Mechanistic Models of Anti-HIV Microbicide Drug Delivery

A new modality for preventing HIV transmission is emerging in the form of topical microbicides. Some clinical trials have shown some promising results of these methods of protection while other trials have failed to show efficacy. Due to the relatively novel nature of microbicide drug transport, a rigorous, deterministic analysis of that transport can help improve the design of microbicide vehicles and understand results from clinical trials. This type of analysis can aid microbicide product design by helping understand and organize the determinants of drug transport and the potential efficacies of candidate microbicide products.

Microbicide drug transport is modeled as a diffusion process with convection and reaction effects in appropriate compartments. This is applied here to vaginal gels and rings and a rectal enema, all delivering the microbicide drug Tenofovir. Although the focus here is on Tenofovir, the methods established in this dissertation can readily be adapted to other drugs, given knowledge of their physical and chemical properties, such as the diffusion coefficient, partition coefficient, and reaction kinetics. Other dosage forms such as tablets and fiber meshes can also be modeled using the perspective and methods developed here.

The analyses here include convective details of intravaginal flows by both ambient fluid and spreading gels with different rheological properties and applied volumes. These are input to the overall conservation equations for drug mass transport in different compartments. The results are Tenofovir concentration distributions in time and space for a variety of microbicide products and conditions. The Tenofovir concentrations in the vaginal and rectal mucosal stroma are converted, via a coupled reaction equation, to concentrations of Tenofovir diphosphate, which is the active form of the drug that functions as a reverse transcriptase inhibitor against HIV. Key model outputs are related to concentrations measured in experimental pharmacokinetic (PK) studies, e.g. concentrations in biopsies and blood. A new measure of microbicide prophylactic functionality, the Percent Protected, is calculated. This is the time dependent volume of the entire stroma (and thus fraction of host cells therein) in which Tenofovir diphosphate concentrations equal or exceed a target prophylactic value, e.g. an EC50.

Results show the prophylactic potentials of the studied microbicide vehicles against HIV infections. Key design parameters for each are addressed in application of the models. For a vaginal gel, fast spreading at small volume is more effective than slower spreading at high volume. Vaginal rings are shown to be most effective if inserted and retained as close to the fornix as possible. Because of the long half-life of Tenofovir diphosphate, temporary removal of the vaginal ring (after achieving steady state) for up to 24h does not appreciably diminish Percent Protected. However, full steady state (for the entire stromal volume) is not achieved until several days after ring insertion. Delivery of Tenofovir to the rectal mucosa by an enema is dominated by surface area of coated mucosa and whether the interiors of rectal crypts are filled with the enema fluid. For the enema 100% Percent Protected is achieved much more rapidly than for vaginal products, primarily because of the much thinner epithelial layer of the mucosa. For example, 100% Percent Protected can be achieved with a one minute enema application, and 15 minute wait time.

Results of these models have good agreement with experimental pharmacokinetic data, in animals and clinical trials. They also improve upon traditional, empirical PK modeling, and this is illustrated here. Our deterministic approach can inform design of sampling in clinical trials by indicating time periods during which significant changes in drug concentrations occur in different compartments. More fundamentally, the work here helps delineate the determinants of microbicide drug delivery. This information can be the key to improved, rational design of microbicide products and their dosage regimens.

A reconciliation of empirical and mechanistic models of the air-sea gas transfer velocity

Models of the air-sea transfer velocity of gases may be either empirical or mechanistic. Extrapolations of empirical models to an unmeasured gas or to another water temperature can be erroneous if the basis of that extrapolation is flawed. This issue is readily demonstrated for the most well-known empirical gas transfer velocity models where the influence of bubble-mediated transfer, which can vary between gases, is not explicitly accounted for. Mechanistic models are hindered by an incomplete knowledge of the mechanisms of air-sea gas transfer. We describe a hybrid model that incorporates a simple mechanistic view—strictly enforcing a distinction between direct and bubble-mediated transfer—but also uses parameterizations based on data from eddy flux measurements of dimethyl sulphide (DMS) to calibrate the model together with dual tracer results to evaluate the model. This model underpins simple algorithms that can be easily applied within schemes to calculate local, regional, or global air-sea fluxes of gases.

A reconciliation of empirical and mechanistic models of the air-sea gas transfer velocity

Models of the air-sea transfer velocity of gases may be either empirical or mechanistic. Extrapolations of empirical models to an unmeasured gas or to another water temperature can be erroneous if the basis of that extrapolation is flawed. This issue is readily demonstrated for the most well-known empirical gas transfer velocity models where the influence of bubble-mediated transfer, which can vary between gases, is not explicitly accounted for. Mechanistic models are hindered by an incomplete knowledge of the mechanisms of air-sea gas transfer. We describe a hybrid model that incorporates a simple mechanistic view—strictly enforcing a distinction between direct and bubble-mediated transfer—but also uses parameterizations based on data from eddy flux measurements of dimethyl sulphide (DMS) to calibrate the model together with dual tracer results to evaluate the model. This model underpins simple algorithms that can be easily applied within schemes to calculate local, regional, or global air-sea fluxes of gases.

Towards the systematic simplification of mechanistic models

Mechanistic models used for prediction should be parsimonious, as models which are over-parameterised may have poor predictive performance. Determining whether a model is parsimonious requires comparisons with alternative model formulations with differing levels of complexity. However, creating alternative formulations for large mechanistic models is often problematic, and usually time-consuming. Consequently, few are ever investigated. In this paper, we present an approach which rapidly generates reduced model formulations by replacing a model’s variables with constants. These reduced alternatives can be compared to the original model, using data based model selection criteria, to assist in the identification of potentially unnecessary model complexity, and thereby inform reformulation of the model. To illustrate the approach, we present its application to a published radiocaesium plant-uptake model, which predicts uptake on the basis of soil characteristics (e.g. pH, organic matter content, clay content). A total of 1024 reduced model formulations were generated, and ranked according to five model selection criteria: Residual Sum of Squares (RSS), AICc, BIC, MDL and ICOMP. The lowest scores for RSS and AICc occurred for the same reduced model in which pH dependent model components were replaced. The lowest scores for BIC, MDL and ICOMP occurred for a further reduced model in which model components related to the distinction between adsorption on clay and organic surfaces were replaced. Both these reduced models had a lower RSS for the parameterisation dataset than the original model. As a test of their predictive performance, the original model and the two reduced models outlined above were used to predict an independent dataset. The reduced models have lower prediction sums of squares than the original model, suggesting that the latter may be overfitted. The approach presented has the potential to inform model development by rapidly creating a class of alternative model formulations, which can be compared.

Mechanistic population Models in Biology: Model Derivation and Application

In general, models of ecological systems can be broadly categorized as ’top-down’ or ’bottom-up’ models, based on the hierarchical level that the model processes are formulated on. The structure of a top-down, also known as phenomenological, population model can be interpreted in terms of population characteristics, but it typically lacks an interpretation on a more basic level. In contrast, bottom-up, also known as mechanistic, population models are derived from assumptions and processes on a more basic level, which allows interpretation of the model parameters in terms of individual behavior. Both approaches, phenomenological and mechanistic modelling, can have their advantages and disadvantages in different situations. However, mechanistically derived models might be better at capturing the properties of the system at hand, and thus give more accurate predictions. In particular, when models are used for evolutionary studies, mechanistic models are more appropriate, since natural selection takes place on the individual level, and in mechanistic models the direct connection between model parameters and individual properties has already been established. The purpose of this thesis is twofold. Firstly, a systematical way to derive mechanistic discrete-time population models is presented. The derivation is based on combining explicitly modelled, continuous processes on the individual level within a reproductive period with a discrete-time maturation process between reproductive periods. Secondly, as an example of how evolutionary studies can be carried out in mechanistic models, the evolution of the timing of reproduction is investigated. Thus, these two lines of research, derivation of mechanistic population models and evolutionary studies, are complementary to each other.

A mechanistic view of mitochondrial death decision pores

Mitochondria increase their outer and inner membrane permeability to solutes, protons and metabolites in response to a variety of extrinsic and intrinsic signaling events. The maintenance of cellular and intraorganelle ionic homeostasis, particularly for Ca2+, can determine cell survival or death. Mitochondrial death decision is centered on two processes: inner membrane permeabilization, such as that promoted by the mitochondrial permeability transition pore, formed across inner membranes when Ca2+ reaches a critical threshold, and mitochondrial outer membrane permeabilization, in which the pro-apoptotic proteins BID, BAX, and BAK play active roles. Membrane permeabilization leads to the release of apoptogenic proteins: cytochrome c, apoptosis-inducing factor, Smac/Diablo, HtrA2/Omi, and endonuclease G. Cytochrome c initiates the proteolytic activation of caspases, which in turn cleave hundreds of proteins to produce the morphological and biochemical changes of apoptosis. Voltage-dependent anion channel, cyclophilin D, adenine nucleotide translocase, and the pro-apoptotic proteins BID, BAX, and BAK may be part of the molecular composition of membrane pores leading to mitochondrial permeabilization, but this remains a central question to be resolved. Other transporting pores and channels, including the ceramide channel, the mitochondrial apoptosis-induced channel, as well as a non-specific outer membrane rupture may also be potential release pathways for these apoptogenic factors. In this review, we discuss the mechanistic models by which reactive oxygen species and caspases, via structural and conformational changes of membrane lipids and proteins, promote conditions for inner/outer membrane permeabilization, which may be followed by either opening of pores or a rupture of the outer mitochondrial membrane.

Comparison of energy evaluation systems and a mechanistic model for milk production by dairy cattle offered fresh grass-based diets

Grass-based diets are of increasing social-economic importance in dairy cattle farming, but their low supply of glucogenic nutrients may limit the production of milk. Current evaluation systems that assess the energy supply and requirements are based on metabolisable energy (ME) or net energy (NE). These systems do not consider the characteristics of the energy delivering nutrients. In contrast, mechanistic models take into account the site of digestion, the type of nutrient absorbed and the type of nutrient required for production of milk constituents, and may therefore give a better prediction of supply and requirement of nutrients. The objective of the present study is to compare the ability of three energy evaluation systems, viz. the Dutch NE system, the agricultural and food research council (AFRC) ME system, and the feed into milk (FIM) ME system, and of a mechanistic model based on Dijkstra et al. [Simulation of digestion in cattle fed sugar cane: prediction of nutrient supply for milk production with locally available supplements. J. Agric. Sci., Cambridge 127, 247-60] and Mills et al. [A mechanistic model of whole-tract digestion and methanogenesis in the lactating dairy cow: model development, evaluation and application. J. Anim. Sci. 79, 1584-97] to predict the feed value of grass-based diets for milk production. The dataset for evaluation consists of 41 treatments of grass-based diets (at least 0.75 g ryegrass/g diet on DM basis). For each model, the predicted energy or nutrient supply, based on observed intake, was compared with predicted requirement based on observed performance. Assessment of the error of energy or nutrient supply relative to requirement is made by calculation of mean square prediction error (MSPE) and by concordance correlation coefficient (CCC). All energy evaluation systems predicted energy requirement to be lower (6-11%) than energy supply. The root MSPE (expressed as a proportion of the supply) was lowest for the mechanistic model (0.061), followed by the Dutch NE system (0.082), FIM ME system (0.097) and AFRCME system(0.118). For the energy evaluation systems, the error due to overall bias of prediction dominated the MSPE, whereas for the mechanistic model, proportionally 0.76 of MSPE was due to random variation. CCC analysis confirmed the higher accuracy and precision of the mechanistic model compared with energy evaluation systems. The error of prediction was positively related to grass protein content for the Dutch NE system, and was also positively related to grass DMI level for all models. In conclusion, current energy evaluation systems overestimate energy supply relative to energy requirement on grass-based diets for dairy cattle. The mechanistic model predicted glucogenic nutrients to limit performance of dairy cattle on grass-based diets, and proved to be more accurate and precise than the energy systems. The mechanistic model could be improved by allowing glucose maintenance and utilization requirements parameters to be variable. (C) 2007 Elsevier B.V. All rights reserved.

Stochastic simulation of time-series models combined with geostatistics to predict water-table scenarios in a Guarani Aquifer System outcrop area, Brazil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Stochastic simulation of time-series models combined with geostatistics to predict water-table scenarios in a Guarani Aquifer System outcrop area, Brazil

Stochastic methods based on time-series modeling combined with geostatistics can be useful tools to describe the variability of water-table levels in time and space and to account for uncertainty. Monitoring water-level networks can give information about the dynamic of the aquifer domain in both dimensions. Time-series modeling is an elegant way to treat monitoring data without the complexity of physical mechanistic models. Time-series model predictions can be interpolated spatially, with the spatial differences in water-table dynamics determined by the spatial variation in the system properties and the temporal variation driven by the dynamics of the inputs into the system. An integration of stochastic methods is presented, based on time-series modeling and geostatistics as a framework to predict water levels for decision making in groundwater management and land-use planning. The methodology is applied in a case study in a Guarani Aquifer System (GAS) outcrop area located in the southeastern part of Brazil. Communication of results in a clear and understandable form, via simulated scenarios, is discussed as an alternative, when translating scientific knowledge into applications of stochastic hydrogeology in large aquifers with limited monitoring network coverage like the GAS.

Crystal structure of the sodium-proton antiporter NhaA dimer and new mechanistic insights

Sodium-proton antiporters rapidly exchange protons and sodium ions across the membrane to regulate intracellular pH, cell volume, and sodium concentration. How ion binding and release is coupled to the conformational changes associated with transport is not clear. Here, we report a crystal form of the prototypical sodium-proton antiporter NhaA from Escherichia coli in which the protein is seen as a dimer. In this new structure, we observe a salt bridge between an essential aspartic acid (Asp163) and a conserved lysine (Lys300). An equivalent salt bridge is present in the homologous transporter NapA, but not in the only other known crystal structure of NhaA, which provides the foundation of most existing structural models of electrogenic sodium-proton antiport. Molecular dynamics simulations show that the stability of the salt bridge is weakened by sodium ions binding to Asp164 and the neighboring Asp163. This suggests that the transport mechanism involves Asp163 switching between forming a salt bridge with Lys300 and interacting with the sodium ion. pKa calculations suggest that Asp163 is highly unlikely to be protonated when involved in the salt bridge. As it has been previously suggested that Asp163 is one of the two residues through which proton transport occurs, these results have clear implications to the current mechanistic models of sodium-proton antiport in NhaA.

Mechanistic modelling of pilling. Part I: Detailing of mechanisms

Mechanistic models of pilling are discussed in general terms, and a framework for pilling simulations is thereby created. A fundamental flaw in earlier models of pilling is revealed. A more comprehensive model of fibre diffusion and withdrawal from the fabric is proposed, and this is solved in general terms to find the rate of fuzz growth. Fuzz wear-off and entanglement into pills are discussed. Fibre fatigue is introduced, and it is demonstrated that this potentially increases the rate of withdrawal of anchor fibres.

A mechanistic description of combined hardening and size effects

Mechanistic models based on geometrically necessary dislocations are re-examined in light of recent experiments exhibiting the indentation size effect. A simple method is developed to combine work hardening, solid solution hardening, radiation hardening and size effects. The model is verified by experiments in ionic salt crystals. © 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Stochastic simulation of time-series models combined with geostatistics to predict water-table scenarios in a Guarani Aquifer System outcrop area, Brazil

Stochastic methods based on time-series modeling combined with geostatistics can be useful tools to describe the variability of water-table levels in time and space and to account for uncertainty. Monitoring water-level networks can give information about the dynamic of the aquifer domain in both dimensions. Time-series modeling is an elegant way to treat monitoring data without the complexity of physical mechanistic models. Time-series model predictions can be interpolated spatially, with the spatial differences in water-table dynamics determined by the spatial variation in the system properties and the temporal variation driven by the dynamics of the inputs into the system. An integration of stochastic methods is presented, based on time-series modeling and geostatistics as a framework to predict water levels for decision making in groundwater management and land-use planning. The methodology is applied in a case study in a Guarani Aquifer System (GAS) outcrop area located in the southeastern part of Brazil. Communication of results in a clear and understandable form, via simulated scenarios, is discussed as an alternative, when translating scientific knowledge into applications of stochastic hydrogeology in large aquifers with limited monitoring network coverage like the GAS.

Effect of Temperature on the Development and Survival of the Argentine Ant, Linepithema humile

The influence of temperature on the developmental times and survival of insects can largely determine their distribution. For invasive species, like the Argentine ant, Linepithema humile Mayr (Hymenoptera: Formicidae), these data are essential for predicting their potential range based on mechanistic models. In the case of this species, such data are too scarce and incomplete to make accurate predictions based on its physiological needs. This research provides comprehensive new data about brood survival and developmental times at a wide range of temperatures under laboratory conditions. Temperature affected both the complete brood development from egg to adult worker and each of the immature stages separately. The higher the temperature, the shorter the development times. Brood survival from egg to adult was low, with the maximum survival rate being only 16% at 26º C. Temperature also affected survival of each of the immature stages differently: eggs were negatively affected by high temperatures, while larvae were negatively affected by low temperatures, and the survival of pupae was apparentlyindependent of environmental temperature. At 32º C no eggs survived, while at 18º C less than 2% of the eggs hatched into larva. The data from the present study are essential for developing prediction models about the distribution range of this tramp species based on its physiological needs in relation to temperature