Embryonic development is a spectacular display of self-organization of multi-cellular systems, combining transformations of tissue mechanics and patterns of gene expression. These processes are driven by the ability of cells to communicate through mechanical and chemical signaling, allowing coordination of both collective movement and patterning of cellular states. 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 principled frameworks to understand how tissues obtain information to generate reproducible patterns. I will discuss how combining dynamical systems models with information theory provides a mathematical language to analyze biological self-organization across diverse systems. Our approach can be used to define and measure the information content of observed patterns, to functionally assess the importance of various patterning mechanisms, and to predict optimal operating regimes of self-organizing systems. I will demonstrate how our framework reveals mechanisms of self-organization of in vitro stem cell systems in direct connection to experimental data, including intestinal organoids and gastruloids. This framework provides an avenue towards unifying the zoo of chemical and mechanical signaling processes that orchestrate embryonic development.

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During organ development cells undergo significant morphological and positional changes. Yet, by the end of organogenesis, internal organ structure is typically robustly defined, with cells tightly packed. It remains an open question as to how the three-dimensional (3D) internal structure of an organ emerges reliably, particularly when there are multiple cell types interacting and dynamic boundary constraints. Here, I discuss recent work from my lab utilising quantitative live imaging and 3D morphological measures of the developing zebrafish myotome to unravel how early muscle organisation emerges. Contrary to the textbook view of muscle fibres as cylindrical, myocytes undergo an ordered chiral twist, the direction and magnitude of which depends on their position within the myotome. Further, cells skew and rearrange, seemingly to facilitate close packing of neighbouring muscle fibres. Cell movement undergoes a rapid decline in speed once the cells span the myotome segment.  We find that cell packing is altered in mutants that disrupt cell fate or cell fusion, even though the final muscle segments remain largely confluent. Biophysical perturbation reveals that the cells are mechanically plastic, able to adjust to changes in the local cellular environment and boundary constraints. Taking these results together, we propose that the early myotome undergoes a structural transition, from a fluid-like state into a frozen state, resembling glass-like behaviour. Cellular plasticity in response to varying boundary constraints may be a general mechanism for ensuring robust organ morphogenesis in dense 3D tissues.

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Ternary lipid membranes—comprising a high-melting species, a low-melting species, and cholesterol—have long served as minimal model systems for studying lipid organization. Despite their ostensible simplicity, they reproduce a surprising range of the complex mixing behavior observed in biological membranes, including fluid-fluid phase coexistence and its associated critical point. A longstanding motivation behind these studies has been the hope that ternary mixtures might help unravel the enduring mystery of lipid rafts. Extensive research on well-controlled model systems has indeed revealed many of the physical principles that govern ternary lipid phase behavior, while complementary discoveries in living cells have added both support and intrigue. Yet the physiological reality remains perplexing.

Recent findings from multiple groups suggest that further progress will likely require addressing a second fundamental feature of biomembranes: their pronounced asymmetry across the two leaflets. This asymmetry is not limited to composition (i.e., the presence of distinct ternary mixtures in each leaflet) but likely extends to mechanical properties as well. There is growing evidence that the two leaflets may experience very different lateral tensions, resulting in a differential stress that strongly influences cholesterol partitioning—arguably one of the central players in membrane organization.

In this talk, I will examine these two intertwined aspects of biomembrane complexity—compositional and mechanical asymmetry—and propose a generic (though not yet very predictive) thermodynamic framework for describing their interplay. I will also present initial coarse-grained simulation results that begin to elucidate the cross-talk between asymmetry and lipid mixing thermodynamics.

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The availability of time- and disease-dependent single-cell gene expression data has opened new opportunities for integrating these datasets into mathematical models representing the evolution and switching between cellular states. In this talk, I will focus on Hopfield recurrent networks, a mathematical framework from statistical physics that captures the multi-stable dynamics inherent in complex cell signaling networks, interpreting gene expression patterns as associative memories. Hopfield recurrent networks can mathematically implement Waddington’s interpretation of normal and abnormal cell phenotypes as dynamical attractors within epigenetic landscapes. I will discuss applications of this framework in modeling the onset of angiogenesis, the dynamics of disease progression in Multiple Myeloma (MM), and the cell cycle. In our angiogenesis model, we use data to visualize the cellular transition from stalk-like to tip-like endothelial cells, corresponding to the formation of capillary sprouts in blood vessels. The MM model employs scRNA-seq data from bone marrow aspirates of MM patients and those diagnosed with two medical conditions that often progress to full MM.

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Protein language models trained on multiple sequence alignments of homologous proteins successfully capture coevolution between amino acids in structural contact: this is one of the ingredients of the success of AlphaFold. We have used such models, especially MSA Transformer, to generate new protein sequences from given protein families, and to predict which proteins interact among the members of two protein families. 

Despite their successes, a drawback of models based on multiple sequence alignments is that sequence alignment can be imperfect. Thus, we developed ProtMamba, a homology-aware but alignment-free protein language model, which is able to generate new protein sequences from given protein families. 

Beyond the amino-acid scale, coevolution also exists between genes that in a genome. To capture it, we trained ProteomeLM on complete proteomes spanning the tree of life. This model allows quick and precise scans of whole protein interaction networks.

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The Arrhenius law explains how a single enzymatic step speeds up with temperature, yet many multi-step complex biological processes still look roughly Arrhenius, until they don’t. Here we will address this question. 

We start with the biochemical cell-cycle oscillator driving early embryonic cleavages. Using new measurements and modeling across ectotherms, we find that cycle periods share similar apparent activation energies and are approximately Arrhenius over a broad range, but break down at cold and hot ends. These deviations are traced to concrete circuit features: biphasic temperature responses in key regulators and imbalances in activation energies across partially rate-determining steps, supported by Xenopus extract and in-vitro assays (Rombouts et al., Nature Comm. 2025).

We then generalize beyond oscillations: viewing biological durations as mean-first-passage times through reversible multi-step networks yields a robust curved middle regime (quadratic-exponential) produced by averaging across many steps, flanked by Arrhenius-like extremes where a few steps dominate. Simple network motifs also account for warm-edge slowdowns and apparent negative activation energies without invoking denaturation. This framework matches more than 100 datasets across species and developmental processes (Jacobs et al., BioRxiv 2025). We then test these rules in new systems and study how they help predict when biological timing will stay coordinated, drift, or fail as environments warm.

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How morphogen gradients are formed has been under debate since the term was first coined by Alan Turing. Can diffusion alone lead to the robust formation of morphogen gradients? Or are cell processes like transcytosis important to move molecules across tissues? How does the complex geometry of the extracellular space determine the diffusive and transport properties of morphogen molecules? In the first part of my talk, I will present a theoretical framework that addresses these questions, and I will discuss the design principles for morphogen gradient formation and the ways these can lead to robustness to perturbations such as tissue size and the molecular numbers in the system. I will then present a combination of experimental and theoretical work where we show that transitions in tissue-scale physical properties are coupled to morphogen signalling and transport during early zebrafish development. Our findings show that morphogen transport are actively regulated by cell and tissue architecture in vivo. We propose that feedback loops between morphogen signalling and tissue organization lock patterning and morphogenesis in a closed feedback loop that ensures that their dynamics are kept in sync. 

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Microbial communities provide countless ecological services essential for sustaining life on Earth, and they perform a wide array of functions in biotechnology—from food production to biofuel synthesis. The quantitative functions delivered by microbial communities depend on their composition, i.e. the specific genotypes present and their relative abundances. To engineer microbial consortia that optimize these functions, we must establish a predictive, quantitative link between community composition and function. Yet, developing mechanistic mathematical models to achieve this is exceptionally challenging due to the complex network of interactions involved. In this talk, I will explore how concepts from fitness landscape theory in genetics can help overcome these challenges and lead to the creation of predictive, quantitative models of community function that can guide the optimization of  synthetic microbial consortia.

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Collective cell motion is ubiquitous in biology, occurring in normal development, wound healing and disease (cancer). Over the past decade I have been collaborating with the lab of Paul Kulesa in Kansas on a study of cranial neural crest cell migration in the chick. In this talk, I will review our work and illustrate how a basic hybrid agent-based mathematical model, combined with experimental studies, has led to new insights into this phenomenon. These include understanding the role of (i) environmentally-induced phenotypic switching, (ii) extracellular matrix degrading factors, (iii) DAN-induced cell velocity control, and (iv) Colec12 and Trial as factors confining cells to move along a corridor.

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Perceptual decisions rely on accumulating sensory evidence. This computation has been studied using phenomenological models, e.g. the drift diffusion model, or neurobiological network models exhibiting attractor dynamics. It remains unclear whether the dynamics of both models are qualitatively equivalent and whether attractor models can integrate evidence optimally. Here, I will present distinctive features of attractor models that allow them to perform flexible temporal weighting of stimulus evidence. In the discrete attractor model, this is due to transitions between decision states that can reverse initially-incorrect categorizations. Moving from categorical choices to continuous perceptual judgments, I will show that a continuous bump attractor network can integrate a circular feature, such as stimulus direction, nearly optimally. As required by optimal integration, the population activity of the network unfolds on a two-dimensional manifold, in which the position of the network’s activity bump tracks the stimulus average, and, simultaneously, the bump amplitude tracks stimulus uncertainty. Moreover, the model can flexibly switch between different temporal weighting profiles by changing a single control parameter, the global excitatory drive. Predictions of the models are validated with psychophysical data. Finally, I will outline how these attractor models can provide a comprehensive and experimentally testable computational framework to study the neural mechanisms underlying stimulus integration and bias effects in combined discrimination-estimation tasks.

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