* joint first author # joint corresponding author

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, Art. No. doi: 10.1016/j.cub.2022.09.034 (2022)
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.

Charlie Duclut✳︎, Joris Paijmans✳︎, Mandar M Inamdar, Carl D. Modes, Frank Jülicher
Nonlinear rheology of cellular networks.
Cells Dev, 168 Art. No. 203746 (2021)
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 Horvat✳︎, 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 Horvat#, 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 Horvat
Tight Localizations of Feedback Sets.
ACM J Exp Algorithmics, 26(1) Art. No. 1.5 (2021)
Open Access PDF 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.

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.

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)
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.

Cyrus Mostajeran, Mark Warner, Carl D. Modes
Frame, metric and geodesic evolution in shape-changing nematic shells.
Soft Matter, 13(46) 8858-8863 (2017)
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)

D Corbett, CD Modes, M Warner
Photomechanics: Bend, Curl, Topography, and Topology
Photomechanical Materials, Composites, and Systems: Wireless Transduction of Light into Work, (2017)


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)


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)


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)


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)


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)


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)


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)


CD Modes, RD Kamien
Hard disks on the hyperbolic plane
Physical review letters 99 (23), 235701 (2007)