Publications

2009
Kraft P, Raychaudhuri S. Complex diseases, complex genes: keeping pathways on the right track [Internet]. Epidemiology 2009;20(4):508-11. Publisher's Version
Raychaudhuri S, Plenge RM, Rossin EJ, Ng ACY, Ng ACY, Purcell SM, Sklar P, Scolnick EM, Xavier RJ, Altshuler D, Daly MJ. Identifying relationships among genomic disease regions: predicting genes at pathogenic SNP associations and rare deletions [Internet]. PLoS Genet 2009;5(6):e1000534. Publisher's VersionAbstract
Translating a set of disease regions into insight about pathogenic mechanisms requires not only the ability to identify the key disease genes within them, but also the biological relationships among those key genes. Here we describe a statistical method, Gene Relationships Among Implicated Loci (GRAIL), that takes a list of disease regions and automatically assesses the degree of relatedness of implicated genes using 250,000 PubMed abstracts. We first evaluated GRAIL by assessing its ability to identify subsets of highly related genes in common pathways from validated lipid and height SNP associations from recent genome-wide studies. We then tested GRAIL, by assessing its ability to separate true disease regions from many false positive disease regions in two separate practical applications in human genetics. First, we took 74 nominally associated Crohn's disease SNPs and applied GRAIL to identify a subset of 13 SNPs with highly related genes. Of these, ten convincingly validated in follow-up genotyping; genotyping results for the remaining three were inconclusive. Next, we applied GRAIL to 165 rare deletion events seen in schizophrenia cases (less than one-third of which are contributing to disease risk). We demonstrate that GRAIL is able to identify a subset of 16 deletions containing highly related genes; many of these genes are expressed in the central nervous system and play a role in neuronal synapses. GRAIL offers a statistically robust approach to identifying functionally related genes from across multiple disease regions--that likely represent key disease pathways. An online version of this method is available for public use (http://www.broad.mit.edu/mpg/grail/).
Kong A, Steinthorsdottir V, Masson G, Thorleifsson G, Sulem P, Besenbacher S, Jonasdottir A, Sigurdsson A, Kristinsson KT, Jonasdottir A, Frigge ML, Gylfason A, Olason PI, Gudjonsson SA, Sverrisson S, Stacey SN, Sigurgeirsson B, Benediktsdottir KR, Sigurdsson H, Jonsson T, Benediktsson R, Olafsson JH, Johannsson OT, Hreidarsson AB, Sigurdsson G, Sigurdsson G, Ferguson-Smith AC, Gudbjartsson DF, Thorsteinsdottir U, Stefansson K. Parental origin of sequence variants associated with complex diseases [Internet]. Nature 2009;462(7275):868-74. Publisher's VersionAbstract
Effects of susceptibility variants may depend on from which parent they are inherited. Although many associations between sequence variants and human traits have been discovered through genome-wide associations, the impact of parental origin has largely been ignored. Here we show that for 38,167 Icelanders genotyped using single nucleotide polymorphism (SNP) chips, the parental origin of most alleles can be determined. For this we used a combination of genealogy and long-range phasing. We then focused on SNPs that associate with diseases and are within 500 kilobases of known imprinted genes. Seven independent SNP associations were examined. Five-one with breast cancer, one with basal-cell carcinoma and three with type 2 diabetes-have parental-origin-specific associations. These variants are located in two genomic regions, 11p15 and 7q32, each harbouring a cluster of imprinted genes. Furthermore, we observed a novel association between the SNP rs2334499 at 11p15 and type 2 diabetes. Here the allele that confers risk when paternally inherited is protective when maternally transmitted. We identified a differentially methylated CTCF-binding site at 11p15 and demonstrated correlation of rs2334499 with decreased methylation of that site.
Lee YC, Raychaudhuri S, Cui J, De Vivo I, Ding B, Alfredsson L, Padyukov L, Costenbader KH, Seielstad M, Graham RR, Klareskog L, Gregersen PK, Plenge RM, Karlson EW. The PRL -1149 G/T polymorphism and rheumatoid arthritis susceptibility. Arthritis Rheum 2009;60(5):1250-4.Abstract
OBJECTIVE: Previous studies have demonstrated that the PRL -1149 T (minor) allele decreases prolactin expression and may be associated with autoimmune disease. The aim of this study was to determine the role of the PRL -1149 G/T polymorphism (rs1341239) in rheumatoid arthritis (RA) susceptibility. METHODS: We examined the association between PRL -1149 G/T and RA risk in 4 separate study populations, consisting of a total of 3,405 RA cases and 4,111 controls of self-reported white European ancestry. Samples were genotyped using 1 of 3 genotyping platforms, and strict quality control metrics were applied. We tested for association using a 2-tailed Cochran-Mantel-Haenszel additive, fixed-effects model. RESULTS: In the individual populations, odds ratios (ORs) for an association between PRL -1149 T and RA risk ranged from 0.80 to 0.97. In a joint meta-analysis across all 4 populations, the OR for an association between PRL -1149 T and RA risk was 0.90 (95% confidence interval 0.84-0.96, P=0.001). CONCLUSION: Our findings indicate a possible association between the PRL -1149 T allele and decreased RA risk. The effect size is small but similar to ORs for other genetic polymorphisms associated with complex traits, including RA.
Raychaudhuri S, Thomson BP, Remmers EF, Eyre S, Hinks A, Guiducci C, Catanese JJ, Xie G, Stahl EA, Chen R, Alfredsson L, Amos CI, Ardlie KG, Ardlie KG, Barton A, Bowes J, Burtt NP, Chang M, Coblyn J, Costenbader KH, Criswell LA, Crusius BJA, Cui J, De Jager PL, Ding B, Emery P, Flynn E, Harrison P, Hocking LJ, Huizinga TWJ, Kastner DL, Ke X, Kurreeman FAS, Lee AT, Liu X, Li Y, Martin P, Morgan AW, Padyukov L, Reid DM, Seielstad M, Seldin MF, Shadick NA, Steer S, Tak PP, Thomson W, van der Helm-van Mil AHM, van der Horst-Bruinsma IE, Weinblatt ME, Wilson AG, Wolbink GJ, Wordsworth P, Wordsworth P, Altshuler D, Karlson EW, Toes REM, de Vries N, Begovich AB, Siminovitch KA, Worthington J, Klareskog L, Gregersen PK, Daly MJ, Plenge RM. Genetic variants at CD28, PRDM1 and CD2/CD58 are associated with rheumatoid arthritis risk [Internet]. Nat Genet 2009;41(12):1313-8. Publisher's VersionAbstract
To discover new rheumatoid arthritis (RA) risk loci, we systematically examined 370 SNPs from 179 independent loci with P < 0.001 in a published meta-analysis of RA genome-wide association studies (GWAS) of 3,393 cases and 12,462 controls. We used Gene Relationships Across Implicated Loci (GRAIL), a computational method that applies statistical text mining to PubMed abstracts, to score these 179 loci for functional relationships to genes in 16 established RA disease loci. We identified 22 loci with a significant degree of functional connectivity. We genotyped 22 representative SNPs in an independent set of 7,957 cases and 11,958 matched controls. Three were convincingly validated: CD2-CD58 (rs11586238, P = 1 x 10(-6) replication, P = 1 x 10(-9) overall), CD28 (rs1980422, P = 5 x 10(-6) replication, P = 1 x 10(-9) overall) and PRDM1 (rs548234, P = 1 x 10(-5) replication, P = 2 x 10(-8) overall). An additional four were replicated (P < 0.0023): TAGAP (rs394581, P = 0.0002 replication, P = 4 x 10(-7) overall), PTPRC (rs10919563, P = 0.0003 replication, P = 7 x 10(-7) overall), TRAF6-RAG1 (rs540386, P = 0.0008 replication, P = 4 x 10(-6) overall) and FCGR2A (rs12746613, P = 0.0022 replication, P = 2 x 10(-5) overall). Many of these loci are also associated to other immunologic diseases.
De Jager PL, Jia X, Wang J, de Bakker PIW, Ottoboni L, Aggarwal NT, Piccio L, Raychaudhuri S, Tran D, Aubin C, Briskin R, Romano S, Romano S, Baranzini SE, McCauley JL, Pericak-Vance MA, Haines JL, Gibson RA, Naeglin Y, Uitdehaag B, Matthews PM, Kappos L, Polman C, McArdle WL, Strachan DP, Evans D, Cross AH, Daly MJ, Compston A, Sawcer SJ, Weiner HL, Hauser SL, Hafler DA, Oksenberg JR. Meta-analysis of genome scans and replication identify CD6, IRF8 and TNFRSF1A as new multiple sclerosis susceptibility loci [Internet]. Nat Genet 2009;41(7):776-82. Publisher's VersionAbstract
We report the results of a meta-analysis of genome-wide association scans for multiple sclerosis (MS) susceptibility that includes 2,624 subjects with MS and 7,220 control subjects. Replication in an independent set of 2,215 subjects with MS and 2,116 control subjects validates new MS susceptibility loci at TNFRSF1A (combined P = 1.59 x 10(-11)), IRF8 (P = 3.73 x 10(-9)) and CD6 (P = 3.79 x 10(-9)). TNFRSF1A harbors two independent susceptibility alleles: rs1800693 is a common variant with modest effect (odds ratio = 1.2), whereas rs4149584 is a nonsynonymous coding polymorphism of low frequency but with stronger effect (allele frequency = 0.02; odds ratio = 1.6). We also report that the susceptibility allele near IRF8, which encodes a transcription factor known to function in type I interferon signaling, is associated with higher mRNA expression of interferon-response pathway genes in subjects with MS.
2008
Raychaudhuri S, Remmers EF, Lee AT, Hackett R, Guiducci C, Burtt NP, Gianniny L, Korman BD, Padyukov L, Kurreeman FAS, Chang M, Catanese JJ, Ding B, Wong S, van der Helm-van Mil AHM, Neale BM, Coblyn J, Cui J, Tak PP, Wolbink GJ, Crusius BJA, van der Horst-Bruinsma IE, Criswell LA, Amos CI, Seldin MF, Kastner DL, Ardlie KG, Alfredsson L, Costenbader KH, Altshuler D, Huizinga TWJ, Shadick NA, Weinblatt ME, de Vries N, Worthington J, Seielstad M, Toes REM, Karlson EW, Begovich AB, Klareskog L, Gregersen PK, Daly MJ, Plenge RM. Common variants at CD40 and other loci confer risk of rheumatoid arthritis [Internet]. Nat Genet 2008;40(10):1216-23. Publisher's VersionAbstract
To identify rheumatoid arthritis risk loci in European populations, we conducted a meta-analysis of two published genome-wide association (GWA) studies totaling 3,393 cases and 12,462 controls. We genotyped 31 top-ranked SNPs not previously associated with rheumatoid arthritis in an independent replication of 3,929 autoantibody-positive rheumatoid arthritis cases and 5,807 matched controls from eight separate collections. We identified a common variant at the CD40 gene locus (rs4810485, P = 0.0032 replication, P = 8.2 x 10(-9) overall, OR = 0.87). Along with other associations near TRAF1 (refs. 2,3) and TNFAIP3 (refs. 4,5), this implies a central role for the CD40 signaling pathway in rheumatoid arthritis pathogenesis. We also identified association at the CCL21 gene locus (rs2812378, P = 0.00097 replication, P = 2.8 x 10(-7) overall), a gene involved in lymphocyte trafficking. Finally, we identified evidence of association at four additional gene loci: MMEL1-TNFRSF14 (rs3890745, P = 0.0035 replication, P = 1.1 x 10(-7) overall), CDK6 (rs42041, P = 0.010 replication, P = 4.0 x 10(-6) overall), PRKCQ (rs4750316, P = 0.0078 replication, P = 4.4 x 10(-6) overall), and KIF5A-PIP4K2C (rs1678542, P = 0.0026 replication, P = 8.8 x 10(-8) overall).
de Bakker PIW, Ferreira MAR, Jia X, Neale BM, Raychaudhuri S, Voight BF. Practical aspects of imputation-driven meta-analysis of genome-wide association studies [Internet]. Hum Mol Genet 2008;17(R2):R122-8. Publisher's VersionAbstract
Motivated by the overwhelming success of genome-wide association studies, droves of researchers are working vigorously to exchange and to combine genetic data to expediently discover genetic risk factors for common human traits. The primary tools that fuel these new efforts are imputation, allowing researchers who have collected data on a diversity of genotype platforms to share data in a uniformly exchangeable format, and meta-analysis for pooling statistical support for a genotype-phenotype association. As many groups are forming collaborations to engage in these efforts, this review collects a series of guidelines, practical detail and learned experiences from a variety of individuals who have contributed to the subject.
2003
Raychaudhuri S, Chang JT, Imam F, Altman RB. The computational analysis of scientific literature to define and recognize gene expression clusters [Internet]. Nucleic Acids Res 2003;31(15):4553-60. Publisher's VersionAbstract
A limitation of many gene expression analytic approaches is that they do not incorporate comprehensive background knowledge about the genes into the analysis. We present a computational method that leverages the peer-reviewed literature in the automatic analysis of gene expression data sets. Including the literature in the analysis of gene expression data offers an opportunity to incorporate functional information about the genes when defining expression clusters. We have created a method that associates gene expression profiles with known biological functions. Our method has two steps. First, we apply hierarchical clustering to the given gene expression data set. Secondly, we use text from abstracts about genes to (i) resolve hierarchical cluster boundaries to optimize the functional coherence of the clusters and (ii) recognize those clusters that are most functionally coherent. In the case where a gene has not been investigated and therefore lacks primary literature, articles about well-studied homologous genes are added as references. We apply our method to two large gene expression data sets with different properties. The first contains measurements for a subset of well-studied Saccharomyces cerevisiae genes with multiple literature references, and the second contains newly discovered genes in Drosophila melanogaster; many have no literature references at all. In both cases, we are able to rapidly define and identify the biologically relevant gene expression profiles without manual intervention. In both cases, we identified novel clusters that were not noted by the original investigators.
Raychaudhuri S, Altman RB. A literature-based method for assessing the functional coherence of a gene group [Internet]. Bioinformatics 2003;19(3):396-401. Publisher's VersionAbstract
MOTIVATION: Many experimental and algorithmic approaches in biology generate groups of genes that need to be examined for related functional properties. For example, gene expression profiles are frequently organized into clusters of genes that may share functional properties. We evaluate a method, neighbor divergence per gene (NDPG), that uses scientific literature to assess whether a group of genes are functionally related. The method requires only a corpus of documents and an index connecting the documents to genes. RESULTS: We evaluate NDPG on 2796 functional groups generated by the Gene Ontology consortium in four organisms: mouse, fly, worm and yeast. NDPG finds functional coherence in 96, 92, 82 and 45% of the groups (at 99.9% specificity) in yeast, mouse, fly and worm respectively.
2002
Raychaudhuri S, Chang JT, Sutphin PD, Altman RB. Associating genes with gene ontology codes using a maximum entropy analysis of biomedical literature [Internet]. Genome Res 2002;12(1):203-14. Publisher's VersionAbstract
Functional characterizations of thousands of gene products from many species are described in the published literature. These discussions are extremely valuable for characterizing the functions not only of these gene products, but also of their homologs in other organisms. The Gene Ontology (GO) is an effort to create a controlled terminology for labeling gene functions in a more precise, reliable, computer-readable manner. Currently, the best annotations of gene function with the GO are performed by highly trained biologists who read the literature and select appropriate codes. In this study, we explored the possibility that statistical natural language processing techniques can be used to assign GO codes. We compared three document classification methods (maximum entropy modeling, naïve Bayes classification, and nearest-neighbor classification) to the problem of associating a set of GO codes (for biological process) to literature abstracts and thus to the genes associated with the abstracts. We showed that maximum entropy modeling outperforms the other methods and achieves an accuracy of 72% when ascertaining the function discussed within an abstract. The maximum entropy method provides confidence measures that correlate well with performance. We conclude that statistical methods may be used to assign GO codes and may be useful for the difficult task of reassignment as terminology standards evolve over time.
Kivi M, Liu X, Raychaudhuri S, Altman RB, Small PM. Determining the genomic locations of repetitive DNA sequences with a whole-genome microarray: IS6110 in Mycobacterium tuberculosis [Internet]. J Clin Microbiol 2002;40(6):2192-8. Publisher's VersionAbstract
The mycobacterial insertion sequence IS6110 has been exploited extensively as a clonal marker in molecular epidemiologic studies of tuberculosis. In addition, it has been hypothesized that this element is an important driving force behind genotypic variability that may have phenotypic consequences. We present here a novel, DNA microarray-based methodology, designated SiteMapping, that simultaneously maps the locations and orientations of multiple copies of IS6110 within the genome. To investigate the sensitivity, accuracy, and limitations of the technique, it was applied to eight Mycobacterium tuberculosis strains for which complete or partial IS6110 insertion site information had been determined previously. SiteMapping correctly located 64% (38 of 59) of the IS6110 copies predicted by restriction fragment length polymorphism analysis. The technique is highly specific; 97% of the predicted insertion sites were true insertions. Eight previously unknown insertions were identified and confirmed by PCR or sequencing. The performance could be improved by modifications in the experimental protocol and in the approach to data analysis. SiteMapping has general applicability and demonstrates an expansion in the applications of microarrays that complements conventional approaches in the study of genome architecture.
Raychaudhuri S, Schütze H, Altman RB. Using text analysis to identify functionally coherent gene groups [Internet]. Genome Res 2002;12(10):1582-90. Publisher's VersionAbstract
The analysis of large-scale genomic information (such as sequence data or expression patterns) frequently involves grouping genes on the basis of common experimental features. Often, as with gene expression clustering, there are too many groups to easily identify the functionally relevant ones. One valuable source of information about gene function is the published literature. We present a method, neighbor divergence, for assessing whether the genes within a group share a common biological function based on their associated scientific literature. The method uses statistical natural language processing techniques to interpret biological text. It requires only a corpus of documents relevant to the genes being studied (e.g., all genes in an organism) and an index connecting the documents to appropriate genes. Given a group of genes, neighbor divergence assigns a numerical score indicating how "functionally coherent" the gene group is from the perspective of the published literature. We evaluate our method by testing its ability to distinguish 19 known functional gene groups from 1900 randomly assembled groups. Neighbor divergence achieves 79% sensitivity at 100% specificity, comparing favorably to other tested methods. We also apply neighbor divergence to previously published gene expression clusters to assess its ability to recognize gene groups that had been manually identified as representative of a common function.
2001
Raychaudhuri S, Sutphin PD, Chang JT, Altman RB. Basic microarray analysis: grouping and feature reduction [Internet]. Trends Biotechnol 2001;19(5):189-93. Publisher's VersionAbstract
DNA microarray technologies are useful for addressing a broad range of biological problems - including the measurement of mRNA expression levels in target cells. These studies typically produce large data sets that contain measurements on thousands of genes under hundreds of conditions. There is a critical need to summarize this data and to pick out the important details. The most common activities, therefore, are to group together microarray data and to reduce the number of features. Both of these activities can be done using only the raw microarray data (unsupervised methods) or using external information that provides labels for the microarray data (supervised methods). We briefly review supervised and unsupervised methods for grouping and reducing data in the context of a publicly available suite of tools called CLEAVER, and illustrate their application on a representative data set collected to study lymphoma.
Chang JT, Raychaudhuri S, Altman RB. Including biological literature improves homology search [Internet]. Pac Symp Biocomput 2001;:374-83. Publisher's VersionAbstract
Annotating the tremendous amount of sequence information being generated requires accurate automated methods for recognizing homology. Although sequence similarity is only one of many indicators of evolutionary homology, it is often the only one used. Here we find that supplementing sequence similarity with information from biomedical literature is successful in increasing the accuracy of homology search results. We modified the PSI-BLAST algorithm to use literature similarity in each iteration of its database search. The modified algorithm is evaluated and compared to standard PSI-BLAST in searching for homologous proteins. The performance of the modified algorithm achieved 32% recall with 95% precision, while the original one achieved 33% recall with 84% precision; the literature similarity requirement preserved the sensitive characteristic of the PSI-BLAST algorithm while improving the precision.
Altman RB, Raychaudhuri S. Whole-genome expression analysis: challenges beyond clustering [Internet]. Curr Opin Struct Biol 2001;11(3):340-7. Publisher's VersionAbstract
Measuring the expression of most or all of the genes in a biological system raises major analytic challenges. A wealth of recent reports uses microarray expression data to examine diverse biological phenomena - from basic processes in model organisms to complex aspects of human disease. After an initial flurry of methods for clustering the data on the basis of similarity, the field has recognized some longer-term challenges. Firstly, there are efforts to understand the sources of noise and variation in microarray experiments in order to increase the biological signal. Secondly, there are efforts to combine expression data with other sources of information to improve the range and quality of conclusions that can be drawn. Finally, techniques are now emerging to reconstruct networks of genetic interactions in order to create integrated and systematic models of biological systems.
2000
Raychaudhuri S, Stuart JM, Liu X, Small PM, Altman RB. Pattern recognition of genomic features with microarrays: site typing of Mycobacterium tuberculosis strains [Internet]. Proc Int Conf Intell Syst Mol Biol 2000;8:286-95. Publisher's VersionAbstract
Mycobacterium tuberculosis (M. tb.) strains differ in the number and locations of a transposon-like insertion sequence known as IS6110. Accurate detection of this sequence can be used as a fingerprint for individual strains, but can be difficult because of noisy data. In this paper, we propose a non-parametric discriminant analysis method for predicting the locations of the IS6110 sequence from microarray data. Polymerase chain reaction extension products generated from primers specific for the insertion sequence are hybridized to a microarray containing targets corresponding to each open reading frame in M. tb. To test for insertion sites, we use microarray intensity values extracted from small windows of contiguous open reading frames. Rank-transformation of spot intensities and first-order differences in local windows provide enough information to reliably determine the presence of an insertion sequence. The nonparametric approach outperforms all other methods tested in this study.
Raychaudhuri S, Stuart JM, Altman RB. Principal components analysis to summarize microarray experiments: application to sporulation time series [Internet]. Pac Symp Biocomput 2000;:455-66. Publisher's VersionAbstract
A series of microarray experiments produces observations of differential expression for thousands of genes across multiple conditions. It is often not clear whether a set of experiments are measuring fundamentally different gene expression states or are measuring similar states created through different mechanisms. It is useful, therefore, to define a core set of independent features for the expression states that allow them to be compared directly. Principal components analysis (PCA) is a statistical technique for determining the key variables in a multidimensional data set that explain the differences in the observations, and can be used to simplify the analysis and visualization of multidimensional data sets. We show that application of PCA to expression data (where the experimental conditions are the variables, and the gene expression measurements are the observations) allows us to summarize the ways in which gene responses vary under different conditions. Examination of the components also provides insight into the underlying factors that are measured in the experiments. We applied PCA to the publicly released yeast sporulation data set (Chu et al. 1998). In that work, 7 different measurements of gene expression were made over time. PCA on the time-points suggests that much of the observed variability in the experiment can be summarized in just 2 components--i.e. 2 variables capture most of the information. These components appear to represent (1) overall induction level and (2) change in induction level over time. We also examined the clusters proposed in the original paper, and show how they are manifested in principal component space. Our results are available on the internet at http:¿www.smi.stanford.edu/project/helix/PCArray .
1997
Raychaudhuri S, Younas F, Karplus PA, Faerman CH, Ripoll DR. Backbone makes a significant contribution to the electrostatics of alpha/beta-barrel proteins [Internet]. Protein Sci 1997;6(9):1849-57. Publisher's VersionAbstract
The electrostatic properties of seven alpha/beta-barrel enzymes selected from different evolutionary families were studied: triose phosphate isomerase, fructose-1,6-bisphosphate aldolase, pyruvate kinase, mandelate racemase, trimethylamine dehydrogenase, glycolate oxidase, and narbonin, a protein without any known enzymatic activity. The backbone of the alpha/beta-barrel has a distinct electrostatic field pattern, which is dipolar along the barrel axis. When the side chains are included in the calculations the general effect is to modulate the electrostatic pattern so that the electrostatic field is generally enhanced and is focused into a specific area near the active site. We use the electrostatic flux through a square surface near the active site to gauge the functionally relevant magnitude of the electrostatic field. The calculations reveal that in six out of the seven cases the backbone itself contributes greater than 45% of the total flux. The substantial electrostatic contribution of the backbone correlates with the known preference of alpha/beta-barrel enzymes for negatively charged substrates.
Van Liew HD, Raychaudhuri S. Stabilized bubbles in the body: pressure-radius relationships and the limits to stabilization [Internet]. J Appl Physiol (1985) 1997;82(6):2045-53. Publisher's VersionAbstract
We previously outlined the fundamental principles that govern behavior of stabilized bubbles, such as the microbubbles being put forward as ultrasound contrast agents. Our present goals are to develop the idea that there are limits to the stabilization and to provide a conceptual framework for comparison of bubbles stabilized by different mechanisms. Gases diffuse in or out of stabilized bubbles in a limited and reversible manner in response to changes in the environment, but strong growth influences will cause the bubbles to cross a threshold into uncontrolled growth. Also, bubbles stabilized by mechanical structures will be destroyed if outside influences bring them below a critical small size. The in vivo behavior of different kinds of stabilized bubbles can be compared by using plots of bubble radius as a function of forces that affect diffusion of gases in or out of the bubble. The two ends of the plot are the limits for unstabilized growth and destruction; these and the curve's slope predict the bubble's practical usefulness for ultrasonic imaging or O2 carriage to tissues.

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