Limitations of entropy maximization in ecology

Applying ideas of statistical mechanics in ecology have recently received quite some attention. The entropy maximization (EM) formalism looks particularly attractive, as it provides a simple algorithm to infer detailed system variables from a limited number of constraints. However, we point out that a blind application of this formalism can easily lead to wrong conclusions. To illustrate this, we reanalyze an ecological data set that has been used to claim the good performance of EM in predicting species abundances from trait measurements. We show that these results are entirely due to the restrictive constraints, and do not provide any support for the applicability of EM in ecology. By comparing with a simple example from physics, we indicate which characteristic mechanism of EM, and of statistical mechanics in general, is missing for the ecological example. This analysis introduces a series of methods to evaluate future attempts to apply EM in ecology.     

Accelerating Computation of DCM for ERP in MATLAB by External Function Calls to the GPU

This study aims to improve the performance of Dynamic Causal Modelling for Event Related Potentials (DCM for ERP) in MATLAB by using external function calls to a graphics processing unit (GPU). DCM for ERP is an advanced method for studying neuronal effective connectivity. DCM utilizes an iterative procedure, the expectation maximization (EM) algorithm, to find the optimal parameters given a set of observations and the underlying probability model. As the EM algorithm is computationally demanding and the analysis faces possible combinatorial explosion of models to be tested, we propose a parallel computing scheme using the GPU to achieve a fast estimation of DCM for ERP. The computation of DCM for ERP is dynamically partitioned and distributed to threads for parallel processing, according to the DCM model complexity and the hardware constraints. The performance efficiency of this hardware-dependent thread arrangement strategy was evaluated using the synthetic data. The experimental data were used to validate the accuracy of the proposed computing scheme and quantify the time saving in practice. The simulation results show that the proposed scheme can accelerate the computation by a factor of 155 for the parallel part. For experimental data, the speedup factor is about 7 per model on average, depending on the model complexity and the data. This GPU-based implementation of DCM for ERP gives qualitatively the same results as the original MATLAB implementation does at the group level analysis. In conclusion, we believe that the proposed GPU-based implementation is very useful for users as a fast screen tool to select the most likely model and may provide implementation guidance for possible future clinical applications such as online diagnosis.     

Three Ways of Implementing the EM Algorithm when Parameters are not Identifiable

We consider situations where the incomplete nature of the observed data causes identifiability problem. Rather than imposing identifiability constraints on the parameters and then implement the EM algorithm subject to these constraints, we argue that for certain problems, an easier option is to ignore the constraints during the M‐steps of the EM procedure. We also suggest a way of carrying out constrained maximization approximately by using Cox and Wermuth's (1990) method for approximating the constrained maximizers from the unconstrained ones at each M‐step. The simplicity and validity of the unconstrained EM procedure are demonstrated using three examples involving bivariate probit regression, multivariate normal order statistics model and the multinominal distribution. Potential applications to more complicated models are also outlined.     

PocketOptimizer 2.0: A modular framework for computer-aided ligand-binding design

The ability to design customized proteins to perform specific tasks is of great interest. We are particularly interested in the design of sensitive and specific small molecule ligand-binding proteins for biotechnological or biomedical applications. Computational methods can narrow down the immense combinatorial space to find the best solution and thus provide starting points for experimental procedures. However, success rates strongly depend on accurate modeling and energetic evaluation. Not only intra- but also intermolecular interactions have to be considered. To address this problem, we developed PocketOptimizer, a modular computational protein design pipeline, that predicts mutations in the binding pockets of proteins to increase affinity for a specific ligand. Its modularity enables users to compare different combinations of force fields, rotamer libraries, and scoring functions. Here, we present a much-improved version––PocketOptimizer 2.0. We implemented a cleaner user interface, an extended architecture with more supported tools, such as force fields and scoring functions, a backbone-dependent rotamer library, as well as different improvements in the underlying algorithms. Version 2.0 was tested against a benchmark of design cases and assessed in comparison to the first version. Our results show how newly implemented features such as the new rotamer library can lead to improved prediction accuracy. Therefore, we believe that PocketOptimizer 2.0, with its many new and improved functionalities, provides a robust and versatile environment for the design of small molecule-binding pockets in proteins. It is widely applicable and extendible due to its modular framework. PocketOptimizer 2.0 can be downloaded at https://github.com/Hoecker-Lab/pocketoptimizer .     

STEME: efficient EM to find motifs in large data sets

MEME and many other popular motif finders use the expectation-maximization (EM) algorithm to optimize their parameters. Unfortunately, the running time of EM is linear in the length of the input sequences. This can prohibit its application to data sets of the size commonly generated by high-throughput biological techniques. A suffix tree is a data structure that can efficiently index a set of sequences. We describe an algorithm, Suffix Tree EM for Motif Elicitation (STEME), that approximates EM using suffix trees. To the best of our knowledge, this is the first application of suffix trees to EM. We provide an analysis of the expected running time of the algorithm and demonstrate that STEME runs an order of magnitude more quickly than the implementation of EM used by MEME. We give theoretical bounds for the quality of the approximation and show that, in practice, the approximation has a negligible effect on the outcome. We provide an open source implementation of the algorithm that we hope will be used to speed up existing and future motif search algorithms.     

A Simple Self-Maintaining Metabolic System: Robustness,Autocatalysis, Bistability

A living organism must not only organize itself from within; it must also maintain its organization in the face of changes in its environment and degradation of its components. We show here that a simple (M,R)-system consisting of three interlocking catalytic cycles, with every catalyst produced by the system itself, can both establish a non-trivial steady state and maintain this despite continuous loss of the catalysts by irreversible degradation. As long as at least one catalyst is present at a sufficient concentration in the initial state, the others can be produced and maintained. The system shows bistability, because if the amount of catalyst in the initial state is insufficient to reach the non-trivial steady state the system collapses to a trivial steady state in which all fluxes are zero. It is also robust, because if one catalyst is catastrophically lost when the system is in steady state it can recreate the same state. There are three elementary flux modes, but none of them is an enzyme-maintaining mode, the entire network being necessary to maintain the two catalysts.     

Exact epidemic models on graphs using graph-automorphism driven lumping

The dynamics of disease transmission strongly depends on the properties of the population contact network. Pair-approximation models and individual-based network simulation have been used extensively to model contact networks with non-trivial properties. In this paper, using a continuous time Markov chain, we start from the exact formulation of a simple epidemic model on an arbitrary contact network and rigorously derive and prove some known results that were previously mainly justified based on some biological hypotheses. The main result of the paper is the illustration of the link between graph automorphisms and the process of lumping whereby the number of equations in a system of linear differential equations can be significantly reduced. The main advantage of lumping is that the simplified lumped system is not an approximation of the original system but rather an exact version of this. For a special class of graphs, we show how the lumped system can be obtained by using graph automorphisms. Finally, we discuss the advantages and possible applications of exact epidemic models and lumping.     

Design, docking, and evaluation of multiple libraries against multiple targets

We present a general approach to the design, docking, and virtual screening of multiple combinatorial libraries against a family of proteins. The method consists of three main stages: docking the scaffold, selecting the best substituents at each site of diversity, and comparing the resultant molecules within and between the libraries. The core "divide-and-conquer" algorithm for side-chain selection, developed from an earlier version (Sun et al., J Comp Aided Mol Design 1998;12:597-604), provides a way to explore large lists of substituents with linear rather than combinatorial time dependence. We have applied our method to three combinatorial libraries and three serine proteases: trypsin, chymotrypsin, and elastase. We show that the scaffold docking procedure, in conjunction with a novel vector-based orientation filter, reproduces crystallographic binding modes. In addition, the free-energy-based scoring procedure (Zou et al., J Am Chem Soc 1999;121:8033-8043) is able to reproduce experimental binding data for P1 mutants of macromolecular protease inhibitors. Finally, we show that our method discriminates between a peptide library and virtual libraries built on benzodiazepine and tetrahydroisoquinolinone scaffolds. Implications of the docking results for library design are explored.     

Mathematical analysis of an age-structured population model with space-limited recruitment

In this paper, we investigate structured population model of marine invertebrate whose life stage is composed of sessile adults and pelagic larvae, such as barnacles contained in a local habitat. First we formulate the basic model as an Cauchy problem on a Banach space to discuss the existence and uniqueness of non-negative solution. Next we define the basic reproduction number R0 to formulate the invasion condition under which the larvae can successfully settle down in the completely vacant habitat. Subsequently we examine existence and stability of steady states. We show that the trivial steady state is globally asymptotically stable if R0 < or = 1, whereas it is unstable if R0 > 1. Furthermore, we show that a positive (non-trivial) steady state uniquely exists if R0 > 1 and it is locally asymptotically stable as far as absolute value of R0 - 1 is small enough.     

Measuring gas vesicle dimensions by electron microscopy

Gas vesicles (GVs) are cylindrical or spindle‐shaped protein nanostructures filled with air and used for flotation by various cyanobacteria, heterotrophic bacteria, and Archaea. Recently, GVs have gained interest in biotechnology applications due to their ability to serve as imaging agents and actuators for ultrasound, magnetic resonance and several optical techniques. The diameter of GVs is a crucial parameter contributing to their mechanical stability, buoyancy function and evolution in host cells, as well as their properties in imaging applications. Despite its importance, reported diameters for the same types of GV differ depending on the method used for its assessment. Here, we provide an explanation for these discrepancies and utilize electron microscopy (EM) techniques to accurately estimate the diameter of the most commonly studied types of GVs. We show that during air drying on the EM grid, GVs flatten, leading to a ~1.5‐fold increase in their apparent diameter. We demonstrate that GVs'' diameter can be accurately determined by direct measurements from cryo‐EM samples or alternatively indirectly derived from widths of flat collapsed and negatively stained GVs. Our findings help explain the inconsistency in previously reported data and provide accurate methods to measure GVs dimensions.     

Stability analysis of predator-prey models via the liapunov method

As is well-known from the classical applications in the electrical and mechanical sciences, energy is a suitable Liapunov function: thus, by analogy, all energy functions proposed in ecology are potential Liapunov functions. In this paper, a generalized Lotka-Volterra model is considered and the stability properties of its non-trivial equilibrium are studied by means of an energy function first proposed by Volterra in the context of conservative ecosystems. The advantage of this Liapunov function with respect to the one that can be induced through linearization is also illustrated.     

The need for stochastic replication of ecological neural networks

Artificial neural networks are becoming increasingly popular as predictive statistical tools in ecosystem ecology and as models of signal processing in behavioural and evolutionary ecology. We demonstrate here that a commonly used network in ecology, the three-layer feed-forward network, trained with the backpropagation algorithm, can be extremely sensitive to the stochastic variation in training data that results from random sampling of the same underlying statistical distribution, with networks converging to several distinct predictive states. Using a random walk procedure to sample error-weight space, and Sammon dimensional reduction of weight arrays, we demonstrate that these different predictive states are not artefactual, due to local minima, but lie at the base of major error troughs in the error-weight surface. We further demonstrate that various gross weight compositions can produce the same predictive state, suggesting the analogy of weight space as a 'patchwork' of multiple predictive states. Our results argue for increased inclusion of stochastic training replication and analysis into ecological and behavioural applications of artificial neural networks.     

Genetic optimization of combinatorial libraries

Most agrochemical and pharmaceutical companies have set up high-throughput screening programs which require large numbers of compounds to screen. Combinatorial libraries provide an attractive way to deliver these compounds. A single combinatorial library with four variable positions can yield more than 10(12) potential compounds, if one assumes that about 1000 reagents are available for each position. This is far more than any high-throughput screening facility can afford to screen. We have proposed a method for iterative compound selection from large databases, which identifies the most active compounds by examining only a small fraction of the database. In this article, we describe the extension of this method to the problem of selecting compounds from large combinatorial libraries. Copyright 1998 John Wiley & Sons, Inc.     

Free and open source geographic information tools for landscape ecology

Geographic Information tools (GI tools) have become an essential component of research in landscape ecology. In this article we review the use of GIS (Geographic Information Systems) and GI tools in landscape ecology, with an emphasis on free and open source software (FOSS) projects. Specifically, we introduce the background and terms related to the free and open source software movement, then compare eight FOSS desktop GIS with proprietary GIS to analyse their utility for landscape ecology research. We also provide a summary of related landscape analysis FOSS applications, and extensions. Our results indicate that (i) all eight GIS provide the basic GIS functionality needed in landscape ecology, (ii) they all facilitate customisation, and (iii) they all provide good support via forums and email lists. Drawbacks that have been identified are related to the fact that most projects are relatively young. This currently affects the size of their user and developer communities, and their ability to include advanced spatial analysis functions and up-to-date documentation. However, we expect these drawbacks to be addressed over time, as systems mature. In general, we see great potential for the use of free and open source desktop GIS in landscape ecology research and advocate concentrated efforts by the landscape ecology community towards a common, customisable and free research platform.     

A novel analytical method for evolutionary graph theory problems

Evolutionary graph theory studies the evolutionary dynamics of populations structured on graphs. A central problem is determining the probability that a small number of mutants overtake a population. Currently, Monte Carlo simulations are used for estimating such fixation probabilities on general directed graphs, since no good analytical methods exist. In this paper, we introduce a novel deterministic framework for computing fixation probabilities for strongly connected, directed, weighted evolutionary graphs under neutral drift. We show how this framework can also be used to calculate the expected number of mutants at a given time step (even if we relax the assumption that the graph is strongly connected), how it can extend to other related models (e.g. voter model), how our framework can provide non-trivial bounds for fixation probability in the case of an advantageous mutant, and how it can be used to find a non-trivial lower bound on the mean time to fixation. We provide various experimental results determining fixation probabilities and expected number of mutants on different graphs. Among these, we show that our method consistently outperforms Monte Carlo simulations in speed by several orders of magnitude. Finally we show how our approach can provide insight into synaptic competition in neurology.     

Self-tolerance and Autoimmunity in a Regulatory T Cell Model

The class of immunosuppressive lymphocytes known as regulatory T cells (Tregs) has been identified as a key component in preventing autoimmune diseases. Although Tregs have been incorporated previously in mathematical models of autoimmunity, we take a novel approach which emphasizes the importance of professional antigen presenting cells (pAPCs). We examine three possible mechanisms of Treg action (each in isolation) through ordinary differential equation (ODE) models. The immune response against a particular autoantigen is suppressed both by Tregs specific for that antigen and by Tregs of arbitrary specificities, through their action on either maturing or already mature pAPCs or on autoreactive effector T cells. In this deterministic approach, we find that qualitative long-term behaviour is predicted by the basic reproductive ratio R ₀ for each system. When R ₀<1, only the trivial equilibrium exists and is stable; when R ₀>1, this equilibrium loses its stability and a stable non-trivial equilibrium appears. We interpret the absence of self-damaging populations at the trivial equilibrium to imply a state of self-tolerance, and their presence at the non-trivial equilibrium to imply a state of chronic autoimmunity. Irrespective of mechanism, our model predicts that Tregs specific for the autoantigen in question play no role in the system’s qualitative long-term behaviour, but have quantitative effects that could potentially reduce an autoimmune response to sub-clinical levels. Our results also suggest an important role for Tregs of arbitrary specificities in modulating the qualitative outcome. A stochastic treatment of the same model demonstrates that the probability of developing a chronic autoimmune response increases with the initial exposure to self antigen or autoreactive effector T cells. The three different mechanisms we consider, while leading to a number of similar predictions, also exhibit key differences in both transient dynamics (ODE approach) and the probability of chronic autoimmunity (stochastic approach).     

qFit 3: Protein and ligand multiconformer modeling for X‐ray crystallographic and single‐particle cryo‐EM density maps

New X‐ray crystallography and cryo‐electron microscopy (cryo‐EM) approaches yield vast amounts of structural data from dynamic proteins and their complexes. Modeling the full conformational ensemble can provide important biological insights, but identifying and modeling an internally consistent set of alternate conformations remains a formidable challenge. qFit efficiently automates this process by generating a parsimonious multiconformer model. We refactored qFit from a distributed application into software that runs efficiently on a small server, desktop, or laptop. We describe the new qFit 3 software and provide some examples. qFit 3 is open‐source under the MIT license, and is available at https://github.com/ExcitedStates/qfit-3.0 .     

Mobilizing and integrating big data in studies of spatial and phylogenetic patterns of biodiversity

The current global challenges that threaten biodiversity are immense and rapidly growing. These biodiversity challenges demand approaches that meld bioinformatics, large-scale phylogeny reconstruction, use of digitized specimen data, and complex post-tree analyses (e.g. niche modeling, niche diversification, and other ecological analyses). Recent developments in phylogenetics coupled with emerging cyberinfrastructure and new data sources provide unparalleled opportunities for mobilizing and integrating massive amounts of biological data, driving the discovery of complex patterns and new hypotheses for further study. These developments are not trivial in that biodiversity data on the global scale now being collected and analyzed are inherently complex. The ongoing integration and maturation of biodiversity tools discussed here is transforming biodiversity science, enabling what we broadly term “next-generation” investigations in systematics, ecology, and evolution (i.e., “biodiversity science”). New training that integrates domain knowledge in biodiversity and data science skills is also needed to accelerate research in these areas. Integrative biodiversity science is crucial to the future of global biodiversity. We cannot simply react to continued threats to biodiversity, but via the use of an integrative, multifaceted, big data approach, researchers can now make biodiversity projections to provide crucial data not only for scientists, but also for the public, land managers, policy makers, urban planners, and agriculture.     

Uses and abuses of fractal methodology in ecology

Fractals have found widespread application in a range of scientific fields, including ecology. This rapid growth has produced substantial new insights, but has also spawned confusion and a host of methodological problems. In this paper, we review the value of fractal methods, in particular for applications to spatial ecology, and outline potential pitfalls. Methods for measuring fractals in nature and generating fractal patterns for use in modelling are surveyed. We stress the limitations and the strengths of fractal models. Strictly speaking, no ecological pattern can be truly fractal, but fractal methods may nonetheless provide the most efficient tool available for describing and predicting ecological patterns at multiple scales.