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.     

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.     

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.     

A quantitative model for linking Na+/Ca2+ exchanger to SERCA during refilling of the sarcoplasmic reticulum to sustain [Ca2+] oscillations in vascular smooth muscle

We have developed a quantitative model for the creation of cytoplasmic Ca²⁺ gradients near the inner surface of the plasma membrane (PM). In particular we simulated the refilling of the sarcoplasmic reticulum (SR) via PM–SR junctions during asynchronous [Ca²⁺]_i oscillations in smooth muscle cells of the rabbit inferior vena cava. We have combined confocal microscopy data on the [Ca²⁺]_i oscillations, force transduction data from cell contraction studies and electron microscopic images to build a basis for computational simulations that model the transport of calcium ions from Na⁺/Ca²⁺ exchangers (NCX) on the PM to sarcoplasmic/endoplasmic reticulum Ca²⁺ ATPase (SERCA) pumps on the SR as a three-dimensional random walk through the PM–SR junctional cytoplasmic spaces. Electron microscopic ultrastructural images of the smooth muscle cells were elaborated with software algorithms to produce a very clear and dimensionally accurate picture of the PM–SR junctions. From this study, we conclude that it is plausible and possible for enough Ca²⁺ to pass through the PM–SR junctions to replete the SR during the regenerative Ca²⁺ release, which underlies agonist induced asynchronous Ca²⁺ oscillations in vascular smooth muscle.     

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.     

Contributions of HERG current to repolarization of the human ventricular action potential

Action potential repolarization in the mammalian heart is governed by interactions of a number of time- and voltage-dependent channel-mediated currents, as well as contributions from the Na⁺/Ca²⁺ exchanger and the Na⁺/K⁺ pump. Recent work has shown that one of the K⁺ currents (HERG) which contributes to repolarization in mammalian ventricle is a locus at which a number of point mutations can have significant functional consequences. In addition, the remarkable sensitivity of this K⁺ channel isoform to inhibition by a variety of pharmacological agents and clinical drugs has resulted in HERG being a major focus for Safety Pharmacology requirements.For these reasons we and others have attempted to define the functional role for HERG-mediated K⁺ currents in repolarization of the action potential in the human ventricle. Here, we describe and evaluate changes in the formulations for two K⁺ currents, I_K1 and HERG (or I_K,r), within the framework of ten Tusscher model of the human ventricular action potential. In this computational study, new mathematical formulations for the two nonlinear K⁺ conductances, I_K1 and HERG, have been developed based upon experimental data obtained from electrophysiological studies of excised human ventricular tissue and/or myocytes. The resulting mathematical model provides much improved simulations of the relative sizes and time courses of the K⁺ currents which modulate repolarization. Our new formulation represents an important first step in defining the mechanism(s) of repolarization of the membrane action potential in the human ventricle. Our overall goal is to understand the genesis of the T-wave of the human electrocardiogram.     

广东省汉族人群的亚群分析

为调查广东地区汉族人群中是否存在着亚群结构,对来自广州、佛山、东莞、江门和中山-珠海5个不同地区的471随机个体血样本进行15个STR的基因分型,并作Hardy-Weinberg平衡检验,比较群体之间的等位基因频率,计算这个5个地区人群间的共祖系数。结果显示,广东汉族人群没有明显的Hardy-Weinberg不平衡,5个地区人群的等位基因分布均没有差异,他们之间的共祖系数小于0.01。因此,广东地区汉族人群中没有明显的亚群结构。 Abstract:To investigate the subpopulation structure within the Han Population in Guandong area,a total of 471 DNA samples from five populations in Guandong Province,including Guangzhou,Foshan,Dongguan,Jiangmen and Zhongshan-Zhuhai region,were genotyped at 15 STR(short tandem repeats) markers.Hardy-Weinberg tests were performed,allele frequencies were compared,and the genetic coancestry coefficient(FST ) was estimated.The results did not show significant departure from Hardy-Weinberg equilibrium in the total population.Difference of allele frequencies among these populations was not observed,and the coancestry coefficient(FST)was less than 0.01.Subpopulation structure within Han Population in Guandong Province could not be detected.     

Effect of vitamin E and polyphenols on ochratoxin A-induced cytotoxicity in liver (HepG2) cells

It has been shown that oxidative damage contributes to the wide range of toxic effects of the mycotoxin ochratoxin A (OTA). Therefore, we examined the effects of alpha-tocopherol (alpha-TOC) and different polyphenols--catechin (CAT), daidzein (DAI), epicatechin (EC), epigallocatechin gallate (EGCG), genistein (GEN), and quercetin (QUE)--on OTA-induced cytotoxicity in HepG2 liver cells. Incubation of HepG2 cells with increasing concentrations of OTA resulted in a dose- and time-dependent cytotoxicity as measured by the neutral red assay. Half lethal concentrations (LC50) of OTA were 35 and 10 microM after 48 and 72 h incubation, respectively. Incubation of HepG2 cells with alpha-TOC as well as with different polyphenols (exhibiting different antioxidant potency as determined by the FRAP, TEAC and DPPH assays) did not counteract OTA-induced cytotoxicity. These findings indicate that OTA may exert its toxic effects by affecting other hepatic mechanisms than those directly modulated by alpha-TOC and polyphenols.     

The evolution of n-player cooperation-threshold games and ESS bifurcations

An evolutionary game of individuals cooperating to obtain a collective benefit is here modelled as an n-player Prisoner's Dilemma game. With reference to biological situations, such as group foraging, we introduce a threshold condition in the number of cooperators required to obtain the collective benefit. In the simplest version, a three-player game, complex behaviour appears as the replicator dynamics exhibits a catastrophic event separating a parameter region allowing for coexistence of cooperators and defectors and a region of pure defection. Cooperation emerges through an ESS bifurcation, and cooperators only thrive beyond a critical point in cost-benefit space. Moreover, a repelling fixed point of the dynamics acts as a barrier to the introduction of cooperation in defecting populations. The results illustrate the qualitative difference between two-player games and multiple player games and thus the limitations to the generality of conclusions from two-player games. We present a procedure to find the evolutionarily stable strategies in any n-player game with cost and benefit depending on the number of cooperators. This was previously done by Motro [1991. Co-operation and defection: playing the field and the ESS. J. Theor. Biol. 151, 145-154] in the special cases of convex and concave benefit functions and constant cost.     

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).     

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.     

Molecular evidence for historical and recent population size reductions of tiger salamanders (Ambystoma tigrinum) in Yellowstone National Park

Population declines caused by natural and anthropogenic factors can quickly erode genetic diversity in natural populations. In this study, we examined genetic variation within 10 tiger salamander populations across northern Yellowstone National Park in Wyoming and Montana, USA using eight microsatellite loci. We tested for the genetic signature of population decline using heterozygosity excess, shifts in allele frequencies, and low ratios of allelic number to allelic size range (M-ratios). We found different results among the three tests. All 10 populations had low M-ratios, five had shifts in allele frequencies and only two had significant heterozygosity excesses. These results support theoretical expectations of different temporal signatures among bottleneck tests and suggest that both historical fish stocking, recent, sustained drought, and possibly an emerging amphibian disease have contributed to declines in effective population size.     

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.     

Using genomic tools to maintain diversity and fitness in conservation programmes

Conservation programmes aim at maximizing the survival probability of populations, by minimizing the loss of genetic diversity, which allows populations to adapt to changes, and controlling inbreeding increases. The best known strategy to achieve these goals is optimizing the contributions of the parents to minimize global coancestry in their offspring. Results on neutral scenarios showed that management based on molecular coancestry could maintain more diversity than management based on genealogical coancestry when a large number of markers were available. However, if the population has deleterious mutations, managing using optimal contributions can lead to a decrease in fitness, especially using molecular coancestry, because both beneficial and harmful alleles are maintained, compromising the long‐term viability of the population. We introduce here two strategies to avoid this problem: The first one uses molecular coancestry calculated removing markers with low minor allele frequencies, as they could be linked to selected loci. The second one uses a coancestry based on segments of identity by descent, which measures the proportion of genome segments shared by two individuals because of a common ancestor. We compare these strategies under two contrasting mutational models of fitness effects, one assuming many mutations of small effect and another with few mutations of large effect. Using markers at intermediate frequencies maintains a larger fitness than using all markers, but leads to maintaining less diversity. Using the segment‐based coancestry provides a compromise solution between maintaining diversity and fitness, especially when the population has some inbreeding load.     

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.     

Changes of enzyme activity in lipid signaling pathways related to substrate reordering

The static fluid mosaic model of biological membranes has been progressively complemented by a dynamic membrane model that includes phospholipid reordering in domains that are proposed to extend from nanometers to microns. Kinetic models for lipolytic enzymes have only been developed for homogeneous lipid phases. In this work, we develop a generalization of the well-known surface dilution kinetic theory to cases where, in a same lipid phase, both domain and nondomain phases coexist. Our model also allows understanding the changes in enzymatic activity due to a decrease of free substrate concentration when domains are induced by peptides. This lipid reordering and domain dynamics can affect the activity of lipolytic enzymes, and can provide a simple explanation for how basic peptides, with a strong direct interaction with acidic phospholipids (such as beta-amyloid peptide), may cause a complex modulation of the activities of many important enzymes in lipid signaling pathways.     

One-hit stochastic decline in a mechanochemical model of cytoskeleton-induced neuron death II: transition state metastability

This is the second of two papers in which we study a mathematical model of cytoskeleton-induced neuron death. Recent evidence indicates that aggravated assembly or destruction of the cytoskeleton can trigger programmed death in neurons, by mechanisms as yet poorly understood. In our model, assembly control of the neuronal cytoskeleton interacts with both cellular stress levels and cytosolic free radical concentrations to trigger neurodegeneration. This trigger mechanism is further modulated by a diffusible toxic factor released from dying neurons. In the companion report we established that the model relates the observed general patterns of neuron decline to specific scales of cytoskeleton reorganization and cell-cell interaction strength. In this paper we study the transit of neurons through states intermediate between initial viability and cell death in our model. We find that the stochastic flow of neuron fate, from viability to cell death, self-organizes into two distinct temporal phases. There is a rapid relaxation of the initial neuron population to a more disordered phase that is long-lived, or metastable, with respect to the time scales of change in single cells. Strikingly, cellular egress from this metastable phase follows the one-hit kinetic pattern of exponential decline now established as a principal hallmark of cell death in neurodegenerative disorders. Intermediate state metastability may therefore be an important element in the systems biology of one-hit neurodegeneration.