On the effective action of confining strings

We study the low-energy effective action on confining strings (in the fundamental representation) in SU(N) gauge theories in D space-time dimensions. We write this action in terms of the physical transverse fluctuations of the string. We show that for any D, the four-derivative terms in the effective action must exactly match the ones in the Nambu-Goto action, generalizing a result of Luscher and Weisz for D=3. We then analyze the six-derivative terms, and we show that some of these terms are constrained. For D=3 this uniquely determines the effective action for closed strings to this order, while for D>3 one term is not uniquely determined by our considerations. This implies that for D=3 the energy levels of a closed string of length L agree with the Nambu-Goto result at least up to order 1/L^5. For any D we find that the partition function of a long string on a torus is unaffected by the free coefficient, so it is always equal to the Nambu-Goto partition function up to six-derivative order. For a closed string of length L, this means that for D>3 its energy can, in principle, deviate from the Nambu-Goto result at order 1/L^5, but such deviations must always cancel in the computation of the partition function. Next, we compute the effective action up to six-derivative order for the special case of confining strings in weakly-curved holographic backgrounds, at one-loop order (leading order in the curvature). Our computation is general, and applies in particular to backgrounds like the Witten background, the Maldacena-Nunez background, and the Klebanov-Strassler background. We show that this effective action obeys all of the constraints we derive, and in fact it precisely agrees with the Nambu-Goto action (the single allowed deviation does not appear).Comment: 71 pages, 7 figures. v2: added reference, minor corrections. v3: removed one term from the effective action since it is trivial. The conclusions on the corrections to energy levels are unchanged, but the claim that the holographic computation shows a deviation from Nambu-Goto was modified. v4: added reference

Brain Organoids—A Bottom-Up Approach for Studying Human Neurodevelopment

Brain organoids have recently emerged as a three-dimensional tissue culture platform to study the principles of neurodevelopment and morphogenesis. Importantly, brain organoids can be derived from human stem cells, and thus offer a model system for early human brain development and human specific disorders. However, there are still major differences between the in vitro systems and in vivo development. This is in part due to the challenge of engineering a suitable culture platform that will support proper development. In this review, we discuss the similarities and differences of human brain organoid systems in comparison to embryonic development. We then describe how organoids are used to model neurodevelopmental diseases. Finally, we describe challenges in organoid systems and how to approach these challenges using complementary bioengineering techniques

Collective Conformations of DNA Polymers Assembled on Surface Density Gradients

To study dense double-stranded DNA (dsDNA) polymer phases, we fabricated continuous density gradients of binding sites for assembly on a photochemical interface and measured both dsDNA occupancy and extension using evanescent fluorescence. Despite the abundance of available binding sites, the dsDNA density saturates after occupation of only a fraction of the available sites along the gradient. The spatial position at which the density saturates marks the onset of collective stretching of dsDNA, a direct manifestation of balancing entropic and excluded-volume interactions. The methodology presented here offers a new means to investigate dense dsDNA compartments

Human neural tube morphogenesis in vitro by geometric constraints

Understanding human organ formation is a scientific challenge with far-reaching medical implications1,2. Three-dimensional stem-cell cultures have provided insights into human cell differentiation3,4. However, current approaches use scaffold-free stem-cell aggregates, which develop non-reproducible tissue shapes and variable cell-fate patterns. This limits their capacity to recapitulate organ formation. Here we present a chip-based culture system that enables self-organization of micropatterned stem cells into precise three-dimensional cell-fate patterns and organ shapes. We use this system to recreate neural tube folding from human stem cells in a dish. Upon neural induction5,6, neural ectoderm folds into a millimetre-long neural tube covered with non-neural ectoderm. Folding occurs at 90% fidelity, and anatomically resembles the developing human neural tube. We find that neural and non-neural ectoderm are necessary and sufficient for folding morphogenesis. We identify two mechanisms drive folding: (1) apical contraction of neural ectoderm, and (2) basal adhesion mediated via extracellular matrix synthesis by non-neural ectoderm. Targeting these two mechanisms using drugs leads to morphological defects similar to neural tube defects. Finally, we show that neural tissue width determines neural tube shape, suggesting that morphology along the anterior-posterior axis depends on neural ectoderm geometry in addition to molecular gradients7. Our approach provides a new route to the study of human organ morphogenesis in health and disease