arXiv subjects

J. M. Schwarz

Publications and source records attributed to J. M. Schwarz.

At least 37 records · Page 2Linked to original sources

arXiv2023

A topologically-protected interior for three-dimensional confluent cellular collectives

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.

cond-mat.soft↗

arXiv2022

Rigidity transitions in zero-temperature polygons

We study geometrical clues of a rigidity transition due to the emergence of a system-spanning state of self stress in under-constrained systems of individual polygons and spring networks constructed from such polygons. When a polygon with harmonic bond edges and an area spring constraint is subject to an expansive strain, we observe that convexity of the polygon is a necessary condition for such a self stress. We prove that the cyclic configuration of the polygon is a sufficient condition for the self stress. This correspondence of geometry and rigidity is akin to the straightening of a one dimensional chain of springs to rigidify it. We predict the onset of the rigidity transition using a purely geometrical method. We also estimate the transition strain for a given initial configuration by approximating irregular polygons as regular polygons. These findings help determine the rigidity of an area-preserving polygon just by looking at it. Since two-dimensional spring networks can be considered as a network of polygons, we look for similar geometric features in under-constrained spring networks under isotropic expansive strain. In particular, we observe that all polygons attain convexity at the rigidity transition such that the fraction of convex, but not cyclic, polygons predicts the onset of the rigidity transition. Interestingly, acyclic polygons in the network correlate with larger tensions, thus, forming effective force chains.

cond-mat.soft↗

arXiv2022

Frequency propagation: Multi-mechanism learning in nonlinear physical networks

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 multi-mechanism learning strategy for physical networks, be it resistive, elastic, or flow networks. Multi-mechanism 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 also falls under the rubric of multi-mechanism learning.

cond-mat.dis-nn↗

arXiv2022

Learning by non-interfering feedback chemical signaling in physical networks

Both non-neural and neural biological systems can learn. So rather than focusing on purely brain-like learning, efforts are underway to study learning in physical systems. Such efforts include equilibrium propagation (EP) and coupled learning (CL), which require storage of two different states-the free state and the perturbed state-during the learning process to retain information about gradients. Inspired by slime mold, we propose a new learning algorithm rooted in chemical signaling that does not require storage of two different states. Rather, the output error information is encoded in a chemical signal that diffuses into the network in a similar way as the activation/feedforward signal. The steady state feedback chemical concentration, along with the activation signal, stores the required gradient information locally. We apply our algorithm using a physical, linear flow network and test it using the Iris data set with 93% accuracy. We also prove that our algorithm performs gradient descent. Finally, in addition to comparing our algorithm directly with EP and CL, we address the biological plausibility of the algorithm.

cond-mat.soft↗

arXiv2022

Thermal Fluctuations of Singular Bar-Joint Mechanisms

A bar-joint mechanism is a deformable assembly of freely rotating joints connected by stiff bars. Here we develop a formalism to study the equilibration of common bar-joint mechanisms with a thermal bath. When the constraints in a mechanism cease to be linearly independent, singularities can appear in its shape space, which is the part of its configuration space after discarding rigid motions. We show that the free-energy landscape of a mechanism at low temperatures is dominated by the neighborhoods of points that correspond to these singularities. We consider two example mechanisms with shape-space singularities and find that they are more likely to be found in configurations near the singularities than others. These findings are expected to help improve the design of nanomechanisms for various applications.

cond-mat.soft↗

arXiv2022

Effective medium theory of random regular networks

Disordered spring networks can exhibit rigidity transitions, due to either the removal of materials in over-constrained networks or the application of strain in under-constrained ones. While an effective medium theory (EMT) exists for the former, there is none for the latter. We, therefore, formulate an EMT for random regular networks, under-constrained spring networks with purely geometrical disorder, to predict their stiffness via the distribution of tensions. We find a linear dependence of stiffness on strain in the rigid phase and a nontrivial dependence on both the mean and standard deviation of the tension distribution. While EMT does not yield highly accurate predictions of shear modulus due to spatial heterogeneities, the noninvasiveness of this EMT makes it an ideal starting point for experimentalists quantifying the mechanics of such networks.

cond-mat.soft↗

arXiv2021

Buckling without bending morphogenesis: Nonlinearities, spatial confinement, and branching hierarchies

During morphogenesis, a featureless convex cerebellum develops folds. As it does so, the cortex thickness is thinnest at the crest (gyri) and thickest at the trough (sulci) of the folds. This observation cannot be simply explained by elastic theories of buckling. A recent minimal model explained this phenomenon by modeling the developing cortex as a growing fluid under the constraints of radially spanning elastic fibers, a plia membrane and a nongrowing sub-cortex (Engstrom, et. al., PRX 2019). In this minimal buckling without bending morphogenesis (BWBM) model, the elastic fibers were assumed to act linearly with strain. Here, we explore how nonlinear elasticity influences shape development within BWBM. The nonlinear elasticity generates a quadratic nonlinearity in the differential equation governing the system's shape and leads to sharper troughs and wider crests, which is an identifying characteristic of cerebellar folds at later stages in development. As developing organs are typically not in isolation, we also explore the effects of steric confinement, and observe flattening of the crests. Finally, as a paradigmatic example, we propose a hierarchical version of BWBM from which a novel mechanism of branching morphogenesis naturally emerges to qualitatively predict later stages of the morphology of the developing cerebellum.

cond-mat.soft↗

arXiv2021

Large-scale cortex-core structure formation in brain organoids

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, as mediated by a dynamic cytoskeleton. 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.

cond-mat.soft↗

arXiv2021

Propagating irreversibility fronts in cyclically-sheared suspensions

The interface separating a liquid from its vapor phase is diffuse: the composition varies continuously from one phase to the other over a finite length. Recent experiments on dynamic jamming fronts in two dimensions [Waitukaitis et al., Europhysics Letters 102, 44001 (2013)] identified a diffuse interface between jammed and unjammed discs. In both cases, the thickness of the interface diverges as a critical transition is approached. We investigate the generality of this behavior using a third system: a model of cyclically-sheared non-Brownian suspensions. As we sediment the particles towards a boundary, we observe a diffuse traveling front that marks the interface between irreversible and reversible phases. We argue that the front width is linked to a diverging correlation lengthscale in the bulk, which we probe by studying avalanches near criticality. Our results show how diffuse interfaces may arise generally when an incompressible phase is brought to a critical point.

cond-mat.soft↗

arXiv2021

The role of vimentin-nuclear interactions in persistent cell motility through confined spaces

The ability of cells to move through small spaces depends on the mechanical properties of the cellular cytoskeleton and on nuclear deformability. In mammalian cells, the cytoskeleton is comprised of three interacting, semi-flexible polymer networks: actin, microtubules, and intermediate filaments (IF). Recent experiments of mouse embryonic fibroblasts with and without vimentin have shown that the IF vimentin plays a role in confined cell motility. We, therefore, develop a minimal model of cells moving through confined geometries that effectively includes all three types of cytoskeletal filaments with a cell consisting of an actomyosin cortex and a deformable cell nucleus and mechanical connections between the two cortices the outer actomyosin one and the inner nuclear one. By decreasing the amount of vimentin, we find that the cell speed is typically faster for vimentin-null cells as compared to cells with vimentin. Vimentin-null cells also contain more deformed nuclei in confinement. Finally, vimentin affects nucleus positioning within the cell. By positing that as the nucleus position deviates further from the center of mass of the cell, microtubules become more oriented in a particular direction to enhance cell persistence or polarity, we show that vimentin-nulls are more persistent than vimentin-full cells. The enhanced persistence indicates that the vimentin-null cells are more subjugated by the confinement since their internal polarization mechanism that depends on cross-talk of the centrosome with the nucleus and other cytoskeletal connections is diminished. In other words, the vimentin-null cells rely more heavily on external cues. Our modeling results present a quantitative interpretation for recent experiments and have implications for understanding the role of vimentin in the epithelial-mesenchymal transition.

physics.bio-ph↗

arXiv2021

A Data-Driven Statistical Description for the Hydrodynamics of Active Matter

Modeling living systems at the collective scale can be very challenging because the individual constituents can themselves be complex and the respective interactions between the constituents are not fully understood. With the advent of high throughput experiments and in the age of big data, data-driven methods are on the rise to overcome these challenges. To directly uncover the underlying physical principles, we present a data-driven method for obtaining the phase-space density such that the solution to the stochastic dynamic equation for active matter readily emerges, from which time and space dependence of physical order parameters can be readily extracted. If the system is near a steady state, we illuminate how to construct a field theory to subsequently make physical predictions about the system. The method is first developed analytically and subsequently calibrated using simulated data. The method is then applied to an experimental system of particles actively driven by a {\it Serratia marcescens} bacterial swarm and in the presence of spatially localized UV light. The analysis demonstrates that the particles are in the steady-state before and sometime after the UV light and obey a Gaussian field theory with a spatially-varying "mass" in those regimes. This novel, yet simple, finding is surprising given the complex dynamics of the bacterial swarm. In response to the UV light, we demonstrate that there is a net flow of the particles away from the UV light and that the entropy of the particles increases away from the light. We conclude with a discussion of additional potential applications of our data-driven method such as when the internal structure of the individual constituents dynamically changes to result in a modified stochastic dynamic equation governing the system.

cond-mat.soft↗

arXiv2021

Dynamic nuclear structure emerges from chromatin crosslinks and motors

The cell nucleus houses the chromosomes, which are linked to a soft shell of lamin filaments. Experiments indicate that correlated chromosome dynamics and nuclear shape fluctuations arise from motor activity. To identify the physical mechanisms, we develop a model of an active, crosslinked Rouse chain bound to a polymeric shell. System-sized correlated motions occur but require both motor activity {\it and} crosslinks. Contractile motors, in particular, enhance chromosome dynamics by driving anomalous density fluctuations. Nuclear shape fluctuations depend on motor strength, crosslinking, and chromosome-lamina binding. Therefore, complex chromatin dynamics and nuclear shape emerge from a minimal, active chromosome-lamina system.

q-bio.SC↗

arXiv2021

Geometric signatures of tissue surface tension in a three-dimensional model of confluent tissue

In dense biological tissues, cell types performing different roles remain segregated by maintaining sharp interfaces. To better understand the mechanisms for such sharp compartmentalization, we study the effect of an imposed heterotypic tension at the interface between two distinct cell types in a fully 3D model for confluent tissues. We find that cells rapidly sort and self-organize to generate a tissue-scale interface between cell types, and cells adjacent to this interface exhibit signature geometric features including nematic-like ordering, bimodal facet areas, and registration, or alignment, of cell centers on either side of the two-tissue interface. The magnitude of these features scales directly with the magnitude of imposed tension, suggesting that biologists can estimate the magnitude of tissue surface tension between two tissue types simply by segmenting a 3D tissue. To uncover the underlying physical mechanisms driving these geometric features, we develop two minimal, ordered models using two different underlying lattices that identify an energetic competition between bulk cell shapes and tissue interface area. When the interface area dominates, changes to neighbor topology are costly and occur less frequently, which generates the observed geometric features.

cond-mat.soft↗

arXiv2020

Loops versus lines and the compression stiffening of cells

Both animal and plant tissue exhibit a nonlinear rheological phenomenon known as compression stiffening, or an increase in moduli with increasing uniaxial compressive strain. Does such a phenomenon exist in single cells, which are the building blocks of tissues? One expects an individual cell to compression soften since the semiflexible biopolymer-based cytoskeletal network maintains the mechanical integrity of the cell and in vitro semiflexible biopolymer networks typically compression soften. To the contrary, we find that mouse embryonic fibroblasts (mEFs) compression stiffen under uniaxial compression via atomic force microscopy (AFM) studies. To understand this finding, we uncover several potential mechanisms for compression stiffening. First, we study a single semiflexible polymer loop modeling the actomyosin cortex enclosing a viscous medium modeled as an incompressible fluid. Second, we study a two-dimensional semiflexible polymer/fiber network interspersed with area-conserving loops, which are a proxy for vesicles and fluid-based organelles. Third, we study two-dimensional fiber networks with angular-constraining crosslinks, i.e. semiflexible loops on the mesh scale. In the latter two cases, the loops act as geometric constraints on the fiber network to help stiffen it via increased angular interactions. We find that the single semiflexible polymer loop model agrees well with our AFM experiments until approximately 35% compressive strain. We also find for the fiber network with area-conserving loops model that the stress-strain curves are sensitive to the packing fraction and size distribution of the area-conserving loops, thereby creating a mechanical fingerprint across different cell types. Finally, we make comparisons between this model and experiments on fibrin networks interlaced with beads as well as discuss the tissue-scale implications of cellular compression stiffening.

physics.bio-ph↗

arXiv2020

How does the extracellular matrix affect the rigidity of an embedded spheroid?

Cellularized tissue and polymer networks can both transition from floppy to rigid as a function of their control parameters, and, yet, the two systems often mechanically interact, which may affect their respective rigidities. To study this interaction, we consider a vertex model with interfacial tension (a spheroid) embedded in a spring network in two dimensions. We identify two regimes with different global spheroid shapes, governed by the pressure resulting from competition between interfacial tension and tension in the network. In the first regime, the tissue remains compact, while in the second, a cavitation-like instability leads to the emergence of gaps at the tissue-network interface. Intriguingly, compression of the tissue promotes fluidization, while tension promotes cellular alignment and rigidification, with the mechanisms driving rigidification differing on either side of the instability.

q-bio.CB↗

arXiv2020

Sponge-like rigid structures in frictional granular packings

We show how rigidity emerges in experiments of sheared frictional granular materials by using generalizations of two methods for identifying rigid structures. Both approaches, the force-based dynamical matrix and the topology-based rigidity percolation, agree with each other and identify similar rigid structures. As the system becomes jammed, at a contact number of $z=2.4\pm 0.1$, a rigid backbone interspersed with floppy, particle-filled holes of a broad range of sizes emerges, creating a sponge-like morphology. We also find that the pressure within rigid structures always exceeds the pressure outside the rigid structures, i.e. that the backbone is load-bearing. These findings shows that it is necessary to go beyond mean-field theory to capture the physics of frictional jamming and also suggests that mechanical stability arises through arch structures and hinges at the mesoscale.

cond-mat.soft↗

arXiv2020

Small-scale demixing in confluent biological tissues

Surface tension governed by differential adhesion can drive fluid particle mixtures to sort into separate regions, i.e., demix. Does the same phenomenon occur in confluent biological tissues? We begin to answer this question for epithelial monolayers with a combination of theory via a vertex model and experiments on keratinocyte monolayers. Vertex models are distinct from particle models in that the interactions between the cells are shape-based, as opposed to distance-dependent. We investigate whether a disparity in cell shape or size alone is sufficient to drive demixing in bidisperse vertex model fluid mixtures. Surprisingly, we observe that both types of bidisperse systems robustly mix on large lengthscales. On the other hand, shape disparity generates slight demixing over a few cell diameters, a phenomenon we term micro-demixing. This result can be understood by examining the differential energy barriers for neighbor exchanges (T1 transitions). Experiments with mixtures of wild-type and E-cadherin-deficient keratinocytes on a substrate are consistent with the predicted phenomenon of micro-demixing, which biology may exploit to create subtle patterning. The robustness of mixing at large scales, however, suggests that despite some differences in cell shape and size, progenitor cells can readily mix throughout a developing tissue until acquiring means of recognizing cells of different types.

cond-mat.soft↗

arXiv2018

Buckling without bending: a new paradigm in morphogenesis

A curious feature of organ and organoid morphogenesis is that in certain cases, spatial oscillations in the thickness of the growing "film" are out-of-phase with the deformation of the slower-growing "substrate," while in other cases, the oscillations are in-phase. The former cannot be explained by elastic bilayer instability, and contradict the notion that there is a universal mechanism by which brains, intestines, teeth, and other organs develop surface wrinkles and folds. Inspired by the microstructure of the embryonic cerebellum, we develop a new model of 2d morphogenesis in which system-spanning elastic fibers endow the organ with a preferred radius, while a separate fiber network resides in the otherwise fluid-like film at the outer edge of the organ and resists thickness gradients thereof. The tendency of the film to uniformly thicken or thin is described via a "growth potential". Several features of cerebellum, +blebbistatin organoid, and retinal fovea morphogenesis, including out-of-phase behavior and a film thickness amplitude that is comparable to the radius amplitude, are readily explained by our simple analytical model, as may be an observed scale-invariance in the number of folds in the cerebellum. We also study a nonlinear variant of the model, propose further biological and bio-inspired applications, and address how our model is and is not unique to the developing nervous system.

physics.bio-ph↗