Curvature gradient drives polarized tissue flow in the Drosophila embryo.

Tissue flow during morphogenesis is commonly driven by local constriction of cell cortices, which is caused by the activation of actomyosin contractility. This can lead to long-range flows due to tissue viscosity. However, in the absence of cell-intrinsic polarized forces or polarity in forces external to the tissue, these flows must be symmetric and centered around the region of contraction. Polarized tissue flows have been previously demonstrated to arise from the coupling of such contractile flows to points of increased friction or adhesion to external structures. However, we show with experiments and modeling that the onset of polarized tissue flow in early Drosophila morphogenesis occurs independent of adhesion and is instead driven by a geometric coupling of apical actomyosin contractility to tissue curvature. Particularly, the onset of polarized flow is driven by a mismatch between the position of apical myosin activation and the position of peak curvature at the posterior pole of the embryo. Our work demonstrates how genetic and geometric information inherited from the mother interact to create polarized flow during embryo morphogenesis.

Programming Directed Motion with DNA-Grafted Particles.

Colloidal particles can be programmed to interact in complex ways by functionalizing them with DNA oligonucleotides. Adding DNA strand-displacement reactions to the system allows these interparticle interactions to respond to specific changes in temperature. We present the requirements for thermally driven directed motion of colloidal particles, and we explore how these conditions can be realized experimentally using strand-displacement reactions. To evaluate the concept, we build and test a colloidal "dancer": a single particle that can be driven to move through a programmed sequence of steps along a one-dimensional track composed of other particles. The results of these tests reveal the capabilities and limitations of using DNA-mediated interactions for applications in dynamic systems. Specifically, we discuss how to design the substrate to limit complexity while permitting full control of the motile component, how to ratchet the interactions to move over many substrate positions with a limited regime of control parameters, and how to use technological developments to reduce the probability of detachment without sacrificing speed.

Mechanochemical Principles of Spatial and Temporal Patterns in Cells and Tissues.

Patterns are ubiquitous in living systems and underlie the dynamic organization of cells, tissues, and embryos. Mathematical frameworks have been devised to account for the self-organization of biological patterns, most famously the Turing framework. Patterns can be defined in space, for example, to form stripes; in time, such as during oscillations; or both, to form traveling waves. The formation of these patterns can have different origins: purely chemical, purely mechanical, or a combination of the two. Beyond the variety of molecular implementations of such patterns, we emphasize the unitary principles associated with them, across scales in space and time, within a general mechanochemical framework. We illustrate where such mechanisms of pattern formation arise in biological systems from cellular to tissue scales, with an emphasis on morphogenesis. Our goal is to convey a picture of pattern formation that draws attention to the principles rather than solely to specific molecular mechanisms.

Using DNA strand displacement to control interactions in DNA-grafted colloids.

Grafting DNA oligonucleotides to colloidal particles leads to specific, reversible interactions between those particles. However, the interaction strength varies steeply and monotonically with temperature, hindering the use of DNA-mediated interactions in self-assembly. We show how the dependence on temperature can be modified in a controlled way by incorporating DNA strand-displacement reactions. The method allows us to make multicomponent systems that can self-assemble over a wide range of temperatures, invert the dependence on temperature to design colloidal systems that melt upon cooling, controllably transition between structures with different compositions, or design systems with multiple melting transitions. This wide range of behaviors can be realized simply by adding a small number of DNA strands to the solution, making the approach modular and straightforward to implement. We conclude with practical considerations for designing systems of DNA-mediated colloidal interactions.