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.     

Discovering structural motifs using a structural alphabet: Application to magnesium-binding sites

Background  

For many metalloproteins, sequence motifs characteristic of metal-binding sites have not been found or are so short that they would not be expected to be metal-specific. Striking examples of such metalloproteins are those containing Mg²⁺, one of the most versatile metal cofactors in cellular biochemistry. Even when Mg²⁺-proteins share insufficient sequence homology to identify Mg²⁺-specific sequence motifs, they may still share similarity in the Mg²⁺-binding site structure. However, no structural motifs characteristic of Mg²⁺-binding sites have been reported. Thus, our aims are (i) to develop a general method for discovering structural patterns/motifs characteristic of ligand-binding sites, given the 3D protein structures, and (ii) to apply it to Mg²⁺-proteins sharing <30% sequence identity. Our motif discovery method employs structural alphabet encoding to convert 3D structures to the corresponding 1D structural letter sequences, where the Mg²⁺-structural motifs are identified as recurring structural patterns.     

Helix formation in model peptides based on nucleolin TPAKK motifs

The structures formed by peptide models of the N-terminal domain of the nucleolar protein nucleolin were studied by CD and nmr. The sequences of the peptides are based on the putative nucleic acid binding sequence motif TPAKK: The peptides TP1 and TP2 have the sequence acetyl-G(ATPAKKAA)_nG-amide, with n = 1 and 2, respectively. CD measurements indicate structural changes in both peptides when the lysine side chains are uncharged by increasing the pH or acetylation of the side-chain amines. When trifluoroethanol (TFE) is added, more extensive structural changes are observed, resembling helical structure based on nmr nuclear Overhauser effect (NOE) and C^α proton chemical shift changes, and CD spectra. The structure formed in 0.5M NaClO₄ as observed by nmr is similar to that when the lysine side chains are acetylated, due presumably to interactions of perchlorate ion with side-chain charges on lysines. The helical structure observed in TPAKK motifs may be stabilized via N-capping interactions involving threonine. The structures observed in TFE suggest that the Thr-Pro sequence initiates short helical segments in TPAKK motifs, and these helical structures might interact with nucleic acids, presumably via interactions between lysines and threonines of nucleolin. © 1995 John Wiley & Sons, Inc.     

基于广义线性混合效应模型的森林树木死亡研究

基于计数模型方法,同时考虑样地的随机效应,构建林分水平死亡模型,探究影响树木死亡的因素,以期为森林资源的监测与管理提供参考依据。以美国德州东部森林连续清查的样地数据为数据源,按4∶1的比例将其进行随机抽样,划分为训练集和验证集数据,将立地因子、林分因子和气候因子作为模型的自变量,林木死亡株数则作为模型的因变量,运用计数模型和混合效应模型方法进行模型的构建,并分析影响林木死亡株数的因子。使用赤池信息准则(AIC)、贝叶斯信息准则(BIC)和-2倍对数似然函数值(-2logL) 3种模型评价指标评估各模型间的拟合效果;采用平均绝对误差(MAE)和均方根误差(RMSE) 2种评价指标评估其预测效果,以便筛选出最佳的林分水平死亡模型。结果表明：立地因子方面,林木死亡株数与海拔(P<0.01)呈显著的负效应,与坡度(P<0.05)呈显著的正效应,说明林木死亡株数随海拔的升高而减少,随坡度的增加而增多;林分因子方面,林木死亡株数与林分年龄(P<0.001)和树木基面积(P<0.001)呈显著的正效应,与林分平方平均胸径(P<0.001)和林分密度(P<0.05)...     

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.     

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.     

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.     

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.     

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.     

Toward a realistic model of mutations affecting fitness

Analysis of a recent mutation accumulation (MA) experiment has led to the suggestion that as many as one-half of spontaneous mutations in Arabidopsis are advantageous for fitness. We evaluate this in the light of data from other MA experiments, along with molecular evidence, that suggest the vast majority of new mutations are deleterious.     

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.     

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.     

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.     

Free-energy landscape of kinesin by a realistic lattice model

Structural fluctuations in the thermal equilibrium of the kinesin motor domain are studied using a lattice protein model with Gō interactions. By means of the multi-self-overlap ensemble Monte Carlo method and the principal component analysis, the free-energy landscape is obtained. It is shown that kinesins have two subdomains that exhibit partial folding/unfolding at functionally important regions: one is located around the nucleotide binding site and the other includes the main microtubule binding site. These subdomains are consistent with structural variability that was reported recently based on experimentally-obtained structures. On the other hand, such large structural fluctuations have not been captured by B-factor or normal mode analyses. Thus, they are beyond the elastic regime, and it is essential to take into account chain connectivity for studying the function of kinesins.