Conditions for Global Dynamic Stability of a Class of Resource-Bounded Model Ecosystems

This paper studies a class of dynamical systems that model multi-species ecosystems. These systems are ‘resource bounded’ in the sense that species compete to utilize an underlying limiting resource or substrate. This boundedness means that the relevant state space can be reduced to a simplex, with coordinates representing the proportions of substrate utilized by the various species. If the vector field is inward pointing on the boundary of the simplex, the state space is forward invariant under the system flow, a requirement that can be interpreted as the presence of non-zero exogenous recruitment. We consider conditions under which these model systems have a unique interior equilibrium that is globally asymptotically stable. The systems we consider generalize classical multi-species Lotka–Volterra systems, the behaviour of which is characterized by properties of the community (or interaction) matrix. However, the more general systems considered here are not characterized by a single matrix, but rather a family of matrices. We develop a set of ‘explicit conditions’ on the basis of a notion of ‘uniform diagonal dominance’ for such a family of matrices, that allows us to extract a set of sufficient conditions for global asymptotic stability based on properties of a single, derived matrix. Examples of these explicit conditions are discussed.     

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.     

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.     

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.     

The Role of Cohesiveness in the Permeability of the Spatial Assemblies of FG Nucleoporins

Nuclear pore complexes (NPCs) conduct selective, bidirectional transport across the nuclear envelope. The NPC passageway is lined by intrinsically disordered proteins that contain hydrophobic phenylalanine-glycine (FG) motifs, known as FG nucleoporins (FG nups), that play the key role in the NPC transport mechanism. Cohesive interactions among the FG nups, which arise from the combination of hydrophobic, electrostatic, and other forces, have been hypothesized to control the morphology of the assemblies of FG nups in the NPC, as well as their permeability with respect to the transport proteins. However, the role of FG nup cohesiveness is still vigorously debated. Using coarse-grained polymer theory and numerical simulations, we study the effects of cohesiveness on the selective permeability of in vitro FG nup assemblies in different geometries that have served as proxies for the morphological and transport properties of the NPC. We show that in high-density FG nup assemblies, increase in cohesiveness leads to the decrease in their permeability, in accordance with the accepted view. On the other hand, the permeability of low-density assemblies is a nonmonotonic function of the cohesiveness, and a moderate increase in cohesiveness can enhance permeability. The density- and cohesiveness-dependent effects on permeability are explained by considering the free-energy cost associated with penetrating the FG nup assemblies. We discuss the implications of these findings for the organization and function of the NPC.     

Bistability Analysis of an Apoptosis Model in the Presence of Nitric Oxide

Bistability in apoptosis, or programmed cell death, is crucial for the healthy functioning of multicellular organisms. The aim in this study is to show the presence of bistability in a mitochondria-dependent apoptosis model under nitric oxide effects using chemical reaction network theory. The model equations are a set of coupled ordinary differential equations arising from the assumed mass action kinetics. Whether these equations have a capacity for bistability (cell survival and apoptosis) is determined using a modular approach in which the model is decomposed into modules. Each module contains only a subset of the whole model and is analyzed separately. It is seen that bistability in a module is preserved throughout the whole model after adding the remaining reactions in the pathway on these modules. It is also found that inhibitor effect of some proteins and the appearance of a reacting protein in a later stage as a product is a desired feature but not sufficient for bistability (in the absence of cooperativity effects). On the whole model, two apoptotic and two cell survival states are obtained depending on the initial cell conditions. The results suggest that the antiapoptotic effects of nitric oxide species are responsible for the bistable character of the apoptotic pathway when cooperativity is not assumed in the apoptosome formation.     

Microenvironmental influences of apoptosis in vivo and in vitro

The apoptosis program of physiological cell death elicits a range of non-phlogistic homeostatic mechanisms—“recognition, response and removal”—that regulate the microenvironments of normal and diseased tissues via multiple modalities operating over short and long distances. The molecular mechanisms mediate intercellular signaling through direct contact with neighboring cells, release of soluble factors and production of membrane-delimited fragments (apoptotic bodies, blebs and microparticles) that allow for interaction with host cells over long distances. These processes effect the selective recruitment of mononuclear phagocytes and the specific activation of both phagocytic and non-phagocytic cells. While much evidence is available concerning the mechanisms underlying the recognition and responses of phagocytes that culminate in the engulfment and removal of apoptotic cell bodies, relatively little is yet known about the non-phagocytic cellular responses to the apoptosis program. These responses regulate inflammatory and immune cell activation as well as cell fate decisions of proliferation, differentiation and death. Here, we review current knowledge of these processes, considering especially how apoptotic cells condition the microenvironments of normal and malignant tissues. We also discuss how apoptotic cells that persist in the absence of phagocytic clearance exert inhibitory effects over their viable neighbors, paying particular attention to the specific case of cell cultures and highlighting how new cell-corpse-clearance devices—Dead-Cert^® Nanoparticles—can significantly improve the efficacy of cell cultures through effective removal of non-viable cells in the absence of phagocytes in vitro.     

Importance of co-cultivation medium pH for successful Agrobacterium-mediated transformation of Lilium × formolongi

An efficient system for Agrobacterium-mediated transformation of Lilium × formolongi was established by preventing the drastic drop of pH in the co-cultivation medium with MES. Meristematic nodular calli were inoculated with an overnight culture of A. tumefaciens strain EHA101 containing the plasmid pIG121-Hm which harbored intron-containing β-glucuronidase (GUS), hygromycin phosphotransferase (HPT), and neomycin phosphotransfease II (NPTII) genes. After three days of co-cultivation on 2 g/l gellan gum-solidified MS medium containing 100 μM acetosyringone, 30 g/l sucrose, 1 mg/l picloram and different concentrations of MES, they were cultured on the same medium containing 12.5 mg/l meropenem to eliminate Agrobacterium for 2 weeks and then transferred onto medium containing the same concentration of meropenem and 25 mg/l hygromycin for selecting putative transgenic calli. Transient GUS expression was only observed by adding MES to co-cultivation medium. Hygromycin-resistant transgenic calli were obtained only when MES was added to the co-cultivation medium especially at 10 mM. The hygromycin-resistant calli were successfully regenerated into plantlets after transferring onto picloram-free medium. Transformation of plants was confirmed by histochemical GUS assay, PCR analysis and Southern blot analysis.     

On 20 years of Lophotrochozoa

Lophotrochozoa is a protostome clade that includes disparate animals such as molluscs, annelids, bryozoans, and flatworms, giving it the distinction of including the most body plans of any of the three major clades of Bilateria. This extreme morphological disparity has prompted numerous conflicting phylogenetic hypotheses about relationships among lophotrochozoan phyla. Here, I review the current understanding of lophotrochozoan phylogeny with emphasis on recent insights gained through approaches taking advantage of high-throughput DNA sequencing (phylogenomics). Of significance, Platyzoa, a hypothesized clade of mostly small-bodied animals, appears to be an artifact of long-branch attraction. Recent studies recovered Gnathifera (Syndermata, Gnathostomulida, and Micrognathozoa) sister to all other lophotrochozoans and a clade called Rouphozoa (Platyhelminthes and Gastrotricha) sister to the remaining non-gnathiferan lophotrochozoans. Although Bryozoa was traditionally grouped with Brachiopoda and Phoronida (Lophophorata), most molecular studies have supported a clade including Entoprocta, Cycliophora, and Bryozoa (Polyzoa). However, recent phylogenomic work has shown that entoprocts and bryozoans have compositionally heterogeneous genomes that may cause systematic artifacts affecting their phylogenetic placement. Lastly, relationships within Trochozoa (Mollusca, Annelida, and relatives) largely remain ambiguous. Recent work has shown that phylogenomic studies must identify and reduce sources of systematic error, such as amino acid compositional heterogeneity and long-branch attraction. Still, other approaches such as the analysis of rare genomic changes may be needed to overcome challenges to standard phylogenomic approaches. Resolving lophotrochozoan phylogeny will provide important insight into how these complex and diverse body plans evolved and provide a much-needed framework for comparative studies.     

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.     

Optimal Timing of Disease Transmission in an Age-Structured Population

It is a common medical folk-practice for parents to encourage their children to contract certain infectious diseases while they are young. This folk-practice is controversial, in part, because it contradicts the long-term public health goal of minimizing disease incidence. We study an epidemiological model of infectious disease in an age-structured population where virulence is age-dependent and show that, in some cases, the optimal behavior will increase disease transmission. This provides a rigorous justification of the concept of “endemic stability,” and demonstrates that folk-practices may have been historically justified.     

Glowworm swarm optimization for simultaneous capture of multiple local optima of multimodal functions

This paper presents glowworm swarm optimization (GSO), a novel algorithm for the simultaneous computation of multiple optima of multimodal functions. The algorithm shares a few features with some better known swarm intelligence based optimization algorithms, such as ant colony optimization and particle swarm optimization, but with several significant differences. The agents in GSO are thought of as glowworms that carry a luminescence quantity called luciferin along with them. The glowworms encode the fitness of their current locations, evaluated using the objective function, into a luciferin value that they broadcast to their neighbors. The glowworm identifies its neighbors and computes its movements by exploiting an adaptive neighborhood, which is bounded above by its sensor range. Each glowworm selects, using a probabilistic mechanism, a neighbor that has a luciferin value higher than its own and moves toward it. These movements—based only on local information and selective neighbor interactions—enable the swarm of glowworms to partition into disjoint subgroups that converge on multiple optima of a given multimodal function. We provide some theoretical results related to the luciferin update mechanism in order to prove the bounded nature and convergence of luciferin levels of the glowworms. Experimental results demonstrate the efficacy of the proposed glowworm based algorithm in capturing multiple optima of a series of standard multimodal test functions and more complex ones, such as stair-case and multiple-plateau functions. We also report the results of tests in higher dimensional spaces with a large number of peaks. We address the parameter selection problem by conducting experiments to show that only two parameters need to be selected by the user. Finally, we provide some comparisons of GSO with PSO and an experimental comparison with Niche-PSO, a PSO variant that is designed for the simultaneous computation of multiple optima. This work is partially supported by a project grant from the Ministry of Human Resources Development, India and by DRDO-IISc Mathematical Engineering Program.     

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.     

Grain of environment explains variation in the strength of genotype × environment interaction

Theory predicts that genetic variation in phenotypic plasticity (genotype × environment interaction or G × E) should be eroded by selection acting across environments. However, it appears that G × E is often maintained under selection, although not universally. This variation in the presence and strength of G × E requires explanation. Here I ask whether the explanation may lie in the grain of the environment at which G × E is expressed. The grain (or grain size) of the environment refers to the scale of environmental heterogeneity relative to generation time – that is, relative to the window of operation of selection – with higher rates of heterogeneity occurring in finer‐grained environments. The hypothesis that the grain of the environment explains variation in the expression of G × E encapsulates variation in the power of selection to shape reaction norms: selection should be able to erode G × E in fine‐grained environments but lose its power as the grain becomes coarser. I survey studies of G × E in sexual traits and demonstrate that the strength of G × E varies with the grain of the environment across which it is expressed, with G × E being stronger in coarser‐grained environments. This result elucidates when G × E is most likely to be sustained in the reaction norms of fitness‐related traits and when its evolutionary consequences will be most pronounced.     

A Dynamical Study of a Cellular Automata Model of the Spread of HIV in a Lymph Node

We conduct a mathematical study of a cellular automata model of the spread of the HIV virus in a lymph node. The model was proposed by Zorzenon dos Santos and Coutinho and captures the unique time scale of the viral spread. We give some rigorous mathematical results about the time scales and other dynamical aspects of the model as well as discuss parameter and model changes and their consequences.     

C-Terminal 23 kDa polypeptide of soybean Gly m Bd 28 K is a potential allergen

Gly m Bd 28 K is a major soybean (Glycine max Merr.) glycoprotein allergen. It was originally identified as a 28 kDa polypeptide in soybean seed flour. However, the full-length protein is encoded by an open reading frame (ORF) of 473 amino acids, and contains a 23 kDa C-terminal polypeptide of as yet unknown allergenic and structural characteristics. IgE-binding (allergenic potential) of the Gly m Bd 28 K protein including the 23 kDa C-terminal portion as well as shorter fragments derived from the full-length ORF were evaluated using sera from soy-sensitive adults. All of these sera contained IgE that efficiently recognized the C-terminal region. Epitope mapping demonstrated that a dominant linear C-terminal IgE binding epitope resides between residues S256 and A270. Alanine scanning of this dominant epitope indicated that five amino acids, Y260, D261, D262, K264 and D266, contribute most towards IgE-binding. A model based on the structure of the subunit of soybean -conglycinin revealed that Gly m Bd 28 K contains two cupin domains. The dominant epitope is on the edge of the first -sheet of the C-terminal cupin domain and is present on a potentially solvent-accessible loop connecting the two cupin domains. Thus, the C-terminal 23 kDa polypeptide of Gly m Bd 28 K present in soy products is allergenic and apparently contains at least one immunodominant epitope near the edge of a cupin domain. This knowledge could be helpful in the future breeding of hypoallergenic soybeans.Abbreviations Ara h 1 Arachis hypogaea allergen 1 - Ara h 3 Arachis hypogaea allergen 3 - BCA Bicinchoninic acid - Gly m Bd 28 K Glycine max band 28 kDa allergen - Gly m Bd 30 K Glycine max band 30 kDa allergen - Gly m Bd 68 K Glycine max band 68 kDa allergen - IgE Immunoglobulin E