Environmental Fluctuations and Level of Density-Compensation Strongly Affects the Probability of Fixation and Fixation Times

The probability of, and time to, fixation of a mutation in a population has traditionally been studied by the classic Wright–Fisher model where population size is constant. Recent theoretical expansions have covered fluctuating populations in various ways but have not incorporated models of how the environment fluctuates in combination with different levels of density-compensation affecting fecundity. We tested the hypothesis that the probability of, and time to, fixation of neutral, advantageous and deleterious mutations is dependent on how the environment fluctuates over time, and on the level of density-compensation. We found that fixation probabilities and times were dependent on the pattern of autocorrelation of carrying capacity over time and interacted with density-compensation. The pattern found was most pronounced at small population sizes. The patterns differed greatly depending on whether the mutation was neutral, advantageous, or disadvantageous. The results indicate that the degree of mismatch between carrying capacity and population size is a key factor, rather than population size per se, and that effective population sizes can be very low also when the census population size is far above the carrying capacity. This study highlights the need for explicit population dynamic models and models for environmental fluctuations for the understanding of the dynamics of genes in populations.     

Mucolipidosis type IV and the mucolipins

MLIV (mucolipidosis type?IV) is a neurodegenerative lysosomal storage disorder caused by mutations in MCOLN1, a gene that encodes TRPML1 (mucolipin-1), a member of the TRPML (transient receptor potential mucolipin) cation channels. Two additional homologues are TRPML2 and TRPML3 comprising the TRPML subgroup in the TRP superfamily. The three proteins play apparently key roles along the endocytosis process, and thus their cellular localization varies among the different group members. Thus TRPML1 is localized exclusively to late endosomes and lysosomes, TRPML2 is primarily located in the recycling clathrin-independent GPI (glycosylphosphatidylinositol)-anchored proteins and early endosomes, and TRPML3 is primarily located in early endosomes. Apparently, all three proteins' main physiological function underlies Ca(2+) channelling, regulating the endocytosis process. Recent findings also indicate that the three TRPML proteins form heteromeric complexes at least in some of their cellular content. The physiological role of these complexes in lysosomal function remains to be elucidated, as well as their effect on the pathophysiology of MLIV. Another open question is whether any one of the TRPMLs bears additional function in channel activity.     

The Final Size of an Epidemic and Its Relation to the Basic Reproduction Number

We study the final size equation for an epidemic in a subdivided population with general mixing patterns among subgroups. The equation is determined by a matrix with the same spectrum as the next generation matrix and it exhibits a threshold controlled by the common dominant eigenvalue, the basic reproduction number R₀{\mathcal{R}_{0}}: There is a unique positive solution giving the size of the epidemic if and only if R₀{\mathcal{R}_{0}} exceeds unity. When mixing heterogeneities arise only from variation in contact rates and proportionate mixing, the final size of the epidemic in a heterogeneously mixing population is always smaller than that in a homogeneously mixing population with the same basic reproduction number R₀{\mathcal{R}_{0}}. For other mixing patterns, the relation may be reversed.     

Erratum to: Attractor Dynamics and Thermodynamic Analogies in the Cerebral Cortex: Synchronous Oscillation,the Background EEG,and the Regulation of Attention

Ongoing changes in attention and cognition depend upon cortical/subcortical interactions, which select sequences of different spatial patterns of activation in the cortex.     

Mediterranean island biodiversity and climate change: the last 10,000 years and the future

Mediterranean islands (MI) are hotspots of global biodiversity and lie in one of the most susceptible to climate change (CC) areas of the world; a big challenge for any conservation strategy. In fact, there is already increasing evidence for CC in the region and associated biological responses in MI ecosystems. These include phenological changes and upward elevation shifts of species and plant communities; although evidence is frequently contrasting for different taxa. Threats are also evident, mainly for endemic species from most taxonomic groups, while communities in mountain and coastal regions are likely to be affected most. For MI conservation under CC additional factors need to be considered: (i) their position at the crossroads of three continents; with which they share common environmental characteristics, (ii) their great variability in sizes and topography and (iii) their climatic differences; with a clear west-east basin divide. CC synergies with changing tourist aspiration and agricultural practices will, in the medium term, modify island landscapes and provide further challenges for biodiversity conservation. Such a combined impact from CC, land-use change, fragmentation of habitats and tourism is difficult to predict. Furthermore, the limited space on islands (especially habitat availability and climatic range limitations) imposes a barrier to species range expansion. Thus, conservation of MI biodiversity under CC requires: (i) future research to focus on improved climate predictions linked to improved understanding of ecological (climate-biotic) responses, incorporating lessons learnt from (island) biogeography, (ii) specific adaptation measures for spatial planning and improvement in regional institutional capacities.     

Novel and recurrent mutations in the tyrosinase gene and the P gene in the German albino population

Albinism is a heterogeneous group of genetic disorders resulting from deficiencies in pigmentation. Clinically, it is divided into ocular (OA) and oculocutaneous albinism (OCA). OCA involves lack of pigment in the skin, hair, and eyes and results from mutations in the tyrosinase gene or in the P gene. OA mainly affects pigmentation in the visual system and may be a mild form of OCA or may be caused by other genetic defects. Clinical diagnosis of albinism type is difficult, because of the observed range of phenotypic variation. Thus, genetic analysis may be helpful with respect to a more accurate diagnosis. Here, we report the mutational profile, determined by genetic analysis of the tyrosinase and P genes, of a large German albino population. We have revealed a total of 42 distinct mutations, 19 of which are novel. Of the 74 unrelated patients screened, 32 (43%) had mutations in the tyrosinase gene, 16 (22%) had P gene mutations, and 26 (35%) patients had no detectable genetic abnormalities. This defines a population of albino patients who are tyrosinase-gene- and P-gene-negative and who thus may represent a good study group for searching for additional genes associated with albinism.     

Serological identification and molecular characterization of B (A) 02 subtype in patients and blood donors from Eastern China

This study was designed to identify the rare?type?ABO?blood?groups, B(A) 02, from Eastern China. Three samples with discordant serological results during routine blood type identification and four samples from one sample’ family were selected. All of them were detected by serological method. The exon 6 and 7 of the ABO genes were amplified by PCR and sequenced. They were typed as AsubB by serology and as BO by genotype. In AsubB samples, nt 700C>G mutation was detected in B gene, which was previously defined as B(A)02 alleles. In these seven samples, six showed B(A)02/O01 and one showed B(A)02/O02.B(A)02 allele was found to be more common in this study than B(A)04 which is considered to be more frequent than B(A)02. The careful identification of rare blood types is important for the safety of clinical blood transfusion.     

Calcineurin ensures a link between the DNA replication checkpoint and microtubule-dependent polarized growth

Microtubules are central to eukaryotic cell morphogenesis. Microtubule plus-end tracking proteins (+TIPs) transport polarity factors to the cell cortex, thereby playing a key role in both microtubule dynamics and cell polarity. However, the signalling pathway linking +TIPs to cell polarity control remains elusive. Here we show that the fission yeast checkpoint kinase Cds1 (Chk2 homologue) delays the transition of growth polarity from monopolar to bipolar (termed NETO; new-end take-off). The +TIPs CLIP170 homologue Tip1 and kinesin Tea2 are responsible for this delay, which is accompanied by a reduction in microtubule dynamics at the cell tip. Remarkably, microtubule stabilization occurs asymmetrically, prominently at the non-growing cell end, which induces abnormal accumulation of the polarity factor Tea1. Importantly, NETO delay requires activation of calcineurin, which is carried out by Cds1, resulting in Tip1 dephosphorylation. Thus, our study establishes a critical link between calcineurin and checkpoint-dependent cell morphogenesis.     

Prey Selection,Vertical Migrations and the Impacts of Harvesting Upon the Population Dynamics of a Predator-Prey System

A model is developed to describe the interaction between a predator and two prey types located in different regions. Conditions for stability and persistence are analysed. The effects of harvesting the predators are investigated by making the predator mortality rate habitat dependent. Results demonstrate that for any given set of parameter values there is a value of the intrinsic preference of the predator for each prey type at which the system undergoes a Hopf bifurcation. Above this critical value the system evolves towards a stable equilibrium, whereas below it, stable limit cycles arise by Hopf bifurcations. Simulations demonstrate that the presence of demographic stochasticity may destabilise oscillatory populations, thereby causing population extinctions. An application of the model to the foraging behaviour of North Sea cod is described. It is shown that if the preferred prey is more productive, it is likely that the equilibrium will be stable, whereas if the less preferred prey is more productive, populations are likely to display cycles and in the stochastic case become extinct. As cod fishing mortality is increased, the point of bifurcation and region of parameter space for which the system is unstable decreases. An increased understanding of how cod behave may enable fish stocks to be managed more successfully, for example by indicating where marine reserves should be placed.     

Elite swimmers and the D allele of the ACE I/D polymorphism

A polymorphism of the human angiotensin-1-converting enzyme (ACE) gene has been identified in which the presence (insertion, I allele) of a 287-bp fragment rather than the absence (deletion, D allele) is associated with lower ACE activity. Several recent studies have shown an association of the I allele with endurance performance, it being found with excess frequency in elite distance runners, rowers and mountaineers. Other workers using heterogeneous cohorts of athletes from mixed sporting disciplines have found no such association. An increasing linear trend of I allele frequency with the distance run amongst Olympic runners and an excess of the D allele amongst sprinters led us to examine whether the ratio of I and D alleles in swimmers competing over different distances would also vary. Swimmers (n=120) from the European and Commonwealth championships and an American college team had their ACE genotype determined and their gene and allele frequencies compared with several control groups, the most closely age-matched of which were 1,248 military recruits. Of the 103 Caucasians, there was a significant excess of the D allele compared with this control group only in the truly elite swimmers of the European and Commonwealth championships (P=0.004). This association remained in those competing over shorter distances (P=0.005 for 400 m and below) but not in the longer events. These findings were confirmed in three further large control groups. A population association study testing whether a genetic marker (the ACE I/D polymorphism) occurs more frequently in cases (elite athletes) than in controls therefore requires a homogeneous cohort of subjects from the same sporting discipline.     

Age and Sex Structured Model for Assessing the Demographic Impact of Mother-to-Child Transmission of HIV/AIDS

Age and sex structured HIV/AIDS model with explicit incubation period is proposed as a system of delay differential equations. The model consists of two age groups that are children (0–14 years) and adults (15–49 years). Thus, the model considers both mother-to-child transmission (MTCT) and heterosexual transmission of HIV in a community. MTCT can occur prenatally, at labour and delivery or postnatally through breastfeeding. In the model, we consider the children age group as a one-sex formulation and divide the adult age group into a two-sex structure consisting of females and males. The important mathematical features of the model are analysed. The disease-free and endemic equilibria are found and their stabilities investigated. We use the Lyapunov functional approach to show the local stability of the endemic equilibrium. Qualitative analysis of the model including positivity and boundedness of solutions, and persistence are also presented. The basic reproductive number (ℛ₀) for the model shows that the adult population is responsible for the spread HIV/AIDS epidemic, thus up-to-date developed HIV/AIDS models to assess intervention strategies have focused much on heterosexual transmission by the adult population and the children population has received little attention. We numerically analyse the HIV/AIDS model to assess the community benefits of using antiretroviral drugs in reducing MTCT and the effects of breastfeeding in settings with high HIV/AIDS prevalence ratio using demographic and epidemiological parameters for Zimbabwe.     

Modelling the Transmission Dynamics and Control of the Novel 2009 Swine Influenza (H1N1) Pandemic

The paper presents a deterministic compartmental model for the transmission dynamics of swine influenza (H1N1) pandemic in a population in the presence of an imperfect vaccine and use of drug therapy for confirmed cases. Rigorous analysis of the model, which stratifies the infected population in terms of their risk of developing severe illness, reveals that it exhibits a vaccine-induced backward bifurcation when the associated reproduction number is less than unity. The epidemiological consequence of this result is that the effective control of H1N1, when the reproduction number is less than unity, in the population would then be dependent on the initial sizes of the subpopulations of the model. For the case where the vaccine is perfect, it is shown that having the reproduction number less than unity is necessary and sufficient for effective control of H1N1 in the population (in such a case, the associated disease-free equilibrium is globally asymptotically stable). The model has a unique endemic equilibrium when the reproduction number exceeds unity. Numerical simulations of the model, using data relevant to the province of Manitoba, Canada, show that it reasonably mimics the observed H1N1 pandemic data for Manitoba during the first (Spring) wave of the pandemic. Further, it is shown that the timely implementation of a mass vaccination program together with the size of the Manitoban population that have preexisting infection-acquired immunity (from the first wave) are crucial to the magnitude of the expected burden of disease associated with the second wave of the H1N1 pandemic. With an estimated vaccine efficacy of approximately 80%, it is projected that at least 60% of Manitobans need to be vaccinated in order for the effective control or elimination of the H1N1 pandemic in the province to be feasible. Finally, it is shown that the burden of the second wave of H1N1 is expected to be at least three times that of the first wave, and that the second wave would last until the end of January or early February, 2010.     

On the Modelling of Biological Patterns with Mechanochemical Models: Insights from Analysis and Computation

The diversity of biological form is generated by a relatively small number of underlying mechanisms. Consequently, mathematical and computational modelling can, and does, provide insight into how cellular level interactions ultimately give rise to higher level structure. Given cells respond to mechanical stimuli, it is therefore important to consider the effects of these responses within biological self-organisation models. Here, we consider the self-organisation properties of a mechanochemical model previously developed by three of the authors in Acta Biomater. 4, 613–621 (2008), which is capable of reproducing the behaviour of a population of cells cultured on an elastic substrate in response to a variety of stimuli. In particular, we examine the conditions under which stable spatial patterns can emerge with this model, focusing on the influence of mechanical stimuli and the interplay of non-local phenomena. To this end, we have performed a linear stability analysis and numerical simulations based on a mixed finite element formulation, which have allowed us to study the dynamical behaviour of the system in terms of the qualitative shape of the dispersion relation. We show that the consideration of mechanotaxis, namely changes in migration speeds and directions in response to mechanical stimuli alters the conditions for pattern formation in a singular manner. Furthermore without non-local effects, responses to mechanical stimuli are observed to result in dispersion relations with positive growth rates at arbitrarily large wavenumbers, in turn yielding heterogeneity at the cellular level in model predictions. This highlights the sensitivity and necessity of non-local effects in mechanically influenced biological pattern formation models and the ultimate failure of the continuum approximation in their absence.     

Resonance assignments of the 56 kDa chimeric avidin in the biotin-bound and free forms

Avidin is a homotetrameric ~56 kDa protein found in chicken egg white. Avidin’s ability to bind biotin with a very high affinity has widely been exploited in biotechnological applications. Protein engineering has further diversified avidin’s feasibility. ChiAVD(I117Y) is a product of rational protein engineering. It is a hyperthermostable synthetic hybrid of avidin and avidin-related protein 4 (AVR4). In this chimeric protein a 23-residue segment in avidin has been replaced with the corresponding sequence found in AVR4, and a point mutation at subunit interface 1–3 (and 2–4) has been introduced. Here we report the backbone and sidechain resonance assignments of the biotin-bound form of ChiAVD(I117Y) as well as the backbone resonance assignments of the free form.     

Molecular Cloning of the Phytase Gene from Citrobacter braakii and its Expression in Saccharomyces cerevisiae

The gene, appA, encoding phytase was cloned from a size-selected genomic library of Citrobacter braakii YH-15 by Southern hybridization using a degenerate probe based on the N-terminal amino acid sequence of the phytase. The deduced amino acid sequence of appA contained the N-terminal RHGXRXP motif and the C-terminal HD motif, which are common in histidine acid phosphatases. It also had significant homology (60% identity) with phytase from Escherichia coli, while the physical mapping analysis of appA revealed that gene organization near appA in C. braakii was similar to that in Salmonella typhimurium genome. C. braakii AppA contained five putative N-glycosylation sites. The recombinant phytases, rAppA_Ec and rAppA_Sc, were produced in E. coli and Saccharomyces cerevisiae, respectively, with both being fused with C-terminal His-tag. After purification, rAppA_Sc was shown to be hyperglycosylated by Endo-H treatment. It had greater thermostability than the wild type phytase and rAppA_Ec.     

Mathematical Study of the Role of Gametocytes and an Imperfect Vaccine on Malaria Transmission Dynamics

A mathematical model is developed to assess the role of gametocytes (the infectious sexual stage of the malaria parasite) in malaria transmission dynamics in a community. The model is rigorously analysed to gain insights into its dynamical features. It is shown that, in the absence of disease-induced mortality, the model has a globally-asymptotically stable disease-free equilibrium whenever a certain epidemiological threshold, known as the basic reproduction number (denoted by ℛ₀), is less than unity. Further, it has a unique endemic equilibrium if ℛ₀>1. The model is extended to incorporate an imperfect vaccine with some assumed therapeutic characteristics. Theoretical analyses of the model with vaccination show that an imperfect malaria vaccine could have negative or positive impact (in reducing disease burden) depending on whether or not a certain threshold (denoted by ∇) is less than unity. Numerical simulations of the vaccination model show that such an imperfect anti-malaria vaccine (with a modest efficacy and coverage rate) can lead to effective disease control if the reproduction threshold (denoted by ℛ_vac) of the disease is reasonably small. On the other hand, the disease cannot be effectively controlled using such a vaccine if ℛ_vac is high. Finally, it is shown that the average number of days spent in the class of infectious individuals with higher level of gametocyte is critically important to the malaria burden in the community.     

Radical changes in the Wadden Sea fauna and flora over the last 2,000 years

Humans have interacted with the Wadden Sea since its origin 7,500 years ago. However, exploitation, habitat alteration and pollution have strongly increased since the Middle Ages, affecting abundance and distribution of many marine mammals, birds, fish, invertebrates and plants. Large whales and some large birds disappeared more than 500 years ago. Most small whales, seals, birds, large fish and oysters were severely reduced by the late 19th and early 20th centuries, leading to the collapse of several traditional fisheries. In the 20th century, conservation efforts have enabled some breeding birds and seals to recover. But other species declined further due to continuing exploitation, habitat destruction, pollution and eutrophication. Moreover, complex three-dimensional habitats such as oyster banks, Sabellaria reefs and subtidal eelgrass beds have been lost completely. In contrast, several opportunistic species such as gulls, polychaetes, green algae and exotic invaders increased during the 20th century. Taken together, multiple human impacts have caused dramatic losses of large predators and habitat-building species in the Wadden Sea over the last 500 years. Although still of high natural value and global importance, the Wadden Sea is a fundamentally changed ecosystem. On the other hand, reduced hunting pressure, increased habitat protection and reduced river pollution have enabled the recent recovery of several species and an increase in environmental quality. These successes, together with a historical vision of what was once possible, should guide current and future conservation, restoration and management efforts towards a more sustainable interaction between man and the sea.     

Genetic and environmental factors influencing the human factor H plasma levels

Factor H is a plasma protein that plays a critical role in the regulation of complement activation in fluid phase and on cellular surfaces. Over the years numerous reports have illustrated the association of factor H deficiencies with chronic renal and infectious diseases. Plasma levels of factor H show a five-fold range of variation in humans (116–562 g/ml), which may also be relevant to disease susceptibility. To quantify the effects of the genetic and environmental factors responsible for the variation in the factor H plasma levels, we have applied variance-component methods to a family-based sample. Factor H plasma levels show an age-dependent increase (P<0.0001) and are decreased in smokers (P<0.0001). Interestingly, the heritability of the factor H trait is very high (h²=0.62±0.07; P<0.0001), indicating that 62% of the factor H phenotypic variance is due to the additive effects of genes. On this premise, we conducted a genome-wide linkage screen in order to identify genes regulating the factor H trait. Three genomic regions (1q32, 2p21–24 and 15q22–24) provided suggestive evidence of linkage (LOD scores 2.03, 2.15 and 2.00, respectively) with the plasma levels of factor H.     

Modeling and Estimation of Kinetic Parameters and Replicative Fitness of HIV-1 from Flow-Cytometry-Based Growth Competition Experiments

Growth competition assays have been developed to quantify the relative fitness of HIV-1 mutants. In this article, we develop mathematical models to describe viral/cellular dynamic interactions in the assay system from which the competitive fitness indices or parameters are defined. In our previous HIV-viral fitness experiments, the concentration of uninfected target cells was assumed to be constant (Wu et al. 2006). But this may not be true in some experiments. In addition, dual infection may frequently occur in viral fitness experiments and may not be ignorable. Here, we relax these two assumptions and extend our earlier viral fitness model (Wu et al. 2006). The resulting models then become nonlinear ODE systems for which closed-form solutions are not achievable. In the new model, the viral relative fitness is a function of time since it depends on the target cell concentration. First, we studied the structure identifiability of the nonlinear ODE models. The identifiability analysis showed that all parameters in the proposed models are identifiable from the flow-cytometry-based experimental data that we collected. We then employed a global optimization approach (the differential evolution algorithm) to directly estimate the kinetic parameters as well as the relative fitness index in the nonlinear ODE models using nonlinear least square regression based on the experimental data. Practical identifiability was investigated via Monte Carlo simulations.