Colloquium: Mechanical formalisms for tissue dynamics

The understanding of morphogenesis in living organisms has been renewed by tremendous progressin experimental techniques that provide access to cell-scale, quantitative information both on theshapes of cells within tissues and on the genes being expressed. This information suggests that ourunderstanding of the respective contributions of gene expression and mechanics, and of their crucialentanglement, will soon leap forward. Biomechanics increasingly benefits from models, which assistthe design and interpretation of experiments, point out the main ingredients and assumptions, andultimately lead to predictions. The newly accessible local information thus calls for a reflectionon how to select suitable classes of mechanical models. We review both mechanical ingredientssuggested by the current knowledge of tissue behaviour, and modelling methods that can helpgenerate a rheological diagram or a constitutive equation. We distinguish cell scale ("intra-cell")and tissue scale ("inter-cell") contributions. We recall the mathematical framework developpedfor continuum materials and explain how to transform a constitutive equation into a set of partialdifferential equations amenable to numerical resolution. We show that when plastic behaviour isrelevant, the dissipation function formalism appears appropriate to generate constitutive equations;its variational nature facilitates numerical implementation, and we discuss adaptations needed in thecase of large deformations. The present article gathers theoretical methods that can readily enhancethe significance of the data to be extracted from recent or future high throughput biomechanicalexperiments.Comment: 33 pages, 20 figures. This version (26 Sept. 2015) contains a few corrections to the published version, all in Appendix D.2 devoted to large deformation

Comparative study of non-invasive force and stress inference methods in tissue

In the course of animal development, the shape of tissue emerges in part from mechanical and biochemical interactions between cells. Measuring stress in tissue is essential for studying morphogenesis and its physical constraints. Experimental measurements of stress reported thus far have been invasive, indirect, or local. One theoretical approach is force inference from cell shapes and connectivity, which is non-invasive, can provide a space-time map of stress and relies on prefactors. Here, to validate force- inference methods, we performed a comparative study of them. Three force-inference methods, which differ in their approach of treating indefiniteness in an inverse problem between cell shapes and forces, were tested by using two artificial and two experimental data sets. Our results using different datasets consistently indicate that our Bayesian force inference, by which cell-junction tensions and cell pressures are simultaneously estimated, performs best in terms of accuracy and robustness. Moreover, by measuring the stress anisotropy and relaxation, we cross-validated the force inference and the global annular ablation of tissue, each of which relies on different prefactors. A practical choice of force-inference methods in distinct systems of interest is discussed.Comment: 12 pages, 8 figures, EPJ E: Topical issue on "Physical constraints on morphogenesis and evolution

Nitric oxide and cyclic nucleotides: Their roles in junction dynamics and spermatogenesis

Spermatogenesis is a highly complicated process in which functional spermatozoa (haploid, 1n) are generated from primitive mitotic spermatogonia (diploid, 2n). This process involves the differentiation and transformation of several types of germ cells as spermatocytes and spermatids undergo meiosis and differentiation. Due to its sophistication and complexity, testis possesses intrinsic mechanisms to modulate and regulate different stages of germ cell development under the intimate and indirect cooperation with Sertoli and Leydig cells, respectively. Furthermore, developing germ cells must translocate from the basal to the apical (adluminal) compartment of the seminiferous epithelium. Thus, extensive junction restructuring must occur to assist germ cell movement. Within the seminiferous tubules, three principal types of junctions are found namely anchoring junctions, tight junctions, and gap junctions. Other less studied junctions are desmosome-like junctions and hemidesmosome junctions. With these varieties of junction types, testes are using different regulators to monitor junction turnover. Among the uncountable junction modulators, nitric oxide (NO) is a prominent candidate due to its versatility and extensive downstream network. NO is synthesized by nitric oxide synthase (NOS). Three traditional NOS, specified as endothelial NOS (eNOS), inducible NOS (iNOS), and neuronal NOS (nNOS), and one testis-specific nNOS (TnNOS) are found in the testis. For these, eNOS and iNOS were recently shown to have putative junction regulation properties. More important, these two NOSs likely rely on the downstream soluble guanylyl cyclase/cGMP/protein kinase G signaling pathway to regulate the structural components at the tight junctions and adherens junctions in the testes. Apart from the involvement in junction regulation, NOS/NO also participates in controlling the levels of cytokines and hormones in the testes. On the other hand, NO is playing a unique role in modulating germ cell viability and development, and indirectly acting on some aspects of male infertility and testicular pathological conditions. Thus, NOS/NO bears an irreplaceable role in maintaining the homeostasis of the microenvironment in the seminiferous epithelium via its different downstream signaling pathways

Upregulation of Forces and Morphogenic Asymmetries in Dorsal Closure during Drosophila Development

Tissue dynamics during dorsal closure, a stage of Drosophila development, provide a model system for cell sheet morphogenesis and wound healing. Dorsal closure is characterized by complex cell sheet movements, driven by multiple tissue specific forces, which are coordinated in space, synchronized in time, and resilient to UV-laser perturbations. The mechanisms responsible for these attributes are not fully understood. We measured spatial, kinematic, and dynamic antero-posterior asymmetries to biophysically characterize both resiliency to laser perturbations and failure of closure in mutant embryos and compared them to natural asymmetries in unperturbed, wild-type closure. We quantified and mathematically modeled two processes that are upregulated to provide resiliency—contractility of the amnioserosa and formation of a seam between advancing epidermal sheets, i.e., zipping. Both processes are spatially removed from the laser-targeted site, indicating they are not a local response to laser-induced wounding and suggesting mechanosensitive and/or chemosensitive mechanisms for upregulation. In mutant embryos, tissue junctions initially fail at the anterior end indicating inhomogeneous mechanical stresses attributable to head involution, another developmental process that occurs concomitant with the end stages of closure. Asymmetries in these mutants are reversed compared to wild-type, and inhomogeneous stresses may cause asymmetries in wild-type closure

Second-order nonlinear least squares estimation

Nonlinear regression, Asymmetric error distribution, Weighted least squares, Minimum distance estimator, Consistency, Asymptotic normality,