In silico estimates of the free energy rates in growing tumor spheroids

The physics of solid tumor growth can be considered at three distinct size scales: the tumor scale, the cell-extracellular matrix (ECM) scale and the sub-cellular scale. In this paper we consider the tumor scale in the interest of eventually developing a system-level understanding of the progression of cancer. At this scale, cell populations and chemical species are best treated as concentration fields that vary with time and space. The cells have chemo-mechanical interactions with each other and with the ECM, consume glucose and oxygen that are transported through the tumor, and create chemical byproducts. We present a continuum mathematical model for the biochemical dynamics and mechanics that govern tumor growth. The biochemical dynamics and mechanics also engender free energy changes that serve as universal measures for comparison of these processes. Within our mathematical framework we therefore consider the free energy inequality, which arises from the first and second laws of thermodynamics. With the model we compute preliminary estimates of the free energy rates of a growing tumor in its pre-vascular stage by using currently available data from single cells and multicellular tumor spheroids.Comment: 27 pages with 5 figures and 2 tables. Figures and tables appear at the end of the pape

Gene synteny comparisons between different vertebrates provide new insights into breakage and fusion events during mammalian karyotype evolution

<p>Abstract</p> <p>Background</p> <p>Genome comparisons have made possible the reconstruction of the eutherian ancestral karyotype but also have the potential to provide new insights into the evolutionary inter-relationship of the different eutherian orders within the mammalian phylogenetic tree. Such comparisons can additionally reveal (i) the nature of the DNA sequences present within the evolutionary breakpoint regions and (ii) whether or not the evolutionary breakpoints occur randomly across the genome. Gene synteny analysis (E-painting) not only greatly reduces the complexity of comparative genome sequence analysis but also extends its evolutionary reach.</p> <p>Results</p> <p>E-painting was used to compare the genome sequences of six different mammalian species and chicken. A total of 526 evolutionary breakpoint intervals were identified and these were mapped to a median resolution of 120 kb, the highest level of resolution so far obtained. A marked correlation was noted between evolutionary breakpoint frequency and gene density. This correlation was significant not only at the chromosomal level but also sub-chromosomally when comparing genome intervals of lengths as short as 40 kb. Contrary to previous findings, a comparison of evolutionary breakpoint locations with the chromosomal positions of well mapped common fragile sites and cancer-associated breakpoints failed to reveal any evidence for significant co-location. Primate-specific chromosomal rearrangements were however found to occur preferentially in regions containing segmental duplications and copy number variants.</p> <p>Conclusion</p> <p>Specific chromosomal regions appear to be prone to recurring rearrangement in different mammalian lineages ('breakpoint reuse') even if the breakpoints themselves are likely to be non-identical. The putative ancestral eutherian genome, reconstructed on the basis of the synteny analysis of 7 vertebrate genome sequences, not only confirmed the results of previous molecular cytogenetic studies but also increased the definition of the inferred structure of ancestral eutherian chromosomes. For the first time in such an analysis, the opossum was included as an outgroup species. This served to confirm our previous model of the ancestral eutherian genome since all ancestral syntenic segment associations were also noted in this marsupial.</p

Onset of collective and cohesive motion

We study the onset of collective motion, with and without cohesion, of groups of noisy self-propelled particles interacting locally. We find that this phase transition, in two space dimensions, is always discontinuous, including for the minimal model of Vicsek et al. [Phys. Rev. Lett. {\bf 75},1226 (1995)] for which a non-trivial critical point was previously advocated. We also show that cohesion is always lost near onset, as a result of the interplay of density, velocity, and shape fluctuations.Comment: accepted for publication in Phys. Rev. Let

Elastic free energy drives the shape of prevascular solid tumors

It is well established that the mechanical environment influences cell functions in health and disease. Here, we address how the mechanical environment influences tumor growth, in particular, the shape of solid tumors. In an in vitro tumor model, which isolates mechanical interactions between tumor cells and a hydrogel, we find that tumors grow as ellipsoids, resembling the same, oft-reported observation of in vivo tumors. Specifically, an oblate ellipsoidal tumor shape robustly occurs when the tumors grow in hydrogels that are stiffer than the tumors, but when they grow in more compliant hydrogels they remain closer to spherical in shape. Using large scale, nonlinear elasticity computations we show that the oblate ellipsoidal shape minimizes the elastic free energy of the tumor-hydrogel system. Having eliminated a number of other candidate explanations, we hypothesize that minimization of the elastic free energy is the reason for predominance of the experimentally observed ellipsoidal shape. This result may hold significance for explaining the shape progression of early solid tumors in vivo and is an important step in understanding the processes underlying solid tumor growth.Comment: Six figures in main text. Supporting Information with 6 additional figure

Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles

We construct the hydrodynamic equations for {\em suspensions} of self-propelled particles (SPPs) with spontaneous orientational order, and make a number of striking, testable predictions:(i) SPP suspensions with the symmetry of a true {\em nematic} are {\em always} absolutely unstable at long wavelengths.(ii) SPP suspensions with {\em polar}, i.e., head-tail {\em asymmetric}, order support novel propagating modes at long wavelengths, coupling orientation, flow, and concentration. (iii) In a wavenumber regime accessible only in low Reynolds number systems such as bacteria, polar-ordered suspensions are invariably convectively unstable.(iv) The variance in the number N of particles, divided by the mean , diverges as $^{2/3}$ in polar-ordered SPP suspensions.Comment: submitted to Phys Rev Let

Contraction-induced cluster formation in cardiac cell culture

Evolution of the spatial arrangement of cells in a primary culture of cardiac tissue derived from newborn rats was studied experimentally over extended period. It was found that cells attract each other spontaneously to form a clustered structure over the timescale of several days. These clusters exhibit spontaneous rhythmic contraction and have been confirmed to consist of cardiac muscle cells. Addition of a contraction inhibitor (2,3-butanedione-2-monoxime) to the culture medium resulted in the inhibition of both the spontaneous contractions exhibited by the cells as well as the formation of clusters. Furthermore, the formation of clusters is suppressed when high concentrations of collagen are used for coating the substratum to which the cells adhere. From these experimental observations, it was deduced that the cells are mechanically stressed by the tension associated with repeated contractions and that this results in the cells becoming compact and attracting each other, finally resulting in the formation of clusters. This process can be interpreted as modulation of a cellular network by the activity associated with contraction, which could be employed to control cellular networks by modifying the dynamics associated with the contractions in cardiac tissue culture.Comment: 12 pages, 12 figure

No severe and global X chromosome inactivation in meiotic male germline of Drosophila

This article is a response to Vibranovski et al

Segmental dataset and whole body expression data do not support the hypothesis that non-random movement is an intrinsic property of Drosophila retrogenes

Background: Several studies in Drosophila have shown excessive movement of retrogenes from the X chromosome to autosomes, and that these genes are frequently expressed in the testis. This phenomenon has led to several hypotheses invoking natural selection as the process driving male-biased genes to the autosomes. Metta and Schlotterer (BMC Evol Biol 2010, 10:114) analyzed a set of retrogenes where the parental gene has been subsequently lost. They assumed that this class of retrogenes replaced the ancestral functions of the parental gene, and reported that these retrogenes, although mostly originating from movement out of the X chromosome, showed female-biased or unbiased expression. These observations led the authors to suggest that selective forces (such as meiotic sex chromosome inactivation and sexual antagonism) were not responsible for the observed pattern of retrogene movement out of the X chromosome. Results: We reanalyzed the dataset published by Metta and Schlotterer and found several issues that led us to a different conclusion. In particular, Metta and Schlotterer used a dataset combined with expression data in which significant sex-biased expression is not detectable. First, the authors used a segmental dataset where the genes selected for analysis were less testis-biased in expression than those that were excluded from the study. Second, sex-biased expression was defined by comparing male and female whole-body data and not the expression of these genes in gonadal tissues. This approach significantly reduces the probability of detecting sex-biased expressed genes, which explains why the vast majority of the genes analyzed (parental and retrogenes) were equally expressed in both males and females. Third, the female-biased expression observed by Metta and Schltterer is mostly found for parental genes located on the X chromosome, which is known to be enriched with genes with female-biased expression. Fourth, using additional gonad expression data, we found that autosomal genes analyzed by Metta and Schlotterer are less up regulated in ovaries and have higher chance to be expressed in meiotic cells of spermatogenesis when compared to X-linked genes. Conclusions: The criteria used to select retrogenes and the sex-biased expression data based on whole adult flies generated a segmental dataset of female-biased and unbiased expressed genes that was unable to detect the higher propensity of autosomal retrogenes to be expressed in males. Thus, there is no support for the authors' view that the movement of new retrogenes, which originated from X-linked parental genes, was not driven by selection. Therefore, selection-based genetic models remain the most parsimonious explanations for the observed chromosomal distribution of retrogenes.National Institutes of Health grant [NIH R0IGM078070-01A1, R01 GM078070-03S1, T32 GM007197]National Institutes of Health grantChicago Community TrustChicago Community TrustChicago Biomedical ConsortiumChicago Biomedical ConsortiumKey Laboratory of the Zoological Systematics and Evolution of the Chinese Academy of Sciences [O952B81P05]Key Laboratory of the Zoological Systematics and Evolution of the Chinese Academy of Science