Trophic structure and dynamical complexity in simple ecological models

We study the dynamical complexity of five non-linear deterministic predator–prey model systems. These simple systems were selected to represent a diversity of trophic structures and ecological interactions in the real world while still preserving reasonable tractability. We find that these systems can dramatically change attractor types, and the switching among different attractors is dependent on system parameters. While dynamical complexity depends on the nature (e.g., inter-specific competition versus predation) and degree (e.g., number of interacting components) of trophic structure present in the system, these systems all evolve principally on intrinsically noisy limit cycles. Our results support the common observation of cycling and rare observation of chaos in natural populations. Our study also allows us to speculate on the functional role of specialist versus generalist predators in food web modeling.     

Repetitive apneas reduce nonlinear dynamical complexity of the human cardiovascular control system.

We tested the hypothesis that intermittent apneas performed by awake subjects simulate obstructive sleep apnea (OSA) and change dynamic complexity of the cardiovascular control system by repetitive short time stimulation of arterial chemoreceptors. Correlation dimension (CD) and reccurent plot quantification calculated as ratio % determinism versus % recurrence (RDR) were used.as indices of chaotic dynamics. Thirty three normotensive subjects of mean age 21,58 +/- 4,1 performed 10 voluntary apneas 1 min. each separated by 1 min free breathing period. Systolic (SYS), diastolic (DIAS) arterial blood pressure was continuously recorded by finger volume clamp. Stroke volume (SV) was estimated by pulse pressure analysis. Cardiac output (CO) and total peripheral resistance (TPR) were calculated by Portapress system. Cardiac inter-beat interval (IBI) was measured from R-R intervals of ECG. Standard deviation (SD), an index of linear variability, was calculated in 1 min epoch. Dynamics of cardiovascular variables was computed in each subject during 20 min. rest (C), 20 min. of 10 apneas, 1 min each, separated by 1 min free breathing (A), and in 20 min. recovery free breathing (R). In A period CD of all circulatory variables was significantly reduced and RDR augmented. In 23 out of 33 subjects decreased nonlinear dynamics of TPR was carried over from A to R. In contrast, SD increased significantly in A. In conclusion, intermittent brief chemoreflex stimulations by repetitive apneas increase blood pressure and TPR and decrease chaotic behaviour and complexity of the cardiovascular autonomic control system, presumably by inhibition of some regulatory loops such as baroreflex, less vital for survival at oxygen deprivation. Reduced complexity could be implicated in the mechanism of arterial hypertension linked with OSA.     

Unraveling aquaporin interaction partners

Background

Insight into protein–protein interactions (PPIs) is highly desirable in order to understand the physiology of cellular events. This understanding is one of the challenges in biochemistry and molecular biology today, especially for eukaryotic membrane proteins where hurdles of production, purification and structural determination must be passed.

Scope of review

We have explored the common strategies used to find medically relevant interaction partners of aquaporins (AQPs). The most frequently used methods to detect direct contact, yeast two-hybrid interaction assay and co-precipitation, are described together with interactions specifically found for the selected targets AQP0, AQP2, AQP4 and AQP5.

Major conclusions

The vast majority of interactions involve the aquaporin C-terminus and the characteristics of the interaction partners are strikingly diverse. While the well-established methods for PPIs are robust, a novel approach like bimolecular fluorescence complementation (BiFC) is attractive for screening many conditions as well as transient interactions. The ultimate goal is structural evaluation of protein complexes in order to get mechanistic insight into how proteins communicate at a molecular level.

General significance

What we learn from the human aquaporin field in terms of method development and communication between proteins can be of major use for any integral membrane protein of eukaryotic origin. This article is part of a Special Issue entitled Aquaporins.     

Unraveling the genomic complexity of sylvatic mosquitoes in changing Neotropical environments

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Unraveling protein interaction networks with near-optimal efficiency

The functional characterization of genes and their gene products is the main challenge of the genomic era. Examining interaction information for every gene product is a direct way to assemble the jigsaw puzzle of proteins into a functional map. Here we demonstrate a method in which the information gained from pull-down experiments, in which single proteins act as baits to detect interactions with other proteins, is maximized by using a network-based strategy to select the baits. Because of the scale-free distribution of protein interaction networks, we were able to obtain fast coverage by focusing on highly connected nodes (hubs) first. Unfortunately, locating hubs requires prior global information about the network one is trying to unravel. Here, we present an optimized 'pay-as-you-go' strategy that identifies highly connected nodes using only local information that is collected as successive pull-down experiments are performed. Using this strategy, we estimate that 90% of the human interactome can be covered by 10,000 pull-down experiments, with 50% of the interactions confirmed by reciprocal pull-down experiments.     

Unraveling regulation and new components of human P-bodies through a protein interaction framework and experimental validation

The cellular factors involved in mRNA degradation and translation repression can aggregate into cytoplasmic domains known as GW bodies or mRNA processing bodies (P-bodies). However, current understanding of P-bodies, especially the regulatory aspect, remains relatively fragmentary. To provide a framework for studying the mechanisms and regulation of P-body formation, maintenance, and disassembly, we compiled a list of P-body proteins found in various species and further grouped both reported and predicted human P-body proteins according to their functions. By analyzing protein-protein interactions of human P-body components, we found that many P-body proteins form complex interaction networks with each other and with other cellular proteins that are not recognized as P-body components. The observation suggests that these other cellular proteins may play important roles in regulating P-body dynamics and functions. We further used siRNA-mediated gene knockdown and immunofluorescence microscopy to demonstrate the validity of our in silico analyses. Our combined approach identifies new P-body components and suggests that protein ubiquitination and protein phosphorylation involving 14-3-3 proteins may play critical roles for post-translational modifications of P-body components in regulating P-body dynamics. Our analyses provide not only a global view of human P-body components and their physical interactions but also a wealth of hypotheses to help guide future research on the regulation and function of human P-bodies.     

Global analysis of dynamical decision-making models through local computation around the hidden saddle

Bistable dynamical switches are frequently encountered in mathematical modeling of biological systems because binary decisions are at the core of many cellular processes. Bistable switches present two stable steady-states, each of them corresponding to a distinct decision. In response to a transient signal, the system can flip back and forth between these two stable steady-states, switching between both decisions. Understanding which parameters and states affect this switch between stable states may shed light on the mechanisms underlying the decision-making process. Yet, answering such a question involves analyzing the global dynamical (i.e., transient) behavior of a nonlinear, possibly high dimensional model. In this paper, we show how a local analysis at a particular equilibrium point of bistable systems is highly relevant to understand the global properties of the switching system. The local analysis is performed at the saddle point, an often disregarded equilibrium point of bistable models but which is shown to be a key ruler of the decision-making process. Results are illustrated on three previously published models of biological switches: two models of apoptosis, the programmed cell death and one model of long-term potentiation, a phenomenon underlying synaptic plasticity.     

Digging through model complexity: using hierarchical models to uncover evolutionary processes in the wild

The growing interest for studying questions in the wild requires acknowledging that eco-evolutionary processes are complex, hierarchically structured and often partially observed or with measurement error. These issues have long been ignored in evolutionary biology, which might have led to flawed inference when addressing evolutionary questions. Hierarchical modelling (HM) has been proposed as a generic statistical framework to deal with complexity in ecological data and account for uncertainty. However, to date, HM has seldom been used to investigate evolutionary mechanisms possibly underlying observed patterns. Here, we contend the HM approach offers a relevant approach for the study of eco-evolutionary processes in the wild by confronting formal theories to empirical data through proper statistical inference. Studying eco-evolutionary processes requires considering the complete and often complex life histories of organisms. We show how this can be achieved by combining sequentially all life-history components and all available sources of information through HM. We demonstrate how eco-evolutionary processes may be poorly inferred or even missed without using the full potential of HM. As a case study, we use the Atlantic salmon and data on wild marked juveniles. We assess a reaction norm for migration and two potential trade-offs for survival. Overall, HM has a great potential to address evolutionary questions and investigate important processes that could not previously be assessed in laboratory or short time-scale studies.     

Xiphophorus interspecies hybrids as genetic models of induced neoplasia

Fishes of the genus Xiphophorus (platyfishes and swordtails) are small, internally fertilizing, livebearing, and derived from freshwater habitats in Mexico, Guatemala, Belize, and Honduras. Scientists have used these fishes in cancer research studies for more than 70 yr. The genus is presently composed of 22 species that are quite divergent in their external morphology. Most cancer studies using Xiphophorus use hybrids, which can be easily produced by artificial insemination. Phenotypic traits, such as macromelanophore pigment patterns, are often drastically altered as a result of lack of gene regulation within hybrid fishes. These fish can develop large exophytic melanomas as a result of upregulated expression of these pigment patterns. Because backcross hybrid fish are susceptible to the development of melanoma and other neoplasms, they can be subjected to potentially deleterious chemical and physical agents. It is thus possible to use gene mapping and cloning methodologies to identify and characterize oncogenes and tumor suppressors implicated in spontaneous or induced neoplasia. This article reviews the history of cancer research using Xiphophorus and recent developments regarding DNA repair capabilities, mapping, and cloning of candidate genes involved in neoplastic phenotypes. The particular genetic complexity of melanoma in these fishes is analyzed and reviewed.     

Combinatorial complexity and dynamical restriction of network flows in signal transduction

The activities and interactions of proteins that govern the cellular response to a signal generate a multitude of protein phosphorylation states and heterogeneous protein complexes. Here, using a computational model that accounts for 307 molecular species implied by specified interactions of four proteins involved in signalling by the immunoreceptor FcepsilonRI, we determine the relative importance of molecular species that can be generated during signalling, chemical transitions among these species, and reaction paths that lead to activation of the protein tyrosine kinase (PTK) Syk. By all of these measures and over two- and ten-fold ranges of model parameters--rate constants and initial concentrations--only a small portion of the biochemical network is active. The spectrum of active complexes, however, can be shifted dramatically, even by a change in the concentration of a single protein, which suggests that the network can produce qualitatively different responses under different cellular conditions and in response to different inputs. Reduced models that reproduce predictions of the full model for a particular set of parameters lose their predictive capacity when parameters are varied over two-fold ranges.     

Unraveling protein dynamics through fast spectral density mapping

Spectral density mapping at multiple NMR field strengths is probably the best method to describe the dynamical behavior of a protein in solution through the analysis of ¹⁵N heteronuclear relaxation parameters. Nevertheless, such analyses are scarcely reported in the literature, probably because this method is excessively demanding in spectrometer measuring time. Indeed, when using n different magnetic fields and assuming the validity of the high frequency approximation, the discrete sampling of the spectral density function with 2n + 1 points needs the measurement of 3n ¹⁵N heteronuclear relaxation measurements (n R ₁, n R ₂, and n¹⁵N{¹H}NOEs). Based on further approximations, we proposed a new strategy that allows us to describe the spectral density with n + 2 points, with the measurement of a total of n + 2 heteronuclear relaxation parameters. Applied to the dynamics analysis of the protein p13 ^MTCP1 at three different NMR fields, this approach allowed us to divide by nearly a factor of two the total measuring time, without altering further results obtained by the “model free” analysis of the resulting spectral densities. Furthermore, simulations have shown that this strategy remains applicable to any low isotropically tumbling protein ( ns), and is valid for the types of motion generally envisaged for proteins.     

基于多Agent仿真解析处理剩余污泥的微生物电解池种群互作关系

【背景】微生物电化学系统耦合了电化学反应和厌氧消化过程,在处理剩余污泥同时实现能源回收,成为具有应用前景的技术之一。揭示电活性生物膜和活性污泥种群互作机制,有助于进一步调控和强化系统性能。高通量核酸测序技术研究微生物群落具有投入大、耗时长和不可预测的缺点,开展微生物群落动态仿真可以更有效地预测群落结构与功能。【目的】研究厌氧消化和生物电化学系统的微生物种间热力学与动力学的演化规律。在考虑电子供体、电子受体、温度、pH值等生态条件下,分析底物的电子流向及微生物群落结构的动态变化。【方法】通过对剩余污泥处理的微生物电解池(Microbial electrolytic cell,MEC)建立一个多Agent仿真(Multi-agent-based simulation,MAS)模型,评估MEC对底物氧化电子转移的能量效率和传质效率,模拟微生物群落结构实时变化,同时耦合动力学和热力学分析;揭示影响MES运行的电子流向决定性因素及相应的微生物种群,为复杂污染物生物处理系统中种间互作和动力学研究提供基础依据。【结果】通过MAS模拟,确定MEC污泥处理工艺的最佳能量传递效率与传质效率为η=0.2,ε=0.5,MAS结合热力学与动力学参数模拟微生物的群落动态与实验组有较高的吻合性。在长期的运行中,微生物电化学系统中丙酮酸没有积累。【结论】证实了MAS结合热力学与动力学参数可以预测微生物的群落动态,并进行实时监测。研究表明多Agent仿真为微生物群落结构动态变化提供了一种新的研究方法,该方法与高通量核酸测序技术进行校验和联用,为人工和自然生态系统中微生物种群预测与评估研究提供一个新的手段。     

Maximum likelihood estimation in dynamical models of HIV

The study of dynamical models of HIV infection, based on a system of nonlinear ordinary differential equations (ODE), has considerably improved the knowledge of its pathogenesis. While the first models used simplified ODE systems and analyzed each patient separately, recent works dealt with inference in non-simplified models borrowing strength from the whole sample. The complexity of these models leads to great difficulties for inference and only the Bayesian approach has been attempted by now. We propose a full likelihood inference, adapting a Newton-like algorithm for these particular models. We consider a relatively complex ODE model for HIV infection and a model for the observations including the issue of detection limits. We apply this approach to the analysis of a clinical trial of antiretroviral therapy (ALBI ANRS 070) and we show that the whole algorithm works well in a simulation study.     

Mapping the complexity of ecological models

We propose to define the complexity of an ecological model as the statistical complexity of the output it produces. This allows for a direct comparison between data and model complexity. Working with univariate time series, we show that this measure ‘blindly’ discriminates among the different dynamical behaviours a model can exhibit. We then search a model parameter space in order to segment it into areas of different dynamical behaviour and calculate the maximum complexity a model can generate. Given a time series, and the problem of choosing among a number of ecological models to study it, we suggest that models whose maximum complexity is lower than the time series complexity should be disregarded because they are unable to reconstruct some of the structures contained in the data. Similar reasoning could be used to disregard models’ subdomains as well as areas of unnecessary high complexity. We suggest that model complexity so defined better captures the difficulty faced by a user in managing and understanding the behaviour of an ecological model than measures based on a model ‘size’.     

Beyond Bt resistance of pests in the context of population dynamical complexity

Complexity in ecological systems often prevents long-term predictions about changes in population size and properties of the population dynamics. Mathematical modeling of such complex system behaviors can provide a rough idea of scenarios of the population dynamics. We use the reaction–diffusion model [Medvinsky, A.B., Morozov, A.Y., Velkov, V.V., Li, B.-L., Sokolov, M.S., Malchow, H., 2004. Modeling the invasion of recessive Bt-resistant insects: an impact on transgenic plants. J. Theor. Biol. 231, 121–127] to study the impact of pests resistant to toxins produced by genetically modified plants on the dynamics of the plant–insect system. Using genetically modified crops is an effective pest management tool for world-wide growers. However, there is a concern that pests may develop resistance to Bt toxins, which are a product of Bacillus thuringiensis genes introduced into genetically modified Bt plants. We show by computer simulations that the Bt plant–Bt-resistant insect dynamics resulting from the invasion of the Bt-resistant pests leads to variety of complex changes in the plant–insect biomass, which underlie the dependence of the Bt plant biomass on the duration of the insect reproduction period. We demonstrate that the plant and insect biomass can undergo both regular and irregular oscillations. We show that the character of such oscillations essentially depends on local insect fluxes resulting from inhomogeneous spatial distributions of the insects. In order to characterize the insect diffusion fluxes we introduce a new parameter, the diffusion number Dn. We show that the dependence between a value of Dn and regularity/irregularity of the plant–insect biomass oscillations is governed by a region in the model parameter space. In one of the regions the growth of the value of the diffusion number correlates with the transformation of regular oscillations into irregular ones, while in the neighboring region of the model parameter space the dependence between the character of the plant–insect oscillations and the value of the diffusion number Dn is more complex. The oscillations are irregular if the values of Dn are between 0.05 and 0.25. On either side of this interval the plant–insect oscillations are regular. The complex character of the response of the Bt crop–pest system to the invasion of Bt-resistant insects can lead to significant complications in attempts to regulate the system dynamics.     

Taming the complexity of large models

There are many complex biological models that fit the data perfectly and yet do not reflect the cellular reality. The process of validating a large model should therefore be viewed as an ongoing mission that refines underlying assumptions by improving low-confidence areas or gaps in the model''s construction.At its most basic, science is about models. Natural phenomena that were perplexing to ancient humans have been systematically illuminated as scientific models have revealed the mathematical order underlying the natural world. But what happens when the models themselves become complex enough that they too must be interpreted to be understood?In 2012, Jonathan Karr, Markus Covert and colleagues at the University of California, San Diego (USA) produced a bold new biological model that attempts to simulate an entire cell: iMg [1]. iMg merges 28 sub-modules of processes within Mycobacterium genitalium, one of the simplest organisms known to man. As a systems biology big-data model, iMg is unique in its scope and is an undeniable paragon of good craft. Because it is probable that this landmark paper will soon be followed by other whole cell models, we feel it is timely to examine this important endeavour, its challenges and potential pitfalls.Building a model requires making many decisions, such as which processes to glaze over and which to reconstruct in detail, how many and what kinds of connections to forge between the model''s constituents, and how to determine values for the model''s parameters. The standard practice has been to tune a model''s parameters and its structure to a best fit with the available data. But this approach breaks down when building a large whole cell model because the number of decisions inflates with the model''s size, and the amount of data required for these decisions to be unequivocal becomes huge. This problem is fundamental, not merely technical, and is rooted in the principle of frugality that underlies all science: Occam''s razor.The problem posed by Occam''s razor is that there are vastly more potential large models that can successfully predict and explain any given body of data than there are small ones. As we can tweak increasingly complex models in an increasing number of ways, we can produce many large models that fit the data perfectly and yet do not reflect the cellular reality. Even if a model fits all the data well, the chance of it happening to be the ‘correct'' model—in other words the one that reflects correctly the underlying cellular architecture and relevant enzymatic parameters—is inversely related to its complexity. A sophisticated large model such as iMg, which has been fitted to many available datasets, will certainly recapture many behaviours of the real system. But it could also recapture many other potentially wrong ones.How do we test a model''s correctness in the sense just mentioned? The intuitive way is to make and test predictions about previously uncharted phenomena. But validating a large biological model is an inherently different challenge than the common practice of “predict, test and validate” customary with smaller ones. Validation using phenotypic ‘emerging'' predictions would require such large amounts of data that it would be highly inefficient and costly at this scale, especially as many of these predictions will turn out to be false leads, with negative results yielding little insight. Rather, the correctness of a whole-cell model is perhaps best validated by using a complementary paradigm: direct testing of the basic decisions that went into the model''s construction. For example, enzymatic rate constants that were fitted in order to make the model behave properly could be experimentally scrutinized for later versions. Performing extensive sensitivity analyses and incorporating known confidence levels of modelling decisions, or harnessing more advanced methods such as ‘active learning'' should all be used in conjunction to determine which parameters to focus on in the future. The process of validating a large model should thus be viewed as an ongoing mission that aims to produce more refined and accurate drafts by improving low-confidence areas or gaps in the model''s construction. Step by step, this paradigm should increase a model''s reliability and ability to make valid new predictions.An open discussion of the potential pitfalls and benefits of building complex biological models could not be timelier, as both the EU and the US have just committed more than a combined 1.4 billion dollars to explicitly model the human brain. Massive data collection and big data analysis are the new norm in most fields, and big models are following closely behind. Their cost, usefulness and application remain open for discussion, but we certainly laud the spirit of the effort. For what is certain is this: only by building these models will we know what usefulness we can attribute to them. Paraphrasing Paul Cezzane, these efforts might be indeed justified and worthy, so long as one is “more or less master of his model”.     

On the nonlinear dynamic plane base-rotator models of DNA: Base-base interaction and dissipation

Nonlinear mechanical plane base-rotator models of DNA are considered. Various expressions for the potential energy of interaction between complementary bases are analyzed. Dissipative functions are introduced into these models: the external function describing the motion of the bases in a solvent and the function describing the internal friction in the molecule. Particle-like solutions of the model without dissipation are obtained and the influence of dissipation on these (soliton) excitations is studied.