A Dynamical Model of Lipoprotein Metabolism

We present a dynamical model of lipoprotein metabolism derived by combining a cascading process in the blood stream and cellular level regulatory dynamics. We analyse the existence and stability of equilibria and show that this low-dimensional, nonlinear model exhibits bistability between a low and a high cholesterol state. A sensitivity analysis indicates that the intracellular concentration of cholesterol is robust to parametric variations while the plasma cholesterol can vary widely. We show how the dynamical response to time-dependent inputs can be used to diagnose the state of the system. We also establish the connection between parameters in the system and medical and genetic conditions.     

Song-related brain regions in the red-winged blackbird are affected by sex and season but not repertoire size

Previous work in songbirds has delimited a neural system responsible for song production and control. Earlier studies have suggested that functional capacity in the song system may be related to the mass of the system in an animal's brain, and that adult plasticity in this neural system may be related to adult capacity for behavioral modification. We now test these hypotheses in adult red-winged blackbirds (Agelaius phoeniceus), a species in which song is produced primarily by males, new song types are added to the male's repertoire in adulthood, and there are substantial differences among males in song complexity. We find that the song system in males is much larger than in females. Song system nuclei become smaller in both sexes as the animals experience shorter days. We do not find any association between repertoire size and size of any of the song system structures examined. Thus, although sex differences in song may be related to differences between sexes in the mass of song system structures, individual differences in song do not appear to be directly related to mass within males. Seasonal change in song system structures in male redwings is consistent with there being a relation between adult plasticity in anatomy and in behavior; the large seasonal change in these structures in females suggests large seasonal changes in the function of these nuclei.     

A cellular automata model of tumor-immune system interactions

We present a hybrid cellular automata-partial differential equation model of moderate complexity to describe the interactions between a growing tumor next to a nutrient source and the immune system of the host organism. The model allows both temporal and two-dimensional spatial evolution of the system under investigation and is comprised of biological cell metabolism rules derived from both the experimental and mathematical modeling literature. We present numerical simulations that display behaviors which are qualitatively similar to those exhibited in tumor-immune system interaction experiments. These include spherical tumor growth, stable and unstable oscillatory tumor growth, satellitosis and tumor infiltration by immune cells. Finally, the relationship between these different growth regimes and key system parameters is discussed.     

Breeding system variation in 10 evening primroses (Oenothera sections Anogra and Kleinia; Onagraceae)

? Premise of the study: We examined two accounts of the relationship between breeding system and life history variation in a clade of evening primroses (Oenothera, Onagraceae): (1) selection for reproductive assurance should generate an association between self-compatibility and monocarpy and (2) phylogenetic conservatism leads to retention of breeding system and life history traits among closely related taxa. ? Methods: We performed over 4000 hand pollinations under greenhouse conditions to determine the compatibility of 10 Oenothera taxa (sections Anogra [17 taxa] and Kleinia [2 taxa)] for which breeding systems had not previously been reported. We used generalized linear mixed models to evaluate the influence of pollination treatment, parents, and population on fruiting success. ? Key results: Among the taxa tested, six were self-incompatible, two were variable in compatibility, and two were self-compatible. We combined these data with published studies in Anogra and Kleinia and mapped breeding system and life history onto a published phylogeny. ? Conclusions: We found no evidence for phylogenetic conservatism, but detected considerable evolutionary lability in both traits. Additionally, we found no evidence for a consistent relationship between breeding system and life history. Only eight of 19 taxa followed the predicted association between self-incompatibility and polycarpy vs. self-compatibility and monocarpy. Instead, many taxa have retained self-incompatibility, regardless of monocarpy or polycarpy.     

Dynamic Artificial Neural Networks with Affective Systems

Artificial neural networks (ANNs) are processors that are trained to perform particular tasks. We couple a computational ANN with a simulated affective system in order to explore the interaction between the two. In particular, we design a simple affective system that adjusts the threshold values in the neurons of our ANN. The aim of this paper is to demonstrate that this simple affective system can control the firing rate of the ensemble of neurons in the ANN, as well as to explore the coupling between the affective system and the processes of long term potentiation (LTP) and long term depression (LTD), and the effect of the parameters of the affective system on its performance. We apply our networks with affective systems to a simple pole balancing example and briefly discuss the effect of affective systems on network performance.     

Dynamic sensitivity and nonlinear interactions influence the system-level evolutionary patterns of phototransduction proteins

Determining the influence of complex, molecular-system dynamics on the evolution of proteins is hindered by the significant challenge of quantifying the control exerted by the proteins on system output. We have employed a combination of systems biology and molecular evolution analyses in a first attempt to unravel this relationship. We employed a comprehensive mathematical model of mammalian phototransduction to predict the degree of influence that each protein in the system exerts on the high-level dynamic behaviour. We found that the genes encoding the most dynamically sensitive proteins exhibit relatively relaxed evolutionary constraint. We also investigated the evolutionary and epistatic influences of the many nonlinear interactions between proteins in the system and found several pairs to have coevolved, including those whose interactions are purely dynamical with respect to system output. This evidence points to a key role played by nonlinear system dynamics in influencing patterns of molecular evolution.     

Transients and tradeoffs of phenotypic switching in a fluctuating limited environment

Phenotypic variability in a microorganism population is thought to be advantageous in fluctuating environments, however much remains unknown about the precise conditions for this advantage to hold. In particular competition for a growth-limiting resource and the dynamics of that resource in the environment modify the tradeoff between different effects of variability. Here we investigate theoretically a model system for variable populations under competition for a flowing resource that governs growth (chemostat model) and changes with time. This environment generally induces density-dependent selection among competing sub-populations. We characterize quantitatively the transient dynamics in this system, and find that equilibration between total population density and environment can occur separately and with a distinct timescale from equilibration between competing sub-populations. We analyze quantitatively the two opposing effects of heterogeneity-transient response to change, and fitness at equilibrium-and find the optimal strategy in a fluctuating environment. We characterize the phase diagram of the system in term of its optimal strategy and find it to be strongly dependent on the typical timescale of the environment and weakly dependent on the internal parameters of the population.     

Adaptive Capacity of Social-Ecological Systems: Lessons from Immune Systems

How do systems respond to disturbances? The capacity of a system to respond to disturbances varies for different types of disturbance regimes. We distinguish two types of responses: one that enables the system to absorb disturbances from an existing disturbance regime, and one that enables a system to reconstruct itself after a fundamental change in a disturbance regime. We use immune systems as a model for how systems can deal with disturbances, and use this model to derive insights in adaptive capacity of social-ecological systems. We identify a tension between the two types of responses where one benefits from learning and memory while the other requires fast-turnover of experience. We discuss how this may affect building up adaptive capacity of social-ecological systems.     

Disentangling the interaction among host resources,the immune system and pathogens

The interaction between the immune system and pathogens is often characterised as a predator–prey interaction. This characterisation ignores the fact that both require host resources to reproduce. Here, we propose novel theory that considers how these resource requirements can modify the interaction between the immune system and pathogens. We derive a series of models to describe the energetic interaction between the immune system and pathogens, from fully independent resources to direct competition for the same resource. We show that increasing within‐host resource supply has qualitatively distinct effects under these different scenarios. In particular, we show the conditions for which pathogen load is expected to increase, decrease or even peak at intermediate resource supply. We survey the empirical literature and find evidence for all three patterns. These patterns are not explained by previous theory, suggesting that competition for host resources can have a strong influence on the outcome of disease.     

On population abundance and niche structure

Recent published evidence indicates a negative correlation between density of populations and the distance of their environments to a suitably defined ‘niche centroid’. This empirical observation lacks theoretical grounds. We provide a theoretical underpinning for the empirical relationship between population density and position in niche space, and use this framework to understand the circumstances under which the relationship will fail. We propose a metapopulation model for the area of distribution, as a system of ordinary differential equations coupled with a dispersal kernel. We present an analytical approximation to the solution of the system as well as R code to solve the full model numerically. We use this tool to analyze various scenarios and assumptions. General and realistic demographic assumptions imply a good correlation between position in niche space and population abundance. Factors that modify this correlation are: transitory states, a heterogeneous spatial structure of suitability, and Allee effects. We also explain why the raw output of the niche modeling algorithm MaxEnt is not a good predictor of environmental suitability. Our results elucidate the empirical results for spatial patterns of population size in niche terms, and provide a theoretical basis for a structured theory of the niche.     

Analysis of the interaction of viral RNA replication proteins by using the yeast two-hybrid assay.

The yeast two-hybrid system has been a useful tool in the genetic evaluation of protein-protein interactions. However, the biological relevance of these two-hybrid interactions to viral positive-strand RNA replication has not been demonstrated. The brome mosaic virus (BMV) system has been characterized extensively both genetically and biochemically, providing numerous mutations in the BMV 1a helicase-like and 2a polymerase-like proteins. We have tested wild-type 1a and 18 insertion mutations of 1a and found a perfect correlation between the in planta phenotypes and their ability to interact with 2a in the two-hybrid system. This finding allowed further characterization of the interaction between and among the BMV viral proteins. Using the two-hybrid assay, we have found that the interaction between the helicase-like region of 1a and the N terminus of 2a is stabilized by the presence of the centrally conserved polymerase-like domain of 2a. We have also identified a novel interaction between the 1a helicase-like protein and itself. Additionally, we have found this interaction in two related tripartite RNA viruses, cowpea chlorotic mottle virus and cucumber mosaic virus. We have demonstrated that this protein-protein interaction is specific to homologous pairings of the protein.     

Extending the HKB model of coordinated movement to oscillators with different eigenfrequencies

We study the dynamics of a system of coupled nonlinear oscillators that has been used to model coordinated human movement behavior. In contrast to earlier work we examine the case where the two component oscillators have different eigenfrequencies. Problems related to the decomposition of a time series (from an experiment) into amplitude and phase are discussed. We show that oscillations at multiples of the main frequency of the oscillator system may occur in the phase and amplitude due to the choice of a coordinate system and how these oscillations can be eliminated. We derive an explicit equation for the dynamics of the relative phase of the oscillator system in phase space that enables a direct comparison between theory and experiment.     

Stability and phase transitions in a mathematical model of Duchenne muscular dystrophy

We present a mathematical model to investigate the role of the immune system in the Duchenne muscular dystrophy disease. It is based on the assumption that the immune system contributes to the tissue damage and indeed its interaction with the muscle tissue after an initial endogenous damage can be described as a predator-prey system showing typical oscillations. In this article we investigate the dynamical properties of the system. We find that, for a biologically relevant parameters range, it shows two phase transitions between qualitative different behaviors corresponding to complete recover or to a state where muscle regeneration and degeneration coexist.     

Recent advances in crayfish hematopoietic stem cell culture: a model for studies of hemocyte differentiation and immunity

Hematopoiesis is the process by which blood cells (hemocytes) mature and subsequently enter the circulation and we have developed a new technique to culture the hematopoietic progenitor cells in vitro. The reason for the successful culture was the isolation of a plasma protein that turned out to be a novel cytokine, astakine 1 (Ast1) containing a domain present in several vertebrates, so-called prokineticins. Now we have detected several astakines from other invertebrate species. Depending on our discovery of the cytokine Ast1 we have an opportunity to study in detail the differentiation of cells in the hematopoietic tissue of a crustacean, a tissue of evolutionary interest for studies of the connection between the vascular system and the nervous system. We have been able to isolate the entire hematopoietic tissue and for the first time detected a link between this tissue and the brain. We have further localized a proliferation center in the tissue and characterized its different parts. We have also used this system to isolate a new hematopoietic factor CHF that is important in the crossroad between apoptosis and hemocyte differentiation. Our technique for culture of crayfish hematopoietic stem cells provides a simple tool for studying the mechanism of hematopoiesis, but also enables detailed studies of immune defense reactions. Further, the culture system has been used for studies of viral defense and the system is suitable for gene silencing which allows functional characterization of different molecules involved in host defense as well as in hemocyte differentiation.     

Family tree analysis of a transformed cell line and the transition probability model for the cell cycle

Variation in intermitotic time between individual cells in culture can be ascribed to the occurrence of random transitions in the cell cycle. We have analysed a family tree of mouse neuroblastoma cells, and observed that variation in difference in intermitotic time between sister cells is smaller than between cousin cells, and this difference is again smaller than between second-cousin and unrelated cells. This observation is incompatible with all transition probability models presented so far. We propose a model for the cell cycle with a single random transition, but with the additional assumption that the (two) system parameters may show variability within the population such that the closer cells are in their relation to each other, the closer their values of the system parameters will be. This model describes correctly the behaviour of the family tree of the cell line and in addition is able to explain why differences in intermitotic time between sister cells are exponentially distributed, while intermitotic times themselves are more or less normally distributed. Methods have been described to quantify the various system parameters.     

Interaction between protein subunits of the type IV secretion system of Bartonella henselae

In this study we used the yeast two-hybrid system to identify interactions between protein subunits of the virB type IV secretion system of Bartonella henselae. We report interactions between inner membrane and periplasmic proteins, the pilus polypeptide, and the core complex and a novel interaction between VirB3 and VirB5.     

Biomass and biodiversity in species-rich tritrophic communities

We consider a tritrophic system with one basal and one top species and a large number of primary consumers, and derive upper and lower bounds for the total biomass of the middle trophic level. These estimates do not depend on dynamical regime, holding for fixed point, periodic, or chaotic dynamics. We have two kinds of estimates, depending on whether the predator abundance is zero. All these results are uniform in a self-limitation parameter, which regulates prey diversity in the system. For strong self-limitation, diversity is large; for weak self-limitation, it is small. Diversity depends on the variance of species’ parameter values. The larger this variance, the lower the diversity, and vice versa. Moreover, variation in the parameters of the Holling type II functional response changes the bifurcation character, with the equilibrium state with nonzero predator abundance losing stability. If that variation is small then the bifurcation can lead to oscillations (the Hopf bifurcation). Under certain conditions, there exists a supercritical Hopf bifurcation. We then find a connection between diversity and Hopf bifurcations. We also show that the system exhibits top-down regulation and a hump-shaped diversity-productivity curve.We then extend the model by allowing species to experience self-regulation. For this extended model, explicit estimates of prey diversity are obtained. We study the dynamics of this system and find the following. First, diversity and system dynamics crucially depend on variation in species parameters. We show that under certain conditions, the system undergoes a supercritical Hopf bifurcation. We also establish a connection between diversity and Hopf bifurcations. For strong self-limitation, diversity is large and complex dynamics are absent. For weak self-limitation, diversity is small and the equilibrium with non-zero predator abundance is unstable.