Discovering topological motifs using a compact notation.

Discovering topological motifs or common topologies in one or more graphs is an important as well as an interesting problem. It had been classically viewed as the subgraph isomorphism problem. This problem and its various flavors are known to be NP-Complete. However, this does not minimize the importance of solving this problem accurately in application areas such as bioinformatics or even larger network studies. The explosion in the size of the output is usually caused by isomorphisms in the motif or graph: we present a method to handle this without sacrificing the correct answers. In this paper, we apply the natural notion of maximality, used extensively in strings, to graphs and present a simple three-step approach to solving this problem completely and exactly (without resorting to heuristics). We handle the natural combinatorial explosion due to isomorphisms inherent in the problem (which could result in output size being exponential in the input size) by the use of "compact location lists." In other words, instead of enumerating k elements out of n, we use the ((n)(k)) form in an implicit manner (k immediate neighbors of a vertex out of n possible immediate neighbors). This drastically reduces the size of the output without any loss of information. The algorithm we present is linear in terms of the size of the output encoded as compact lists.     

Correction for missed events based on a realistic model of a detector.

Quantitative patch-clamp analysis based on dwell-time histograms has to deal with the problem of missed events. The correction of the evaluated time constants has to take into account the characteristics of the detector used for the reconstruction of the time series. In previous approaches a simple model of the detector has been used, which is based on the assumption that all events shorter than the temporal resolution tres were missed, irrespective of the preceding events. Rather than the standard assumption of a fixed dead time, we introduce a more realistic model of a detector by a continuous-time version of the Hinkley detector. The combined state of the channel and the detector obeys a Markov model, which is governed by a Fokker-Planck-Kolmogorov partial differential equation. The steady-state solution leads to the determination of the apparent time constants tau o and tau c depending on the true rate constants koc and kco and the temporal resolution tres of the detector. Simulations with different kinds of detectors, including the Bessel filter with half-amplitude threshold detection, are performed. They show that our new equation predicts the dependence of tau c and tau o on koc, kco, and tres better than the standard equation used until now.     

基于对数线性模型的酵母基因转录调控模体分析

识别真核基因的转录因子结合位点(或称模体)是后基因组时代的一项主要工作,对共表达或共调控的基因同时进行分析可以提高模体识别的准确性.本文基于2×2列联表的对数线性模型,以模体出现的基因条数计数,对酵母核糖体蛋白(RP)基因普遍使用的转录调控模体进行分析,然后用U-检验进一步筛选出相对于背景序列来说过表达的模体.这些模体为酵母RP基因潜在的转录调控元件,与实验获得的转录因子结合位点的符合率达90%.本方法的优点在于用严格的统计标准在一组基因启动子中搜索普遍使用的模体,克服了以往分析中对模体使用普遍性的模糊判断.本文的方法也可以有效地搜索共表达基因族的组合调控模体对.研究中还发现一个现象:2×2列联表中反映属性相关程度的Pearson相关系数与对数线性模型的交互效应之间存在着明显的相关性.这一结果提示,可以用对数线性模型的交互效应来评价两属性的关联情况.     

Respiratory flow in a realistic tracheostenosis model

The possible mechanism of wheeze generation in tracheostenosis was identified by measuring inspiratory and expiratory flow in a "morphological and distensible" realistic tracheostenosis model. The shape of the model was based on CT (Computed Tomography) images of a patient that had tracheostenosis. A trachea consists of tracheal cartilage rings and smooth muscle. Spatial variation of wall distensibility was achieved in the model by varying the wall thickness based on the elastic modulus measured in pig airways. The spatial variation influenced the flow in the airway and the turbulence production rate decreased faster at smooth muscles. Using the model, we investigated the mechanism of wheeze generation by focusing on the turbulence intensity. The turbulence intensity in expiratory flow was about twice that in inspiratory flow, and larger vortices existed in post-stenosis in expiratory flow, and thus might contribute to wheeze generation.     

A computer based model for realistic simulations of neural networks

The use of computer simulations as a neurophysiological tool creates new possibilities to understand complex systems and to test whether a given model can explain experimental findings. Simulations, however, require a detailed specification of the model, including the nerve cell action potential and synaptic transmission. We describe a neuron model of intermediate complexity, with a small number of compartments representing the soma and the dendritic tree, and equipped with Na⁺, K⁺, Ca²⁺, and Ca²⁺ dependent K⁺ channels. Conductance changes in the different compartments are used to model conventional excitatory and inhibitory synaptic interactions. Voltage dependent NMDA-receptor channels are also included, and influence both the electrical conductance and the inflow of Ca²⁺ ions. This neuron model has been designed for the analysis of neural networks and specifically for the simulation of the network generating locomotion in a simple vertebrate, the lamprey. By assigning experimentally established properties to the simulated cells and their synapses, it has been possible to verify the sufficiency of these properties to account for a number of experimental findings of the network in operation. The model is, however, sufficiently general to be useful for realistic simulation also of other neural systems.     

Towards a more biologically realistic use of Droop's equations to model growth under multiple nutrient limitation

Droop's model was originally designed to describe the growth of unicellular phytoplankton species in chemostats but it is now commonly used for a variety of organisms in models of trophic interactions, ecosystem functioning, and evolution. Despite its ubiquitous use, Droop's model is still limited by several simplifying assumptions. For example, the assumption of equal theoretical maximum growth rates for all nutrients is commonly used to describe growth limited by multiple nutrients. This assumption, however, is both biologically unrealistic and potentially misleading. We propose the alternative hypothesis of equal realized maximum growth rates for all nutrients. We support our hypothesis with empirical and theoretical arguments and discuss how it may improve our understanding of the biology of growth, while avoiding some of the pitfalls of the previous assumption.     

Protein precipitation by polyethylene glycol: a generalized model based on hydrodynamic radius

PEGs for protein precipitation are usually classified by molecular weight. The higher molecular weight precipitants are more efficient but result in higher viscosity. Following empirical evidence that the precipitation efficiency is more comprehensively characterized by PEG hydrodynamic radius (r_h,PEG) than molecular weight, this paper proposes a model to explicate the significance of r_h,PEG. A general expression was formulated to characterize the PEG effect exclusively by r_h,PEG. The coefficients of a linearized form were then fitted using empirical solubility data. The result is a simple numerical relation that models the efficiency of general-shaped PEG precipitants as a function of r_h,PEG and protein hydrodynamic radius (r_h,prot). This equation also explains the effects of environmental conditions and PEG branching. While predictions by the proposed correlation agree reasonably well with independent solubility data, its simplicity gives rise to potential quantitative deviations when involving small proteins, large proteins and protein mixtures. Nonetheless, the model offers a new insight into the precipitation mechanism by clarifying the significance of r_h,PEG. This in turn helps to refine the selection criterion for PEG precipitants.     

Chimeric HTH motifs based on EF-hands

The design of a new peptide construct from two structurally equivalent basis motifs is reported. A chimera was designed from the helical regions of a helix-turn-helix (HTH) domain, incorporating the consensus EF-hand Ca-binding loop at the turn. Two 33-residue peptides were constructed: one (P3, designed) includes the 12-residue consensus EF-hand loop, while the other (P2, control) contains the reversed EF-hand loop sequence. The Eu(III) and Ca(II) binding properties of P2 and P3 were investigated by circular dichroism and NMR. The designed peptide (P3) is 25% helical in its Eu(III)-saturated form, and 14% helical with excess Ca(II). Both the free and Eu-bound peptides have inherent solution structure, as demonstrated by the helicity induced by the addition of trifluoroethanol solvent. While Eu(III) binding stabilizes the structure of P3, it destabilizes the structure of P2. The NMR titration of P3 with Eu(III) resulted in new resonances characteristic of Ca-bound EF-hand loops. As observed for isolated EF-hands, the resonances appear within the first 0.5 equivalents of Eu(III) added, suggesting that one metal ion organizes two equivalents of peptide to fold into the back-to-back dimer structure of native EF-hands. The EuP3 chimera, but not EuP2, has significant affinity for supercoiled plasmid DNA, causing a gel shift at concentrations as low as 10 microM EuP3 (50 microM base pairs). These results show our chimeric peptide combines the characteristics of the parent motifs, maintaining both metal binding and DNA affinity.     

The generalized multiplicative model for viability selection at multiple loci

Selection due to differential viability is studied in an n-locus two-allele model using a set indexation that allows the simplicity of the one-locus two-allele model to be carried to multi-locus models. The existence condition is analyzed for polymorphic equilibria with linkage equilibrium: Robbins' equilibria. The local stability condition is given for the Robbins' equilibria on the boundaries in the generalized non-epistatic selection regimes of Karlin and Liberman (1979). These generalized non-epistatic regimes include the additive selection model, the multiplicative selection model and the multiplicative interaction model, and their symmetric versions cover all the symmetric viability models.Research supported by grant no. 11-7805 from the Danish Natural Science Research Council, by NIH grant GM 28016, by a fellowship from the Research Foundation of Aarhus University, and by a visiting fellowship from the University of New England, N.S.W.     

Discrete breathers in a realistic coarse-grained model of proteins

We report the results of molecular dynamics simulations of an off-lattice protein model featuring a physical force-field and amino-acid sequence. We show that localized modes of nonlinear origin, discrete breathers (DBs), emerge naturally as continuations of a subset of high-frequency normal modes residing at specific sites dictated by the native fold. DBs are time-periodic, space-localized vibrational modes that exist generically in nonlinear discrete systems and are known for their resilience and ability to concentrate energy for long times. In the case of the small β-barrel structure that we consider, DB-mediated localization occurs on the turns connecting the strands. At high energies, DBs stabilize the structure by concentrating energy on a few sites, while their collapse marks the onset of large-amplitude fluctuations of the protein. Furthermore, we show how breathers develop as energy-accumulating centres following perturbations even at distant locations, thus mediating efficient and irreversible energy transfers. Remarkably, due to the presence of angular potentials, the breather induces a local static distortion of the native fold. Altogether, the combination of these two nonlinear effects may provide a ready means for remotely controlling local conformational changes in proteins.     

Discovering relational-based association rules with multiple minimum supports on microarray datasets

MOTIVATION: Association rule analysis methods are important techniques applied to gene expression data for finding expression relationships between genes. However, previous methods implicitly assume that all genes have similar importance, or they ignore the individual importance of each gene. The relation intensity between any two items has never been taken into consideration. Therefore, we proposed a technique named REMMAR (RElational-based Multiple Minimum supports Association Rules) algorithm to tackle this problem. This method adjusts the minimum relation support (MRS) for each gene pair depending on the regulatory relation intensity to discover more important association rules with stronger biological meaning. RESULTS: In the actual case study of this research, REMMAR utilized the shortest distance between any two genes in the Saccharomyces cerevisiae gene regulatory network (GRN) as the relation intensity to discover the association rules from two S.cerevisiae gene expression datasets. Under experimental evaluation, REMMAR can generate more rules with stronger relation intensity, and filter out rules without biological meaning in the protein-protein interaction network (PPIN). Furthermore, the proposed method has a higher precision (100%) than the precision of reference Apriori method (87.5%) for the discovered rules use a literature survey. Therefore, the proposed REMMAR algorithm can discover stronger association rules in biological relationships dissimilated by traditional methods to assist biologists in complicated genetic exploration.     

Instability in a generalized Keller-Segel model

We present a generalized Keller-Segel model where an arbitrary number of chemical compounds react, some of which are produced by a species, and one of which is a chemoattractant for the species. To investigate the stability of homogeneous stationary states of this generalized model, we consider the eigenvalues of a linearized system. We are able to reduce this infinite dimensional eigenproblem to a parametrized finite dimensional eigenproblem. By matrix theoretic tools, we then provide easily verifiable sufficient conditions for destabilizing the homogeneous stationary states. In particular, one of the sufficient conditions is that the chemotactic feedback is sufficiently strong. Although this mechanism was already known to exist in the original Keller-Segel model, here we show that it is more generally applicable by significantly enlarging the class of models exhibiting this instability phenomenon which may lead to pattern formation.     

Dystroglycan versatility in cell adhesion: a tale of multiple motifs

In the last fifteen years, rapid progress has been made in delineating the cellular response to DNA damage. The DNA damage response network is composed of a large number of proteins with different functions that detect and signal the presence of DNA damage in order to coordinate DNA repair with a variety of cellular processes, notably cell cycle progression. This signal, which radiates from the chromatin template, is driven primarily by phosphorylation events, mainly on serine and threonine residues. While we have accumulated detailed information about kinases and their substrates our understanding of the role of phosphatases in the DNA damage response is still preliminary. Identifying the phosphatases and their regulation will be instrumental to obtain a complete picture of the dynamics of the DNA damage response. Here we give an overview of the DNA damage response in mammalian cells and then review the data on the role of different phosphatases and discuss their biological relevance.     

Computerization of a population projection model based on generalized age-dependent branching processes: a connection with the Leslie matrix

The population projection model based on generalized age-dependent branching processes developed by Mode and Busby (1981) involves the solution of a large number of renewal type equations. It is shown that these equations may be solved recursively. Such a solution has two implications. One is that the projection model may be very efficiently computerized. Second, the recursive algorithm developed has striking similarities to two traditional methods of population projection used by demographers: the Leslie matrix and cohort component methods. The results presented here associate traditional projection techniques with the theory of age-dependent branching processes.     

Host-parasitoid dynamics of a generalized Thompson model

A discrete-time host-parasitoid model including host-density dependence and a generalized Thompson escape function is analyzed. This model assumes that parasitoids are egg-limited but not search-limited, and is proven to exhibit five types of dynamics: host failure in which the host goes extinct in the parasitoid's presence or absence, unconditional parasitoid failure in which the parasitoid always goes extinct while the host persists, conditional parasitoid failure in the host and the parasitoid go extinct or coexist depending on the initial host-parasitoid ratio, parasitoid driven extinction in which the parasitoid invariably drives the host to extinction, and coexistence in which the host and parasitoid coexist about a global attractor. The latter two dynamics only occur when the parasitoid's maximal rate of growth exceeds the host's maximal rate of growth. Moreover, coexistence requires parasitism events to be sufficiently aggregated. Small additive noise is proven to alter the dynamical outcomes in two ways. The addition of noise to parasitoid driven extinction results in random outbreaks of the host and parasitoid with varying intensity. Additive noise converts conditional parasitoid failure to unconditional parasitoid failure. Implications for classical biological control are discussed.     

A generalized model of a resource-population system

Summary A system of nonlinear differential equations describing a resource-population system is analyzed in terms of the existence and characteristics of its equilibrium states.It is proved that, under the condition that k< (necessary condition for the population being able to grow under optimal conditions), it is a necessary and sufficient condition for the system to have a steady state that the resource input rate to the system be constant.When the resource input rate is a constant different from zero, the system has only one equilibrium point, at M ⁰=/⁰/k, A ⁰=–(/⁰/k)ln(1–k/), and this equilibrium point is always stable. In other words, the system population-resource will always reach the steady state, either monotonically (node) or by damped oscillations (focus), from any arbitrary initial condition in the positive quadrant.When the resource input rate is equal to zero, the system has an infinite number of equilibrium points at M ₀=0, A ₀=constant. All these equilibrium points are unstable in the sense that any slight increase in M will move the system away from the equilibrium states, except for the point M ₀=0, A ₀=0, which is the only stable equilibrium point, to which the system will tend. This stable equilibrium point corresponds to the condition of complete annihilation of both resource and population.Finally, it is proved that the system does not have limit cycles in the positive quadrant and is therefore incapable of self-oscillations.This work was partially supported by a Ford Foundation fellowship and various Cornell University fellowships.     

Pattern formation in a generalized chemotactic model

Many models have been proposed for spatial pattern formation in embryology and analyzed for the standard case of zero-flux boundary conditions. However, relatively little attention has been paid to the role of boundary conditions on the form of the final pattern. Here we investigate, numerically, the effect of nonstandard boundary conditions on a model pattern generator, which we choose to be of a cell-chemotactic type. We specifically focus on the role of boundary conditions and the effects of scale and aspect ratio, and study the spatiotemporal dynamics of pattern formation. We illustrate the properties of the model by application to the spatiotemporal sequence of skeletal development.     

Developing a realistic sexual network model of chlamydia transmission in Britain

Background  

A national chlamydia screening programme is currently being rolled out in the UK and other countries. However, much of the epidemiology remains poorly understood. In this paper we present a stochastic, individual based, dynamic sexual network model of chlamydia transmission and its parameterisation. Mathematical models provide a theoretical framework for understanding the key epidemiological features of chlamydia: sexual behaviour, health care seeking and transmission dynamics.