Deriving the probabilities of water loss and ammonia loss for amino acids from tandem mass spectra

In protein identification through tandem mass spectrometry, it is critical to accurately predict the theoretical spectrum for a peptide sequence. The widely used prediction models, such as SEQUEST and MASCOT, ignore the intensity of the ions with important neutral losses, including water loss and ammonia loss. However, ignoring these neutral losses results in a significant deviation between the predicted theoretical spectrum and its experimental counterpart. Here, based on the "one peak, multiple explanations" observation, we proposed an expectation-maximization (EM) method to automatically learn the probabilities of water loss and ammonia loss for each amino acid. Then we employed these probabilities to design an improved statistical model for theoretical spectrum prediction. We implemented these methods and tested them on practical data. On a training set containing 1803 spectra, the experimental results show a good agreement with some known knowledge about neutral losses, such as the tendency of water loss from Asp, Glu, Ser, and Thr. Furthermore, on a testing set containing 941 spectra, the improved similarity between the experimental and predicted spectra demonstrates that this method can generate more reasonable predictions relative to the model that ignores neutral losses. As an application of the derived probabilities, we implemented a database searching method adopting the improved theoretical spectrum model with neutral loss ions estimated. Experimental results on Keller's data set demonstrate that this method can identify peptides more accurately than SEQUEST. In another application to validate SEQUEST's results, the reported peptide-spectrum pairs are reranked with respect to the similarity between experimental and predicted spectra. Experimental results on both LTQ and QSTAR data sets suggest that this reranking strategy can effectively distinguish the false negative predictions reported by SEQUEST.     

Modes and cuts in metabolic networks: complexity and algorithms

Constraint-based approaches recently brought new insight into our understanding of metabolism. By making very simple assumptions such as that the system is at steady-state and some reactions are irreversible, and without requiring kinetic parameters, general properties of the system can be derived. A central concept in this methodology is the notion of an elementary mode (EM for short) which represents a minimal functional subsystem. The computation of EMs still forms a limiting step in metabolic studies and several algorithms have been proposed to address this problem leading to increasingly faster methods. However, although a theoretical upper bound on the number of elementary modes that a network may possess has been established, surprisingly, the complexity of this problem has never been systematically studied. In this paper, we give a systematic overview of the complexity of optimisation problems related to modes. We first establish results regarding network consistency. Most consistency problems are easy, i.e., they can be solved in polynomial time. We then establish the complexity of finding and counting elementary modes. We show in particular that finding one elementary mode is easy but that this task becomes hard when a specific EM (i.e. an EM containing some specified reactions) is sought. We then show that counting the number of elementary modes is musical sharpP-complete. We emphasize that the easy problems can be solved using currently existing software packages. We then analyse the complexity of a closely related task which is the computation of so-called minimum reaction cut sets and we show that this problem is hard. We then present two positive results which both allow to avoid computing EMs as a prior to the computation of reaction cuts. The first one is a polynomial approximation algorithm for finding a minimum reaction cut set. The second one is a test for verifying whether a set of reactions constitutes a reaction cut; this test can be readily included in existing algorithms to improve their performance. Finally, we discuss the complexity of other cut-related problems.     

Comparative dynamics of avian communities across edges and interiors of North American ecoregions

Aim Based on a priori hypotheses, we developed predictions about how avian communities might differ at the edges vs. interiors of ecoregions. Specifically, we predicted lower species richness and greater local turnover and extinction probabilities for regional edges. We tested these predictions using North American Breeding Bird Survey (BBS) data across nine ecoregions over a 20‐year time period. Location Data from 2238 BBS routes within nine ecoregions of the United States were used. Methods The estimation methods used accounted for species detection probabilities < 1. Parameter estimates for species richness, local turnover and extinction probabilities were obtained using the program COMDYN. We examined the difference in community‐level parameters estimated from within exterior edges (the habitat interface between ecoregions), interior edges (the habitat interface between two bird conservation regions within the same ecoregion) and interior (habitat excluding interfaces). General linear models were constructed to examine sources of variation in community parameters for five ecoregions (containing all three habitat types) and all nine ecoregions (containing two habitat types). Results Analyses provided evidence that interior habitats and interior edges had on average higher bird species richness than exterior edges, providing some evidence of reduced species richness near habitat edges. Lower average extinction probabilities and turnover rates in interior habitats (five‐region analysis) provided some support for our predictions about these quantities. However, analyses directed at all three response variables, i.e. species richness, local turnover, and local extinction probability, provided evidence of an interaction between habitat and region, indicating that the relationships did not hold in all regions. Main conclusions The overall predictions of lower species richness, higher local turnover and extinction probabilities in regional edge habitats, as opposed to interior habitats, were generally supported. However, these predicted tendencies did not hold in all regions.     

Constructing and counting phylogenetic invariants.

The method of invariants is an approach to the problem of reconstructing the phylogenetic tree of a collection of m taxa using nucleotide sequence data. Models for the respective probabilities of the 4m possible vectors of bases at a given site will have unknown parameters that describe the random mechanism by which substitution occurs along the branches of a putative phylogenetic tree. An invariant is a polynomial in these probabilities that, for a given phylogeny, is zero for all choices of the substitution mechanism parameters. If the invariant is typically non-zero for another phylogenetic tree, then estimates of the invariant can be used as evidence to support one phylogeny over another. Previous work of Evans and Speed showed that, for certain commonly used substitution models, the problem of finding a minimal generating set for the ideal of invariants can be reduced to the linear algebra problem of finding a basis for a certain lattice (that is, a free Z-module). They also conjectured that the cardinality of such a generating set can be computed using a simple "degrees of freedom" formula. We verify this conjecture. Along the way, we explain in detail how the observations of Evans and Speed lead to a simple, computationally feasible algorithm for constructing a minimal generating set.     

Estimation in a semi-Markov transformation model

Semi-Markov and modulated renewal processes provide a large class of multi-state models which can be used for analysis of longitudinal failure time data. In biomedical applications, models of this kind are often used to describe evolution of a disease and assume that patient may move among a finite number of states representing different phases in the disease progression. Several authors proposed extensions of the proportional hazard model for regression analysis of these processes. In this paper, we consider a general class of censored semi-Markov and modulated renewal processes and propose use of transformation models for their analysis. Special cases include modulated renewal processes with interarrival times specified using transformation models, and semi-Markov processes with with one-step transition probabilities defined using copula-transformation models. We discuss estimation of finite and infinite dimensional parameters and develop an extension of the Gaussian multiplier method for setting confidence bands for transition probabilities and related parameters. A transplant outcome data set from the Center for International Blood and Marrow Transplant Research is used for illustrative purposes.     

Simple mathematical model of pathologic microsatellite expansions: when self-reparation does not work

We propose a simple model of pathologic microsatellite expansion, and describe an inherent self-repairing mechanism working against expansion. We prove that if the probabilities of elementary expansions and contractions are equal, microsatellite expansions are always self-repairing. If these probabilities are different, self-reparation does not work. Mosaicism, anticipation and reverse mutation cases are discussed in the framework of the model. We explain these phenomena and provide some theoretical evidence for their properties, for example, the rarity of reverse mutations.     

A control theory approach to the analysis and synthesis of the experimentally observed motion primitives

Recent experiments on frogs and rats, have led to the hypothesis that sensory-motor systems are organized into a finite number of linearly combinable modules; each module generates a motor command that drives the system to a predefined equilibrium. Surprisingly, in spite of the infiniteness of different movements that can be realized, there seems to be only a handful of these modules. The structure can be thought of as a vocabulary of "elementary control actions". Admissible controls, which in principle belong to an infinite dimensional space, are reduced to the linear vector space spanned by these elementary controls. In the present paper we address some theoretical questions that arise naturally once a similar structure is applied to the control of nonlinear kinematic chains. First of all, we show how to choose the modules so that the system does not loose its capability of generating a "complete" set of movements. Secondly, we realize a "complete" vocabulary with a minimal number of elementary control actions. Subsequently, we show how to modify the control scheme so as to compensate for parametric changes in the system to be controlled. Remarkably, we construct a set of modules with the property of being invariant with respect to the parameters that model the growth of an individual. Robustness against uncertainties is also considered showing how to optimally choose the modules equilibria so as to compensate for errors affecting the system. Finally, the motion primitive paradigm is extended to locomotion and a related formalization of internal (proprioceptive) and external (exteroceptive) variables is given.     

Cell motion, contractile networks, and the physics of interpenetrating reactive flow.

In this paper we propose a physical model of contractile biological polymer networks based on the notion of reactive interpenetrating flow. We show how our model leads to a mathematical formulation of the dynamical laws governing the behavior of contractile networks. We also develop estimates of the various parameters that appear in our equations, and we discuss some elementary predictions of the model concerning the general scaling principles that pertain to the motions of contractile networks.     

Construction of Estimation Regions for the Parameters of Explicit Functional Relationships

Assuming that some explicit functional relationship acts as a mathematical model we consider the case that we are given a finite set of hypercuboids, each of which contains at least one point of the true functional relationship with a certain given probability. We present a procedure to construct sets for the unknown parameters and probabilities for the event that those contain the true parameter value. The procedure is illustrated by an example from pharmaceutical technology.     

Estimating survival of a streamside salamander: importance of temporary emigration,capture response,and location

Estimating survival for highly secretive aquatic animals, such as stream salamanders, presents numerous challenges. Salamanders often spend a considerable time in refugia where they are difficult to capture. Few studies have calculated vital rates for stream salamanders, yet the need is substantial as they are threatened by a wide range of land-use stressors, especially urban development. In this study, we used 34 months of continuous field samples collected at an urban and undisturbed stream and robust design mark-recapture analysis to evaluate the importance of temporary emigration, capture response, and location on survival estimates of the salamander Desmognathus fuscus. We constructed a set of candidate models incorporating combinations of time- and location-varying capture and recapture probabilities, capture responses, temporary emigration, and survival estimates and ranked models using Akaike’s Information Criterion. We found strong support for month-specific capture probabilities, recapture probabilities, temporary emigration and a negative behavioral response to capture in the majority of months. We found no support for variation in capture probabilities, recapture probabilities, and temporary emigration between locations. However, we found that location strongly influenced survival estimates. Specifically, survival estimates were significantly higher at the undisturbed site than at the urban site. Our results emphasize the importance of estimating capture probabilities, recapture probabilities, capture response, and temporary emigration when evaluating survival in highly secretive aquatic animals. Failure to account for these population parameters will likely yield biased estimates of survival in freshwater animal populations.     

Three-stage stochastic epidemic model: an application to AIDS.

A three-stage stochastic epidemic model extending the so-called classical epidemic process to one that includes time-dependent transition probabilities is described, and a solution to the appropriate set of forward differential-difference equations is given. When an individual can move from being a susceptible to one infected with the HIV virus to one diagnosed as having AIDS, we can use this general model to describe an AIDS epidemic process. We obtain expressions for the mean and variance of the number of AIDS cases for some special cases. By comparing these with actual data, it is suggested that, for some categories of cases (in particular, children), this model might be a plausible model to describe the underlying mechanism of the AIDS epidemic.     

Parameter identification in N-compartment mamillary models

We consider a general mamillary model with a central compartment (compartment 1) and n?1 peripheral compartments, each bidirectionally connected to the first. Elimination is allowed from any compartment and effectively occurs from the system. With input introduced into an arbitrary compartment and measurement performed in an arbitrary compartment, explicit equations are given to derive the parameters of the model from the input-output procedure. The calculations include essentially the determination of the roots of a polynomial plus some elementary algebra. If input and measurement are performed in the same compartment, then a set of 2n elementary combinations of the model parameters can be uniquely determined. However, the model parameters themselves can only be localized, each within an interval. These intervals are explicitly calculated and their width discussed.     

Using prior information to build probabilistic invasive species risk assessments

Understanding why some introduced species become naturalized and invasive whereas others do not is a major focus of invasion ecology. Invasive species risk assessments address this same question, but are not typically based on the results from recent ecological studies. Applying results from the ecological literature to risk assessment is difficult, in part because there are no general explanations of invasion likelihood across taxa. Most ecological studies are also specific to a particular region and it is unclear whether outcomes in one region will necessarily apply to another. Here we show how a hierarchical Bayesian statistical framework can make better use of ecological studies for applied risk assessments. We focus on three key opportunities afforded by these models: (1) the ability to leverage information from one region to form prior expectations for other regions about which little is known, (2) the ability to quantify uncertainty of predictions, and (3) flexibility to incorporate within-group heterogeneities in probabilities of naturalization. We illustrate these principles using a case study where we predict the probability of plant taxa naturalizing in New Zealand and Australia, showing how prior information can be particularly valuable when data are limited. As more studies document invasion patterns around the world, a framework that can formally incorporate prior information will help link the accumulating data on species introductions to risk assessments.     

Effects of dilation and translation on a perceptron-type learning rule for higher order Hopfield neural networks

In this paper, we will take a further look at a generalized perceptron-like learning rule which uses dilation and translation parameters in order to enhance the recall performance of higher order Hopfield neural networks without significantly increasing their complexity. We will practically study the influence of these parameters on the perceptron learning and recall process, using a generalized version of the Hebbian learning rule for initialization. Our analysis will be based on a pattern recognition problem with random patterns. We will see that in case of a highly correlated set of patterns, there can be gained some improvements concerning the learning and recall performance. On the other hand, we will show that the dilation and translation parameters have to be chosen carefully for a positive result.     

PATTERNS IN THE GEOGRAPHICAL RANGES OF SPECIES

1. A growing number of studies have documented patterns in species geographic ranges relevant to the study of community structure. These include patterns in the frequency of geographic ranges of different sizes, and in the interaction of range sizes with population abundances and variabilities, body sizes, trophic characteristics and extinction probabilities.
2. Agreement between hypothesized and observed relationships is reasonably good, but we do not know how general the patterns are. Analysis of patterns has focused upon a few taxonomic groups, a bias largely resulting from a lack of information on the geographic distributions of most taxa.
3. Many of the patterns are interrelated, and although theoretical bases to all the patterns can be suggested, it is possible that some are artifacts.
4. Taylor power plots give us a means of making predictions about population behaviour as it pertains to geographic ranges. Some of these predictions suggest that previous conceptions of such interactions have been too narrow, but empirical analyses of these patterns will be hampered by the difficulty of measuring population variability.
5. In general, our knowledge of the structure, and spatial and temporal behaviour, of species geographic ranges remains poor.     

Parametric Analysis of Alignment and Phylogenetic Uncertainty

To infer a phylogenetic tree from a set of DNA sequences, typically a multiple alignment is first used to obtain homologous bases. The inferred phylogeny can be very sensitive to how the alignment was created. We develop tools for analyzing the robustness of phylogeny to perturbations in alignment parameters in the NW algorithm. Our main tool is parametric alignment, with novel improvements that are of general interest in parametric inference. Using parametric alignment and a Gaussian distribution on alignment parameters, we derive probabilities of optimal alignment summaries and inferred phylogenies. We apply our method to analyze intronic sequences from Drosophila flies. We show that phylogeny estimates can be sensitive to the choice of alignment parameters, and that parametric alignment elucidates the relationship between alignment parameters and reconstructed trees.     

小球藻联产油脂和虾青素的基元模式分析

构建了包含虾青素合成途径的小球藻代谢网络模型,集成文献报道同位素标定的小球藻代谢通量数据,估算了胞内代谢通量分布。在正常和缺氮培养条件下,虾青素的代谢通量分别为0.38和0.35。计算得到基元模式共640条,通过最大熵原理算法求取了正常培养和缺氮培养条件下的基元模式概率。存在4条关键基元模式,在2种培养条件下,其基元模式概率之和分别为60.95%和77.53%。虾青素的最大理论合成产率为11.27%,但是这4条关键基元模式并不包括虾青素的合成反应。     

A method for defining steady-state unidirectional fluxes through branched chemical, osmotic and chemiosmotic reactions

A general mathematical technique is described for deriving analytical expressions and obtaining numerical solutions for the steady-state unidirectional fluxes between two chemical states via any set of intermediate states present within any hypothetical system of unbranched or branched and overlapping elementary processes. The technique is a restricted application of the theory of Markov processes with conditional probabilities being assigned to the chemical state transitions constituting the system of reactions. While, in principle, the technique requires the summation of an infinite power series of a matrix defining the conditional probabilities of single state transitions, the power series is evaluated by means of the Taylor series expansion for matrices. As this technique allows isotopic exchange velocity equations to be derived from systems of reactions in which no distinction between the labelled and unlabelled species is required it provides a distinct and independent alternative to previously proposed methods. The technique is illustrated by application to a mechanism for second-order carrier-mediated transport.     

Estimating rates of local extinction and colonization in colonial species and an extension to the metapopulation and community levels

Coloniality has mainly been studied from an evolutionary perspective, but relatively few studies have developed methods for modelling colony dynamics. Changes in number of colonies over time provide a useful tool for predicting and evaluating the responses of colonial species to management and to environmental disturbance. Probabilistic Markov process models have been recently used to estimate colony site dynamics using presence–absence data when all colonies are detected in sampling efforts. Here, we define and develop two general approaches for the modelling and analysis of colony dynamics for sampling situations in which all colonies are, and are not, detected. For both approaches, we develop a general probabilistic model for the data and then constrain model parameters based on various hypotheses about colony dynamics. We use Akaike's Information Criterion (AIC) to assess the adequacy of the constrained models. The models are parameterised with conditional probabilities of local colony site extinction and colonization. Presence–absence data arising from Pollock's robust capture–recapture design provide the basis for obtaining unbiased estimates of extinction, colonization, and detection probabilities when not all colonies are detected. This second approach should be particularly useful in situations where detection probabilities are heterogeneous among colony sites. The general methodology is illustrated using presence–absence data on two species of herons. Estimates of the extinction and colonization rates showed interspecific differences and strong temporal and spatial variations. We were also able to test specific predictions about colony dynamics based on ideas about habitat change and metapopulation dynamics. We recommend estimators based on probabilistic modelling for future work on colony dynamics. We also believe that this methodological framework has wide application to problems in animal ecology concerning metapopulation and community dynamics.