Mathematical Model of Viral Kinetics In Vitro Estimates the Number of E2-CD81 Complexes Necessary for Hepatitis C Virus Entry

Interaction between the hepatitis C virus (HCV) envelope protein E2 and the host receptor CD81 is essential for HCV entry into target cells. The number of E2-CD81 complexes necessary for HCV entry has remained difficult to estimate experimentally. Using the recently developed cell culture systems that allow persistent HCV infection in vitro, the dependence of HCV entry and kinetics on CD81 expression has been measured. We reasoned that analysis of the latter experiments using a mathematical model of viral kinetics may yield estimates of the number of E2-CD81 complexes necessary for HCV entry. Here, we constructed a mathematical model of HCV viral kinetics in vitro, in which we accounted explicitly for the dependence of HCV entry on CD81 expression. Model predictions of viral kinetics are in quantitative agreement with experimental observations. Specifically, our model predicts triphasic viral kinetics in vitro, where the first phase is characterized by cell proliferation, the second by the infection of susceptible cells and the third by the growth of cells refractory to infection. By fitting model predictions to the above data, we were able to estimate the threshold number of E2-CD81 complexes necessary for HCV entry into human hepatoma-derived cells. We found that depending on the E2-CD81 binding affinity, between 1 and 13 E2-CD81 complexes are necessary for HCV entry. With this estimate, our model captured data from independent experiments that employed different HCV clones and cells with distinct CD81 expression levels, indicating that the estimate is robust. Our study thus quantifies the molecular requirements of HCV entry and suggests guidelines for intervention strategies that target the E2-CD81 interaction. Further, our model presents a framework for quantitative analyses of cell culture studies now extensively employed to investigate HCV infection.

Rapid and quantitative detection of the microbial spoilage of meat by Fourier Transform Infrared Spectroscopy and machine learning

Ellis, D. I., Broadhurst, D., Kell, D. B., Rowland, J. J., Goodacre, R. (2002). Rapid and quantitative detection of the microbial spoilage of meat by Fourier Transform Infrared Spectroscopy and machine learning. ? Applied and Environmental Microbiology, 68, (6), 2822-2828 Sponsorship: BBSRC

QUANTITATIVE THREE DIMENSIONAL ELASTICITY IMAGING

Neoplastic tissue is typically highly vascularized, contains abnormal concentrations of extracellular proteins (e.g. collagen, proteoglycans) and has a high interstitial fluid pres- sure compared to most normal tissues. These changes result in an overall stiffening typical of most solid tumors. Elasticity Imaging (EI) is a technique which uses imaging systems to measure relative tissue deformation and thus noninvasively infer its mechanical stiffness. Stiffness is recovered from measured deformation by using an appropriate mathematical model and solving an inverse problem. The integration of EI with existing imaging modal- ities can improve their diagnostic and research capabilities. The aim of this work is to develop and evaluate techniques to image and quantify the mechanical properties of soft tissues in three dimensions (3D). To that end, this thesis presents and validates a method by which three dimensional ultrasound images can be used to image and quantify the shear modulus distribution of tissue mimicking phantoms. This work is presented to motivate and justify the use of this elasticity imaging technique in a clinical breast cancer screening study. The imaging methodologies discussed are intended to improve the specificity of mammography practices in general. During the development of these techniques, several issues concerning the accuracy and uniqueness of the result were elucidated. Two new algorithms for 3D EI are designed and characterized in this thesis. The first provides three dimensional motion estimates from ultrasound images of the deforming ma- terial. The novel features include finite element interpolation of the displacement field, inclusion of prior information and the ability to enforce physical constraints. The roles of regularization, mesh resolution and an incompressibility constraint on the accuracy of the measured deformation is quantified. The estimated signal to noise ratio of the measured displacement fields are approximately 1800, 21 and 41 for the axial, lateral and eleva- tional components, respectively. The second algorithm recovers the shear elastic modulus distribution of the deforming material by efficiently solving the three dimensional inverse problem as an optimization problem. This method utilizes finite element interpolations, the adjoint method to evaluate the gradient and a quasi-Newton BFGS method for optimiza- tion. Its novel features include the use of the adjoint method and TVD regularization with piece-wise constant interpolation. A source of non-uniqueness in this inverse problem is identified theoretically, demonstrated computationally, explained physically and overcome practically. Both algorithms were test on ultrasound data of independently characterized tissue mimicking phantoms. The recovered elastic modulus was in all cases within 35% of the reference elastic contrast. Finally, the preliminary application of these techniques to tomosynthesis images showed the feasiblity of imaging an elastic inclusion.

Quantitative genetics of preference and performance on chickpeas in the noctuid moth, Helicoverpa armigera

If a novel, resistant host-plant genotype arises in the environment, insect populations utilising that host must be able to overcome that resistance in order that they can maintain their ability to feed on that host. The ability to evolve resistance to host-plant defences depends upon additive genetic variation in larval performance and adult host-choice preference. To investigate the potential of a generalist herbivore to respond to a novel resistant host, we estimated the heritability of larval performance in the noctuid moth, Helicoverpa armigera, on a resistant and a susceptible variety of the chickpea, Cicer arietinum, at two different life stages. Heritability estimates were higher for neonates than for third-instar larvae, suggesting that their ability to establish on plants could be key to the evolution of resistance in this species; however, further information regarding the nature of selection in the field would be required to confirm this prediction. There was no genetic correlation between larval performance and oviposition preference, indicating that female moths do not choose the most suitable plant for their offspring. We also found significant genotype by environment interactions for neonates (but not third-instar larvae), suggesting that the larval response to different plant genotypes is stage-specific in this species.

Detection of quantitative trait loci for androstenone, skatole and boar taint in a cross between Large White and Meishan pigs

'Boar taint' is a strong perspiration-like, urine-like unpleasant odour given off upon heating or cooking of meat from some intact (uncastrated) male pigs. Data from the F(2) generation of a Large White (LW) x Meishan (MS) crossbred population were analysed to detect quantitative trait loci (QTL) for traits associated with boar taint. Fat samples from 178 intact male pigs slaughtered at 85 +/- 5 kg were analysed for the major contributors to boar taint (androstenone, indole and skatole). Fat and lean samples from cooked meat were scored for boar, abnormal and pork flavour and odour by a trained sensory panel (SP). A scan with 117 markers covering the whole genome was performed in the F(2) individuals, together with their F(1) parents and purebred grandparents. At the 5% chromosomal significance threshold (approximately equal to the genome-wide suggestive significance threshold), QTL were detected for the laboratory estimate of androstenone on chromosomes 2, 4, 6, 7 and 9. However, only on chromosome 6 were there QTL for boar flavour (BF) traits in the same or adjacent marker intervals as a QTL for the laboratory estimate of androstenone. On chromosome 14, QTL were detected for the laboratory estimates of indole and skatole, the SP score for skatole and the scores for BF in lean and BF in fat. In all five cases, the MS allele generally increased the estimate or score, compared with the LW allele, but it appeared that desirable and undesirable alleles were present in both breeds. This locus on chromosome 14 has considerable potential for use to reduce the incidence of boar taint, especially if further research can identify the causative polymorphism or strongly associated markers.

Device-specific weighted T-score for two quantitative ultrasounds: operational propositions for the management of osteoporosis for 65 years and older women in Switzerland.

The World Health Organization (WHO) criteria for the diagnosis of osteoporosis are mainly applicable for dual X-ray absorptiometry (DXA) measurements at the spine and hip levels. There is a growing demand for cheaper devices, free of ionizing radiation such as promising quantitative ultrasound (QUS). In common with many other countries, QUS measurements are increasingly used in Switzerland without adequate clinical guidelines. The T-score approach developed for DXA cannot be applied to QUS, although well-conducted prospective studies have shown that ultrasound could be a valuable predictor of fracture risk. As a consequence, an expert committee named the Swiss Quality Assurance Project (SQAP, for which the main mission is the establishment of quality assurance procedures for DXA and QUS in Switzerland) was mandated by the Swiss Association Against Osteoporosis (ASCO) in 2000 to propose operational clinical recommendations for the use of QUS in the management of osteoporosis for two QUS devices sold in Switzerland. Device-specific weighted "T-score" based on the risk of osteoporotic hip fractures as well as on the prediction of DXA osteoporosis at the hip, according to the WHO definition of osteoporosis, were calculated for the Achilles (Lunar, General Electric, Madison, Wis.) and Sahara (Hologic, Waltham, Mass.) ultrasound devices. Several studies (totaling a few thousand subjects) were used to calculate age-adjusted odd ratios (OR) and area under the receiver operating curve (AUC) for the prediction of osteoporotic fracture (taking into account a weighting score depending on the design of the study involved in the calculation). The ORs were 2.4 (1.9-3.2) and AUC 0.72 (0.66-0.77), respectively, for the Achilles, and 2.3 (1.7-3.1) and 0.75 (0.68-0.82), respectively, for the Sahara device. To translate risk estimates into thresholds for clinical application, 90% sensitivity was used to define low fracture and low osteoporosis risk, and a specificity of 80% was used to define subjects as being at high risk of fracture or having osteoporosis at the hip. From the combination of the fracture model with the hip DXA osteoporotic model, we found a T-score threshold of -1.2 and -2.5 for the stiffness (Achilles) determining, respectively, the low- and high-risk subjects. Similarly, we found a T-score at -1.0 and -2.2 for the QUI index (Sahara). Then a screening strategy combining QUS, DXA, and clinical factors for the identification of women needing treatment was proposed. The application of this approach will help to minimize the inappropriate use of QUS from which the whole field currently suffers.

Continuous quantification of HER2 expression by microfluidic precision immunofluorescence estimates HER2 gene amplification in breast cancer.

Chromogenic immunohistochemistry (IHC) is omnipresent in cancer diagnosis, but has also been criticized for its technical limit in quantifying the level of protein expression on tissue sections, thus potentially masking clinically relevant data. Shifting from qualitative to quantitative, immunofluorescence (IF) has recently gained attention, yet the question of how precisely IF can quantify antigen expression remains unanswered, regarding in particular its technical limitations and applicability to multiple markers. Here we introduce microfluidic precision IF, which accurately quantifies the target expression level in a continuous scale based on microfluidic IF staining of standard tissue sections and low-complexity automated image analysis. We show that the level of HER2 protein expression, as continuously quantified using microfluidic precision IF in 25 breast cancer cases, including several cases with equivocal IHC result, can predict the number of HER2 gene copies as assessed by fluorescence in situ hybridization (FISH). Finally, we demonstrate that the working principle of this technology is not restricted to HER2 but can be extended to other biomarkers. We anticipate that our method has the potential of providing automated, fast and high-quality quantitative in situ biomarker data using low-cost immunofluorescence assays, as increasingly required in the era of individually tailored cancer therapy.

Quantitative response of the longevity of seed of twelve crops to temperature and moisture in hermetic storage

Seeds of 39 seed lots of a total of twelve different crops were stored hermetically in a wide range of air-dry environments (2-25% moisture content at 0-50 degrees C), viability assessed periodically, and the seed viability equation constants estimated. Within a species, estimates of the constants which quantify absolute longevity (K-E) and the relative effects on longevity of moisture content (C-W) and temperature (C-H and C-Q) did not differ (P >0.05 to P >0.25) among lots. Comparison among the 12 crops provided variant estimates of K-E and C-W (P< 0.01), but common values of C-H and C-Q (0.0322 and 0.000454, respectively, P >0.25). Maize (Zea mays) provided the greatest estimate of K-E (9.993, s.e.= 0.456), followed by sorghum (Sorghum bicolor) (9.381, s.e. 0.428), pearl millet (Pennisetum typhoides) (9.336, s.e.= 0.408), sugar beet (Beta vulgaris) (8.988, s.e.= 0.387), African rice (Oryza glaberrima) (8.786, s.e.= 0.484), wheat (Triticum aestivum) (8.498, s.e.= 0.431), foxtail millet (Setaria italica) (8.478, s.e.= 0.396), sugarcane (Saccharum sp.) (8.454, s.e.= 0.545), finger millet (Eleusine coracana) (8.288, s.e.= 0.392), kodo millet (Paspalum scrobiculatum) (8.138, s.e.= 0.418), rice (Oryza sativa) (8.096, s.e.= 0.416) and potato (Solanum tuberosum) (8.037, s.e.= 0.397). Similarly, estimates of C-W were ranked maize (5.993, s.e.= 0.392), pearl millet (5.540, s.e.= 0.348), sorghum (5.379, s.e.=0.365), potato (5.152, s.e.= 0.347), sugar beet (4.969, s.e.= 0.328), sugar cane (4.964, s.e.= 0.518), foxtail millet (4.829, s.e.= 0.339), wheat (4.836, s.e.= 0.366), African rice (4.727, s.e.= 0.416), kodo millet (4.435, s.e.= 0.360), finger millet (4.345, s.e.= 0.336) and rice (4.246, s.e.= 0.355). The application of these constants to long-term seed storage is discussed.

The effect of surface heterogeneity on cloud absorption estimates

This study presents a systematic and quantitative analysis of the effect of inhomogeneous surface albedo on shortwave cloud absorption estimates. We used 3D radiative transfer modeling over a checkerboard surface albedo to calculate cloud absorption. We have found that accounting for surface heterogeneity enhances cloud absorption. However, the enhancement is not sufficient to explain the reported difference between measured and modeled cloud absorption.

Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation

We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the $L^2$ condition numbers for these formulations, and also on the norms of the classical acoustic single- and double-layer potential operators. These bounds to some extent make explicit the dependence of condition numbers on the wave number $k$, the geometry of the scatterer, and the coupling parameter. For example, with the usual choice of coupling parameter they show that, while the condition number grows like $k^{1/3}$ as $k\to\infty$, when the scatterer is a circle or sphere, it can grow as fast as $k^{7/5}$ for a class of `trapping' obstacles. In this paper we prove further bounds, sharpening and extending our previous results. In particular we show that there exist trapping obstacles for which the condition numbers grow as fast as $\exp(\gamma k)$, for some $\gamma>0$, as $k\to\infty$ through some sequence. This result depends on exponential localisation bounds on Laplace eigenfunctions in an ellipse that we prove in the appendix. We also clarify the correct choice of coupling parameter in 2D for low $k$. In the second part of the paper we focus on the boundary element discretisation of these operators. We discuss the extent to which the bounds on the continuous operators are also satisfied by their discrete counterparts and, via numerical experiments, we provide supporting evidence for some of the theoretical results, both quantitative and asymptotic, indicating further which of the upper and lower bounds may be sharper.

Quantitative precipitation estimation over ocean using Bayesian approach from microwave observations during the typhoon season

We have developed a new Bayesian approach to retrieve oceanic rain rate from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), with an emphasis on typhoon cases in the West Pacific. Retrieved rain rates are validated with measurements of rain gauges located on Japanese islands. To demonstrate improvement, retrievals are also compared with those from the TRMM/Precipitation Radar (PR), the Goddard Profiling Algorithm (GPROF), and a multi-channel linear regression statistical method (MLRS). We have found that qualitatively, all methods retrieved similar horizontal distributions in terms of locations of eyes and rain bands of typhoons. Quantitatively, our new Bayesian retrievals have the best linearity and the smallest root mean square (RMS) error against rain gauge data for 16 typhoon overpasses in 2004. The correlation coefficient and RMS of our retrievals are 0.95 and ~2 mm hr-1, respectively. In particular, at heavy rain rates, our Bayesian retrievals outperform those retrieved from GPROF and MLRS. Overall, the new Bayesian approach accurately retrieves surface rain rate for typhoon cases. Accurate rain rate estimates from this method can be assimilated in models to improve forecast and prevent potential damages in Taiwan during typhoon seasons.

Bollène-2002 experiment: radar quantitative precipitation estimation in the Cévennes–Vivarais region, France

The Bollène-2002 Experiment was aimed at developing the use of a radar volume-scanning strategy for conducting radar rainfall estimations in the mountainous regions of France. A developmental radar processing system, called Traitements Régionalisés et Adaptatifs de Données Radar pour l’Hydrologie (Regionalized and Adaptive Radar Data Processing for Hydrological Applications), has been built and several algorithms were specifically produced as part of this project. These algorithms include 1) a clutter identification technique based on the pulse-to-pulse variability of reflectivity Z for noncoherent radar, 2) a coupled procedure for determining a rain partition between convective and widespread rainfall R and the associated normalized vertical profiles of reflectivity, and 3) a method for calculating reflectivity at ground level from reflectivities measured aloft. Several radar processing strategies, including nonadaptive, time-adaptive, and space–time-adaptive variants, have been implemented to assess the performance of these new algorithms. Reference rainfall data were derived from a careful analysis of rain gauge datasets furnished by the Cévennes–Vivarais Mediterranean Hydrometeorological Observatory. The assessment criteria for five intense and long-lasting Mediterranean rain events have proven that good quantitative precipitation estimates can be obtained from radar data alone within 100-km range by using well-sited, well-maintained radar systems and sophisticated, physically based data-processing systems. The basic requirements entail performing accurate electronic calibration and stability verification, determining the radar detection domain, achieving efficient clutter elimination, and capturing the vertical structure(s) of reflectivity for the target event. Radar performance was shown to depend on type of rainfall, with better results obtained with deep convective rain systems (Nash coefficients of roughly 0.90 for point radar–rain gauge comparisons at the event time step), as opposed to shallow convective and frontal rain systems (Nash coefficients in the 0.6–0.8 range). In comparison with time-adaptive strategies, the space–time-adaptive strategy yields a very significant reduction in the radar–rain gauge bias while the level of scatter remains basically unchanged. Because the Z–R relationships have not been optimized in this study, results are attributed to an improved processing of spatial variations in the vertical profile of reflectivity. The two main recommendations for future work consist of adapting the rain separation method for radar network operations and documenting Z–R relationships conditional on rainfall type.

Wild bird feeding in a large UK urban area: characteristics and estimates of energy input and individuals supported

Wild bird feeding is popular in domestic gardens across the world. Nevertheless, there is surprisingly little empirical information on certain aspects of the activity and no year-round quantitative records of the amounts and nature of the different foods provided in individual gardens. We sought to characterise garden bird feeding in a large UK urban area in two ways. First, we conducted face-to-face questionnaires with a representative cross-section of residents. Just over half fed birds, the majority doing so year round and at least weekly. Second, a two-year study recorded all foodstuffs put out by households on every provisioning occasion. A median of 628 kcal/garden/day was given. Provisioning level was not significantly influenced by weather or season. Comparisons between the data sets revealed significantly less frequent feeding amongst these ‘keen’ feeders than the face-to-face questionnaire respondents, suggesting that one-off questionnaires may overestimate provisioning frequency. Assuming 100% uptake, the median provisioning level equates to sufficient supplementary resources across the UK to support 196 million individuals of a hypothetical average garden-feeding bird species (based on 10 common UK garden-feeding birds’ energy requirements). Taking the lowest provisioning level recorded (101 kcal/day) as a conservative measure, 31 million of these average individuals could theoretically be supported.

Incorporating toxicokinetics into an individual-based model for more realistic pesticide exposure estimates: A case study of the wood mouse

The potential risk of agricultural pesticides to mammals typically depends on internal concentrations within individuals, and these are determined by the amount ingested and by absorption, distribution, metabolism, and excretion (ADME). Pesticide residues ingested depend, amongst other things, on individual spatial choices which determine how much and when feeding sites and areas of pesticide application overlap, and can be calculated using individual-based models (IBMs). Internal concentrations can be calculated using toxicokinetic (TK) models, which are quantitative representations of ADME processes. Here we provide a population model for the wood mouse (Apodemus sylvaticus) in which TK submodels were incorporated into an IBM representation of individuals making choices about where to feed. This allows us to estimate the contribution of individual spatial choice and TK processes to risk. We compared the risk predicted by four IBMs: (i) “AllExposed-NonTK”: assuming no spatial choice so all mice have 100% exposure, no TK, (ii) “AllExposed-TK”: identical to (i) except that the TK processes are included where individuals vary because they have different temporal patterns of ingestion in the IBM, (iii) “Spatial-NonTK”: individual spatial choice, no TK, and (iv) “Spatial-TK”: individual spatial choice and with TK. The TK parameters for hypothetical pesticides used in this study were selected such that a conventional risk assessment would fail. Exposures were standardised using risk quotients (RQ; exposure divided by LD50 or LC50). We found that for the exposed sub-population including either spatial choice or TK reduced the RQ by 37–85%, and for the total population the reduction was 37–94%. However spatial choice and TK together had little further effect in reducing RQ. The reasons for this are that when the proportion of time spent in treated crop (PT) approaches 1, TK processes dominate and spatial choice has very little effect, and conversely if PT is small spatial choice dominates and TK makes little contribution to exposure reduction. The latter situation means that a short time spent in the pesticide-treated field mimics exposure from a small gavage dose, but TK only makes a substantial difference when the dose was consumed over a longer period. We concluded that a combined TK-IBM is most likely to bring added value to the risk assessment process when the temporal pattern of feeding, time spent in exposed area and TK parameters are at an intermediate level; for instance wood mice in foliar spray scenarios spending more time in crop fields because of better plant cover.

Quantitative variation in the tropical maize population, ESALQ-PB1

A boa produtividade e os valores intermediários para altura da planta e altura da espiga caracterizam a população de milho ESALQ-PB1 como agronomicamente promissora. São relatadas estimativas de parâmetros para 13 caracteres: altura da planta (PH), altura da espiga (EH), posição relativa da espiga (EP), comprimento do pendão (TL), peso do pendão (TW), número de ramificações do pendão (TB), peso de espigas (EW), peso de grãos (GW), comprimento da espiga (EL), diâmetro da espiga (ED), número de fileiras de grãos (RN), número de grãos por fileira (KR) e prolificidade (PR). Os resultados se referem a um único ambiente (um local e um ano). Foi detectada variação genética para todos os caracteres, e são apresentadas estimativas da variância genética aditiva. Os coeficientes de herdabilidade (indivíduos) variaram de 0,14 a 0,72 e foram considerados altos para PH, EH e TB; intermediários para EP, TL, TW, EL e ED, e baixos para EW, GW, KR e PR. O coeficiente de herdabilidade para médias de progênies mostrou aproximadamente a mesma tendência, variando de 0,40 a 0,75. O maior ganho esperado por seleção foi para TB (27% por ciclo) sob seleção massal e para TW (16,4%) por seleção entre progênies; o menor ganho esperado foi para ED, tanto por seleção massal (1,9%) como por seleção entre progênies (2,9%). Coeficientes de correlação aditiva (rA) 0.5