Minimal output sets for identifiability

Ordinary differential equation models in biology often contain a large number of parameters that must be determined from measurements by parameter estimation. For a parameter estimation procedure to be successful, there must be a unique set of parameters that can have produced the measured data. This is not the case if a model is not uniquely structurally identifiable with the given set of outputs selected as measurements. In designing an experiment for the purpose of parameter estimation, given a set of feasible but resource-consuming measurements, it is useful to know which ones must be included in order to obtain an identifiable system, or whether the system is unidentifiable from the feasible measurement set. We have developed an algorithm that, from a user-provided set of variables and parameters or functions of them assumed to be measurable or known, determines all subsets that when used as outputs give a locally structurally identifiable system and are such that any output set for which the system is structurally identifiable must contain at least one of the calculated subsets. The algorithm has been implemented in Mathematica and shown to be feasible and efficient. We have successfully applied it in the analysis of large signalling pathway models from the literature.     

Domain is a moving target for relational learning

The domain for relational learning was manipulated by varying the training set size for pigeons that had learned the same/different (S/D) concept. Six pigeons that had learned a S/D task with pairs of pictures with a set size of 1024 picture items had their training set size reduced to 8 items. Training on the reduced 8-item set was followed by transfer testing that was repeated four times. Transfer performance following reduction of the training set to 8 items was 9.2% less than it had been when the pigeons were trained with the 1024-item set, but 25.8% above chance. This partial abstract-concept learning remained constant over the four tests with novel stimuli. The results show that a broad domain established by a large expanding training set can once again become restricted by further training with a small training set.     

Structural templates for modeling homodimers

Oligomeric proteins are more abundant in nature than monomeric proteins, and involved in all biological processes. In the absence of an experimental structure, their subunits can be modeled from their sequence like monomeric proteins, but reliable procedures to build the oligomeric assembly are scarce. Template‐based methods, which start from known protein structures, are commonly applied to model subunits. We present a method to model homodimers that relies on a structural alignment of the subunits, and test it on a set of 511 target structures recently released by the Protein Data Bank, taking as templates the earlier released structures of 3108 homodimeric proteins (H‐set), and 2691 monomeric proteins that form dimer‐like assemblies in crystals (M‐set). The structural alignment identifies a H‐set template for 97% of the targets, and in half of the cases, it yields a correct model of the dimer geometry and residue–residue contacts in the target. It also identifies a M‐set template for most of the targets, and some of the crystal dimers are very similar to the target homodimers. The procedure efficiently detects homology at low levels of sequence identities, and points to erroneous quaternary structures in the Protein Data Bank. The high coverage of the target set suggests that the content of the Protein Data Bank already approaches the structural diversity of protein assemblies in nature, and that template‐based methods should become the choice method for modeling oligomeric as well as monomeric proteins.     

Evolutionary stability conditions for signaling games with costly signals

The paper investigates the class of signaling games with the following properties: (a) the interests of sender and receiver coincide, (b) different signals incur differential costs, and (c) different events (meanings/types) have different probabilities. Necessary and sufficient conditions are presented for a profile to be evolutionarily stable and neutrally stable, and for a set of profiles to be an evolutionarily stable set.The main finding is that a profile belongs to some evolutionarily stable set if and only if a maximal number of events can be reliably communicated. Furthermore, it is shown that under the replicator dynamics, a set of states with a positive measure is attracted to “sub-optimal” equilibria that do not belong to any asymptotically stable set.     

A knowledge-based move set for protein folding

The free energy landscape of protein folding is rugged, occasionally characterized by compact, intermediate states of low free energy. In computational folding, this landscape leads to trapped, compact states with incorrect secondary structure. We devised a residue-specific, protein backbone move set for efficient sampling of protein-like conformations in computational folding simulations. The move set is based on the selection of a small set of backbone dihedral angles, derived from clustering dihedral angles sampled from experimental structures. We show in both simulated annealing and replica exchange Monte Carlo (REMC) simulations that the knowledge-based move set, when compared with a conventional move set, shows statistically significant improved ability at overcoming kinetic barriers, reaching deeper energy minima, and achieving correspondingly lower RMSDs to native structures. The new move set is also more efficient, being able to reach low energy states considerably faster. Use of this move set in determining the energy minimum state and for calculating thermodynamic quantities is discussed.     

An Efficient Soft Set-Based Approach for Conflict Analysis

Conflict analysis has been used as an important tool in economic, business, governmental and political dispute, games, management negotiations, military operations and etc. There are many mathematical formal models have been proposed to handle conflict situations and one of the most popular is rough set theory. With the ability to handle vagueness from the conflict data set, rough set theory has been successfully used. However, computational time is still an issue when determining the certainty, coverage, and strength of conflict situations. In this paper, we present an alternative approach to handle conflict situations, based on some ideas using soft set theory. The novelty of the proposed approach is that, unlike in rough set theory that uses decision rules, it is based on the concept of co-occurrence of parameters in soft set theory. We illustrate the proposed approach by means of a tutorial example of voting analysis in conflict situations. Furthermore, we elaborate the proposed approach on real world dataset of political conflict in Indonesian Parliament. We show that, the proposed approach achieves lower computational time as compared to rough set theory of up to 3.9%.     

Identifying Gene Interaction Enrichment for Gene Expression Data

Gene set analysis allows the inclusion of knowledge from established gene sets, such as gene pathways, and potentially improves the power of detecting differentially expressed genes. However, conventional methods of gene set analysis focus on gene marginal effects in a gene set, and ignore gene interactions which may contribute to complex human diseases. In this study, we propose a method of gene interaction enrichment analysis, which incorporates knowledge of predefined gene sets (e.g. gene pathways) to identify enriched gene interaction effects on a phenotype of interest. In our proposed method, we also discuss the reduction of irrelevant genes and the extraction of a core set of gene interactions for an identified gene set, which contribute to the statistical variation of a phenotype of interest. The utility of our method is demonstrated through analyses on two publicly available microarray datasets. The results show that our method can identify gene sets that show strong gene interaction enrichments. The enriched gene interactions identified by our method may provide clues to new gene regulation mechanisms related to the studied phenotypes. In summary, our method offers a powerful tool for researchers to exhaustively examine the large numbers of gene interactions associated with complex human diseases, and can be a useful complement to classical gene set analyses which only considers single genes in a gene set.     

Integrative network biology: graph prototyping for co-expression cancer networks

Network-based analysis has been proven useful in biologically-oriented areas, e.g., to explore the dynamics and complexity of biological networks. Investigating a set of networks allows deriving general knowledge about the underlying topological and functional properties. The integrative analysis of networks typically combines networks from different studies that investigate the same or similar research questions. In order to perform an integrative analysis it is often necessary to compare the properties of matching edges across the data set. This identification of common edges is often burdensome and computational intensive. Here, we present an approach that is different from inferring a new network based on common features. Instead, we select one network as a graph prototype, which then represents a set of comparable network objects, as it has the least average distance to all other networks in the same set. We demonstrate the usefulness of the graph prototyping approach on a set of prostate cancer networks and a set of corresponding benign networks. We further show that the distances within the cancer group and the benign group are statistically different depending on the utilized distance measure.     

An Entangled Model for Sustainability Indicators

Nowadays the challenge for humanity is to find pathways towards sustainable development. Decision makers require a set of sustainability indicators to know if the sustainability strategies are following those pathways. There are more than one hundred sustainability indicators but they differ on their relative importance according to the size of the locality and change on time. The resources needed to follow these sustainability indicators are scarce and in some instances finite, especially in smaller regions. Therefore strategies to select set of these indicators are useful for decision makers responsible for monitoring sustainability. In this paper we propose a model for the identification and selection of a set of sustainability indicators that adequately represents human systems. In developing this model, we applied evolutionary dynamics in a space where sustainability indicators are fundamental entities interconnected by an interaction matrix. we used a fixed interaction that simulates the current context for the city of Cuernavaca, México as an example. We were able to identify and define relevant sets indicators for the system by using the Pareto principle. In this case we identified a set of sixteen sustainability indicators with more than 80% of the total strength. This set presents resilience to perturbations. For the Tangled Nature framework we provided a manner of treating different contexts (i.e., cities, counties, states, regions, countries, continents or the whole planet), dealing with small dimensions. This model provides decision makers with a valuable tool to select sustainability indicators set for towns, cities, regions, countries, continents or the entire planet according to a coevolutionary framework. The social legitimacy can arise from the fact that each individual indicator must be selected from those that are most important for the subject community.     

Assessing the implications of the loss of set‐aside for farmland birds

Between 1988 and 2007, set‐aside, a European Commission production control measure, took an average of 10% of arable farmland in the EU out of production each year. In 2007, the set‐aside rate was set to 0% and the scheme was later abandoned altogether. By assessing associations of farmland birds with set‐aside and quantifying the extent of set‐aside loss, this study aims to assess the implications of set‐aside loss for farmland bird conservation. During the lifespan of set‐aside, a large number of studies assessed the biodiversity value of set‐aside and other agricultural crops and habitats. Where possible we considered measurable benefits of set‐aside. However, some studies did not specify the type of set‐aside and in some cases set‐aside fields were grouped with cereal stubble fields. In these cases, we took the pragmatic approach of assessing the value of generic stubble fields as a conservative minimum estimate of the value of set‐aside fields. A re‐analysis of data from 30 intensive studies demonstrates that farmland bird densities tended to be higher on set‐aside than on either cereal or oilseed rape crops. Without mitigation, these are the two crops likely to replace most set‐aside fields. We estimate that 26–52% of the farmland populations of key granivorous passerines were present on stubble fields, giving an indication of the proportion of birds likely to be present on set‐aside fields within this broader category. An extensive survey of lowland farmland during winters 1999/2000, 2000/2001 and 2002/2003, repeated in February 2008, showed a doubling of the number of 1‐km squares with no stubble and a halving of the number of squares with more than 10 ha of stubble. After set‐aside abandonment, 72% of squares had no stubble in the important late winter period, confirming that many of the former stubble fields were retained as set‐aside. A simple correlative model suggests that this could cause a small increase in the rate of decline of Skylark Alauda arvensis and Yellowhammer Emberiza citrinella populations, assuming causal links between stubble area and demography. However, even if this assumption cannot be supported, these results clearly indicate that a significant proportion of some farmland bird populations will need to find alternative breeding and foraging habitats.     

A proposed max-product threshold unit for classification of pattern vectors

This paper proposes a max-product threshold unit (maptu) that can successfully perform dichotomous classifications of pattern vectors. Maptu, with weight vector, w, classifies a pattern vector, x, by comparing x max-prod w to 0.5. Results obtained by other methods in classification of benchmark data are used for comparison to the method using maptu. The benchmark data consists of the Australian credit data set, cervical cell data set, diabetes data set and the iris data set.     

Guidelines for the use and interpretation of assays for monitoring autophagy in higher eukaryotes

Research in autophagy continues to accelerate,(1) and as a result many new scientists are entering the field. Accordingly, it is important to establish a standard set of criteria for monitoring macroautophagy in different organisms. Recent reviews have described the range of assays that have been used for this purpose.(2,3) There are many useful and convenient methods that can be used to monitor macroautophagy in yeast, but relatively few in other model systems, and there is much confusion regarding acceptable methods to measure macroautophagy in higher eukaryotes. A key point that needs to be emphasized is that there is a difference between measurements that monitor the numbers of autophagosomes versus those that measure flux through the autophagy pathway; thus, a block in macroautophagy that results in autophagosome accumulation needs to be differentiated from fully functional autophagy that includes delivery to, and degradation within, lysosomes (in most higher eukaryotes) or the vacuole (in plants and fungi). Here, we present a set of guidelines for the selection and interpretation of the methods that can be used by investigators who are attempting to examine macroautophagy and related processes, as well as by reviewers who need to provide realistic and reasonable critiques of papers that investigate these processes. This set of guidelines is not meant to be a formulaic set of rules, because the appropriate assays depend in part on the question being asked and the system being used. In addition, we emphasize that no individual assay is guaranteed to be the most appropriate one in every situation, and we strongly recommend the use of multiple assays to verify an autophagic response.     

Efficient algorithms for counting and reporting segregating sites in genomic sequences.

The number of segregating sites provides an indicator of the degree of DNA sequence variation that is present in a sample, and has been of great interest to the biological, pharmaceutical and medical professions. In this paper, we first provide linear- and expected-sublinear-time algorithms for finding all the segregating sites of a given set of DNA sequences. We also describe a data structure for tracking segregating sites in a set of sequences, such that every time the set is updated with the insertion of a new sequence or removal of an existing one, the segregating sites are updated accordingly without the need to re-scan the entire set of sequences.     

Three-dimensional biofilm image reconstruction for assessing structural parameters

Parameters representing three-dimensional (3D) biofilm structure are quantified from confocal laser-scanning microscope (CLSM) images. These 3D parameters describe the distribution of biomass pixels within the space occupied by a biofilm; however, they lack a direct connection to biofilm activity. As a result, researchers choose a handful of parameters without there being a consensus on a standard set of parameters. We hypothesized that a select 3D parameter set could be used to reconstruct a biofilm image and that the reconstructed and original biofilm images would have similar activities. To test this hypothesis, an algorithm was developed to reconstruct a biofilm image with parameters identical to those of the original CLSM image. We introduced an objective method to assess the reconstruction algorithm by comparing the activities of the original and reconstructed biofilm images. We found that biofilm images with identical structural parameters showed nearly identical activities and substrate concentration profiles. This implies that the set containing all common structural parameters can successfully describe biofilm structure. This finding is significant, as it opens the door to the next step, of finding a smaller standard set of biofilm structural parameters that can be used to compare biofilm structure.     

Clustering algorithms for identifying core atom sets and for assessing the precision of protein structure ensembles

An important open question in the field of NMR-based biomolecular structure determination is how best to characterize the precision of the resulting ensemble of structures. Typically, the RMSD, as minimized in superimposing the ensemble of structures, is the preferred measure of precision. However, the presence of poorly determined atomic coordinates and multiple "RMSD-stable domains"--locally well-defined regions that are not aligned in global superimpositions--complicate RMSD calculations. In this paper, we present a method, based on a novel, structurally defined order parameter, for identifying a set of core atoms to use in determining superimpositions for RMSD calculations. In addition we present a method for deciding whether to partition that core atom set into "RMSD-stable domains" and, if so, how to determine partitioning of the core atom set. We demonstrate our algorithm and its application in calculating statistically sound RMSD values by applying it to a set of NMR-derived structural ensembles, superimposing each RMSD-stable domain (or the entire core atom set, where appropriate) found in each protein structure under consideration. A parameter calculated by our algorithm using a novel, kurtosis-based criterion, the epsilon-value, is a measure of precision of the superimposition that complements the RMSD. In addition, we compare our algorithm with previously described algorithms for determining core atom sets. The methods presented in this paper for biomolecular structure superimposition are quite general, and have application in many areas of structural bioinformatics and structural biology.     

Quantitative self-organizing maps for clustering electron tomograms

Tomography emerges as a powerful methodology for determining the complex architectures of biological specimens that are better regarded from the structural point of view as singular entities. However, once the structure of a sufficiently large number of singular specimens is solved, quite possibly structural patterns start to emerge. This latter situation is addressed here, where the clustering of a set of 3D reconstructions using a novel quantitative approach is presented. In general terms, we propose a new variant of a self-organizing neural network for the unsupervised classification of 3D reconstructions. The novelty of the algorithm lies in its rigorous mathematical formulation that, starting from a large set of noisy input data, finds a set of "representative" items, organized onto an ordered output map, such that the probability density of this set of representative items resembles at its possible best the probability density of the input data. In this study, we evaluate the feasibility of application of the proposed neural approach to the problem of identifying similar 3D motifs within tomograms of insect flight muscle. Our experimental results prove that this technique is suitable for this type of problem, providing the electron microscopy community with a new tool for exploring large sets of tomogram data to find complex patterns.     

Screening human populations for chromosome aberrations

In order to determine the usefulness of micronuclear counts (MNC) for identifying people with relatively high frequencies of chromosome aberrations we have examined factors that influence the MNC in a learning set of blood samples obtained from 28 adults. The presence of cells with chromosome aberrations among approximately 170 metaphase cells per sample was the most important factor. Controlling for the effect of chromosome aberrations we found that age had a significant effect on MNC, but that donor sex, the mitotic index, the per cent of metaphase cells in the second or third division or the frequency of abnormal anaphase cells did not. Using logistic regression analysis we found that MNC was an excellent predictor of the presence of cells with chromosome aberrations among both the learning set and a test set of 17 additional blood samples.     

A new strategy for the detection of subtelomeric rearrangements

We present a new strategy for the detection of subtelomeric rearrangements. This approach is based on two hybridizations with different probe sets. The first set consists of microdissected subtelomeric probes (each 5-10 megabases in size) labeled combinatorially employing 7 different fluorochromes. With this set, subtelomeric interchromosomal exchanges can be detected in a 24-color experiment. The second set comprises a second generation of subtelomeric PAC-, P1- and BAC-clones. Probes for p- and q-arms are labeled with two different colors. This second set detects small deletions; in addition it provides regional information, so that translocated material identified by the first probe set can be assigned to the p- or q-arm of a chromosome. The test has been evaluated in a blind study on a series of subtle translocations and deletions.