Stress relaxation behavior of tessellated cartilage from the jaws of blue sharks

AbstractMuch of the skeleton of sharks, skate and rays (Elasmobranchii) is characterized by a tessellated structure, composed of a shell of small, mineralized plates (tesserae) joined by intertesseral ligaments overlaying a soft cartilage core. Although tessellated cartilage is a defining feature of this group of fishes, the significance of this skeletal tissue type – particularly from a mechanical perspective – is unknown. The aim of the present work was to perform stress relaxation experiments with tessellated cartilage samples from the jaws of blue sharks to better understand the time dependent behavior of this skeletal type.In order to facilitate this aim, the resulting relaxation behavior for different loading directions were simulated using the transversely isotropic biphasic model and this model combined with generalized Maxwell elements to represent the tessellated layer. Analysis of the ability of the models to simulate the observed experimental behavior indicates that the transversely isotropic biphasic model can provide good predictions of the relaxation behavior of the hyaline cartilage. However, the incorporation of Maxwell elements into this model can achieve a more accurate simulation of the dynamic behavior of calcified cartilage when the loading is parallel to the tessellated layer. Correlation of experimental data with present combined composite models showed that the equilibrium modulus of the tessellated layer for this loading direction is about 45 times greater than that for uncalcified cartilage. Moreover, tessellation has relatively little effect on the viscoelasticity of shark cartilage under loading that is normal to the tessellated layer

Determining the control networks regulating stem cell lineages in colonic crypts

The question of stem cell control is at the center of our understanding of tissue functioning, both in healthy and cancerous conditions. It is well accepted that cellular fate decisions (such as divisions, differentiation, apoptosis) are orchestrated by a network of regulatory signals emitted by different cell populations in the lineage and the surrounding tissue. The exact regulatory network that governs stem cell lineages in a given tissue is usually unknown. Here we propose an algorithm to identify a set of candidate control networks that are compatible with (a) measured means and variances of cell populations in different compartments, (b) qualitative information on cell population dynamics, such as the existence of local controls and oscillatory reaction of the system to population size perturbations, and (c) statistics of correlations between cell numbers in different compartments. Using the example of human colon crypts, where lineages are comprised of stem cells, transit amplifying cells, and differentiated cells, we start with a theoretically known set of 32 smallest control networks compatible with tissue stability. Utilizing near-equilibrium stochastic calculus of stem cells developed earlier, we apply a series of tests, where we compare the networks' expected behavior with the observations. This allows us to exclude most of the networks, until only three, very similar, candidate networks remain, which are most compatible with the measurements. This work demonstrates how theoretical analysis of control networks combined with only static biological data can shed light onto the inner workings of stem cell lineages, in the absence of direct experimental assessment of regulatory signaling mechanisms. The resulting candidate networks are dominated by negative control loops and possess the following properties: (1) stem cell division decisions are negatively controlled by the stem cell population, (2) stem cell differentiation decisions are negatively controlled by the transit amplifying cell population

Mathematical Modeling of Cancer Stem Cells and Therapeutic Intervention Methods

We develop a multispecies continuum model to simulate the spatiotemporal dynamics of cell lineages in solid tumors is discussed. The model accounts for protein signaling factors produced by cells in lineages, and nutrients supplied by the microenvironment. We find that the combination therapy involving differentiation promoters and radiotherapy is very effective in eradicating such a tumor. We investigate the effect of production of various feedback factors by healthy tissue on tumor morphologies. Our simulation results show that the larger production rate of the negative feedback factor by healthy tissue surrounding the tumor, in general lead to smaller, more compact and more circular tumor shapes. However, the increase in the concentration of these feedback factors may have non-monotone effect on the tumor morphologies. We investigate the effect of initial shape on therapy effectiveness. The results from the simulations show that the initial tumor geometry might play an important role in tumor prognostic and the effectiveness of a specific treatment. We observe that the therapy is more effective on tumors that still respond to the signals received from the healthy tissue in comparison with the ones that do not respond to signaling factors (in this case differentiation signals) by stromal tissue or healthy tissue surrounding the tumor. It is shown that the tumors with larger shape factors and smaller areas (more elongated and thinner) respond better to treatment, and the combination therapy is more successful on tumors with such characteristics. We applied mathematical modeling of radiotherapy using experimental data provided from our collaborative work with radiational oncology department of University of California, Los Angeles. Our investigations show that in order to match the experimental results with the simulations, the dedifferentiation rate of non-stem cells should be increased as a function of radiation dose. It is also observed that the population of induced stem cells followed such exponential relationship with respect to therapy dose. The results from simulations and the analysis of the equations suggest that in order for the simulation results to match with the experimental data, the original stem cells and the induced stem cells may undergo direct differentiation

Multispecies model of cell lineages and feedback control in solid tumors.

We develop a multispecies continuum model to simulate the spatiotemporal dynamics of cell lineages in solid tumors. The model accounts for protein signaling factors produced by cells in lineages, and nutrients supplied by the microenvironment. Together, these regulate the rates of proliferation, self-renewal and differentiation of cells within the lineages, and control cell population sizes and distributions. Terminally differentiated cells release proteins (e.g., from the TGFβ superfamily) that feedback upon less differentiated cells in the lineage both to promote differentiation and decrease rates of proliferation (and self-renewal). Stem cells release a short-range factor that promotes self-renewal (e.g., representative of Wnt signaling factors), as well as a long-range inhibitor of this factor (e.g., representative of Wnt inhibitors such as Dkk and SFRPs). We find that the progression of the tumors and their response to treatment is controlled by the spatiotemporal dynamics of the signaling processes. The model predicts the development of spatiotemporal heterogeneous distributions of the feedback factors (Wnt, Dkk and TGFβ) and tumor cell populations with clusters of stem cells appearing at the tumor boundary, consistent with recent experiments. The nonlinear coupling between the heterogeneous expressions of growth factors and the heterogeneous distributions of cell populations at different lineage stages tends to create asymmetry in tumor shape that may sufficiently alter otherwise homeostatic feedback so as to favor escape from growth control. This occurs in a setting of invasive fingering, and enhanced aggressiveness after standard therapeutic interventions. We find, however, that combination therapy involving differentiation promoters and radiotherapy is very effective in eradicating such a tumor

Multispecies model of cell lineages and feedback control in solid tumors.

We develop a multispecies continuum model to simulate the spatiotemporal dynamics of cell lineages in solid tumors. The model accounts for protein signaling factors produced by cells in lineages, and nutrients supplied by the microenvironment. Together, these regulate the rates of proliferation, self-renewal and differentiation of cells within the lineages, and control cell population sizes and distributions. Terminally differentiated cells release proteins (e.g., from the TGFβ superfamily) that feedback upon less differentiated cells in the lineage both to promote differentiation and decrease rates of proliferation (and self-renewal). Stem cells release a short-range factor that promotes self-renewal (e.g., representative of Wnt signaling factors), as well as a long-range inhibitor of this factor (e.g., representative of Wnt inhibitors such as Dkk and SFRPs). We find that the progression of the tumors and their response to treatment is controlled by the spatiotemporal dynamics of the signaling processes. The model predicts the development of spatiotemporal heterogeneous distributions of the feedback factors (Wnt, Dkk and TGFβ) and tumor cell populations with clusters of stem cells appearing at the tumor boundary, consistent with recent experiments. The nonlinear coupling between the heterogeneous expressions of growth factors and the heterogeneous distributions of cell populations at different lineage stages tends to create asymmetry in tumor shape that may sufficiently alter otherwise homeostatic feedback so as to favor escape from growth control. This occurs in a setting of invasive fingering, and enhanced aggressiveness after standard therapeutic interventions. We find, however, that combination therapy involving differentiation promoters and radiotherapy is very effective in eradicating such a tumor