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Spatio-temporal modeling of benthic biological species.

The spatial and temporal distribution of the number of benthic species located in an important area under ecological stress (Puerto CALICA, Quintana Roo, Mexico) is analyzed by means of Gaussian Spatial Linear Mixed Models. Following a model-based approach we derive spatial predictions taking into account temporal variations between May 1996 and June 1999. The proposed models were evaluated in terms of their ability to detect the underlying spatial structure for further interpolation. Uncertainty in the prediction could be evaluated by using the Bayesian paradigm. The results can be used as a guide for further environmental management policies in the region.

Animals↗

Methyl substituents at the 11 or 12 position of retinal profoundly and differentially affect photochemistry and signalling activity of rhodopsin.

The C-11=C-12 double bond of the retinylidene chromophore of rhodopsin holds a central position in its light-induced photoisomerization and hence the photosensory function of this visual pigment. To probe the local environment of the HC-11=C-12H element we have prepared the 11-methyl and 12-methyl derivatives of 11-Z retinal and incorporated these into opsin to generate the rhodopsin analogs 11-methyl and 12-methyl rhodopsin. These analog pigments form with much slower kinetics and lower efficiency than the native pigment. The initial photochemistry and the signaling activity of the analog pigments were investigated by UV-vis and FTIR spectroscopy, and by a G protein activation assay. Our data indicate that the ultrafast formation of the first photointermediate is strongly perturbed by the presence of an 11-methyl substituent, but much less by a 12-methyl substituent. These results support the current concept of the mechanism of the primary photoisomerization event in rhodopsin. An important stronghold of this concept is an out-of-plane movement of the C-12H element, which is facilitated by torsion as well as extended positive charge delocalization into the C-10-C-13 segment of the chromophore. We argue that this mechanism is maintained principally with a methyl substituent at C-12. In addition, we show that both an 11-methyl and a 12-methyl substitutent perturb the photointermediate cascade and finally yield a low-activity state of the receptor. The 11-methyl pigment retains about 30% of the G protein activation rate of native rhodopsin, while the 12-methyl chromophore behaves like an inverse agonist up to at least 20 degrees C, trapping the protein in a perturbed Meta-I-like conformation. We conclude that the isomerization region of the chromophore and the spatial structure of the binding site are finely tuned, in order to achieve a high photosensory potential with an efficient pathway to a high-activity state.

Animals↗

Evolution of mutualism through spatial effects.

Mutualism among species is ubiquitous in natural ecosystems but its evolution is not well understood. We provided a simple lattice model to clarify the importance of spatial structure for the evolution of mutualism. We assumed reproductive rates of two species are modified through interaction between species and examine conditions where mutualists of both species, that give some benefit to the other species with their own cost, invade non-mutualists populations. When dispersal of offspring is unlimited, we verified the evolution of mutualism is impossible under any condition. On the other hand, when the dispersal is limited to neighboring lattice sites, mutualists can invade if the ratio of cost to benefit is low and the intrinsic reproductive rate is low in case where the parameter values are symmetric between species. Under the same conditions, non-mutualists cannot invade mutualist populations, that is, the latter are evolutionarily stable. In case of asymmetric parameters, mutualists tend to invade if the average value of costs to two species is low or that of benefits is high, and if the intrinsic reproductive rate is low for one of the two species. A mechanistic explanation of why mutualists increase when the dispersal is limited is given by showing that mutualist pairs of the two species at the same lattice site rapidly increase at the initial phase of the invasion.

Altruism↗

On moment closures for population dynamics in continuous space.

A first-order moment closure, the mean-field assumption that organisms encounter one another in proportion to their spatial average densities, lies at the heart of much theoretical ecology. This assumption ignores all spatial information and, at the very least, needs to be replaced by a second-order closure to gain understanding of ecological dynamics in spatially structured populations. We describe a number of conditions that a second-order closure should satisfy and use these conditions to evaluate some closures currently available in the literature. Two conditions are particularly helpful in discriminating among the alternatives: that the closure should be positive, and that the dynamics should be unaltered when identical individuals are given different labels. On this basis, a class of closures we refer to as 'power-2' turns out to provide a good compromise between positivity and dynamical invariance under relabelling.

Animals↗

Evolution of searching and life history characteristics in individual-based models of host-parasitoid-microbe associations.

In this paper we develop a novel discrete, individual-based mathematical model of the evolution of life history, dispersal and other behavioural characteristics in insect host-parasitoid-microbe associations, and use it to investigate their evolutionary dynamics. For any individual characteristic the model begins with an even, rectangular distribution of characteristic values. Selection is then allowed to act, and the change in the distribution of the characteristic values is observed. Evolutionary change in the population variance of the characteristic value is also observed, since we would expect this to decline under selection in most cases. The paper, therefore, introduces a general framework for modeling problems of evolution in stochastic, spatially structured environments, where movement and dispersal are under selection. The model then extends this approach to include the sex-distorting bacterium Wolbachia in order to investigate aspects of its horizontal and vertical transmission under different levels of superparasitism by parasitoids. The model also includes a neutral genetic marker, in order to be able to detect changes in phenotype frequency caused by genetic drift, as well as a simplified simulation of sexual reproduction so as to allow the possibility of recombination between genotypes. Key results from the model simulations show that: (i) the refractory time after oviposition affects the value of superparasitism, with short refractory times favouring high rates of superparasitism; (ii) variable levels of superparasitism do not affect the stable proportion of the population of parasitoids infected with Wolbachia, but this is achieved by different evolutionary pathways under low and high superparasitism, respectively. In the case of low superparasitism Wolbachia spreads mainly by vertical transmission, leading to population replacement, whereas when superparasitism rates are high there is significant horizontal transfer.

Animals↗

Pattern formation of leaf veins by the positive feedback regulation between auxin flow and auxin efflux carrier.

The generation of vascular pattern formation in plants is an interesting process of pattern formation in organisms. It is well known that the plant hormone auxin is involved in plant vascular differentiation and that the PIN1 protein, an auxin efflux carrier, localizes to one side of the cell membrane. Several hypotheses have been proposed to explain the formation of leaf venation. One is the canalization hypothesis that is based on the assumption that a positive feedback regulation exists between the flow of a signal molecule and the capacity of its flow. Here, we attempted to integrate the canalization hypothesis and experimental data. We investigated models of the positive feedback regulation between the auxin flow and PIN1 localization. Model 1, with conserved PIN1 amount in each cell, can generate a branching pattern similar to that of plant leaf venation. We introduced the diffusible enhancer "e" into the model as unknown factor. The obtained patterns show a quasi-periodic distribution of auxin flow paths, when the model dynamics includes domain growth. In order to understand the early initiation process that generates an inhomogeneity from an almost homogeneous distribution, we introduced model 2, a simplified version of model 1. Model 2 can generate inhomogeneity with a parameter dependency similar to that of model 1. To analyse parameter condition required for pattern development, approximated equations are obtained from model 2. The isocline analysis of the equations without spatial structure shows that the inhomogeneous distribution occurs from an almost homogeneous distribution. This parameter condition for generating inhomogeneity is consistent with the results of models 1 and 2.

Arabidopsis Proteins↗

Probing the effects of the well-mixed assumption on viral infection dynamics.

Viral kinetics have been extensively studied in the past through the use of spatially well-mixed ordinary differential equations describing the time evolution of the diseased state. However, emerging spatial structures such as localized populations of dead cells might adversely affect the spread of infection, similar to the manner in which a counter-fire can stop a forest fire from spreading. In a previous publication [Beauchemin, C., Samuel, J., Tuszynski, J., 2005. A simple cellular automaton model for influenza A viral infections. J. Theor. Biol. 232(2), 223-234], a simple two-dimensional cellular automaton model was introduced and shown to be accurate enough to model an uncomplicated infection with influenza A. Here, this model is used to investigate the effects of relaxing the well-mixed assumption. Particularly, the effects of the initial distribution of infected cells, the regeneration rule for dead epithelial cells, and the proliferation rule for immune cells are explored and shown to have an important impact on the development and outcome of the viral infection in our model.

Animals↗

Bifurcations and phase transitions in spatially extended two-member hypercycles.

Mounting theoretical and experimental evidence indicates that the success of molecular replicators is strongly tied to the local nature of their interactions. Local dispersal in a given spatial domain, particularly on surfaces, might strongly enhance the growth and selection of fit molecules and their resistance to parasites. In this work the spatial dynamics of a simple hypercycle model consisting of two molecular species is analysed. In order to characterize it, both mean field models and stochastic, spatially explicit approaches are considered. The mean field approach predicts the presence of a saddle-node bifurcation separating a phase involving stable hypercycles from extinction, consistently with spatially explicit models, where an absorbing first-order phase transition is shown to exist and diffusion is explicitly introduced. The saddle-node bifurcation is shown to leave a ghost in the phase plane. A metapopulation-based model is also developed in order to account for the observed phases when both diffusion and reaction are considered. The role of information and diffusion as well as the relevance of these phases and the underlying spatial structures are discussed, and their potential implications for the evolution of early replicators are outlined.

Animals↗

Review of solutions for 3D hydrodynamic modeling applied to aquaculture in South Pacific atoll lagoons.

A workshop organized in French Polynesia in November 2004 allowed reviewing the current methods to model the three-dimensional hydrodynamic circulation in semi-enclosed atoll lagoons for aquaculture applications. Mollusk (e.g. pearl oyster, clam) aquaculture is a major source of income for South Pacific countries such as French Polynesia or Cook Islands. This aquaculture now requires a better understanding of circulation patterns to improve the spatial use of the lagoons, especially to define the best area to set larvae collectors. The pelagic larval duration of the relevant species (<20 days) and the size of the semi-closed lagoons (few hundreds of km2) drive the specifications of the model in terms of the spatial and temporal scale. It is considered that, in contrast with fish, mollusk larvae movements are limited and that their cycle occurs completely in the lagoon, without an oceanic stage. Atolls where aquaculture is productive are generally well-bounded, or semi-closed, without significant large and deep openings to the ocean. Nevertheless part of the lagoon circulation is driven by oceanic water inputs through the rim, ocean swells, tides and winds. Therefore, boundary conditions of the lagoon system are defined by the spatial structure of a very shallow rim (exposition and number of hoas), the deep ocean swell climate, tides and wind regimes. To obtain a realistic 3D numerical model of lagoon circulation with adequate forcing, it is thus necessary to connect in an interdisciplinary way a variety of methods (models, remote sensing and in situ data collection) to accurately represent the different components of the lagoon system and its specific boundary conditions. We review here the current methods and tools used to address these different components for a hypothetical atoll of the Tuamotu Archipelago (French Polynesia), representative of the semi-closed lagoons of the South Pacific Ocean. We hope this paper will serve as a guide for similar studies elsewhere and we provide guidelines in terms of costs for all the different stages involved.

Animals↗

A mathematical analysis on public goods games in the continuous space.

We consider the population dynamics of two competing species sharing the same resource, which is modeled by the carrying capacity term of logistic equation. One species (farmer) increases the carrying capacity in exchange for a decreased survival rate, while the other species (exploiter) does not. As the carrying capacity is shared by both species, farmer is altruistic. The effect of continuous spatial structure on the performance of such strategies is studied using the reaction diffusion equations. Mathematical analysis on the traveling wave solution of the system revealed; (1) Farmers can never expel exploiters in any traveling wave solution. (2) The expanding velocity of the exploiter population invading the farmer population can be analytically determined and it depends only on a cost of altruism and the diffusion coefficients while it is independent of the benefit of altruism. (3) When the effect of altruism is small, the dynamics of the invasion of exploiters obeys the Fisher-KPP equation. Numerical calculations confirm these results.

Altruism↗

Super Enhanced Purification of Denatured-Refolded Ubiquitinated Proteins by ThUBD Revealed Ubiquitinome Dysfunction in Liver Fibrosis.

Ubiquitination is crucial for maintaining protein homeostasis and plays a vital role in diverse biological processes. Ubiquitinome profiling and quantification are of great scientific significance. Artificial ubiquitin-binding domains (UBDs) have been widely employed to capture ubiquitinated proteins. The success of this enrichment relies on recognizing native spatial structures of ubiquitin and ubiquitin chains by UBDs under native conditions. However, the use of native lysis conditions presents significant challenges, including insufficient protein extraction, heightened activity of deubiquitinating enzymes and proteasomes in removing the ubiquitin signal, and purification of a substantial number of contaminant proteins, all of which undermine the robustness and reproducibility of ubiquitinomics. In this study, we introduced a novel approach that combines denatured-refolded ubiquitinated sample preparation (DRUSP) with a tandem hybrid UBD for ubiquitinomic analysis. The samples were effectively extracted using strongly denatured buffers and subsequently refolded using filters. DRUSP yielded a significantly stronger ubiquitin signal, nearly three times greater than that of the Control method. Then, eight types of ubiquitin chains were quickly and accurately restored; therefore, they were recognized and enriched by tandem hybrid UBD with high efficiency and no biases. Compared with the Control method, DRUSP showed extremely high efficiency in enriching ubiquitinated proteins, improving overall ubiquitin signal enrichment by approximately 10-fold. Moreover, when combined with ubiquitin chain-specific UBDs, DRUSP had also been proven to be a versatile approach. This new method significantly enhanced the stability and reproducibility of ubiquitinomics research. Finally, DRUSP was successfully applied to deep ubiquitinome profiling of early mouse liver fibrosis with increased accuracy, revealing novel insights for liver fibrosis research.

Animals↗

Area-level risks for BSE in British cattle before and after the July 1988 meat and bone meal feed ban.

In this paper we investigate area-level risk factors for BSE for the cattle population present in Great Britain between 1986 and 1997. By dividing this population into two birth cohorts, those born before the July 1988 ban on feeding ruminant-derived meat and bone meal to ruminants and those born after, second-order regional influences are distinguished from the strong first-order south-to-north gradient of area-level BSE risk using Bayesian hierarchical models that account for structured (spatially correlated) and unstructured heterogeneity in the data. For both cohorts area-level risk of BSE was increased by a more southerly location and greater numbers of dairy cattle, relative to non-dairy cattle. For the cohort of cattle born after the July 1988 ban on feeding ruminant-derived meat and bone meal area-level BSE risk was additionally associated with greater numbers of pigs, relative to cattle. These findings support the role of low level cross-contamination of cattle feed by pig feed as an influence on BSE incidence risk as the epidemic evolved. Prior to the 1988 meat and bone meal ban unexplained BSE risk was relatively uniformly distributed across the country whereas after the ban there were spatially aggregated areas of unexplained risk in the northern and eastern regions of England suggesting that local influences allowed BSE control measures to be less-successfully applied in these areas, compared with the rest of the country. We conclude that spatially localised influences were operating in divergent ways during the two phases of the epidemic.

Animal Feed↗

Spatial statistical modeling of disease outbreaks with particular reference to the UK foot and mouth disease (FMD) epidemic of 2001.

In this paper we examine issues relating to the analysis of spatially-referenced disease data. Initially, we discuss the use of exploratory statistical tools such as density estimation and nonparametric regression. We then consider the need for descriptive epidemic models in space, time, and space-time models for epidemic dynamics. Implicitly space-time must be considered in any analysis of the spatial structure of epidemics. The use of Bayesian models for disease spread is discussed and applied to the recent foot and mouth outbreak in the UK.

Animals↗

Competition landscapes: scaling up local biotic and abiotic processes in heterogeneous environments.

I present a model based on benthic populations by first defining a competition landscape where competitive interactions are confined to small areas, defined by the distribution of resource renewal from a global pool. Using truncated kernels and results from 1-dimensional percolation theory, I then derive an approximation allowing the scaling up of local interactions among individuals to patch and landscape levels. This approximation is used to explore how spatially structured habitats can affect competition intensity. The competition landscape is then compared to a simulation of mussel colonization under various flow velocity patterns, and is shown to predict the qualitative effect of the scale of patchiness in habitat quality on total competition intensity. The interaction between large scale hydrodynamic forcing and local competition is also shown to provide an alternate hypothesis explaining the observed among-year reversal of the relationship between topographic scale and mussel abundance in some intertidal communities. The model more generally highlights the nonlinear scaling up of competitive interactions in competition landscapes, and provides a framework for the study of self-organization in heterogeneous ecosystems.

Cluster Analysis↗

Identification of pentadecapeptide mimicking muramyl peptide.

We used monoclonal antibody, generated against N-acetylglucosaminyl-beta1-4-N-acetylmuramyl-alanyl-D-isoglutamine (GMDP), and phage display libraries of random peptides to select for oligopeptides, that mimic GMDP in their biological activity. Selected phage clones displayed a peptide RVPPRYHAKISPMVN (called RN-peptide) on their surface. This peptide was synthesized. RN-peptide was shown to augment the antibody response to ovalbumin in mice while the peptide was non-immunogenic and non-pyrogenic. We also characterized adjuvant activity of 14-, 10- and 7-mer analogs of RN-peptide truncated at the C-terminus and found them to be active. Because both carbohydrate and peptide fragments are critical for the biological activity of muramyl peptides, the results indicate that RN-peptide mimicks the spatial structure of intact GMDP.

Acetylmuramyl-Alanyl-Isoglutamine↗

Effects of contrast and size on orientation discrimination.

Motivated by the recent physiological finding that a neuron's receptive field can increase in size by a factor of 2-4-fold at low contrast [Nat. Neurosci. 2 (1999) 733, Proc. Natl. Acad. Sci. USA 96 (1999) 12073], we sought to examine whether a psychophysical task might reflect the contrast dependent changes in the size/structure of a receptive field. We postulate that since spatial summation is not contrast invariant, a task that relies on the spatial structure of a receptive field, such as orientation discrimination, should also be affected by changes in contrast. Previously, orientation discrimination thresholds have been reported to be roughly independent of the contrast of a stimulus for most of the visible range of contrasts [i.e. J. Neurophysiol. 57 (1987) 773, J. Opt. Soc. Am. 6 (1989) 713, Vis. Res. 30 (1990) 449, Vis. Res. 39 (1999) 1631]. Here, we found large improvements in orientation discrimination with contrast that were dependent on stimulus area. Furthermore, the apparent constancy of orientation discrimination for large area stimuli is possibly a result of a floor effect on the threshold. Therefore we conclude that there is not strong evidence for contrast invariant orientation discrimination. We interpret these results in the context of recent neurophysiological results about the expansion of cortical cells' receptive fields at low contrast.

Contrast Sensitivity↗

Aftereffect of adaptation to Glass patterns.

Our visual systems constantly adapt their representation of the environment to match the prevailing input. Adaptation phenomena provide striking examples of perceptual plasticity and offer valuable insight into the mechanisms of sensory coding. Here, we describe an aftereffect of adaptation to a spatially structured image whereby an unstructured test stimulus takes on illusory structure locally perpendicular to that of the adaptor. Objective measurement of the strength of the aftereffect for different patterns suggests a neural locus of adaptation prior to the extraction of complex form in the visual processing hierarchy, probably at the level of primary visual cortex. This view is supported by further experiments showing that the aftereffect exhibits partial interocular transfer but complete transfer across opposite contrast polarities. However, the aftereffect does show weak position invariance, suggesting that adaptation at higher levels of the visual system may also contribute to the effect.

Adaptation, Ocular↗

Optic-flow and egocentric-direction strategies in walking: central vs peripheral visual field.

The impact of a central or peripheral visual field loss on the vision strategy used to guide walking was determined by measuring walking paths of visually impaired participants. An immersive virtual environment was used to dissociate the expected paths of the optic-flow and egocentric-direction strategies by offsetting the walker's point of view from the actual direction of walking. Environments consisted of a goal within a forest, the goal alone, or the forest alone following a brief presentation of the goal. The first two environments allowed an evaluation of the visual information used in a goal-directed task whereas the third environment investigated the information used in a memory-guided task. Participants had either a central (CFL) or peripheral visual field loss (PFL) or were fully sighted (FS). Results showed that, for the goal-directed task, the CFL group was less influenced by optic flow than was an age-matched FS group. Optic flow decreased heading error by only 1.3 degrees (16%) in the CFL group compared to 3.6 degrees (42%) in the FS group. The PFL group showed an optic-flow influence (2.4 degrees or 26%) comparable to an older, age-matched FS group (2.9 degrees or 31%). For the memory-guided task, all but the PFL group had heading errors comparable to those obtained in the goal-alone scene, demonstrating the ability to use an egocentric-direction strategy with a stored representation of either the goal's position or an offset relative to a landmark instead of a visible goal. The paths of the PFL group veered significantly from the predicted paths of both the optic-flow and egocentric-direction strategies. The findings of this study suggest that central vision is important for using optic flow to guide walking, whereas peripheral vision is important for establishing and/or updating an accurate representation of spatial structure for navigation.

Adult↗