A finite-element model of mechanosensation by a Pacinian corpuscle cluster in human skin

The Pacinian corpuscle (PC) is the cutaneous mechanoreceptor responsible for sensation of high-frequency (20–1000 Hz) vibrations. PCs lie deep within the skin, often in multicorpuscle clusters with overlapping receptive fields. We developed a finite-element mechanical model of one or two PCs embedded within human skin, coupled to a multiphysics PC model to simulate action potentials elicited by each PC. A vibration was applied to the skin surface, and the resulting mechanical signal was analyzed using two metrics: the deformation amplitude ratio (\({\rho }_{\mathrm{1S}} \), \({\rho }_{\mathrm{2S}} )\) and the phase shift of the vibration (\({\delta }_{\mathrm{S}1}^{\mathrm{mech}} \), \({\delta }_{\mathrm{S}2}^{\mathrm{mech}} )\) between the stimulus and the PC. Our results showed that the amplitude attenuation and phase shift at a PC increased with distance from the stimulus to the PC. Differences in amplitude (\(\rho _{12} )\) and phase shift (\({\delta }_{12}^{\mathrm{mech}} )\) between the two PCs in simulated clusters directly affected the interspike interval between the action potentials elicited by each PC (\({\delta }_{12}^{\mathrm{spike}} )\). While \({\delta }_{12}^{\mathrm{mech}} \) had a linear relationship with \({\delta }_{12}^{\mathrm{spike}} \), \(\rho _{12} \)’s effect on \({\delta }_{12}^{\mathrm{spike}} \) was greater for lower values of \(\rho _{12} \). In our simulations, the separation between PCs and the distance of each PC from the stimulus location resulted in differences in amplitude and phase shift at each PC that caused \({\delta }_{12}^{\mathrm{spike}} \) to vary with PC location. Our results suggest that PCs within a cluster receive different mechanical stimuli which may enhance source localization of vibrotactile stimuli, drawing parallels to sound localization in binaural hearing.     

Mathematical Analysis of the Transmission Dynamics of HIV Syphilis Co-infection in the Presence of Treatment for Syphilis

The re-emergence of syphilis has become a global public health issue, and more persons are getting infected, especially in developing countries. This has also led to an increase in the incidence of human immunodeficiency virus (HIV) infections as some studies have shown in the recent decade. This paper investigates the synergistic interaction between HIV and syphilis using a mathematical model that assesses the impact of syphilis treatment on the dynamics of syphilis and HIV co-infection in a human population where HIV treatment is not readily available or accessible to HIV-infected individuals. In the absence of HIV, the syphilis-only model undergoes the phenomenon of backward bifurcation when the associated reproduction number (\({\mathcal {R}}_{T}\)) is less than unity, due to susceptibility to syphilis reinfection after recovery from a previous infection. The complete syphilis–HIV co-infection model also undergoes the phenomenon of backward bifurcation when the associated effective reproduction number (\({\mathcal {R}}_{C}\)) is less than unity for the same reason as the syphilis-only model. When susceptibility to syphilis reinfection after treatment is insignificant, the disease-free equilibrium of the syphilis-only model is shown to be globally asymptotically stable whenever the associated reproduction number (\({\mathcal {R}}_{T}\)) is less than unity. Sensitivity and uncertainty analysis show that the top three parameters that drive the syphilis infection (with respect to the associated response function, \({\mathcal {R}}_{T}\)) are the contact rate (\(\beta _S\)), modification parameter that accounts for the increased infectiousness of syphilis-infected individuals in the secondary stage of the infection (\(\theta _1\)) and treatment rate for syphilis-only infected individuals in the primary stage of the infection (\(r_1\)). The co-infection model was numerically simulated to investigate the impact of various treatment strategies for primary and secondary syphilis, in both singly and dually infected individuals, on the dynamics of the co-infection of syphilis and HIV. It is observed that if concerted effort is exerted in the treatment of primary and secondary syphilis (in both singly and dually infected individuals), especially with high treatment rates for primary syphilis, this will result in a reduction in the incidence of HIV (and its co-infection with syphilis) in the population.     

Study of the Population Dynamics of <Emphasis Type="Italic">Busseola fusca</Emphasis>, Maize Pest

Busseola fusca is a maize and sorghum pest that can cause significant damage to both crops. Given that maize is one of the main cereals grown in the worldwide, this pest is a major challenge for maize production and therefore for the economies of several countries . In this paper , based on the life cycle of B. fusca, we propose a mathematical model to study the population dynamics of this insect pest . A sensitivity analysis using the eFast method was performed to show the most important parameters of the model. We present the theoretical analysis of the model. More precisely, we derive a threshold parameter \({\mathcal {N}}_0\), called basic offspring number and show that the trivial equilibrium is globally asymptotically stable whenever \({\mathcal {N}}_0\le 1\), while if \({\mathcal {N}}_0>1\), the non trivial equilibrium is globally asymptotically stable. The theoretical results are supported by numerical simulations.     

Multi-stage Vector-Borne Zoonoses Models: A Global Analysis

A class of models that describes the interactions between multiple host species and an arthropod vector is formulated and its dynamics investigated. A host-vector disease model where the host’s infection is structured into n stages is formulated and a complete global dynamics analysis is provided. The basic reproduction number acts as a sharp threshold, that is, the disease-free equilibrium is globally asymptotically stable (GAS) whenever \({\mathcal {R}}_0^2\le 1\) and that a unique interior endemic equilibrium exists and is GAS if \({\mathcal {R}}_0^2>1\). We proceed to extend this model with m host species, capturing a class of zoonoses where the cross-species bridge is an arthropod vector. The basic reproduction number of the multi-host-vector, \({\mathcal {R}}_0^2(m)\), is derived and shown to be the sum of basic reproduction numbers of the model when each host is isolated with an arthropod vector. It is shown that the disease will persist in all hosts as long as it persists in one host. Moreover, the overall basic reproduction number increases with respect to the host and that bringing the basic reproduction number of each isolated host below unity in each host is not sufficient to eradicate the disease in all hosts. This is a type of “amplification effect,” that is, for the considered vector-borne zoonoses, the increase in host diversity increases the basic reproduction number and therefore the disease burden.     

Stability of a Stochastic Model of an SIR Epidemic with Vaccination

We prove almost sure exponential stability for the disease-free equilibrium of a stochastic differential equations model of an SIR epidemic with vaccination. The model allows for vertical transmission. The stochastic perturbation is associated with the force of infection and is such that the total population size remains constant in time. We prove almost sure positivity of solutions. The main result concerns especially the smaller values of the diffusion parameter, and describes the stability in terms of an analogue \(\mathcal{R}_\sigma\) of the basic reproduction number \(\mathcal{R}_0\) of the underlying deterministic model, with \(\mathcal{R}_\sigma \le \mathcal{R}_0\). We prove that the disease-free equilibrium is almost sure exponentially stable if \(\mathcal{R}_\sigma <1\).     

Qualitative Analysis of an ODE Model of a Class of Enzymatic Reactions

The present paper analyzes an ODE model of a certain class of (open) enzymatic reactions. This type of model is used, for instance, to describe the interactions between messenger RNAs and microRNAs. It is shown that solutions defined by positive initial conditions are well defined and bounded on \([0, \infty )\) and that the positive octant of \({\mathbb {R}}^3\) is a positively invariant set. We prove further that in this positive octant there exists a unique equilibrium point, which is asymptotically stable and a global attractor for any initial state with positive components; a controllability property is emphasized. We also investigate the qualitative behavior of the QSSA system in the phase plane \({\mathbb {R}}^2\). For this planar system we obtain similar results regarding global stability by using Lyapunov theory, invariant regions and controllability.     

Physical parameter estimation from porcine ex vivo vocal fold dynamics in an inverse problem framework

This study presents a framework for a direct comparison of experimental vocal fold dynamics data to a numerical two-mass-model (2MM) by solving the corresponding inverse problem of which parameters lead to similar model behavior. The introduced 2MM features improvements such as a variable stiffness and a modified collision force. A set of physiologically sensible degrees of freedom is presented, and three optimization algorithms are compared on synthetic vocal fold trajectories. Finally, a total of 288 high-speed video recordings of six excised porcine larynges were optimized to validate the proposed framework. Particular focus lay on the subglottal pressure, as the experimental subglottal pressure is directly comparable to the model subglottal pressure. Fundamental frequency, amplitude and objective function values were also investigated. The employed 2MM is able to replicate the behavior of the porcine vocal folds very well. The model trajectories’ fundamental frequency matches the one of the experimental trajectories in \(98.6\%\) of the recordings. The relative error of the model trajectory amplitudes is on average \(9.5\%\). The experiments feature a mean subglottal pressure of 10.16 (SD \(= 2.31\)) \({\text {cmH}}_2{\text {O}}\); in the model, it was on average 7.61 (SD \(= 2.40\)) \({\text {cmH}}_2{\text {O}}\). A tendency of the model to underestimate the subglottal pressure is found, but the model is capable of inferring trends in the subglottal pressure. The average absolute error between the subglottal pressure in the model and the experiment is 2.90 (SD \(= 1.80\)) \({\text {cmH}}_2{\text {O}}\) or \(27.5\%\). A detailed analysis of the factors affecting the accuracy in matching the subglottal pressure is presented.     

A Mathematical Model of Anthrax Transmission in Animal Populations

A general mathematical model of anthrax (caused by Bacillus anthracis) transmission is formulated that includes live animals, infected carcasses and spores in the environment. The basic reproduction number \(\mathcal {R}_0\) is calculated, and existence of a unique endemic equilibrium is established for \(\mathcal {R}_0\) above the threshold value 1. Using data from the literature, elasticity indices for \(\mathcal {R}_0\) and type reproduction numbers are computed to quantify anthrax control measures. Including only herbivorous animals, anthrax is eradicated if \(\mathcal {R}_0 < 1\). For these animals, oscillatory solutions arising from Hopf bifurcations are numerically shown to exist for certain parameter values with \(\mathcal {R}_0>1\) and to have periodicity as observed from anthrax data. Including carnivores and assuming no disease-related death, anthrax again goes extinct below the threshold. Local stability of the endemic equilibrium is established above the threshold; thus, periodic solutions are not possible for these populations. It is shown numerically that oscillations in spore growth may drive oscillations in animal populations; however, the total number of infected animals remains about the same as with constant spore growth.     

Potential use of sulfite as a supplemental electron donor for wastewater denitrification

Biological denitrification typically requires the addition of a supplemental electron donor, which can add a significant operating expense to wastewater treatment facilities. Most common electron donors are organic, but reduced inorganic sulfur compounds (RISCs), such as sulfide (HS^?) and elemental sulfur (S⁰), may be more cost-effective. S⁰ is an inexpensive and well characterized electron donor, but it provides slow denitrification rates due to its low solubility. A lesser-known RISC is sulfite (\({\text{SO}}_{3}^{2 - }\)), which can be easily produced from S⁰ by a simple combustion process. Unlike S⁰, \({\text{SO}}_{3}^{2 - }\) is highly soluble, and therefore may provide higher denitrification rates. However, very little is known about microbial denitrification with \({\text{SO}}_{3}^{2 - }\). Also, \({\text{SO}}_{3}^{2 - }\) is a strong reductant that reacts abiotically with oxygen and has toxic effects on microorganisms. This paper reviews \({\text{SO}}_{3}^{2 - }\) in the environment, \({\text{SO}}_{3}^{2 - }\) chemistry, microbiology, toxicity, and its potential use for denitrification. Since \({\text{SO}}_{3}^{2 - }\) is an intermediate in the sulfur oxidation pathway of most sulfur-oxidizing microorganisms, it is an energetic electron donor and it should select for a \({\text{SO}}_{3}^{2 - }\)-oxidizing community. Our review of the literature, as well as our own lab experience, suggests that \({\text{SO}}_{3}^{2 - }\) can effectively serve as an electron donor for denitrification. Further research is needed to determine the kinetics of \({\text{SO}}_{3}^{2 - }\)-based denitrification, its toxic threshold for sulfur-oxidizing microorganisms, and its potential inhibition of sensitive species such as nitrifying microorganisms and potential formation of nitrous oxide. Its effect on sludge settling efficiency also should be explored.     

<Superscript>1</Superscript>H, <Superscript>13</Superscript>C, <Superscript>15</Superscript>N resonance assignments of the extracellular loop 1 domain (ECL1) of <Emphasis Type="Italic">Streptococcus pneumoniae</Emphasis> D39 FtsX,an essential cell division protein

FtsX is an integral membrane protein from Streptococcus pneumoniae (pneumococcus) that harbors an extracellular loop 1 domain (\({\text{FtsX}}^{\text{ECL1}}_{Spn}\)) that interacts with PcsB, an peptidoglycan hydrolase that is essential for cell growth and division. Here, we report nearly complete backbone and side chain resonance assignments and a secondary structural analysis of \({\text{FtsX}}^{\text{ECL1}}_{Spn}\) (residues 47–168 of FtsX) as first steps toward structure determination of \({\text{FtsX}}^{\text{ECL1}}_{Spn}\).     

Measuring the signs of the methyl <Superscript>1</Superscript>H chemical shift differences between major and ‘invisible’ minor protein conformational states using methyl <Superscript>1</Superscript>H multi-quantum spectroscopy

Carr–Purcell–Meiboom–Gill (CPMG) type relaxation dispersion experiments are now routinely used to characterise protein conformational dynamics that occurs on the μs to millisecond (ms) timescale between a visible major state and ‘invisible’ minor states. The exchange rate(s) (\( k_{{{\text{ex}}}} \)), population(s) of the minor state(s) and the absolute value of the chemical shift difference \(|{\Delta \varpi }|\) (ppm) between different exchanging states can be extracted from the CPMG data. However the sign of \({\Delta \varpi }\) that is required to reconstruct the spectrum of the ‘invisible’ minor state(s) cannot be obtained from CPMG data alone. Building upon the recently developed triple quantum (TQ) methyl \( ^{1} {\text{H}} \) CPMG experiment (Yuwen in Angew Chem 55:11490–11494, 2016) we have developed pulse sequences that use carbon detection to generate and evolve single quantum (SQ), double quantum (DQ) and TQ coherences from methyl protons in the indirect dimension to measure the chemical exchange-induced shifts of the SQ, DQ and TQ coherences from which the sign of \({\Delta \varpi }\) is readily obtained for two state exchange. Further a combined analysis of the CPMG data and the difference in exchange induced shifts between the SQ and DQ resonances and between the SQ and TQ resonances improves the estimates of exchange parameters like the population of the minor state. We demonstrate the use of these experiments on two proteins undergoing exchange: (1) the ~ 18 kDa cavity mutant of T4 Lysozyme (\( k_{{{\text{ex}}}} \sim\,3500{\text{ s}}^{{ - 1}} \)) and (2) the \(\sim\,4.7\) kDa Peripheral Sub-unit Binding Domain (PSBD) from the acetyl transferase of Bacillus stearothermophilus (\(k_{ex} \sim\,13,000\hbox { s}^{-1}\)).     

Uptake of ammonium and soluble reactive phosphorus in forested streams: influence of dissolved organic matter composition

Many microbes responsible for inorganic nutrient uptake and transformation utilize dissolved organic matter (DOM) as a nutrient or energy source, but little is known about whether DOM composition is an important driver of nutrient uptake in streams. Our goal was to determine whether incorporating DOM composition metrics with other more commonly considered biological, physical, and chemical variables improved our ability to explain patterns of ammonium (\({\text{NH}}_{4}^{ + }\)–N) and soluble reactive phosphorus (SRP) uptake across 11 Lake Superior tributaries. Nutrient uptake velocities (V_f) ranged from undetectable to 14.6 mm min^?1 for \({\text{NH}}_{4}^{ + }\)–N and undetectable to 7.2 mm min^?1 for SRP. Logistic regressions suggested that DOM composition was a useful predictor of where SRP uptake occurred (4/11 sites) and \({\text{NH}}_{4}^{ + }\)–N concentration was a useful predictor of where \({\text{NH}}_{4}^{ + }\)–N uptake occurred (9/11 sites). Multiple regression analysis revealed that the best models included temperature, specific discharge, and canopy cover, and DOM composition as significant predictors of \({\text{NH}}_{4}^{ + }\)–N V_f. Partial least squares revealed fluorescence index (describing the source of aquatic fulvic acids), specific ultraviolet absorbance at 254 nm (an indicator of DOM aromaticity), temperature, and conductivity were highly influential predictors of \({\text{NH}}_{4}^{ + }\)–N V_f. Therefore, streams with higher temperatures, lower solute concentrations, more terrestrial DOM signal and greater aromaticity had greater \({\text{NH}}_{4}^{ + }\)–N V_f. Our results suggest that DOM composition may be an important, yet often overlooked, predictor of \({\text{NH}}_{4}^{ + }\)–N and SRP uptake in deciduous forest streams that should be considered along with commonly measured predictors.     

Optimal Therapy Scheduling Based on a Pair of Collaterally Sensitive Drugs

Despite major strides in the treatment of cancer, the development of drug resistance remains a major hurdle. One strategy which has been proposed to address this is the sequential application of drug therapies where resistance to one drug induces sensitivity to another drug, a concept called collateral sensitivity. The optimal timing of drug switching in these situations, however, remains unknown. To study this, we developed a dynamical model of sequential therapy on heterogeneous tumors comprised of resistant and sensitive cells. A pair of drugs (DrugA, DrugB) are utilized and are periodically switched during therapy. Assuming resistant cells to one drug are collaterally sensitive to the opposing drug, we classified cancer cells into two groups, \(A_\mathrm{R}\) and \(B_\mathrm{R}\), each of which is a subpopulation of cells resistant to the indicated drug and concurrently sensitive to the other, and we subsequently explored the resulting population dynamics. Specifically, based on a system of ordinary differential equations for \(A_\mathrm{R}\) and \(B_\mathrm{R}\), we determined that the optimal treatment strategy consists of two stages: an initial stage in which a chosen effective drug is utilized until a specific time point, T, and a second stage in which drugs are switched repeatedly, during which each drug is used for a relative duration (i.e., \(f \Delta t\)-long for DrugA and \((1-f) \Delta t\)-long for DrugB with \(0 \le f \le 1\) and \(\Delta t \ge 0\)). We prove that the optimal duration of the initial stage, in which the first drug is administered, T, is shorter than the period in which it remains effective in decreasing the total population, contrary to current clinical intuition. We further analyzed the relationship between population makeup, \(\mathcal {A/B} = A_\mathrm{R}/B_\mathrm{R}\), and the effect of each drug. We determine a critical ratio, which we term \(\mathcal {(A/B)}^{*}\), at which the two drugs are equally effective. As the first stage of the optimal strategy is applied, \(\mathcal {A/B}\) changes monotonically to \(\mathcal {(A/B)}^{*}\) and then, during the second stage, remains at \(\mathcal {(A/B)}^{*}\) thereafter. Beyond our analytic results, we explored an individual-based stochastic model and presented the distribution of extinction times for the classes of solutions found. Taken together, our results suggest opportunities to improve therapy scheduling in clinical oncology.     

Vector-Borne Pathogen and Host Evolution in a Structured Immuno-Epidemiological System

Vector-borne disease transmission is a common dissemination mode used by many pathogens to spread in a host population. Similar to directly transmitted diseases, the within-host interaction of a vector-borne pathogen and a host’s immune system influences the pathogen’s transmission potential between hosts via vectors. Yet there are few theoretical studies on virulence–transmission trade-offs and evolution in vector-borne pathogen–host systems. Here, we consider an immuno-epidemiological model that links the within-host dynamics to between-host circulation of a vector-borne disease. On the immunological scale, the model mimics antibody-pathogen dynamics for arbovirus diseases, such as Rift Valley fever and West Nile virus. The within-host dynamics govern transmission and host mortality and recovery in an age-since-infection structured host-vector-borne pathogen epidemic model. By considering multiple pathogen strains and multiple competing host populations differing in their within-host replication rate and immune response parameters, respectively, we derive evolutionary optimization principles for both pathogen and host. Invasion analysis shows that the \({\mathcal {R}}_0\) maximization principle holds for the vector-borne pathogen. For the host, we prove that evolution favors minimizing case fatality ratio (CFR). These results are utilized to compute host and pathogen evolutionary trajectories and to determine how model parameters affect evolution outcomes. We find that increasing the vector inoculum size increases the pathogen \({\mathcal {R}}_0\), but can either increase or decrease the pathogen virulence (the host CFR), suggesting that vector inoculum size can contribute to virulence of vector-borne diseases in distinct ways.     

Seasonal transmission dynamics of measles in China

Measles, a highly contagious infection caused by the measles virus, is a major public health problem in China. The reported measles cases decreased dramatically from 2004 to 2012 due to the mandatory measles vaccine program started in 2005 and the goal of eliminating measles by 2012. However, after reaching its lowest level in 2012, measles has resurged again since 2013. Since the monthly data of measles cases exhibit a seasonally fluctuating pattern, based on the measles model in Earn et al. (Science 287:667–670, 2000), we propose a susceptible, exposed, infectious, and recovered model with periodic transmission rate to investigate the seasonal measles epidemics and the effect of vaccination. We calculate the basic reproduction number \({\mathcal {R}}_{0}\), analyze the dynamical behavior of the model, and use the model to simulate the monthly data of measles cases reported in China. We also carry out some sensitivity analysis of \({\mathcal {R}}_{0}\) in the terms of various model parameters which shows that measles can be controlled and eventually eradicated by increasing the immunization rate, improving the effective vaccine management, and enhancing the awareness of people about measles.     

When is a Phylogenetic Network Simply an Amalgamation of Two Trees?

Phylogenetic networks generalise phylogenetic (evolutionary) trees by allowing for the representation of reticulation (non-treelike) events. The structure of such networks is often viewed by the phylogenetic trees they embed. In this paper, we determine when a phylogenetic network \({\mathcal {N}}\) has two phylogenetic tree embeddings which collectively contain all of the edges of \({\mathcal {N}}\). This determination leads to a polynomial-time algorithm for recognising such networks and an unexpected characterisation of the class of reticulation-visible networks.     

Cell Volume Regulation in the Proximal Tubule of Rat Kidney

We developed a dynamic model of a rat proximal convoluted tubule cell in order to investigate cell volume regulation mechanisms in this nephron segment. We examined whether regulatory volume decrease (RVD), which follows exposure to a hyposmotic peritubular solution, can be achieved solely via stimulation of basolateral K\(^+\) and \(\hbox {Cl}^-\) channels and \(\hbox {Na}^+\)–\(\hbox {HCO}_3^-\) cotransporters. We also determined whether regulatory volume increase (RVI), which follows exposure to a hyperosmotic peritubular solution under certain conditions, may be accomplished by activating basolateral \(\hbox {Na}^+\)/H\(^+\) exchangers. Model predictions were in good agreement with experimental observations in mouse proximal tubule cells assuming that a 10% increase in cell volume induces a fourfold increase in the expression of basolateral K\(^+\) and \(\hbox {Cl}^-\) channels and \(\hbox {Na}^+\)–\(\hbox {HCO}_3^-\) cotransporters. Our results also suggest that in response to a hyposmotic challenge and subsequent cell swelling, \(\hbox {Na}^+\)–\(\hbox {HCO}^-_3\) cotransporters are more efficient than basolateral K\(^+\) and \(\hbox {Cl}^-\) channels at lowering intracellular osmolality and reducing cell volume. Moreover, both RVD and RVI are predicted to stabilize net transcellular \(\hbox {Na}^+\) reabsorption, that is, to limit the net \(\hbox {Na}^+\) flux decrease during a hyposmotic challenge or the net \(\hbox {Na}^+\) flux increase during a hyperosmotic challenge.     

Performance and kinetics of ANAMMOX granular sludge with pH shock in a sequencing batch reactor

As an efficient and cost-effective nitrogen removal process, anaerobic ammonium oxidation (ANAMMOX) could be well operated at suitable pH condition. However, pH shock occurred in different kinds of wastewater and affected ANANNOX process greatly. The present research aimed at studying the performance and kinetics of ANAMMOX granular sludge with pH shock. When influent pH was below 7.5, effluent \({\text{NH}}_{4}^{ + }\)–N and \({\text{NO}}_{2}^{ - }\)–N increased with decreasing pH. At Ph 6.0, effluent \({\text{NO}}_{2}^{ - }\)–N approached 100 mg/L, and the ratios of \(\Delta {\text{NO}}_{2}^{ - } - {\text{N}}:\Delta {\text{NH}}_{4}^{ + } - {\text{N and }}\Delta {\text{NO}}_{3}^{ - } - {\text{N}}:\Delta {\text{NH}}_{4}^{ + } - {\text{N}}\) approached 2.2 and 1.3, respectively. Both greatly deviated from theoretical values. When influent pH was above 7.5, effluent \({\text{NH}}_{4}^{ + }\)–N and \({\text{NO}}_{2}^{ - }\)–N increased with increasing pH. At pH 9.0, ammonium removal rate (ARR) and nitrite removal rate (NRR) decreased to 0.011 ± 0.004 and 0.035 ± 0.004 kg/(m³·d), respectively. Besides, \(\Delta {\text{NO}}_{2}^{ - }\)–N:\(\Delta {\text{NH}}_{4}^{ + }\)–N deviated from theoretical value. Longer recovery time from pH 9.0 than from pH 6.0 indicated that alkaline surroundings inhibited anaerobic ammonium oxidizing bacteria (AAOB) greater. The sludge settling velocity was 2.15 cm/s at pH 7.5. However, it decreased to 2.02 cm/s when pH was 9.0. Acidic pH had little effect on sludge size, but disintegration of ANAMMOX granule was achieved with pH of 9.0. The Bell-shaped (A) model and the Ratkowsky model were more applicable to simulate the effect resulting from pH shock on ANAMMOX activity (R² > 0.95), and both could describe ANAMMOX activity well with pH shock. They indicated that q_max was 0.37 kg \(\Delta {\text{NH}}_{4}^{ + }\)–N/(kgMLSS·d) at the optimum pH value (7.47) in present study. The minimum pH during which ANAMMOX occurred was 5.68 while the maximum pH for ANAMMOX reaction was 9.26. Based on nitrogen removal performance with different pH, strongly acidic (pH ≤ 6.5) or alkaline (pH ≥ 8.5) inhibited ANAMMOX process. Besides, ANAMMOX appeared to be more susceptible to alkaline wastewater. Compared to extremely acidic condition (low pH), extremely alkaline condition (high pH) affected ANAMMOX granules much more.     

Analysis of two susceptibility SNPs in HLA region and evidence of interaction between rs6457617 in <Emphasis Type="BoldItalic">HLA-DQB1</Emphasis> and <Emphasis Type="BoldItalic">HLA-DRB1</Emphasis>*04 locus on Tunisian rheumatoid arthritis

Previous genomewide association studies (GWAS) and meta-analyses have enumerated several genes/loci in major histocompatibility complex region, which are consistently associated with rheumatoid arthritis (RA) in different ethnic populations. Given the genetic heterogeneity of the disease, it is necessary to replicate these susceptibility loci in other populations. In this case, we investigate the analysis of two SNPs, rs13192471 and rs6457617, from the human leukocyte antigen (HLA) region with the risk of RA in Tunisian population. These SNPs were previously identified to have a strong RA association signal in several GWAS studies. A case–control sample composed of 142 RA patients and 123 healthy controls was analysed. Genotyping of rs13192471 and rs6457617 was carried out using real-time PCR methods by TaqMan allelic discrimination assay. A trend of significant association was found in rs6457617 TT genotype with susceptibility to RA (\(P = 0.04\), \(p_{c} = 0.08\), \(\hbox {OR} = 1.73\)). Moreover, using multivariable analysis, the combination of rs6457617*TT–HLA-DRB1*\(04^{+}\) increased risk of RA (\(\hbox {OR} = 2.38\)), which suggest a gene–gene interaction event between rs6457617 located within the HLA-DQB1 and HLA-DRB1. Additionally, haplotypic analysis highlighted a significant association of rs6457617*T–HLA-DRB1*\(04^{+}\) haplotype with susceptibility to RA (\(P = 0.018\), \(p_{c} = 0.036\), \(\hbox {OR} = 1.72\)). An evidence of association was shown subsequently in \(\hbox {antiCCP}^{+}\) subgroup with rs6457617 both in T allele and TT genotype (\(P = 0.01\), \(p_{c} = 0.03\), \(\hbox {OR} = 1.66\) and \(P = 0.008\), \(p_{c} = 0.024\), \(\hbox {OR} = 1.28\), respectively). However, no association was shown for rs13192471 polymorphism with susceptibility and severity to RA. This study suggests the involvement of rs6457617 locus as risk variant for susceptibility/severity to RA in Tunisian population. Secondly, it highlights the gene–gene interaction between HLA-DQB1 and HLA-DRB1.