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PubMed1993

Heterogeneity testing for Alzheimer's disease within and between data sets.

We examined the three Alzheimer's disease (AD) family data sets for heterogeneity. Four markers that were represented in all three data sets were selected for analysis. Markers BCL3/EcoR-Mlu and D19S13/TaqI were chosen for chromosome 19 and D21S13/TaqI and D21S16/XbaI for chromosome 21. Homogeneity testing was performed on the data by use of Morton's pre-divided samples test (PS-test) and Smith's admixture test (A-test). The C-test of MacLean et al. [1992] was also used to test for linkage in the presence of heterogeneity. Assuming homogeneity, there was significant evidence of linkage to AD for BCL3, D19S13, D21S16 in the Duke data set and D19S13, D21S16 in the Boston data set. C-tests also provided evidence of linkage for BCL3 and D21S13 in the Duke data set, and D21S16 in the Boston data set. No evidence for heterogeneity within the data sets was found for any of the four markers using either the A-test or the C-test. For marker BCL3, PS-tests found evidence of heterogeneity between the three data sets and between early-versus late-onset families combined over all data sets.

Aged↗
PubMed1993

A bootstrap approach to estimating power for linkage heterogeneity.

We examined the power of detecting linkage heterogeneity when the null hypothesis is that all families are linked to one locus (A) and the two alternative hypotheses are either 1) a proportion of the families are linked to locus A and the remaining families are linked to a second locus B or 2) a proportion of the families are linked to locus A or B and a third proportion of the families are unlinked to either locus. The power of detecting linkage heterogeneity is estimated for various proportions of families linked to loci A, B or unlinked to either locus (sampling under the alternative hypothesis). To estimate the significance level, the data set is sampled under the null hypothesis. For sampling under both hypotheses, a bootstrap approach is employed, sampling the simulated pedigrees with replacement. The power to detect linkage heterogeneity is strongest when the recombination fraction is 0 and equal proportions of the families are linked to loci A and B. The power decreases as the recombination fraction increases, the proportion of unlinked families increases and the disparity between the proportion of the families linked to either locus A or B increases. In the data set of 32 Duke Familial Alzheimer Disease families, when equal proportions of families are linked to loci A and B, the power to detect linkage heterogeneity is 0.94 using a likelihood ratio criterion of 10:1. The p value that corresponds to the likelihood ratio of 10:1 is estimated as 0.013 with a 95% confidence interval for p ranging from 0.012 to 0.014.

Aged↗
PubMed2006

Cellular mitochondrial heterogeneity in cultured astrocytes as demonstrated by immunogold labeling of alpha-ketoglutarate dehydrogenase.

In brain cells, various metabolites and metabolic pathways, largely of mitochondrial origin, have been shown to be compartmentalized. Attention has therefore been focused on the possible existence of mitochondrial heterogeneity in the brain at the cellular level. To determine whether mitochondria in cultured cortical and cerebellar astrocytes are heterogeneous at the single cell level, immunogold electron microscopy and an antibody against the alpha-ketoglutarate dehydrogenase component of the alpha-ketoglutarate dehydrogenase complex, a marker enzyme for the tricarboxylic acid (TCA) cycle, were employed. The number of gold particles was counted in the mitochondria of 36 and 42 cells from cultured cerebellar and cortical astrocytes, respectively. A test for random distribution (Poisson distribution) of mitochondria according to the number of gold particles was subsequently performed for every one of the 36 and 42 cells as the ratio variance/mean (= index of dispersion). This should be approximately distributed as chi2/degrees of freedom (df) = n - 1, n = number of mitochondria), if the observations obeyed a Poisson distribution. For 26 of the 36 (cerebellar astrocytes) distributions and for 28 of the 42 (cortical astrocytes) distributions a random distribution had to be rejected. These findings therefore strongly indicate that alpha-ketoglutarate dehydrogenase is heterogeneously distributed in mitochondria within individual astrocytes originating either from cerebellum or cerebral cortex. In conclusion, this study underlines the probability that mitochondrial heterogeneity at the single cell level might be extended to involve other metabolic pathways and metabolites.

Algorithms↗
PubMed2006

Income-related reporting heterogeneity in self-assessed health: evidence from France.

This paper tests for income-related reporting heterogeneity in self-assessed health (SAH). It also constructs a synthetic measure of clinical health to decompose the effect of income on SAH into an effect on clinical health (which is called a health production effect) and a reporting heterogeneity effect. We find health production effects essentially for low-income individuals, and reporting heterogeneity for the choice between the medium labels, i.e. 'fair' vs 'good' and for high-income individuals. As such, SAH should be used cautiously for the assessment of income-related health inequalities in France. It is however possible to minimize the reporting heterogeneity bias by converting SAH into a binary variable for poor health vs other health statuses.

Adult↗
PubMed2004

Distinguishing between heterogeneity and inefficiency: stochastic frontier analysis of the World Health Organization's panel data on national health care systems.

The most commonly used approaches to parametric (stochastic frontier) analysis of efficiency in panel data, notably the fixed and random effects models, fail to distinguish between cross individual heterogeneity and inefficiency. This blending of effects is particularly problematic in the World Health Organization's (WHO) panel data set on health care delivery, which is a 191 country, 5-year panel. The wide variation in cultural and economic characteristics of the worldwide sample produces a large amount of unmeasured heterogeneity in the data. This study examines several alternative approaches to stochastic frontier analysis with panel data, and applies some of them to the WHO data. A more general, flexible model and several measured indicators of cross country heterogeneity are added to the analysis done by previous researchers. Results suggest that there is considerable heterogeneity that has masqueraded as inefficiency in other studies using the same data.

Cultural Diversity↗
PubMed2001

Tumor heterogeneity in small hepatocellular carcinoma: analysis of tumor cell proliferation, expression and mutation of p53 AND beta-catenin.

Most hepatocellular carcinomas (HCCs) first occur as well-differentiated HCCs, from which poorly differentiated HCC cells develop because of dedifferentiation. In this study, we try to clarify the changes of dedifferentiation and cell proliferative activity and their relationship in small HCCs (less than 3.0 cm in diameter) and try to learn the mechanism of these changes by analysing the expressions and genetic changes of proliferation-related genes p53 and beta-catenin. Of 41 surgically resected small HCCs, 11 were identified to have tumor heterogeneity. DNA from the 11 small HCCs, consisting of 29 intratumoral lesions and 11 noncancerous liver tissues adjacent to HCCs, was extracted from paraffin embedded tissue sections. Exons 5-8 of p53 gene and exon 3 of beta-catenin gene were amplified by polymerase chain reaction and analyzed by direct sequence. The serial sections were also immunostained by anti-Ki-67, p53 and beta-catenin antibody. Immunohistochemistry showed that the p53 overexpression was significantly related to the proliferative activities as evaluated by Ki-67 immunostaining and to the histological differentiation. The expression of beta-catenin was found to be heterogeneously distributed not only in various histological grades of the same tumor but also in areas of the same histological grade. p53 and beta-catenin gene mutations were detected in 1 tumor respectively, both of which were second primary HCCs and also recurred later. The p53 mutation showed the same mutation pattern in heterogeneous subpopulations. beta-catenin mutation was detected only in the less differentiated lesion but not in the well-differentiated lesion of tumor. In conclusion, our findings suggest that there was histological heterogeneity in small but established HCC, which was accompanied by increased proliferative activity and p53 overexpression. The overexpression of beta-catenin may be related to the proliferative activity and dedifferentiation of HCC.

Aged↗
PubMed1980

The generation of tumor heterogeneity in vivo.

In order to determine whether host factors may contribute to the generation of tumor heterogeneity, the phenotypic stability of cells from a cloned tumor was examined during proliferation in tissue culture and in the syngeneic host. Growth of this cloned tumor was initiated both in vivo and in vitro, and the tumor populations were sampled at different time intervals by subcloning. The susceptibility of these tumor subclones to the cytotoxic action of natural antibodies and complement was used as a marker of their membrane phenotype. The extent of phenotypic variation of the clones in one sample was considered to be a measure of tumor heterogeneity. Following these procedures, we observed that a clone of the L5178Y murine lymphoma maintained its homogeneity during 5 months of in vitro culture. In contrast, a single passage of the same tumor clone for 3 1/2 weeks or 3 months in the syngeneic host resulted in the generation of a population of cells exhibiting a significant increase in heterogeneity. This relative instability of tumor phenotype in vivo suggests that the host milieu may allow the generation of tumor heterogeneity. Genetic or epigenetic mechanism(s) may be involved although the high frequency of new phenotypes argues against a role for somatic mutation.

Animals↗
PubMed1991

Heterogeneity for integrin expression and cytokine-mediated VLA modulation can influence the adhesion of human melanoma cells to extracellular matrix proteins.

Expression of alpha and beta subunits of VLA and VNR integrins was analyzed by cytofluorimetric analysis on 6 different human primary and metastatic melanoma cell cultures. Marked inter-tumor heterogeneity was observed, and expression of VLA-alpha I, VLA-alpha 2 and VLA-alpha 6 was lower on primary melanomas than on metastatic lesions. The function of VLA products on melanoma cells was assessed by adhesion assays to extracellular matrix (ECM) proteins using a panel of melanoma clones previously characterized for the presence and heterogeneity of expression of the distinct VLA-alpha subunits. These experiments indicated that intra-tumor heterogeneity in the integrin profile can influence the interaction of neoplastic cells with ECM proteins. Inhibition of adhesion with antibodies to VLA-alpha subunits revealed that the presence on melanoma cells of VLA-alpha 2, VLA-alpha 5 and VLA-alpha 6 is relevant for the adhesion to type-IV collagen, fibronectin and laminin respectively. Culture of tumor cells in the presence of cytokines such as rIL-I beta, rTNF-alpha, rIFN-gamma or TGF-beta I could induce up- or down-modulation in the level of expression of multiple VLA integrins. Cytokine-mediated antigenic shifts in the VLA profile of melanoma cells were detected by cytofluorimetric analysis as early as 24 hr after cytokine exposure. The cytokine-dependent change in the matrix receptor profile of melanoma cells also affected the adhesion to ECM proteins as revealed by the enhanced adhesion of rTNF-alpha-treated cells to fibronectin. These data indicate that constitutive heterogeneity in the integrin profile or cytokine-mediated shifts in VLA expression can affect the ability of human melanoma cells to interact with different ECM components.

Cell Adhesion↗
PubMed1993

Intracellular glutathione heterogeneity in L1210 murine leukemia sublines made resistant to DNA-interacting anti-neoplastic agents.

Intracellular glutathione (GSH) content was measured by flow cytometry using monochlorobimane (mBCl) and by the enzymatic assay in a set of 6 sublines of murine L1210 leukemia cells made resistant to DNA-interacting agents having distinct mechanisms of action: L-phenylalanine mustard (L-PAM), 1,3-bis(2-chloroethyl)-I-nitrosourea (BCNU), cisplatin (DDP), N-deformyl-N-(4-N,N-bis(2-chloroethylamino) benzoyl) distamycin A (FCE 24517), doxorubicin (DX) and 3'-deamino-3' (2-methoxy-4-morpholinyl)-doxorubicin (FCE 23762). A significant correlation was demonstrated between the mean intracellular mBCl fluorescence values measured by flow cytometry and levels of GSH measured by the classical enzymatic assay, despite the possible influence of glutathione-S-transferases and of other thiols on the mBCl fluorescence. Although less specific, the flow cytometric method is more informative than the enzymatic assay, allowing detection of fluorescence distributions, which we proved to be characteristic of each subline. In order to assess a procedure enabling a quantitative analysis to be made of intercellular GSH heterogeneity, we propose the use of appropriate thresholds and parameters of the mBCl flow cytometric distribution. By use of this analysis procedure, distinct types of alterations, with respect to the heterogeneity distribution of the parental L1210 cell line, have been evidenced in resistant cells. A uniform increase in mBCl fluorescence was observed among cells of the sublines resistant to L-PAM and FCE-24517. The mean mBCl fluorescence increase in sublines resistant to DX and DDP was due to a higher number of cells with fairly high mBCl fluorescence, but still within the range spanned by the parental cell line. A less heterogeneous mBCl fluorescence distribution was found in the L1210 subline resistant to FCE 23762, which was, however, similar to a cloned sensitive line. Though GSH was linked to the principal cause of drug resistance only in the L-PAM-resistant cell line, alterations in heterogeneity, as detected by mBCl fluorescence distributions, were found in 5 out of 6 resistant lines.

Animals↗
PubMed1994

A repertoire of monoclonal antibodies reveals extensive epitope heterogeneity in CEA purified from neoplasms originating from different organs.

The heterogeneity of carcinoembryonic antigen (CEA) from 5 individual hepatic metastases of tumours originating in different organs (1 colon, 1 stomach and 3 breast adenocarcinomas) was analyzed with a repertoire of 56 alpha CEA murine MAbs. In each tumour preparation, the MAbs disclosed 2 distinct molecular species displaying remarkable variability in their apparent molecular weights (e.g. 130-170 kDa for the fast-migrating CEA variant and 180-260 kDa for the slowly-migrating one). After chemical deglycosylation this heterogeneity was abolished and 2 main proteins of 84 and 64 kDa were generated; the difference in their molecular weights could not be accounted for by differential glycosylation. Although 3 of the analyzed preparations were derived from individual adenocarcinomas of the breast, the glycosylated molecules differed considerably from one another, in their relative molecular mass. The MAbs used showed essentially 3 different recognition patterns according to their reactivity either with both CEA molecular weight variants, or just with the higher or the lower one. In a quantitative comparison of the immunoprecipitation yields of the MAbs with CEA, considerable immunological variability (ranging up to 26-fold), as well as preferential expression of CEA epitopes, could be demonstrated among the 5 different preparations. Here again no uniform epitope presentation could be observed among the 3 breast tumours thus far tested. Comparison of the precipitation yields with the glycosylated and deglycosylated CEA species revealed that, whereas the CEA antigenic heterogeneity remained in some cases unchanged, most of the MAbs exhibited, in carbohydrate-free CEA, the appearance of a new heterogeneity.

Adenocarcinoma↗
PubMed1992

Heterogeneity in the mobilization of cytoplasmic calcium by human polymorphonuclear leukocytes in response to fMLP, C5a and IL-8/NAP-1.

The visible excitation and emission wave-lengths of the recently developed fluorescent Ca2+ indicator fluo-3 permit analysis of the intracellular Ca2+ concentration, [Ca2+]i, in flow cytometry with a 488-nm argon laser. The role of [Ca2+]i in human polymorphonuclear leukocyte heterogeneity was investigated in response to formyl-methionyl-leucyl-phenylalanine (fMLP), C5a, and interleukin 8/neutrophil attractant/activation protein 1 (IL-8/NAP-1) by flow cytometry. The [Ca2+]i changes in different subpopulations within a heterogeneous cell suspension were resolved upon stimulation with fMLP. Using an anti-CD16 phycoerythrin-conjugated antibody and fluo-3 simultaneously, neutrophils affected and nonaffected in Ca2+ mobilization were distinguished in two patients suffering from glycogen storage disease type 1b. In normal neutrophils, a different time course of Ca2+ mobilization of neutrophil subpopulations immediately after stimulation with fMLP was detected. In addition, after stimulation with a low concentration of IL-8/NAP-1 (10(-10) M) two subsets of neutrophils appeared; one of them showed an increase in [Ca2+]i, while the other did not. These results indicate heterogeneity in the neutrophil signal transduction process involved in Ca2+ mobilization. Therefore, flow cytometric analyses can resolve changes in single-cell [Ca2+]i distribution patterns, which is important for the understanding of [Ca2+]i in neutrophil heterogeneous activation processes.

Aniline Compounds↗
PubMed1997

Development, significance, and heterogeneity of mast cells with particular regard to the mast cell-specific proteases chymase and tryptase.

Mast cells are one of the major effector cells in the pathogenesis of the immediate-type hypersensitivity reaction in a number of non-allergic immune disorders as well as in normal physiological processes. In addition, it has been shown recently that mast cells also play a significant role in a life-saving host response to bacterial reactions. But as much as the immunopathological role of mast cells has been acknowledged, these cells have also aroused much controversy and confusion. By now it is clear that one explanation for the sometimes even contradictory opinions on mast cell function arise from mast cell heterogeneity. This heterogeneity can express itself as differences in histochemical, biochemical, and functional characteristics. In vitro systems provided a powerful tool for the investigation of the basic mechanisms for mast cell development and differentiation and helped to demonstrate that mast cell heterogeneity can be traced back to certain cytokine patterns that are present in different microenvironments. In this context it has also been shown that the growth factors required for human mast cell differentiation are somewhat different than those for rodents. In rodents, the atypical, T cell-dependent mucosal type mast cell can be distinguished from the T cell-independent connective tissue-type mast cell. In humans, the strict classification into mucosal and connective tissue-type mast cells is not possible and the content of mast cell-specific proteases chymase and tryptase is the main criterion for mast cell subtypes in humans. The large quantities of tryptase and chymase that are synthesized by mast cells suggest and emphasize the significance of these proteinases in mast cell function and stimulated investigations about the biological properties of these mast cell-specific proteases. Comparing their biological activities it becomes clear that they share some activities. On the other hand, tryptase seems to participate in proinflammatory mast cell function, whereas chymase seems to be more involved in inflammatory reactions. This review provides a short overview of the discovery, origin, development, and biological significance of mast cells and will then concentrate on mast cell heterogeneity in rodents and humans with respect to the mast cell proteases tryptase and chymase and their function.

Animals↗
PubMed2006

Spatial and spectral heterogeneity of time-varying shear stress profiles in the carotid bifurcation by phase-contrast MRI.

PURPOSE: To determine the heterogeneity of the time-varying shear stress profiles in the human carotid bifurcation, a region prone to atherosclerosis. MATERIALS AND METHODS: Lagrangian bicubic interpolation of phase-contrast MRI images was used to determine the shear stress profiles for three adult healthy male volunteers. Frequency spectra for the common and internal carotid artery (CCA and ICA, respectively)-derived shear stresses were examined in order to determine the presence of significant heterogeneity in the intensity distribution. RESULTS: Hemodynamic characteristics (peak, minimum, average shear stress, and oscillatory shear index [OSI]) were highly heterogeneous both along the length of the vessel as well as circumferentially around the CCA and ICA. In the frequency domain, intensities below 4 Hz were significantly higher in the CCA compared to the sinus region of the ICA, indicating that shear stress heterogeneity can be detected in the frequency domain. The harmonic index, a measure of the relative contributions of dynamic and static components of the shear stress signal, colocalizes with OSI, which implies a relationship between specific frequency components and atherosclerosis development. CONCLUSION: These findings indicate that the time and frequency dependent parameters of in vivo shear stress have important implications for regional development of atherosclerosis.

Adult↗
PubMed1993

Heterogeneity in early and advanced gastric carcinomas by flow cytometric DNA analysis.

We investigated 230 systematically sampled fresh specimens from 12 early and 26 advanced gastric cancer patients by DNA flow cytometry for heterogeneity in DNA content. Fifty-eight percent of the 12 early gastric cancers were uniformly diploid and 42% were uniformly aneuploid. Fifty-four percent of advanced cancers were uniformly diploid in superficial layers and 42% were uniformly diploid in deep layers, whereas 46% were uniformly aneuploid in superficial layers, and 50% were uniformly aneuploid and 8% were heterogeneously aneuploid and diploid in deep layers. Both diploid and aneuploid samples were obtained from 15% for advanced cancers, but ploidy heterogeneity did not occur in early cancers. Heterogeneity for DNA index (more than one aneuploid DNA index) occurred in 46% of whole thickness of advanced cancers, in 19% of superficial layers of advanced cancers, and in 8% of early cancers. We concluded that DNA ploidy determination using superficial layer specimens may be reliable in early gastric cancer but must be interpreted with care in advanced cancer.

Aneuploidy↗
PubMed2006

Water diffusion heterogeneity index in the human brain is insensitive to the orientation of applied magnetic field gradients.

The alpha diffusion-weighted imaging (DWI) method was developed to study heterogeneous water diffusion in the human brain using magnetic resonance imaging (MRI). An advantage of this model is that it does not require an assumption about the shape of the intravoxel distribution of apparent diffusion rates, and it has a calculable relationship to this distribution. The alpha-DWI technique is useful for detecting microstructural tissue changes associated with brain tumor invasion, and may be useful for directing therapy to invading tumor cells. In previous work, alpha-DWI was performed with magnetic field gradients applied along a single direction in order to avoid artificially introducing a source of heterogeneity to the decay. However, it is known that restricted diffusion is anisotropic in the brain, and the alpha-DWI method must take this into account to be complete. In this work the relationship between the applied magnetic field gradients and the fitted stretched-exponential model parameters was studied in the human brain. It was found the distributed diffusion coefficient (DDC) varies with the direction of applied gradients, while the heterogeneity index alpha is relatively direction-insensitive. It is proposed that in clinical use, maps of alpha can be created using diffusion-weighting gradients applied in a single direction that reflect the tissue heterogeneity.

Algorithms↗
PubMed1995

DNA heterogeneity determined by flow cytometry in prostatic adenocarcinoma--necessitating multiple site analysis.

Although DNA ploidy analysis of prostate cancer is generally associated with grade, stage, clinical outcome, and responsiveness to androgen therapy, one possible reason cited for contrary reports may be tumor heterogeneity. A preliminary report using flow cytometric analysis of punch biopsies demonstrated DNA heterogeneity in five of nine patients. We evaluated 75 patients by cutting whole mounts of formalin fixed prostatectomy tissue every 0.6 cm. All malignant areas and a selected normal area were circumscribed, excised, remounted, and 1-3 50 mu thick sections removed. The nuclei were extracted by a Hedley technique and the DNA stained with propidium iodide. Each whole mount had an average of 1 distinct malignant area (range of 1-6 areas per whole mount block). Nuclei were analyzed on a Becton Dickinson (San Jose, CA) FACScan flow cytometer equipped with RFIT DNA software program. After excluding histograms with CVs > 8.0% and/or "suspicious" diploid histograms having a right "shoulder," 75 or 87 patients still had > or = 2 malignant sites available for analysis (average 4, range 2-9 malignant sites/patient). The 322 histograms had an average CV of 4.4%. Thirty of 75 patients (40%) showed DNA heterogeneity in multiple samples taken from the same prostate. There were 37 prostates with only diploid (D), 1 with only tetraploid (T), 7 with only aneuploid (A), 20 with D plus A, 7 with D plus T, 2 with D plus T plus A, and 1 with a D plus suspected hypodiploid DNA content. Exclusion of the tetraploid and "near diploid aneuploid" cases still resulted in 16% (12/75) of the patients having a diploid versus aneuploid DNA content heterogeneity. Because 40% of the prostates contained a different ploidy depending on which area was sampled, this report suggests multiple sites of malignancy must be analyzed to more accurately assess the ploidy status of prostatic adenocarcinoma.

Adenocarcinoma↗
PubMed2006

Folding pathway dependence on energetic frustration and interaction heterogeneity for a three-dimensional hydrophobic protein model.

Monte Carlo simulations of a hydrophobic protein model of 40 monomers in the cubic lattice are used to explore the effect of energetic frustration and interaction heterogeneity on its folding pathway. The folding pathway is described by the dependence of relevant conformational averages on an appropriate reaction coordinate, pfold, defined as the probability for a given conformation to reach the native structure before unfolding. We compare the energetically frustrated and heterogeneous hydrophobic potential, according to which individual monomers have a higher or lower tendency to form contacts unspecifically depending on their hydrophobicities, to an unfrustrated homogeneous Go-type potential with uniformly attractive native interactions and neutral non-native interactions (called Go1 in this study), and to an unfrustrated heterogeneous potential with neutral non-native interactions and native interactions having the same energy as the hydrophobic potential (called Go2 in this study). Folding kinetics are slowed down dramatically when energetic frustration increases, as expected and previously observed in a two-dimensional model. Contrary to our previous results in two dimensions, however, it appears that the folding pathway and transition state ensemble can be significantly dependent on the energy function used to stabilize the native structure. The sequence of events along the reaction coordinate, or the order along this coordinate in which different regions of the native conformation become structured, turns out to be similar for the hydrophobic and Go2 potentials, but with analogous events tending to occur at lower pfold values in the first case. In particular, the transition state obtained from the ensemble around pfold = 0.5 is more structured for the hydrophobic potential. For Go1, not only the transition state ensemble but the order of events itself is modified, suggesting that interaction heterogeneity, in addition to energetic frustration, can have significant effects on the folding mechanism, most likely by modifying the probability of different contacts in the unfolded state, the starting point for the folding reaction. Although based on a simple model, these results provide interesting insight into how sequence-dependent switching between folding pathways might occur in real proteins.

Kinetics↗
PubMed2000

Fast subsystem bifurcations in strongly coupled heterogeneous collections of excitable cells.

A continuum model for a heterogeneous collection of excitable cells electrically coupled through gap junctions is introduced and analysed using spatial averaging, asymptotic and numerical techniques. Heterogeneity is modelled by imposing a spatial dependence on parameters which define the single cell model and a diffusion term is used to model the gap junction coupling. For different parameter values, single cell models can exhibit bursting, beating and a myriad of other complex oscillations. A procedure for finding asymptotic estimates of the thresholds between these (synchronous) behaviors in the cellular aggregates is described for the heterogeneous case where the coupling strength is strong. This procedure is tested on a model of a strongly coupled heterogeneous collection of bursting and beating cells. Since isolated pancreatic beta-cells have been observed to both burst and beat, this test of the spatial averaging techniques provides a possible explanation to measured discrepancies between the electrical activities of isolated beta-cells and coupled collections (islets) of beta-cells.

Computer Simulation↗