Human brain wrinkling has been implicated in neurodevelopmental disorders and yet its origins remain unknown. Polymer gel models suggest that wrinkling emerges spontaneously due to compression forces arising during differential swelling, but these ideas have not been tested in a living system. Here, we report the appearance of surface wrinkles during the in vitro development and self-organization of human brain organoids in a micro-fabricated compartment that supports in situ imaging over a timescale of weeks. We observe the emergence of convolutions at a critical cell density and maximal nuclear strain, which are indicative of a mechanical instability. We identify two opposing forces contributing to differential growth: cytoskeletal contraction at the organoid core and cell-cycle-dependent nuclear expansion at the organoid perimeter. The wrinkling wavelength exhibits linear scaling with tissue thickness, consistent with balanced bending and stretching energies. Lissencephalic (smooth brain) organoids display reduced convolutions, modified scaling and a reduced elastic modulus. Although the mechanism here does not include the neuronal migration seen in in vivo, it models the physics of the folding brain remarkably well. Our on-chip approach offers a means for studying the emergent properties of organoid development, with implications for the embryonic human brain.

The assembly of artificial cells capable of executing synthetic DNA programs has been an important goal for basic research and biotechnology. We assembled two-dimensional DNA compartments fabricated in silicon as artificial cells capable of metabolism, programmable protein synthesis, and communication. Metabolism is maintained by continuous diffusion of nutrients and products through a thin capillary, connecting protein synthesis in the DNA compartment with the environment. We programmed protein expression cycles, autoregulated protein levels, and a signaling expression gradient, equivalent to a morphogen, in an array of interconnected compartments at the scale of an embryo. Gene expression in the DNA compartment reveals a rich, dynamic system that is controlled by geometry, offering a means for studying biological networks outside a living cell.

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 Lüscher 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 (so that the sum of the deviations of all states at each energy level must vanish). In particular there is no correction at this order to the ground state energy of a winding string. 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-Nuñez 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).

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Understanding how human embryos develop their shape is a fundamental question in physics of life with strong medical implications. However, it is challenging to study the dynamics of organ formation in humans. Animals differ from humans in key aspects, and in particular in the development of the nervous system. Conventional organoids are quantitatively unreproducible and exhibit highly variable morphology. Here we present a morphologically reproducible and scalable approach for studying human organogenesis in a dish, which is compatible with live imaging. We achieve this by precisely controlling cell fate pattern formation in 2D stem cell sheets, while allowing for self-organization of tissue shape in 3D. Upon triggering neural pattern formation, the initially flat stem cell sheet undergoes folding morphogenesis and self-organizes into a millimeter long anatomically accurate model of the neural tube, covered by epidermis. We find that neural and epidermal human tissues are necessary and sufficient for folding morphogenesis in the absence of mesoderm activity. Furthermore, we find that molecular inhibition of tissue contractility leads to defects similar to neural tube closure defects, consistent with in vivo studies. Finally, we discover that neural tube shape, including the number and location of hinge points, depends on neural tissue size. This suggests that neural tube morphology along the anterior posterior axis depends on neural plate geometry in addition to molecular gradients. Our approach provides a new path to study human organ morphogenesis in health and disease.