RÉSUMÉ
To understand the difference between benign and severe outcomes after Coronavirus infection, we urgently need ways to clarify and quantify the time course of tissue and immune responses. Here we re-analyze 72-hour time-series microarrays generated in 2013 by Sims and collaborators for SARS-CoV-1 in vitro infection of a human lung epithelial cell line. Transcriptograms, a Bioinformatics tool to analyze genome-wide gene expression data, allow us to define an appropriate context-dependent threshold for mechanistic relevance of gene differential expression. Without knowing in advance which genes are relevant, classical analyses detect every gene with statistically-significant differential expression, leaving us with too many genes and hypotheses to be useful. Using a Transcriptogram-based top-down approach, we identified three major, differentially-expressed gene sets comprising 219 mainly immune-response-related genes. We identified timescales for alterations in mitochondrial activity, signaling and transcription regulation of the innate and adaptive immune systems and their relationship to viral titer. The methods can be applied to RNA data sets for SARS-CoV-2 to investigate the origin of differential responses in different tissue types, or due to immune or preexisting conditions or to compare cell culture, organoid culture, animal models and human-derived samples.
RÉSUMÉ
Active-Matter models commonly consider particles with overdamped dynamics subject to a force (speed) with constant modulus and random direction. Some models also include random noise in particle displacement (a Wiener process), resulting in diffusive motion at short time scales. On the other hand, Ornstein-Uhlenbeck processes apply Langevin dynamics to the particles' velocity and predict motion that is not diffusive at short time scales. Experiments show that migrating cells have gradually varying speeds at intermediate and long time scales, with short-time diffusive behavior. While Ornstein-Uhlenbeck processes can describe the moderate-and long-time speed variation, Active-Matter models for over-damped particles can explain the short-time diffusive behavior. Isotropic models cannot explain both regimes, because short-time diffusion renders instantaneous velocity ill-defined, and prevents the use of dynamical equations that require velocity time-derivatives. On the other hand, both models correctly describe some of the different temporal regimes seen in migrating biological cells and must, in the appropriate limit, yield the same observable predictions. Here we propose and solve analytically an Anisotropic Ornstein-Uhlenbeck process for polarized particles, with Langevin dynamics governing the particle's movement in the polarization direction and a Wiener process governing displacement in the orthogonal direction. Our characterization provides a theoretically robust way to compare movement in dimensionless simulations to movement in experiments in which measurements have meaningful space and time units. We also propose an approach to deal with inevitable finite-precision effects in experiments and simulations.
RÉSUMÉ
To understand the difference between benign and severe outcomes after Coronavirus infection, we urgently need ways to clarify and quantify the time course of tissue and immune responses. Here we re-analyze 72-hour time-series microarrays generated in 2013 by Sims and collaborators for SARS-CoV-1 in vitro infection of a human lung epithelial cell line. Transcriptograms, a Bioinformatics tool to analyze genome-wide gene expression data, allow us to define an appropriate context-dependent threshold for mechanistic relevance of gene differential expression. Without knowing in advance which genes are relevant, classical analyses detect every gene with statistically-significant differential expression, leaving us with too many genes and hypotheses to be useful. Using a Transcriptogram-based top-down approach, we identified three major, differentially-expressed gene sets comprising 219 mainly immune-response-related genes. We identified timescales for alterations in mitochondrial activity, signaling and transcription regulation of the innate and adaptive immune systems and their relationship to viral titer. At the individual-gene level, EGR3 was significantly upregulated in infected cells. Similar activation in T-cells and fibroblasts in infected lung could explain the T-cell anergy and eventual fibrosis seen in SARS-CoV-1 infection. The methods can be applied to RNA data sets for SARS-CoV-2 to investigate the origin of differential responses in different tissue types, or due to immune or preexisting conditions or to compare cell culture, organoid culture, animal models, and human-derived samples.
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Mesenchymal cell crawling is a critical process in normal development, in tissue function, and in many diseases. Quantitatively predictive numerical simulations of cell crawling thus have multiple scientific, medical, and technological applications. However, we still lack a low-computational-cost approach to simulate mesenchymal three-dimensional (3D) cell crawling. Here, we develop a computationally tractable 3D model (implemented as a simulation in the CompuCell3D simulation environment) of mesenchymal cells crawling on a two-dimensional substrate. The Fürth equation, the usual characterization of mean-squared displacement (MSD) curves for migrating cells, describes a motion in which, for increasing time intervals, cell movement transitions from a ballistic to a diffusive regime. Recent experiments have shown that for very short time intervals, cells exhibit an additional fast diffusive regime. Our simulations' MSD curves reproduce the three experimentally observed temporal regimes, with fast diffusion for short time intervals, slow diffusion for long time intervals, and intermediate time -interval-ballistic motion. The resulting parameterization of the trajectories for both experiments and simulations allows the definition of time- and length scales that translate between computational and laboratory units. Rescaling by these scales allows direct quantitative comparisons among MSD curves and between velocity autocorrelation functions from experiments and simulations. Although our simulations replicate experimentally observed spontaneous symmetry breaking, short-timescale diffusive motion, and spontaneous cell-motion reorientation, their computational cost is low, allowing their use in multiscale virtual-tissue simulations. Comparisons between experimental and simulated cell motion support the hypothesis that short-time actomyosin dynamics affects longer-time cell motility. The success of the base cell-migration simulation model suggests its future application in more complex situations, including chemotaxis, migration through complex 3D matrices, and collective cell motion.
Sujet(s)
Modèles biologiques , Mouvement cellulaire , Simulation numérique , Diffusion , DéplacementRÉSUMÉ
Soybean is an economically important plant, and its production is affected in soils with high salinity levels. It is important to understand the adaptive mechanisms through which plants overcome this kind of stress and to identify potential genes for improving abiotic stress tolerance. RNA-Seq data of two Glycine max cultivars, a drought-sensitive (C08) and a tolerant (Conquista), subjected to different periods of salt stress were analyzed. The transcript expression profile was obtained using a transcriptogram approach, comparing both cultivars and different times of treatment. After 4 h of salt stress, Conquista cultivar had 1400 differentially expressed genes, 647 induced and 753 repressed. Comparative expression revealed that 719 genes share the same pattern of induction or repression between both cultivars. Among them, 393 genes were up- and 326 down-regulated. Salt stress also modified the expression of 54 isoforms of miRNAs in Conquista, by the maturation of 39 different pre-miRNAs. The predicted targets for 12 of those mature miRNAs also have matches with 15 differentially expressed genes from our analyses. We found genes involved in important pathways related to stress adaptation. Genes from both ABA and BR signaling pathways were modulated, with possible crosstalk between them, and with a likely post-transcriptional regulation by miRNAs. Genes related to ethylene biosynthesis, DNA repair, and plastid translation process were those that could be regulated by miRNA.
Sujet(s)
Glycine max/génétique , Stress salin/génétique , Tolérance au sel/génétique , Adaptation physiologique/génétique , Agriculture/méthodes , Sécheresses , Analyse de profil d'expression de gènes/méthodes , Régulation de l'expression des gènes végétaux/génétique , Salinité , Transduction du signal/génétique , Stress physiologique/génétique , Facteurs de transcription/génétique , Transcriptome/génétiqueRÉSUMÉ
Lead poisoning effects are wide and include nervous system impairment, peculiarly during development, leading to neural damage. Lead interaction with calcium and zinc-containing metalloproteins broadly affects cellular metabolism since these proteins are related to intracellular ion balance, activation of signaling transduction cascades, and gene expression regulation. In spite of lead being recognized as a neurotoxin, there are gaps in knowledge about the global effect of lead in modulating the transcription of entire cellular systems in neural cells. In order to investigate the effects of lead poisoning in a systemic perspective, we applied the transcriptogram methodology in an RNA-seq dataset of human embryonic-derived neural progenitor cells (ES-NP cells) treated with 30 µM lead acetate for 26 days. We observed early downregulation of several cellular systems involved with cell differentiation, such as cytoskeleton organization, RNA, and protein biosynthesis. The downregulated cellular systems presented big and tightly connected networks. For long treatment times (12 to 26 days), it was possible to observe a massive impairment in cell transcription profile. Taking the enriched terms together, we observed interference in all layers of gene expression regulation, from chromatin remodeling to vesicle transport. Considering that ES-NP cells are progenitor cells that can originate other neural cell types, our results suggest that lead-induced gene expression disturbance might impair cells' ability to differentiate, therefore influencing ES-NP cells' fate.
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Cell migration is essential to cell segregation, playing a central role in tissue formation, wound healing, and tumor evolution. Considering random mixtures of two cell types, it is still not clear which cell characteristics define clustering time scales. The mass of diffusing clusters merging with one another is expected to grow as t^{d/d+2} when the diffusion constant scales with the inverse of the cluster mass. Cell segregation experiments deviate from that behavior. Explanations for that could arise from specific microscopic mechanisms or from collective effects, typical of active matter. Here we consider a power law connecting diffusion constant and cluster mass to propose an analytic approach to model cell segregation where we explicitly take into account finite-size corrections. The results are compared with active matter model simulations and experiments available in the literature. To investigate the role played by different mechanisms we considered different hypotheses describing cell-cell interaction: differential adhesion hypothesis and different velocities hypothesis. We find that the simulations yield normal diffusion for long time intervals. Analytic and simulation results show that (i) cluster evolution clearly tends to a scaling regime, disrupted only at finite-size limits; (ii) cluster diffusion is greatly enhanced by cell collective behavior, such that for high enough tendency to follow the neighbors, cluster diffusion may become independent of cluster size; (iii) the scaling exponent for cluster growth depends only on the mass-diffusion relation, not on the detailed local segregation mechanism. These results apply for active matter systems in general and, in particular, the mechanisms found underlying the increase in cell sorting speed certainly have deep implications in biological evolution as a selection mechanism.
Sujet(s)
Mouvement cellulaire , Modèles biologiques , Adhérence cellulaire , Analyse de regroupements , Simulation numérique , Diffusion , Facteurs tempsRÉSUMÉ
Microbial biofilms are highly structured and dynamic communities in which phenotypic diversification allows microorganisms to adapt to different environments under distinct conditions. The environmentally ubiquitous pathogen Cryptococcus neoformans colonizes many niches of the human body and implanted medical devices in the form of biofilms, an important virulence factor. A new approach was used to characterize the underlying geometrical distribution of C. neoformans cells during the adhesion stage of biofilm formation. Geometrical aspects of adhered cells were calculated from the Delaunay triangulation and Voronoi diagram obtained from scanning electron microscopy images (SEM). A correlation between increased biofilm formation and higher ordering of the underlying cell distribution was found. Mature biofilm aggregates were analyzed by applying an adapted protocol developed for ultrastructure visualization of cryptococcal cells by SEM. Flower-like clusters consisting of cells embedded in a dense layer of extracellular matrix were observed as well as distinct levels of spatial organization: adhered cells, clusters of cells and community of clusters. The results add insights into yeast motility during the dispersion stage of biofilm formation. This study highlights the importance of cellular organization for biofilm growth and presents a novel application of the geometrical method of analysis.
RÉSUMÉ
BACKGROUND: Autosomal dominant polycystic kidney disease (ADPKD) causes progressive loss of renal function in adults as a consequence of the accumulation of cysts. ADPKD is the most common genetic cause of end-stage renal disease. Mutations in polycystin-1 occur in 87% of cases of ADPKD and mutations in polycystin-2 are found in 12% of ADPKD patients. The complexity of ADPKD has hampered efforts to identify the mechanisms underlying its pathogenesis. No current FDA (Federal Drug Administration)-approved therapies ameliorate ADPKD progression. RESULTS: We used the de Almeida laboratory's sensitive new transcriptogram method for whole-genome gene expression data analysis to analyze microarray data from cell lines developed from cell isolates of normal kidney and of both non-cystic nephrons and cysts from the kidney of a patient with ADPKD. We compared results obtained using standard Ingenuity Volcano plot analysis, Gene Set Enrichment Analysis (GSEA) and transcriptogram analysis. Transcriptogram analysis confirmed the findings of Ingenuity, GSEA, and published analysis of ADPKD kidney data and also identified multiple new expression changes in KEGG (Kyoto Encyclopedia of Genes and Genomes) pathways related to cell growth, cell death, genetic information processing, nucleotide metabolism, signal transduction, immune response, response to stimulus, cellular processes, ion homeostasis and transport and cofactors, vitamins, amino acids, energy, carbohydrates, drugs, lipids, and glycans. Transcriptogram analysis also provides significance metrics which allow us to prioritize further study of these pathways. CONCLUSIONS: Transcriptogram analysis identifies novel pathways altered in ADPKD, providing new avenues to identify both ADPKD's mechanisms of pathogenesis and pharmaceutical targets to ameliorate the progression of the disease.
Sujet(s)
Polykystose rénale autosomique dominante/métabolisme , Transcriptome , Adulte , Études cas-témoins , Lignée cellulaire , Analyse de profil d'expression de gènes , Gene Ontology , Humains , Mâle , Voies et réseaux métaboliques , Adulte d'âge moyen , Polykystose rénale autosomique dominante/anatomopathologie , Canaux cationiques TRPP/génétique , Canaux cationiques TRPP/métabolismeRÉSUMÉ
In wet liquid foams, slow diffusion of gas through bubble walls changes bubble pressure, volume and wall curvature. Large bubbles grow at the expenses of smaller ones. The smaller the bubble, the faster it shrinks. As the number of bubbles in a given volume decreases in time, the average bubble size increases: i.e. the foam coarsens. During coarsening, bubbles also move relative to each other, changing bubble topology and shape, while liquid moves within the regions separating the bubbles. Analyzing the combined effects of these mechanisms requires examining a volume with enough bubbles to provide appropriate statistics throughout coarsening. Using a Cellular Potts model, we simulate these mechanisms during the evolution of three-dimensional foams with wetnesses of Ï = 0.00, 0.05 and 0.20. We represent the liquid phase as an ensemble of many small fluid particles, which allows us to monitor liquid flow in the region between bubbles. The simulations begin with 2 × 105 bubbles for Ï = 0.00 and 1.25 × 105 bubbles for Ï = 0.05 and 0.20, allowing us to track the distribution functions for bubble size, topology and growth rate over two and a half decades of volume change. All simulations eventually reach a self-similar growth regime, with the distribution functions time independent and the number of bubbles decreasing with time as a power law whose exponent depends on the wetness.
RÉSUMÉ
BACKGROUND: Transcriptogram profiling is a method to present and analyze transcription data in a genome-wide scale that reduces noise and facilitates biological interpretation. An ordered gene list is produced, such that the probability that the genes are functionally associated exponentially decays with their distance on the list. This list presents a biological logic, evinced by the selective enrichment of successive intervals with Gene Ontology terms or KEGG pathways. Transcriptograms are expression profiles obtained by taking the average of gene expression over neighboring genes on this list. Transcriptograms enhance reproducibility and precision for expression measurements of functionally correlated gene sets. RESULTS: Here we present an ordering list for Homo sapiens and apply the transcriptogram profiling method to different datasets. We show that this method enhances experiment reproducibility and enhances signal. We applied the method to a diabetes study by Hwang and collaborators, which focused on expression differences between cybrids produced by the hybridization of mitochondria of diabetes mellitus donors with osteosarcoma cell lines, depleted of mitochondria. We found that the transcriptogram method revealed significant differential expression in gene sets linked to blood coagulation and wound healing pathways, and also to gene sets that do not represent any metabolic pathway or Gene Ontology term. These gene sets are connected to ECM-receptor interaction and secreted proteins. CONCLUSION: The transcriptogram profiling method provided an automatic way to define sets of genes with correlated expression, reduce noise in genome-wide transcription profiles, and enhance measure reproducibility and sensitivity. These advantages enabled biologic interpretation and pointed to differentially expressed gene sets in diabetes mellitus which were not previously defined.
Sujet(s)
Analyse de profil d'expression de gènes , Régulation de l'expression des gènes , Génome humain , Analyse de regroupements , Biologie informatique/méthodes , Analyse de profil d'expression de gènes/méthodes , Analyse de profil d'expression de gènes/normes , Études d'associations génétiques/méthodes , Études d'associations génétiques/normes , Étude d'association pangénomique/méthodes , Étude d'association pangénomique/normes , Humains , Annotation de séquence moléculaire , Reproductibilité des résultats , TranscriptomeRÉSUMÉ
Whole genome protein-protein association networks are not random and their topological properties stem from genome evolution mechanisms. In fact, more connected, but less clustered proteins are related to genes that, in general, present more paralogs as compared to other genes, indicating frequent previous gene duplication episodes. On the other hand, genes related to conserved biological functions present few or no paralogs and yield proteins that are highly connected and clustered. These general network characteristics must have an evolutionary explanation. Considering data from STRING database, we present here experimental evidence that, more than not being scale free, protein degree distributions of organisms present an increased probability for high degree nodes. Furthermore, based on this experimental evidence, we propose a simulation model for genome evolution, where genes in a network are either acquired de novo using a preferential attachment rule, or duplicated with a probability that linearly grows with gene degree and decreases with its clustering coefficient. For the first time a model yields results that simultaneously describe different topological distributions. Also, this model correctly predicts that, to produce protein-protein association networks with number of links and number of nodes in the observed range for Eukaryotes, it is necessary 90% of gene duplication and 10% of de novo gene acquisition. This scenario implies a universal mechanism for genome evolution.
Sujet(s)
Cellules eucaryotes/métabolisme , Évolution moléculaire , Duplication de gène , Génome , Algorithmes , Simulation numérique , Bases de données génétiques , Eucaryotes/génétique , Eucaryotes/métabolisme , Réseaux de régulation génique , Modèles génétiques , Cartographie d'interactions entre protéines , Cartes d'interactions protéiquesRÉSUMÉ
We study the topology and geometry of two-dimensional coarsening foam with an arbitrary liquid fraction. To interpolate between the dry limit described by von Neumann's law and the wet limit described by Marqusee's equation, the relevant bubble characteristics are the Plateau border radius and a new variable: the effective number of sides. We propose an equation for the individual bubble growth rate as the weighted sum of the growth through bubble-bubble interfaces and through bubble-Plateau border interfaces. The resulting prediction is successfully tested, without an adjustable parameter, using extensive bidimensional Potts model simulations. The simulations also show that a self-similar growth regime is observed at any liquid fraction, and they also determine how the average size growth exponent, side number distribution, and relative size distribution interpolate between the extreme limits. Applications include concentrated emulsions, grains in polycrystals, and other domains with coarsening that is driven by curvature.
Sujet(s)
Modèles chimiques , Transition de phase , Cristallisation , Émulsions/composition chimique , Gaz/composition chimiqueRÉSUMÉ
BACKGROUND: Genetic plasticity may be understood as the ability of a functional gene network to tolerate alterations in its components or structure. Usually, the studies involving gene modifications in the course of the evolution are concerned to nucleotide sequence alterations in closely related species. However, the analysis of large scale data about the distribution of gene families in non-exclusively closely related species can provide insights on how plastic or how conserved a given gene family is. Here, we analyze the abundance and diversity of all Eukaryotic Clusters of Orthologous Groups (KOG) present in STRING database, resulting in a total of 4,850 KOGs. This dataset comprises 481,421 proteins distributed among 55 eukaryotes. RESULTS: We propose an index to evaluate the evolutionary plasticity and conservation of an orthologous group based on its abundance and diversity across eukaryotes. To further KOG plasticity analysis, we estimate the evolutionary distance average among all proteins which take part in the same orthologous group. As a result, we found a strong correlation between the evolutionary distance average and the proposed evolutionary plasticity index. Additionally, we found low evolutionary plasticity in Saccharomyces cerevisiae genes associated with inviability and Mus musculus genes associated with early lethality. At last, we plot the evolutionary plasticity value in different gene networks from yeast and humans. As a result, it was possible to discriminate among higher and lower plastic areas of the gene networks analyzed. CONCLUSIONS: The distribution of gene families brings valuable information on evolutionary plasticity which might be related with genetic plasticity. Accordingly, it is possible to discriminate among conserved and plastic orthologous groups by evaluating their abundance and diversity across eukaryotes.
Sujet(s)
Évolution moléculaire , Réseaux de régulation génique , Animaux , Biologie informatique , Humains , Souris , Saccharomyces cerevisiae/génétique , Levures/génétiqueRÉSUMÉ
Analysis of genome-wide expression data poses a challenge to extract relevant information. The usual approaches compare cellular expression levels relative to a pre-established control and genes are clustered based on the correlation of their expression levels. This implies that cluster definitions are dependent on the cellular metabolic state, eventually varying from one experiment to another. We present here a computational method that order genes on a line and clusters genes by the probability that their products interact. Protein-protein association information can be obtained from large data bases as STRING. The genome organization obtained this way is independent from specific experiments, and defines functional modules that are associated with gene ontology terms. The starting point is a gene list and a matrix specifying interactions. Considering the Saccharomyces cerevisiae genome, we projected on the ordering gene expression data, producing plots of transcription levels for two different experiments, whose data are available at Gene Expression Omnibus database. These plots discriminate metabolic cellular states, point to additional conclusions, and may be regarded as the first versions of 'transcriptograms'. This method is useful for extracting information from cell stimuli/responses experiments, and may be applied with diagnostic purposes to different organisms.
Sujet(s)
Analyse de profil d'expression de gènes/méthodes , Génomique/méthodes , Saccharomyces cerevisiae/génétique , Algorithmes , Génome fongique , Méthode de Monte Carlo , Cartographie d'interactions entre protéines , Saccharomyces cerevisiae/métabolismeRÉSUMÉ
A Green's function method is developed to approach the spatiotemporal equations describing the cAMP production in Dictyostelium discoideum, markedly reducing numerical calculations times: cAMP concentrations and gradients are calculated just at the amoeba locations. A single set of parameters is capable of reproducing the different observed behaviors, from cAMP synchronization, spiral waves and reaction-diffusion patterns to streaming and mound formation. After aggregation, the emergence of a circular motion of amoebas, breaking the radial cAMP field symmetry, is observed.
Sujet(s)
Algorithmes , AMP cyclique/composition chimique , Dictyostelium/composition chimique , Modèles biologiques , Modèles chimiques , Simulation numériqueRÉSUMÉ
UNLABELLED: ViaComplex is an open-source application that builds landscape maps of gene expression networks. The motivation for this software comes from two previous publications (Nucleic Acids Res., 35, 1859-1867, 2007; Nucleic Acids Res., 36, 6269-6283, 2008). The first article presents a network-based model of genome stability pathways where we defined a set of genes that characterizes each genetic system. In the second article we analyzed this model by projecting functional information from several experiments onto the gene network topology. In order to systematize the methods developed in these articles, ViaComplex provides tools that may help potential users to assess different high-throughput experiments in the context of six core genome maintenance mechanisms. This model illustrates how different gene networks can be analyzed by the same algorithm. AVAILABILITY: (http://lief.if.ufrgs.br/pub/biosoftwares/viacomplex).
Sujet(s)
Analyse de profil d'expression de gènes/méthodes , Expression des gènes , Réseaux de régulation génique/génétique , Génome/génétique , Logiciel , Interface utilisateurRÉSUMÉ
Apoptosis is essential for complex multicellular organisms and its failure is associated with genome instability and cancer. Interactions between apoptosis and genome-maintenance mechanisms have been extensively documented and include transactivation-independent and -dependent functions, in which the tumor-suppressor protein p53 works as a 'molecular node' in the DNA-damage response. Although apoptosis and genome stability have been identified as ancient pathways in eukaryote phylogeny, the biological evolution underlying the emergence of an integrated system remains largely unknown. Here, using computational methods, we reconstruct the evolutionary scenario that linked apoptosis with genome stability pathways in a functional human gene/protein association network. We found that the entanglement of DNA repair, chromosome stability and apoptosis gene networks appears with the caspase gene family and the antiapoptotic gene BCL2. Also, several critical nodes that entangle apoptosis and genome stability are cancer genes (e.g. ATM, BRCA1, BRCA2, MLH1, MSH2, MSH6 and TP53), although their orthologs have arisen in different points of evolution. Our results demonstrate how genome stability and apoptosis were co-opted during evolution recruiting genes that merge both systems. We also provide several examples to exploit this evolutionary platform, where we have judiciously extended information on gene essentiality inferred from model organisms to human.
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Apoptose/génétique , Évolution moléculaire , Réseaux de régulation génique , Instabilité du génome , Animaux , Biologie informatique , Gènes létaux , Gènes tumoraux , Génome humain , Humains , Souris , Saccharomyces cerevisiae/génétiqueRÉSUMÉ
A self-propelled particle model is introduced to study cell sorting occurring in some living organisms. This allows us to evaluate the influence of intrinsic cell motility separately from differential adhesion with fluctuations, a mechanism previously shown to be sufficient to explain a variety of cell rearrangement processes. We find that the tendency of cells to actively follow their neighbors greatly reduces segregation time scales. A finite-size analysis of the sorting process reveals clear algebraic growth laws as in physical phase-ordering processes, albeit with unusual scaling exponents.