Clusters,factories and domains

During S-phase of the cell cycle, chromosomal DNA is replicated according to a complex replication timing program, with megabase-sized domains replicating at different times. DNA fibre analysis reveals that clusters of adjacent replication origins fire near-synchronously. Analysis of replicating cells by light microscopy shows that DNA synthesis occurs in discrete foci or factories. The relationship between timing domains, origin clusters and replication foci is currently unclear. Recent work, using a hybrid Xenopus/hamster replication system, has shown that when CDK levels are manipulated during S-phase the activation of replication factories can be uncoupled from progression through the replication timing program. Here, we use data from this hybrid system to investigate potential relationships between timing domains, origin clusters and replication foci. We suggest that each timing domain typically comprises several replicon clusters, which are usually processed sequentially by replication factories. We discuss how replication might be regulated at different levels to create this complex organisation and the potential involvement of CDKs in this process.     

Two-criteria model assessment shows that foliage maintenance in old-growth Pseudotsuga menziesii requires both delayed and sequential reiteration

Functional structural models (FSMs) are valuable tools to explore relationships between plant form and function, yet they lack rigorous methods for development and assessment. We use multi-criteria assessment of an architectural FSM to show that both traumatic sequential and adaptive delayed reiteration (ADR) are necessary components of foliage maintenance in branches of old-growth Pseudotsuga menziesii. ADR has previously been established as a process that maintains foliage in old-growth P. menziesii. We use a simulation model of branch development in the species to evaluate morphogenesis in the context of this ADR. The structure of the model is a theoretical representation of how P. menziesii branch morphology develops throughout the branch lifespan, and this model structure is assessed with two criteria that are optimized simultaneously; the criteria measure foliage demography by the number of foliated shoots, and how those foliated shoots are organized into independent clusters. Assessment results indicated that improvements in model structure were required. Anomalous parameter vectors from the assessment search uncovered an inadequacy in the process of foliage maintenance, and the model was modified to include traumatic sequential reiteration in addition to ADR. The modes of the resulting parameter distributions were consistent with empirical observations. We discuss why the assessment of FSMs is an essential procedure that requires multiple criteria.     

RECOGNITION OF TAXONOMICALLY SIGNIFICANT CLUSTERS NEAR THE SPECIES LEVEL,USING COMPUTATIONALLY INTENSE METHODS,WITH EXAMPLES FROM THE STEPHANODISCUS NIAGARAE COMPLEX (BACILLARIOPHYCEAE)1

Since the early 1960s, numerical techniques have produced a wide variety of methods to suggest classifications of organisms based on quantitative measurements. A long-recognized shortcoming of these methods is that they will suggest classifications for any group of organisms and any set of measurements, whether or not the clusters in the suggested classification have any natural meaning or significance. Some progress has been made in assessing the reality of clusters determined by various methods. Data simulated to reflect known cluster structure have been used to test the accuracy of different methods, Various methods have been applied to the same data sets to compare how well they realize various desirable properties. Here we define a data-based model of randomness to represent what might be meant by “no natural basis for subdivision into clusters” and use it to compare an observed measure of cluster distinctness to the distribution of this measure predicted by this model of randomness. In this way, unwarranted subdivision can be statistically avoided, and significant subdivisions can be investigated with confidence. Our methods are illustrated with some examples from the Stephanodiscus niagarae Ehrenb. species complex. Significant differences in morphologic expression are identified in S. reimerii Theriot and Stoermer in Theriot, S. superiorensis Theriot and Stoermer and S. yellowstonensis Theriot and Stoermer. In addition, statistically significant clusters are identified in S. niagarae populations from different geographic locations and in members of the same population grown in different environments. These results suggest current criteria for resolving diatom taxa may not be sufficient to discern subtle differences that occur between real species.     

Biofilm image reconstruction for assessing structural parameters

The structure of biofilms can be numerically quantified from microscopy images using structural parameters. These parameters are used in biofilm image analysis to compare biofilms, to monitor temporal variation in biofilm structure, to quantify the effects of antibiotics on biofilm structure and to determine the effects of environmental conditions on biofilm structure. It is often hypothesized that biofilms with similar structural parameter values will have similar structures; however, this hypothesis has never been tested. The main goal was to test the hypothesis that the commonly used structural parameters can characterize the differences or similarities between biofilm structures. To achieve this goal (1) biofilm image reconstruction was developed as a new tool for assessing structural parameters, (2) independent reconstructions using the same starting structural parameters were tested to see how they differed from each other, (3) the effect of the original image parameter values on reconstruction success was evaluated, and (4) the effect of the number and type of the parameters on reconstruction success was evaluated. It was found that two biofilms characterized by identical commonly used structural parameter values may look different, that the number and size of clusters in the original biofilm image affect image reconstruction success and that, in general, a small set of arbitrarily selected parameters may not reveal relevant differences between biofilm structures.     

Bismuth autometallography: protocol, specificity, and differentiation.

We provide a detailed protocol of the autometallographic bismuth technique and evaluate the specificity of the technique. We show by the multi-element technique "proton-induced X-ray microanalysis" (PIXE) that the autometallographic grains contain silver, bismuth, and sulfur, proving that autometallography can be used for specific tracing of bismuth bound as bismuth sulfide clusters in tissue sections from Bi-exposed animals or humans. In sections from animals exposed concurrently to selenium and bismuth, the autometallographic grains also contain selenium. This demonstrates that, if present in excess in the organisms, selenium will bind to exogenous bismuth, creating bismuth selenide clusters. As a further possible control for specificity and as a tool for differentiating among autometallographically detectable metals in sections containing more than one, we describe how bismuth sulfide clusters can be removed from Epon-embedded tissue sections by potassium cyanide.     

Genetic structure and assignment tests demonstrate illegal translocation of red deer (Cervus elaphus) into a continuous population

Molecular forensic methods are being increasingly used to help enforce wildlife conservation laws. Using multilocus genotyping, illegal translocation of an animal can be demonstrated by excluding all potential source populations as an individual's population of origin. Here, we illustrate how this approach can be applied to a large continuous population by defining the population genetic structure and excluding suspect animals from each identified cluster. We aimed to test the hypothesis that recreational hunters had illegally introduced a group of red deer into a hunting area in Luxembourg. Reference samples were collected over a large area in order to test the possibility that the suspect individuals might be recent immigrants. Due to isolation-by-distance relationships in the data set, inferring the number of genetic clusters using Bayesian methods was not straightforward. Biologically meaningful clusters were only obtained by simultaneously analysing spatial and genetic information using the program baps 4.1. We inferred the presence of three genetic clusters in the study region. Using partial Mantel tests, we detected barriers to gene flow other than distance, probably created by a combination of urban areas, motorways and a river valley used for viticulture. The four focal animals could be excluded with a high certainty from the three genetic subpopulations and it was therefore likely that they had been released illegally.     

Structural sensitivity and resilience in a predator–prey model with density-dependent mortality

Numerous formulations with the same mathematical properties can be relevant to model a biological process. Different formulations can predict different model dynamics like equilibrium vs. oscillations even if they are quantitatively close (structural sensitivity). The question we address in this paper is: does the choice of a formulation affect predictions on the number of stable states? We focus on a predator–prey model with predator competition that exhibits multiple stable states. A bifurcation analysis is realized with respect to prey carrying capacity and species body mass ratio within range of values found in food web models. Bifurcation diagrams built for two type-II functional responses are different in two ways. First, the kind of stable state (equilibrium vs. oscillations) is different for 26.0–49.4% of the parameter values, depending on the parameter space investigated. Using generalized modelling, we highlight the role of functional response slope in this difference. Secondly, the number of stable states is higher with Ivlev's functional response for 0.1–14.3% of the parameter values. These two changes interact to create different model predictions if a parameter value or a state variable is altered. In these two examples of disturbance, Holling's disc equation predicts a higher system resilience. Indeed, Ivlev's functional response predicts that disturbance may trap the system into an alternative stable state that can be escaped from only by a larger alteration (hysteresis phenomena). Two questions arise from this work: (i) how much complex ecological models can be affected by this sensitivity to model formulation? and (ii) how to deal with these uncertainties in model predictions?     

Trapping by Clusters of Channels,Receptors, and Transporters: Quantitative Description

Various membrane functional units such as receptors, transporters, and channels, whose action necessarily involves capturing diffusing molecules, are often organized into multimeric complexes forming clusters on the cell and organelle membranes. These functional units themselves are usually oligomers of several integral proteins, which have their own symmetry. Depending on the symmetry, they form clusters on different packing lattices. Moreover, local membrane inhomogeneities, e.g., the so-called membrane domains, rafts, stalks, etc., lead to different patterns even within the structures on the same packing lattice. Units in the cluster compete for diffusing molecules and screen each other. Here we propose a general approach that allows one to quantify the screening effects. The approach is used to derive simple approximate formulas giving the trapping rates of diffusing molecules by clusters of absorbers on lattices of different packing symmetries. The obtained results describe smooth variation of the trapping rate from the sum of the rates of individual absorbers forming the cluster to the effective collective rate. The latter shows how the trapping efficiency of an individual absorber decreases as the number of absorbers in the cluster increases and/or the inter-absorber distance decreases. Numerical tests demonstrate good agreement between the rates predicted by the theory and obtained from Brownian dynamics simulations for clusters of different shapes and sizes.     

Parameter redundancy in mark‐recovery models

We provide a definitive guide to parameter redundancy in mark‐recovery models, indicating, for a wide range of models, in which all the parameters are estimable, and in which models they are not. For these parameter‐redundant models, we identify the parameter combinations that can be estimated. Simple, general results are obtained, which hold irrespective of the duration of the studies. We also examine the effect real data have on whether or not models are parameter redundant, and show that results can be robust even with very sparse data. Covariates, as well as time‐ or age‐varying trends, can be added to models to overcome redundancy problems. We show how to determine, without further calculation, whether or not parameter‐redundant models are still parameter redundant after the addition of covariates or trends.     

Trapping by Clusters of Channels,Receptors, and Transporters: Quantitative Description

Various membrane functional units such as receptors, transporters, and channels, whose action necessarily involves capturing diffusing molecules, are often organized into multimeric complexes forming clusters on the cell and organelle membranes. These functional units themselves are usually oligomers of several integral proteins, which have their own symmetry. Depending on the symmetry, they form clusters on different packing lattices. Moreover, local membrane inhomogeneities, e.g., the so-called membrane domains, rafts, stalks, etc., lead to different patterns even within the structures on the same packing lattice. Units in the cluster compete for diffusing molecules and screen each other. Here we propose a general approach that allows one to quantify the screening effects. The approach is used to derive simple approximate formulas giving the trapping rates of diffusing molecules by clusters of absorbers on lattices of different packing symmetries. The obtained results describe smooth variation of the trapping rate from the sum of the rates of individual absorbers forming the cluster to the effective collective rate. The latter shows how the trapping efficiency of an individual absorber decreases as the number of absorbers in the cluster increases and/or the inter-absorber distance decreases. Numerical tests demonstrate good agreement between the rates predicted by the theory and obtained from Brownian dynamics simulations for clusters of different shapes and sizes.     

Silhouette width using generalized mean—A flexible method for assessing clustering efficiency

Cluster analysis plays vital role in pattern recognition in several fields of science. Silhouette width is a widely used index for assessing the fit of individual objects in the classification, as well as the quality of clusters and the entire classification. Silhouette combines two clustering criteria, compactness and separation, which imply that spherical cluster shapes are preferred over others—a property that can be seen as a disadvantage in the presence of complex, nonspherical clusters, which is common in real situations. We suggest a generalization of the silhouette width using the generalized mean. By changing the p parameter of the generalized mean between ?∞ and +∞, several specific summary statistics, including the minimum, maximum, the arithmetic, harmonic, and geometric means, can be reproduced. Implementing the generalized mean in the calculation of silhouette width allows for changing the sensitivity of the index to compactness versus connectedness. With higher sensitivity to connectedness, the preference of silhouette width toward spherical clusters should reduce. We test the performance of the generalized silhouette width on artificial data sets and on the Iris data set. We examine how classifications with different numbers of clusters prepared by different algorithms are evaluated, if p is set to different values. When p was negative, well‐separated clusters achieved high silhouette widths despite their elongated or circular shapes. Positive values of p increased the importance of compactness; hence, the preference toward spherical clusters became even more detectable. With low p, single linkage clustering was deemed the most efficient clustering method, while with higher parameter values the performance of group average, complete linkage, and beta flexible with beta = ?0.25 seemed better. The generalized silhouette allows for adjusting the contribution of compactness and connectedness criteria, thus avoiding underestimation of clustering efficiency in the presence of clusters with high internal heterogeneity.     

How seals divide up the world: environment, life history, and conservation

Pinnipeds display a remarkable variation in life history adaptations while successfully inhabiting almost every marine environment. We explore how they have done this by grouping the world’s pinniped species according to their environmental conditions, mating systems, lactation strategies, and timing of life histories. Next, we tested whether any of these clusters provide information about risk of extinction (using the International Union for Nature and the Conservation of Natural Resources status ranks). Seals at risk were not characterized by differences in lactation pattern (22% short vs. 46% long), mating system (24% multi-male vs. 35% harems), or timing of life history events (23% fast vs. 42% slow) but did differ based on four environmental groupings. Grouping traits (rather than seals) described two clusters: one that included the environmental trait, primary productivity, and a second one that included all other environmental variables (seasonality, latitude, and temperature). Based on this result and theoretical considerations, we plotted seals according to energy (primary productivity) and variation (seasonality) and found a pattern analogous to that of the same four groups determined by cluster analysis of all environmental variables. Of the two pinniped groups representing low variation (equatorial and high productivity), ten of 21 seal species have been designated at risk, in contrast to none of the 13 seal species adapted to high variation. We conclude that seals appear to be best adapted to seasonal environments and thus, conservation efforts may benefit by concentrating on species inhabiting less variable environments.     

Stability of two cluster solutions in pulse coupled networks of neural oscillators

Phase response curves (PRCs) have been widely used to study synchronization in neural circuits comprised of pacemaking neurons. They describe how the timing of the next spike in a given spontaneously firing neuron is affected by the phase at which an input from another neuron is received. Here we study two reciprocally coupled clusters of pulse coupled oscillatory neurons. The neurons within each cluster are presumed to be identical and identically pulse coupled, but not necessarily identical to those in the other cluster. We investigate a two cluster solution in which all oscillators are synchronized within each cluster, but in which the two clusters are phase locked at nonzero phase with each other. Intuitively, one might expect this solution to be stable only when synchrony within each isolated cluster is stable, but this is not the case. We prove rigorously the stability of the two cluster solution and show how reciprocal coupling can stabilize synchrony within clusters that cannot synchronize in isolation. These stability results for the two cluster solution suggest a mechanism by which reciprocal coupling between brain regions can induce local synchronization via the network feedback loop.