The cell interior is an active bath driven by a myriad of enzymes. It is an open problem as to how this background activity can affect physical processes in the cell including liquid-liquid phase separation. We seek to experimentally reconstitute a model system for an active bath of enzymes to determine the effects on the liquid phase separation of a model condensate protein. We will use urease, an exothermic and kinetically fast enzyme that converts urea to carbon dioxide and ammonia, as the background enzyme.

We introduce frequency propagation, a learning algorithm for nonlinear physical networks. In a resistive electrical circuit with variable resistors, an activation current is applied at a set of input nodes at one frequency and an error current is applied at a set of output nodes at another frequency. The voltage response of the circuit to these boundary currents is the superposition of an activation signal and an error signal whose coefficients can be read in different frequencies of the frequency domain. Each conductance is updated proportionally to the product of the two coefficients. The learning rule is local and proved to perform gradient descent on a loss function. We argue that frequency propagation is an instance of a multimechanism learning strategy for physical networks, be it resistive, elastic, or flow networks. Multimechanism learning strategies incorporate at least two physical quantities, potentially governed by independent physical mechanisms, to act as activation and error signals in the training process. Locally available information about these two signals is then used to update the trainable parameters to perform gradient descent. We demonstrate how earlier work implementing learning via chemical signaling in flow networks (Anisetti, Scellier, et al., 2023) also falls under the rubric of multimechanism learning.

Chromatin plays an essential role in the nuclear mechanical response and determining nuclear shape, which maintain nuclear compartmentalization and function. However, major genomic functions, such as transcription activity, might also impact cell nuclear shape via blebbing and rupture through their effects on chromatin structure and dynamics. To test this idea, we inhibited transcription with several RNA polymerase II inhibitors in wild-type cells and perturbed cells that presented increased nuclear blebbing. Transcription inhibition suppressed nuclear blebbing for several cell types, nuclear perturbations and transcription inhibitors. Furthermore, transcription inhibition suppressed nuclear bleb formation, bleb stabilization and bleb-based nuclear ruptures. Interestingly, transcription inhibition did not alter the histone H3 lysine 9 (H3K9) modification state, nuclear rigidity, and actin compression and contraction, which typically control nuclear blebbing. Polymer simulations suggested that RNA polymerase II motor activity within chromatin could drive chromatin motions that deform the nuclear periphery. Our data provide evidence that transcription inhibition suppresses nuclear blebbing and rupture, in a manner separate and distinct from chromatin rigidity.

The hypothalamus in the mammalian brain is responsible for regulating functions associated with survival and reproduction representing a complex set of highly interconnected, yet anatomically and functionally distinct, sub-regions. It remains unclear what factors drive the spatial organization of sub-regions within the hypothalamus. One potential factor may be structural connectivity of the network that promotes efficient function with well-connected sub-regions placed closer together geometrically, i.e., the strongest axonal signal transferred through the shortest geometrical distance. To empirically test for such efficiency, we use hypothalamic data derived from the Allen Mouse Brain Connectivity Atlas, which provides a structural connectivity map of mouse brain regions derived from a series of viral tracing experiments. Using both cost function minimization and comparison with a weighted, sphere-packing ensemble, we demonstrate that the sum of the distances between hypothalamic sub-regions are not close to the minimum possible distance, consistent with prior whole brain studies. However, if such distances are weighted by the inverse of the magnitude of the connectivity, their sum is among the lowest possible values. Specifically, the hypothalamus appears within the top 94th percentile of neural efficiencies of randomly packed configurations and within one standard deviation of the median efficiency when packings are optimized for maximal neural efficiency. Our results, therefore, indicate that a combination of geometrical and topological constraints help govern the structure of the hypothalamus.

Cross-sections of cell shapes in a tissue monolayer typically resemble a tiling of convex polygons. Yet, examples exist where the polygons are not convex with curved cell-cell interfaces, as seen in the adaxial epidermis. To date, two-dimensional vertex models predicting the structure and mechanics of cell monolayers have been mostly limited to convex polygons. To overcome this limitation, we introduce a framework to study curvy cell-cell interfaces at the subcellular scale within vertex models by using a parameterized curve between vertices that is expanded in a Fourier series and whose coefficients represent additional degrees of freedom. This extension to non-convex polygons allows for cells with same shape index, or dimensionless perimeter, to be, for example, either elongated or globular with lobes. In the presence of applied, anisotropic stresses, we find that local, subcellular curvature, or buckling, can be energetically more favorable than larger scale deformations involving groups of cells. Inspired by recent experiments, we also find that local, subcellular curvature at cell-cell interfaces emerges in a group of cells in response to the swelling of additional cells surrounding the group. Our framework, therefore, can account for a wider array of multi-cellular responses to constraints in the tissue environment.

The mechanics of a foam depends on bubble shape, bubble network topology, and the material at hand, be it metallic or polymeric, for example. While the shapes of bubbles are the consequence of minimizing surface area for a given bubble volume in a space-filling packing, if one were to consider biological tissue as a foam-like material, the zoology of observed shapes of cells perhaps motivates different energetic contributions. Building on earlier two-dimensional results, here, we focus on a mean field approach to obtain the elastic moduli for an ordered, three-dimensional vertex model. We use the space-filling shape of a truncated octahedron and an energy functional containing a restoring surface area spring and a restoring volume spring. The tuning of the three-dimensional shape index exhibits a rigidity transition via a compatible-incompatible transition. Specifically, for smaller shape indices, both the target surface area and volume cannot be achieved, while beyond some critical value of the three-dimensional shape index, they can be, resulting in a zero-energy state. In addition to analytically determining the location of the transition in mean field, we find that the rigidity transition and the elastic moduli depend on the parameterization of the cell shape. This parameterization effect is more pronounced in three dimensions than in two dimensions given the zoology of shapes that a polyhedron can take on (as compared to a polygon). We also uncover nontrivial dependence of the elastic moduli on the deformation protocol in which some deformations result in affine motion of the vertices, while others result in nonaffine motion. Such dependencies on the shape parameterization and deformation protocol give rise to a nontrivial shape landscape and, therefore, nontrivial mechanical response even in the absence of topology changes.

We present analysis of neuronal activity recordings from a subset of neurons in the medial prefrontal cortex of rats before and after the administration of cocaine. Using an underlying modern Hopfield model as a description for the neuronal network, combined with a machine learning approach, we compute the underlying functional connectivity of the neuronal network. We find that the functional connectivity changes after the administration of cocaine with both functional-excitatory and functional-inhibitory neurons being affected. Using conventional network analysis, we find that the diameter of the graph, or the shortest length between the two most distant nodes, increases with cocaine, suggesting that the neuronal network is less robust. We also find that the betweenness centrality scores for several of the functional-excitatory and functional-inhibitory neurons decrease significantly, while other scores remain essentially unchanged, to also suggest that the neuronal network is less robust. Finally, we study the distribution of neuronal activity and relate it to energy to find that cocaine drives the neuronal network towards destabilization in the energy landscape of neuronal activation. While this destabilization is presumably temporary given one administration of cocaine, perhaps this initial destabilization indicates a transition towards a new stable state with repeated cocaine administration. However, such analyses are useful more generally to understand how neuronal networks respond to perturbations.

The viscoelasticity of tissues impacts their shape, as well as the growth and differentiation of their cells. Nevertheless, little is known about changes in viscoelastic properties during brain malformations. Lissencephaly is a severe malformation of cortical development caused by LIS1 mutations, which results in a lack of cortical convolutions. Here, we show that human-derived brain organoids with LIS1 mutation are stiffer than control ones at multiple developmental times. This stiffening is accompanied by abnormal ECM expression and organization, as well as elevated water content, as measured by diffusion-weighted MRI. Proteolytic cleavage of ECM components by short-term treatment with the catalytic subunit of MMP9 reduced the stiffening and water diffusion levels of mutated organoids to control levels. Finally, based on the molecular and rheological properties obtained, we generated a computational microstructure mechanical model that can successfully predict mechanical changes that follow differential ECM localization and integrity in the developing brain. Overall, our study reveals that LIS1 is essential for the expression and organization of ECM proteins during brain development, and its mutation leads to a substantial viscoelastic change. To our knowledge, this is the first study to elucidate how tissue mechanics change in disease states using human brain organoids.### Competing Interest StatementThe authors have declared no competing interest.

By training linear physical networks to learn linear transformations, we discern how their physical properties evolve due to weight update rules. Our findings highlight a striking similarity between the learning behaviors of such networks and the processes of aging and memory formation in disordered and glassy systems. We show that the learning dynamics resembles an aging process, where the system relaxes in response to repeated application of the feedback boundary forces in presence of an input force, thus encoding a memory of the input-output relationship. With this relaxation comes an increase in the correlation length, which is indicated by the two-point correlation function for the components of the network. We also observe that the square root of the mean-squared error as a function of epoch takes on a non-exponential form, which is a typical feature of glassy systems. This physical interpretation suggests that by encoding more detailed information into input and feedback boundary forces, the process of emergent learning can be rather ubiquitous and, thus, serve as a very early physical mechanism, from an evolutionary standpoint, for learning in biological systems.

In the realm of biological flow networks, the ability to dynamically adjust to varying demands is paramount. Drawing inspiration from the remarkable adaptability of Physarum polycephalum, we present a novel physical mechanism tailored to optimize flow networks. Central to our approach is the principle that each network component -- specifically, the tubes -- harnesses locally available information to collectively minimize a global cost function. Our findings underscore the scalability of this mechanism, making it feasible for larger, more complex networks. We construct a comprehensive phase diagram, pinpointing the specific network parameters under which successful adaptation, or tuning, is realized. There exists a phase boundary in the phase diagram, revealing a distinct satisfiability-unsatisfiability (SAT-UNSAT) phase transition delineating successful and unsuccessful adaptation.

We explore rectification phenomena in a system where two-dimensional random walkers interact with a funnel-shaped ratchet under two distinct classes of reflection rules. The two classes include the angle of reflection exceeding the angle of incidence ($\theta_{reflect} > \theta_{incident}$), or vice versa ($\theta_{reflect} < \theta_{incident}$). These generalized boundary reflection rules are indicative of non-equilibrium conditions due to the introduction of energy flows at the boundary. Our findings reveal that the nature of such particle-wall interactions dictates the system's behavior: the funnel either acts as a pump, directing flow, or as a collector, demonstrating a ratchet reversal. Importantly, we provide a geometric proof elucidating the underlying mechanism of rectification, thereby offering insights into why certain interactions lead to directed motion, while others do not.

Organs in the human body have complex networks of fluid-filled tubes and loops with different geometries and topologies. By studying self-organized, synthetic tissues, the link between topological transitions and the emergence of tissue architecture was revealed.

How genes affect tissue scale organization remains a longstanding biological puzzle. As experimental efforts are underway to solve this puzzle via quantification of gene expression, chromatin organization, cellular structure, and tissue structure, computational modeling efforts remain far behind. To help accelerate the computational modeling efforts, we review two recent publications, the first on a cellular-based model for tissues and the second on a model of a cell nucleus that includes a lamina shell and chromatin. We then address how the two models can be combined to ultimately test multiscale hypotheses linking the chromatin scale and the tissue scale. To be concrete, we turn to an in vitro system for the brain known as a brain organoid. We provide a multiscale hypothesis to distinguish structural differences between brain organoids built from induced-pluripotent human stem cells and from induced-pluripotent gorilla and chimpanzee stem cells. Recent experiments discover that a cell fate transition from neuroepithelial cells to radial glial cells includes a new intermediate state that is delayed in human-derived brain organoids as compared to their genetically-close relatives, which significantly narrows and lengthens the cells on the apical side [1]. Additional experiments revealed that the protein ZEB2 plays a major role in the emergence of this new intermediate state with ZEB2 mRNA levels peaking at the onset of the emergence [1]. We postulate that the enhancement of ZEB2 expression driving this intermediate state is potentially due to chromatin reorganization. More precisely, there exists critical strain triggering the reorganization that is higher for human-derived stem cells, thereby resulting in a delay. Such a hypothesis can readily be tested experimentally within individual cells and within brain organoids as well as computationally to help work towards solving the gene-to-tissue organization puzzle.

Brain organoids recapitulate a number of brain properties, including neuronal diversity. However, do they recapitulate brain structure? Using a hydrodynamic description for cell nuclei as particles interacting initially via an effective , attractive force as mediated by the respective, surrounding cytoskeletons, we quantify structure development in brain organoids to determine what physical mechanism regulates the number of cortex-core structures. Regions of cell nuclei overdensity in the linear regime drive the initial seeding for cortex-core structures, which ultimately develop in the non-linear regime, as inferred by the emergent form of an effective interaction between cell nuclei and with the extracellular environment. Individual cortex-core structures then provide a basis upon which we build an extended version of the buckling without bending morphogenesis (BWBM) model, with its proliferating cortex and constraining core, to predict foliations/folds of the cortex in the presence of a nonlinearity due to cortical cells actively regulating strain. In doing so, we obtain asymmetric foliations/folds with respect to the trough (sulci) and the crest (gyri). In addition to laying new groundwork for the design of more familiar and less familiar brain structures, the hydrodynamic description for cell nuclei during the initial stages of brain organoid development provides an intriguing quantitative connection with large-scale structure formation in the universe.

Organoids are in vitro cellular collectives from which brain-like, or gut-like, or kidney-like structures emerge. To make quantitative predictions regarding the morphology and rheology of a cellular collective in its initial stages of development, we construct and study a three-dimensional vertex model. In such a model, the cells are represented as deformable polyhedrons with cells sharing faces such that there are no gaps between them, otherwise known as confluent. In a bulk model with periodic boundary conditions, we find a rigidity transition as a function of the target cell shape index $s_0$ with a critical value $s_0^*=5.39\pm0.01$. For a confluent cellular collective with a finite boundary, and in the presence of lateral extensile and in-plane, radial extensile deformations, we find a significant boundary-bulk effect that is one-cell layer thick. More specifically, for lateral extensile deformations, the cells in the bulk are much less aligned with the direction of the lateral deformation than the cells at the boundary. For in-plane, radial deformations, the cells in the bulk exhibit much less reorientation perpendicular to the radial direction than the cells at the boundary. In other words, for both deformations, the bulk, interior cells are topologically-protected from the deformations, at least over time scales much slower than the timescale for cellular rearrangements and up to reasonable amounts of strain. Our results provide an underlying mechanism for some observed cell shape patterning in organoids. Finally, we discuss the use of a cellular-based approach to designing organoids with new types of morphologies to study the intricate relationship between structure and function at the multi-cellular scale for example.