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PubMed2006

Visualizing hidden heterogeneity in isogenic populations of C. elegans.

Age-specific mortality levels off at advanced ages in many species; one explanation for this phenomenon is provided by the population heterogeneity theory. Although mortality at advanced ages can be well fit by heterogeneity models, population heterogeneity remains theoretical, lacking much direct evidence to support the existence of unobserved heterogeneity. Here, we provide direct evidence to support the heterogeneity theory by using isogenic population of worms of Caenorhabditis elegans. We measure the ability of individual worms to respond to a heat stress using an HSP-16.2 promoter that has been attached to GFP, a fluorescent marker that can be assessed in living animals. Worms differ substantially in their response; worms with high response have a long lifespan, and worms with low response to stress have a short life. Each of these classes results from a mix of two distinct, heterogeneous classes of worms and the addition of more classes does not result in a better fit.

Aging↗
PubMed2005

Random effects survival models gave a better understanding of heterogeneity in individual patient data meta-analyses.

BACKGROUND AND OBJECTIVE: Individual patient data meta-analysis consists in combining data from all available trials dealing with a therapeutic problem in order to increase the power of statistical analyses. A key issue when analyzing these pooled data sets is intertrial heterogeneity. In survival data, heterogeneity manifests itself either by differing treatment effects between the included trials or by a baseline hazard that differs between studies. One way to investigate and accommodate this heterogeneity is to use models that include random effects. METHODS: We apply this class of models to the Meta-Analysis of Chemotherapy in Head and Neck Cancers, in which strong heterogeneity is exhibited. This meta-analysis pooled 63 trials involving 10,741 patients. RESULTS: We show that such modeling permits a better understanding of heterogeneity in the MACH-NC data, both from a frequentist and from a Bayesian point of view. In particular, the modeling suggests the presence of two outlying sets of trials whose baseline risk could explain the apparent efficacy or inefficacy of some treatment protocols. CONCLUSION: We conclude that this family of random-effects models is a useful tool for exploring heterogeneity in meta-analyses of time-to-event data, and that its features can be applied to a very wide range of studies.

Chemotherapy, Adjuvant↗
PubMed2004

Spatial heterogeneity and the persistence of infectious diseases.

The endemic persistence of infectious diseases can often not be understood without taking into account the relevant heterogeneities of host mixing. Here, we consider spatial heterogeneity, defined as 'patchiness' of the host population. After briefly reviewing how disease persistence is influenced by population size, reproduction number and infectious period, we explore its dependence on the level of spatial heterogeneity. Analysis and simulation of disease transmission in a symmetric meta-population suggest that disease persistence typically becomes worse as spatial heterogeneity increases, although local persistence optima can occur for infections with oscillatory population dynamics. We obtain insight into the dynamics that underlie the observed persistence patterns by studying the infection prevalence correlation between patches and by comparing full-model simulations to results obtained using simplified patch-level descriptions of the interplay between local extinctions and between-patch transmissions. The observed patterns are interpreted in terms of rescue effects for strong spatial heterogeneity and in terms of between-patch coherence and synchronization effects at intermediate and weak levels of heterogeneity.

Communicable Diseases↗
PubMed2000

Chest radiograph heterogeneity predicts functional improvement with volume reduction surgery.

BACKGROUND: Using a historical cohort study model, we tested the hypothesis that heterogeneity of emphysematous changes on the preoperative chest radiograph correlated with favorable outcome of lung volume reduction surgery. METHODS: The test population consisted of 21 patients with severe emphysema who were being treated at a 1,000-bed university-affiliated tertiary teaching hospital. A simple but quantitative index of heterogeneity has been devised, whereby the preoperative posteroanterior chest radiographic lung fields are divided into four geometric quadrants. Each quadrant is scored (0 to 4) for emphysematous changes by two radiologists blinded as to subsequent patient management and outcome. Criteria for determining presence of emphysema were hyperlucency, decreased vascular markings, and parenchymal crowding indicating compressed lung. Heterogeneity index is the sum of the two highest scores minus the two lowest, with a maximum index of 8 and a minimum of 0. Preoperative chest radiographs and postoperative changes in forced expiratory volume in 1 second were examined. RESULTS: The heterogeneity index was positively correlated with change in forced expiratory volume in 1 second after operation with an r2 of 0.31 and an average increase of 117 mL per unit increase in heterogeneity index (p < 0.009). CONCLUSIONS: This simple index of heterogeneity may be useful as a predictor of improved pulmonary function after lung volume reduction surgery.

Aged↗
PubMed1997

Analysis of phosphorescence in heterogeneous systems using distributions of quencher concentration.

A continuous distribution approach, instead of the traditional mono- and multiexponential analysis, for determining quencher concentration in a heterogeneous system has been developed. A mathematical model of phosphorescence decay inside a volume with homogeneous concentration of phosphor and heterogeneous concentration of quencher was formulated to obtain pulse-response fitting functions for four different distributions of quencher concentration: rectangular, normal (Gaussian), gamma, and multimodal. The analysis was applied to parameter estimates of a heterogeneous distribution of oxygen tension (PO2) within a volume. Simulated phosphorescence decay data were randomly generated for different distributions and heterogeneity of PO2 inside the excitation/emission volume, consisting of 200 domains, and then fit with equations developed for the four models. Analysis using a monoexponential fit yielded a systematic error (underestimate) in mean PO2 that increased with the degree of heterogeneity. The fitting procedures based on the continuous distribution approach returned more accurate values for parameters of the generated PO2 distribution than did the monoexponential fit. The parameters of the fit (M = mean; sigma = standard deviation) were investigated as a function of signal-to-noise ratio (SNR = maximum signal amplitude/peak-to-peak noise). The best-fit parameter values were stable when SNR > or = 20. All four fitting models returned accurate values of M and sigma for different PO2 distributions. The ability of our procedures to resolve two different heterogeneous compartments was also demonstrated using a bimodal fitting model. An approximate scheme was formulated to allow calculation of the first moments of a spatial distribution of quencher without specifying the distribution. In addition, a procedure for the recovery of a histogram, representing the quencher concentration distribution, was developed and successfully tested.

Light↗
PubMed1999

Functional heterogeneity of oxygen supply-consumption ratio in the heart.

In this review, the regional heterogeneity of the oxygen supply-consumption ratio within the heart is discussed. This is an important functional parameter because it determines whether regions within the heart are normoxic or dysoxic. Although the heterogeneity of the supply side of oxygen has been primarily described by flow heterogeneity, the diffusional component of oxygen supply should not be ignored, especially at high resolution (tissue regions << 1 g). Such oxygen diffusion does not seem to take place from arterioles or venules within the heart, but seems to occur between capillaries, in contrast to data recently obtained from other tissues. Oxygen diffusion may even become the primary determinant of oxygen supply during obstructed flow conditions. Studies aimed at modelling regional blood flow and oxygen consumption have demonstrated marked regional heterogeneity of oxygen consumption matched by flow heterogeneity Direct, non-invasive indicators of the balance between oxygen supply and consumption include NADH videofluorimetry (mitochondrial energy state) and microvascular PO2 measurement by the Pd-porphyrin phosphorescence technique. These indicators have shown a relatively homogeneous distribution during physiological conditions supporting the notion of regional matching of oxygen supply with oxygen consumption. NADH videofluorimetry, however, has demonstrated large increases in functional heterogeneity of this ratio in compromised hearts (ischemia, hypoxia, hypertrophy and endotoxemia) with specific areas, referred to as microcirculatory weak units, predisposed to showing the first signs of dysoxia. It has been suggested that these weak units show the largest relative reduction in flow (independent of absolute flow levels) during compromising conditions, with dysoxia initially developing at the venous end of the capillary.

Animals↗
PubMed1996

Heterogeneity of glyceryl trinitrate response in isolated bovine coronary arteries.

Factors determining heterogeneity of response to glyceryl trinitrate in coronary microvessels have been extensively documented in recent years, but determinants of heterogeneity between conduit and large resistance vessels are poorly understood. The current study has characterised heterogeneity to glyceryl trinitrate and other vasodilators in bovine isolated proximal (4.5 mm i.d.) and distal (0.5 mm i.d.) segments of left anterior descending artery. Compared with proximal segments, distal segments were less responsive to glyceryl trinitrate and sodium nitroprusside, equi-responsive to S-nitroso-N-acetylpenicillamine, and more responsive to isoprenaline. Heterogeneity to glyceryl trinitrate was unaffected by the presence of the thiols (cysteine or N-acetylcysteine, 100 microM). The results are interpreted as evidence that heterogeneity of vascular responsiveness to glyceryl trinitrate reflects impairment in the small artery of the cellular events which precede activation of the cyclic GMP pathway. An implication is that the impairment is not a consequence of limited thiol availability, and in this respect the cellular mechanism of heterogeneity differs from those proposed for the coronary microvasculature.

15-Hydroxy-11 alpha,9 alpha-(epoxymethano)prosta-5↗
PubMed2003

Statistical analysis and biological interpretation of the flow cytometric heterogeneity observed in bacterial axenic cultures.

Histogram comparison and meaningful statistics in flow cytometry is probably the most widely encountered mathematical problem in flow cytometry. Ideally, a test for determining the statistical equality or difference of flow cytometric distributions will identify the significant differences or similarities of the obtained histograms. This situation is of particular interest when flow cytometry is used to study the heterogeneity of axenic bacterial populations. We have statistically measured the heterogeneity of successive cytometric measures, the modifications produced after 20 transfers from the same culture, and the differences between 20 subcultures of identical origin. The heterogeneity of the bacterial populations and the similarity of the obtained 360 histograms were analysed by standard statistical methods. We have studied bacterial axenic cultures in order to detect, quantify and interpret their cytometric heterogeneity, and to assess intrinsic differences and differences produced by laboratory manipulations. We concluded that the standard axenic cultures have a considerable intrinsic cellular and molecular heterogeneity. We suggest that the heterogeneity we have detected basically has two origins: cell size diversity and cell cycle variations.

Bacteria↗
PubMed2002

Virus transport in physically and geochemically heterogeneous subsurface porous media.

A two-dimensional model for virus transport in physically and geochemically heterogeneous subsurface porous media is presented. The model involves solution of the advection-dispersion equation, which additionally considers virus inactivation in the solution, as well as virus removal at the solid matrix surface due to attachment (deposition), release, and inactivation. Two surface inactivation models for the fate of attached inactive viruses and their subsequent role on virus attachment and release were considered. Geochemical heterogeneity, portrayed as patches of positively charged metal oxyhydroxide coatings on collector grain surfaces, and physical heterogeneity, portrayed as spatial variability of hydraulic conductivity, were incorporated in the model. Both layered and randomly (log-normally) distributed physical and geochemical heterogeneities were considered. The upstream weighted multiple cell balance method was employed to numerically solve the governing equations of groundwater flow and virus transport. Model predictions show that the presence of subsurface layered geochemical and physical heterogeneity results in preferential flow paths and thus significantly affect virus mobility. Random distributions of physical and geochemical heterogeneity have also notable influence on the virus transport behavior. While the solution inactivation rate was found to significantly influence the virus transport behavior, surface inactivation under realistic field conditions has probably a negligible influence on the overall virus transport. It was further demonstrated that large virus release rates result in extended periods of virus breakthrough over significant distances downstream from the injection sites. This behavior suggests that simpler models that account for virus adsorption through a retardation factor may yield a misleading assessment of virus transport in "hydrogeologically sensitive" subsurface environments.

Adsorption↗
PubMed2001

Heterogeneity of hepatic parenchymal enhancement on computed tomography during arterial portography: quantitative analysis of correlation with severity of hepatic fibrosis.

Background/Aims: In patients with chronic liver disease, heterogeneous enhancement of liver parenchyma is often noted on computed tomography during arterial portography (CTAP). We investigated the factors contributing to the heterogeneous enhancement and its relationship with postoperative histopathological findings. Methodology: Eighty-seven patients who had undergone a right lobectomy for liver tumor after CTAP were evaluated. The heterogeneity of hepatic parenchymal enhancement on CTAP was assessed quantitatively using standard deviation of mean CT numbers for five ROIs (S.D.) set in the right hepatic lobe, and comparatively evaluated among three histological groups (liver cirrhosis (LC, n=41), chronic hepatitis (CH, n=33), and normal liver (Normal, n=13)). Severity of fibrosis and degree of splenomegaly (Sp) were taken up as factors contributory to the heterogeneity, and were assessed for correlation with the S.D. Results: The range (mean) of S.D. was LC, 3.07-17.64 (9.10); CH, 1.83-11.12 (6.77); and Normal, 2.06-8.89 (5.64) (Scheffe's F-test: LC vs CH, P<0.0005; LC vs Normal, P<0.0002). The higher fibrosis group exhibited significantly greater S.D. values as compared with the lower fibrosis group (Scheffe's F-test: P<0.00003). Coefficient of correlation between the S.D. and the Sp was 0.295 (P<0.005). Conclusion: There was a fair possibility of LC in patients with heterogeneous enhancement of liver parenchyma on CTAP. The severity of liver fibrosis and the degree of splenomegaly were considered to be factors contributing to the heterogeneous enhancement.

Journal Article↗
PubMed2004

Translocation of carbon by Rhizoctonia solani in nutritionally-heterogeneous microcosms.

Responses of Rhizoctonia solani to spatial heterogeneity in sources of carbon, and associated translocation of carbon (C), were studied in a simple microcosm system comprising two discrete domains of agar gels separated on a glass slide and overlain with a porous membrane. Two arrangements of the gel pairs were used, one containing two equally large resources (representing 'homogeneous' conditions) and one containing a large and a negligible resource (representing 'heterogeneous' conditions). The nutrient sources were a standard mineral salt medium with or without glucose as sole C source. The fungus was inoculated onto one domain and growth responses determined by direct measurement of biomass. Translocation of C was quantified by use of 13C-enriched glucose. This substrate was either added to the agar at the outset, when studying newly developing colonies, or as a pulse into already established colonies. When growing in heterogeneous conditions, the fungus actively translocated C from a glucose-containing domain to sustain growth in the adjacent region lacking such a resource. In homogeneous conditions there was evidence of passive translocation (diffusion), but the fungus preferentially used local resource to maintain growth. Active translocation was only observed in newly growing colonies, whereas passive translocation occurred in both growing and established colonies. When the fungus was pulsed with a 13C-enriched glucose solution after 10 d growth, 2.5 times more 13C was taken up by the fungus grown in heterogeneous than homogeneous conditions, suggesting uptake exceeded local demands. In heterogeneous conditions, the total amount of 13C enriched glucose taken up by the fungus was independent of the location of the enriched glucose in the underlying medium. When the nylon membrane was replaced by Cellophane (an additional C source), degradation of the membrane and an increase in biomass occurred only in the heterogeneous system. The possible implications for these results in soil systems are discussed.

Biomass↗
PubMed2004

Characterization of the imprint effect and the influence of imprinting conditions on affinity, capacity, and heterogeneity in molecularly imprinted polymers using the Freundlich isotherm-affinity distribution analysis.

Molecularly imprinted polymers (MIPs) have been used in a wide range of analytical applications in particular in chromatography and sensing. However, the binding properties in MIPs are typically measured only in a narrow concentration range, which corresponds to only a subset of the sites in MIPs. This limited analytical window and binding site heterogeneity of MIPs leads to inaccuracies and inconsistencies in the estimation of their binding properties. This has hampered the characterization and optimization of MIPs for analytical applications. In this study, the origins of the molecular imprinting effect were studied using the newly developed Freundlich isotherm-affinity distribution (FIAD) analysis. The analysis is able to readily calculate an affinity distribution for MIPs from the limited analytical window. The FIAD analysis also yields an estimate of number, affinity, and heterogeneity for this subset of binding sites. Consistent with previous studies, MIPs were found to have higher capacities than the corresponding nonimprinted polymers (NIPs). Interestingly, MIPs were also found to be more heterogeneous than NIPs. Examination of variables in the imprinting process including temperature, template concentration, and cross-linking percentages further confirmed these trends. Based on these observations, a model for the imprinting effect was developed. The larger population of high-affinity sites in MIPs appears to arise from a broadening of the heterogeneous distribution. This suggests that noncovalent MIPs may be ill-suited for chromatographic applications and other applications that are detrimentally affected by binding site heterogeneity and better suited to applications that are less affected by heterogeneity such as sensing.

Journal Article↗
PubMed2004

Box model investigation of the effect of soot particles on ozone downwind from an urban area through heterogeneous reactions.

Soot can provide additional surface area where heterogeneous reactions can take place in the atmosphere. These reactions are dependent on the number of reactive sites on the soot surface rather than the soot surface area per se. A box model, MOCCA, is used to investigate the effects of introducing heterogeneous reactions on soot into air parcel passing over an urban area and traveling downwind. The model was run at two soot mass concentrations of 2 microg/m3 and 20 microg/m3 with a surface density of n-hexane and decane. Signifcant change in gasphase concentration was only observed for the higher soot concentration. Due to the noncatalytic nature of the heterogeneous reactions, soot sites are rapidly consumed, and soot site concentrations are greatly reduced shortly after emissions are turned off. Notable changes in gaseous concentrations due to the introduction of heterogeneous reactions are not observed in the urban setting. The impact of heterogeneous reactions is more evident after emissions are turned off (i.e. downwind from the urban center). These changes are minimal for the condition that used n-hexane surface density. For conditions that used decane soot, NOx concentrations showed a slight increase, with NO being higher in the daytime and NO2 at night. The maximum O3 reduction observed when using the higher soot concentration is 7 ppb, downwind of the urban center. Change in O3 concentration was less than 1 ppb when using the lower soot loading. The observed effects of heterogeneous reactions on soot decrease with time.

Air Pollutants↗
PubMed2005

Chemical heterogeneity of organic soil colloids investigated by scanning transmission X-ray microscopy and C-1s NEXAFS microspectroscopy.

Colloid release and deposition in soils and sorption of inorganic and organic pollutants to soil colloids are strongly influenced by the composition and chemical heterogeneity of colloidal soil particles. To investigate the chemical heterogeneity of organic soil colloids at the particle scale, we used synchrotron scanning transmission X-ray microscopy (STXM) and C-1s near-edge X-ray absorption fine structure (NEXAFS) spectroscopy on 49 individual particles isolated from the surface horizons of three forest soils. Stacks of 130 images of each particle were collected at different X-ray energies between 280 and 310 eV. From these image arrays, NEXAFS spectra were obtained for each pixel and analyzed by principle component analysis and cluster analysis (PCA-CA) to characterize the intraparticle heterogeneity of the organic components. The results demonstrate that the organic matter associated with water-dispersible soil colloids is chemically heterogeneous at the single-particle scale. PCA-CA identified at least two distinct regions within single particles. However, the spectral variations between these regions were much smaller than the variations of averaged NEXAFS spectra representing different particles from the same soil horizon, implying that interparticle heterogeneity is much larger than intraparticle heterogeneity. Especially the contents of aromatic and carboxyl carbon exhibited a large variability. Overall, the NEXAFS spectra of water-dispersible soil colloids were similar to the NEXAFS spectrum of the humic acid fraction, but differed clearly from the fulvic acid and dissolved organic matter fractions extracted from the same soil horizon using conventional techniques.

Colloids↗
PubMed2006

Dissecting and reducing the heterogeneity of excited-state energy transport in DNA-based photonic wires.

Molecular photonic wires are one-dimensional representatives of a family of nanoscale molecular devices that transport excited-state energy over considerable distances in analogy to optical waveguides in the far-field. In particular, the design and synthesis of such complex supramolecular devices is challenging concerning the desired homogeneity of energy transport. On the other hand, novel optical techniques are available that permit direct investigation of heterogeneity by studying one device at a time. In this article, we describe our efforts to synthesize and study DNA-based molecular photonic wires that carry several chromophores arranged in an energetic downhill cascade and exploit fluorescence resonance energy transfer to convey excited-state energy. The focus of this work is to understand and control the heterogeneity of such complex systems, applying single-molecule fluorescence spectroscopy (SMFS) to dissect the different sources of heterogeneity, i.e., chemical heterogeneity and inhomogeneous broadening induced by the nanoenvironment. We demonstrate that the homogeneity of excited-state energy transport in DNA-based photonic wires is dramatically improved by immobilizing photonic wires in aqueous solution without perturbation by the surface. In addition, our study shows that the in situ construction of wire molecules, i.e., the stepwise hybridization of differently labeled oligonucleotides on glass cover slides, further decreases the observed heterogeneity in overall energy-transfer efficiency. The developed strategy enables efficient energy transfer between up to five chromophores in the majority of molecules investigated along a distance of approximately 14 nm. Finally, we used multiparameter SMFS to analyze the energy flow in photonic wires in more detail and to assign residual heterogeneity under optimized conditions in solution to different leakages and competing energy-transfer processes.

DNA↗
PubMed1998

Synchronization and oscillatory dynamics in heterogeneous, mutually inhibited neurons.

We study some mechanisms responsible for synchronous oscillations and loss of synchrony at physiologically relevant frequencies (10-200 Hz) in a network of heterogeneous inhibitory neurons. We focus on the factors that determine the level of synchrony and frequency of the network response, as well as the effects of mild heterogeneity on network dynamics. With mild heterogeneity, synchrony is never perfect and is relatively fragile. In addition, the effects of inhibition are more complex in mildly heterogeneous networks than in homogeneous ones. In the former, synchrony is broken in two distinct ways, depending on the ratio of the synaptic decay time to the period of repetitive action potentials (tau s/T), where T can be determined either from the network or from a single, self-inhibiting neuron. With tau s/T > 2, corresponding to large applied current, small synaptic strength or large synaptic decay time, the effects of inhibition are largely tonic and heterogeneous neurons spike relatively independently. With tau s/T < 1, synchrony breaks when faster cells begin to suppress their less excitable neighbors; cells that fire remain nearly synchronous. We show numerically that the behavior of mildly heterogeneous networks can be related to the behavior of single, self-inhibiting cells, which can be studied analytically.

Computer Simulation↗
PubMed2000

Determination of the origin of charge heterogeneity in a murine monoclonal antibody.

PURPOSE: The aim of this study was to elucidate the molecular basis of charge heterogeneity found in a purified monoclonal IgG1 antibody, MMA383. METHODS: Cation exchange chromatography (CEX) and isoelectric focusing (IEF) were used to monitor charge heterogeneity. CEX in conjunction with carboxypeptidase B digests of the antibody was used to determine the contribution of C-terminal lysines to MMA383 charge heterogeneity. Potential chemical degradation sites were identified by peptide mapping of individual chains, with peptide identification by mass spectrometry (MALDI-TOF MS). Peptide sequencing was used to determine specific deamidation sites. Binding constants of predominant isoforms were compared by surface plasmon resonance (SPR). RESULTS: Extensive charge heterogeneity of purified MMA383 was detected by CEX and IEF. Removal of C-terminal lysines simplified the IEF pattern to nine predominant isoforms. Quantitation of isoaspartate in each of the isoforms indicated deamidation of MMA383 as a major cause of charge heterogeneity. CEX of the individual isoform chains suggested the presence of one deamidation site on each of the heavy and light chains. The two sites of deamidation were identified using peptide mapping, sequencing and mass spectrometry. SPR results showed no significant difference in the binding parameters among the isoforms. CONCLUSIONS: C-terminal lysine microheterogeneity and deamidation of Asn141 in the heavy chain and Asn161 in the light chain are the major causes of MMA383 charge heterogeneity. Identification of the two deamidation sites will allow replacement of these amino acids in order to create a product less susceptible to degradation.

Antibodies, Monoclonal↗
PubMed2005

Investigating population heterogeneity with factor mixture models.

Sources of population heterogeneity may or may not be observed. If the sources of heterogeneity are observed (e.g., gender), the sample can be split into groups and the data analyzed with methods for multiple groups. If the sources of population heterogeneity are unobserved, the data can be analyzed with latent class models. Factor mixture models are a combination of latent class and common factor models and can be used to explore unobserved population heterogeneity. Observed sources of heterogeneity can be included as covariates. The different ways to incorporate covariates correspond to different conceptual interpretations. These are discussed in detail. Characteristics of factor mixture modeling are described in comparison to other methods designed for data stemming from heterogeneous populations. A step-by-step analysis of a subset of data from the Longitudinal Survey of American Youth illustrates how factor mixture models can be applied in an exploratory fashion to data collected at a single time point.

Child↗