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PubMed2005

The spread of infectious diseases in spatially structured populations: an invasory pair approximation.

The invasion of new species and the spread of emergent infectious diseases in spatially structured populations has stimulated the study of explicit spatial models such as cellular automata, network models and lattice models. However, the analytic intractability of these models calls for the development of tractable mathematical approximations that can capture the dynamics of discrete, spatially-structured populations. Here we explore moment closure approximations for the invasion of an SIS epidemic on a regular lattice. We use moment closure methods to derive an expression for the basic reproductive number, R(0), in a lattice population. On lattices, R(0) should be bounded above by the number of neighbors per individual. However, we show that conventional pair approximations actually predict unbounded growth in R(0) with increasing transmission rates. To correct this problem, we propose an 'invasory' pair approximation which yields a relatively simple expression for R(0) that remains bounded above, and also predicts R(0) values from lattice model simulations more accurately than conventional pair and triple approximations. The invasory pair approximation is applicable to any spatial model, since it takes into account characteristics of invasions that are common to all spatially structured populations.

Animals↗
PubMed1993

Two-dimensional 1H-NMR study of the spatial structure of neurotoxin II from Naja naja oxiana.

The spatial structure of neurotoxin II from the venom of the central Asian cobra Naja naja oxiana was determined by two-dimensional 1H-NMR techniques and computational analysis. Nearly complete proton resonance assignments for 61 amino acid residues have been made using two-dimensional (2D) homonuclear total correlated spectroscopy, 2D homonuclear double-quantum-filtered correlated spectroscopy and 2D homonuclear NOE spectroscopy (NOESY) experiments. The cross-peak volumes in NOESY spectra spin-spin coupling constants of vicinal protons NH-C alpha H and C alpha H-C beta H and the observation of slow deuterium exchange of amide protons were used to define local structure and a set of constraints for distance geometry program DIANA. The average root-mean-square deviations are 53 pm for backbone heavy atoms and 118 pm for all heavy atoms of 19 final neurotoxin II conformations. The spatial structure is characterized by a short double-stranded (residues 1-5 and 13-17) and a triple-stranded (residues 22-30, 33-41 and 50-54) antiparallel beta-sheets.

Amino Acid Sequence↗
PubMed2004

Forecasting spatially structured populations: the role of dispersal and scale.

We forecasted spatially structured population models with complex dynamics, focusing on the effect of dispersal and spatial scale on the predictive capability of nonlinear forecasting (NLF). Dispersal influences NLF ability by its influence on population dynamics. For simple 2-cell models, when dispersal is small, our ability to predict abundance in subpopulations decreased and then increased with increasing dispersal. Spatial heterogeneity, dispersal manner, and environmental noise did not qualitatively change this result. But results are not clear for complex spatial configurations because of complicated dispersal interactions across subpopulations. Populations undergoing periodic fluctuations could be forecasted perfectly for all deterministic cases that we studied, but less reliably when environmental noise was incorporated. More importantly, for all models that we have examined, NLF was much worse at larger spatial scales as a consequence of the asynchronous dynamics of subpopulations when the dispersal rate was below some critical value. The only difference among models was the critical value of dispersal rate, which varied with growth rate, carrying capacity, mode of dispersal, and spatial configuration. These results were robust even when environmental noise was incorporated. Intermittency, common in the dynamics of spatially structured populations, lowered the predictive capability of NLF. Forecasting population behaviour is of obvious value in resource exploitation and conservation. We suggest that forecasting at local scales holds promise, whereas forecasting abundance at regional scales may yield poor results. Improved understanding of dispersal can enhance the management and conservation of natural resources, and may help us to understand resource-exploitation strategies employed by local indigenous humans.

Animals↗
PubMed1987

[Relation between the spatial structure and antigenic activity of trophoblast-specific beta1-glycoprotein].

Temperature- and pH-dependence of spatial structure of a native trophoblast-specific beta-glycoprotein (TSG), its desialated and deglycosylated derivatives, as well as of a fragment obtained by partial acid hydrolysis on the temperature and pH variations has been studied using CD and UV spectroscopy. Within the range 45-50 degrees C a conformational transition of the protein moiety of TSG, leading to partially reversible alterations in tertiary and secondary structures of this glycoprotein after cooling the solution to 20 degrees C has been found out. The results of spectral studies of the spatial structure of the TSG protein component have been compared with the data on antigen activity of native, temperature- and pH-denaturated, desialated, and deglycosilated TSG. It has been concluded that the protein moiety of TSG consists mainly of beta-structures; the greater part of antigen determinants of TSG is topographic and belongs to the protein component of TSG, and only 15% of antigen determinants are not connected with TSG's spatial structure.

Circular Dichroism↗
PubMedDate not supplied

[Spatial structure of BAM-12P dodecapeptide and its analogues].

Theoretical conformational analysis was used to study the spatial structure and conformational properties of the bovine adrenal medulla dodecapeptide BAM-12P (Tyr1-Gly2-Gly3-Phe4-Met5-Arg6-Arg7-Val8-Gly9-Arg10-Pro11-Glu12). Twenty-three low-energy conformations of the BAM-12P backbone were shown to represent the spatial structure of the peptide. The inverse structural problem was solved, and synthetic analogues of BAM-12P were proposed, the spatial structures of which correspond to a set of low-energy potentially physiologically active conformations of the natural dodecapeptide. The English version of the paper: Russian Journal of Bioorganic Chemistry, 2005, vol. 31, no. 3; see also http://www.maik.ru.

Animals↗
PubMed2006

Fine scale spatial structuring of sex and mitochondria in Silene vulgaris.

Fine scale spatial structure (FSSS) of cytoplasmic genes in plants is thought to be generated via founder events and can be amplified when seeds germinate close to their mother. In gynodioecious species these processes are expected to generate FSSS in sex ratio because maternally inherited cytoplasmic male sterility genes partially influence sex expression. Here we document a striking example of FSSS in both mitochondrial genetic markers and sex in roadside populations of Silene vulgaris. We show that in one population FSSS of sexes influences relative fruit production of females compared to hermaphrodites. Furthermore, FSSS in sex ratio is expected to persist into future generations because offspring sex ratios from females are female-biased whereas offspring sex ratios from hermaphrodites are hermaphrodite-biased. Earlier studies indicated that pollen limitation is the most likely mechanism underlying negative frequency dependent fitness of females. Our results support the theoretical predictions that FSSS in sex ratio can reduce female fitness by decreasing the frequency at which females experience hermaphrodites. We argue that the influence of FSSS on female fitness is complementary to the influence of larger scale population structure on female fitness, and that population structure at both scales will act to decrease female frequencies in gynodioecious species. Better comprehension of the spatial structure of genders and genes controlling sex expression at a local scale is required for future progress toward understanding sex ratio evolution in gynodioecious plants.

DNA, Mitochondrial↗
PubMedDate not supplied

Hierarchy of regions of amino acid sequence with respect to their role in the protein spatial structure.

The method of the representation of amino acid sequence by graph of the interactions energy between parts of spatial structure has been elaborated. Our method provides the possibility to establish the compatibility between each point of a polypeptide chain and the Van der Waals interactions energy of regions of a native globule adjacent to this amino acid residue. We have undertaken an exhaustive analysis of a set of proteins. Boundaries of domain and module structures have been found. Nonequivalence of different parts of sequences in respect to their contribution to stabilization of the spatial structure of the protein macromolecules has been revealed. On the basis of the number of energetic levels which are necessary to identify all independent parts of the globule, the contribution from each part of the sequence to stabilization of the spatial structure of the globule is defined. Thus, it has been found that the sequence of amino acid residues coincides with the sequence of the numerical values which can be used in turn in formal procedures, such as an alignment, a search of consensus, the recognition of composition peculiarities, etc. An example of the comparison of proteins with various sequence identities is considered to demonstrate the scheme of an alignment procedure.

Amino Acid Sequence↗
PubMed1997

Estimation of evolutionary distances from protein spatial structures.

New equations are derived to estimate the number of amino acid substitutions per site between two homologous proteins from the root mean square (RMS) deviation between two spatial structures and from the fraction of identical residues between two sequences. The equations are based on evolutionary models, analyzing predominantly structural changes and not sequence changes. Evolution of spatial structure is treated as a diffusion in an elastic force field. Diffusion accounts for structural changes caused by amino acid substitutions, and elastic force reflects selection, which preserves protein fold. Obtained equations are supported by analysis of protein spatial structures.

Amino Acid Sequence↗
PubMed2005

Computer-aided analysis of spatial structure of some hydrolytic enzymes.

Using the MolScript version 2.1 computer program for protein molecule modeling and X-ray structure analysis data the spatial structures of several hydrolytic enzymes have been compared. These include glucoamylase from Aspergillus awamori and Saccharomycopsis fibuligera and lipases from Rhizopus japonicus. Results on homology of amino acid sequences and topology of secondary structure elements were obtained. 3D models of these enzymes with positioning of functionally important groups in the active site cavity were built.

Amino Acid Sequence↗
PubMed1986

Spatial structures in mitochondrial suspension induced by cation efflux.

The formation of spatial structures in a thin unstirred layer of a mitochondrial suspension has been studied. It is shown that the structure formation depends on the state of the ion-transporting systems of mitochondria and that pattern development coincides with the activation of cation efflux from preloaded mitochondria. Spatial structure formation is an energy-dependent process and is suppressed by respiratory chain inhibitors. Patterning is also inhibited by EGTA, EDTA and ruthenium red, reflecting the requirement for divalent cation translocation in mitochondria for the studied phenomenon.

Animals↗
PubMed2006

Adaptive evolution in a spatially structured asexual population.

We study the process of adaptation in a spatially structured asexual haploid population. The model assumes a local competition for replication, where each organism interacts only with its nearest neighbors. We observe that the substitution rate of beneficial mutations is smaller for a spatially structured population than that seen for populations without structure. The difference between structured and unstructured populations increases as the adaptive mutation rate increases. Furthermore, the substitution rate decreases as the number of neighbors for local competition is reduced. We have also studied the impact of structure on the distribution of adaptive mutations that fix during adaptation.

Adaptation, Biological↗
PubMed2003

Field stimulation of cardiac fibers with random spatial structure.

Polarization of individual cells ("sawtooth") has been proposed as a mechanism for field stimulation and defibrillation. To date, the modeling work has concentrated on the myocardium with periodic spatial structure; this paper investigates potentials arising in cardiac fibers with random spatial structure. Ten different random fibers consisting of cells with varying length (l(c) = 100 +/- 50 microm), diameter (d(c) = 20 +/- 10 microm), thickness of extracellular space (t(e) = 1.18 +/- 0.59 microm), and junctional resistance (R(j) = 2 +/- 1 M(omega)) are studied. Simulations demonstrate that randomizing spatial structure introduces to the field-induced potential (V(m)) a randomly varying baseline, which arises due to polarization of groups of cells. This polarization appears primarily in response to randomizing t(e); R(j), l(c), and d(c) have less influence. The maximum V(m) increases from 3.5 mV in a periodic fiber to 20.5+/-4.7 mV in random fibers (1 V/cm field applied for 5 ms). Field stimulation threshold E(th) decreases from 6.9 to 1.59 +/- 0.43 V/cm, which is within the range of experimental measurements. Thresholds for normal and reversed field polarities are statistically equivalent: 1.59 +/- 0.43 versus 1.44 +/- 0.41 V/cm (p value = 0.453). Thus, V(m) arising due to random structure of the myocardium may play an important role in field stimulation and defibrillation.

Computer Simulation↗
PubMed2004

Assumed and inferred spatial structure of populations: the Scandinavian brown bears revisited.

We reanalysed the spatial structure of the Scandinavian brown bear (Ursus arctos) population based on multilocus genotypes. We used data from a former study that had presumed a priori a specific population subdivision based on four subpopulations. Using two independent methods (neighbour-joining trees and Bayesian assignment tests), we analysed the data without any prior presumption about the spatial structure. A subdivision of the population into three subpopulations emerged from our study. The genetic pattern of these subpopulations matched the three geographical clusters of individuals present in the population. We recommend considering the Scandinavian brown bear population as consisting of three (instead of four) subpopulations. Our results underline the importance of determining genetic structure from the data, without presupposing a structure, even when there seems to be good reason to do so.

Animals↗
PubMed2000

Testing local dependence of spatial structures on images

Associations between two spatial processes can be due to a real dependence between the two processes or to the dependence on common underlying variables. We propose to test the existence of a real dependence by use of local tests, leading to a global test of real dependence and a map of local interactions. We present first how classical interaction tests based on random rotations between completely observed processes such as those developed by Berman (Berman. Appl. Statist. (1986) 35, 54-62), can be integrated in local analyses. For this purpose, tests are first performed locally, and the distribution of their p-values is then compared to the corresponding value under the null hypothesis. A similar approach is proposed to test non-stationarity of a point pattern by using distance statistics popularized by Diggle (Diggle. Statistical Analysis of Spatial Point Patterns. (1983) Academic Press, New York). The problem of testing the interaction between a random field and a censoring area pattern process is discussed and an approach similar to the preceding ones is then proposed. The methods are mainly applied to agricultural examples but they can be applied to any microscopical images for which one wishes to analyse the spatial structure.

Journal Article↗
PubMedDate not supplied

Radar determination of the spatial structure of hydraulic conductivity.

Spatial variability of hydraulic conductivity exerts a predominant control on the flow of fluid through porous media. Heterogeneities influence advective pathways, hydrodynamic dispersion, and density-dependent dispersion; they are, therefore, a key concern for studies of ground water resource development, contaminant transport, and reservoir engineering. Ground-penetrating radar contributes to the remote, geophysical characterization of the macroscale variability of natural porous media. On a controlled excavation of a glacial-fluvial sand and gravel deposit in the Fanshawe Delta area (Ontario, Canada), the hydraulic conductivity field of a 45 x 3 m vertical exposure was characterized using constant-head permeameter measurements performed on undisturbed horizontal sediment cores. Ground-penetrating radar data were collected along the excavation face in the form of both reflection and common midpoint surveys. Comparison of geostatistical analyses of the permeameter measurements and the radar data suggests thatthe horizontal correlation structure of radar stack velocity can be used to directly infer the horizontal correlation structure of hydraulic conductivity. The averaging nature of the common midpoint survey is manifest in the vertical correlation structure of stack velocity, making it less useful. Radar reflection data do not exhibit a spatial structure similar to that of hydraulic conductivity possibly because reflections are a result of material property contrasts rather than the material properties themselves.

Data Collection↗
PubMed2005

Mutation at high rates reduces spatial structure within populations.

The question of whether or not the high rates (mu) of mutation that occur for some hypervariable markers can affect commonly used empirical measures of spatial structure of genetic variation within populations is addressed. The results show that values of these measures are approximately halved when mu is 10(-2). Finest spatial-scale correlations, measured by either Moran's I-statistics or conditional kinship, are reduced by 30%-50%. When the mutation rate is 10 times lower, much smaller reductions result, e.g. averaging 7% for the finest scale correlations. Still smaller orders of magnitude of mu cause negligible changes in spatial structure, where any effects normally would not be detectable. The reductions are caused by forward mutations, and when the reductions are measured as percentages, they are nearly independent of the amount of structure produced sans mutation, except when dispersal is nearly minimal. The percent reductions are also nearly independent of the number of alleles and of back mutations, hence of the nature of the mutation process (e.g. stepwise or not). The results demonstrate that some hypervariable loci should have reduced spatial structuring, and that marker choice may affect the values observed in experimental surveys. Moreover, if fine-scale correlations are used to indirectly estimate dispersal distances, then mutation at high rates could inflate estimates, easily up to two- to three-fold.

Computer Simulation↗
PubMed1989

The spatial structure of migration: an analysis of flows between states in the USA over three decades.

"Migration flows between states in the [United States] over three decades are analysed using a general spatial interaction model. The role of geographic distance and a more general distance conception are examined, as is the stability of the spatial structure over time. Results imply that although migration structures reflect geographic distance, other stable factors, reflecting idiosyncratic ties between locations, are important as well. This suggests that the common practice in migration research of ignoring spatial structure to focus on individual locations is misleading. The particular ties between locations cannot be ignored in examining total migration at a location at one point in time. In examining changes over time, however, we can limit consideration to the relative draw and sending effects at each location because the spatial structure is quite stable over extended periods." (SUMMARY IN FRE AND GER)

Americas↗
PubMed2006

Spatially structured superinfection and the evolution of disease virulence.

When pathogen strains differing in virulence compete for hosts, spatial structuring of disease transmission can govern both evolved levels of virulence and patterns in strain coexistence. We develop a spatially detailed model of superinfection, a form of contest competition between pathogen strains; the probability of superinfection depends explicitly on the difference in levels of virulence. We apply methods of adaptive dynamics to address the interplay of spatial dynamics and evolution. The mean-field approximation predicts evolution to criticality; any small increase in virulence capable of dynamical persistence is favored. Both pair approximation and simulation of the detailed model indicate that spatial structure constrains disease virulence. Increased spatial clustering reduces the maximal virulence capable of single-strain persistence and, more importantly, reduces the convergent-stable virulence level under strain competition. The spatially detailed model predicts that increasing the probability of superinfection, for given difference in virulence, increases the likelihood of between-strain coexistence. When strains differing in virulence can coexist ecologically, our results may suggest policies for managing diseases with localized transmission. Comparing equilibrium densities from the pair approximation, we find that introducing a more virulent strain into a host population infected by a less virulent strain can sometimes reduce total host mortality and increase global host density.

Adaptation, Physiological↗