How well do reduced models capture the dynamics in models of interacting neurons?

This paper introduces a class of stochastic models of interacting neurons with emergent dynamics similar to those seen in local cortical populations. Rigorous results on existence and uniqueness of nonequilibrium steady states are proved. These network models are then compared to very simple reduced models driven by the same mean excitatory and inhibitory currents. Discrepancies in firing rates between network and reduced models are investigated and explained by correlations in spiking, or partial synchronization, working in concert with “nonlinearities” in the time evolution of membrane potentials. The use of simple random walks and their first passage times to simulate fluctuations in neuronal membrane potentials and interspike times is also considered.

     

Individual behavioral variation in predator–prey models

The role of individual behavioral variation in community dynamics was studied. Behavioral variation in this study does not refer to differences in average responses (e.g., average response between presence and absence of antipredator behavior). Rather it refers to the variation around the average response that is not explained by trivial experimental treatments. First, the effect of behavioral variation was examined based on Jensen’s inequality. In cases of commonly used modeling framework with type II functional response, neglecting behavioral variation (a component of encounter rate) causes overestimation of predation effects. The effect of this bias on community processes was examined by incorporating the behavioral variation in a commonly used consumer-resource model (Rosenzweig–MacArthur model). How such a consideration affects a model prediction (paradox of enrichment) was examined. The inclusion of behavioral variation can both quantitatively and qualitatively alter the model characteristics. Behavioral variation can substantially increase the stability of the community with respect to enrichment.     

Mathematical models of α-synuclein transport in axons

To investigate possible effects of diffusion on α-synuclein (α-syn) transport in axons, we developed two models of α-syn transport, one that assumes that α-syn is transported only by active transport, as part of multiprotein complexes, and a second that assumes an interplay between motor-driven and diffusion-driven α-syn transport. By comparing predictions of the two models, we were able to investigate how diffusion could influence axonal transport of α-syn. The predictions obtained could be useful for future experimental work aimed at elucidating the mechanisms of axonal transport of α-syn. We also attempted to simulate possible defects in α-syn transport early in Parkinson's disease (PD). We assumed that in healthy axons α-syn localizes in the axon terminal while in diseased axons α-syn does not localize in the terminal (this was simulated by postulating a zero α-syn flux into the terminal). We found that our model of a diseased axon predicts the build-up of α-syn close to the axon terminal. This build-up could cause α-syn accumulation in Lewy bodies and the subsequent axonal death pattern observed in PD (‘dying back’ of axons).     

Mobility unevenness in rock–paper–scissors models

We investigate a tritrophic system whose cyclic dominance is modelled by the rock–paper–scissors game. We consider that organisms of one or two species are affected by movement limitations, which unbalances the cyclic spatial game. Performing stochastic simulations, we show that mobility unevenness controls the population dynamics. In the case of one slow species, the predominant species depends on the level of mobility restriction, with the slow species being preponderant if the mobility limitations are substantial. If two species face mobility limitations, our outcomes show that being higher dispersive does not constitute an advantage in terms of population growth. On the contrary, if organisms move with higher mobility, they expose themselves to enemies more frequently, being more vulnerable to being eliminated. Finally, our findings show that biodiversity benefits in regions where species are slowed. Biodiversity loss for high mobility organisms, common to cyclic systems, may be avoided with coexistence probability being higher for robust mobility limitations. Our results may help biologists understand the dynamics of unbalanced spatial systems where organisms’ dispersal is fundamental to biodiversity conservation.     

Nitrogen fixation in eukaryotes – New models for symbiosis

Background  

Nitrogen, a component of many bio-molecules, is essential for growth and development of all organisms. Most nitrogen exists in the atmosphere, and utilisation of this source is important as a means of avoiding nitrogen starvation. However, the ability to fix atmospheric nitrogen via the nitrogenase enzyme complex is restricted to some bacteria. Eukaryotic organisms are only able to obtain fixed nitrogen through their symbiotic interactions with nitrogen-fixing prokaryotes. These symbioses involve a variety of host organisms, including animals, plants, fungi and protists.     

Parkinson��s disease mouse models in translational research

Animal models with high predictive power are a prerequisite for translational research. The closer the similarity of a model to Parkinson??s disease (PD), the higher is the predictive value for clinical trials. An ideal PD model should present behavioral signs and pathology that resemble the human disease. The increasing understanding of PD stratification and etiology, however, complicates the choice of adequate animal models for preclinical studies. An ultimate mouse model, relevant to address all PD-related questions, is yet to be developed. However, many of the existing models are useful in answering specific questions. An appropriate model should be chosen after considering both the context of the research and the model properties. This review addresses the validity, strengths, and limitations of current PD mouse models for translational research.     

Spiral blood flow in aorta–renal bifurcation models

The presence of a spiral arterial blood flow pattern in humans has been widely accepted. It is believed that this spiral component of the blood flow alters arterial haemodynamics in both positive and negative ways. The purpose of this study was to determine the effect of spiral flow on haemodynamic changes in aorta–renal bifurcations. In this regard, a computational fluid dynamics analysis of pulsatile blood flow was performed in two idealised models of aorta–renal bifurcations with and without flow diverter. The results show that the spirality effect causes a substantial variation in blood velocity distribution, while causing only slight changes in fluid shear stress patterns. The dominant observed effect of spiral flow is on turbulent kinetic energy and flow recirculation zones. As spiral flow intensity increases, the rate of turbulent kinetic energy production decreases, reducing the region of potential damage to red blood cells and endothelial cells. Furthermore, the recirculation zones which form on the cranial sides of the aorta and renal artery shrink in size in the presence of spirality effect; this may lower the rate of atherosclerosis development and progression in the aorta–renal bifurcation. These results indicate that the spiral nature of blood flow has atheroprotective effects in renal arteries and should be taken into consideration in analyses of the aorta and renal arteries.     

Mechanistic understanding of β-cryptoxanthin and lycopene in cancer prevention in animal models

To better understand the potential function of carotenoids in the chemoprevention of cancers, mechanistic understanding of carotenoid action on genetic and epigenetic signaling pathways is critically needed for human studies. The use of appropriate animal models is the most justifiable approach to resolve mechanistic issues regarding protective effects of carotenoids at specific organs and tissue sites. While the initial impetus for studying the benefits of carotenoids in cancer prevention was their antioxidant capacity and pro-vitamin A activity, significant advances have been made in the understanding of the action of carotenoids with regards to other mechanisms. This review will focus on two common carotenoids, provitamin A carotenoid β-cryptoxanthin and non-provitamin A carotenoid lycopene, as promising chemopreventive agents or chemotherapeutic compounds against cancer development and progression. We reviewed animal studies demonstrating that β-cryptoxanthin and lycopene effectively prevent the development or progression of various cancers and the potential mechanisms involved. We highlight recent research that the biological functions of β-cryptoxanthin and lycopene are mediated, partially via their oxidative metabolites, through their effects on key molecular targeting events, such as NF-κB signaling pathway, RAR/PPARs signaling, SIRT1 signaling pathway, and p53 tumor suppressor pathways. The molecular targets by β-cryptoxanthin and lycopene, offer new opportunities to further our understanding of common and distinct mechanisms that involve carotenoids in cancer prevention.This article is part of a Special Issue entitled Carotenoids recent advances in cell and molecular biology edited by Johannes von Lintig and Loredana Quadro.     

Patterns of patchy spread in multi-species reaction–diffusion models

Spread of populations in space often takes place via formation, interaction and propagation of separated patches of high species density, without formation of continuous fronts. This type of spread is called a ‘patchy spread’. In earlier models, this phenomenon was considered to be a result of a pronounced environmental or/and demographic stochasticity. Recently, it was found that a patchy spread can arise in a fully deterministic predator–prey system and in models of infectious diseases; in each case the process takes place in a homogeneous environment. It is well recognized that the observed patterns of patchy spread in nature are a result of interplay between stochastic and deterministic factors. However, the models considering deterministic mechanism of patchy spread are developed and studied much less compared to those based on stochastic mechanisms. A further progress in the understanding of the role of deterministic factors in the patchy spread would be extremely helpful. Here we apply multi-species reaction–diffusion models of two spatial dimensions in a homogeneous environment. We demonstrate that patterns of patchy spread are rather common for the considered approach, in particular, they arise both in mutualism and competition models influenced by predation. We show that this phenomenon can occur in a system without a strong Allee effect, contrary to what was assumed to be crucial in earlier models. We show, as well, a pattern of patchy spread having significantly different speeds in different spatial directions. We analyze basic features of spatiotemporal dynamics of patchy spread common for the reaction–diffusion approach. We discuss in which ecosystems we would observe patterns of deterministic patchy spread due to the considered mechanism.     

Can cellular models revolutionize drug discovery in Parkinson's disease?

The study of mechanisms that underlie Parkinson's disease (PD), as well as translational drug development, has been hindered by the lack of appropriate models. Both cell culture systems and animal models have limitations, and to date none faithfully recapitulate all of the clinical and pathological phenotypes of the disease. In this review we examine the various cell culture model systems of PD, with a focus on different stem cell models that can be used for investigating disease mechanisms as well as drug discovery for PD. We conclude with a discussion of recent discoveries in the field of stem cell biology that have led to the ability to reprogram somatic cells to a pluripotent state via the use of a combination of genetic factors; these reprogrammed cells are termed “induced pluripotent stem cells” (iPSCs). This groundbreaking technique allows for the derivation of patient-specific cell lines from individuals with sporadic forms of PD and also those with known disease-causing mutations. Such cell lines have the potential to serve as a human cellular model of neurodegeneration and PD when differentiated into dopaminergic neurons. The hope is that these iPSC-derived dopaminergic neurons can be used to replicate the key molecular aspects of neural degeneration associated with PD. If so, this approach could lead to transformative new tools for the study of disease mechanisms. In addition, such cell lines can be potentially used for high-throughput drug screening. While not the focus of this review, ultimately it is envisioned that techniques for reprogramming of somatic cells may be optimized to a point sufficient to provide potential new avenues for stem cell-based restorative therapies.     

Dealing with many correlated covariates in capture–recapture models

Capture–recapture models for estimating demographic parameters allow covariates to be incorporated to better understand population dynamics. However, high-dimensionality and multicollinearity can hamper estimation and inference. Principal component analysis is incorporated within capture–recapture models and used to reduce the number of predictors into uncorrelated synthetic new variables. Principal components are selected by sequentially assessing their statistical significance. We provide an example on seabird survival to illustrate our approach. Our method requires standard statistical tools, which permits an efficient and easy implementation using standard software.     

What ecological factors shape species-area curves in neutral models?

Understanding factors that shape biodiversity and species coexistence across scales is of utmost importance in ecology, both theoretically and for conservation policies. Species-area relationships (SARs), measuring how the number of observed species increases upon enlarging the sampled area, constitute a convenient tool for quantifying the spatial structure of biodiversity. While general features of species-area curves are quite universal across ecosystems, some quantitative aspects can change significantly. Several attempts have been made to link these variations to ecological forces. Within the framework of spatially explicit neutral models, here we scrutinize the effect of varying the local population size (i.e. the number of individuals per site) and the level of habitat saturation (allowing for empty sites). We conclude that species-area curves become shallower when the local population size increases, while habitat saturation, unless strongly violated, plays a marginal role. Our findings provide a plausible explanation of why SARs for microorganisms are flatter than those for larger organisms.     

D-β-hydroxybutyrate is protective in mouse models of Huntington's disease

Abnormalities in mitochondrial function and epigenetic regulation are thought to be instrumental in Huntington's disease (HD), a fatal genetic disorder caused by an expanded polyglutamine track in the protein huntingtin. Given the lack of effective therapies for HD, we sought to assess the neuroprotective properties of the mitochondrial energizing ketone body, D-β-hydroxybutyrate (DβHB), in the 3-nitropropionic acid (3-NP) toxic and the R6/2 genetic model of HD. In mice treated with 3-NP, a complex II inhibitor, infusion of DβHB attenuates motor deficits, striatal lesions, and microgliosis in this model of toxin induced-striatal neurodegeneration. In transgenic R6/2 mice, infusion of DβHB extends life span, attenuates motor deficits, and prevents striatal histone deacetylation. In PC12 cells with inducible expression of mutant huntingtin protein, we further demonstrate that DβHB prevents histone deacetylation via a mechanism independent of its mitochondrial effects and independent of histone deacetylase inhibition. These pre-clinical findings suggest that by simultaneously targeting the mitochondrial and the epigenetic abnormalities associated with mutant huntingtin, DβHB may be a valuable therapeutic agent for HD.     

Analysis of gene × environment interactions in sibships using mixed models

Background

Gene × environment models are widely used to assess genetic and environmental risks and their association with a phenotype of interest for many complex diseases. Mixed generalized linear models were used to assess gene × environment interactions with respect to systolic blood pressure on sibships adjusting for repeated measures and hierarchical nesting structures. A data set containing 410 sibships from the Framingham Heart Study offspring cohort (part of the Genetic Analysis Workshop 13 data) was used for all analyses. Three mixed gene × environment models, all adjusting for repeated measurement and varying levels of nesting, were compared for precision of estimates: 1) all sibships with adjustment for two levels of nesting (sibs within sibships and sibs within pedigrees), 2) all sibships with adjustment for one level of nesting (sibs within sibships), and 3) 100 data sets containing random draws of one sibship per extended pedigree adjusting for one level of nesting.

Results

The main effects were: gender, baseline age, body mass index (BMI), hypertensive treatment, cigarettes per day, grams of alcohol per day, and marker GATA48G07A. The interaction fixed effects were: baseline age by gender, baseline age by cigarettes per day, baseline age by hypertensive treatment, baseline age by BMI, hypertensive treatment by BMI, and baseline age by marker GATA48G07A. The estimates for all three nesting techniques were not widely discrepant, but precision of estimates and determination of significant effects did change with the change in adjustment for nesting.

Conclusion

Our results show the importance of the adjustment for all levels of hierarchical nesting of sibs in the presence of repeated measures.

     

Large amplification in stage-structured models: Arnol’d tongues revisited

The coexistence of periodic and point attractors has been confirmed for a range of stage-structured discrete time models. The periodic attractor cycles have large amplitude, with the populations cycling between extremely low and surprisingly high values when compared to the equilibrium level. In this situation a stable state can be shocked by noise of sufficient strength into a state of high volatility. We found that the source of these large amplitude cycles are Arnold tongues, special regions of parameter space where the system exhibits periodic behaviour. Most of these tongues lie entirely in that part of parameter space where the system is unstable, but there are exceptions and these exceptions are the tongues that lead to attractor coexistence. Similarity in the geometry of Arnold tongues over the range of models considered might suggest that this is a common feature of stage-structured models but in the absence of proof this can only be a useful working hypothesis. The analysis shows that although large amplitude cycles might exist mathematically they might not be accessible biologically if biological constraints, such as non-negativity of population densities and vital rates, are imposed. Accessibility is found to be highly sensitive to model structure even though the mathematical structure is not. This highlights the danger of drawing biological conclusions from particular models. Having a comprehensive view of the different mechanisms by which periodic states can arise in families of discrete time models is important in the debate on whether the causes of periodicity in particular ecological systems are intrinsic, environmental or trophic. This paper is a contribution to that continuing debate.     

Cartilage-specific autoimmunity in animal models and clinical aspects in patients – focus on relapsing polychondritis

Relapsing polychondritis is an autoimmune disease in which an inappropriate immune response destroys cartilage. Cartilage of the ears, larynx and nose rather than spine and joint cartilage is affected by a chronic relapsing and erosive inflammation. Several animal models for relapsing polychondritis have been published in which immunization with various cartilage proteins induces a variety of chondritis symptoms that mimic those seen in patients. In this review we describe the collagens, matrilin-1 and cartilage oligomeric matrix protein as potential autoantigens able to trigger the tissue-specific immune response seen both in patients and in animal models for relapsing polychondritis and related autoimmune diseases.     

Elastin calcification in in vitro models and its prevention by MGP’s N-terminal peptide

Medial calcification has been associated with diabetes, chronic kidney disease, and genetic disorders like pseudoxanthoma elasticum. Recently, we showed that genetic reduction of arterial elastin content reduces the severity of medial calcification in matrix Gla protein (MGP)-deficient and Eln haploinsufficient Mgp?/?;Eln+/? mice. This study suggests that there might be a direct effect of elastin amount on medial calcification. We studied this using novel in vitro systems, which are based on elastin or elastin-like polypeptides. We first examined the mineral deposition properties of a transfected pigmented epithelial cell line that expresses elastin and other elastic lamina proteins. When grown in inorganic phosphate-supplemented medium, these cells deposited calcium phosphate minerals, which could be prevented by an N’-terminal peptide of MGP (m3pS) carrying phosphorylated serine residues. We next confirmed these findings using a cell-free elastin-like polypeptide (ELP₃) scaffold, where the peptide prevented mineral maturation. Overall, this work describes a novel cell culture model for elastocalcinosis and examines the inhibition of mineral deposition by the m3pS peptide in this and a cell-free elastin-based scaffold. Our study provides strong evidence suggesting the critical functional roles of MGP’s phosphorylated serine residues in the prevention of elastin calcification and proposes a possible mechanism of their action.