Inverse-power-law behavior of cellular motility reveals stromal-epithelial cell interactions in 3D co-culture by OCT fluctuation spectroscopy.
ABSTRACT: The progression of breast cancer is known to be affected by stromal cells within the local microenvironment. Here we study the effect of stromal fibroblasts on the in-place motions (motility) of mammary epithelial cells within organoids in 3D co-culture, inferred from the speckle fluctuation spectrum using optical coherence tomography (OCT). In contrast to Brownian motion, mammary cell motions exhibit an inverse power-law fluctuation spectrum. We introduce two complementary metrics for quantifying fluctuation spectra: the power-law exponent and a novel definition of the motility amplitude, both of which are signal- and position-independent. We find that the power-law exponent and motility amplitude are positively (p<0.001) and negatively (p<0.01) correlated with the density of stromal cells in 3D co-culture, respectively. We also show how the hyperspectral data can be visualized using these metrics to observe heterogeneity within organoids. This constitutes a simple and powerful tool for detecting and imaging cellular functional changes with OCT.
Project description:Myxococcus xanthus is a bacterium capable of complex social organization. Its characteristic social ("S")-motility mechanism is mediated by type IV pili (TFP), linear actuator appendages that propel the bacterium along a surface. TFP are known to bind to secreted exopolysaccharides (EPS), but it is unclear how M. xanthus manages to use the TFP-EPS technology common to many bacteria to achieve its unique coordinated multicellular movements. We examine M. xanthus S-motility, using high-resolution particle-tracking algorithms, and observe aperiodic stick-slip movements. We show that they are not due to chemotaxis, but are instead consistent with a constant TFP-generated force interacting with EPS, which functions both as a glue and as a lubricant. These movements are quantitatively homologous to the dynamics of earthquakes and other crackling noise systems. These systems exhibit critical behavior, which is characterized by a statistical hierarchy of discrete "avalanche" motions described by a power law distribution. The measured critical exponents from M. xanthus are consistent with mean field theoretical models and with other crackling noise systems, and the measured Lyapunov exponent suggests the existence of highly branched EPS. Such molecular architectures, which are common for efficient lubricants but rare in bacterial EPS, may be necessary for S-motility: We show that the TFP of leading "locomotive" cells initiate the collective motion of follower cells, indicating that lubricating EPS may alleviate the force generation requirements on the lead cell and thus make S-motility possible.
Project description:The human mammary gland is a complex and heterogeneous organ, where the interactions between mammary epithelial cells (MEC) and stromal fibroblasts are known to regulate normal biology and tumorigenesis. We aimed to longitudinally evaluate morphology and size of organoids in 3D co-cultures of normal (MCF10A) or pre-malignant (MCF10DCIS.com) MEC and hTERT-immortalized fibroblasts from reduction mammoplasty (RMF). This co-culture model, based on an isogenic panel of cell lines, can yield insights to understand breast cancer progression. However, 3D cultures pose challenges for quantitative assessment and imaging, especially when the goal is to measure the same organoid structures over time. Using optical coherence tomography (OCT) as a non-invasive method to longitudinally quantify morphological changes, we found that OCT provides excellent visualization of MEC-fibroblast co-cultures as they form ductal acini and remodel over time. Different concentrations of fibroblasts and MEC reflecting reported physiological ratios  were evaluated, and we found that larger, hollower, and more aspherical acini were formed only by pre-malignant MEC (MCF10DCIS.com) in the presence of fibroblasts, whereas in comparable conditions, normal MEC (MCF10A) acini remained smaller and less aspherical. The ratio of fibroblast to MEC was also influential in determining organoid phenotypes, with higher concentrations of fibroblasts producing more aspherical structures in MCF10DCIS.com. These findings suggest that stromal-epithelial interactions between fibroblasts and MEC can be modeled in vitro, with OCT imaging as a convenient means of assaying time dependent changes, with the potential for yielding important biological insights about the differences between benign and pre-malignant cells.
Project description:Cell sorting, whereby a heterogeneous cell mixture organizes into distinct tissues, is a fundamental patterning process in development. Hydra is a powerful model system for carrying out studies of cell sorting in three dimensions, because of its unique ability to regenerate after complete dissociation into individual cells. The physicists Alfred Gierer and Hans Meinhardt recognized Hydra's self-organizing properties more than 40 years ago. However, what drives cell sorting during regeneration of Hydra from cell aggregates is still debated. Differential motility and differential adhesion have been proposed as driving mechanisms, but the available experimental data are insufficient to distinguish between these two. Here, we answer this longstanding question by using transgenic Hydra expressing fluorescent proteins and a multiscale experimental and numerical approach. By quantifying the kinematics of single cell and whole aggregate behaviors, we show that no differences in cell motility exist among cell types and that sorting dynamics follow a power law with an exponent of ?0.5. Additionally, we measure the physical properties of separated tissues and quantify their viscosities and surface tensions. Based on our experimental results and numerical simulations, we conclude that tissue interfacial tensions are sufficient to explain cell sorting in aggregates of Hydra cells. Furthermore, we demonstrate that the aggregate's geometry during sorting is key to understanding the sorting dynamics and explains the exponent of the power law behavior. Our results answer the long standing question of the physical mechanisms driving cell sorting in Hydra cell aggregates. In addition, they demonstrate how powerful this organism is for biophysical studies of self-organization and pattern formation.
Project description:It is well-known that word frequencies arrange themselves according to Zipf's law. However, little is known about the dependency of the parameters of the law and the complexity of a communication system. Many models of the evolution of language assume that the exponent of the law remains constant as the complexity of a communication systems increases. Using longitudinal studies of child language, we analysed the word rank distribution for the speech of children and adults participating in conversations. The adults typically included family members (e.g., parents) or the investigators conducting the research. Our analysis of the evolution of Zipf's law yields two main unexpected results. First, in children the exponent of the law tends to decrease over time while this tendency is weaker in adults, thus suggesting this is not a mere mirror effect of adult speech. Second, although the exponent of the law is more stable in adults, their exponents fall below 1 which is the typical value of the exponent assumed in both children and adults. Our analysis also shows a tendency of the mean length of utterances (MLU), a simple estimate of syntactic complexity, to increase as the exponent decreases. The parallel evolution of the exponent and a simple indicator of syntactic complexity (MLU) supports the hypothesis that the exponent of Zipf's law and linguistic complexity are inter-related. The assumption that Zipf's law for word ranks is a power-law with a constant exponent of one in both adults and children needs to be revised.
Project description:Previous work [Burgess et al., Med. Phys. 28, 419-437 (2001)] has shown that anatomical noise in projection mammography results in a power spectrum well modeled over a range of frequencies by a power law, and the exponent (beta) of this power law plays a critical role in determining the size at which a growing lesion reaches the threshold for detection. In this study, the authors evaluated the power-law model for breast computed tomography (bCT) images, which can be thought of as thin sections through a three-dimensional (3D) volume. Under the assumption of a 3D power law describing the distribution of attenuation coefficients in the breast parenchyma, the authors derived the relationship between the power-law exponents of bCT and projection images and found it to be betasection=betaproj-1. They evaluated this relationship on clinical images by comparing bCT images from a set of 43 patients to Burgess' findings in mammography. They were able to make a direct comparison for 6 of these patients who had both a bCT exam and a digitized film-screen mammogram. They also evaluated segmented bCT images to investigate the extent to which the bCT power-law exponent can be explained by a binary model of attenuation coefficients based on the different attenuation of glandular and adipose tissue. The power-law model was found to be a good fit for bCT data over frequencies from 0.07 to 0.45 cyc/mm, where anatomical variability dominates the spectrum. The average exponent for bCT images was 1.86. This value is close to the theoretical prediction using Burgess' published data for projection mammography and for the limited set of mammography data available from the authors' patient sample. Exponents from the segmented bCT images (average value: 2.06) were systematically slightly higher than bCT images, with substantial correlation between the two (r=0.84).
Project description:Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Using the idea from general fractals and scaling, I propose a dual competition hypothesis of city development to explain the value intervals and the special value, 1, of the power exponent. Zipf's law and Pareto's law can be mathematically transformed into one another, but represent different processes of urban evolution, respectively. Based on the Pareto distribution, a frequency correlation function can be constructed. By scaling analysis and multifractals spectrum, the parameter interval of Pareto exponent is derived as (0.5, 1]; Based on the Zipf distribution, a size correlation function can be built, and it is opposite to the first one. By the second correlation function and multifractals notion, the Pareto exponent interval is derived as [1, 2). Thus the process of urban evolution falls into two effects: one is the Pareto effect indicating city number increase (external complexity), and the other the Zipf effect indicating city size growth (internal complexity). Because of struggle of the two effects, the scaling exponent varies from 0.5 to 2; but if the two effects reach equilibrium with each other, the scaling exponent approaches 1. A series of mathematical experiments on hierarchical correlation are employed to verify the models and a conclusion can be drawn that if cities in a given region follow Zipf's law, the frequency and size correlations will follow the scaling law. This theory can be generalized to interpret the inverse power-law distributions in various fields of physical and social sciences.
Project description:The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to -1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesis for neuronal avalanches by using more stringent statistical analyses. In particular, we performed the following steps: (i) analysis of finite-size scaling to identify scale-free dynamics in neuronal avalanches, (ii) model parameter estimation to determine the specific exponent of the power law, and (iii) comparison of the power law to alternative model distributions. Consistent with critical state dynamics, avalanche size distributions exhibited robust scaling behavior in which the maximum avalanche size was limited only by the spatial extent of sampling ("finite size" effect). This scale-free dynamics suggests the power law as a model for the distribution of avalanche sizes. Using both the Kolmogorov-Smirnov statistic and a maximum likelihood approach, we found the slope to be close to -1.5, which is in line with previous reports. Finally, the power law model for neuronal avalanches was compared to the exponential and to various heavy-tail distributions based on the Kolmogorov-Smirnov distance and by using a log-likelihood ratio test. Both the power law distribution without and with exponential cut-off provided significantly better fits to the cluster size distributions in neuronal avalanches than the exponential, the lognormal and the gamma distribution. In summary, our findings strongly support the power law scaling in neuronal avalanches, providing further evidence for critical state dynamics in superficial layers of cortex.
Project description:For decades, the work of cell and developmental biologists has demonstrated the striking ability of the mesenchyme and the stroma to instruct epithelial form and function in the mammary gland, but the role of extracellular matrix (ECM) molecules in mammary pattern specification has not been elucidated. Here, we show that stromal collagen I (Col-I) fibers in the mammary fat pad are axially oriented prior to branching morphogenesis. Upon puberty, the branching epithelium orients along these fibers, thereby adopting a similar axial bias. To establish a causal relationship from Col-I fiber to epithelial orientation, we embedded mammary organoids within axially oriented Col-I fiber gels and observed dramatic epithelial co-orientation. Whereas a constitutively active form of Rac1, a molecule implicated in cell motility, prevented a directional epithelial response to Col-I fiber orientation, inhibition of the RhoA/Rho-associated kinase (ROCK) pathway did not. However, time-lapse studies revealed that, within randomly oriented Col-I matrices, the epithelium axially aligns fibers at branch sites via RhoA/ROCK-mediated contractions. Our data provide an explanation for how the stromal ECM encodes architectural cues for branch orientation as well as how the branching epithelium interprets and reinforces these cues through distinct signaling processes.
Project description:BACKGROUND:Though earlier works on modelling transcript abundance from vertebrates to lower eukaroytes have specifically singled out the Zip's law, the observed distributions often deviate from a single power-law slope. In hindsight, while power-laws of critical phenomena are derived asymptotically under the conditions of infinite observations, real world observations are finite where the finite-size effects will set in to force a power-law distribution into an exponential decay and consequently, manifests as a curvature (i.e., varying exponent values) in a log-log plot. If transcript abundance is truly power-law distributed, the varying exponent signifies changing mathematical moments (e.g., mean, variance) and creates heteroskedasticity which compromises statistical rigor in analysis. The impact of this deviation from the asymptotic power-law on sequencing count data has never truly been examined and quantified. RESULTS:The anecdotal description of transcript abundance being almost Zipf's law-like distributed can be conceptualized as the imperfect mathematical rendition of the Pareto power-law distribution when subjected to the finite-size effects in the real world; This is regardless of the advancement in sequencing technology since sampling is finite in practice. Our conceptualization agrees well with our empirical analysis of two modern day NGS (Next-generation sequencing) datasets: an in-house generated dilution miRNA study of two gastric cancer cell lines (NUGC3 and AGS) and a publicly available spike-in miRNA data; Firstly, the finite-size effects causes the deviations of sequencing count data from Zipf's law and issues of reproducibility in sequencing experiments. Secondly, it manifests as heteroskedasticity among experimental replicates to bring about statistical woes. Surprisingly, a straightforward power-law correction that restores the distribution distortion to a single exponent value can dramatically reduce data heteroskedasticity to invoke an instant increase in signal-to-noise ratio by 50% and the statistical/detection sensitivity by as high as 30% regardless of the downstream mapping and normalization methods. Most importantly, the power-law correction improves concordance in significant calls among different normalization methods of a data series averagely by 22%. When presented with a higher sequence depth (4 times difference), the improvement in concordance is asymmetrical (32% for the higher sequencing depth instance versus 13% for the lower instance) and demonstrates that the simple power-law correction can increase significant detection with higher sequencing depths. Finally, the correction dramatically enhances the statistical conclusions and eludes the metastasis potential of the NUGC3 cell line against AGS of our dilution analysis. CONCLUSIONS:The finite-size effects due to undersampling generally plagues transcript count data with reproducibility issues but can be minimized through a simple power-law correction of the count distribution. This distribution correction has direct implication on the biological interpretation of the study and the rigor of the scientific findings. REVIEWERS:This article was reviewed by Oliviero Carugo, Thomas Dandekar and Sandor Pongor.
Project description:Epidemics, flame propagation, and cardiac rhythms are classic examples of reaction-diffusion waves that describe a switch from one alternative state to another. Only two types of waves are known: pulled, driven by the leading edge, and pushed, driven by the bulk of the wave. Here, we report a distinct class of semipushed waves for which both the bulk and the leading edge contribute to the dynamics. These hybrid waves have the kinetics of pushed waves, but exhibit giant fluctuations similar to pulled waves. The transitions between pulled, semipushed, and fully pushed waves occur at universal ratios of the wave velocity to the Fisher velocity. We derive these results in the context of a species invading a new habitat by examining front diffusion, rate of diversity loss, and fluctuation-induced corrections to the expansion velocity. All three quantities decrease as a power law of the population density with the same exponent. We analytically calculate this exponent, taking into account the fluctuations in the shape of the wave front. For fully pushed waves, the exponent is -1, consistent with the central limit theorem. In semipushed waves, however, the fluctuations average out much more slowly, and the exponent approaches 0 toward the transition to pulled waves. As a result, a rapid loss of genetic diversity and large fluctuations in the position of the front occur, even for populations with cooperative growth and other forms of an Allee effect. The evolutionary outcome of spatial spreading in such populations could therefore be less predictable than previously thought.