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Figure 2. Blastopore closure at high and low temperatures.(A) Upper: vegetal view of an embryo showing the blastopore soon after the start of dorsal superficial involution. Lower left: kymograph of blastopore closure at 26°C, taken along the yellow line from the dorsal side to the ventral side, showing the points when dorsal (DI) and ventral (VI) superficial involution begin, and when the blastopore closes (BC). Right: kymograph taken along a line from the dorsal to the ventral side at 16°C. (B) The ratio (RCP) of the time for blastopore closure to the time for dorsal-to-ventral progression of involution versus the time (tP) for dorsal-to-ventral progression of involution. Dots indicate individual embryos. X's indicate medians for clutches (4 to 8 embryos each).
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Figure 3. Comparison of viscoelastic models of morphogenesis for ramped versus stepped forces.(A) Diagram of model. Summed contractions (wavy lines) average out to stepped or ramped stresses (σ) depending on when cells begin contracting. When applied to the viscoelastic material with compliance J[t], the deformations (strains, ε) follow the time course of ramped forces more closely than stepped force. This can be visualized as adding up strains due to a series of stepped forces applied over time (dotted lines on right). (B) Predictions for RCP, the ratio of the time for morphogenesis (blastopore closure) to the time for patterning (D-V progression of involution), as a function of the time for patterning at temperature T, normalized to the time for patterning at 16°C, for ramped vs. stepped models for different values of β. Yellow dots: grand mean of experimentally observed values. The curves automatically converge to the right hand dot (at 16°C) where T2 = T1 since tC at T1 is used to calculate RCP at T2. (C) Comparison of the observed RCP at 26°C to the predictions for models with ramped or stepped forces, and with temperature invariant or varying mechanical properties (inset: prediction for stepped force model with temperature dependent mechanical properties on a log scale.) Error bars indicate confidence intervals. (D) Histogram of bootstrap resampling estimates of RCP at 26°C for each model (10,000 resamples total).
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Figure 4. Duration of actomyosin contractions depends on temperature.(A) Sequential frames from a representative time-lapse sequence collected from the basal cortex of an animal cap ectoderm explant cultured on fibronectin-coated glass substrate. F-actin dynamics are revealed in cells expressing the actin-binding domain from moesin coupled to EGFP (moe-GFP) (left column). This sample collected at 16°C. (A′) Schematic of frames matching those in (A) highlighting the cell outline (dotted line) and hexagonal regions of the cell cortex identified as “F-actin contractions.” Regions are categorized as contractions when their integrated intensities are 50% greater than the mean intensity of the basal cell cortex. (B) Duration of individual F-actin contractions across the three temperature regimes. (C) Frequency distribution of the duration F-actin contractions at three temperatures. Note abundant short duration contractions at the low temperature regime.
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Figure 5. Model schematic.(A) Diagrams of blastopore closure from the lateral side. The ectoderm and neurectoderm (gray) spreads over the embryo during gastrulation. Involution begins on the dorsal side at t = 0, and begins on the ventral side at tP; the blastopore closes at tC. In the generalized model (Model 1) we assumed all morphogenetic durations (tP, tC, etc) changed by the same proportion with temperature. In the step and ramp models (Models 2A & B) tP is used, as an estimate of the timing of cell behaviors that exert morphogenetic forces, to predict tC. A strip of tissue (A, to right of each whole embryo schematic) experiences spatially and temporally varying stresses (open arrows; stresses from deep tissues not shown), which elongate it and change its shape. We approximate this deformation as uniform stretching of a strip of material (B). The generalized model (Model 1) assumes temperature only affects the speed of morphogenesis, therefore each morphogenetic event occurs at fixed, but unspecified strains (εP,εC,…). In the step and ramp models (Models 2A & B) the main forces driving blastopore closure begin near the start of ventral involution (so ε[0]≈0), and blastopore closure occurs at a fixed strain (ε[tC] = εC); however, the strain at tP varies with temperature.
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Figure 6. Differences among models.Hypothetical stress (left), creep compliance (middle), and deformation (strain, ε; right) in the tissue. (A) The generalized model (Model 1) assumes the relative timing (ô) and the strains, of all events (1, 2, 3,…) are independent of temperature (cool (blue) vs warm (red)), as in a movie played faster. The generalized model does not specify the developmental course of strain or stress, only that timing scales with temperature. The generalized model predicts how stress and compliance vary together as temperature changes (Model 1, eqn.16). (B) Step and ramp models (Models 2A & 2B). The step and ramp models assume morphogenetic stresses are stepped (top) or ramped (bottom) with time. For a step stress (upper), the change in tP with temperature does not affect the time tC to reach strain εC (when the blastopore closes) because peak stress and compliance are unchanged (Model 2A, eqns. 21–22). A ramp is the sum of stress increments (gray lines; bottom left). Stress timing (hence the slope of the ramp) scales with tP, and therefore with temperature (red, warm; blue, cool). The time tC varies with tP (and therefore temperature) for the ramp model (upper; Model 2B, eqns. 25–26), because strain increments follow the change in timing of stress increments (gray lines).
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Figure 1. Temperature dependence of compliance and strength of induced contraction.(A) Representative kymographs of microaspiration with electrically induced contractions at 900 seconds at 16°C (upper) and 26°C (lower). (B) Fit of power law viscoelastic model to the aspirated length from 600 to 900 s for the 26°C case. (C) Flow chart for analysis of contractions. (D) Contraction analysis. ‘X's indicate half-max, max, and return to half-max for each curve. Panels B and D show data from the lower embryo in A. Arrowheads in A and B indicate electrical stimuli. (E) β, (F) maximum displacement during induced contraction, (G) duration (half-maximum until return to half-maximum displacement) of contraction, (H) compliance at 1 s (triangles) and at 300 s (circles), (I) maximum apical tension during induced contraction, (J) duration of apical tension. Triangles and circles: individual embryos; X's: means.
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