Publications

In this work, we develop a spectral theory for hypergraph limits. We prove the convergence of the spectra of adjacency and Laplacian matrices for hypergraph sequences converging in the 1-cut metric. On the other hand, we give examples of matrix operators associated with hypergraphs whose spectra are not continuous with respect to the 1-cut metric. Furthermore, we show that these operators are continuous with respect to other cut norms

AlphaFold has enabled large-scale prediction of protein-protein and protein-nucleic acid complexes, but ranking and assessing the quality of predicted models remain challenging. Existing confidence scores are often highly parametrized and provide limited interpretability. We introduce a simple geometric framework that converts AlphaFold-predicted aligned error (PAE) into conditional contact probability. We show that these probabilities are well calibrated to the fraction of native contacts observed across experimentally determined structures. Motivated by this, we define the Pinc score (Probability of interface native contacts) as the mean contact probability between interacting chains. Because the probabilistic interpretation extends to individual residues, Pinc captures local structural constraint beyond interfacial burial, enabling residue-level prioritization of hotspot positions for mutational studies. Depending solely on a single empirically fixed contact radius, Pinc offers an interpretable path from PAE to interface confidence, matching or exceeding the classification performance of more complex methods across five independent benchmark sets. We provide a portable, dependency-free C program and a Google Colab notebook for calculating Pinc scores for AlphaFold models at https://git.mpi-cbg.de/tothpetroczylab/Pinc.

Network-based biocomputing (NBC) presents an energy-efficient, parallel computing approach for solving nondeterministic polynomial time (NP) complete problems by leveraging motor-driven cytoskeletal filaments that explore all possible solutions through nanofabricated networks in a massively parallel fashion. However, guiding errors at pass junctions, where filaments deviate from their intended path, currently limit the scalability of NBC systems. In this study, we addressed this critical challenge by fabricating sub-200 nm channel geometries using modified electron-beam-lithography and reactive-ion-etching protocols to physically constrain the trajectories of kinesin-driven microtubules and enhance path fidelity. Investigating junction designs with varying channel widths, we demonstrate that reducing channel width significantly lowers junction error rates. Practically error-free junction performance was achieved by scaling down the entire network geometry by a factor of two. These optimized junctions were incorporated into NBC networks that successfully solved 24- and 25-set instances of the Exact Cover problem, representing solution spaces of approximately 16 and 33 million, respectively. This work establishes a new benchmark in NBC performance and represents a computational scale far beyond what has been achieved in prior demonstrations.

We show that coupling enzymatic activity to condensation under limited resource conditions drives emergent self-regulation via droplet formation and dissolution. Our kinetic models show that in situ phase separation of in-vitro-transcribed mRNA with an intrinsically disordered protein (mutant G3BP1) modulates transcription and degradation kinetics. When resources for mRNA production are limited, condensates spontaneously dissolve, driven by the feedback from compartmentalization on reaction rate constants-with slower degradation within condensates than in the mRNA-protein-poor phase. Consequently, the lifetime of mRNA is prolonged upon condensation compared to the case without condensates. Extending the model to sustained and oscillatory resource supply reveals that condensates elevate mean mRNA levels and buffer deviations from the mean compared to the non-condensate scenario. These findings provide a general mechanism of cross-regulation and feedback between phase separation and enzymatic reactions, highlighting condensates as active regulators of biochemical flux rather than as passive organizers.

The ability to follow transcription in individual cells with live imaging has revealed key dynamical mechanisms of gene regulation. However, such measurements are lacking in the context of vertebrate embryos. We addressed this deficit by applying MS2-MCP mRNA labeling to the quantification of transcription in zebrafish, a model vertebrate. We developed a platform of transgenic organisms, light-sheet fluorescence microscopy, and optimized image analysis that enables visualization and quantification of MS2 reporters. With these tools, we obtained single-cell, real-time measurements of the transcriptional dynamics of the segmentation clock. Our measurements reveal that smooth clock protein oscillations arise from discrete transcriptional bursts that are organized in space and time. Together, these results highlight how measuring single-cell transcriptional activity in the context of vertebrate organisms can reveal unexpected features of gene regulation and how this data can fuel the dialogue between theory and experiment.

While pancreatic cysts have been described in syndromic ciliopathies, the pancreas is not commonly recognised as a target organ. However, several ciliary gene knockout mouse models develop a pancreatic phenotype combining acinar atrophy and adipocyte accumulation, here called adipopancreatosis, suggesting a link between ciliary dysfunction and pancreatic disease.

Live cells in tissue are plastic, phenotypically dynamic, and modify their function in response to genetic and environmental perturbations. To unleash the power of live-cell imaging to identify phenotype-genotype-function coupling over time, we report the development of a standardized Shape-Appearance-Motion (SAM) "phenome" and SAM-Phenotype-Observation-Tool (SPOT), that act as an image-"transcriptome" and image-"transcriptome analyzer" respectively, and provide an unbiased and comprehensive description of morpho-dynamic phenotypes without prior knowledge. We apply SAM-SPOT to our simulated organoids database with known ground-truth and >1.6 million mouse and human organoid instances with defined genetic and chemical perturbations. SAM-SPOT can effectively and robustly characterize 3D morpho-dynamics from 2D projection videos. Combined with single-cell RNA sequencing, SAM-SPOT reveals that altered WNT signaling, but not mutant RAS or p53, predisposes intestinal organoids to irregular morphogenesis. SAM-SPOT advances biomedical discovery by empowering live-cell imaging to identify phenotype-genotype-function relationships through large-scale and cost-effective label-free live-cell imaging.

Cells are plastic, highly heterogeneous and change over time. High-content timelapse imaging promises to reveal dynamic cell behaviors, enabling more accurate identification of cell state and cell fate prediction for biological hypothesis generation and perturbation screens. To empower live-cell imaging based screening, we report the development of (1) a Shape, Appearance, Motion (SAM) "phenome"; a universal set of 2185 image-derived features that act as a image-"transcriptome" to comprehensively quantify an object's instantaneous phenotype; (2) the SAM-Phenotype-Observation-Tool (SPOT), for image-"sequencing" analysis of phenomes. We validate the effectiveness of unbiased SAM-SPOT workflow on publicly available computer vision and 2D single cell imaging datasets. Importantly, we demonstrate that SAM-phenome outperforms features generated by deep learning AI models trained on >1 million fixed single cell and >5000 single cell video frames, respectively. SAM-phenome and SPOT deliver high-throughput, object-treatment-agnostic, comprehensive screening readouts of dynamics, promising to advance novel molecular target discovery and new medicine development.

MALT1 (mucosa-associated lymphoid tissue lymphoma/leukemia protein 1)-TRAF6 [tumor necrosis factor receptor (TNFR)-associated factor 6] interaction drives lymphocyte activation and adaptive immunity, but it also contributes to maintaining immune homeostasis. MALT1 exists in two isoforms that differ only by either encoding two (MALT1A) or one (MALT1B) TRAF6 binding motif (T6BM). The human mutation MALT1 E806D in T6BM2, expressed in both MALT1A and MALT1B, has been associated with an immune disorder combining symptoms of immune deficiency and autoimmunity. Here, we report that the orthologous germline mutation MALT1 E814D is sufficient to induce a fatal autoimmune syndrome in mice. We demonstrate that species-specific differences in the effects of T6BM2 disruptions can be attributed to alterations in MALT1 splicing and that immune homeostasis is restored by genetically enforcing expression of MALT1A in MALT1 E814D mice. Thus, alternative MALT1 splicing allows tuning of TRAF6 association, thereby functioning as a molecular rheostat to balance between optimal immune activation and maintenance of peripheral tolerance.

The active inference framework provides a principled approach to modeling sentient behavior. In this framework perception and action selection are treated in a unified way. The resulting agents form an internal generative model of the relevant dynamics of the world in order to infer their future observations, their internal states and to select actions. We combine this modeling framework with the Integrated Information Theory of consciousness and are therefore able to analyze the active inference agents from the perspective of integrated information. The Integrated Information Theory aims at quantifying the level of consciousness of a system by assessing its capability to integrate information. Here, we define a measure of integrated information for the generative model by making an additional structural assumption. Experiments with simulated agents reveal a correlation between integrated information measures and the free energy of the active inference agents that increases with the size of the generative model.