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Intracellular space is demarcated into membraneless bodies and compartments via the process of liquid-liquid phase separation (LLPS). Phase separated condensates formed by proteins, RNA and/or other biomolecules are associated with many cellular functions including gene expression regulation. Here we describe how the genome organizer SATB1 utilizes its prion-like domains for LLPS. We have identified two SATB1 isoforms which display distinct biophysical behavior. We further showed how phosphorylation and interaction with nuclear RNA impact their phase transitions, leading to formation of aggregates when dysregulated. Moreover, we show that SATB1 is involved in the regulation of transcription and splicing, both of which displayed deregulation in Satb1 knockout murine thymocytes. Thus, the tight regulation of different SATB1 isoform expression levels, combined with protein post-translational modifications, are imperative for SATB1’s physiological roles in T cell development while their deregulation may be linked to disorders such as cancer.

The regulatory circuits that define developmental decisions of thymocytes are still incompletely resolved. SATB1 protein is predominantly expressed at the CD4+CD8+cell stage exerting its broad transcription regulation potential with both activatory and repressive roles. A series of post-translational modifications and the presence of potential SATB1 protein isoforms indicate the complexity of its regulatory potential. The most apparent mechanism of its involvement in gene expression regulation is via the orchestration of long-range chromatin loops between genes and their regulatory elements. Multiple SATB1 perturbations in mice uncovered a link to autoimmune diseases while clinical investigations on cancer research uncovered that SATB1 has a promoting role in several types of cancer and can be used as a prognostic biomarker. SATB1 is a multivalent tissue-specific factor with a broad and yet undetermined regulatory potential. Future investigations on this protein could further uncover T cell-specific regulatory pathways and link them to (patho)physiology.

SummaryMechanisms of tissue-specific gene expression regulation via spatial coordination of gene promoters and distal regulatory elements are still poorly understood. We investigated the 3D genome organization of developing murine T cells and identified SATB1, a tissue-specific genome organizer, enriched at the anchors of promoter-enhancer chromatin loops. We assessed the function of SATB1 in T cell chromatin organization and compared it to the conventional genome organizer CTCF. SATB1 builds a more refined layer of genome organization upon a CTCF scaffold. To understand the regulatory implications of SATB1 loopscape structure, we generatedSatb1fl/flCd4-Cre+(Satb1cKO) conditional knockout animals which suffered from autoimmunity. We aimed to identify molecular mechanisms responsible for the deregulation of the immune system inSatb1cKO animals. H3K27ac HiChIP and Hi-C experiments indicated that SATB1 primarily mediates promoter-enhancer loops affecting master regulator genes (such asBcl6), the T cell receptor locus and adhesion molecule genes, collectively being critical for cell lineage specification and immune system homeostasis. Our findings unravel the function of a tissue-specific factor that controls transcription programs, via spatial chromatin arrangements complementary to the chromatin structure imposed by ubiquitously expressed genome organizers.

microRNAs are of vital importance for the regulation of the adaptive and innate immune responses, modulating gene expression at the post transcriptional level. Although there is cumulative information regarding the steady state mature microRNA levels and their respective targets, little is known about the effect of the three-dimensional chromatin architecture on the transcriptional regulation of microRNA gene loci. Here, we sought to investigate the effect of subnuclear localization on the transcriptional activation of eight murine microRNA loci in the immune system. Our results show that microRNA genes display a preferential monoallelic gene expression profile accompanied with perinuclear localization irrespectively of their transcription status or differentiation state. The expression profile and perinuclear localization are developmentally conserved while microRNA gene loci localization outside constitutive lamin associated domains is cross-species conserved. Our findings provide support for an active nuclear periphery and its role in chromatin organization of the non-coding genome.

The infiltration and subsequent in situ subtype specification of monocytes to effector/inflammatory and repair macrophages is indispensable for tissue repair upon acute sterile injury. However, the chromatin-level mediators and regulatory events controlling this highly dynamic macrophage phenotype switch are not known. In this study, we used a murine acute muscle injury model to assess global chromatin accessibility and gene expression dynamics in infiltrating macrophages during sterile physiological inflammation and tissue regeneration. We identified a heme-binding transcriptional repressor, BACH1, as a novel regulator of this process. Bach1 knockout mice displayed impaired muscle regeneration, altered dynamics of the macrophage phenotype transition, and transcriptional deregulation of key inflammatory and repair-related genes. We also found that BACH1 directly binds to and regulates distal regulatory elements of these genes, suggesting a novel role for BACH1 in controlling a broad spectrum of the repair response genes in macrophages upon injury. Inactivation of heme oxygenase-1 (Hmox1), one of the most stringently deregulated genes in the Bach1 knockout in macrophages, impairs muscle regeneration by changing the dynamics of the macrophage phenotype switch. Collectively, our data suggest the existence of a heme–BACH1­–HMOX1 regulatory axis, that controls the phenotype and function of the infiltrating myeloid cells upon tissue damage, shaping the overall tissue repair kinetics.

The functional implications of the three-dimensional genome organization are becoming increasingly recognized. The Hi-C and HiChIP research approaches belong among the most popular choices for probing long-range chromatin interactions. A few methodical protocols have been published so far, yet their reproducibility and efficiency may vary. Most importantly, the high frequency of the dangling ends may dramatically affect the number of usable reads mapped to valid interaction pairs. Additionally, more obstacles arise from the chromatin compactness of certain investigated cell types, such as primary T cells, which due to their small and compact nuclei, impede limitations for their use in various genomic approaches. Here we systematically optimized all the major steps of the HiChIP protocol in T cells. As a result, we reduced the number of dangling ends to nearly zero and increased the proportion of long-range interaction pairs. Moreover, using three different mouse genotypes and multiple biological replicates, we demonstrated the high reproducibility of the optimized protocol. Although our primary goal was to optimize HiChIP, we also successfully applied the optimized steps to Hi-C, given their significant protocol overlap. Overall, we describe the rationale behind every optimization step, followed by a detailed protocol for both HiChIP and Hi-C experiments.

Endotoxin tolerance occurs to protect the organism from hyperactivation of innate immune responses, primarily mediated by macrophages. Regulation of endotoxin tolerance occurs at multiple levels of cell responses and requires significant changes in gene expression. In the process of macrophage activation, induced expression of microRNA (miR)-155 and miR-146a contributes to the regulation of the inflammatory response and endotoxin tolerance. In this article, we demonstrate that expression of both miRNAs is coordinately regulated during endotoxin tolerance by a complex mechanism that involves monoallelic interchromosomal association, alterations in histone methyl marks, and transcription factor binding. Upon activation of naive macrophages, Histone3 was trimethylated at lysine4 and NFκBp65 was bound on both miR-155 and miR-146a gene loci. However, at the stage of endotoxin tolerance, both miR gene loci were occupied by C/EBPβ, NFκBp50, and the repressive Histone3 marks trimethylation of K9 of H3. DNA fluorescence in situ hybridization experiments revealed monoallelic interchromosomal colocalization of miR-155 and miR-146a gene loci at the stage of endotoxin tolerance, whereas RNA-DNA-fluorescence in situ hybridization experiments showed that the colocalized alleles were silenced, suggesting a common repression mechanism. Genetic ablation of Akt1, which is known to abrogate endotoxin tolerance, abolished induction of loci colocalization and C/EBPβ binding, further supporting that this mechanism occurs specifically in endotoxin tolerance. Overall, this study demonstrates that two miRNAs are coordinately regulated via gene colocalization at the three-dimensional chromatin space, same transcriptional machinery, and similar Histone3 methylation profile, contributing to the development of endotoxin tolerance.

Current research on the cytokine-mediated signalling towards the polarization and differentiation of a T-helper cell lineage lacks mechanistic insights on the transcriptional regulation of cytokine receptor genes. Here, we propose a new mechanism for the transcriptional regulation of the interferon gamma receptor 1 gene via long-range intrachromosomal interactions with the Ifnγ locus mediated by the protein CTCF. These interactions sustain the monoallelic expression of the differentially methylated IfnγR1 gene and are persistent on blockade of active transcription. Our findings suggest that regulatory elements for a cytokine gene locus can also positively regulate the transcription of its receptor.

The nucleus is an ordered three-dimensional entity, and organization of the genome within the nuclear space might have implications for orchestrating gene expression. Recent technological developments have revealed that chromatin is folded into loops bringing distal regulatory elements into intimate contact with the genes that they regulate. Such intrachromosomal contacts appear to be a general mechanism of enhancer-promoter communication ‘in cis’. Tantalizing evidence is also emerging that regulatory elements might have the capacity to act ‘in trans’ to regulate genes on other chromosomes. However, unequivocal data required to prove that interchromosomal gene regulation truly represents another level of control within the nucleus is still lacking, and this concept remains highly contentious. Such controversy only emphasizes that our current understanding of the mechanisms that govern gene expression are far from complete.

The rates of activation and unitary properties of Na+-activated K+ (KNa) currents have been found to vary substantially in different types of neurones. One class of KNa channels is encoded by the Slack gene. We have now determined that alternative RNA splicing gives rise to at least five different transcripts for Slack, which produce Slack channels that differ in their predicted cytoplasmic amino-termini and in their kinetic properties. Two of these, termed Slack-A channels, contain an amino-terminus domain closely resembling that of another class of KNa channels encoded by the Slick gene. Neuronal expression of Slack-A channels and of the previously described Slack isoform, now called Slack-B, are driven by independent promoters. Slack-A mRNAs were enriched in the brainstem and olfactory bulb and detected at significant levels in four different brain regions. When expressed in CHO cells, Slack-A channels activate rapidly upon depolarization and, in single channel recordings in Xenopus oocytes, are characterized by multiple subconductance states with only brief transient openings to the fully open state. In contrast, Slack-B channels activate slowly over hundreds of milliseconds, with openings to the fully open state that are ∼6-fold longer than those for Slack-A channels. In numerical simulations, neurones in which outward currents are dominated by a Slack-A-like conductance adapt very rapidly to repeated or maintained stimulation over a wide range of stimulus strengths. In contrast, Slack-B currents promote rhythmic firing during maintained stimulation, and allow adaptation rate to vary with stimulus strength. Using an antibody that recognizes all amino-termini isoforms of Slack, Slack immunoreactivity is present at locations that have no Slack-B-specific staining, including olfactory bulb glomeruli and the dendrites of hippocampal neurones, suggesting that Slack channels with alternate amino-termini such as Slack-A channels are present at these locations. Our data suggest that alternative promoters of the Slack gene differentially modulate the properties of neurones.

Cilia are present on nearly all cell types in mammals and perform remarkably diverse functions. However, the mechanisms underlying ciliogenesis are unclear. Here, we cloned a previously uncharacterized highly conserved gene, stumpy , located on mouse chromosome 7. Stumpy was ubiquitously expressed, and conditional loss in mouse resulted in complete penetrance of perinatal hydrocephalus (HC) and severe polycystic kidney disease (PKD). We found that cilia in stumpy mutant brain and kidney cells were absent or markedly deformed, resulting in defective flow of cerebrospinal fluid. Stumpy colocalized with ciliary basal bodies, physically interacted with γ-tubulin, and was present along ciliary axonemes, suggesting that stumpy plays a role in ciliary axoneme extension. Therefore, stumpy is essential for ciliogenesis and may be involved in the pathogenesis of human congenital malformations such as HC and PKD.

Naive CD4 T cells differentiate into several effector lineages, which generate a stronger and more rapid response to previously encountered immunological challenges. Although effector function is a key feature of adaptive immunity, the molecular basis of this process is poorly understood. Here, we investigated the spatiotemporal regulation of cytokine gene expression in resting and restimulated effector T helper 1 (Th1) cells. We found that the Lymphotoxin (LT)/TNF alleles, which encode TNF-α, were closely juxtaposed shortly after T-cell receptor (TCR) engagement, when transcription factors are limiting. Allelic pairing required a nuclear myosin, myosin VI, which is rapidly recruited to the LT/TNF locus upon restimulation. Furthermore, transcription was paused at the TNF locus and other related genes in resting Th1 cells and released in a myosin VI-dependent manner following activation. We propose that homologous pairing and myosin VI-mediated transcriptional pause release account for the rapid and efficient expression of genes induced by an external stimulus.

Physiological processes rely on the regulation of total mRNA levels in a cell. In diploid organisms, the transcriptional activation of one or both alleles of a gene may involve trans-allelic interactions that provide a tight spatial and temporal level of gene expression regulation. The mechanisms underlying such interactions still remain poorly understood. Here, we demonstrate that lipopolysaccharide stimulation of murine macrophages rapidly resulted in the actin-mediated and transient homologous spatial proximity of Tnfα alleles, which was necessary for the mono- to biallelic switch in gene expression. We identified two new complementary long noncoding RNAs transcribed from the TNFα locus and showed that their knockdown had opposite effects in Tnfα spatial proximity and allelic expression. Moreover, the observed spatial proximity of Tnfα alleles depended on pyruvate kinase muscle isoform 2 (PKM2) and T-helper-inducing POZ-Krüppel-like factor (ThPOK). This study suggests a role for lncRNAs in the regulation of somatic homologous spatial proximity and allelic expression control necessary for fine-tuning mammalian immune responses.

The deacetylase inhibitor Trichostatin A (TSA) induces the transcription of the Major Histocompatibility Class II (MHC II) DRA gene in a way independent of the master coactivator CIITA. To analyze the molecular mechanisms by which this epigenetic regulator stimulates MHC II expression, we used chromatin immunoprecipitation (ChIP) assays to monitor the alterations in histone modifications that correlate with DRA transcription after TSA treatment. We found that a dramatic increase in promoter linked histone acetylation is followed by an increase in Histone H3 lysine 4 methylation and a decrease of lysine 9 methylation. Fluorescence recovery after photobleaching (FRAP) experiments showed that TSA increases the mobility of HDAC while decreasing the mobility of the class II enhanceosome factor RFX5. These data, in combination with ChIP experiments, indicate that the TSA-mediated induction of DRA transcription involves HDAC relocation and enhanceosome stabilization. In order to gain a genome-wide view of the genes responding to inhibition of deacetylases, we compared the transcriptome of B cells before and after TSA treatment using Affymetrix microarrays. This analysis showed that in addition to the DRA gene, the entire MHC II family and the adjacent histone cluster that are located in chromosome 6p21-22 locus are strongly induced by TSA. A complex pattern of gene reprogramming by TSA involves immune recognition, antiviral, apoptotic and inflammatory pathways and extends the rationale for using Histone Deacetylase Inhibitors (HDACi) to modulate the immune response.

The immune system is influenced by environmental factors such as hormones and nutrients. Previous studies have suggested that vitamins A and D influence the process of naive T helper (Th) cell differentiation into Th1 or Th2 cells. Vitamins A and D signal through the retinoid X receptor (RXR), which partners with either the retinoic acid receptor or the vitamin D receptor. Most previous studies into the role of RXR in Th differentiation have been performed in vitro and it was necessary for these to be verified in a physiological environment. However, in vivo study has been hindered since RXRα deficient mice are embryonic lethal. Du et al. in this issue of the European Journal of Immunology, overcome this obstacle using “pinkie” mice that harbor a hypomorphic mutation in the Rxrα gene. The authors report that the mutant mice have an exaggerated Th1 immune response which is attributed to the aberrant antigen-presenting cell and CD4 T cell function. This study confirms previous studies indicating that RXR signaling plays an important role in Th cell differentiation and also provides a valuable tool with which to study the mechanisms and the in vivo functions of this signaling pathway. See accompanying article: http://dx.doi.org/10.1002/eji.200535366

Several regulatory regions are important for the expression of genes encoding T helper type 2 (T(H)2) cytokines, including T(H)2-specific DNase I hypersensitivity sites in the T(H)2 cytokine locus control region. Among these sites, Rad50 hypersensitive site 7 (RHS7) shows rapid T(H)2-specific demethylation after antigenic stimulation. To investigate the function of RHS7 in T(H)2 cell differentiation, we have generated RHS7-deficient mice. CD4(+) T cells and mast cells showed a notable reduction in T(H)2 cytokine expression in vitro and T(H)2 responses in vivo were considerably impaired in RHS7-deficient mice. Deletion of RHS7 did not affect the expression of a linked Rad50 gene, but it did reduce long-range intrachromosomal interactions between the locus control region and promoters of the T(H)2 cytokine genes. Our findings show that RHS7 is essential for the proper regulation of T(H)2 cytokine gene expression.

The T helper type 2 (T(H)2) locus control region is important in the regulation of the genes encoding the cytokines interleukins 4, 5 and 13. Using the chromosome conformation capture technique, we found that in T cells, natural killer cells, B cells and fibroblasts, the promoters for the genes encoding T(H)2 cytokines are located in close spatial proximity, forming an initial chromatin core configuration. In CD4(+) T cells and natural killer cells, but not B cells and fibroblasts, the T(H)2 locus control region participates in this configuration. The transcription factors GATA3 and STAT6 are essential for the establishment and/or maintenance of these interactions. Intrachromosomal interactions in the T(H)2 cytokine locus may form the basis for the coordinated transcriptional regulation of cytokine-encoding genes by the T(H)2 locus control region.

It is becoming increasingly appreciated that the non-coding genome may have a great impact on the regulation of chromatin structure and gene expression. The innate immune response can be mediated upon lipopolysaccharide stimulation of macrophages which leads to immediate transcriptional activation of early responsive genes including tumor necrosis factor alpha (Tnfα). The functional role of non-coding RNAs, such as lncRNAs and microRNAs, on the transcriptional activation of proinflammatory genes and the subsequent regulation of the innate immune response is still lacking mechanistic insights. In this study we wanted to unravel the functional role of the lncRNA SeT, which is encoded from the murine Tnfα gene locus, and miR-155 on the transcriptional regulation of the Tnfα gene. We utilized genetically modified mice harboring either a deletion of the SeT promoter elements or the mature miR-155 and studied the response of macrophages to lipopolysaccharide (LPS) stimulation. We found that decreased expression of the lncRNA SeT in murine primary macrophages resulted in increased mortality of mice challenged with LPS, which was corroborated by increased Tnfα steady state mRNA levels and a higher frequency of biallelically expressing macrophages. On the contrary, miR-155 deletion resulted in reduced Tnfα mRNA levels supported by a lower frequency of biallelically expressing macrophages upon stimulation with LPS. In both cases, in the absence of either lncRNA SeT or miR-155 we observed a deregulation of the Tnfα allele homologous pairing, previously shown to regulate the switch from mono- to bi-allelic gene expression. Although lncRNA SeT was not found to be a direct target of miR-155 its stability was increased upon miR-155 deletion. This study suggests a role of the non-coding genome in mediating Tnfα mRNA dosage control based on the regulation of homologous pairing of gene alleles and their subsequent biallelic expression.

Intensive characterization of the locus encoding interferon-γ provides new insight into how proper gene expression is achieved in polarizing T cells.NOTE: In the version of this News & Views initially published, the figure credit is missing. This figure should be credited to Ann Thomson. The error has been corrected in the HTML and PDF versions of the article.

The T helper type 2 (Th2) cytokine genes Il4 , Il5 , and Il13 are contained within a 140-kb region of mouse chromosome 11 and their expression is controlled by a locus control region (LCR) embedded within this locus. The LCR is composed of a number of DNase I–hypersensitive sites (HSs), which are believed to encompass the regulatory core of the LCR. To determine the function of these sites, mutant mice were generated in which combinations of these HSs had been deleted from the endogenous LCR, and the effect on Th2 cytokine expression was assessed through the use of in vivo and in vitro models. These experiments revealed that, although all of the hypersensitive sites analyzed are important for appropriate LCR function, some sites are more important than others in regulating cytokine expression. Interestingly, each LCR mutation showed contrasting effects on cytokine expression, in some cases with mutants displaying opposing phenotypes between in vitro cultures and in vivo immunizations. These studies indicated that Rad50 hypersensitive site 6 was the singularly most important HS for Th2 cytokine expression, displaying consistent reductions in cytokine levels in all models tested. Furthermore analysis of chromatin modifications revealed that deletion of Rad50 hypersensitive site 6 impacted epigenetic modifications at the promoters of the Il4 , Il5 , and Il13 genes as well as other regulatory sites within the Th2 locus.

Differentiation of T(H)1 and T(H)2 effector cells proceeds through several phases: First, naive CD4(+) precursor cells are instructed to differentiate as appropriate to optimally fight the infectious threat encountered. This process is governed by the IL12 and IL4 cytokines, as well as by signaling through the Notch receptor. In response to these signals, transcription is initiated of lineage specific cytokine genes including the Ifngamma and Il4 genes as well as of genes encoding transcriptional regulators, such as T-bet and Gata3. The respective differentiation programs are reinforced by both positive and negative feedback mechanisms. Furthermore, epigenetic modifications of the lineage specific genes result in the emergence of regulatory elements, which control high level lineage restricted expression by both intrachromosomal and interchromosomal associations. Together, these mechanisms ensure stable inheritance of the differentiated fate in the numerous progeny of the original naive CD4(+) T cells.

The rates of activation and unitary properties of Na+-activated K+ (K(Na)) currents have been found to vary substantially in different types of neurones. One class of K(Na) channels is encoded by the Slack gene. We have now determined that alternative RNA splicing gives rise to at least five different transcripts for Slack, which produce Slack channels that differ in their predicted cytoplasmic amino-termini and in their kinetic properties. Two of these, termed Slack-A channels, contain an amino-terminus domain closely resembling that of another class of K(Na) channels encoded by the Slick gene. Neuronal expression of Slack-A channels and of the previously described Slack isoform, now called Slack-B, are driven by independent promoters. Slack-A mRNAs were enriched in the brainstem and olfactory bulb and detected at significant levels in four different brain regions. When expressed in CHO cells, Slack-A channels activate rapidly upon depolarization and, in single channel recordings in Xenopus oocytes, are characterized by multiple subconductance states with only brief transient openings to the fully open state. In contrast, Slack-B channels activate slowly over hundreds of milliseconds, with openings to the fully open state that are approximately 6-fold longer than those for Slack-A channels. In numerical simulations, neurones in which outward currents are dominated by a Slack-A-like conductance adapt very rapidly to repeated or maintained stimulation over a wide range of stimulus strengths. In contrast, Slack-B currents promote rhythmic firing during maintained stimulation, and allow adaptation rate to vary with stimulus strength. Using an antibody that recognizes all amino-termini isoforms of Slack, Slack immunoreactivity is present at locations that have no Slack-B-specific staining, including olfactory bulb glomeruli and the dendrites of hippocampal neurones, suggesting that Slack channels with alternate amino-termini such as Slack-A channels are present at these locations. Our data suggest that alternative promoters of the Slack gene differentially modulate the properties of neurones.

Cytokine loci undergo changes in chromatin structure when naive CD4 + T cells differentiate into Th1 or Th2 cells and have also been examined for regulatory sequences underlying such changes and their functional correlates. Studies have shown that distal regulatory elements control the Ifng and Th2 cytokine loci and are primary targets for tissue-specific transcription factors, serving as centers for epigenetic changes that mark heritable traits in effector cells. Reports of intra- and, remarkably, interchromosomal interactions between these regulatory elements shed light on the mechanisms by which they regulate gene expression, revealing an extraordinary new picture that conceptually extends our views on how genes are regulated from two to three dimensions. Here, we summarize these recent findings on the role of regulatory elements and their mechanisms of action, which are of broad significance for gene regulation, not only of the immune system but also of many, if not all, coregulated genes.

The T-helper-cell 1 and 2 (T(H)1 and T(H)2) pathways, defined by cytokines interferon-gamma (IFN-gamma) and interleukin-4 (IL-4), respectively, comprise two alternative CD4+ T-cell fates, with functional consequences for the host immune system. These cytokine genes are encoded on different chromosomes. The recently described T(H)2 locus control region (LCR) coordinately regulates the T(H)2 cytokine genes by participating in a complex between the LCR and promoters of the cytokine genes Il4, Il5 and Il13. Although they are spread over 120 kilobases, these elements are closely juxtaposed in the nucleus in a poised chromatin conformation. In addition to these intrachromosomal interactions, we now describe interchromosomal interactions between the promoter region of the IFN-gamma gene on chromosome 10 and the regulatory regions of the T(H)2 cytokine locus on chromosome 11. DNase I hypersensitive sites that comprise the T(H)2 LCR developmentally regulate these interchromosomal interactions. Furthermore, there seems to be a cell-type-specific dynamic interaction between interacting chromatin partners whereby interchromosomal interactions are apparently lost in favour of intrachromosomal ones upon gene activation. Thus, we provide an example of eukaryotic genes located on separate chromosomes associating physically in the nucleus via interactions that may have a function in coordinating gene expression.

Genes present on different chromosomes can be coordinately expressed through a transcription regulatory factor that brings them together in a region of active transcription in the nucleus.

Nat. Immun. 8, 681–683 (2007); published online 19 June 2007; corrected after print 22 June 2007 In the version of this News & Views initially published, the figure credit is missing. This figure should be credited to Ann Thomson. The error has been corrected in the HTML and PDF versions of the article.