@article{21282, abstract = {Developmental patterning comprises processes that range from purely instructed, where external signals specify cell fates, to fully self-organized, where spatial patterns emerge autonomously through cellular interactions. We propose that both extremes—as well as the continuum of intermediate cases—can be conceptualized as information-processing systems, whose operation can be described using “Marr's three levels of analysis”: the computational problem being solved, the algorithms employed, and their molecular implementation. At the first level, we argue that normative theories, such as information-theoretic optimization principles, provide a formalization of the computational problem. At the second level, we show how simplified information-processing architectures provide a framework for developmental algorithms, which are formalized mathematically using dynamical systems theory. At the third level, the implementation of developmental algorithms is described by mechanistic biophysical and gene regulatory network models.}, author = {Brückner, David and Tkačik, Gašper}, issn = {2835-8279}, journal = {PRX Life}, publisher = {American Physical Society}, title = {{Marr's three levels for embryonic development: Information, dynamical systems, gene networks}}, doi = {10.1103/fdcf-dkws}, volume = {4}, year = {2026}, } @article{20056, abstract = {Theoretical studies have shown that stochasticity can affect the dynamics of ecosystems in counterintuitive ways. However, without knowing the equations governing the dynamics of populations or ecosystems, it is difficult to ascertain the role of stochasticity in real datasets. Therefore, the inverse problem of inferring the governing stochastic equations from datasets is important. Here, we present an equation discovery methodology that takes time series data of state variables as input and outputs a stochastic differential equation. We achieve this by combining traditional approaches from stochastic calculus with the equation discovery techniques. We demonstrate the generality of the method via several applications. First, we deliberately choose various stochastic models with fundamentally different governing equations, yet they produce nearly identical steady-state distributions. We show that we can recover the correct underlying equations, and thus infer the structure of their stability, accurately from the analysis of time series data alone. We demonstrate our method on two real-world datasets—fish schooling and single-cell migration—that have vastly different spatiotemporal scales and dynamics. We illustrate various limitations and potential pitfalls of the method and how to overcome them via diagnostic measures. Finally, we provide our open-source code via a package named PyDaDDy (Python Library for Data-Driven Dynamics).}, author = {Nabeel, Arshed and Karichannavar, Ashwin and Palathingal, Shuaib and Jhawar, Jitesh and Brückner, David and Raj M, Danny and Guttal, Vishwesha}, issn = {1537-5323}, journal = {The American Naturalist}, number = {4}, pages = {E100--E117}, publisher = {University of Chicago Press}, title = {{Discovering stochastic dynamical equations from ecological time series data}}, doi = {10.1086/734083}, volume = {205}, year = {2025}, } @article{20259, abstract = {Cell migration in narrow microenvironments occurs in numerous physiological processes. It involves successive cycles of confinement and release that drive important morphological changes. However, it remains unclear whether migrating cells can retain a memory of their past morphological states that could potentially facilitate their navigation through confined spaces. We demonstrate that local geometry governs a switch between two cell morphologies, thereby facilitating cell passage through long and narrow gaps. We combined cell migration assays on standardized microsystems with biophysical modelling and biochemical perturbations to show that migrating cells have a long-term memory of past confinement events. The morphological cell states correlate across transitions through actin cortex remodelling. These findings indicate that mechanical memory in migrating cells plays an active role in their migratory potential in confined environments.}, author = {Kalukula, Yohalie and Luciano, Marine and Simanov, Gleb and Charras, Guillaume and Brückner, David and Gabriele, Sylvain}, issn = {1745-2481}, journal = {Nature Physics}, pages = {1451--1461}, publisher = {Springer Nature}, title = {{The actin cortex acts as a mechanical memory of morphology in confined migrating cells}}, doi = {10.1038/s41567-025-02980-z}, volume = {21}, year = {2025}, } @article{20431, abstract = {Haptotaxis is the process of directed cell migration along gradients of extracellular matrix density and is central to morphogenesis, immune responses and cancer invasion. It is commonly assumed that cells respond to these gradients by migrating directionally towards the regions of highest ligand density. In contrast with this view, here we show that cells exposed to micropatterned fibronectin gradients exhibit a wide range of complex trajectories, including directed haptotactic migration up the gradient but also linear oscillations and circles with extended periods of migration down the gradient. To explain this behaviour, we developed a biophysical model of haptotactic cell migration based on a coarse-grained molecular clutch model coupled to persistent stochastic polarity dynamics. Although initial haptotactic migration is explained by the differential friction at the front and back of the cell, the observed complex trajectories over longer timescales arise from the interplay between differential friction, persistence and physical confinement. Overall, our study reveals that confinement and persistence modulate the ability of cells to sense and respond to haptotactic cues and provides a framework for understanding how cells navigate complex environments.}, author = {Fortunato, Isabela Corina and Brückner, David and Grosser, Steffen and Nautiyal, Rohit and Rossetti, Leone and Bosch-Padrós, Miquel and Trebicka, Jonel and Roca-Cusachs, Pere and Sunyer, Raimon and Hannezo, Edouard B and Trepat, Xavier}, issn = {1745-2481}, journal = {Nature Physics}, pages = {1638--1647}, publisher = {Springer Nature}, title = {{Single-cell migration along and against confined haptotactic gradients}}, doi = {10.1038/s41567-025-03015-3}, volume = {21}, year = {2025}, } @article{18960, abstract = {The importance of physical forces in the morphogenesis, homeostatic function, and pathological dysfunction of multicellular tissues is being increasingly characterized, both theoretically and experimentally. Analogies between biological systems and inert materials such as foams, gels, and liquid crystals have provided striking insights into the core design principles underlying multicellular organization. However, these connections can seem surprising given that a key feature of multicellular systems is their ability to constantly consume energy, providing an active origin for the forces that they produce. Key emerging questions are, therefore, to understand whether and how this activity grants tissues novel properties that do not have counterparts in classical materials, as well as their consequences for biological function. Here, we review recent discoveries at the intersection of active matter and tissue biology, with an emphasis on how modeling and experiments can be combined to understand the dynamics of multicellular systems. These approaches suggest that a number of key biological tissue-scale phenomena, such as morphogenetic shape changes, collective migration, or fate decisions, share unifying design principles that can be described by physical models of tissue active matter.}, author = {Brückner, David and Hannezo, Edouard B}, issn = {1943-0264}, journal = {Cold Spring Harbor Perspectives in Biology}, number = {4}, publisher = {Cold Spring Harbor Laboratory Press}, title = {{Tissue active matter: Integrating mechanics and signaling into dynamical models}}, doi = {10.1101/cshperspect.a041653}, volume = {17}, year = {2025}, } @article{19404, abstract = {Cell migration is a fundamental process during embryonic development. Most studies in vivo have focused on the migration of cells using the extracellular matrix (ECM) as their substrate for migration. In contrast, much less is known about how cells migrate on other cells, as found in early embryos when the ECM has not yet formed. Here, we show that lateral mesendoderm (LME) cells in the early zebrafish gastrula use the ectoderm as their substrate for migration. We show that the lateral ectoderm is permissive for the animal-pole-directed migration of LME cells, while the ectoderm at the animal pole halts it. These differences in permissiveness depend on the lateral ectoderm being more cohesive than the animal ectoderm, a property controlled by bone morphogenetic protein (BMP) signaling within the ectoderm. Collectively, these findings identify ectoderm tissue cohesion as one critical factor in regulating LME migration during zebrafish gastrulation.}, author = {Tavano, Ste and Brückner, David and Tasciyan, Saren and Tong, Xin and Kardos, Roland and Schauer, Alexandra and Hauschild, Robert and Heisenberg, Carl-Philipp J}, issn = {2211-1247}, journal = {Cell Reports}, number = {3}, publisher = {Elsevier}, title = {{BMP-dependent patterning of ectoderm tissue material properties modulates lateral mesendoderm cell migration during early zebrafish gastrulation}}, doi = {10.1016/j.celrep.2025.115387}, volume = {44}, year = {2025}, } @article{21236, abstract = {The migration behavior of colliding cells is critically determined by transient contact interactions. During these interactions, the motility machinery, including the front-rear polarization of the cell, dynamically responds to surface protein-mediated transmission of forces and biochemical signals between cells. While biomolecular details of such contact interactions are increasingly well understood, it remains unclear what biophysical interaction mechanisms govern the cell-level dynamics of colliding cells and how these mechanisms vary across cell types. Here we develop a phenomenological theory based on 14 candidate contact-interaction mechanisms coupling cell position, protrusion, and polarity. Using high-throughput micropattern experiments, we detect which of these phenomenological contact interactions captures the interaction behaviors of cells. We find that various cell types—ranging from mesenchymal to epithelial cells—are accurately captured by a single model with only two interaction mechanisms: polarity-protrusion coupling and polarity-polarity coupling. Remarkably, the qualitatively different interaction behaviors of distinct cells, as well as cells subject to molecular perturbations of surface protein-mediated signaling, can all be quantitatively captured by varying the strength and sign of the polarity-polarity coupling mechanism. Altogether, our data-driven phenomenological theory of cell-cell interactions reveals polarity-polarity coupling as a versatile and general contact-interaction mechanism, which may underlie diverse collective migration behaviors of motile cells.}, author = {Brandstätter, Tom and Brieger, Emily and Brückner, David and Ladurner, Georg and Rädler, Joachim O. and Broedersz, Chase P.}, issn = {2835-8279}, journal = {PRX Life}, number = {3}, publisher = {American Physical Society}, title = {{Data-driven theory reveals protrusion and polarity interactions governing collision behavior of distinct motile cells}}, doi = {10.1103/3hhj-rt1n}, volume = {3}, year = {2025}, } @article{18807, abstract = {Developing tissues interpret dynamic changes in morphogen activity to generate cell type diversity. To quantitatively study bone morphogenetic protein (BMP) signaling dynamics in the mouse neural tube, we developed an embryonic stem cell differentiation system tailored for growing tissues. Differentiating cells form striking self-organized patterns of dorsal neural tube cell types driven by sequential phases of BMP signaling that are observed both in vitro and in vivo. Data-driven biophysical modeling showed that these dynamics result from coupling fast negative feedback with slow positive regulation of signaling by the specification of an endogenous BMP source. Thus, in contrast to relays that propagate morphogen signaling in space, we identify a BMP signaling relay that operates in time. This mechanism allows for a rapid initial concentration-sensitive response that is robustly terminated, thereby regulating balanced sequential cell type generation. Our study provides an experimental and theoretical framework to understand how signaling dynamics are exploited in developing tissues.}, author = {Rus, Stefanie and Brückner, David and Minchington, Thomas and Greunz, Martina and Merrin, Jack and Hannezo, Edouard B and Kicheva, Anna}, issn = {1534-5807}, journal = {Developmental Cell}, number = {4}, pages = {567--580}, publisher = {Elsevier}, title = {{Self-organized pattern formation in the developing mouse neural tube by a temporal relay of BMP signaling}}, doi = {10.1016/j.devcel.2024.10.024}, volume = {60}, year = {2025}, } @misc{20121, abstract = {PyDaddy is an open source package which is a key contribution of the manuscript Nabeel et al, arXiv:2205.02645. The basic scientific premise for this package is to discover the nature of stochasticity in ecological time series datasets. It is well known that the stochasticity can affect the dynamics of ecological systems in counter-intuitive ways. Without understanding the equations (typically, in the form of stochastic differential equations or SDEs, in short) that govern the dynamics of populations or ecosystems, it's challenging to determine the impact of randomness on real datasets. In this manuscript and accompanying package, we introduce a methodology for discovering equations (SDEs) that transforms time series data of state variables into stochastic differential equations. This approach merges traditional stochastic calculus with modern equation-discovery techniques. We showcase the generality of our method through various applications and discuss its limitations and potential pitfalls, offering diagnostic measures to address these challenges.}, author = {Nabeel, Arshed and Karichannavar, Ashwin and Palathingal, Shuaib and Jhawar, Jitesh and Brückner, David and Danny Raj, Masila and Guttal, Vishwesha}, publisher = {Zenodo}, title = {{PyDaddy: A Python Package for Discovering SDEs from Time Series Data}}, doi = {10.5281/ZENODO.7137151}, year = {2024}, } @article{15315, abstract = {Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description.}, author = {Brückner, David and Broedersz, Chase P.}, issn = {1361-6633}, journal = {Reports on Progress in Physics}, number = {5}, publisher = {IOP Publishing}, title = {{Learning dynamical models of single and collective cell migration: a review}}, doi = {10.1088/1361-6633/ad36d2}, volume = {87}, year = {2024}, } @article{17123, abstract = {A key feature of many developmental systems is their ability to self-organize spatial patterns of functionally distinct cell fates. To ensure proper biological function, such patterns must be established reproducibly, by controlling and even harnessing intrinsic and extrinsic fluctuations. While the relevant molecular processes are increasingly well understood, we lack a principled framework to quantify the performance of such stochastic self-organizing systems. To that end, we introduce an information-theoretic measure for self-organized fate specification during embryonic development. We show that the proposed measure assesses the total information content of fate patterns and decomposes it into interpretable contributions corresponding to the positional and correlational information. By optimizing the proposed measure, our framework provides a normative theory for developmental circuits, which we demonstrate on lateral inhibition, cell type proportioning, and reaction–diffusion models of self-organization. This paves a way toward a classification of developmental systems based on a common information-theoretic language, thereby organizing the zoo of implicated chemical and mechanical signaling processes.}, author = {Brückner, David and Tkačik, Gašper}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, number = {23}, publisher = {National Academy of Sciences}, title = {{Information content and optimization of self-organized developmental systems}}, doi = {10.1073/pnas.2322326121}, volume = {121}, year = {2024}, } @article{17269, abstract = {The directed migration of epithelial cell collectives through coordinated movements plays a crucial role in various physiological processes and is increasingly understood at the level of large confluent monolayers. However, numerous processes rely on the migration of small groups of polarized epithelial clusters in complex environments, and their responses to external geometries remain poorly understood. To address this, we cultivate primary epithelial keratocyte tissues on adhesive microstripes to create autonomous epithelial clusters with well-defined geometries. We show that their migration efficiency is strongly influenced by the contact geometry and the orientation of cell–cell contacts with respect to the direction of migration. A combination of velocity and polarity alignment with contact regulation of locomotion in an active matter model captures quantitatively the experimental data. Furthermore, we predict that this combination of rules enables efficient navigation in complex geometries, which we confirm experimentally. Altogether, our findings provide a conceptual framework for extracting the interaction rules of active systems from their interaction with physical boundaries, as well as design principles for collective navigation in complex microenvironments.}, author = {Vercruysse, Eléonore and Brückner, David and Gómez-González, Manuel and Remson, Alexandre and Luciano, Marine and Kalukula, Yohalie and Rossetti, Leone and Trepat, Xavier and Hannezo, Edouard B and Gabriele, Sylvain}, issn = {1745-2481}, journal = {Nature Physics}, pages = {1492--1500}, publisher = {Springer Nature}, title = {{Geometry-driven migration efficiency of autonomous epithelial cell clusters}}, doi = {10.1038/s41567-024-02532-x}, volume = {20}, year = {2024}, } @article{12818, abstract = {The multicellular organization of diverse systems, including embryos, intestines, and tumors relies on coordinated cell migration in curved environments. In these settings, cells establish supracellular patterns of motion, including collective rotation and invasion. While such collective modes have been studied extensively in flat systems, the consequences of geometrical and topological constraints on collective migration in curved systems are largely unknown. Here, we discover a collective mode of cell migration in rotating spherical tissues manifesting as a propagating single-wavelength velocity wave. This wave is accompanied by an apparently incompressible supracellular flow pattern featuring topological defects as dictated by the spherical topology. Using a minimal active particle model, we reveal that this collective mode arises from the effect of curvature on the active flocking behavior of a cell layer confined to a spherical surface. Our results thus identify curvature-induced velocity waves as a mode of collective cell migration, impacting the dynamical organization of 3D curved tissues.}, author = {Brandstätter, Tom and Brückner, David and Han, Yu Long and Alert, Ricard and Guo, Ming and Broedersz, Chase P.}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{Curvature induces active velocity waves in rotating spherical tissues}}, doi = {10.1038/s41467-023-37054-2}, volume = {14}, year = {2023}, } @article{13261, abstract = {Chromosomes in the eukaryotic nucleus are highly compacted. However, for many functional processes, including transcription initiation, the pairwise motion of distal chromosomal elements such as enhancers and promoters is essential and necessitates dynamic fluidity. Here, we used a live-imaging assay to simultaneously measure the positions of pairs of enhancers and promoters and their transcriptional output while systematically varying the genomic separation between these two DNA loci. Our analysis reveals the coexistence of a compact globular organization and fast subdiffusive dynamics. These combined features cause an anomalous scaling of polymer relaxation times with genomic separation leading to long-ranged correlations. Thus, encounter times of DNA loci are much less dependent on genomic distance than predicted by existing polymer models, with potential consequences for eukaryotic gene expression.}, author = {Brückner, David and Chen, Hongtao and Barinov, Lev and Zoller, Benjamin and Gregor, Thomas}, issn = {1095-9203}, journal = {Science}, number = {6652}, pages = {1357--1362}, publisher = {American Association for the Advancement of Science}, title = {{Stochastic motion and transcriptional dynamics of pairs of distal DNA loci on a compacted chromosome}}, doi = {10.1126/science.adf5568}, volume = {380}, year = {2023}, } @article{14827, abstract = {Understanding complex living systems, which are fundamentally constrained by physical phenomena, requires combining experimental data with theoretical physical and mathematical models. To develop such models, collaborations between experimental cell biologists and theoreticians are increasingly important but these two groups often face challenges achieving mutual understanding. To help navigate these challenges, this Perspective discusses different modelling approaches, including bottom-up hypothesis-driven and top-down data-driven models, and highlights their strengths and applications. Using cell mechanics as an example, we explore the integration of specific physical models with experimental data from the molecular, cellular and tissue level up to multiscale input. We also emphasize the importance of constraining model complexity and outline strategies for crosstalk between experimental design and model development. Furthermore, we highlight how physical models can provide conceptual insights and produce unifying and generalizable frameworks for biological phenomena. Overall, this Perspective aims to promote fruitful collaborations that advance our understanding of complex biological systems.}, author = {Schwayer, Cornelia and Brückner, David}, issn = {1477-9137}, journal = {Journal of Cell Science}, keywords = {Cell Biology}, number = {24}, publisher = {The Company of Biologists}, title = {{Connecting theory and experiment in cell and tissue mechanics}}, doi = {10.1242/jcs.261515}, volume = {136}, year = {2023}, } @article{12277, abstract = {Cell migration in confining physiological environments relies on the concerted dynamics of several cellular components, including protrusions, adhesions with the environment, and the cell nucleus. However, it remains poorly understood how the dynamic interplay of these components and the cell polarity determine the emergent migration behavior at the cellular scale. Here, we combine data-driven inference with a mechanistic bottom-up approach to develop a model for protrusion and polarity dynamics in confined cell migration, revealing how the cellular dynamics adapt to confining geometries. Specifically, we use experimental data of joint protrusion-nucleus migration trajectories of cells on confining micropatterns to systematically determine a mechanistic model linking the stochastic dynamics of cell polarity, protrusions, and nucleus. This model indicates that the cellular dynamics adapt to confining constrictions through a switch in the polarity dynamics from a negative to a positive self-reinforcing feedback loop. Our model further reveals how this feedback loop leads to stereotypical cycles of protrusion-nucleus dynamics that drive the migration of the cell through constrictions. These cycles are disrupted upon perturbation of cytoskeletal components, indicating that the positive feedback is controlled by cellular migration mechanisms. Our data-driven theoretical approach therefore identifies polarity feedback adaptation as a key mechanism in confined cell migration.}, author = {Brückner, David and Schmitt, Matthew and Fink, Alexandra and Ladurner, Georg and Flommersfeld, Johannes and Arlt, Nicolas and Hannezo, Edouard B and Rädler, Joachim O. and Broedersz, Chase P.}, issn = {2160-3308}, journal = {Physical Review X}, keywords = {General Physics and Astronomy}, number = {3}, publisher = {American Physical Society}, title = {{Geometry adaptation of protrusion and polarity dynamics in confined cell migration}}, doi = {10.1103/physrevx.12.031041}, volume = {12}, year = {2022}, } @article{10530, abstract = {Cell dispersion from a confined area is fundamental in a number of biological processes, including cancer metastasis. To date, a quantitative understanding of the interplay of single cell motility, cell proliferation, and intercellular contacts remains elusive. In particular, the role of E- and N-Cadherin junctions, central components of intercellular contacts, is still controversial. Combining theoretical modeling with in vitro observations, we investigate the collective spreading behavior of colonies of human cancer cells (T24). The spreading of these colonies is driven by stochastic single-cell migration with frequent transient cell-cell contacts. We find that inhibition of E- and N-Cadherin junctions decreases colony spreading and average spreading velocities, without affecting the strength of correlations in spreading velocities of neighboring cells. Based on a biophysical simulation model for cell migration, we show that the behavioral changes upon disruption of these junctions can be explained by reduced repulsive excluded volume interactions between cells. This suggests that in cancer cell migration, cadherin-based intercellular contacts sharpen cell boundaries leading to repulsive rather than cohesive interactions between cells, thereby promoting efficient cell spreading during collective migration. }, author = {Zisis, Themistoklis and Brückner, David and Brandstätter, Tom and Siow, Wei Xiong and d’Alessandro, Joseph and Vollmar, Angelika M. and Broedersz, Chase P. and Zahler, Stefan}, issn = {0006-3495}, journal = {Biophysical Journal}, keywords = {Biophysics}, number = {1}, pages = {P44--60}, publisher = {Elsevier}, title = {{Disentangling cadherin-mediated cell-cell interactions in collective cancer cell migration}}, doi = {10.1016/j.bpj.2021.12.006}, volume = {121}, year = {2022}, }