binding parameters are in agreement with equilibrium thermodynamic parameters. We conclude that despite its simplicity, this one-dimensional Ising model is a reliable model for analyzing and interpreting the energetics and kinetics of cooperative cofilin-actin filament interactions. The model predicts that severing activity associated with boundaries between bare and decorated segments will not be linear, but display a transient burst at short times on cofilin activation then dissipate due to a kinetic competition between severing activity and cofilin binding. A second peak of severing activity is predicted to arise from irreversible cofilin dissociation on inactivation. These behaviors predict what we believe to be novel mechanisms of cofilin severing and spatial regulation of actin filament turnover in cells. The methods developed for this system are generally applicable to the kinetic analysis of cooperative ligand binding to linear polymers.     

Pathogen invasion and host extinction in lattice structured populations

We examined the propagation of an infectious disease and the eventual extinction of the host population in a lattice-structured population. Both the host colonization and pathogen transmission processes are assumed to be restricted to act between the nearest neighbor sites. The model is analyzed by an improved version of pair approximation (IPA). Pair approximation is a technique to trace the dynamics of the number of nearest neighbor pairs having particular states, and IPA takes account of the clustering property of lattice models more precisely. The results are checked by computer simulations. The analysis shows: (i) in a one-dimensional lattice population, a pathogen cannot invade a host population no matter how large is the transmission rate; (ii) in a two-dimensional lattice population, pathogens will drive the host to extinction if the transmission rate is larger than a threshold. These results indicate that spatially structured population models may give qualitatively different results from conventional population models, such as Lotka-Volterra ones, without spatial structure.     

Nearest neighbor parameters for inosine x uridine pairs in RNA duplexes

An enzyme family known as adenosine deaminases that act on RNA (ADARs) catalyzes adenosine deamination in RNA. ADARs act on RNA that is largely double-stranded and convert adenosine to inosine, resulting, in many cases, in an I x U pair. Thermodynamic parameters derived from optical melting studies are reported for a series of 14 oligoribonucleotides containing single I x U pairs adjacent to Watson-Crick pairs. In order to determine unique linearly independent nearest neighbor parameters for I x U pairs, four duplexes containing 3'-terminal I x U pairs and four duplexes containing 5'-terminal I x U pairs have also been thermodynamically characterized. This data was combined with previously published data of seven duplexes containing internal, terminal, or tandem I x U pairs from Strobel et al. [Strobel, S. A., Cech, T. R., Usman, N., and Beigelman, L. (1994) Biochemistry 33, 13824-13838] and Serra et al. [Serra, M. J., Smolter, P. E., and Westhof, E. (2004) Nucleic Acids Res. 32, 1824-1828]. On average, a duplex with an internal I x U pair is 2.3 kcal/mol less stable than the same duplex with an A-U pair, however, a duplex with a terminal I x U pair is 0.8 kcal/mol more stable than the same duplex with an A-U pair. Although isosteric with a G-U pair, on average, a duplex with an internal I x U pair is 1.9 kcal/mol less stable than the same duplex with a G-U pair, however, a duplex with a terminal I x U pair is 0.9 kcal/mol more stable than the same duplex with a G-U pair. Duplexes with tandem I x U pairs are on average 5.9 and 3.8 kcal/mol less stable than the same duplex with tandem A-U or tandem G-U pairs, respectively. Using the combined thermodynamic data and a complete linear least-squares fitting routine, nearest neighbor parameters for all nearest neighbor combinations of I x U pairs and an additional parameter for terminal I x U pairs have been derived.     

Spatial arrangement and diet overlap between colonies of desert ants

Summary The spatial patterns and diets of three desert ant species were examined. The results indicate that food competition may account for the spatial arrangement of these species, and that only intraspecific interactions may be required. Each ant species was significantly overdispersed, and the average intraspecific nearest neighbor distances were greater than the interspecific nearest neighbor distances. A test of pairwise spatial arrangment showed that all three species pairs were aggregated interspecifically. The level of the interspecific aggregation was related to the diet similarity of the species. The two species pairs with the lowest diet overlaps were significantly aggregated, and the species pair with the most similar diets was not significantly aggregated. Pairwise dietary overlaps between colonies showed that average intraspecific overlaps were significantly greater than interspecific diet overlaps. Furthermore, the diet overlap was significantly positively correlated to the mean nearest neighbor distance for the three intraspecific and three interspecific comparisons. These data indicate competition for food, especially within species, may be regulating the intercolony distances of these ant species. A computer simulation tested whether only intraspecific territoriality is necessary to produce the observed nearest neighbor distances. A simulation that placed colonies randomly on a patch confirmed that these colonies are intraspecifically overdispersed. By adding intraspecific territoriality, the simulation nearest neighbor distances fit the empirical data reasonably well. Thus interspecific competitive interactions seem unnecessary to account for the spatial arrangement of these species.     

Glutamine synthetase of Bacillus stearothermophilus. Regulation, site interactions, and functional information.

The action of various feedback modifiers on Bacillus stearothermophilus glutamine synthetase has been investigated by initial velocity kinetics, using the Mn2+-stimulated biosynthetic assay at 55 degrees C. The most potent inhibitors, used singly, are AMP, L-glutamine, and L-alanine. Other modifiers of significance include glycine, CTP, L-histidine, glucosamine 6-phosphate, and GDP. Marked synergism of action is observed for AMP in the presence of L-glutamine, L-histidine, ADP, or glucosamine 6-phosphate (glucosamine-6-P), and for CTP with ADP or GDP. Inhibition by saturating levels of many modifiers is either less than 100%, or is not overcome by elevated substrate levels, or both. This argues for modifier binding sites separate from substrate sites, notably in the cases of AMP, L-glutamine, glycine, L-alanine, glucosamine-6-P, and CTP. Glycine and L-alanine are Vmax inhibitors, whereas L-glutamine, glucosamine-6-P, GDP, and CTP alter the binding of L-glutamate. ADP and L-histidine apparently can compete directly with MnATP, but AMP alters Mn-ATP binding from a separate site. The action of several modifiers requires or is enhanced by bound substrates. Considerable antagonistic interaction is observed in experiments with modifier pairs, but the most potent inhibitors show synergistic or cumulative (independent) interactions. One may interpret antagonistic effects as due to (a) overlapping modifier domains, or (b) separate but antagonistically interacting sites. Either interpretation leads to a scheme for modifier-substrate and modifier-modifier site interactions in which the thermophilic enzyme must maintain and stabilize a great deal of complex functional information under extreme environmental conditions.     

Rice chitinases: sugar recognition specificities of the individual subsites

Sugar recognition specificities of class III (OsChib1a) and class I (OsChia1cDeltaChBD) chitinases from rice, Oryza sativa L., were investigated by analyzing (1)H- and (13)C-nuclear magnetic resonance spectra of the enzymatic products from partially N-acetylated chitosans. The reducing end residue of the enzymatic products obtained by the class III enzyme was found to be exclusively acetylated, whereas both acetylated and deacetylated units were found at the nearest neighbor to the reducing end residue. Both acetylated and deacetylated units were also found at the nonreducing end residue and its nearest neighbor of the class III enzyme products. Thus, only subsite (-1) among the contiguous subsites (-2) to (+2) of the class III enzyme was found to be specific to an acetylated residue. For the class I enzyme, the reducing end residue was preferentially acetylated, although the specificity was not absolute. The nearest neighbor to the acetylated reducing end residue was specifically acetylated. Moreover, the nonreducing end residue produced by the class I enzyme was exclusively acetylated, although there was a low but significant preference for deacetylated units at the nearest neighbor to the nonreducing end. These results suggest that the three contiguous subsites (-2), (-1), and (+1) of the class I enzyme are specific to three consecutive GlcNAc residues of the substrate. In rice plants, the target of the class I enzyme might be a consecutive GlcNAc sequence probably in the cell wall of fungal pathogen, whereas the class III enzyme might act toward an endogenous complex carbohydrate containing GlcNAc residue.     

Circular dichroism of double-helical oligoribonucleotides

The ultraviolet circular dichroism and absorption of 15 double-stranded helical oligoribonucleotides have been measured. These molecules of chain-length 6 to 12 contain all 10 possible nearest neighbors of Watson-Crick base pairs. They are thus good models for short double-stranded regions in RNA molecules. The contribution to the circular dichroism of each of the nearest neighbor base pairs has been obtained. The circular dichroism is found to be very sequence-dependent and may be useful in distinguishing possible secondary structures. However, the nearest neighbor approximation for circular dichroism fails to give a quantitative measure of the circular dichroism of double-strand regions.     

Acid pairs increase the N-terminal Ca2+ affinity of CaM by increasing the rate of Ca2+ association

A series of N-terminal calmodulin (CaM) mutants was generated to probe the relationship between the N-terminal Ca(2+) affinity and the number of paired, negatively charged Ca(2+) chelating residues in the N-terminal Ca(2+)-binding sites of CaM. When the number of acid pairs [negatively charged residues at positions +x and -x (X-axis), +y and -y (Y-axis), and +z and -z (Z-axis)] was increased from zero to one and then to two, a progressive increase was seen in the N-terminal Ca(2+) affinities. The maximal ranges of the increases observed in the N-terminal Ca(2+) affinity were approximately 8-8.5-fold for site I, approximately 4.5-5-fold for site II, and approximately 11-fold for both sites, in comparison to the mutants containing no acid pairs. The maximal values of N-terminal Ca(2+) affinity were bestowed by the presence of five acidic chelating residues in site I or II, individually. Addition of the sixth acidic chelating residue (third acid pair) to both N-terminal Ca(2+)-binding sites reduced the N-terminal Ca(2+) affinity. The increases in Ca(2+) affinity observed were caused by an increase in the Ca(2+) association rates for the Y- and Z-axis acid pairs, while the X-axis acid pair caused a reduction in the Ca(2+) dissociation rates.     

A tetrahedral coordination of Zinc during transmembrane transport by P-type Zn(2+)-ATPases

Zn(2+) is an essential transition metal required in trace amounts by all living organisms. However, metal excess is cytotoxic and leads to cell damage. Cells rely on transmembrane transporters, with the assistance of other proteins, to establish and maintain Zn(2+) homeostasis. Metal coordination during transport is key to specific transport and unidirectional translocation without the backward release of free metal. The coordination details of Zn(2+) at the transmembrane metal binding site responsible for transport have now been established. Escherichia coli ZntA is a well-characterized Zn(2+)-ATPase responsible for intracellular Zn(2+) efflux. A truncated form of the protein lacking regulatory metal sites and retaining the transport site was constructed. Metrical parameters of the metal-ligand coordination geometry for the zinc bound isolated form were characterized using x-ray absorption spectroscopy (XAS). Our data support a nearest neighbor ligand environment of (O/N)(2)S(2) that is compatible with the proposed invariant metal coordinating residues present in the transmembrane region. This ligand identification and the calculated bond lengths support a tetrahedral coordination geometry for Zn(2+) bound to the TM-MBS of P-type ATPase transporters.     

The ATP-Mg2+ binding site and cytoplasmic domain interactions of Na+,K+-ATPase investigated with Fe2+-catalyzed oxidative cleavage and molecular modeling

This work utilizes Fe(2+)-catalyzed cleavages and molecular modeling to obtain insight into conformations of cytoplasmic domains and ATP-Mg(2+) binding sites of Na(+),K(+)-ATPase. In E(1) conformations the ATP-Fe(2+) complex mediates specific cleavages at 712VNDS (P domain) and near 440VAGDA (N domain). In E(2)(K), ATP-Fe(2+) mediates cleavages near 212TGES (A domain), near 440VAGDA, and between residues 460-490 (N domain). Cleavages at high ATP-Fe(2+) concentrations do not support suggestions for two ATP sites. A new reagent, fluorescein-DTPA, has been synthesized. The fluorescein-DTPA-Fe(2+) complex mediates cleavages similar to those mediated by ATP-Fe(2+). The data suggest the existence of N to P domain interactions in E(1)Na, with bound ATP-Fe(2+) or fluorescein-DPTA-Fe(2+), A-N, and A-P interactions in E(2)(K), and provide testable constraints for model building. Molecular models based on the Ca(2+)-ATPase structure are consistent with the predictions. Specifically, high-affinity ATP-Mg(2+) binding in E(1) is explained with the N domain tilted ca. 80 degrees toward the P domain, by comparison with well-separated N and P domains in the Ca-ATPase crystal structure. With ATP-Mg(2+) docked, bound Mg(2+) is close to both D710 (in 710DGVNDS) and D443 (in 440VAGDASE). D710 is known to be crucial for Mg(2+) binding. The cleavage and modeling data imply that D443 could also be a candidate for Mg(2+) binding. Comparison of E(1).ATP,Mg(2+) and E(2) models suggests an explanation of the high or low ATP affinities, respectively. We propose a scheme of ATP-Mg(2+) and Mg(2+) binding and N, P, and A domain interactions in the different conformations of the catalytic cycle.