Michael F Staddon#, Carl D. Modes# Curved-edge vertex models and increased tissue fluidity. Phys Rev Research, 7(1) Art. No. 013218 (2025)
Open Access DOI
The vertex model for epithelia models the apical surface of a tissue by a tiling, with polygons representing cells and edges representing cell-cell junctions. The mechanics are described by an energy governed by deviations from a target area and target perimeter for each cell. It has been shown that the target perimeter p0 governs a solid-to-fluid phase transition: when the target perimeter is low, there is an energy barrier to rearrangement, and when it is high, cells may rearrange for free and the tissue can flow like a liquid. One simplification often made is modeling junctions using straight edges. However, the Young-Laplace equation states that interfaces should be circular arcs, with the curvature being equal to the pressure difference between the neighboring cells divided by the interfacial tension. Here, we investigate how including curved edges alters the mechanical properties of the vertex model and the equilibrium shape of individual cells. Importantly, we show how curved edges shift the solid-to-fluid transition point, from p0 = 3.81 to p0 = 3.73, allowing tissues to fluidize sooner than in the traditional model with straight edges.
Arthur Genthon, Carl D. Modes, Frank Jülicher#, Stephan W. Grill# Nonequilibrium Transitions in a Template Copying Ensemble. Phys Rev Lett, 134(6) Art. No. 68402 (2025)
Open Access DOI
The fuel-driven process of replication in living systems generates distributions of copied entities with varying degrees of copying accuracy. Here we introduce a thermodynamically consistent ensemble for investigating universal population features of template copying systems. In the context of copolymer copying, coarse-graining over molecular details, we establish a phase diagram of copying accuracy. We discover sharp non-equilibrium transitions between populations of random and accurate copies. Maintaining a population of accurate copies requires a minimum energy expenditure that depends on the configurational entropy of copolymer sequences.
2024
Michael F Staddon How the zebra got its stripes: Curvature-dependent diffusion orients Turing patterns on three-dimensional surfaces. Phys Rev E, 110(3) Art. No. 034402 (2024)
Open Access DOI
Many animals have patterned fur, feathers, or scales, such as the stripes of a zebra. Turing models, or reaction- diffusion systems, are a class of mathematical models of interacting species that have been successfully used to generate animal-like patterns for many species. When diffusion of the inhibitor is high enough relative to the activator, a diffusion-driven instability can spontaneously form patterns. However, it is not just the type of pattern but also the orientation that matters, and it remains unclear how patterns are oriented in practice. Here, we propose a mechanism by which the curvature of the surface influences the rate of diffusion, and can recapture the correct orientation of stripes on models of a zebra and of a cat in numerical simulations. Previous work has shown how anisotropic diffusion can give stripe forming reaction-diffusion systems a bias in orientation. From the observation that zebra stripes run around the direction of highest curvature, that is around the torso and legs, we apply this result by modifying the anisotropic diffusion rates based on the local curvature. These results show how local geometry can influence the reaction dynamics to give robust, global-scale patterns. Overall, this model proposes a coupling between the system geometry and reaction-diffusion dynamics that can give global control over the patterning by using only local curvature information. Such a model can give shape and positioning information in animal development without the need for spatially dependent morphogen gradients.
Jana Fuhrmann*, Abhijeet Krishna*, Joris Paijmans, Charlie Duclut, Greta Cwikla, Suzanne Eaton, Marko Popović, Frank Jülicher, Carl D. Modes#, Natalie Dye# Active shape programming drives Drosophila wing disc eversion. Sci Adv, 10(32) Art. No. eadp0860 (2024)
Open Access DOI
How complex 3D tissue shape emerges during animal development remains an important open question in biology and biophysics. Here, we discover a mechanism for 3D epithelial shape change based on active, in-plane cellular events that is analogous to inanimate "shape programmable" materials, which undergo blueprinted 3D shape transformations from in-plane gradients of spontaneous strains. We study eversion of the Drosophila wing disc pouch, when the epithelium transforms from a dome into a curved fold, quantifying 3D tissue shape changes and mapping spatial patterns of cellular behaviors on the evolving geometry using cellular topology. Using a physical model inspired by shape programming, we find that active cell rearrangements are the major contributor to pouch eversion and validate this conclusion using a knockdown of MyoVI, which reduces rearrangements and disrupts morphogenesis. This work shows that shape programming is a mechanism for animal tissue morphogenesis and suggests that patterns in nature could present design strategies for shape-programmable materials.
Carlos M Duque, Douglas M Hall, Botond Tyukodi, Michael F Hagan, Christian D Santangelo, Gregory M Grason Limits of economy and fidelity for programmable assembly of size-controlled triply periodic polyhedra. Proc Natl Acad Sci U.S.A., 121(18) Art. No. e2315648121 (2024)
Open Access DOI
We propose and investigate an extension of the Caspar-Klug symmetry principles for viral capsid assembly to the programmable assembly of size-controlled triply periodic polyhedra, discrete variants of the Primitive, Diamond, and Gyroid cubic minimal surfaces. Inspired by a recent class of programmable DNA origami colloids, we demonstrate that the economy of design in these crystalline assemblies-in terms of the growth of the number of distinct particle species required with the increased size-scale (e.g., periodicity)-is comparable to viral shells. We further test the role of geometric specificity in these assemblies via dynamical assembly simulations, which show that conditions for simultaneously efficient and high-fidelity assembly require an intermediate degree of flexibility of local angles and lengths in programmed assembly. Off-target misassembly occurs via incorporation of a variant of disclination defects, generalized to the case of hyperbolic crystals. The possibility of these topological defects is a direct consequence of the very same symmetry principles that underlie the economical design, exposing a basic tradeoff between design economy and fidelity of programmable, size controlled assembly.
Botond Molnár, Ildikó-Beáta Márton, Szabolcs Horvát#, Mária Ercsey-Ravasz# Community detection in directed weighted networks using Voronoi partitioning. Sci Rep, 14(1) Art. No. 8124 (2024)
Open Access DOI
Community detection is a ubiquitous problem in applied network analysis, however efficient techniques do not yet exist for all types of network data. Directed and weighted networks are an example, where the different information encoded by link weights and the possibly high graph density can cause difficulties for some approaches. Here we present an algorithm based on Voronoi partitioning generalized to deal with directed weighted networks. As an added benefit, this method can directly employ edge weights that represent lengths, in contrast to algorithms that operate with connection strengths, requiring ad-hoc transformations of length data. We demonstrate the method on inter-areal brain connectivity, air transportation networks, and several social networks. We compare the performance with several other well-known algorithms, applying them on a set of randomly generated benchmark networks. The algorithm can handle dense graphs where weights are the main factor determining communities. The hierarchical structure of networks can also be detected, as shown for the brain. Its time efficiency is comparable or even outperforms some of the state-of-the-art algorithms, the part with the highest time-complexity being Dijkstra's shortest paths algorithm ( O(|E|+|V|log|V|) ).
Ferenc Molnár, Szabolcs Horvát, Ana R. Ribeiro Gomes, Jorge Martinez Armas, Botond Molnár, Robert F Hevner, Kenneth Knoblauch, Henry Kennedy, Zoltan Toroczkai Predictability of cortico-cortical connections in the mammalian brain. Network Neuroscience, 8(1) 138-157 (2024)
Open Access DOI
Despite a five order of magnitude range in size, the brains of mammals share many anatomical and functional characteristics that translate into cortical network commonalities. Here we develop a machine learning framework to quantify the degree of predictability of the weighted interareal cortical matrix. Partial network connectivity data were obtained with retrograde tract-tracing experiments generated with a consistent methodology, supplemented by projection length measurements in a nonhuman primate (macaque) and a rodent (mouse). We show that there is a significant level of predictability embedded in the interareal cortical networks of both species. At the binary level, links are predictable with an area under the ROC curve of at least 0.8 for the macaque. Weighted medium and strong links are predictable with an 85%-90% accuracy (mouse) and 70%-80% (macaque), whereas weak links are not predictable in either species. These observations reinforce earlier observations that the formation and evolution of the cortical network at the mesoscale is, to a large extent, rule based. Using the methodology presented here, we performed imputations on all area pairs, generating samples for the complete interareal network in both species. These are necessary for comparative studies of the connectome with minimal bias, both within and across species.
Revealed by tract-tracing datasets, communication between the functional areas of the cortex operates via a complex, dense, and weighted network of physical connections with little apparent regularity. Although there are studies showing the existence of nonrandom topological features, their extent has not been clear. Employing a machine learning-based approach, which efficiently extracts structural models from such datasets, here we show that there is a significant amount of regularity embedded in the mammalian connectome. This regularity allows predicting interareal connections and their weights with good accuracy and can be used to infer properties of experimentally untested connections. The structural models are well learned even with small training sets, without overfitting, suggesting the existence of a low-dimensional, universal mechanism for mesoscale cortical network formation and evolution.
2023
Romina Piscitello-Gómez*, Franz Gruber*, Abhijeet Krishna, Charlie Duclut, Carl D. Modes, Marko Popović, Frank Jülicher, Natalie Dye, Suzanne Eaton Core PCP mutations affect short-time mechanical properties but not tissue morphogenesis in the Drosophila pupal wing. Elife, 12 Art. No. e85581 (2023)
Open Access DOI
How morphogenetic movements are robustly coordinated in space and time is a fundamental open question in biology. We study this question using the wing of Drosophila melanogaster, an epithelial tissue that undergoes large-scale tissue flows during pupal stages. Previously, we showed that pupal wing morphogenesis involves both cellular behaviors that allow relaxation of mechanical tissue stress, as well as cellular behaviors that appear to be actively patterned (Etournay et al., 2015). Here, we show that these active cellular behaviors are not guided by the core planar cell polarity (PCP) pathway, a conserved signaling system that guides tissue development in many other contexts. We find no significant phenotype on the cellular dynamics underlying pupal morphogenesis in mutants of core PCP. Furthermore, using laser ablation experiments, coupled with a rheological model to describe the dynamics of the response to laser ablation, we conclude that while core PCP mutations affect the fast timescale response to laser ablation they do not significantly affect overall tissue mechanics. In conclusion, our work shows that cellular dynamics and tissue shape changes during Drosophila pupal wing morphogenesis do not require core PCP as an orientational guiding cue.
Arthur Hernandez, Michael F Staddon, Michael Moshe, M Cristina Marchetti Finite elasticity of the vertex model and its role in rigidity of curved cellular tissues. Soft Matter, 19(40) 7744-7752 (2023)
DOI
Using a mean field approach and simulations, we study the non-linear mechanical response of the vertex model (VM) of biological tissue to compression and dilation. The VM is known to exhibit a transition between solid and fluid-like, or floppy, states driven by geometric incompatibility. Target perimeter and area set a target shape which may not be geometrically achievable, thereby engendering frustration. Previously, an asymmetry in the linear elastic response was identified at the rigidity transition between compression and dilation. Here we show that the asymmetry extends away from the transition point for finite strains. Under finite compression, an initially solid VM can completely relax perimeter tension, resulting in a drop discontinuity in the mechanical response. Conversely, an initially floppy VM under dilation can rigidify and have a higher response. These observations imply that re-scaling of cell area shifts the transition between rigid and floppy states. Based on this insight, we calculate the re-scaling of cell area engendered by intrinsic curvature and write a prediction for the rigidity transition in the presence of curvature. The shift of the rigidity transition in the presence of curvature for the VM provides a new metric for predicting tissue rigidity from image data of curved tissues in a manner analogous to the flat case.
Ana P. Ramos, Alicja Szalapak, Lucrezia Camilla Ferme, Carl D. Modes From cells to form: A roadmap to study shape emergence in vivo. Biophys J, 122(18) 3587-3599 (2023)
Open Access DOI
Organogenesis arises from the collective arrangement of cells into progressively 3D-shaped tissue. The acquisition of a correctly shaped organ is then the result of a complex interplay between molecular cues, responsible for differentiation and patterning, and the mechanical properties of the system, which generate the necessary forces that drive correct shape emergence. Nowadays, technological advances in the fields of microscopy, molecular biology, and computer science are making it possible to see and record such complex interactions in incredible, unforeseen detail within the global context of the developing embryo. A quantitative and interdisciplinary perspective of developmental biology becomes then necessary for a comprehensive understanding of morphogenesis. Here, we provide a roadmap to quantify the events that lead to morphogenesis from imaging to image analysis, quantification, and modeling, focusing on the discrete cellular and tissue shape changes, as well as their mechanical properties.
Felix Kramer#, Carl D. Modes# Biological flow networks: Antagonism between hydrodynamic and metabolic stimuli as driver of topological transitions. Phys Rev Research, 5(2) Art. No. 023106 (2023)
Open Access DOI
A plethora of computational models have been developed in recent decades to account for the morphogenesis of complex biological fluid networks, such as capillary beds. Contemporary adaptation models are based on optimization schemes where networks react and adapt vessel conductance toward given flow patterns. Recent numeric studies on network morphogenesis, incorporating uptake of metabolites by the embedding tissue, have indicated this conventional approach to be insufficient. Here, we systematically study a hybrid model intended to generate space-filling perfusion as well as optimal filtration of metabolites. As a result, we find hydrodynamic stimuli (wall-shear stress) and filtration based stimuli (uptake of metabolites) to be antagonistic as hydrodynamically optimized systems have suboptimal uptake qualities and vice versa. We show that a switch between optimization regimes is typically accompanied with a transition between topologically redundant meshes and spanning trees. Depending on the metabolite demand and uptake capabilities of the adapting networks, we further demonstrate the existence of nullity reentrance as a function of dissipation and the development of compromised phenotypes such as dangling nonperfused vessels and bottlenecks.
Michael F Staddon, Arthur Hernandez#, Mark J Bowick#, Michael Moshe#, M Cristina Marchetti# The role of non-affine deformations in the elastic behavior of the cellular vertex model. Soft Matter, 19(17) 3080-3091 (2023)
Open Access DOI
The vertex model of epithelia describes the apical surface of a tissue as a tiling of polygonal cells, with a mechanical energy governed by deviations in cell shape from preferred, or target, area, A0, and perimeter, P0. The model exhibits a rigidity transition driven by geometric incompatibility as tuned by the target shape index, . For with p*(6) the perimeter of a regular hexagon of unit area, a cell can simultaneously attain both the preferred area and preferred perimeter. As a result, the tissue is in a mechanically soft compatible state, with zero shear and Young's moduli. For p0 < p*(6), it is geometrically impossible for any cell to realize the preferred area and perimeter simultaneously, and the tissue is in an incompatible rigid solid state. Using a mean-field approach, we present a complete analytical calculation of the linear elastic moduli of an ordered vertex model. We analyze a relaxation step that includes non-affine deformations, leading to a softer response than previously reported. The origin of the vanishing shear and Young's moduli in the compatible state is the presence of zero-energy deformations of cell shape. The bulk modulus exhibits a jump discontinuity at the transition and can be lower in the rigid state than in the fluid-like state. The Poisson's ratio can become negative which lowers the bulk and Young's moduli. Our work provides a unified treatment of linear elasticity for the vertex model and demonstrates that this linear response is protocol-dependent.
2022
Karen Soans, Ana P. Ramos, Jaydeep Sidhaye, Abhijeet Krishna, Anastasia Solomatina, Karl Hoffmann, Raimund Schlüßler, Jochen Guck, Ivo F. Sbalzarini, Carl D. Modes#, Caren Norden# Collective cell migration during optic cup formation features changing cell-matrix interactions linked to matrix topology. Curr Biol, 32(22) 4817-4831 (2022)
DOI
Cell migration is crucial for organismal development and shapes organisms in health and disease. Although a lot of research has revealed the role of intracellular components and extracellular signaling in driving single and collective cell migration, the influence of physical properties of the tissue and the environment on migration phenomena in vivo remains less explored. In particular, the role of the extracellular matrix (ECM), which many cells move upon, is currently unclear. To overcome this gap, we use zebrafish optic cup formation, and by combining novel transgenic lines and image analysis pipelines, we study how ECM properties influence cell migration in vivo. We show that collectively migrating rim cells actively move over an immobile extracellular matrix. These cell movements require cryptic lamellipodia that are extended in the direction of migration. Quantitative analysis of matrix properties revealed that the topology of the matrix changes along the migration path. These changes in matrix topologies are accompanied by changes in the dynamics of cell-matrix interactions. Experiments and theoretical modeling suggest that matrix porosity could be linked to efficient migration. Indeed, interfering with matrix topology by increasing its porosity results in a loss of cryptic lamellipodia, less-directed cell-matrix interactions, and overall inefficient migration. Thus, matrix topology is linked to the dynamics of cell-matrix interactions and the efficiency of directed collective rim cell migration during vertebrate optic cup morphogenesis.
Charlie Duclut, Joris Paijmans, Mandar M Inamdar, Carl D. Modes, Frank Jülicher Active T1 transitions in cellular networks. Eur Phys J E Soft Matter, 45(3) Art. No. 29 (2022)
Open Access DOI
In amorphous solids as in tissues, neighbor exchanges can relax local stresses and allow the material to flow. In this paper, we use an anisotropic vertex model to study T1 rearrangements in polygonal cellular networks. We consider two different physical realizations of the active anisotropic stresses: (i) anisotropic bond tension and (ii) anisotropic cell stress. Interestingly, the two types of active stress lead to patterns of relative orientation of T1 transitions and cell elongation that are different. Our work suggests that these two realizations of anisotropic active stresses can be observed in vivo. We describe and explain these results through the lens of a continuum description of the tissue as an anisotropic active material. We furthermore discuss the energetics of the dynamic tissue and express the energy balance in terms of internal elastic energy, mechanical work, chemical work and heat. This allows us to define active T1 transitions that can perform mechanical work while consuming chemical energy.
2021
Charlie Duclut*, Joris Paijmans*, Mandar M Inamdar, Carl D. Modes, Frank Jülicher Nonlinear rheology of cellular networks. Cells Dev, 168 Art. No. 203746 (2021)
DOI
Morphogenesis depends crucially on the complex rheological properties of cell tissues and on their ability to maintain mechanical integrity while rearranging at long times. In this paper, we study the rheology of polygonal cellular networks described by a vertex model in the presence of fluctuations. We use a triangulation method to decompose shear into cell shape changes and cell rearrangements. Considering the steady-state stress under constant shear, we observe nonlinear shear-thinning behavior at all magnitudes of the fluctuations, and an even stronger nonlinear regime at lower values of the fluctuations. We successfully capture this nonlinear rheology by a mean-field model that describes the tissue in terms of cell elongation and cell rearrangements. We furthermore introduce anisotropic active stresses in the vertex model and analyze their effect on rheology. We include this anisotropy in the mean-field model and show that it recapitulates the behavior observed in the simulations. Our work clarifies how tissue rheology is related to stochastic cell rearrangements and provides a simple biophysical model to describe biological tissues. Further, it highlights the importance of nonlinearities when discussing tissue mechanics.
D. Duffy, L. Cmok, J.S. Biggins, A. Krishna, Carl D. Modes, M.K. Abdelrahman, M. Javed, T.H. Ware, F. Feng, M. Warner Shape programming lines of concentrated Gaussian curvature. J Appl Phys, 129(22) Art. No. 224701 (2021)
Open Access DOI
Liquid crystal elastomers (LCEs) can undergo large reversible contractions along their nematic director upon heating or illumination. A spatially patterned director within a flat LCE sheet, thus, encodes a pattern of contraction on heating, which can morph the sheet into a curved shell, akin to how a pattern of growth sculpts a developing organism. Here, we consider theoretically, numerically, and experimentally patterns constructed from regions of radial and circular director, which, in isolation, would form cones and anticones. The resultant surfaces contain curved ridges with sharp V-shaped cross sections, associated with the boundaries between regions in the patterns. Such ridges may be created in positively and negatively curved variants and, since they bear Gauss curvature (quantified here via the GaussBonnet theorem), they cannot be flattened without energetically prohibitive stretch. Our experiments and numerics highlight that, although such ridges cannot be flattened isometrically, they can deform isometrically by trading the (singular) curvature of the V angle against the (finite) curvature of the ridge line. Furthermore, in finite thickness sheets, the sharp ridges are inevitably non-isometrically blunted to relieve bend, resulting in a modest smearing out of the encoded singular Gauss curvature. We close by discussing the use of such features as actuating linear features, such as probes, tongues, and grippers. We speculate on similarities between these patterns of shape change and those found during the morphogenesis of several biological systems. Published under an exclusive license by AIP Publishing.
Szabolcs Horvát*, Adeeba Fathima*, Stefan Goerlich, Michael Schlierf#, Carl D. Modes#, Nils Kroeger# Computational analysis of the effects of nitrogen source and sin1 knockout on biosilica morphology in the model diatom Thalassiosira pseudonana. Discover Materials, 1 Art. No. 8 (2021)
Open Access DOI
Morphogenesis of the silica based cell walls of diatoms, a large group of microalgae, is a paradigm for the self-assembly
of complex 3D nano- and microscale patterned inorganic materials. In recent years, loss-of-function studies using genetic
manipulation were successfully applied for the identification of genes that guide silica morphogenesis in diatoms. These
studies revealed that the loss of one gene can affect multiple morphological parameters, and the morphological changes
can be rather subtle being blurred by natural variations in morphology even within the same clone. Both factors severely
hamper the identification of morphological mutants using subjective by-eye inspection of electron micrographs. Here
we have developed automated image analysis for objectively quantifying the morphology of ridge networks and pore
densities from numerous electron micrographs of diatom biosilica. This study demonstrated differences in ridge network
morphology and pore density in diatoms growing on ammonium rather than nitrate as the sole nitrogen source. Fur-
thermore, it revealed shortcomings in previous by-eye evaluation of the biosilica phenotype of the silicanin-1 knockout
mutant. We anticipate that the computational methods established in the present work will be invaluable for unraveling
genotype–phenotype correlations in diatom biosilica morphogenesis.
Szabolcs Horvát#, Carl D. Modes# Connectedness matters: construction and exact random sampling of connected networks. J Phys Complex, 2(1) Art. No. 015008 (2021)
Open Access DOI
We describe a new method for the random sampling of connected networks with a specified degree
sequence. We consider both the case of simple graphs and that of loopless multigraphs. The
constraints of fixed degrees and of connectedness are two of the most commonly needed ones when
constructing null models for the practical analysis of physical or biological networks. Yet handling
these constraints, let alone combining them, is non-trivial. Our method builds on a recently
introduced novel sampling approach that constructs graphs with given degrees independently
(unlike edge-switching Markov chain Monte Carlo methods) and efficiently (unlike the
configuration model), and extends it to incorporate the constraint of connectedness. Additionally,
we present a simple and elegant algorithm for directly constructing a single connected realization
of a degree sequence, either as a simple graph or a multigraph. Finally, we demonstrate our
sampling method on a realistic scale-free example, as well as on degree sequences of connected
real-world networks, and show that enforcing connectedness can significantly alter the properties
of sampled networks.
Michael Hecht, Krzysztof Gonciarz, Szabolcs Horvát Tight Localizations of Feedback Sets. ACM J Exp Algorithmics, 26(1) Art. No. 1.5 (2021)
Open AccessPDF
DOI
The classical NP–hard feedback arc set problem (FASP) and feedback vertex set problem (FVSP) ask for a minimum set of arcs ε ⊆ E or vertices ν ⊆ V whose removal G ∖ ε, G ∖ ν makes a given multi–digraph G=(V, E) acyclic, respectively. Though both problems are known to be APX–hard, constant ratio approximations or proofs of inapproximability are unknown. We propose a new universal O(|V||E|4)–heuristic for the directed FASP. While a ratio of r ≈ 1.3606 is known to be a lower bound for the APX–hardness, at least by empirical validation we achieve an approximation of r ≤ 2. Most of the relevant applications, such as circuit testing, ask for solving the FASP on large sparse graphs, which can be done efficiently within tight error bounds with our approach.
2020
Stephan Daetwyler, Carl D. Modes, Reto Fiolka Fiji plugin for annotating movies with custom arrows. Biol Open, 9(11) Art. No. bio056200 (2020)
Open Access DOI
Annotation of time-lapse data provides an important tool to highlight dynamic processes. Particularly, arrows, circles and arrowheads are useful to pinpoint a specific process, stationary or evolving over time. Here, we describe a user-friendly Fiji plugin to facilitate annotation of movies with arrows, arrowheads and circles. The plugin also enables saving and loading of annotated tracks.
Felix Kramer#, Carl D. Modes# How to pare a pair: Topology control and pruning in intertwined complex networks. Phys Rev Research, 2(4) Art. No. 043171 (2020)
Open Access DOI
Recent work on self-organized remodeling of vasculature in slime molds, leaf venation systems, and vesselsystems in vertebrates has put forward a plethora of potential adaptation mechanisms. All these share theunderlying hypothesis of a flow-driven machinery, meant to alter rudimentary vessel networks in order tooptimize the system’s dissipation, flow uniformity, or more, with different versions of constraints. Nevertheless,the influence of environmental factors on the long-term adaptation dynamics as well as the network structureand function have not been fully understood. Therefore, interwoven capillary systems such as those found inthe liver, kidney, and pancreas present a novel challenge and key opportunity regarding the field of coupleddistribution networks. We here present an advanced version of the discrete Hu-Cai model, coupling two spatialnetworks in three dimensions. We show that spatial coupling of two flow-adapting networks can control the onsetof topological complexity in concert with short-term flow fluctuations. We find that both fluctuation-inducedand spatial coupling induced topology transitions undergo curve collapse, obeying simple functional rescaling.Further, our approach results in an alternative form of Murray’s law, which incorporates local vessel interactionsand flow interactions. This geometric law allows for the estimation of the model parameters in ideal Kirchhoffnetworks and respective experimentally acquired network skeletons.
Mohammadreza Bahadorian, Christoph Zechner#, Carl D. Modes# Gift of gab: Probing the limits of dynamic concentration-sensing across a network of communicating cells. Phys Rev Research, 2(2) Art. No. 023403 (2020)
Open Access DOI
Many systems in biology and other sciences employ collaborative, collective communication strategies for improved efficiency and adaptive benefit. One such paradigm of particular interest is the community estimation of a dynamic signal, when, for example, an epithelial tissue of cells must decide whether to react to a given dynamic external concentration of stress-signaling molecules. At the level of dynamic cellular communication, however, it remains unknown what effect, if any, arises from communication beyond the mean field level. What are the limits and benefits to communication across a network of neighbor interactions? What is the role of Poissonian versus super-Poissonian dynamics in such a setting? How does the particular topology of connections impact the collective estimation and that of the individual participating cells? In this article we construct a robust and general framework of signal estimation over continuous-time Markov chains in order to address and answer these questions. Our results show that in the case of Possonian estimators, the communication solely enhances convergence speed of the mean squared error (MSE) of the estimators to their steady-state values while leaving these values unchanged. However, in the super-Poissonian regime, the MSE of estimators significantly decreases by increasing the number of neighbors. Surprisingly, in this case, the clustering coefficient of an estimator does not enhance its MSE while still reducing the total MSE of the population.
2019
Iskra Yanakieva, Anna Erzberger, Marija Matejčić, Carl D. Modes, Caren Norden Cell and tissue morphology determine actin-dependent nuclear migration mechanisms in neuroepithelia. J Cell Biol, 218(10) 3272-3289 (2019)
DOI
Correct nuclear position is crucial for cellular function and tissue development. Depending on cell context, however, the cytoskeletal elements responsible for nuclear positioning vary. While these cytoskeletal mechanisms have been intensely studied in single cells, how nuclear positioning is linked to tissue morphology is less clear. Here, we compare apical nuclear positioning in zebrafish neuroepithelia. We find that kinetics and actin-dependent mechanisms of nuclear positioning vary in tissues of different morphology. In straight neuroepithelia, nuclear positioning is controlled by Rho-ROCK-dependent myosin contractility. In contrast, in basally constricted neuroepithelia, a novel formin-dependent pushing mechanism is found for which we propose a proof-of-principle force generation theory. Overall, our data suggest that correct nuclear positioning is ensured by the adaptability of the cytoskeleton to cell and tissue shape. This in turn leads to robust epithelial maturation across geometries. The conclusion that different nuclear positioning mechanisms are favored in tissues of different morphology highlights the importance of developmental context for the execution of intracellular processes.
Stephan Daetwyler, Ulrik Günther, Carl D. Modes, Kyle Harrington#, Jan Huisken# Multi-sample SPIM image acquisition, processing and analysis of vascular growth in zebrafish. Development, 146(6) Art. No. dev173757 (2019)
Open Access DOI
To quantitatively understand biological processes that occur over many hours or days, it is desirable to image multiple samples simultaneously, and automatically process and analyse the resulting datasets. Here, we present a complete multi-sample preparation, imaging, processing and analysis workflow to determine the development of the vascular volume in zebrafish. Up to five live embryos were mounted and imaged simultaneously over several days using selective plane illumination microscopy (SPIM). The resulting large imagery dataset of several terabytes was processed in an automated manner on a high-performance computer cluster and segmented using a novel segmentation approach that uses images of red blood cells as training data. This analysis yielded a precise quantification of growth characteristics of the whole vascular network, head vasculature and tail vasculature over development. Our multi-sample platform demonstrates effective upgrades to conventional single-sample imaging platforms and paves the way for diverse quantitative long-term imaging studies.
2017
Cyrus Mostajeran, Mark Warner, Carl D. Modes Frame, metric and geodesic evolution in shape-changing nematic shells. Soft Matter, 13(46) 8858-8863 (2017)
DOI
Non-uniform director fields in flat, responsive, glassy nematic sheets lead to the induction of shells with non-trivial topography on the application of light or heat. Contraction along the director causes metric change, with, in general, the induction of Gaussian curvature, that drives the topography change. We describe the metric change, the evolution of the director field, and the transformation of reference state material curves, e.g. spirals into radii, as curvature develops. The non-isometric deformations associated with heat or light change the geodesics of the surface, intriguingly even in regions where no Gaussian curvature results.
Christoph Kirst, Carl D. Modes, Marcelo O. Magnasco Shifting attention to dynamics: Self-reconfiguration of neural networks Curr Opin Syst Biol, 3 132-140 (2017)
DOI
--- D Corbett, CD Modes, M Warner Photomechanics: Bend, Curl, Topography, and Topology Photomechanical Materials, Composites, and Systems: Wireless Transduction of Light into Work, (2017)
2016
CD Modes, MO Magnasco, E Katifori Extracting Hidden Hierarchies in 3D Distribution Networks Physical Review X 6, 031009 (2016) --- CD Modes, M Warner Shape-programmable materials Physics Today 69 (1), 32-38 (2016)
2015
CD Modes, M Warner Negative Gaussian curvature from induced metric changes Physical Review E 92 (1), 010401 (2015) --- J Gräwer, CD Modes, MO Magnasco, E Katifori Structural self-assembly and avalanchelike dynamics in locally adaptive networks Physical Review E 92 (1), 012801 (2015)
2013
CD Modes, RD Kamien Spherical foams in flat space Soft Matter 9, 11078 - 11084 (2013) --- CD Modes, M Warner, C Sánchez-Somolinos, LT de Haan, D Broer Angular deficits in flat space: remotely controllable apertures in nematic solid sheets 469. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (2013) --- CD Modes, MO Magnasco A Geometric Knotspace Template arXiv preprint arXiv:1302.1146 (2013)
2012
CD Modes, M Warner The activated morphology of grain boundaries in nematic solid sheets Emerging Liquid Crystal Technologies VII 8279, 82790Q (2012) --- CD Modes, M Warner Responsive nematic solid shells: Topology, compatibility, and shape EPL (Europhysics Letters) 97 (3), 36007 (2012) --- CD Modes, M Warner, C Sánchez-Somolinos, LT de Haan, D Broer Mechanical frustration and spontaneous polygonal folding in active nematic sheets Physical Review E 86 (6), 060701 (2012)
2011
CD Modes, M Warner Blueprinting nematic glass: Systematically constructing and combining active points of curvature for emergent morphology Physical Review E 84 (2), 021711 (2011) --- CD Modes, K Bhattacharya, M Warner Gaussian curvature from flat elastica sheets Proceedings of the Royal Society of London A: Mathematical, Physical and … (2011)
2010
CD Modes, M Warner, CL Van Oosten, D Corbett Anisotropic response of glassy splay-bend and twist nematic cantilevers to light and heat Physical Review E 82 (4), 041111 (2010) --- CD Modes, K Bhattacharya, M Warner Disclination-mediated thermo-optical response in nematic glass sheets Physical Review E 81 (6), 060701(2010) --- M Warner, CD Modes, D Corbett Suppression of curvature in nematic elastica 466. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (2010) --- M Warner, CD Modes, D Corbett Curvature in nematic elastica responding to light and heat 466. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (2010)
2008
CD Modes, RD Kamien Geometrical frustration in two dimensions: Idealizations and realizations of a hard-disk fluid in negative curvature Physical Review E 77 (4), 041125 (2008) --- CD Modes Uniform background curvature: Foam families and frustrated discs University of Pennsylvania (2008)
2007
CD Modes, RD Kamien Hard disks on the hyperbolic plane Physical review letters 99 (23), 235701 (2007)
