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 F€ urth equation, the usual characterization of meansquared 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 longertime 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.

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BackgroundTranscriptogram 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.ResultsHere 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.ConclusionThe 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.Electronic supplementary materialThe online version of this article (doi:10.1186/1471-2164-15-1181) contains supplementary material, which is available to authorized users.

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