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.     

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.     

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.     

Beauveria Bassiana Pathogenicity to the Citrus Rust Mite Phyllocoptruta Oleivora

The pathogenicity of Beauveria bassiana to one of the major pests of citrus crops, Phyllocoptruta oleivora, was assessed by inoculating mites with different concentrations of conidia (1×10⁶, 5×10⁶, 1×10⁷, 5×10⁷ and 1×10⁸). Treated mites were kept at controlled conditions (25 ± 0.5°C, 12 h photoperiod and 98% relative humidity) and mite survivorship was evaluated daily. Mortality was found to increase in time and was dependent on the conidia concentration, with values ranging from 24 to 91% for the lowest and highest conidia concentration, respectively. The calculated LC₅₀ on the fifth day was 4.23×10⁶ conidia/ml. Mean lethal time was 3.98, 9.79, 3.09 and 2.74 days for 5×10⁶, 1×10⁷, 5×10⁷ and 1×10⁸ conidia/ml, respectively. Conidia were found to adhere all over the mite body surface, especially at the anal region, where vegetative mycelium was found entering the mite body. We noticed the formation of small crystals inside the mite’s body that were produced during colonization of the body cavity by the fungus. This is the first report of B. bassiana pathogenicity for this species.     

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.     

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.     

A Mechanism for Ultra-Slow Oscillations in the Cortical Default Network

When the brain is in its noncognitive “idling” state, functional MRI measurements reveal the activation of default cortical networks whose activity is suppressed during cognitive processing. This default or background mode is characterized by ultra-slow BOLD oscillations (∼0.05 Hz), signaling extremely slow cycling in cortical metabolic demand across distinct cortical regions. Here we describe a model of the cortex which predicts that slow cycling of cortical activity can arise naturally as a result of nonlinear interactions between temporal (Hopf) and spatial (Turing) instabilities. The Hopf instability is triggered by delays in the inhibitory postsynaptic response, while the Turing instability is precipitated by increases in the strength of the gap-junction coupling between interneurons. We comment on possible implications for slow dendritic computation and information processing.     

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.     

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.     

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.     

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.     

Efficient Semiparametric Marginal Estimation for the Partially Linear Additive Model for Longitudinal/Clustered Data

We consider the efficient estimation of a regression parameter in a partially linear additive nonparametric regression model from repeated measures data when the covariates are multivariate. To date, while there is some literature in the scalar covariate case, the problem has not been addressed in the multivariate additive model case. Ours represents a first contribution in this direction. As part of this work, we first describe the behavior of nonparametric estimators for additive models with repeated measures when the underlying model is not additive. These results are critical when one considers variants of the basic additive model. We apply them to the partially linear additive repeated-measures model, deriving an explicit consistent estimator of the parametric component; if the errors are in addition Gaussian, the estimator is semiparametric efficient. We also apply our basic methods to a unique testing problem that arises in genetic epidemiology; in combination with a projection argument we develop an efficient and easily computed testing scheme. Simulations and an empirical example from nutritional epidemiology illustrate our methods.     

Angiotensin IV in the central nervous system

The mammalian brain harbors a renin-angiotensin system (RAS), which is independent from the peripheral RAS. Angiotensin II is a well-studied member of the RAS and exerts most of the known angiotensin-mediated effects on fluid and electrolyte homeostasis, autonomic activity, neuroendocrine regulation, and behavior. This review summarizes a mass of compelling new evidence for the biological role of an active (3-8) fragment of angiotensin II, named angiotensin IV. Angiotensin IV binds to a widely distributed binding site in the brain, but which is different from the known angiotensin II receptors AT1 and AT2. Angiotensin IV has been implicated in a number of physiological actions, including the regulation of blood flow, the modulation of exploratory behavior, and processes attributed to learning and memory. Furthermore, angiotensin IV may also be involved in neuronal development. Collectively, the available evidence suggests that angiotensin IV is a potent neuropeptide, involved in a broad range of brain functions.     

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.     

Visual system: prostriata - a visual area off the beaten path

Recent work establishes that Prostriata, a little-studied area of the visual cortex neighboring V1, has distinct but hybrid visual properties which are suggestive of an unsuspected role in the rapid analysis and integration of peripheral visual stimuli.     

Human Genetics: Message from the Mesolithic

DNA extracted from the remains of two Mesolithic individuals reveals that they had genetically little in common with modern Europeans. The ancestors of most modern Europeans thus most likely entered Europe only with the advent of farming.