Divining the Essence of Symbiosis: Insights from the Squid-Vibrio Model

Biology has a big elephant in the room. Researchers are learning that microorganisms are critical for every aspect of the biosphere''s health. Even at the scale of our own bodies, we are discovering the unexpected necessity and daunting complexity of our microbial partners. How can we gain an understanding of the form and function of these “ecosystems” that are an individual animal? This essay explores how development of experimental model systems reveals basic principles that underpin the essence of symbiosis and, more specifically, how one symbiosis, the squid-vibrio association, provides insight into the persistent microbial colonization of animal epithelial surfaces.     

Wnt Signaling from Development to Disease: Insights from Model Systems

One of the early surprises in the study of cell adhesion was the discovery that β-catenin plays dual roles, serving as an essential component of cadherin-based cell–cell adherens junctions and also serving as the key regulated effector of the Wnt signaling pathway. Here, we review our current model of Wnt signaling and discuss how recent work using model organisms has advanced our understanding of the roles Wnt signaling plays in both normal development and in disease. These data help flesh out the mechanisms of signaling from the membrane to the nucleus, revealing new protein players and providing novel information about known components of the pathway.Modern biomedical science is a partnership between scientists studying basic cell and developmental processes in model systems and clinicians exploring the basis of human disease. Few fields exemplify this better than Wnt signaling, born 22 years ago with the realization that the oncogene int1 and the Drosophila developmental patterning gene wingless (wg) are homologs (Cabrera et al. 1987; Rijsewijk et al. 1987). Additional connections further fueled research. Drosophila Armadillo (Arm), a component of the Wg pathway, is the homolog of the cell junction proteins β-catenin (βcat) and plakoglobin (McCrea et al. 1991; Peifer et al. 1992; Peifer and Wieschaus 1990) joining Wnt signaling and cadherin-based cell adhesion, a connection we still do not fully understand (see Heuberger and Birchmeier 2009). Adenomatous polyposis coli (APC), the tumor suppressor mutated in most colon cancers, binds βcat and is a key regulator of Wnt signaling (Rubinfeld et al. 1993; Su et al. 1993), putting the Wnt field even more squarely in the center of cancer research. Here, we outline recent advances in understanding Wnt signaling, casting new light on these critical regulators of development, homeostasis, and disease.     

On the Importance of Countergradients for the Development of Retinotopy: Insights from a Generalised Gierer Model

During the development of the topographic map from vertebrate retina to superior colliculus (SC), EphA receptors are expressed in a gradient along the nasotemporal retinal axis. Their ligands, ephrin-As, are expressed in a gradient along the rostrocaudal axis of the SC. Countergradients of ephrin-As in the retina and EphAs in the SC are also expressed. Disruption of any of these gradients leads to mapping errors. Gierer''s (1981) model, which uses well-matched pairs of gradients and countergradients to establish the mapping, can account for the formation of wild type maps, but not the double maps found in EphA knock-in experiments. I show that these maps can be explained by models, such as Gierer''s (1983), which have gradients and no countergradients, together with a powerful compensatory mechanism that helps to distribute connections evenly over the target region. However, this type of model cannot explain mapping errors found when the countergradients are knocked out partially. I examine the relative importance of countergradients as against compensatory mechanisms by generalising Gierer''s (1983) model so that the strength of compensation is adjustable. Either matching gradients and countergradients alone or poorly matching gradients and countergradients together with a strong compensatory mechanism are sufficient to establish an ordered mapping. With a weaker compensatory mechanism, gradients without countergradients lead to a poorer map, but the addition of countergradients improves the mapping. This model produces the double maps in simulated EphA knock-in experiments and a map consistent with the Math5 knock-out phenotype. Simulations of a set of phenotypes from the literature substantiate the finding that countergradients and compensation can be traded off against each other to give similar maps. I conclude that a successful model of retinotopy should contain countergradients and some form of compensation mechanism, but not in the strong form put forward by Gierer.     

Effects of an Introduced Piscivore on Native Trout: Insights from a Demographic Model

Introductions of exotic species pose a significant threat to the persistence of many native populations, including many inland fishes. In 1994, piscivorous lake trout (Salvelinus namaycush) were discovered in Yellowstone Lake, Yellowstone National Park, Wyoming, USA, one of the last strongholds of the native Yellowstone cutthroat trout (Oncorhynchus clarki bouvieri). Predation by lake trout is expected to lead to a substantial decline in the native cutthroat trout population, which may have significant negative consequences for terrestrial predators that depend on cutthroat trout for prey and for the recreational fishery of the Park. We developed a matrix demographic model for the cutthroat trout population in Yellowstone Lake to identify the life stages that are most critical for understanding population dynamics. Parameter estimates (vital rates) were manipulated to explore the possible consequences of lake trout invasion. Comparisons of our results with current estimates of population trend and age structure suggested that our model reflected current conditions of the system. Elasticity analysis of the model revealed that population growth was most sensitive to annual survival of young trout, the group that is expected to be most vulnerable to lake trout predation. Projection of our deterministic model suggested that, in addition to a decline in abundance of cutthroat trout, the effects of lake trout may be manifest as changes in age and breeding structure of the population. Simulations of a stochastic version of the model indicated that a 60% or greater decline in the cutthroat trout population could be expected within 100 years if the lake trout population were permitted to grow uncontrolled. However, an effective control strategy that prevented the establishment of a large population of lake trout substantially reduced population decline, although the reduction in the availability of adult trout to terrestrial predators and anglers may be still be substantial (20–40%). In addition to current control activities in place in the Park, we recommend a renewed emphasis on understanding and monitoring juvenile life stages of cutthroat trout. Our results demonstrate the value of existing data sets for developing models to estimate the potential impact of biological invasions on the management and conservation of native populations, especially when opportunities and resources for additional empirical studies are limited.     

Mapping the Prion Protein Distribution in Marsupials: Insights from Comparing Opossum with Mouse CNS

The cellular form of the prion protein (PrP^C) is a sialoglycoprotein widely expressed in the central nervous system (CNS) of mammalian species during neurodevelopment and in adulthood. The location of the protein in the CNS may play a role in the susceptibility of a species to fatal prion diseases, which are also known as the transmissible spongiform encephalopathies (TSEs). To date, little is known about PrP^C distribution in marsupial mammals, for which no naturally occurring prion diseases have been reported. To extend our understanding of varying PrP^C expression profiles in different mammals we carried out a detailed expression analysis of PrP^C distribution along the neurodevelopment of the metatherian South American short-tailed opossum (Monodelphis domestica). We detected lower levels of PrP^C in white matter fiber bundles of opossum CNS compared to mouse CNS. This result is consistent with a possible role for PrP^C in the distinct neurodevelopment and neurocircuitry found in marsupials compared to other mammalian species.     

一类带时滞竞争模型的周期解

研究了来源于水生种群植化相克的模型,提出了带时滞的半线性抛物系统．用上下解方法讨论了抛物方程组周期解存在性的原理,利用特征函数构造所提出抛物系统的上解,给出了正周期解存在的充分条件．     

Robust Unidirectional Airflow through Avian Lungs: New Insights from a Piecewise Linear Mathematical Model

Avian lungs are remarkably different from mammalian lungs in that air flows unidirectionally through rigid tubes in which gas exchange occurs. Experimental observations have been able to determine the pattern of gas flow in the respiratory system, but understanding how the flow pattern is generated and determining the factors contributing to the observed dynamics remains elusive. It has been hypothesized that the unidirectional flow is due to aerodynamic valving during inspiration and expiration, resulting from the anatomical structure and the fluid dynamics involved, however, theoretical studies to back up this hypothesis are lacking. We have constructed a novel mathematical model of the airflow in the avian respiratory system that can produce unidirectional flow which is robust to changes in model parameters, breathing frequency and breathing amplitude. The model consists of two piecewise linear ordinary differential equations with lumped parameters and discontinuous, flow-dependent resistances that mimic the experimental observations. Using dynamical systems techniques and numerical analysis, we show that unidirectional flow can be produced by either effective inspiratory or effective expiratory valving, but that both inspiratory and expiratory valving are required to produce the high efficiencies of flows observed in avian lungs. We further show that the efficacy of the inspiratory and expiratory valving depends on airsac compliances and airflow resistances that may not be located in the immediate area of the valving. Our model provides additional novel insights; for example, we show that physiologically realistic resistance values lead to efficiencies that are close to maximum, and that when the relative lumped compliances of the caudal and cranial airsacs vary, it affects the timing of the airflow across the gas exchange area. These and other insights obtained by our study significantly enhance our understanding of the operation of the avian respiratory system.     

Hydrological Forecasting in the Oder Estuary using a Three-Dimensional Hydrodynamic Model

A three-dimensional operational hydrodynamic model, developed at the Institute of Oceanography, University of Gdańsk was used to forecast hydrological conditions in the Oder Estuary. The model was based on the coastal ocean circulation model known as the Princeton Ocean Model (POM). Because of wind-driven water backup in the Oder mouth, a simplified operational model of river discharge, based on water budget in a stream channel, was developed. Linking these two models into a single system made it possible to forecast water levels, currents, water temperature, and salinity in the estuary. A good fit between the observed and computed data allowed to consider the model as a reliable environmental tool. Obtaining a hydrological forecast via a quick website access gives potential users an opportunity to predict the day-by-day course of processes that may affect different areas of human life and activities, e.g., navigation, port operations, flood protection of coastal areas; the predictions may also be used in studies of coastal processes in the estuary.     

Quercetin-Induced Melanogenesis in a Reconstituted Three-Dimensional Human Epidermal Model

Quercetin (3,5,7,3',4'-pentahydroxyflavone) is one of the most abundant natural flavonoids. It is present in various common vegetables and fruits. In this report, we examined the effect of quercetin on melanogenesis using a three-dimensional reconstituted human epidermal culture model, MelanoDerm, which is a new commercially-available cultured human epidermis containing functional melanocytes. Treatment with 10 microM quercetin induced an increase of tyrosinase activity in cultured epidermis after 3-5 days in time-dependent manner. In the quercetin-treated epidermis, furthermore, melanin content and tyrosinase expression were markedly increased, as shown by immunohistochemistry after a 7-day culture period. Ultrastructural studies clearly indicated an accumulation of mature melanosomes (stages III and IV) inside the basal layer of the cultured epidermis after the quercetin treatment. In addition, the dendrites of melanocytes extended further towards the adjacent keratinocytes after quercetin treatment. These results suggest that quercetin has an effect on maturation of melanosomes and that quercetin has the potential to induced melanogenesis in human epidermis.     

Site-Specific Phosphorylation of VEGFR2 Is Mediated by Receptor Trafficking: Insights from a Computational Model

Matrix-binding isoforms and non-matrix-binding isoforms of vascular endothelial growth factor (VEGF) are both capable of stimulating vascular remodeling, but the resulting blood vessel networks are structurally and functionally different. Here, we develop and validate a computational model of the binding of soluble and immobilized ligands to VEGF receptor 2 (VEGFR2), the endosomal trafficking of VEGFR2, and site-specific VEGFR2 tyrosine phosphorylation to study differences in induced signaling between these VEGF isoforms. In capturing essential features of VEGFR2 signaling and trafficking, our model suggests that VEGFR2 trafficking parameters are largely consistent across multiple endothelial cell lines. Simulations demonstrate distinct localization of VEGFR2 phosphorylated on Y1175 and Y1214. This is the first model to clearly show that differences in site-specific VEGFR2 activation when stimulated with immobilized VEGF compared to soluble VEGF can be accounted for by altered trafficking of VEGFR2 without an intrinsic difference in receptor activation. The model predicts that Neuropilin-1 can induce differences in the surface-to-internal distribution of VEGFR2. Simulations also show that ligated VEGFR2 and phosphorylated VEGFR2 levels diverge over time following stimulation. Using this model, we identify multiple key levers that alter how VEGF binding to VEGFR2 results in different coordinated patterns of multiple downstream signaling pathways. Specifically, simulations predict that VEGF immobilization, interactions with Neuropilin-1, perturbations of VEGFR2 trafficking, and changes in expression or activity of phosphatases acting on VEGFR2 all affect the magnitude, duration, and relative strength of VEGFR2 phosphorylation on tyrosines 1175 and 1214, and they do so predictably within our single consistent model framework.     

Towards Predicting the Response of a Solid Tumour to Chemotherapy and Radiotherapy Treatments: Clinical Insights from a Computational Model

In this paper we use a hybrid multiscale mathematical model that incorporates both individual cell behaviour through the cell-cycle and the effects of the changing microenvironment through oxygen dynamics to study the multiple effects of radiation therapy. The oxygenation status of the cells is considered as one of the important prognostic markers for determining radiation therapy, as hypoxic cells are less radiosensitive. Another factor that critically affects radiation sensitivity is cell-cycle regulation. The effects of radiation therapy are included in the model using a modified linear quadratic model for the radiation damage, incorporating the effects of hypoxia and cell-cycle in determining the cell-cycle phase-specific radiosensitivity. Furthermore, after irradiation, an individual cell''s cell-cycle dynamics are intrinsically modified through the activation of pathways responsible for repair mechanisms, often resulting in a delay/arrest in the cell-cycle. The model is then used to study various combinations of multiple doses of cell-cycle dependent chemotherapies and radiation therapy, as radiation may work better by the partial synchronisation of cells in the most radiosensitive phase of the cell-cycle. Moreover, using this multi-scale model, we investigate the optimum sequencing and scheduling of these multi-modality treatments, and the impact of internal and external heterogeneity on the spatio-temporal patterning of the distribution of tumour cells and their response to different treatment schedules.     

Mathematical Model of Contractile Ring-Driven Cytokinesis in a Three-Dimensional Domain

In this paper, a mathematical model of contractile ring-driven cytokinesis is presented by using both phase-field and immersed-boundary methods in a three-dimensional domain. It is one of the powerful hypotheses that cytokinesis happens driven by the contractile ring; however, there are only few mathematical models following the hypothesis, to the author’s knowledge. I consider a hybrid method to model the phenomenon. First, a cell membrane is represented by a zero-contour of a phase-field implicitly because of its topological change. Otherwise, immersed-boundary particles represent a contractile ring explicitly based on the author’s previous work. Here, the multi-component (or vector-valued) phase-field equation is considered to avoid the emerging of each cell membrane right after their divisions. Using a convex splitting scheme, the governing equation of the phase-field method has unique solvability. The numerical convergence of contractile ring to cell membrane is proved. Several numerical simulations are performed to validate the proposed model.     

Crawling with Virus: Translational Insights from a Neonatal Mouse Model on the Pathogenesis of Respiratory Syncytial Virus in Infants

The infant immune response to respiratory syncytial virus (RSV) remains incompletely understood. Here we review the use of a neonatal mouse model of RSV infection to mimic severe infection in human infants. We describe numerous age-specific responses, organized by cell type, observed in RSV-infected neonatal mice and draw comparisons (when possible) to human infants.     

Three-Dimensional Solid-State NMR Study of a Seven-Helical Integral Membrane Proton Pump—Structural Insights

Proteorhodopsin (PR) is a recently discovered ubiquitous eubacterial retinal-binding light-driven proton pump. Almost 1000 PR variants are widely distributed in species of marine and freshwater bacteria, suggesting PR's important photobiological role. PR is a typical seven-transmembrane α-helical membrane protein and as such poses a significant challenge to structural studies. Attempts to crystallize PR have not been successful, and its three-dimensional structure remains unknown. We show that PR reconstituted in lipids gives well-resolved magic-angle spinning NMR spectra of high signal-to-noise ratio. We report sequential assignment of ¹³C and ¹⁵N backbone and side-chain chemical shifts for 103 of 238 residues in PR, achieved by three-dimensional chemical shift correlation experiments performed on two samples with different patterns of reverse labeling. The chemical shift analysis gives a number of important structural insights not available from other studies: we have established protonation states of several carboxylic acids, identified the boundaries and distortions of transmembrane α-helices, and detected secondary structure elements in the loops. We confirmed that internal Asp227, which was proposed to form part of the Schiff base counterion, is ionized, while Glu142, which is located close to the extracellular surface, is neutral, in agreement with earlier predictions. We infer that, similar to bacteriorhodopsin's structure, PR has a proline kink in helix C, a non-proline kink in helix G, a short β-turn in the B-C loop, and a short α-helical segment in the E-F loop.     

一个单种群时滞微分方程模型的全局吸引性

研究了一个单种群时滞微分方程模型,给出了其平衡点吸引其正解得充分条件,应用本文结论对于两个例子进行讨论,得到其平衡点全局吸引性的新结果。     

A Reduce and Replace Strategy for Suppressing Vector-Borne Diseases: Insights from a Stochastic,Spatial Model

Two basic strategies have been proposed for using transgenic Aedes aegypti mosquitoes to decrease dengue virus transmission: population reduction and population replacement. Here we model releases of a strain of Ae. aegypti carrying both a gene causing conditional adult female mortality and a gene blocking virus transmission into a wild population to assess whether such releases could reduce the number of competent vectors. We find this “reduce and replace” strategy can decrease the frequency of competent vectors below 50% two years after releases end. Therefore, this combined approach appears preferable to releasing a strain carrying only a female-killing gene, which is likely to merely result in temporary population suppression. However, the fixation of anti-pathogen genes in the population is unlikely. Genetic drift at small population sizes and the spatially heterogeneous nature of the population recovery after releases end prevent complete replacement of the competent vector population. Furthermore, releasing more individuals can be counter-productive in the face of immigration by wild-type mosquitoes, as greater population reduction amplifies the impact wild-type migrants have on the long-term frequency of the anti-pathogen gene. We expect the results presented here to give pause to expectations for driving an anti-pathogen construct to fixation by relying on releasing individuals carrying this two-gene construct. Nevertheless, in some dengue-endemic environments, a spatially heterogeneous decrease in competent vectors may still facilitate decreasing disease incidence.     

Watkinson时滞差分方程模型的全局渐近稳定性

考虑差分方程ｘｎ＋１＝λｘｎ／（１＋ａｘｎ－ｋ）＾ｐ＋ｂλｘｎ－ｍ,ｎ＝０,１,２,…,其中ａ,ｂ,ｐ＞０,λ＞１,ｋ,ｍ∈｛０,１,２,…｝,当ｋ＝ｍ＝０时,Ｗａｔｋｉｎｓｏｎ用此方程来描述热带地区季蜀黍属作物的生长规律,当Ｐ＝１时,此方程就是著名的含多个滞量的Ｌｏｇｉｓｔｉｃ微分方程的离散模拟,本文主要目的是研究该方程唯一正平衡解的全局渐近稳定性。     

Calcium Involvement in Regulation of Neuronal Bursting in Disinhibited Neuronal Networks: Insights from Calcium Studies in a Spherical Cell Model

Cytosolic calcium is involved in the regulation of many intracellular processes. Intracellular calcium may therefore potentially affect the behavior of both single neurons and synaptically connected neuronal assemblies. In computer model studies, we investigated calcium dynamics in spherical neurons during periods of recurrent neuronal bursting that were simulated in a disinhibited neuronal network. The model takes into account calcium influx via voltage-gated calcium channels, extrusion through the cell membrane, and binding to two different buffers representing fixed and mobile endogenous calcium buffers. Throughout the duration of the simulated recurrent neuronal bursting, the concentration of free fixed buffers shows a hyperbolic decrease in time at a rate that is not uniform inside a neuron. Recurrent calcium influxes associated with bursting lead to the formation of gradients in the concentration of the fixed buffer in the radial direction, and are accompanied by the redistribution of mobile buffers acting to compensate for these gradients. Simulated intracellular calcium transients have a slow component characterized by a gradual increase in the calcium baseline level that reaches a plateau 120-200 s after the onset of recurrent bursting. Using this model, we demonstrate what we believe is a novel mechanism of regulation of network excitability that occurs in conditions of prolonged and recurrent neuronal bursting in disinhibited networks. This mechanism is expressed via interaction of calcium clearance systems inside neurons with calcium-dependent potassium regulation of neuronal excitability in membranes. This is a network phenomenon because it arises largely by synaptic interactions. Therefore, it can serve as a network safety mechanism to prevent excessive and uncontrolled neuronal firing resulting from the lack of inhibition or after acute suppression of the inhibitory drive.