The legacies of Langmuir, Ising, and Pauling: ligand binding and the helix-coil transition

Multiple, independent sites or domains behave, on chemical change, in a manner predicted by Langmuir. Distortions of this behavior have been attributed to interactions between the domains, which vary with the progress of the changes occurring at the sites or domains. The two main models for nearest neighbor interactions perturbing the Langmuir prediction for independent domains are those of Ising and Pauling. If we designate the initial site as (-) and the changed site as (+), then the Langmuir requirement for independence of sites yields a set of nearest neighbor interactions such that the (- -), (- +), (+ -), and (+ +) interactions are all identical. This identity is usually characterized as "no interactions." Ising, in dealing with electron pairs, invoked nearest neighbor interactions such that the interactions of the (- -) paris equaled those of the (+ +) pairs, but with the (- +) and (+ -) pairs differing from the reference (- -) pair. Pauling, on the other hand, postulated that only the (- -) and (+ -) pairs interacted differently. A dichotomy has arisen in the application of these two models, with some investigators ignoring or overlooking one of the models. We explore these models, alone and combined, with exact partition functions generated in reasonable computer times for hundreds of sites employing our combinatorial algorithm.     

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.     

Spatial pattern,regeneration and growth rates of Brachystegia spiciformis and Julbernardia globiflora

Past work on tree-to-tree interactions in semi-arid savannas, through the use of nearest neighbour analysis, has shown both a regular dispersion pattern and a positive correlation between the size of a tree and the distance to its nearest neighbour. From these results, the importance of competition has been inferred. In the present study, tree-to-tree interactions in a mesic savanna woodland at Marondera, Zimbabwe, dominated by relatively small-sized individuals of Brachystegia spiciformis and Julbernardia globiflora, were examined. Results show that the regular dispersion pattern is uncommon; that there are few significant positive correlations between size of individual and distance to nearest neighbour; and that growth rate is not consistently correlated with size and distance of nearest neighbour. Results of a study of regeneration relative to canopy cover suggest a possible mechanism for these findings: unlike semi-arid savannas, young plants often grow in under-canopy environments so that early spacing of young trees does not occur. Significant positive correlations between the size of a tree and the distance to its nearest neighbour were found in a stand of larger, presumably older, trees, suggesting that such a relationship only develops in mesic miombo woodland through a thinning process as the trees mature. Familial clumping, which is common in the study area, may mask spatial patterns.Abbreviations RBAI Relative basal area increment     

Combined hopping-superexchange mechanism of charge transfer in DNA; a model with nearest interactions

In the framework of the earlier developed combined hopping-superexchange mechanism of charge transfer in DNA, a model with all nearest interactions between nucleobases is proposed. It is shown that the transfer rates for various types of nucleotide sequences calculated within this model are in a good agreement with experimental data.     

南亚热带鹤山主要人工林生态系统C、N累积及分配格局的模拟研究

 以南亚热带鹤山的马占相思（Acacia mangium）、湿地松（Pinus elliotii）和荷木（Schima uperba）3种代表性人工林生态系统为对象,利用气象、水文、土壤及植物等方面的资料对CENTURY模型进行了参数化,模拟了3种人工林生态系统1985～2100年的C、N累积动态及其分配格局变化,并利用实测资料对模拟结果进行了独立样本的双尾t检验,模拟值与实测值之间没有显著差异（p=0.995）。模拟结果表明,马占相思林的净初级生产力（NPP）呈指数函数形式下降,约在20龄（2005年）时趋于稳定;荷木林的NPP持续缓慢增加;湿地松林的NPP基本维持恒定;20龄以前3种林分的年均NPP分别为12.2 t·hm-2·a-1、6.7 t·hm-2·a-1和2.5 t·hm-2·a-1。马占相思林生物量呈对数函数形式增加,20龄后增加很少;荷木林与湿地松林的生物量呈直线增加,约在2050年时,荷木林的NPP和生物量将超过马占相思林;2100年时马占相思、荷木与湿地松林的生物量将分别达到252.7 t·hm-2、352.4t·hm-2和226.3t·hm-2。荷木林具有更大C累积潜力。3种人工林生态系统的N累积动态与其生物量累积动态相似,但马占相思林生态系统的N累积量远高于荷木林与湿地松林,至2100年时它们的N累积量将分别达到7.2t·hm-2、1.9t·hm-2和2.2t·hm-2。3种林分的C、N随着林分的发育将更多地分配到茎、枝和根部。马占相思林的叶C、N累积量约在2005年后分别下降1.85t·hm-2和0.20t·hm-2,荷木林的叶C、N累积则分别增加0.09t·hm-2和0.05 t·hm-2,湿地松林叶C、N累积分别增加0.57t·hm-2和0.02 t·hm-2,这一模拟结果显示了马占相思林冠层萎缩的内在原因。外来树种组成的马占相思林先锋群落冠层衰退过早,阳生性灌木的大量入侵和定居可能会滞缓地带性森林植被的恢复进程。因此认为我国南亚热带地区进行地带性森林植被恢复时,先锋森林群落的构建应以荷木等本地树种为主。     

Map analysis of ligand binding to a linear lattice

A one-dimensional mapping of the binding properties of a linear lattice offers an exact analytical solution for the site-specific properties of the lattice once the length N and the parameter for nearest neighbor interactions are specified. The solution is derived independent of the definition of the partition function or the transfer matrix, nor does it involve combinatorial arguments. This result provides a simple and effective way of analyzing experimental data for protein-ligand interactions and broadens our understanding of site-specific properties in biological macromolecules.     

A cellular basis for pattern formation in the insect epidermis

Developmental and genetic studies of the detailed patterns visible on the cuticle of many insects indicates that they are generated, progressively, through cellular interactions between nearest neighbours rather than instructed by gradients of diffusible morphogens.     

Fagus sylvatica L. recruitment across a fragmented Mediterranean Landscape, importance of long distance effective dispersal, abiotic conditions and biotic interactions

Native tree populations have been fragmented by anthropogenic disturbance worldwide, leaving them at risk from extinction. The possibility of sizable recovery of fragmented populations is a function of their dispersal, the abiotic conditions, and the biotic interactions. The relative importance of these three drivers for the recruitment rate of a fragmented population of the late-successional Fagus sylvatica L. was analysed at the landscape scale in Causse du Larzac, southern margins of the Massif Central, in the South of France. We used regression models on observational data to analyse the response of Fagus recruitment rate to the distance to the nearest mature population, to climatic and geological variables, and to variables describing biotic interactions (pine vs. grassland, light, shrub cover). Distance to the nearest F. sylvatica adult population was the most important explanatory variable. Recruitment rate was also influenced by facilitative biotic interactions with shrubs, and by the climatic conditions of the plot. Recruitment occurred at a greater distance from the nearest mature population of Fagus in pine forests than in grassland. Dispersal was the major limitation to recruitment of F. sylvatica in this landscape. The recruitment rate was then modulated by the climate and positive biotic interactions. The activity of the European jay could be of great importance for such fragmented populations, because it can lead to long-distance dispersal events and may result in a preferential dispersal towards pine forests.     

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.     

On the adsorption of ions at charged sites in an electric field: I

Considering only nearest neighbor interactions, an expression is obtained for the grand partition function for the adsorption of two kinds of monovalent positive ions at a long chain of one type of monovalent negative fixed sites in an electric field. Expressions are obtained for the fractions of sites which are occupied by each kind of ion as well as of those which are unoccupied as a function of the potential of the electric field.     

Removal of tropomyosin overlap modifies cooperative binding of myosin S-1 to reconstituted thin filaments of rabbit striated muscle

Cooperative binding of myosin S-1.ADP to regulated F-actin was previously reported and has been interpreted by a two-state model in which an important source of cooperativity is nearest neighbor interactions between the 7-actin.tropomyosin (TM).troponin units (functional units) (Hill, T.L., Eisenberg, E., and Greene, L. (1980) Proc. Natl. Acad. Sci. U.S.A. 77, 3186-3190). It has been postulated that the head-to-tail overlap between adjacent TM molecules is the structural basis of the nearest neighbor interactions. We tested the hypothesis by examining S-1.ADP binding to reconstituted regulated F-actin containing either intact TM or nonpolymerizable TM from which the COOH-terminal 11 residues were removed. In the absence of Ca2+, substitution of nonpolymerizable TM for TM reduced significantly the slope of the steeply rising phase of the sigmoidal S-1.ADP binding curve. Nevertheless, considerable residual cooperativity remained. Analysis of the data using the two-state model of Hill et al. suggests that removal of TM overlap abolishes nearest neighbor interactions, while the concerted change of the state of 7 actins in a functional unit can account for the residual cooperativity.     

Aggression and nest spacing in single and mixed species groups of seabirds

When heterospecific seabirds are part of a nesting colony, there may be less opportunity for conspecifics to come in direct contact with each other, resulting in lower intraspecific aggressiveness. To determine if individuals spend less time in aggressive behavior when nesting in conspecific rather than heterospecific groups, we compared the behavior of black skimmers (Rhynchops niger) nesting with gull-billed terns (Sterna nilotica) in three mixed species subcolonies to those of black skimmers in three single species subcolonies. In contrast to our predictions, black skimmers spent significantly less time in aggressive behaviors when nesting in single species subcolonies than when nesting with heterospecifics. Although skimmers in mixed species subcolonies tended to have more aggressive interactions with skimmers than terns, this may be a function of subcolony composition; the proportions of aggressive interactions with conspecifics were similar to the proportions of conspecifics in each subcolony. However, within the mixed species subcolonies, skimmers that nested nearer to terns were involved in aggressive interactions significantly less than skimmers that nested closer to conspecifics. Also, skimmers nested closer to their nearest neighbor when it was a gull-billed tern than when it was another skimmer. Regardless of which species they nested closest to, skimmers were more aggressive towards other skimmers than to terns within the mixed species subcolonies. Distance to nearest neighbor's nest did not differ significantly between the colony types, and did not seem to influence the duration of aggressive activity in the single species subcolonies. In the mixed species subcolonies, however, the time spent in aggressive behavior increased as the distance to nearest neighbor increased. It appears that of the several benefits that have been proposed of mixed species colonies, reduced time spent in conspecific aggression is not among them. However, within a mixed species colony, an individual can reduce time spent in aggressive interactions by nesting near heterospecifics. Received: 16 September 1996 / Accepted: 24 February 1997     

Combined hopping-superexchange mechanism of charge transfer in DNA: Consideration of nearest interactions

Within the framework of a previously developed combined hopping-superexchange mechanism, a model of charge transfer in DNA is proposed that takes into account all nearest interactions. The charge transfer rate constants calculated using this model for a number of nucleotide sequences agree well with the experimentally measured values.     

Evaluation of short-range interactions as secondary structure energies for protein fold and sequence recognition.

Short-range interactions for secondary structures of proteins are evaluated as potentials of mean force from the observed frequencies of secondary structures in known protein structures which are assumed to have an equilibrium distribution with the Boltzmann factor of secondary structure energies. A secondary conformation at each residue position in a protein is described by a tripeptide, including one nearest neighbor on each side. The secondary structure potentials are approximated as additive contributions from neighboring residues along the sequence. These are part of an empirical potential to provide a crude estimate of protein conformational energy at a residue level. Unlike previous works, interactions are decoupled into intrinsic potentials of residues, potentials of backbone-backbone interactions, and of side chain-backbone interactions. Also interactions are decoupled into one-body, two-body, and higher order interactions between peptide backbone and side chain and between backbones. These decouplings are essential to correctly evaluate the total secondary structure energy of a protein structure without overcounting interactions. Each interaction potential is evaluated separately by taking account of the correlation in the amino acid order of protein sequences. Interactions among side chains are neglected, because of the relatively limited number of protein structures. Proteins 1999;36:347-356. Published 1999 Wiley-Liss, Inc.     

Stochastic treatment of cooperative specific adsorption

A stochastic treatment of cooperative specific adsorption of ions at a linear chain of discrete sites leads to a set of differential equations for the various probabilities involved in which the coefficients are determined by nearest neighbor interactions and relative adsorption specificities of the ions for the sites. It is shown that the cooperative specific adsorption isotherm derived earlier on the basis of statistical mechanics for essentially a very large number of sites can be obtained with maximum deviations of only three per cent with this approach by considering only five sites.     

Spatial pattern analysis and competition between Acacia karroo trees in humid savannas

It is unclear whether inter-tree competition plays a role in determining the woody plant cover of humid savannas. Spatial point-pattern analysis can give insights to the underlying processes affecting the individuals in a population. We assessed the spatial patterns of Acacia karroo trees from savannas in KwaZulu-Natal, using conventional nearest neighbour analysis and second-order spatial statistics such as Ripley??s K- and L-functions, and the univariate and bivariate O-ring statistics. We predicted that juvenile trees would be spatially aggregated, because of facilitation between shrubs when zones of overlap are relatively small, while adult trees would be regularly spaced because of the effects of density-dependent mortality (i.e. consistent with the honeycomb rippling model). We found that juvenile trees were more aggregated than expected by chance, and the overall spatial distribution of all trees was also found to be aggregated, with no evidence of regularity among large individuals. Nearest neighbour analysis, however, revealed significant positive correlations between the sum of the distances to the four nearest neighbours and the sum of the canopy diameters of the target tree and its four nearest neighbours, indicating the presence of competition. In sum, these findings suggest that competitive interactions between A. karroo trees at these sites are relatively weak, and result in decreased performance (smaller canopy diameters) rather than mortality, thus preventing a regular pattern of tree distribution. We advocate the use of both methods of detecting competitive interactions in the field, especially if the effects of competition are too subtle to result in differential mortality.     

Cooperativity in nucleosomes assembly on supercoiled pBR322 DNA.

Many studies have shown that in reconstituted chromatin model systems, containing only purified DNA and histone octamer, nucleosomes can adopt well defined locations with respect to DNA nucleotide sequence. Recently, nucleosome-nucleosome interactions were suggested as one of the factors underlying preferential nucleosomes positioning. In the present paper this aspect has been studied by topological analysis and electron microscopy visualization of minichromosomes reconstituted at different histone/DNA ratios. Both methods suggest that cooperativity plays a role in nucleosomes formation. A linear cooperative model in which nucleosomes are formed on discrete sites with cooperative interactions occurring only between nearest neighbours allows to calculate the cooperative constant. The reported results show that basic interactions, which are of relevance in the process of chromatin folding, are present also in very simple model system.     

Impurity and end effects on finite polymer chains--Ising model approach

By the use of a new trick, the open one-dimensional Ising model with nearest neighbor interactions is solved exactly to examine impurity and end effects on finite polymer chains. Melting curves are plotted for various distributions of AT and GC bonds as a function of interaction strength and chain length. Results are compared with previous calculations on infinite length chains by Montroll &; Goel. Correlation effects between impurity bonds on a finite, pure-basis chain are also studied and their implications to further studies of polymer chains indicated.     

Structural determinants of nitroxide motion in spin-labeled proteins: solvent-exposed sites in helix B of T4 lysozyme

Site-directed spin labeling provides a means for exploring structure and dynamics in proteins. To interpret the complex EPR spectra that often arise, it is necessary to characterize the rotamers of the spin-labeled side chain and the interactions they make with the local environment in proteins of known structure. For this purpose, crystal structures have been determined for T4 lysozyme bearing a nitroxide side chain (R1) at the solvent-exposed helical sites 41 and 44 in the B helix. These sites are of particular interest in that the corresponding EPR spectra reveal two dynamic states of R1, one of which is relatively immobilized suggesting interactions of the nitroxide with the environment. The crystal structures together with the effect of mutagenesis of nearest neighbors on the motion of R1 suggest intrahelical interactions of 41R1 with the i + 4 residue and of 44R1 with the i + 1 residue. Such interactions appear to be specific to particular rotamers of the R1 side chain.