Calibration methodology of low-cost sensors for high-quality monitoring of fine particulate matter.

Low concentrations of pollutants may already be associated with significant health effects. An accurate assessment of individual exposure to pollutants therefore requires measuring pollutant concentrations at the finest possible spatial and temporal scales. Low-cost sensors (LCS) of particulate matter (PM) meet this need so well that their use is constantly growing worldwide. However, everyone agrees that LCS must be calibrated before use. Several calibration studies have already been published, but there is not yet a standardized and well-established methodology for PM sensors. In this work, we develop a method combining an adaptation of an approach developed for gas-phase pollutants with a dust event preprocessing to calibrate PM LCS (PMS7003) commonly used in urban environments. From the selection of outliers to model tuning and error estimation, the developed protocol allows to analyze, process and calibrate LCS data using multilinear (MLR) and random forest (RFR) regressions for comparison with a reference instrument. We demonstrate that the calibration performance was very good for PM1 and PM2.5 but turns out less good for PM10 (R2 = 0.94, RMSE = 0.55 µg/m3, NRMSE = 12 % for PM1 with MLR, R2 = 0.92, RMSE = 0.70 µg/m3, NRMSE = 12 % for PM2.5 with RFR and R2 = 0.54, RMSE = 2.98 µg/m3, NRMSE = 27 % for PM10 with RFR). Dust events removal significantly improved LCS accuracy for PM2.5 (11 % increase of R2 and 49 % decrease of RMSE) but no significant changes for PM1. Best calibration models included internal relative humidity and temperature for PM2.5 and only internal relative humidity for PM1. It turns out that PM10 cannot be properly measured and calibrated because of technical limitations of the PMS7003 sensor. This work therefore provides guidelines for PM LCS calibration. This represents a first step toward standardizing calibration protocols and facilitating collaborative research.

Modeling of the combined dynamics of leptospirosis transmission and seroconversion in herds.

Leptospirosis is a zoonotic disease-causing illness in both humans and animals resulting in related economic impacts due to production loss as well as prevention and control efforts. Several mathematical models have been proposed to study the dynamics of infection but none of them has so far taken into account the dynamics of seroconversion. In this study, we have developed a general framework, based on the kinetic model for animal leptospirosis, that combines both the antibody (exposure marker) and infection dynamics to simultaneously follows both seroconversion and infection status of leptospirosis in a herd population. It is a stochastic compartmental model (for transition rates) with time delay (for seroconversion) which describes the progression of infection by a SEIRS (susceptible, exposed, infected, removed and susceptible) approach and seroconversion by four-state antibody kinetics (antibody negative and three antibody positive states of different antibody levels). The model shows that it is possible to assess and follow both seroconversion and infection status through the prism of diagnostic testing. Such an approach of combined kinetics could prove very useful to assist the competent authorities in their analyzes of epidemic situations and in the implementation of strategies for controlling and managing the associated risks.

In vitro reconstitution of kallikrein-kinin system and progress curve analysis.

Human kallikrein-kinin system (KKS) is a proteolytic cascade with two serine-protease zymogen couples (Factor XII and prekallikrein (PK) and their activated forms, FXIIa, PKa, respectively), releasing bradykinin by cleavage of native high-molecular-weight kininogen (nHK) into cleaved HK. For KKS investigation in human plasma, this cascade is usually triggered on ice eventually by mixing with purified proteins. It has been established that purified FXIIa, PK, and nHK required a fixed order and timing for mixing protein on ice to ensure reproducibility of testing, we investigated the activation kinetics of both enzymes. The activation process of this in vitro minimal reconstitution of KKS was studied by progress curve analysis, in condition of high enzyme/substrate ratio and by using on natural rather than peptide substrates. FXIIa and PKa were found five-times less active on ice than at 37°C: kcat = 0.133 ± 0.034 and 0.0119 ± 0.0027 s-1, KM = 672 ± 150 and 115 ± 24 nM, respectively. The progress curve analysis of our in vitro KKS reconstitutions differed from a Michaelis-Menten mathematical simulation by a faster initial rate and a slower late rate. These two features were also observed ex vivo by using dextran sulfate-activated plasma and could reinforce the hypothesis of a maximal local effect (bradykinin release) and a minimal systemic consequence (PK preservation) in KKS activation process. Analyzing the complete curve of cold KKS activation would provide valuable information for ex vivo investigation of KKS in samples from patients presenting with hereditary angioedema and other inflammatory conditions.

Population dynamics of a poultry hematophagous mite: characterization of the population growth and identification of factors of its slowdown using closed mesocosms.

BACKGROUND: A thorough knowledge of the population dynamics of pests and of the main factors affecting population growth is an important prerequisite for the development of effective control strategies. Failures of various treatments aimed at regulating populations of Dermanyssus gallinae are regularly reported in poultry farms and pullulations occur very quickly after first detection. To finely characterize population dynamics of D. gallinae, and to identify the factors modulating population growth, we conducted two successive multi-generation experiments using closed mesocosms equipped with or without automatic counters and housing a host full- or part-time (three nights per week). RESULTS: Population growth was very rapid and the adult to juvenile ratio very different from the prediction by a mathematical model. A male-biased sex ratio was observed in some mesocosms from 21 days and in most mesocosms from 35 days of population growth originating from an inoculum of adult females. A dramatic slowdown in growth was measured in mesocosms equipped with trackers, where the mites' path to the host was constrained. The slowdown in population growth induced by the intermittent presence of the host compared to its full-time presence was much less marked. CONCLUSION: These findings suggest avenues of research for new management methods. They question the relevance of a critical threshold based on traditional trap monitoring to manage D. gallinae. Our results highlight a unique characteristic of D. gallinae that makes it a recalcitrant case to threshold-based practices recommended for integrated pest management (IPM) against other arthropod pests. The dramatic effect of a physical constraint for the mite to access the host (unnatural constrained path) confirms an observation made in 1917 and is a reason to design perches that are less conducive to parasite traffic. © 2022 The Authors. Pest Management Science published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry.

The dynamical Matryoshka model: 3. Diffusive nature of the atomic motions contained in a new dynamical model for deciphering local lipid dynamics.

In accompanying papers [Bicout et al., BioRxiv https://doi.org/10.1101/2021.09.21.461198 (2021); Cissé et al., BioRxiv https://doi.org/10.1101/2022.03.30.486370 (2022)], a new model called Matryoshka model has been proposed to describe the geometry of atomic motions in phospholipid molecules in bilayers and multilamellar vesicles based on their quasielastic neutron scattering (QENS) spectra. Here, in order to characterize the relaxational aspects of this model, the energy widths of the QENS spectra of the samples were analyzed first in a model-free way. The spectra were decomposed into three Lorentzian functions, which are classified as slow, intermediate, and fast motions depending on their widths. The analysis provides the diffusion coefficients, residence times, and geometrical parameters for the three classes of motions. The results corroborate the parameter values such as the amplitudes and the mobile fractions of atomic motions obtained by the application of the Matryoshka model to the same samples. Since the current analysis was carried out independently of the development of the Matryoshka model, the present results enhance the validity of the model. The model will serve as a powerful tool to decipher the dynamics of lipid molecules not only in model systems, but also in more complex systems such as mixtures of different kinds of lipids or natural cell membranes.

The dynamical Matryoshka model: 2. Modeling of local lipid dynamics at the sub-nanosecond timescale in phospholipid membranes.

Biological membranes are generally formed by lipids and proteins. Often, the membrane properties are studied through model membranes formed by phospholipids only. They are molecules composed by a hydrophilic head group and hydrophobic tails, which can present a panoply of various motions, including small localized movements of a few atoms up to the diffusion of the whole lipid or collective motions of many of them. In the past, efforts were made to measure these motions experimentally by incoherent neutron scattering and to quantify them, but with upcoming modern neutron sources and instruments, such models can now be improved. In the present work, we expose a quantitative and exhaustive study of lipid dynamics on DMPC and DMPG membranes, using the Matryoshka model recently developed by our group. The model is confronted here to experimental data collected on two different membrane samples, at three temperatures and two instruments. Despite such complexity, the model describes reliably the data and permits to extract a series of parameters. The results compare also very well to other values found in the literature.

The dynamical Matryoshka model: 1. Incoherent neutron scattering functions for lipid dynamics in bilayers.

Fluid lipid bilayers are the building blocks of biological membranes. Although there is a large amount of experimental data using incoherent quasi-elastic neutron scattering (QENS) techniques to study membranes, very little theoretical works have been developed to study the local dynamics of membranes. The main objective of this work is to build a theoretical framework to study and describe the local dynamics of lipids and derive analytical expressions of intermediate scattering functions (ISF) for QENS. As results, we developed the dynamical Matryoshka model which describes the local dynamics of lipid molecules in membrane layers as a nested hierarchical convolution of three motional processes: (i) individual motions described by the vibrational motions of H-atoms; (ii) internal motions including movements of the lipid backbone, head groups and tails, and (iii) molecule movements of the lipid molecule as a whole. The analytical expressions of the ISF associated with these movements are all derived. For use in analyzing the QENS experimental data, we also derived an analytical expression for the aggregate ISF of the Matryoshka model which involves an elastic term plus three inelastic terms of well-separated time scales and whose amplitudes and rates are functions of the lipid motions. And as an illustrative application, we used the aggregated ISF to analyze the experimental QENS data on a lipid sample of multilamellar bilayers of DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine). It is clear from this analysis that the dynamical Matryoshka model describes very well the experimental data and allow extracting the dynamical parameters of the studied system.

Air pollution and health impacts during the COVID-19 lockdowns in Grenoble, France.

It is undeniable that exposure to outdoor air pollution impacts the health of populations and therefore constitutes a public health problem. Any actions or events causing variations in air quality have repercussions on populations' health. Faced with the worldwide COVID-19 health crisis that began at the end of 2019, the governments of several countries were forced, in the beginning of 2020, to put in place very strict containment measures that could have led to changes in air quality. While many works in the literature have studied the issue of changes in the levels of air pollutants during the confinements in different countries, very few have focused on the impact of these changes on health risks. In this work, we compare the 2020 period, which includes two lockdowns (March 16 - May 10 and a partial shutdown Oct. 30 - Dec. 15) to a reference period 2015-2019 to determine how these government-mandated lockdowns affected concentrations of NO2, O3, PM2.5, and PM10, and how that affected human health factors, including low birth weight, lung cancer, mortality, asthma, non-accidental mortality, respiratory, and cardiovascular illnesses. To this end, we structured 2020 into four periods, alternating phases of freedom and lockdowns characterized by a stringency index. For each period, we calculated (1) the differences in pollutant levels between 2020 and a reference period (2015-2019) at both background and traffic stations; and (2) the resulting variations in the epidemiological based relative risks of health outcomes. As a result, we found that relative changes in pollutant levels during the 2020 restriction period were as follows: NO2 (-32%), PM2.5 (-22%), PM10 (-15%), and O3 (+10.6%). The pollutants associated with the highest health risk reductions in 2020 were PM2.5 and NO2, while PM10 and O3 changes had almost no effect on health outcomes. Reductions in short-term risks were related to reductions in PM2.5 (-3.2% in child emergency room visits for asthma during the second lockdown) and NO2 (-1.5% in hospitalizations for respiratory causes). Long-term risk reductions related to PM2.5 were low birth weight (-8%), mortality (-3.3%), and lung cancer (-2%), and to NO2 for mortality (-0.96%). Overall, our findings indicate that the confinement period in 2020 resulted in a substantial improvement in air quality in the Grenoble area.

Modelling of the transmission dynamics of carbapenem-resistant Klebsiella pneumoniae in hospitals and design of control strategies.

Carbapenem-resistant Klebsiella pneumoniae (CRKP) has emerged as a major threat to global public health. Epidemiological and infection controls associated with CRKP are challenging because of several potential elements involved in a complicated cycle of transmission. Here, we proposed a comprehensive mathematical model to investigate the transmission dynamics of CRKP, determine factors affecting the prevalence, and evaluate the impact of interventions on transmission. The model includes the essential compartments, which are uncolonized, asymptomatic colonized, symptomatic colonized, and relapsed patients. Additionally, symptomatic colonized and relapsed patients were further classified into subpopulations according to their number of treatment failures or relapses. We found that the admission of colonized patients and use of antibiotics significantly impacted the endemic transmission in health care units. Thus, we introduced the treatment efficacy, defined by combining the treatment duration and probability of successful treatment, to characterize and describe the effects of antibiotic treatment on transmission. We showed that a high antibiotic treatment efficacy results in a significantly reduced likelihood of patient readmission in the health care unit. Additionally, our findings demonstrate that CRKP transmission with different epidemiological characteristics must be controlled using distinct interventions.

Health risk assessment with multiple reference indices.

BACKGROUND: Conducting a risk assessment can be challenging, especially when dealing with several reference indices, which could lead to conflicting conclusions between studies. The common approach is to use a reference index from a single source based on the risk assessor's preference. OBJECTIVES: To propose an approach for constructing a multi-reference index-based aggregated risk estimate using mathematical objectivity to reflect all of the available information. METHODS: The aggregated risk estimate based on multiple reference indices (AREMRI) results from the weighted linear combination of risk distributions that were obtained with each reference index available. The weights were calculated using the degree of agreement among the reference index-based risk distributions. The approach is illustrated through three practical cases of benzene inhalation cancer risk assessment using inhalation unit risks (IURs) from six different regulatory agencies. RESULTS: The degrees of agreement between the reference index-based risk distribution, obtained with the six IURs, ranged from 0.7 to 92%. The highest weights were attributed to reference index-based risk distributions that had the highest degree of agreement with the maximum number of other reference index-based risk distributions. Regardless of the practical case considered, the AREMRI risk distribution resulted in the third highest risk compared to the six single risk distributions. CONCLUSION: Our approach can be useful in the presence of several reference indices by providing useful insights, consistency and direct comparisons between studies to support better-informed risk assessment and management decisions. This approach can shed some light on some of the uncertainties associated with the toxicological reference values in a risk assessment associated with the toxicological reference values. If the uncertainty is large, more detailed evaluation of the toxicological reference values would be needed.

Population-level impact of native arthropod predators on the poultry red mite Dermanyssus gallinae.

Stimulating the regulation of pests by their natural enemies is a way to improve the sustainability of agriculture and respect for the environment. However, the presence of natural enemies does not guarantee the existence of a pest control service. To what extent are predatory mites commonly found in henhouses actually able to regulate a major egg industry pest mite, Dermanyssus gallinae? To answer this question, we have experimentally recreated portions of a poultry house ecosystem allowing the development of the pest over several generations in the presence of a chick and detritivorous mites (Astigmata) that are ubiquitous and abundant in layer farms. In these conditions, we compared the growth of D. gallinae populations in the presence and absence of native predatory arthropods. No effect of native predators on the growth of the D. gallinae population could be detected despite high initial predator-to-prey ratios and satisfactory growth of predator populations. Prey switching to the alternative prey Astigmata likely dilutes the effect of predation on the target prey. Further exploration is needed to see whether action could be taken to enhance the effect of top-down regulation.

Added-value of mosquito vector breeding sites from street view images in the risk mapping of dengue incidence in Thailand.

Dengue is an emerging vector-borne viral disease across the world. The primary dengue mosquito vectors breed in containers with sufficient water and nutrition. Outdoor containers can be detected from geotagged images using state-of-the-art deep learning methods. In this study, we utilize such container information from street view images in developing a risk mapping model and determine the added value of including container information in predicting dengue risk. We developed seasonal-spatial models in which the target variable dengue incidence was explained using weather and container variable predictors. Linear mixed models with fixed and random effects are employed in our models to account for different characteristics of containers and weather variables. Using data from three provinces of Thailand between 2015 and 2018, the models are developed at the sub-district level resolution to facilitate the development of effective targeted intervention strategies. The performance of the models is evaluated with two baseline models: a classic linear model and a linear mixed model without container information. The performance evaluated with the correlation coefficients, R-squared, and AIC shows the proposed model with the container information outperforms both baseline models in all three provinces. Through sensitivity analysis, we investigate the containers that have a high impact on dengue risk. Our findings indicate that outdoor containers identified from street view images can be a useful data source in building effective dengue risk models and that the resulting models have potential in helping to target container elimination interventions.

Metabotypes of Pseudomonas aeruginosa Correlate with Antibiotic Resistance, Virulence and Clinical Outcome in Cystic Fibrosis Chronic Infections.

Pseudomonas aeruginosa (P.a) is one of the most critical antibiotic resistant bacteria in the world and is the most prevalent pathogen in cystic fibrosis (CF), causing chronic lung infections that are considered one of the major causes of mortality in CF patients. Although several studies have contributed to understanding P.a within-host adaptive evolution at a genomic level, it is still difficult to establish direct relationships between the observed mutations, expression of clinically relevant phenotypes, and clinical outcomes. Here, we performed a comparative untargeted LC/HRMS-based metabolomics analysis of sequential isolates from chronically infected CF patients to obtain a functional view of P.a adaptation. Metabolic profiles were integrated with expression of bacterial phenotypes and clinical measurements following multiscale analysis methods. Our results highlighted significant associations between P.a "metabotypes", expression of antibiotic resistance and virulence phenotypes, and frequency of clinical exacerbations, thus identifying promising biomarkers and therapeutic targets for difficult-to-treat P.a infections.

A consensus approach for estimating health risk: Application to inhalation cancer risks.

Conducting a risk assessment is challenging because various and contrasting risk indicators are available, which can lead to discrepancies and, sometimes, conflicting conclusions. Constructing and using a consensus risk indicator (CRI) could provide a reliable alternative that is consistent and supports direct comparisons. The goal of this study is to propose a structured and pragmatic approach for constructing a CRI distribution and demonstrate its feasibility and easy implementation when conducting risk assessments. A CRI distribution is constructed as a weighted combination of existing indicators where the weights are obtained by using the overlapping areas of an individual indicator's distribution and an aggregated reference distribution. The approach is illustrated through an assessment of human cancer risk following inhalation exposure. The CRI is constructed using eight risk indicators. The CRI distribution parameters for 199 human carcinogenic chemicals associated with inhalation exposure were determined and are presented in an interactive table. To aid the wider implementation of the CRI approach, a user-friendly and interactive web application, named InCaRisk, was created to facilitate the cancer risk estimation following inhalation exposure. Our approach could be useful for enhancing the quality of regulatory decisions and protecting human health from environmental pollutants; our approach can be applied for a given health outcome, route of exposure and exposure setting.

How the individual human mobility spatio-temporally shapes the disease transmission dynamics.

Human mobility plays a crucial role in the temporal and spatial spreading of infectious diseases. During the past few decades, researchers have been extensively investigating how human mobility affects the propagation of diseases. However, the mechanism of human mobility shaping the spread of epidemics is still elusive. Here we examined the impact of human mobility on the infectious disease spread by developing the individual-based SEIR model that incorporates a model of human mobility. We considered the spread of human influenza in two contrasting countries, namely, Belgium and Martinique, as case studies, to assess the specific roles of human mobility on infection propagation. We found that our model can provide a geo-temporal spreading pattern of the epidemics that cannot be captured by a traditional homogenous epidemic model. The disease has a tendency to jump to high populated urban areas before spreading to more rural areas and then subsequently spread to all neighboring locations. This heterogeneous spread of the infection can be captured by the time of the first arrival of the infection [Formula: see text], which relates to the landscape of the human mobility characterized by the relative attractiveness. These findings can provide insights to better understand and forecast the disease spreading.

Bird Species Involved in West Nile Virus Epidemiological Cycle in Southern Québec.

Despite many studies on West Nile Virus (WNV) in the US, including the reservoir role of bird species and the summer shifts of the Culex mosquito, feeding from birds to mammals, there have been few equivalent studies in the neighboring regions of Canada where WNV is endemic. Here, a priority list of bird species likely involved in WNV transmission in the greater Montréal area is constructed by combining three sources of data: (i) from WNV surveillance in wild birds (2002-2015); (ii) blood meal analysis of Culex pipiens-restuans (CPR), the primary enzootic vectors of WNV in the region, collected from surveillance in 2008 and 2014; (iii) literature review on the sero-prevalence/host competence of resident birds. Each of these data sources yielded 18, 23 and 53 species, and overall, 67 different bird species were identified as potential WNV amplifiers/reservoirs. Of those identified from CPR blood meals, Common starlings, American robins, Song sparrows and House sparrows ranked the highest and blood meal analysis demonstrated a seasonal shift in feed preference from birds to mammals by CPR. Our study indicates that there are broad similarities in the ecology of WNV between our region and the northeastern US, although the relative importance of bird species varies somewhat between regions.

Occupational Co-exposures to Multiple Chemical Agents from Workplace Measurements by the US Occupational Safety and Health Administration.

OBJECTIVES: The occupational environment represents an important source of exposures to multiplehazards for workers' health. Although it is recognized that mixtures of agents may have differenteffects on health compared to their individual effects, studies generally focus on the assessment ofindividual exposures. Our objective was to identify occupational co-exposures occurring in the United States using the multi-industry occupational exposure databank of the Occupational Safety and Health Administration (OSHA). METHODS: Using OSHA's Integrated Management Information System (IMIS), measurement data from workplace inspections occurring from 1979 to 2015 were examined. We defined a workplace situation (WS) by grouping measurements that occurred within a company, within the same occupation (i.e. job title) within 1 year. All agents present in each WS were listed and the resulting databank was analyzed with the Spectrosome approach, a methodology inspired by network science, to determine global patterns of co-exposures. The presence of an agent in a WS was defined either as detected, or measured above 20% of a relevant occupational exposure limit (OEL). RESULTS: Among the 334 648 detected exposure measurements of 105 distinct agents collected from 14 513 US companies, we identified 125 551 WSs, with 31% involving co-exposure. Fifty-eight agents were detected with others in >50% of WSs, 29 with a proportion >80%. Two clusters were highlighted, one for solvents and one for metals. Toluene, xylene, acetone, hexone, 2-butanone, and N-butyl acetate formed the basis of the solvent cluster. The main agents of the metal cluster were zinc, iron, lead, copper, manganese, nickel, cadmium, and chromium. 68 556 WS were included in the analyses based on levels of exposure above 20% of their OEL, with 12.4% of co-exposure. In this analysis, while the metal cluster remained, only the combinations of toluene with xylene or 2-butanone were frequently observed among solvents. An online web application allows the examination of industry specific patterns. CONCLUSIONS: We identified frequent co-exposure situations in the IMIS databank. Using the spectrome approach, we revealed global combination patterns and the agents most often implicated. Future work should endeavor to explore the toxicological effects of prevalent combinations of exposures on workers' health to prioritize research and prevention efforts.

Fireworks-like surveillance approach: The case of HPAI H5N1 in wild birds in Europe.

Highly pathogenic avian influenza (HPAI) risk management requires efficient surveillance of the infection in wild birds for early warning purposes. In this study, our aim was to describe the spread of continent-wide infection cases using a fireworks model and therefore improve current surveillance systems. The fireworks model is a metaphor illustrating the spread of HPAI as a point source epizootic. The approach is based on early detection of the outbreak seeds (sparks from the fireworks) and uses a predictive model of the probability of the occurrence of new cases following a seed introduction; this then determines the spatiotemporal perimeter for intense surveillance investigations. For a case study, we used surveillance data on HPAI H5N1 in wild birds across Europe between 2005 and 2010 to describe the outbreaks and determine the success of the case detection used to inform management of the disease. The fireworks description assumes simultaneous introductions of 'seeds' of cases, which then 'explode' in local foci but do not merge into a progressive disease wave. This model fits the data well. Using this predictive approach for HPAI cases in EU countries, we found that the investigation radius needed to achieve a detection level of 90% of new cases after an outbreak ranged from 10 km to more than 300 km, depending on the outbreak pattern. Based on these findings, the fireworks approach can be a valuable method for identifying the perimeters and risk areas to be targeted for enhanced surveillance. The rationale of the fireworks approach is quite generic and can easily be adapted to different situations and contexts.

Dynamical decoration of stabilized-microtubules by Tau-proteins.

Tau is a microtubule-associated protein that regulates axonal transport, stabilizes and spatially organizes microtubules in parallel networks. The Tau-microtubule pair is crucial for maintaining the architecture and integrity of axons. Therefore, it is essential to understand how these two entities interact to ensure and modulate the normal axonal functions. Based on evidence from several published experiments, we have developed a two-dimensional model that describes the interaction between a population of Tau proteins and a stabilized microtubule at the scale of the tubulin dimers (binding sites) as an adsorption-desorption dynamical process in which Tau can bind on the microtubule outer surface via two distinct modes: a longitudinal (along a protofilament) and lateral (across adjacent protofilaments) modes. Such a process yields a dynamical distribution of Tau molecules on the microtubule surface referred to as microtubule decoration that we have characterized at the equilibrium using two observables: the total microtubule surface coverage with Tau's and the distribution of nearest neighbors Tau's. Using both analytical and numerical approaches, we have derived expressions and computed these observables as a function of key parameters controlling the binding reaction: the stoichiometries of the Taus in the two binding modes, the associated dissociation constants and the ratio of the Tau concentration to that of microtubule tubulin dimers.

Determining the binding parameters from co-sedimentation assays.

The stoichiometry n and the dissociation constant [Formula: see text] are key binding parameters characterizing the ligand-macromolecule interactions and equilibria. Equilibrium co-sedimentation experiments are performed in varying the concentration of one of the reactant while keeping constant that of the other reactant. The measured observable is the fraction [Formula: see text] of bound ligands when the ligand concentration is kept constant while that of macromolecules is varying whereas it is the macromolecule coverage [Formula: see text] with bound ligands when the ligand concentration is varying while that of macromolecules is kept constant. We have derived general expressions for [Formula: see text] and [Formula: see text] and subsequently showed that those expressions are in perfect agreement with simulations for a system of large ligands binding on macromolecules. Approximations have been developed to derive mathematical simple analytical expressions for [Formula: see text] and [Formula: see text] that can be used to fit the experimental data and thus extract, n and [Formula: see text] within the framework of equilibrium co-sedimentation assays. The method usefulness is illustrated and demonstrated by fitting the data from the literature using the derived formulas to determine the binding parameters.