Seasonal Invasion Dynamics in a Spatially Heterogeneous River with Fluctuating Flows

A key problem in environmental flow assessment is the explicit linking of the flow regime with ecological dynamics. We present a hybrid modeling approach to couple hydrodynamic and biological processes, focusing on the combined impact of spatial heterogeneity and temporal variability on population dynamics. Studying periodically alternating pool-riffle rivers that are subjected to seasonally varying flows, we obtain an invasion ratchet mechanism. We analyze the ratchet process for a caricature model and a hybrid physical–biological model. The water depth and current are derived from a hydrodynamic equation for variable stream bed water flows and these quantities feed into a reaction-diffusion-advection model that governs population dynamics of a river species. We establish the existence of spreading speeds and the invasion ratchet phenomenon, using a mixture of mathematical approximations and numerical computations. Finally, we illustrate the invasion ratchet phenomenon in a spatially two-dimensional hydraulic simulation model of a meandering river structure. Our hybrid modeling approach strengthens the ecological component of stream hydraulics and allows us to gain a mechanistic understanding as to how flow patterns affect population survival.     

Evolution under Spatially Heterogeneous Selection in Solid Tumors

Spatial genetic and phenotypic diversity within solid tumors has been well documented. Nevertheless, how this heterogeneity affects temporal dynamics of tumorigenesis has not been rigorously examined because solid tumors do not evolve as the standard population genetic model due to the spatial constraint. We therefore, propose a neutral spatial (NS) model whereby the mutation accumulation increases toward the periphery; the genealogical relationship is spatially determined and the selection efficacy is blunted (due to kin competition). In this model, neutral mutations are accrued and spatially distributed in manners different from those of advantageous mutations. Importantly, the distinctions could be blurred in the conventional model. To test the NS model, we performed a three-dimensional multiple microsampling of two hepatocellular carcinomas. Whole-genome sequencing (WGS) revealed a 2-fold increase in mutations going from the center to the periphery. The operation of natural selection can then be tested by examining the spatially determined clonal relationships and the clonal sizes. Due to limited migration, only the expansion of highly advantageous clones can sweep through a large part of the tumor to reveal the selective advantages. Hence, even multiregional sampling can only reveal a fraction of fitness differences in solid tumors. Our results suggest that the NS patterns are crucial for testing the influence of natural selection during tumorigenesis, especially for small solid tumors.     

Adaptation Dynamics in Densely Clustered Chemoreceptors

In many sensory systems, transmembrane receptors are spatially organized in large clusters. Such arrangement may facilitate signal amplification and the integration of multiple stimuli. However, this organization likely also affects the kinetics of signaling since the cytoplasmic enzymes that modulate the activity of the receptors must localize to the cluster prior to receptor modification. Here we examine how these spatial considerations shape signaling dynamics at rest and in response to stimuli. As a model system, we use the chemotaxis pathway of Escherichia coli, a canonical system for the study of how organisms sense, respond, and adapt to environmental stimuli. In bacterial chemotaxis, adaptation is mediated by two enzymes that localize to the clustered receptors and modulate their activity through methylation-demethylation. Using a novel stochastic simulation, we show that distributive receptor methylation is necessary for successful adaptation to stimulus and also leads to large fluctuations in receptor activity in the steady state. These fluctuations arise from noise in the number of localized enzymes combined with saturated modification kinetics between the localized enzymes and the receptor substrate. An analytical model explains how saturated enzyme kinetics and large fluctuations can coexist with an adapted state robust to variation in the expression levels of the pathway constituents, a key requirement to ensure the functionality of individual cells within a population. This contrasts with the well-mixed covalent modification system studied by Goldbeter and Koshland in which mean activity becomes ultrasensitive to protein abundances when the enzymes operate at saturation. Large fluctuations in receptor activity have been quantified experimentally and may benefit the cell by enhancing its ability to explore empty environments and track shallow nutrient gradients. Here we clarify the mechanistic relationship of these large fluctuations to well-studied aspects of the chemotaxis system, precise adaptation and functional robustness.     

The Impact of the Allee Effect in Dispersal and Patch-Occupancy Age on the Dynamics of Metapopulations

In this paper, we introduce a Levins-type metapopulation model with empty and occupied patches, and dispersing population. We structure the proportion of occupied patches according to the patch-occupancy age. We observe that patch-occupancy age may destabilize the metapopulation, leading to persistent oscillations. We also allow for the dispersal rate to vary with the proportion of empty patches in a monotone or unimodal way. The unimodal dependence leads to multiple non-trivial equilibria and bistability when the reproduction number of the metapopulation < 1 but greater than a lower critical value ^*. We show that the metapopulation will persist independently of its initial status if > 1.     

The Urban Funnel Model and the Spatially Heterogeneous Ecological Footprint

Urban ecological systems are characterized by complex interactions between the natural environment and humans at multiple scales; for an individual urban ecosystem, the strongest interactions may occur at the local or regional spatial scale. At the regional scale, external ecosystems produce resources that are acquired and transported by humans to urban areas, where they are processed and consumed. The assimilation of diffuse human wastes and pollutants also occurs at the regional scale, with much of this process occurring external to the urban system. We developed the urban funnel model to conceptualize the integration of humans into their ecological context. The model captures this pattern and process of resource appropriation and waste generation by urban ecosystems at various spatial scales. This model is applied to individual cities using a modification of traditional ecological footprint (EF) analysis that is spatially explicit; the incorporation of spatial heterogeneity in calculating the EF greatly improves its accuracy. The method for EF analysis can be further modified to ensure that a certain proportion of potential ecosystem services are left for in situ processes. Combining EF models of human appropriation with ecosystem process models would help us to learn more about the effects of ecosystem service appropriation. By comparing the results for food and water, we were able to identify some of the potentially limiting ecological factors for cities. A comparison of the EFs for the 20 largest US cities showed the importance of urban location and interurban competition for ecosystem services. This study underscores the need to take multiple scales and spatial heterogeneity into consideration to expand our current understanding of human–ecosystem interactions. The urban funnel model and the spatially heterogeneous EF provide an effective means of achieving this goal. Received 17 October 2000; accepted 31 May 2001.     

Thermal Adaptation of Conformational Dynamics in Ribonuclease H

The relationship between inherent internal conformational processes and enzymatic activity or thermodynamic stability of proteins has proven difficult to characterize. The study of homologous proteins with differing thermostabilities offers an especially useful approach for understanding the functional aspects of conformational dynamics. In particular, ribonuclease HI (RNase H), an 18 kD globular protein that hydrolyzes the RNA strand of RNA:DNA hybrid substrates, has been extensively studied by NMR spectroscopy to characterize the differences in dynamics between homologs from the mesophilic organism E. coli and the thermophilic organism T. thermophilus. Herein, molecular dynamics simulations are reported for five homologous RNase H proteins of varying thermostabilities and enzymatic activities from organisms of markedly different preferred growth temperatures. For the E. coli and T. thermophilus proteins, strong agreement is obtained between simulated and experimental values for NMR order parameters and for dynamically averaged chemical shifts, suggesting that these simulations can be a productive platform for predicting the effects of individual amino acid residues on dynamic behavior. Analyses of the simulations reveal that a single residue differentiates between two different and otherwise conserved dynamic processes in a region of the protein known to form part of the substrate-binding interface. Additional key residues within these two categories are identified through the temperature-dependence of these conformational processes.     

Optimal Dynamics for Quality Control in Spatially Distributed Mitochondrial Networks

Recent imaging studies of mitochondrial dynamics have implicated a cycle of fusion, fission, and autophagy in the quality control of mitochondrial function by selectively increasing the membrane potential of some mitochondria at the expense of the turnover of others. This complex, dynamical system creates spatially distributed networks that are dependent on active transport along cytoskeletal networks and on protein import leading to biogenesis. To study the relative impacts of local interactions between neighboring mitochondria and their reorganization via transport, we have developed a spatiotemporal mathematical model encompassing all of these processes in which we focus on the dynamics of a health parameter meant to mimic the functional state of mitochondria. In agreement with previous models, we show that both autophagy and the generation of membrane potential asymmetry following a fusion/fission cycle are required for maintaining a healthy mitochondrial population. This health maintenance is affected by mitochondrial density and motility primarily through changes in the frequency of fusion events. Health is optimized when the selectivity thresholds for fusion and fission are matched, providing a mechanistic basis for the observed coupling of the two processes through the protein OPA1. We also demonstrate that the discreteness of the components exchanged during fusion is critical for quality control, and that the effects of limiting total amounts of autophagy and biogenesis have distinct consequences on health and population size, respectively. Taken together, our results show that several general principles emerge from the complexity of the quality control cycle that can be used to focus and interpret future experimental studies, and our modeling framework provides a road-map for deconstructing the functional importance of local interactions in communities of cells as well as organelles.     

Generalization in Adaptation to Stable and Unstable Dynamics

Humans skillfully manipulate objects and tools despite the inherent instability. In order to succeed at these tasks, the sensorimotor control system must build an internal representation of both the force and mechanical impedance. As it is not practical to either learn or store motor commands for every possible future action, the sensorimotor control system generalizes a control strategy for a range of movements based on learning performed over a set of movements. Here, we introduce a computational model for this learning and generalization, which specifies how to learn feedforward muscle activity in a function of the state space. Specifically, by incorporating co-activation as a function of error into the feedback command, we are able to derive an algorithm from a gradient descent minimization of motion error and effort, subject to maintaining a stability margin. This algorithm can be used to learn to coordinate any of a variety of motor primitives such as force fields, muscle synergies, physical models or artificial neural networks. This model for human learning and generalization is able to adapt to both stable and unstable dynamics, and provides a controller for generating efficient adaptive motor behavior in robots. Simulation results exhibit predictions consistent with all experiments on learning of novel dynamics requiring adaptation of force and impedance, and enable us to re-examine some of the previous interpretations of experiments on generalization.     

Predators Reduce Extinction Risk in Noisy Metapopulations

Background

Spatial structure across fragmented landscapes can enhance regional population persistence by promoting local “rescue effects.” In small, vulnerable populations, where chance or random events between individuals may have disproportionately large effects on species interactions, such local processes are particularly important. However, existing theory often only describes the dynamics of metapopulations at regional scales, neglecting the role of multispecies population dynamics within habitat patches.

Findings

By coupling analysis across spatial scales we quantified the interaction between local scale population regulation, regional dispersal and noise processes in the dynamics of experimental host-parasitoid metapopulations. We find that increasing community complexity increases negative correlation between local population dynamics. A potential mechanism underpinning this finding was explored using a simple population dynamic model.

Conclusions

Our results suggest a paradox: parasitism, whilst clearly damaging to hosts at the individual level, reduces extinction risk at the population level.     

Inferring Diffusion Dynamics from FCS in Heterogeneous Nuclear Environments

Fluorescence correlation spectroscopy (FCS) is a noninvasive technique that probes the diffusion dynamics of proteins down to single-molecule sensitivity in living cells. Critical mechanistic insight is often drawn from FCS experiments by fitting the resulting time-intensity correlation function, G(t), to known diffusion models. When simple models fail, the complex diffusion dynamics of proteins within heterogeneous cellular environments can be fit to anomalous diffusion models with adjustable anomalous exponents. Here, we take a different approach. We use the maximum entropy method to show—first using synthetic data—that a model for proteins diffusing while stochastically binding/unbinding to various affinity sites in living cells gives rise to a G(t) that could otherwise be equally well fit using anomalous diffusion models. We explain the mechanistic insight derived from our method. In particular, using real FCS data, we describe how the effects of cell crowding and binding to affinity sites manifest themselves in the behavior of G(t). Our focus is on the diffusive behavior of an engineered protein in 1) the heterochromatin region of the cell’s nucleus as well as 2) in the cell’s cytoplasm and 3) in solution. The protein consists of the basic region-leucine zipper (BZip) domain of the CCAAT/enhancer-binding protein (C/EBP) fused to fluorescent proteins.     

Dynamics of Heterogeneous Liners with Prolonged Plasma Creation

Prolonged plasma creation in heterogeneous liners, in which the liner substance is separated into two phase states (a hot plasma and a cold skeleton), is investigated both experimentally and theoretically. This situation is typical of multiwire, foam, and even gas liners in high-current high-voltage facilities. The main mechanisms governing the rate at which the plasma is created are investigated, and the simplest estimates of the creation rate are presented. It is found that, during prolonged plasma creation, the electric current flows through the entire cross section of the produced plasma shell, whose thickness is comparable with the liner radius; in other words, a current skin layer does not form. During compression, such a shell is fairly stable because of its relatively high resilience. It is shown that, under certain conditions, even a thick plasma shell can be highly compressed toward the discharge axis. A simplified numerical simulation of the compression of a plasma shell in a liner with prolonged plasma creation is employed in order to determine the conditions for achieving regimes of fairly compact and relatively stable radial compression of the shell.     

Longitudinal Study of Spatially Heterogeneous Emphysema Progression in Current Smokers with Chronic Obstructive Pulmonary Disease

Background

Cigarette smoke is the main risk factor for emphysema, which is a key pathology in chronic obstructive pulmonary disease (COPD). Low attenuation areas (LAA) in computed tomography (CT) images reflect emphysema, and the cumulative size distribution of LAA clusters follows a power law characterized by the exponent D. This property of LAA clusters can be explained by model simulation, where mechanical force breaks alveolar walls causing local heterogeneous lung tissue destruction. However, a longitudinal CT study has not investigated whether continuous smoking causes the spatially heterogeneous progression of emphysema.

Methods

We measured annual changes in ratios of LAA (LAA%), D and numbers of LAA clusters (LAN) in CT images acquired at intervals of ≥3 years from 22 current and 31 former smokers with COPD to assess emphysema progression. We constructed model simulations using CT images to morphologically interpret changes in current smokers.

Results

D was decreased in current and former smokers, whereas LAA% and LAN were increased only in current smokers. The annual changes in LAA%, D, and LAN were greater in current, than in former smokers (1.03 vs. 0.37%, p = 0.008; −0.045 vs. −0.01, p = 0.004; 13.9 vs. 1.1, p = 0.007, respectively). When LAA% increased in model simulations, the coalescence of neighboring LAA clusters decreased D, but the combination of changes in D and LAN in current smokers could not be explained by the homogeneous emphysema progression model despite cluster coalescence. Conversely, a model in which LAAs heterogeneously increased and LAA clusters merged somewhat in relatively advanced emphysematous regions could reflect actual changes.

Conclusions

Susceptibility to parenchymal destruction induced by continuous smoking is not uniform over the lung, but might be higher in local regions of relatively advanced emphysema. These could result in the spatially heterogeneous progression of emphysema in current smokers.     

Optimizing Carbon Storage Within a Spatially Heterogeneous Upland Grassland Through Sheep Grazing Management

Livestock grazing is known to influence carbon (C) storage in vegetation and soil. Yet, for grazing management to be used to optimize C storage, large scale investigations that take into account the typically heterogeneous distribution of grazers and C across the landscape are required. In a landscape-scale grazing experiment in the Scottish uplands, we quantified C stored in swards dominated by the widespread tussock-forming grass species Molinia caerulea. The impact of three sheep stocking treatments (‘commercial’ 2.7 ewes ha^?1 y^?1, ‘low’ 0.9 ewes ha^?1 y^?1 and no livestock) on plant C stocks was determined at three spatial scales; tussock, sward and landscape, and these data were used to predict long-term changes in soil organic carbon (SOC). We found that tussocks were particularly dense C stores (that is, high C mass per unit area) and that grazing reduced their abundance and thus influenced C stocks held in M. caerulea swards across the landscape; C stocks were 3.83, 5.01 and 6.85 Mg C ha^?1 under commercial sheep grazing, low sheep grazing and no grazing, respectively. Measured vegetation C in the three grazing treatments provided annual C inputs to RothC, an organic matter turnover model, to predict changes in SOC over 100 years. RothC predicted SOC to decline under commercial sheep stocking and increase under low sheep grazing and no grazing. Our findings suggest that no sheep and low-intensity sheep grazing are better upland management practices for enhancing plant and soil C sequestration than commercial sheep grazing. This is evaluated in the context of other upland management objectives.     

Synchronization and Oscillatory Dynamics in Heterogeneous, Mutually Inhibited Neurons

We study some mechanisms responsible for synchronous oscillations and loss of synchrony at physiologically relevant frequencies (10–200 Hz) in a network of heterogeneous inhibitory neurons. We focus on the factors that determine the level of synchrony and frequency of the network response, as well as the effects of mild heterogeneity on network dynamics. With mild heterogeneity, synchrony is never perfect and is relatively fragile. In addition, the effects of inhibition are more complex in mildly heterogeneous networks than in homogeneous ones. In the former, synchrony is broken in two distinct ways, depending on the ratio of the synaptic decay time to the period of repetitive action potentials (_s/T), where T can be determined either from the network or from a single, self-inhibiting neuron. With _s/T > 2, corresponding to large applied current, small synaptic strength or large synaptic decay time, the effects of inhibition are largely tonic and heterogeneous neurons spike relatively independently. With _s/T < 1, synchrony breaks when faster cells begin to suppress their less excitable neighbors; cells that fire remain nearly synchronous. We show numerically that the behavior of mildly heterogeneous networks can be related to the behavior of single, self-inhibiting cells, which can be studied analytically.