von Dassow M et al. (2010), Surprisingly simple mechanical behavior of a co...

XB-ART-42570

PLoS One 2010 Dec 28;512:e15359. doi: 10.1371/journal.pone.0015359.

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Surprisingly simple mechanical behavior of a complex embryonic tissue.

von Dassow M , Strother JA , Davidson LA .

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BACKGROUND: Previous studies suggest that mechanical feedback could coordinate morphogenetic events in embryos. Furthermore, embryonic tissues have complex structure and composition and undergo large deformations during morphogenesis. Hence we expect highly non-linear and loading-rate dependent tissue mechanical properties in embryos. METHODOLOGY/PRINCIPAL FINDINGS: We used micro-aspiration to test whether a simple linear viscoelastic model was sufficient to describe the mechanical behavior of gastrula stage Xenopus laevis embryonic tissue in vivo. We tested whether these embryonic tissues change their mechanical properties in response to mechanical stimuli but found no evidence of changes in the viscoelastic properties of the tissue in response to stress or stress application rate. We used this model to test hypotheses about the pattern of force generation during electrically induced tissue contractions. The dependence of contractions on suction pressure was most consistent with apical tension, and was inconsistent with isotropic contraction. Finally, stiffer clutches generated stronger contractions, suggesting that force generation and stiffness may be coupled in the embryo. CONCLUSIONS/SIGNIFICANCE: The mechanical behavior of a complex, active embryonic tissue can be surprisingly well described by a simple linear viscoelastic model with power law creep compliance, even at high deformations. We found no evidence of mechanical feedback in this system. Together these results show that very simple mechanical models can be useful in describing embryo mechanics.

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	Figure 1. Mechanical response to micro-aspiration was independent of loading rate.A) Diagram of X. laevis gastrula (stage 11): vegetal view (left); cross section (right). Hatched areas indicate where measurements were made. B) Diagram of the micro-aspirator (not to scale) on the stage of an inverted microscope. An embryo (em) is pressed to the channel (ch) using a polished glass rod (not shown). The pressures in the high- and low- pressure reservoirs (hpr and lpr) are adjusted hydrostatically. The aspirated tissue is imaged from below. C) Aspirated tissue (arrow) is visible in the channel. The bulk of the embryo is on the right of the channel opening (dashed line) but is hidden by reflections off the channel block surface. D–F) Tissue positions and curve fits using the power-law model for three different pressure histories. G-I) Viscoelastic parameters at different suction rates: compliance at 60 s (G), compliance at 300 s (H) and power-law exponent (I). Different symbols indicate which part of the data were fitted: "suction": −120 to +600 s; "release": +540 to +1200 s; "whole series": −120 to +1200 s.
	Figure 2. Mechanical response to micro-aspiration is independent of loading pressure.Effect of loading pressure on (A) compliance at 60 s (J[60]) and 300 s (J[300]), and (B) the power-law exponent, β. Lines for least squares fits are shown for visual clarity only. Viscoelastic parameters were calculated from tissue positions between −30 and +300 s after application of loading pressure.
	Figure 3. The effect of non-linear material properties.(A) Aspirated length L as a function of pressure P in an FEM model for different degrees of material non-linearity (increasing α). Aspirated length was normalized to channel radius, and pressure was normalized to the Young's modulus (‘E’). Solid lines: frictional coefficient of 0; dotted lines: frictional coefficient of 0.5. (B) There was no detectable effect of initial aspirated length on the measured compliance for either the loading rate experiment (‘R’, triangles) or the load magnitude experiment (‘M’, squares).
	Figure 4. Micro-aspiration produces complex patterns of stretch and compression.Maps of the three principal stretch ratios, λi, for different values of α and different aspirated lengths ‘L’ (relative to channel radius, ‘Rc’), and no friction between the tissue and the channel. Only half of the channel is shown because the model was axisymmetric. The plots were cropped as indicated by dotted lines in the insets (‘Ch’: channel; ‘Em’: embryo). Deformations outside of the enlarged region were low and nearly uniform. Note that the color scales differ for different principal stretches, and for different aspirated lengths.
	Figure 5. Pressure time courses can be reconstructed from displacements.A) An example of an applied pressure pulse (see Fig. 1F). The viscoelastic model was fitted to the tissue position vs. time data prior to the pressure pulse (dashed line) given the applied pressure (dotted gray line). The fitted viscoelastic parameters were then used to calculate subsequent pressure changes (black dotted line) from tissue displacements allowing comparison of applied and calculated pressure pulse. B) The magnitude of actual applied pressure pulses versus the maximum pressure during the pulse calculated based on the viscoelastic model.
	Figure 6. Comparing two models of induced contractions.Loading pressure versus magnitude of induced contractions calculated as A) equivalent pressure, B) apical tension, or C) the ratio of the maximal displacement during the contraction, ‘m’, to the pre-contraction aspirated length, L[300]. Lines for linear least squares fits are shown for clarity only. D) Average compliance for each clutch versus average apical tension for each clutch. Compliance was calculated at 60 s (J[60]) and 300 s (J[300]); n = 3 to 4 for each clutch.

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