Spectral sensitivity in linear biological models

Properties of spectral components of the system matrix of linear time-invariant discrete or continuous models are investigated. It is shown that the entries in these matrices have the interpretation of being the sensitivity of the system matrix eigenvalues with respect to the model parameters. The spectral resolution formula for linear operators is used to get explicit results about component matrices and eigenvalue sensitivity. In biological modeling, particular interest is in the real maximal or minimal roots of the system matrix. Exact formulation of the related spectral components is made in important system matrix cases such as companion, Leslie, ecosystem, compartmental, and stochastic matrices.     

A framework for models of biological behaviour

Modelling is most clearly understood as a adjunct in the process of deriving predictions from hypotheses. By representing a hypothesised mechanism in a model we hope by manipulating the model to understand the hypotheses' consequences. Eight dimensions on which models of biological behaviour can vary are described: the degree of realism with which they apply to biology; the level of biology they represent; the generality or range of systems the model is supposed to cover; the abstraction or amount of biological detail represented; the accuracy of representation of the mechanisms; the medium in which the model is built; the match of the model behaviour to biological behaviour; and the utility of the model in providing biological understanding and/or technical insight. It is hoped this framework will help to clarify debates over different approaches to modelling, particularly by pointing out how the above dimensions are relatively independent and should not be conflated.     

Structural sensitivity of biological models revisited

Enhancing the predictive power of models in biology is a challenging issue. Among the major difficulties impeding model development and implementation are the sensitivity of outcomes to variations in model parameters, the problem of choosing of particular expressions for the parametrization of functional relations, and difficulties in validating models using laboratory data and/or field observations. In this paper, we revisit the phenomenon which is referred to as structural sensitivity of a model. Structural sensitivity arises as a result of the interplay between sensitivity of model outcomes to variations in parameters and sensitivity to the choice of model functions, and this can be somewhat of a bottleneck in improving the models predictive power. We provide a rigorous definition of structural sensitivity and we show how we can quantify the degree of sensitivity of a model based on the Hausdorff distance concept. We propose a simple semi-analytical test of structural sensitivity in an ODE modeling framework. Furthermore, we emphasize the importance of directly linking the variability of field/experimental data and model predictions, and we demonstrate a way of assessing the robustness of modeling predictions with respect to data sampling variability. As an insightful illustrative example, we test our sensitivity analysis methods on a chemostat predator-prey model, where we use laboratory data on the feeding of protozoa to parameterize the predator functional response.     

A framework for structural equation models in general pedigrees

Background/Aims: Structural Equation Modeling (SEM) is an analysis approach that accounts for both the causal relationships between variables and the errors associated with the measurement of these variables. In this paper, a framework for implementing structural equation models (SEMs) in family data is proposed. Methods: This framework includes both a latent measurement model and a structural model with covariates. It allows for a wide variety of models, including latent growth curve models. Environmental, polygenic and other genetic variance components can be included in the SEM. Kronecker notation makes it easy to separate the SEM process from a familial correlation model. A limited information method of model fitting is discussed. We show how missing data and ascertainment may be handled. We give several examples of how the framework may be used. Results: A simulation study shows that our method is computationally feasible, and has good statistical properties. Conclusion: Our framework may be used to build and compare causal models using family data without any genetic marker data. It also allows for a nearly endless array of genetic association and/or linkage tests. A preliminary Matlab program is available, and we are currently implementing a more complete and user-friendly R package.     

Defining and detecting crossover-interference mutants in yeast

The analysis of crossover interference in many creatures is complicated by the presence of two kinds of crossovers, interfering and noninterfering. In such creatures, the values of the traditional indicators of interference are subject not only to the strength of interference but also to the relative frequencies of crossing over contributed by the two kinds. We formalize the relationship among these variables and illustrate the possibilities and limitations of classical interference analysis with meiotic tetrad data from wild-type Saccharomyces cerevisiae and from mlh1 and ndj1 mutants.     

Driving reservoir models with oscillations: a solution to the extreme structural sensitivity of chaotic networks

A large body of experimental and theoretical work on neural coding suggests that the information stored in brain circuits is represented by time-varying patterns of neural activity. Reservoir computing, where the activity of a recurrently connected pool of neurons is read by one or more units that provide an output response, successfully exploits this type of neural activity. However, the question of system robustness to small structural perturbations, such as failing neurons and synapses, has been largely overlooked. This contrasts with well-studied dynamical perturbations that lead to divergent network activity in the presence of chaos, as is the case for many reservoir networks. Here, we distinguish between two types of structural network perturbations, namely local (e.g., individual synaptic or neuronal failure) and global (e.g., network-wide fluctuations). Surprisingly, we show that while global perturbations have a limited impact on the ability of reservoir models to perform various tasks, local perturbations can produce drastic effects. To address this limitation, we introduce a new architecture where the reservoir is driven by a layer of oscillators that generate stable and repeatable trajectories. This model outperforms previous implementations while being resistant to relatively large local and global perturbations. This finding has implications for the design of reservoir models that capture the capacity of brain circuits to perform cognitively and behaviorally relevant tasks while remaining robust to various forms of perturbations. Further, our work proposes a novel role for neuronal oscillations found in cortical circuits, where they may serve as a collection of inputs from which a network can robustly generate complex dynamics and implement rich computations.     

Defining fitness in evolutionary models

The analysis of evolutionary models requires an appropriate definition for fitness. In this paper, I review such definitions in relation to the five major dimensions by which models may be described, namely (i) finite versus infinite (or very large) population size, (ii) type of environment (constant, fixed length, temporally stochastic, temporally predictable, spatially stochastic, spatially predictable and social environment), (iii) density-independent or density-dependent, (iv) inherent population dynamics (equilibrium, cyclical and chaotic), and (v) frequency-dependent or independent. In simple models, the Malthusian parameter ‘r’ or the net reproductive rate R ₀ may be satisfactory, but once density-dependence or complex population dynamics is introduced the invasion exponent should be used. Defining fitness in a social environment or when there is frequency-dependence requires special consideration.     

Catch bonds: physical models, structural bases, biological function and rheological relevance

Force can shorten the lifetimes of macromolecular complexes (e.g., receptor-ligand bonds) by accelerating their dissociation. Perhaps paradoxical at first glance, bond lifetimes can also be prolonged by force. This counterintuitive behavior was named catch bonds, which is in contrast to the ordinary slip bonds that describe the intuitive behavior of lifetimes being shortened by force. Fifteen years after their theoretical proposal, catch bonds have finally been observed. In this article we review recently published data that have demonstrated catch bonds in the selectin system and suggested catch bonds in other systems, the theoretical models for their explanations, possible structural bases, their relation to flow-enhanced adhesion, and the potential biorheological relevance.     

LUMPY: a probabilistic framework for structural variant discovery

Comprehensive discovery of structural variation (SV) from whole genome sequencing data requires multiple detection signals including read-pair, split-read, read-depth and prior knowledge. Owing to technical challenges, extant SV discovery algorithms either use one signal in isolation, or at best use two sequentially. We present LUMPY, a novel SV discovery framework that naturally integrates multiple SV signals jointly across multiple samples. We show that LUMPY yields improved sensitivity, especially when SV signal is reduced owing to either low coverage data or low intra-sample variant allele frequency. We also report a set of 4,564 validated breakpoints from the NA12878 human genome. https://github.com/arq5x/lumpy-sv.     

Lipid-protein interactions in biological membranes: a structural perspective

Lipid molecules bound to membrane proteins are resolved in some high-resolution structures of membrane proteins. An analysis of these structures provides a framework within which to analyse the nature of lipid-protein interactions within membranes. Membrane proteins are surrounded by a shell or annulus of lipid molecules, equivalent to the solvent layer surrounding a water-soluble protein. The lipid bilayer extends right up to the membrane protein, with a uniform thickness around the protein. The surface of a membrane protein contains many shallow grooves and protrusions to which the fatty acyl chains of the surrounding lipids conform to provide tight packing into the membrane. An individual lipid molecule will remain in the annular shell around a protein for only a short period of time. Binding to the annular shell shows relatively little structural specificity. As well as the annular lipid, there is evidence for other lipid molecules bound between the transmembrane alpha-helices of the protein; these lipids are referred to as non-annular lipids. The average thickness of the hydrophobic domain of a membrane protein is about 29 A, with a few proteins having significantly smaller or greater thicknesses than the average. Hydrophobic mismatch between a membrane protein and the surrounding lipid bilayer generally leads to only small changes in membrane thickness. Possible adaptations in the protein to minimise mismatch include tilting of the helices and rotation of side chains at the ends of the helices. Packing of transmembrane alpha-helices is dependent on the chain length of the surrounding phospholipids. The function of membrane proteins is dependent on the thickness of the surrounding lipid bilayer, sometimes on the presence of specific, usually anionic, phospholipids, and sometimes on the phase of the phospholipid.     

Lipid-protein interactions in biological membranes: a structural perspective

Lipid molecules bound to membrane proteins are resolved in some high-resolution structures of membrane proteins. An analysis of these structures provides a framework within which to analyse the nature of lipid-protein interactions within membranes. Membrane proteins are surrounded by a shell or annulus of lipid molecules, equivalent to the solvent layer surrounding a water-soluble protein. The lipid bilayer extends right up to the membrane protein, with a uniform thickness around the protein. The surface of a membrane protein contains many shallow grooves and protrusions to which the fatty acyl chains of the surrounding lipids conform to provide tight packing into the membrane. An individual lipid molecule will remain in the annular shell around a protein for only a short period of time. Binding to the annular shell shows relatively little structural specificity. As well as the annular lipid, there is evidence for other lipid molecules bound between the transmembrane α-helices of the protein; these lipids are referred to as non-annular lipids. The average thickness of the hydrophobic domain of a membrane protein is about 29 Å, with a few proteins having significantly smaller or greater thicknesses than the average. Hydrophobic mismatch between a membrane protein and the surrounding lipid bilayer generally leads to only small changes in membrane thickness. Possible adaptations in the protein to minimise mismatch include tilting of the helices and rotation of side chains at the ends of the helices. Packing of transmembrane α-helices is dependent on the chain length of the surrounding phospholipids. The function of membrane proteins is dependent on the thickness of the surrounding lipid bilayer, sometimes on the presence of specific, usually anionic, phospholipids, and sometimes on the phase of the phospholipid.     

Vertebrate animal models of glioma: Understanding the mechanisms and developing new therapies

Glioblastoma Multiforme (GBM) is recognized as one of the most deadly cancers characterized by cellular atypia, severe necrosis, and high rate of angiogenesis. In this review, we discuss a diversified group of GBM xenograft models and compare them with the genetically engineered mouse (GEM) model systems. Next, we describe common genetic defects observed in GBM and numerous GEM models that recapitulate these abnormalities. Finally, we focus on the clinical value of other vertebrate animal models such as the canine model by examining their contributions to GBM research.     

'Genomemark': detecting word periodicity in biological sequences

Identifying and predicting the structural characteristics of novel repeats throughout the genome can lend insight into biological function. Specific repeats are believed to have biological significance as a function of their distribution patterns. We have developed 'GenomeMark,' a computer program that detects and statistically analyzes candidate repeats. Specifically, 'GenomeMark' identifies the periodic distribution of unique words, calculating their chi2 and Z-score values. Using 'GenomeMark,' we identified novel sequence words present in tandem throughout genomes. We found that these sequences have remarkable spacer sequence distributions and many were genome specific, validating the genome signature theory. Further analysis confirmed that many of these sequences have a specific biological function. The program is available from the authors upon request and is freely available for non-commercial and academic entities.     

LFM-Pro: a tool for detecting significant local structural sites in proteins

MOTIVATION: The rapidly growing protein structure repositories have opened up new opportunities for discovery and analysis of functional and evolutionary relationships among proteins. Detecting conserved structural sites that are unique to a protein family is of great value in identification of functionally important atoms and residues. Currently available methods are computationally expensive and fail to detect biologically significant local features. RESULTS: We propose Local Feature Mining in Proteins (LFM-Pro) as a framework for automatically discovering family-specific local sites and the features associated with these sites. Our method uses the distance field to backbone atoms to detect geometrically significant structural centers of the protein. A feature vector is generated from the geometrical and biochemical environment around these centers. These features are then scored using a statistical measure, for their ability to distinguish a family of proteins from a background set of unrelated proteins, and successful features are combined into a representative set for the protein family. The utility and success of LFM-Pro are demonstrated on trypsin-like serine proteases family of proteins and on a challenging classification dataset via comparison with DALI. The results verify that our method is successful both in identifying the distinctive sites of a given family of proteins, and in classifying proteins using the extracted features. AVAILABILITY: The software and the datasets are freely available for academic research use at http://bioinfo.ceng.metu.edu.tr/Pub/LFMPro.