Identifying Essential Mechanisms for Cortical Actomyosin Contractions with Computational Modeling

The success of embryogenesis requires coordinated cell-cell signaling, tissue patterning, and morphogenetic movements. In order to understand how birth defects such as spin bifid a occur, we must understand how signaling and patterning integrate mechanically to drive morphogenetic movements. Although there are many different scales to consider (molecular, cellular or tissue), this dissertation is unique in its attempt to bridge molecular biophysics to cell- and tissue-scale biomechanics. On the molecular level, filamentous actin (F-actin) and non-muscle myosin II (NMM II) motors are cytoskeletal proteins responsible for cell motility and shape change. Currently, there are no techniques for measuring in vivo forces generated by actomyosin. In order to gain a better understanding of the behavior of actomyosin in vivo, we have developed theoretical models, beginning with a simple rotational model for actomyosin, and extended the theory to a simple sliding filament system. Based on the results and intuition gained from these simple models, we developed a 2D model where we can study the emergent morphology of the filaments and motors. In vivo, we observe actomyosin punctuated contractions which initiate from a quiescent background of F-actin to flow into a region of high intensity and disassemble, returning to baseline levels. Previous research showed the correlation between the locations of these punctuated contractions and the resultant cell shape change during development. The 2D model allows us to explore the kinematics of F-actin arrays and the dynamics of their force production as we vary biophysical parameters. We can also test the model results against in vitro observations of purified actin and myosin. Although still simplified, our model has set the groundwork for future studies on the role of actin binding proteins in actomyosin dynamics, simulating the role of actomyosin in cell shape change, and making comparative measurements for experimental studies of purified cytoskeletal actomyosin

Biomechanics and the thermotolerance of development

Successful completion of development requires coordination of patterning events with morphogenetic movements. Environmental variability challenges this coordination. For example, developing organisms encounter varying environmental temperatures that can strongly influence developmental rates. We hypothesized that the mechanics of morphogenesis would have to be finely adjusted to allow for normal morphogenesis across a wide range of developmental rates. We formulated our hypothesis as a simple model incorporating time-dependent application of force to a viscoelastic tissue. This model suggested that the capacity to maintain normal morphogenesis across a range of temperatures would depend on how both tissue viscoelasticity and the forces that drive deformation vary with temperature. To test this model we investigated how the mechanical behavior of embryonic tissue (Xenopus laevis) changed with temperature; we used a combination of micropipette aspiration to measure viscoelasticity, electrically induced contractions to measure cellular force generation, and confocal microscopy to measure endogenous contractility. Contrary to expectations, the viscoelasticity of the tissues and peak contractile tension proved invariant with temperature even as rates of force generation and gastrulation movements varied three-fold. Furthermore, the relative rates of different gastrulation movements varied with temperature: the speed of blastopore closure increased more slowly with temperature than the speed of the dorsal-to-ventral progression of involution. The changes in the relative rates of different tissue movements can be explained by the viscoelastic deformation model given observed viscoelastic properties, but only if morphogenetic forces increase slowly rather than all at once. © 2014 von Dassow et al

Duration of actomyosin contractions depends on temperature.

<p>(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.</p

Model schematic.

<p>(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 t_P; the blastopore closes at t_C. In the generalized model (Model 1) we assumed all morphogenetic durations (t_P, t_C, etc) changed by the same proportion with temperature. In the step and ramp models (Models 2A & B) t_P is used, as an estimate of the timing of cell behaviors that exert morphogenetic forces, to predict t_C. 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 (ε_P,ε_C,…). 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[t_C] = ε_C); however, the strain at t_P varies with temperature.</p

Temperature dependence of mechanical and morphogenetic parameters.

<p>*<i>P</i>≤0.05;</p><p>**<i>P</i>≤0.01:</p><p>Significant difference between 16 and 26°C for log transformed parameters.</p>1<p>Estimated mean and confidence interval for log-transformed parameters were determined using ANOVA (mechanics and actin) and Tukey's honestly significant difference criterion, or T-tests (morphogenesis).</p><p>Values were then transformed back to a linear scale to provide estimates of the lower and upper bounds (LB, UB) on the ratio.</p>2<p>Comparing 17° and 27°C. Ratios for the durations of actin contractions were 0.9 between 16.9°C and 21.3°C, and 1.5 between 21.3°C and 26.7°C.</p><p>To obtain confidence bounds here, we used ANOVA with temperature treatment as a categorical variable, and explant as a random factor; clutch was excluded because it was non-significant.</p

Differences among models.

<p>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, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095670#pone.0095670.e016" target="_blank">eqn.16</a>). (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 t_P with temperature does not affect the time t_C to reach strain ε_C (when the blastopore closes) because peak stress and compliance are unchanged (Model 2A, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095670#pone.0095670.e021" target="_blank">eqns. 21</a>–<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095670#pone.0095670.e022" target="_blank">22</a>). A ramp is the sum of stress increments (gray lines; bottom left). Stress timing (hence the slope of the ramp) scales with t_P, and therefore with temperature (red, warm; blue, cool). The time t_C varies with t_P (and therefore temperature) for the ramp model (upper; Model 2B, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095670#pone.0095670.e025" target="_blank">eqns. 25</a>–<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095670#pone.0095670.e026" target="_blank">26</a>), because strain increments follow the change in timing of stress increments (gray lines).</p

Symbols.

<p>Symbols.</p

Temperature dependence of compliance and strength of induced contraction.

<p>(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.</p

Comparison of viscoelastic models of morphogenesis for ramped versus stepped forces.

<p>(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 R_CP, 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 <i>vs.</i> 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 t_C at T₁ is used to calculate R_CP at T₂. (C) Comparison of the observed R_CP 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 R_CP at 26°C for each model (10,000 resamples total).</p

Blastopore closure at high and low temperatures.

<p>(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 (R_CP) of the time for blastopore closure to the time for dorsal-to-ventral progression of involution versus the time (t_P) for dorsal-to-ventral progression of involution. Dots indicate individual embryos. X's indicate medians for clutches (4 to 8 embryos each).</p