Population differentiation and migration: coalescence times in a two-sex island model for autosomal and X-linked loci

Evolutionists have debated whether population-genetic parameters, such as effective population size and migration rate, differ between males and females. In humans, most analyses of this problem have focused on the Y chromosome and the mitochondrial genome, while the X chromosome has largely been omitted from the discussion. Past studies have compared F_ST values for the Y chromosome and mitochondrion under a model with migration rates that differ between the sexes but with equal male and female population sizes. In this study we investigate rates of coalescence for X-linked and autosomal lineages in an island model with different population sizes and migration rates for males and females, obtaining the mean time to coalescence for pairs of lineages from the same deme and for pairs of lineages from different demes. We apply our results to microsatellite data from the Human Genome Diversity Panel, and we examine the male and female migration rates implied by observed F_ST values.     

Genetic diversity of microsatellite loci in hierarchically structured populations

Microsatellite loci are widely used for investigating patterns of genetic variation within and among populations. Those patterns are in turn determined by population sizes, migration rates, and mutation rates. We provide exact expressions for the first two moments of the allele frequency distribution in a stochastic model appropriate for studying microsatellite evolution with migration, mutation, and drift under the assumption that the range of allele sizes is bounded. Using these results, we study the behavior of several measures related to Wright’s F_ST, including Slatkin’s R_ST. Our analytical approximations for F_ST and R_ST show that familiar relationships between N_em and F_ST or R_ST hold when the migration and mutation rates are small. Using the exact expressions for F_ST and R_ST, our numerical results show that, when the migration and mutation rates are large, these relationships no longer hold. Our numerical results also show that the diversity measures most closely related to F_ST depend on mutation rates, mutational models (stepwise versus two-phase), migration rates, and population sizes. Surprisingly, R_ST is relatively insensitive to the mutation rates and mutational models. The differing behaviors of R_ST and F_ST suggest that properties of the among-population distribution of allele frequencies may allow the roles of mutation and migration in producing patterns of diversity to be distinguished, a topic of continuing investigation.     

The role of low avidity T cells in the protection against type 1 diabetes: a modeling investigation

Cytotoxic T lymphocytes (CTLs) play a dominant role in the pathogenesis of autoimmune diabetes, commonly denoted Type 1 Diabetes (T1D). These CTLs (notably CD8⁺ T cells) recognize and kill insulin-secreting pancreatic β cells, reducing their number by ∼90%. The resulting reduction of insulin secretion causes the defective regulation of glucose metabolism, leading to the characteristic symptoms of diabetes. Recognition of β cells as targets by CTLs depends on the interactions between MHC-peptide complexes on the surface of β cells and receptors (TCRs) on T cells. Those CTLs with high affinity TCRs (also called high avidity T cells) cause most of the harm, while those with low affinity TCRs (also called low avidity T cells) play a more mysterious role. Recent experimental evidence suggests that low avidity T cells accumulate as memory T cells during the disease and may be protective in NOD mice (a strain prone to developing T1D), delaying disease progression. It has been hypothesized that such low avidity T cells afford disease protection either by crowding the islets of Langerhans, where β cells reside, or by killing antigen presenting cells (APCs).In this paper, we explore the hypothesized mechanisms for this protective effect in the context of a series of models for (1) the interactions of low and high avidity T cells, (2) the effect of APCs and (3) the feedback from β cell killing to autoantigen-induced T cell proliferation. We analyze properties of these models, noting consistency of predictions with observed behaviour. We then use the models to examine the influence of various treatment strategies on the progression of the disease. The model reveals that progressive accumulation of memory low avidity autoreactive T cells during disease progression makes treatments aimed at expanding these protective T cell types more effective close to, or at the onset of clinical disease. It also provides evidence for the hypothesis that low avidity T cells kill APCs (rather than the alternate hypothesis that they crowd the islets).     

Melanoblast proliferation dynamics during mouse embryonic development. Modeling and validation

In this paper, we are looking for mathematical modeling of mouse embryonic melanoblast proliferation dynamics, taking into account, the expression level of β‐catenin. This protein plays an important role into the whole signal pathway process. Different assumptions on some unobservable features lead to different candidate models. From real data measured, from biological experiments and from a priori biological knowledge, it was able to validate or invalidate some of the candidate models. Data assimilation and parameter identification allowed us to derive a mathematical model that is in very good agreement with biological data. As a result, the produced model can give tracks for biologists into their biological investigations and experimental evidence. Another interest is the use of this model for robust hidden parameter identification like double times or number of founder melanoblasts.     

Self-organization at the origin of life

The concept of an (M,R) system with organizational invariance allows one to understand how a system may be able to maintain itself indefinitely if it is coupled to an external source of energy and materials. However, although this constitutes an important step towards understanding the difference between a living and a non-living system, it is not clear that an (M,R) system with organizational invariance is sufficient to define a living system. To take a further step towards defining what it means to be alive it is necessary to add to a simple (M,R) system some property that represents its identity, and which can be maintained and modified in subsequent generations.     

E versus Z geometry in β-d-arabino-hexopyranosidulose oximes

Koenigs-Knorr-type glycosidations of peracylated 2Z-benzoyloxyimino-glycopyranosyl bromides invariably proceed with retention of the Z-geometry. Accordingly, the many β-d-hexosidulose oximes in literature which were prepared in this way and for which the oxime geometry has not been addressed explicitly, are the Z-oximes throughout. By contrast, oximation of β-d-hexopyranosid-2-uloses leads to mixtures of E and Z oximes readily separable and structurally verifiable by ¹H and ¹³C NMR. Configurational assignments rested on comparative evaluation of NMR data of E and Z isomers, and, most notably on an X-ray structural analysis of the pivaloylated isopropyl 2E-benzoyloxyimino-2-deoxy-β-d-arabino-hexopyranoside revealing the unusual ¹S₅?^1,4B conformation for the pyranoid ring.     

Uncovering operational interactions in genetic networks using asynchronous Boolean dynamics

Biological networks of large dimensions, with their diagram of interactions, are often well represented by a Boolean model with a family of logical rules. The state space of a Boolean model is finite, and its asynchronous dynamics are fully described by a transition graph in the state space. In this context, a model reduction method will be developed for identifying the active or operational interactions responsible for a given dynamic behaviour. The first step in this procedure is the decomposition of the asynchronous transition graph into its strongly connected components, to obtain a “reduced” and hierarchically organized graph of transitions. The second step consists of the identification of a partial graph of interactions and a sub-family of logical rules that remain operational in a given region of the state space. This model reduction method and its usefulness are illustrated by an application to a model of programmed cell death. The method identifies two mechanisms used by the cell to respond to death-receptor stimulation and decide between the survival and apoptotic pathways.     

Kinetics and mechanism of the aquation of the trinuclear cation, [μ3-oxo-triaqua-hexakis(acetato)tris(iron(III))]in perchloric acid media

The aquation of the title complex cation in aqueous perchloric acid proceeded via two steps, both postulated to be the proton attack on the oxygen atom which binds the acetate ligand to the metal centre, followed by Fe-O bond cleavage. This was followed by rapid decomposition to produce aqueous iron(III) and acetate ions. The first-order rate constants for the first and second steps at 25 °C are: k₁ = (4.16 ± 0.58) × 10⁻² s⁻¹ and k₂ = (2.09 ± 0.42) × 10⁻³ s⁻¹, respectively, and their corresponding activation parameters are . The spontaneous hydrolysis rate constants for the first and second steps were also determined at 25 °C and ionic strength of 1 mol dm⁻³ and they are k₀ = (3.10 ± 0.82) × 10⁻³ s⁻¹ and , respectively. The corresponding activation parameters are .     

The shared reward dilemma

One of the most direct human mechanisms of promoting cooperation is rewarding it. We study the effect of sharing a reward among cooperators in the most stringent form of social dilemma, namely the prisoner's dilemma (PD). Specifically, for a group of players that collect payoffs by playing a pairwise PD game with their partners, we consider an external entity that distributes a fixed reward equally among all cooperators. Thus, individuals confront a new dilemma: on the one hand, they may be inclined to choose the shared reward despite the possibility of being exploited by defectors; on the other hand, if too many players do that, cooperators will obtain a poor reward and defectors will outperform them. By appropriately tuning the amount to be shared a vast variety of scenarios arises, including the traditional ones in the study of cooperation as well as more complex situations where unexpected behavior can occur. We provide a complete classification of the equilibria of the n-player game as well as of its evolutionary dynamics.     

Molecular characterization of β1,4-galactosyltransferase 7 genetic mutations linked to the progeroid form of Ehlers-Danlos syndrome (EDS)

β1,4-Galactosyltransferase 7 (β4GalT7) is a key enzyme initiating glycosaminoglycan (GAG) synthesis. Based on in vitro and ex vivo kinetics studies and structure-based modelling, we molecularly characterized β4GalT7 mutants linked to the progeroid form of Ehlers-Danlos syndrome (EDS), a severe connective tissue disorder. Our results revealed that loss of activity upon L206P substitution due to altered protein folding is the primary cause for the GAG synthesis defect in patients carrying the compound A186D and L206P mutations. We showed that R270C substitution strongly reduced β4GalT7 affinity towards xyloside acceptor, thus affecting GAG chains formation. This study establishes the molecular basis for β4GalT7 defects associated with altered GAG synthesis in EDS.     

Evolutionary stability of first-order-information indirect reciprocity in sizable groups

Indirect reciprocity is considered as a key mechanism for explaining the evolution of cooperation in situations where the same individuals interact only a few times. Under indirect reciprocity, an individual who helps others gets returns indirectly from others who know her good reputation. Recently, many studies have discussed the effect of reputation criteria based only on the former actions of the others (first-order information) and of those based also on the former reputation of opponents of the others (second-order information) on the evolution of indirect reciprocity. In this study, we investigate the evolutionary stability of the indirectly reciprocal strategy (discriminating strategy: DIS), which cooperates only with opponents who have good reputations, in -person games where more than two individuals take part in a single group (interaction). We show that in n-person games, DIS is an evolutionarily stable strategy (ESS) even under the image-scoring reputation criterion, which is based only on first-order information and where cooperations (defections) are judged to be good (bad). This result is in contrast to that of 2-person games where DIS is not an ESS under reputation criteria based only on first-order information.     

Generalized population models and the nature of genetic drift

The Wright–Fisher model of allele dynamics forms the basis for most theoretical and applied research in population genetics. Our understanding of genetic drift, and its role in suppressing the deterministic forces of Darwinian selection has relied on the specific form of sampling inherent to the Wright–Fisher model and its diffusion limit. Here we introduce and analyze a broad class of forward-time population models that share the same mean and variance as the Wright–Fisher model, but may otherwise differ. The proposed class unifies and further generalizes a number of population-genetic processes of recent interest, including the Λ and Cannings processes. Even though these models all have the same variance effective population size, they encode a rich diversity of alternative forms of genetic drift, with significant consequences for allele dynamics. We characterize in detail the behavior of standard population-genetic quantities across this family of generalized models. Some quantities, such as heterozygosity, remain unchanged; but others, such as neutral absorption times and fixation probabilities under selection, deviate by orders of magnitude from the Wright–Fisher model. We show that generalized population models can produce startling phenomena that differ qualitatively from classical behavior — such as assured fixation of a new mutant despite the presence of genetic drift. We derive the forward-time continuum limits of the generalized processes, analogous to Kimura’s diffusion limit of the Wright–Fisher process, and we discuss their relationships to the Kingman and non-Kingman coalescents. Finally, we demonstrate that some non-diffusive, generalized models are more likely, in certain respects, than the Wright–Fisher model itself, given empirical data from Drosophila populations.     

Compressible gas gills of diving insects: Measurements and models

Many diving insects collect a bubble of air from the surface to supply their oxygen requirements while submerged. It has been theorised that these air bubbles may also act as compressible gas gills, as the low oxygen partial pressure (PO₂) within the bubble caused by the insect's respiration creates a gradient capable of driving the diffusion of oxygen from the water into the bubble. Under these conditions nitrogen diffuses in the opposite direction, resulting in a situation where the volume of the bubble is continually shrinking while oxygen is obtained. This study measures changes in volume and PO₂ within the gas gills held by a tethered water bug, Agraptocorixa eurynome. Both gill volume and PO₂ drop rapidly at the beginning of a dive, but eventually the PO₂ reaches an apparently stable level while volume continually declines at a slower rate. Active ventilation of the gill is crucial to maintaining oxygen uptake. These measurements are used to calculate oxygen flux into the gas gill and the oxygen consumption rate of the bug. The effectiveness of a gas gill as a respiratory organ is also demonstrated by determining the critical PO₂ of the water bug and comparing this with measured gas gill PO₂ and calculated .     

Topology is the Principal Determinant in the Folding of a Complex All-alpha Greek Key Death Domain from Human FADD

In order to elucidate the relative importance of secondary structure and topology in determining folding mechanism, we have carried out a phi-value analysis of the death domain (DD) from human FADD. FADD DD is a 100 amino acid domain consisting of six anti-parallel alpha helices arranged in a Greek key structure. We asked how does the folding of this domain compare with that of (a) other all-alpha-helical proteins and (b) other Greek key proteins? Is the folding pathway determined mainly by secondary structure or is topology the principal determinant? Our Φ-value analysis reveals a striking resemblance to the all-beta Greek key immunoglobulin-like domains. Both fold via diffuse transition states and, importantly, long-range interactions between the four central elements of secondary structure are established in the transition state. The elements of secondary structure that are less tightly associated with the central core are less well packed in both cases. Topology appears to be the dominant factor in determining the pathway of folding in all Greek key domains.     

A multilevel approach to cancer growth modeling

Cancer growth models may be divided into macroscopic models, which describe the tumor as a single entity, and microscopic ones, which consider the tumor as a complex system whose behavior emerges from the local dynamics of its basic components, the neoplastic cells. Mesoscopic models (e.g. as based on the Local Interaction Simulation Approach [Delsanto, P.P., Mignogna, R., Scalerandi, M., Schechter, R., 1998. In: Delsanto, P.P. Saenz, A.W. (Eds.), New Perspectives on Problems in Classical and Quantum Physics, vol. 2. Gordon & Breach, New Delhi, p. 5174]), which explicitly consider the behavior of cell clusters and their interactions, may be used instead of the microscopic ones, in order to study the properties of cancer biology that strongly depend on the interactions of small groups of cells at intermediate spatial and temporal scales. All these approaches have been developed independently, which limits their usefulness, since they all include relevant features and information that should be cross-correlated for a deeper understanding of the mechanisms involved. In this contribution we consider multicellular tumor spheroids as biological reference systems and propose an intermediate model to bridge the gap between a macroscopic formulation of tumor growth and a mesoscopic one. Thus we are able to establish, as an important result of our formalism, a direct correspondence between parameters characterizing processes occurring at different scales. In particular, we analyze their dependence on an important limiting factor to tumor growth, i.e. the extra-cellular matrix pressure. Since the macro and meso-models stem from totally different roots (energy conservation and clinical observations vs. cell groups dynamics), their consistency may be used to validate both approaches. It may also be interesting to note that the proposed formalism fits well into a recently proposed conjecture of growth laws universality.     

Transmission dynamics of Toxoplasma gondii along an urban-rural gradient

Recently, several authors have proposed that the availability of intermediate hosts (IHs) for definitive hosts (DHs) may contribute to determining the dynamics and evolutionary ecology of parasites with facultative complex life cycles. The protozoa Toxoplasma gondii may be transmitted to DHs either via predation of infected IHs through a complex life cycle (CLC) or directly from a contaminated environment through a simple life cycle (SLC). This parasite is also present in contrasting host density environments. We tested the hypothesis that the relative contributions of the CLC and SLC along an urban-rural gradient depend on the IH supply. We built and analysed a deterministic model of the T. gondii transmission cycle. The SLC relative contribution is important only in urban-type environments, i.e., with low predation rate on IHs. In contrast, the parasite is predominantly transmitted through a CLC in suburban and rural environments. The association of the two cycles enables the parasite to spread in situations of low IH availability and low DH population size for which each cycle alone is insufficient.     

Metabolic and energetic aspects of biohydrogen production of Clostridium tyrobutyricum: The effects of hydraulic retention time and peptone addition

This study evaluates the microbial metabolism and energy demand in fermentative biohydrogen production using Clostridium tyrobutyricum FYa102 at different hydraulic retention times (HRT) over a period of 1-18 h. The hydrogen yield shows a positive correlation with the butyrate yield, the B/A ratio, and the Y_H2/2(Y_HAc+Y_HBu) ratio, but a negative correlation with the lactate yield. A decrease in HRT, which is accompanied by an increased biomass growth, tends to decrease the B/A ratio, due presumably to a higher energy demand for microbial growth. The production of lactate at a low HRT, however, may involve an unfavorable change in e⁻ equiv distribution to result in a reduced hydrogen production. Finally, the relatively high hydrogen yields observed in the bioreactor with the peptone addition may be ascribed to the utilization of peptone as an additional energy and/or amino-acid source, thus reducing the glucose demand for biomass growth during the hydrogen production process.     

Computation of threshold conditions for epidemiological models and global stability of the disease-free equilibrium (DFE)

One goal of this paper is to give an algorithm for computing a threshold condition for epidemiological systems arising from compartmental deterministic modeling. We calculate a threshold condition T(0) of the parameters of the system such that if T(0)<1 the disease-free equilibrium (DFE) is locally asymptotically stable (LAS), and if T(0)>1, the DFE is unstable. The second objective, by adding some reasonable assumptions, is to give, depending on the model, necessary and sufficient conditions for global asymptotic stability (GAS) of the DFE. In many cases, we can prove that a necessary and sufficient condition for the global asymptotic stability of the DFE is R(0)< or =1, where R(0) is the basic reproduction number [O. Diekmann, J.A. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, Wiley, New York, 2000]. To illustrate our results, we apply our techniques to examples taken from the literature. In these examples we improve the results already obtained for the GAS of the DFE. We show that our algorithm is relevant for high dimensional epidemiological models.