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With carbon particles we analyzed patterns of growth in Acetabularia acetabulum (Lam.) P.C. Silva, a giant unicell famous for classic development studies. We focused on the stalk apex, which generates the stalk, whorls of hairs, and whorls of gametophores. To gain visual and physical accessibility, we amputated the youngest whorls of hair and the original apex and performed experiments on the apex that regenerated. Video analysis indicated that most growth occurred near the tip of the new apex. Less growth occured throughout the cut-interwhorl. We also analyzed cell wall thickness along stalks cleared of cytoplasm. Correlating growth data to wall morphology suggests growth near the apex may be proportional to stress on the cell wall. We propose that turgor-pressure wall stress modulates local apical cell wall growth rates. A supplementary model, relating cell wall curvature and growth rate in the cut-interwhorl, characterizes how the stalk's final dimensions and nearly cylindrical shap may arise. See http://faculty.washington.edu/mandoli/vondassow for supplementary data, analysis, and mathematical appendices. We believe this is the first quantiative description of apex morphogenesis of A. acetabulum.

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All insects possess homologous segments, but segment specification differs radically among insect orders. In Drosophila, maternal morphogens control the patterned activation of gap genes, which encode transcriptional regulators that shape the patterned expression of pair-rule genes. This patterning cascade takes place before cellularization. Pair-rule gene products subsequently 'imprint' segment polarity genes with reiterated patterns, thus defining the primordial segments. This mechanism must be greatly modified in insect groups in which many segments emerge only after cellularization. In beetles and parasitic wasps, for instance, pair-rule homologues are expressed in patterns consistent with roles during segmentation, but these patterns emerge within cellular fields. In contrast, although in locusts pair-rule homologues may not control segmentation, some segment polarity genes and their interactions are conserved. Perhaps segmentation is modular, with each module autonomously expressing a characteristic intrinsic behaviour in response to transient stimuli. If so, evolution could rearrange inputs to modules without changing their intrinsic behaviours. Here we suggest, using computer simulations, that the Drosophila segment polarity genes constitute such a module, and that this module is resistant to variations in the kinetic constants that govern its behaviour.

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We studied cyclic reorganizations of filamentous actin, myosin II and microtubules in syncytial Drosophila blastoderms using drug treatments, time-lapse movies and laser scanning confocal microscopy of fixed stained embryos (including multiprobe three-dimensional reconstructions). Our observations imply interactions between microtubules and the actomyosin cytoskeleton. They provide evidence that filamentous actin and cytoplasmic myosin II are transported along microtubules towards microtubule plus ends, with actin and myosin exhibiting different affinities for the cell's cortex. Our studies further reveal that cell cycle phase modulates the amounts of both polymerized actin and myosin II associated with the cortex. We analogize pseudocleavage furrow formation in the Drosophila blastoderm with how the mitotic apparatus positions the cleavage furrow for standard cytokinesis, and relate our findings to polar relaxation/global contraction mechanisms for furrow formation.

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Progress of a cell through its reproductive cycle of DNA synthesis and division is governed by a complex network of biochemical reactions controlling the activities of both M-phase- and S-phase-promoting factors. Standard chemical kinetic theory provides a disciplined method for expressing the molecular biologists' diagrams and intuition in precise mathematical form, so that qualitative and quantitative implications of our 'working models' can be derived and compared with experiment.

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We present here a model for how chemical reactions generate protrusive forces by rectifying Brownian motion. This sort of energy transduction drives a number of intracellular processes, including filopodial protrusion, propulsion of the bacterium Listeria, and protein translocation.

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The steroid hormone 20-hydroxyecdysone (20HE) and the Broad-Complex locus (BRC) are involved in regulating developmental changes in gene expression around the time of metamorphosis in Drosophila. We have investigated the regulatory interactions between 20HE, BRC, and a set of genes expressed in the fat body of third-instar Drosophila larvae. RNA levels for two hormone-inducible genes, Larval Serum Protein-2 and P1, accumulate to normal levels in BRC-mutant larvae. In contrast, RNA levels for the P6 gene were affected by mutations at BRC. On the basis of the results of experiments in which hormone concentrations were varied in BRC-mutant or wild-type larvae, we conclude that 20HE can both increase and decrease P6 RNA levels in the absence of BRC product(s). BRC appears to be a trans-acting modulator of the response of P6 to the hormone. We propose that BRC attenuates the repressive effect of the hormone, expanding the range of hormone concentrations that induce the gene, thus allowing P6 RNA to reach high levels during the third larval instar. The results are discussed in relation to other genes that are regulated by the same two trans-acting factors. A model is presented that refines the model of Ashburner et al. (1974, Cold Spring Harbor Symp. Quant. Biol. 38: 655-662) for the hormonal regulation of gene activity.

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The pair-rule genes hairy, runt, even-skipped, and fushi tarazu express their mRNAs and proteins in striped patterns in the Drosophila embryo at the blastoderm stage. Previous studies have shown that the generation of these patterns depends upon products of the gap genes and upon interactions between the pair-rule genes themselves. Here we show that blocking protein synthesis induces expression of each of the pair-rule mRNAs in virtually all regions of the embryo. Our observations together with genetic studies carried out in other laboratories suggest that negative feedback between the pair-rule genes plays a key role in striped expression of pair-rule genes. We propose that stable proteins, present in all regions of the embryo, first activate transcription of these pair-rule genes constitutively. Then, various combinations of unstable proteins repress their transcription in a patterned fashion; each stripe of accumulated products of a given pair-rule gene marks a region where it was not repressed. We develop this idea in mathematical form and demonstrate that a network of mutual repression by pair-rule genes can make each blastoderm nucleus into a genetic switch with two stable states. If preexisting gap gene patterns provide initial bias to the blastoderm nuclei, then the "bistable switch behavior" of the nuclei can refine an initially weak spatial bias into a final pattern of sharp stripes.

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In the Drosophila embryo at the blastoderm stage, the segmentation gene fushi tarazu (ftz) is expressed in a seven-banded pattern. The generation of this pattern, like many other segmentation gene expression patterns, coincides with the formation of cell membranes around the blastoderm nuclei. To test the role of cellularization in resolving the banded ftz pattern, we used cytoskeletal inhibitors (colcemid and cytochalasin B) to block cellularization. We found that banded ftz RNA and protein patterns can form without cellular structure. We also tested the importance of rapid degradation of the ftz RNA, using cycloheximide to block degradation. RNA degradation is essential to maintain the banded ftz pattern in a syncytium, but is not required to maintain the pattern in a cellularized embryo. A latticework of cytoskeletal microtubules that forms during cellularization appears to be a key component in localizing the ftz mRNA. We conclude that RNA degradation and cellular structure normally work together to localize ftz RNA to its sites of synthesis.

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We present here a new model for epithelial morphogenesis, which we call the 'cortical tractor model'. This model assumes that the motile activities of epithelial cells are similar to those of mesenchymal cells, with the added constraint that the cells in an epithelial sheet remain attached at their apical circumference. In particular, we assert that there is a time-averaged motion of cortical cytoplasm which flows from the basal and lateral surfaces to the apical region. This cortical flow carries with it membrane and adhesive structures that are inserted basally and resorbed apically. Thus the apical seal that characterizes epithelial sheets is a dynamic structure: it is continuously created by the cortical flow which piles up components near where they are recycled in the apical region. By use of mechanical analyses and computer simulations we demonstrate that the cortical tractor motion can reproduce a variety of epithelial motions, including columnarization (placode formation), invagination and rolling. It also provides a mechanism for driving active cell rearrangements within an epithelial sheet, while maintaining the integrity of the apical seal. Active repacking of epithelial cells appears to drive a number of morphogenetic processes. Neurulation in amphibians provides an example of a process in which all four of the above morphogenetic movements appear to play a role. Here we reexamine the process of neurulation in amphibians in light of the cortical tractor model, and find that it provides an integrated view of this important morphogenetic process.

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If each of many cells of an embryo (or different zones in a single cell) possess identical active cytogel machinery, having the 'right' mechanochemical response properties, then the collective interaction among those identical participants leads automatically to the globally coherent tissue deformations seen in embryogenesis, and to shuttle streaming in the plasmodial slime mould Physarum polycephalum. Biologically plausible, and experimentally verifiable hypotheses are proposed concerning how the tension generated by a strand of cytogel is determined by the deformation it suffers and by the concentration of a contraction trigger chemical, Ca2+, whose kinetics involve coupling to mechanical strain. The consequences of these hypotheses, deduced by solving the appropriate differential equation systems numerically, and displayed in computer-animated films, closely imitate diverse tissue deformation events seen in developing embryos. The same hypotheses on cytogel behaviour are used to model a thick-walled Physarum vein segment, and two such segments are set up to be able to pump endoplasm back and forth between them. Under certain conditions, this model exhibits spontaneous rhythmic mechanochemical oscillations, many features of which correlate well with shuttle streaming in Physarum. Small gradual variations of parameters, presumably under genetic control, are shown to cause abrupt and biologically interesting bifurcations of the qualitative behaviour of the model.

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The contractility of actomyosin gels is the basis for a variety of cellular motility phenomena. We present here a mechanical analysis of contractile gels. By making certain hypotheses on the chemical regulation of cytogel contraction we formulate a model for the rhythmic contractions of plasmodia in the slime mold Physarum polycephalum which is in accord with a number of experimental observations.

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A continuum theory is proposed for the chemically controlled cytoplasmic streaming observed in pseudopodium extension in Chaos Carolinensis. Amoeboid cytoplasm is assumed to consist of submicroscopic contractile fibers bathed by viscous fluid. The fiber constituent models the actin-like and myosin-like contractile machinery known to be present in Chaos Carolinensis cytoplasm. A "trigger chemical", produced at the pseudopodium tip, moves by diffusion in, and convection by, the viscous fluid, and causes the contractile fibers to contract in their own length. The contracting fibers, attached at the tip and running continuously back toward the amoeba cell body, pull the fluid constituent of the cytoplasm forward and ultimately crosslink to form the outer gel tube of the advancing pseudopodium. That is, streaming cytoplasm is modeled as a two constituent porous medium, with the fluid constituent free to flow through a porous matrix of oriented (contractile fiber) rods, while the matrix of rods itself moves as the fibers contract, with fiber contraction controlled by a trigger chemical born by the fluid constituent. According to this theory, in the region behind the advancing pseudopodium tip, the contractile fiber rods move forward toward the tip faster than the fluid constituent. The hydrostatic pressure in the fluid therefore increases from the cell body toward the tip (Just the opposite from flow driven by pressure excess generated in the cell body). The excess of hydrostatic pressure above ambient built up at the tip provides the force to roll out the advancing pseudopodium tip. The cell membrane plays no active mechanical role. The mathematical transcription makes a precise theory of R. D. Allen's "frontal (or fountain zone) contraction model". The general system of coupled, non-linear, partial differential equations is solved for its simplest non-trivial special case, that of a steady-state motion, as seen from a coordinate system attached to the advancing tip. Solutions exist, and, for each distinct forward speed (which is left to the discretion of the amoeba) the solution is unique. The theory predicts both upper and lower bounds for possible pseudopodium lengths.

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