This seminar explores the modeling of biological growth and patterning across diverse systems — the filamentous cyanobacterium Anabaena, Arabidopsis thaliana plants, Drosophila melanogaster flies, and an epidemic spreading across a population. We delve into how genetic and environmental factors influence the quasi-regular patterning of nitrogen-fixing specialized cells, called heterocysts, in Anabaena. The model highlights key genes and cellular processes that govern pattern appearance and maintenance, illustrating the impact of physical boundary conditions in biological systems. For Arabidopsis, we examine how light and temperature cues affect the growth of the hypocotyl through interactions between photoreceptors and thermal sensors, shedding light on plant morphogenesis. In Drosophila, we focus on how BMP2/4 signaling regulates cell proliferation and apoptosis to ensure precise organ size during development. Finally, epidemic spread has been a topic of grave concern in recent years, and it provides a perfect example to discuss both the limitations of mathematical prediction and the right level of complexity a model should have.

In 1967 Francis Crick and Sydney Brenner proposed that we need mathematical models of cells to understand their complexity and their behaviour; in 2001 mathematical modelling of cells was identified as a grand challenge of 21st Century science. In order to understand the complexity of life, in order to integrate and interpret experimental data, and in order to control cellular processes in biotechnology and synthetic biology we need a conceptual, analytical, and predictive framework – referred to as the CellMap by Sydney Brenner. I will discuss three facets, centred around cell differentiation and developmental process, of how we can start to distill “design principles” underlying cellular behaviour. Here design principles are understood as the essential properties that a system needs to possess to be able to fulfil certain functions. I will discuss the interplay of cell lineages, molecular networks, and phenotypic landscapes, their intricate interdependencies, and how they shape cell-fate decision making processes. These are, of course, only baby-steps towards Brenner’s dream of a CellMap, but taking them has already allowed us to map out and embark on a feasible path towards such models.

Early development across vertebrates and insects critically relies on robustly reorganizing the cytoplasm of fertilized eggs into individualized cells. This intricate process is orchestrated by large microtubule structures that traverse the embryo, partitioning the cytoplasm into physically distinct and stable compartments. Despite the robustness of embryonic development, here we uncover an intrinsic instability in cytoplasmic partitioning driven by the microtubule cytoskeleton. We reveal that embryos circumvent this instability through two distinct mechanisms: either by matching the cell cycle duration to the time needed for the instability to unfold or by limiting microtubule nucleation. These regulatory mechanisms give rise to two possible strategies to fill the cytoplasm, which we experimentally demonstrate in zebrafish and Drosophila embryos, respectively. In zebrafish embryos, unstable microtubule waves fill the geometry of the entire embryo from the first division. Conversely, in Drosophila embryos, stable microtubule asters resulting from reduced microtubule nucleation gradually fill the cytoplasm throughout multiple divisions. Our results indicate that the temporal control of microtubule dynamics could have driven the evolutionary emergence of species-specific mechanisms for effective cytoplasmic organization. Furthermore, our study unveils a fundamental synergy between physical instabilities and biological clocks, uncovering universal strategies for rapid, robust, and efficient spatial ordering in biological systems.

Amyloid fibrils form and precipitate in more than 50 incurable human diseases, including Alzheimer’s (AD) and Parkinson’s disease. Only a small number of human proteins and protein variants are known to form amyloids, limiting our ability to understand, predict and engineer amyloid aggregation from sequence. The initial events in amyloid formation are particularly challenging to study by classic biophysical methods, due to the transient and high-energy nature of transition states, but they are also the most critical steps to understand, as these events control the rate of the aggregation reaction and can be targeted to prevent or slow down amyloid formation for therapeutic purposes. 

We have developed a multiplex assay of variant effects (MAVE) approach that is able to quantify the rate of aggregation of thousands of protein sequences in parallel. We have shown that this MAVE accurately classifies insertions, deletions, and missense variants in Amyloid Beta (Aß), the protein which is mutated in familial forms of AD and which aggregates in all forms of AD. In this talk I will show how, by employing the same approach on different amyloids, we find that mutational effects in one single amyloid are not enough to predict mutational impact in another amyloid forming sequence. This provides a rationale for generating MAVEs for all human amyloids, an approach which will greatly impact clinical variant classification. 

Finally, I will show how, by expanding our strategy to cover hundreds of thousands of random sequences, it is now possible to train an interpretable model that is able to predict the ability of any sequence to form amyloids, demonstrating how the power of massive experimental random sequence-space exploration is now opening the way for a systematic and global understanding of amyloid formation.

Nonequilibrium pervades nature, from the expanding universe to climate dynamics, living cells and molecular machines. Key to nonequilibrium states is the entropy production rate σ  at which energy is dissipated to the environment. Despite its importance, σ  remains challenging to measure, especially in nanoscale systems with limited access to microscopic variables. Here I present a recently introduced variance sum rule for displacement and force variances that permits to measure σ  by constraining energetics through modelling [1,2]. We apply it to measure the first heat map of human red blood cells in experiments with laser optical tweezers and ultrafast life-imaging microscopy. We find a spatially heterogeneous σ  with finite-correlation length of half a micron ξ~0.5μm and global σ~ 10⁶ k_BT/s per single cell, in agreement with calorimetry estimates. The variance sum rule sets a new resource for measuring entropy production rates in active and living matter [3].

References

[1]  Di Terlizzi, I., Gironella, M., Herráez-Aguilar, D., Betz, T., Monroy, F., Baiesi, M., & Ritort, F. (2024). Variance sum rule for entropy production. Science, 383(6686), 971-976.

[2] Di Terlizzi, I., Baiesi, M., & Ritort, F. (2024). Variance sum rule: proofs and solvable models. New Journal of Physics, DOI: 10.1088/1367-2630/ad4fb9.

[3] Roldán, É. (2024). Thermodynamic probes of life. Science, 383(6686), 952-953.

One of the greatest mysteries concerning the origin of life is how it has emerged so quickly after the formation of the earth. In particular, it is not understood how the intricate structures of metabolic cycles, which power the non-equilibrium activity of cells and support their functions under homeostatic conditions, have come into existence in the first instances. These structures have emerged from a dilute primordial soup of chemicals that have turned out to be suitable partners in certain reactions in the roles of reactants and catalysts. While it is generally expected that non-equilibrium conditions would have been necessary for the formation of these primitive metabolic structures, the focus has so far been on externally imposed non-equilibrium conditions, such as temperature or proton gradients. I introduce an alternative paradigm in which naturally occurring non-reciprocal interactions between catalysts that can potentially partner together in a cyclic reaction lead to their rapid recruitment into self-organized functional structures [1]. Within this paradigm, we uncover different classes of self-organized cycles that form through exponentially rapid coarsening processes, depending on the parity of the cycle and the nature of the interaction motifs, which are all generic but have readily tuneable features. Our results also shed light on possibilities that may be explored in designing efficient synthetic cycles. Moreover, we identify programmable non-reciprocal interactions as a tool to achieve the ability to employ a common set of building blocks that can self-organize into a multitude of different structures [2]. The design rule is composed of reciprocal interactions that lead to the equilibrium assembly of the different structures, through a process denoted as multifarious self-assembly, and non-reciprocal interactions that give rise to non-equilibrium dynamical transitions between the structures. The design of such self-organized shape-shifting structures can be implemented at different scales, from nucleic acids and peptides to proteins and colloids.

[1] Vincent Ouazan-Reboul, Jaime Agudo-Canalejo, and Ramin Golestanian, Nature Communications 14, 4496 (2023)

[2] Saeed Osat and Ramin Golestanian, Nature Nanotechnology 18, 79–85 (2023)

Transcriptomic data provide a systematic multivariate snapshot measurement of the state of a biological system. In my team, we develop transcriptomics data integration and modelling frameworks to reconstruct systems dynamics, identify and precisely quantify hidden phenotypic variation at multiple scales, from the molecular level to organismal physiology, and to make quantitative predictions about genetic and non-genetic cellular and molecular and mechanisms of phenotypic variation including at single-cell and single-individual level. In contrast to others, our strategies privilege interpretability and robustness. I will present examples of how I applied these strategies to predict complex phenotypes and mechanisms at the single-cell and single-organism level.  In particular, I will present RAPToR, a simple but precise computational method to infer absolute physiological age of a system from its transcriptome exploiting existing time series data as reference1. Importantly, ages estimated on the same reference are comparable across conditions, genetic backgrounds even across species. RAPToR, works in multiple model organisms or humans for both development and aging, for bulk, dissected tissues, single-individual and single-cell data. Moreover, provided with tissue/process -specific annotation RAPToR can provide tissue specific age estimates from whole-animal data.  Estimated physiological ages, (in combination with chronological age) can be used not only to precisely quantify the effect (and time of action) of genetic, environmental and inter-individual variation on development or aging speed but also to quantify their specific effects of on gene expression, suggesting their specific molecular determinants. In summary, large scale transcriptomic data can be exploited to both quantify complex phenotypes and learn molecular and cellular determinants of these phenotypes. These quantities inferred from gene expression can then be used to parametrize mathematical models to predict phenotypes.

References

1.Bulteau, R. & Francesconi, M. Real age prediction from the transcriptome with RAPToR. Nat Methods 1–7 (2022) doi:10.1038/s41592-022-01540-0

Fate decisions in developing tissues involve cells transitioning between a set of discrete cell states. Geometric models, often referred to as Waddington landscapes, are an appealing way to describe differentiation dynamics and developmental decisions. We consider the differentiation of neural and mesodermal cells from pluripotent mouse embryonic stem cells exposed to different combinations and durations of signalling factors. We developed a principled statistical approach using flow cytometry data to quantify differentiating cell states. Then, using a framework based on Catastrophe Theory and approximate Bayesian computation, we constructed the corresponding dynamical landscape. The result was a quantitative model that accurately predicted the proportions of neural and mesodermal cells differentiating in response to specific signalling regimes. Taken together, the approach we describe is broadly applicable for the quantitative analysis of differentiation dynamics and for determining the logic of developmental cell fate decisions.

Bacteria employ various strategies to survive environmental stress. One of these strategies is filamentation wherein bacterial cells elongate instead of dividing. This adaptive response, essential for survival, is also associated with virulence. In this talk I will review our research on the topic where we have focused on understanding the mechanobiology cues driving this process and their implications. Thus, using quantitative fluorescent time-lapse microscopy, micropatterning, modeling, microfluidics, and FRAP we reveal how Min dynamics is coupled to the mechanical stress originating from bacterial filamentation and ultimately influences the post-stress bacterial division process.