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.     

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.     

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.     

Spatiotemporal Dynamics of the Epidemic Transmission in a Predator-Prey System

Epidemic transmission is one of the critical density-dependent mechanisms that affect species viability and dynamics. In a predator-prey system, epidemic transmission can strongly affect the success probability of hunting, especially for social animals. Predators, therefore, will suffer from the positive density-dependence, i.e., Allee effect, due to epidemic transmission in the population. The rate of species contacting the epidemic, especially for those endangered or invasive, has largely increased due to the habitat destruction caused by anthropogenic disturbance. Using ordinary differential equations and cellular automata, we here explored the epidemic transmission in a predator-prey system. Results show that a moderate Allee effect will destabilize the dynamics, but it is not true for the extreme Allee effect (weak or strong). The predator-prey dynamics amazingly stabilize by the extreme Allee effect. Predators suffer the most from the epidemic disease at moderate transmission probability. Counter-intuitively, habitat destruction will benefit the control of the epidemic disease. The demographic stochasticity dramatically influences the spatial distribution of the system. The spatial distribution changes from oil-bubble-like (due to local interaction) to aggregated spatially scattered points (due to local interaction and demographic stochasticity). It indicates the possibility of using human disturbance in habitat as a potential epidemic-control method in conservation.     

On the Evolution of the Timing of Reproduction with Non-equilibrium Resident Dynamics

We study the evolution of an individual’s reproductive strategy in a mechanistic modeling framework. We assume that the total number of juveniles one adult individual can produce is a finite constant, and we study how this number should be distributed during the season, given the types of inter-individual interactions and mortality processes included in the model. The evolution of the timing of reproduction in this modeling framework has already been studied earlier in the case of equilibrium resident dynamics, but we generalize the situation to also fluctuating population dynamics. We find that, as in the equilibrium case, the presence or absence of inter-juvenile aggression affects the functional form of the evolutionarily stable reproductive strategy. If an ESS exists, it can have an absolutely continuous part only if inter-juvenile aggression is included in the model. If inter-juvenile aggression is not included in the model, an ESS can have no continuous parts, and only Dirac measures are possible.     

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.     

Engineered Bi-Histidine Metal Chelation Sites Map the Structure of the Mechanical Unfolding Transition State of an Elastomeric Protein Domain GB1

Determining the structure of the transition state is critical for elucidating the mechanism behind how proteins fold and unfold. Due to its high free energy, however, the transition state generally cannot be trapped and studied directly using traditional structural biology methods. Thus, characterizing the structure of the transition state that occurs as proteins fold and unfold remains a major challenge. Here, we report a novel (to our knowledge) method that uses engineered bi-histidine (bi-His) metal-binding sites to directly map the structure of the mechanical unfolding transition state of proteins. This method is adapted from the traditional ψ-value analysis, which uses engineered bi-His metal chelation sites to probe chemical (un)folding transition-state structure. The ϕ^M2+_U-value is defined as ΔΔG_‡-N/ΔΔG_U-N, which is the energetic effects of metal chelation by the bi-His site on the unfolding energy barrier (ΔG_‡-N) relative to its thermodynamic stability (ΔG_U-N) and can be used to obtain information about the transition state in the mutational site. As a proof of principle, we used the small protein GB1 as a model system and set out to map its mechanical unfolding transition-state structure. Using single-molecule atomic force microscopy and spectrofluorimetry, we directly quantified the effect of divalent metal ion binding on the mechanical unfolding free energy and thermodynamic stability of GB1, which allowed us to quantify ϕ^M2+_U-values for different sites in GB1. Our results enabled us to map the structure of the mechanical unfolding transition state of GB1. Within GB1’s mechanical unfolding transition state, the interface between force-bearing β-strands 1 and 4 is largely disrupted, and the first β-hairpin is partially disordered while the second β-hairpin and the α-helix remain structured. Our results demonstrate the unique application of ψ-value analysis in elucidating the structure of the transition state that occurs during the mechanical unfolding process, offering a potentially powerful new method for investigating the design of novel elastomeric proteins.     

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.     

Pressure-Temperature Analysis of the Stability of the CTL9 Domain Reveals Hidden Intermediates

The observation of two-state unfolding for many small single-domain proteins by denaturants has led to speculation that protein sequences may have evolved to limit the population of partially folded states that could be detrimental to fitness. How such strong cooperativity arises from a multitude of individual interactions is not well understood. Here, we investigate the stability and folding cooperativity of the C-terminal domain of the ribosomal protein L9 in the pressure-temperature plane using site-specific NMR. In contrast to apparent cooperative unfolding detected with denaturant-induced and thermal-induced unfolding experiments and stopped-flow refolding studies at ambient pressure, NMR-detected pressure unfolding revealed significant deviation from two-state behavior, with a core region that was selectively destabilized by increasing temperature. Comparison of pressure-dependent NMR signals from both the folded and unfolded states revealed the population of at least one invisible excited state at atmospheric pressure. The core destabilizing cavity-creating I98A mutation apparently increased the cooperativity of the loss of folded-state peak intensity while also increasing the population of this invisible excited state present at atmospheric pressure. These observations highlight how local stability is subtly modulated by sequence to tune protein conformational landscapes and illustrate the ability of pressure- and temperature-dependent studies to reveal otherwise hidden states.     

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.     

A genome-wide analysis of the expansin genes in Malus × Domestica

Expansins were first identified as cell wall-loosening proteins; they are involved in regulating cell expansion, fruits softening and many other physiological processes. However, our knowledge about the expansin family members and their evolutionary relationships in fruit trees, such as apple, is limited. In this study, we identified 41 members of the expansin gene family in the genome of apple (Malus × Domestica L. Borkh). Phylogenetic analysis revealed that expansin genes in apple could be divided into four subfamilies according to their gene structures and protein motifs. By phylogenetic analysis of the expansins in five plants (Arabidopsis, rice, poplar, grape and apple), the expansins were divided into 17 subgroups. Our gene duplication analysis revealed that whole-genome and chromosomal-segment duplications contributed to the expansion of Mdexpansins. The microarray and expressed sequence tag (EST) data showed that 34 Mdexpansin genes could be divided into five groups by the EST analysis; they may also play different roles during fruit development. An expression model for MdEXPA16 and MdEXPA20 showed their potential role in developing fruit. Overall, our study provides useful data and novel insights into the functions and regulatory mechanisms of the expansin genes in apple, as well as their evolution and divergence. As the first step towards genome-wide analysis of the expansin genes in apple, our results have established a solid foundation for future studies on the function of the expansin genes in fruit development.     

Quantification of the interceptor action of caffeine on the in vitro biological effect of the anti-tumour agent topotecan

Using published in vitro data on the dependence of the percentage of apoptosis induced by the anti-cancer drug topotecan in a leukaemia cell line on the concentration of added caffeine, and a general model of competitive binding in a system containing two aromatic drugs and DNA, it has been shown to be possible to quantify the relative change in the biological effect just using a set of component concentrations and equilibrium constants of the complexation of the drugs. It is also proposed that a general model of competitive binding and parameterization of that model may potentially be applied to any system of DNA-targeting aromatic drugs under in vitro conditions. The main reasons underpinning the proposal are the general feature of the complexation of aromatic drugs with DNA and their interaction in physiological media via hetero-association.     

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.     

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.     

Impacts of Incubation Delay on the Dynamics of an Eco-Epidemiological System—A Theoretical Study

Parasite and predator play significant role in trophic interaction, productivity and stability of an ecosystem. In this paper, we have studied a host-parasite-predator interaction that incorporates incubation delay. How the qualitative and quantitative behaviors of the system alter with the incubation delay have been discussed both from mathematical and biological point of views. It is observed that for a lower infection rate, the system is stable for all delays; but for a higher infection rate, there exists a threshold value of the delay above which the system is unstable and below which the system is stable leading to the persistence of all the species. Also, the instability arising from the incubation delay may be controlled if somehow the growth rate of predator population is increased. Numerical studies have also been performed to illustrate different analytical findings. Research is supported by UGC, India; F No. 32-173/2006(SR).     

A Geometric Buildup Algorithm for the Solution of the Distance Geometry Problem Using Least-Squares Approximation

We propose a new geometric buildup algorithm for the solution of the distance geometry problem in protein modeling, which can prevent the accumulation of the rounding errors in the buildup calculations successfully and also tolerate small errors in given distances. In this algorithm, we use all instead of a subset of available distances for the determination of each unknown atom and obtain the position of the atom by using a least-squares approximation instead of an exact solution to the system of distance equations. We show that the least-squares approximation can be obtained by using a special singular value decomposition method, which not only tolerates and minimizes small distance errors, but also prevents the rounding errors from propagation effectively, especially when the distance data is sparse. We describe the least-squares formulations and their solution methods, and present the test results from applying the new algorithm for the determination of a set of protein structures with varying degrees of availability and accuracy of the distances. We show that the new development of the algorithm increases the modeling ability, and improves stability and robustness of the geometric buildup approach significantly from both theoretical and practical points of view.     

Side-effects of pesticides on the life cycle of the mite pathogenic fungus Neozygites floridana

The tomato red spider mite, Tetranychus evansi Baker and Pritchard, is an invasive species in Africa causing considerable damage to Solanaceous crops. The fungal pathogen Neozygites floridana Weiser and Muma from Brazil has been considered a potential candidate for introduction into Africa for the control of T. evansi. To be incorporated in the tomato production system, N. floridana has to be compatible with the pesticides used for the control of other pests and diseases. Pesticides used in tomatoes that might affect the fungus were therefore studied by the use of different methods. Two insecticides (Lambda-cyhalothrin and Methomyl), two acaricides (Propargite and Abamectin), and two fungicides (Captan and Mancozeb) were tested in two concentrations: the mean commercial rate (CR) and 50% of the mean commercial rate (CR/2). Fungus-killed mite cadavers or the substrates used for sporulation (leaf discs and coverslips) were either immersed or sprayed with the pesticides before testing their effects on sporulation, germination of primary conidia and infectivity of N. floridana. Direct immersion of cadavers, coverslips or leaf discs into pesticides affected sporulation and germination stronger than the spray tower method, although infectivity of capilliconidia was neither affected by the method of application nor the concentration of the pesticides. The fungicides Captan and Mancozeb resulted in a high reduction in sporulation and germination at both concentrations. Propargite did not inhibit sporulation but affected germination of primary conidia. Methomyl and Abamectin resulted in less effects on N. floridana.