A Mathematical Model of Rift Valley Fever with Human Host

Rift Valley Fever is a vector-borne disease mainly transmitted by mosquito. To gain some quantitative insights into its dynamics, a deterministic model with mosquito, livestock, and human host is formulated as a system of nonlinear ordinary differential equations and analyzed. The disease threshold [Formula: see text] is computed and used to investigate the local stability of the equilibria. A sensitivity analysis is performed and the most sensitive model parameters to the measure of initial disease transmission [Formula: see text] and the endemic equilibrium are determined. Both [Formula: see text] and the disease prevalence in mosquitoes are more sensitive to the natural mosquito death rate, d(m). The disease prevalence in livestock and humans are more sensitive to livestock and human recruitment rates, [Formula: see text] and [Formula: see text], respectively, suggesting isolation of livestock from humans is a viable preventive strategy during an outbreak. Numerical simulations support the analytical results in further exploring theoretically the long-term dynamics of the disease at the population level.     

The dynamics, causes and possible prevention of hepatitis e outbreaks

Rapidly spreading infectious diseases are a serious risk to public health. The dynamics and the factors causing outbreaks of these diseases can be better understood using mathematical models, which are fit to data. Here we investigate the dynamics of a Hepatitis E outbreak in the Kitgum region of northern Uganda during 2007 to 2009. First, we use the data to determine that [Formula: see text] is approximately 2.25 for the outbreak. Secondly, we use a model to estimate that the critical level of latrine and bore hole coverages needed to eradicate the epidemic is at least [Formula: see text] and [Formula: see text] respectively. Lastly, we further investigate the relationship between the co-infection factor for malaria and Hepatitis E on the value of [Formula: see text] for Hepatitis E. Taken together, these results provide us with a better understanding of the dynamics and possible causes of Hepatitis E outbreaks.     

Unifying Time to Contact Estimation and Collision Avoidance across Species

The [Formula: see text]-function and the [Formula: see text]-function are phenomenological models that are widely used in the context of timing interceptive actions and collision avoidance, respectively. Both models were previously considered to be unrelated to each other: [Formula: see text] is a decreasing function that provides an estimation of time-to-contact (ttc) in the early phase of an object approach; in contrast, [Formula: see text] has a maximum before ttc. Furthermore, it is not clear how both functions could be implemented at the neuronal level in a biophysically plausible fashion. Here we propose a new framework - the corrected modified Tau function - capable of predicting both [Formula: see text]-type ("[Formula: see text]") and [Formula: see text]-type ("[Formula: see text]") responses. The outstanding property of our new framework is its resilience to noise. We show that [Formula: see text] can be derived from a firing rate equation, and, as [Formula: see text], serves to describe the response curves of collision sensitive neurons. Furthermore, we show that [Formula: see text] predicts the psychophysical performance of subjects determining ttc. Our new framework is thus validated successfully against published and novel experimental data. Within the framework, links between [Formula: see text]-type and [Formula: see text]-type neurons are established. Therefore, it could possibly serve as a model for explaining the co-occurrence of such neurons in the brain.     

Critical motor number for fractional steps of cytoskeletal filaments in gliding assays

In gliding assays, filaments are pulled by molecular motors that are immobilized on a solid surface. By varying the motor density on the surface, one can control the number [Formula: see text] of motors that pull simultaneously on a single filament. Here, such gliding assays are studied theoretically using Brownian (or Langevin) dynamics simulations and taking the local force balance between motors and filaments as well as the force-dependent velocity of the motors into account. We focus on the filament stepping dynamics and investigate how single motor properties such as stalk elasticity and step size determine the presence or absence of fractional steps of the filaments. We show that each gliding assay can be characterized by a critical motor number, [Formula: see text]. Because of thermal fluctuations, fractional filament steps are only detectable as long as [Formula: see text]. The corresponding fractional filament step size is [Formula: see text] where [Formula: see text] is the step size of a single motor. We first apply our computational approach to microtubules pulled by kinesin-1 motors. For elastic motor stalks that behave as linear springs with a zero rest length, the critical motor number is found to be [Formula: see text], and the corresponding distributions of the filament step sizes are in good agreement with the available experimental data. In general, the critical motor number [Formula: see text] depends on the elastic stalk properties and is reduced to [Formula: see text] for linear springs with a nonzero rest length. Furthermore, [Formula: see text] is shown to depend quadratically on the motor step size [Formula: see text]. Therefore, gliding assays consisting of actin filaments and myosin-V are predicted to exhibit fractional filament steps up to motor number [Formula: see text]. Finally, we show that fractional filament steps are also detectable for a fixed average motor number [Formula: see text] as determined by the surface density (or coverage) of the motors on the substrate surface.     

Limits to the rate of adaptive substitution in sexual populations

In large populations, many beneficial mutations may be simultaneously available and may compete with one another, slowing adaptation. By finding the probability of fixation of a favorable allele in a simple model of a haploid sexual population, we find limits to the rate of adaptive substitution, [Formula: see text], that depend on simple parameter combinations. When variance in fitness is low and linkage is loose, the baseline rate of substitution is [Formula: see text], where [Formula: see text] is the population size, [Formula: see text] is the rate of beneficial mutations per genome, and [Formula: see text] is their mean selective advantage. Heritable variance [Formula: see text] in log fitness due to unlinked loci reduces [Formula: see text] by [Formula: see text] under polygamy and [Formula: see text] under monogamy. With a linear genetic map of length [Formula: see text] Morgans, interference is yet stronger. We use a scaling argument to show that the density of adaptive substitutions depends on [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] only through the baseline density: [Formula: see text]. Under the approximation that the interference due to different sweeps adds up, we show that [Formula: see text], implying that interference prevents the rate of adaptive substitution from exceeding one per centimorgan per 200 generations. Simulations and numerical calculations confirm the scaling argument and confirm the additive approximation for [Formula: see text]; for higher [Formula: see text], the rate of adaptation grows above [Formula: see text], but only very slowly. We also consider the effect of sweeps on neutral diversity and show that, while even occasional sweeps can greatly reduce neutral diversity, this effect saturates as sweeps become more common-diversity can be maintained even in populations experiencing very strong interference. Our results indicate that for some organisms the rate of adaptive substitution may be primarily recombination-limited, depending only weakly on the mutation supply and the strength of selection.     

(13)C NMR Reveals No Evidence of n-π* Interactions in Proteins

An [Formula: see text] interaction between neighboring carbonyl groups has been postulated to stabilize protein structures. Such an interaction would affect the [Formula: see text]C chemical shielding of the carbonyl groups, whose paramagnetic component is dominated by [Formula: see text] and [Formula: see text] excitations. Model compound calculations indicate that both the interaction energetics and the chemical shielding of the carbonyl group are instead dominated by a classical dipole-dipole interaction. A set of high-resolution protein structures with associated carbonyl [Formula: see text]C chemical shift assignments verifies this correlation and provides no evidence for an inter-carbonyl [Formula: see text] interaction.     

Specificity of Hpa II and Hae III DNA methylases

The methylases M.HaeIII and M.HpaII recognize the tetranucleotide sequences [Formula: see text] and [Formula: see text] respectively, in DNA, and transfer a methyl group from S-adenosylmethionine to the 5-position of cytosine on each strand as indicated by the asterisks. Restriction endonuclease R.HaeIII does not cleave the methylated sequence [Formula: see text] but can cleave [Formula: see text] in which methylation is introduced on the unnatural external cytosine positions. Similarly, R.HpaII does not cleave [Formula: see text] but can cleave [Formula: see text].Images     

Optimizing vaccine allocation at different points in time during an epidemic

Background

Pandemic influenza A(H1N1) 2009 began spreading around the globe in April of 2009 and vaccination started in October of 2009. In most countries, by the time vaccination started, the second wave of pandemic H1N1 2009 was already under way. With limited supplies of vaccine, we are left to question whether it may be a good strategy to vaccinate the high-transmission groups earlier in the epidemic, but it might be a better use of resources to protect instead the high-risk groups later in the epidemic. To answer this question, we develop a deterministic epidemic model with two age-groups (children and adults) and further subdivide each age group in low and high risk.

Methods and Findings

We compare optimal vaccination strategies started at various points in time in two different settings: a population in a developed country where children account for 24% of the population, and a population in a less developed country where children make up the majority of the population, 55%. For each of these populations, we minimize mortality or hospitalizations and we find an optimal vaccination strategy that gives the best vaccine allocation given a starting vaccination time and vaccine coverage level. We find that population structure is an important factor in determining the optimal vaccine distribution. Moreover, the optimal policy is dynamic as there is a switch in the optimal vaccination strategy at some time point just before the peak of the epidemic. For instance, with 25% vaccine coverage, it is better to protect the high-transmission groups before this point, but it is optimal to protect the most vulnerable groups afterward.

Conclusions

Choosing the optimal strategy before or early in the epidemic makes an important difference in minimizing the number of influenza infections, and consequently the number of influenza deaths or hospitalizations, but the optimal strategy makes little difference after the peak.     

An epidemiological framework for modelling fungicide dynamics and control

Defining appropriate policies for controlling the spread of fungal disease in agricultural landscapes requires appropriate theoretical models. Most existing models for the fungicidal control of plant diseases do not explicitly include the dynamics of the fungicide itself, nor do they consider the impact of infection occurring during the host growth phase. We introduce a modelling framework for fungicide application that allows us to consider how "explicit" modelling of fungicide dynamics affects the invasion and persistence of plant pathogens. Specifically, we show that "explicit" models exhibit bistability zones for values of the basic reproductive number ([Formula: see text]) less than one within which the invasion and persistence threshold depends on the initial infection levels. This is in contrast to classical models where invasion and persistence thresholds are solely dependent on [Formula: see text]. In addition if initial infection occurs during the growth phase then an additional "invasion zone" can exist for even smaller values of [Formula: see text]. Within this region the system will experience an epidemic that is not able to persist. We further show that ideal fungicides with high levels of effectiveness, low rates of application and low rates of decay lead to the existence of these bistability zones. The results are robust to the inclusion of demographic stochasticity.     

Reactive vaccination in the presence of disease hotspots

Reactive vaccination has recently been adopted as an outbreak response tool for cholera and other infectious diseases. Owing to the global shortage of oral cholera vaccine, health officials must quickly decide who and where to distribute limited vaccine. Targeted vaccination in transmission hotspots (i.e. areas with high transmission efficiency) may be a potential approach to efficiently allocate vaccine, however its effectiveness will likely be context-dependent. We compared strategies for allocating vaccine across multiple areas with heterogeneous transmission efficiency. We constructed metapopulation models of a cholera-like disease and compared simulated epidemics where: vaccine is targeted at areas of high or low transmission efficiency, where vaccine is distributed across the population, and where no vaccine is used. We find that connectivity between populations, transmission efficiency, vaccination timing and the amount of vaccine available all shape the performance of different allocation strategies. In highly connected settings (e.g. cities) when vaccinating early in the epidemic, targeting limited vaccine at transmission hotspots is often optimal. Once vaccination is delayed, targeting the hotspot is rarely optimal, and strategies that either spread vaccine between areas or those targeted at non-hotspots will avert more cases. Although hotspots may be an intuitive outbreak control target, we show that, in many situations, the hotspot-epidemic proceeds so fast that hotspot-targeted reactive vaccination will prevent relatively few cases, and vaccination shared across areas where transmission can be sustained is often best.     

Complete determination of the Pin1 catalytic domain thermodynamic cycle by NMR lineshape analysis

The phosphorylation-specific peptidyl-prolyl isomerase Pin1 catalyzes the isomerization of the peptide bond preceding a proline residue between cis and trans isomers. To best understand the mechanisms of Pin1 regulation, rigorous enzymatic assays of isomerization are required. However, most measures of isomerase activity require significant constraints on substrate sequence and only yield rate constants for the cis isomer, [Formula: see text] and apparent Michaelis constants, [Formula: see text]. By contrast, NMR lineshape analysis is a powerful tool for determining microscopic rates and populations of each state in a complex binding scheme. The isolated catalytic domain of Pin1 was employed as a first step towards elucidating the reaction scheme of the full-length enzyme. A 24-residue phosphopeptide derived from the amyloid precurser protein intracellular domain (AICD) phosphorylated at Thr668 served as a biologically-relevant Pin1 substrate. Specific (13)C labeling at the Pin1-targeted proline residue provided multiple reporters sensitive to individual isomer binding and on-enzyme catalysis. We have performed titration experiments and employed lineshape analysis of phosphopeptide (13)C-(1)H constant time HSQC spectra to determine [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] for the catalytic domain of Pin1 acting on this AICD substrate. The on-enzyme equilibrium value of [E·trans]/[E·cis]?=?3.9 suggests that the catalytic domain of Pin1 is optimized to operate on this substrate near equilibrium in the cellular context. This highlights the power of lineshape analysis for determining the microscopic parameters of enzyme catalysis, and demonstrates the feasibility of future studies of Pin1-PPIase mutants to gain insights on the catalytic mechanism of this important enzyme.     

Optimizing Real-Time Vaccine Allocation in a Stochastic SIR Model

Real-time vaccination following an outbreak can effectively mitigate the damage caused by an infectious disease. However, in many cases, available resources are insufficient to vaccinate the entire at-risk population, logistics result in delayed vaccine deployment, and the interaction between members of different cities facilitates a wide spatial spread of infection. Limited vaccine, time delays, and interaction (or coupling) of cities lead to tradeoffs that impact the overall magnitude of the epidemic. These tradeoffs mandate investigation of optimal strategies that minimize the severity of the epidemic by prioritizing allocation of vaccine to specific subpopulations. We use an SIR model to describe the disease dynamics of an epidemic which breaks out in one city and spreads to another. We solve a master equation to determine the resulting probability distribution of the final epidemic size. We then identify tradeoffs between vaccine, time delay, and coupling, and we determine the optimal vaccination protocols resulting from these tradeoffs.     

Trans-Theta Logistics: A New Family of Population Growth Sigmoid Functions

Sigmoid functions have been applied in many areas to model self limited population growth. The most popular functions; General Logistic (GL), General von Bertalanffy (GV), and Gompertz (G), comprise a family of functions called Theta Logistic ([Formula: see text] L). Previously, we introduced a simple model of tumor cell population dynamics which provided a unifying foundation for these functions. In the model the total population (N) is divided into reproducing (P) and non-reproducing/quiescent (Q) sub-populations. The modes of the rate of change of ratio P/N was shown to produce GL, GV or G growth. We now generalize the population dynamics model and extend the possible modes of the P/N rate of change. We produce a new family of sigmoid growth functions, Trans-General Logistic (TGL), Trans-General von Bertalanffy (TGV) and Trans-Gompertz (TG)), which as a group we have named Trans-Theta Logistic (T [Formula: see text] L) since they exist when the [Formula: see text] L are translated from a two parameter into a three parameter phase space. Additionally, the model produces a new trigonometric based sigmoid (TS). The [Formula: see text] L sigmoids have an inflection point size fixed by a single parameter and an inflection age fixed by both of the defining parameters. T [Formula: see text] L and TS sigmoids have an inflection point size defined by two parameters in bounding relationships and inflection point age defined by three parameters (two bounded). While the Theta Logistic sigmoids provided flexibility in defining the inflection point size, the Trans-Theta Logistic sigmoids provide flexibility in defining the inflection point size and age. By matching the slopes at the inflection points we compare the range of values of inflection point age for T [Formula: see text] L versus [Formula: see text] L for model growth curves.     

Copper(I)-alkyl sulfide and -cysteine tri-nuclear clusters as models for metallo proteins: a structural density functional analysis

After having set up the computational methodology for Cu(I)-sulfur systems as models for copper proteins, namely using the simple ligands H(2)S, HS(-), CH(3)SH, and CH(3)S(-), the Cu(I)-Cysteine systems have been investigated: [Cu(I)( S -H(2)Cys) (n) ](+) (H(2)Cys, cysteine, NH(2),SH,COOH) [Cu(I)( S -HCys) (n) ](1-) (n) (NH(2),S(-),COOH). Finally, the structures for bi-nuclear [Formula: see text] (Et, CH(2)CH(3)), [Formula: see text] and tri-nuclear [Cu(I)( S -SH)](3), [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] (NH(2),SH,COOH), [Formula: see text] (NH(2),S(-),COOH, and NH(2),SH,COO(-)), as well as [Formula: see text] (NH(2),S(-),COO(-)), were also optimized to mimic the active center for a metallo-chaperone copper transport protein (CopZ). The X-ray structures for the biomolecules were matched fairly well as regards the Cu-S bond distances and Cu…Cu contact distances in the case the model cysteine S atom is deprotonated. Upon protonation of ligand S atoms, the conformation of clusters is altered and might bring about the di- and tri-nuclear core breakage. These findings suggest that subtle protonation/deprotonation steps, i.e. small and/or local pH changes play a significant role for copper transport processes.     

Fracture Faces in the Cell Envelope of Escherichia coli

Freeze-fracturing of Escherichia coli cells in the presence of 30% (v/v) glycerol resulted in a double cleavage of the cell envelope exposing two convex and two concave fracture faces ([Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text]) with characteristic patterns. Complementary replicas revealed the relationship of the fracture faces to their corresponding fracture planes. The inner fracture plane splits the plasma membrane at one particular level. Apparently the outer fracture plane was located in the outer part of the wall, as it was separated by a layer ([Formula: see text]) from the fractured profile (CW1) presumably corresponding to the murein layer. The outer fracture plane did alternate toward the cell periphery, exposing complementary smooth areas ([Formula: see text] and [Formula: see text]). When cells were freeze-fractured in the absence of glycerol, the outer cell surface appeared as an etching face rather than a fracture face. A schematic representation of the relative location of the different fracture faces in the E. coli cell envelope is given.     

The IspA protease's involvement in the regulation of the sporulation process of Bacillus thuringiensis is revealed by proteomic analysis

We have observed that the process of sporulation of the ispA-deficient mutant was delayed under phase-contrast microscopy. The protein profiles of the ispA-deficient mutant have been analyzed using two-dimensional gel electrophoresis. The results of a proteomic analysis using MALDI-TOF MS indicated that a sporulation-associated protein, pro- [Formula: see text], was upregulated, while two other sporulation-associated proteins, SpoVD and SpoVR, were downregulated in the ispA-deficient mutant. It has been known that pro- [Formula: see text] is a precursor of [Formula: see text] and is required for gene expression related to the late stage of sporulation. Moreover, SpoVD and SpoVR are known to be involved in the formation of the spore cortex. Based on these observations, we propose that the delay in the sporulation process observed in the ispA-deficient mutant may be due to a failure of [Formula: see text] to signal sporulation. This phenomenon may be further enhanced by insufficient amount of SpoVD and SpoVR for cortex formation. In this study, we have revealed for the first time a possible pathway for the regulation of sporulation-associated proteins via IspA.     

Optimal Vaccination Policies for an SIR Model with Limited Resources

The purpose of the paper is to use analytical method and optimization tool to suggest a vaccination program intensity for a basic SIR epidemic model with limited resources for vaccination. We show that there are two different scenarios for optimal vaccination strategies, and obtain analytical solutions for the optimal control problem that minimizes the total cost of disease under the assumption of daily vaccine supply being limited. These solutions and their corresponding optimal control policies are derived explicitly in terms of initial conditions, model parameters and resources for vaccination. With sufficient resources, the optimal control strategy is the normal Bang–Bang control. However, with limited resources, the optimal control strategy requires to switch to time-variant vaccination.     

Robustness and information propagation in attractors of random boolean networks

Attractors represent the long-term behaviors of Random Boolean Networks. We study how the amount of information propagated between the nodes when on an attractor, as quantified by the average pairwise mutual information ([Formula: see text]), relates to the robustness of the attractor to perturbations ([Formula: see text]). We find that the dynamical regime of the network affects the relationship between [Formula: see text] and [Formula: see text]. In the ordered and chaotic regimes, [Formula: see text] is anti-correlated with [Formula: see text], implying that attractors that are highly robust to perturbations have necessarily limited information propagation. Between order and chaos (for so-called "critical" networks) these quantities are uncorrelated. Finite size effects cause this behavior to be visible for a range of networks, from having a sensitivity of 1 to the point where [Formula: see text] is maximized. In this region, the two quantities are weakly correlated and attractors can be almost arbitrarily robust to perturbations without restricting the propagation of information in the network.     

Lack of histamine type-1 receptors impairs the thermal response of respiration during hypoxia in mice (Mus musculus)

Thermoregulation and the hypoxic ventilatory response are modulated by histamine type-1 (H1) receptors in the brain. In this study, we tested the hypothesis that activation of H1 receptors is required for the thermal control of ventilation during normoxia and hypoxia, using conscious male wild-type and H1 receptor-knockout (H1RKO) mice (Mus musculus). Under normoxic conditions, hyperthermia (39 degrees C) decreased minute ventilation (V (E)) and oxygen consumption [Formula: see text] in both genotypes, suggesting that H1 receptors are not involved in thermal ventilatory control during normoxia. Pa(CO2) was unchanged in both hyperthermia and normothermia, suggesting that the thermal decrease in V (E) is optimized by metabolic demand. Acute hypoxic gas exposure (7% O(2)+3% CO(2) in N(2)) increased, and then decreased, V (E) in wild-type mice; this increase was augmented and sustained by hyperthermia. Hypoxic gas exposure reduced [Formula: see text] and [Formula: see text] in wild-type mice at both body temperatures; the reduced [Formula: see text] during combined hyperthermia and hypoxia was higher than during normothermia and hypoxia. In H1RKO mice, hyperthermia did not augment the V (E) response to hypoxia, and did not affect [Formula: see text] and [Formula: see text] during hypoxia. In conclusion, histamine participates in the thermal increase of ventilation during hypoxia by activating H1 receptors.     

Suicide inactivation of tyrosinase in its action on tetrahydropterines

Tetrahydrobiopterin (BH(4)), methyl-tetrahydropterin (MBH(4)) and dimethyl-tetrahydropterin (DMBH(4)) are oxidized by tyrosinase in a process during which the suicide inactivation of tyrosinase may occur. From the kinetic study of this process, [Formula: see text] (apparent maximum constant for the suicide inactivation), [Formula: see text] (Michaelis constant for the substrate) and r (number of turnovers that the enzyme makes before the inactivation) can be obtained. From the results obtained, it can be deduced that the velocity of the inactivation governed by ([Formula: see text]) and the potency of the same ([Formula: see text]) follow the order: BH(4) > MBH(4) > DMBH(4).