We suggest a rule-based approach to modeling the development of organs and body plans of animals. We subdivide the problem into gene-regulated cell differentiation, cell-cell signaling, and the physical dynamics of interacting cells that shape organs and bodies. In this talk I will focus on the latter, starting with the overall phenomenology of our bodies as a collection of sheets that forms hollow spheres, tubes and branching tubes. The physics of these two symmetry-breaking events is governed by two types of cell-cell interactions: the Apical-Basal polarity (AB) that directs sheet formation, and the Planar Cell Polarity (PCP) that direct tube formation.  I describe a working dynamical model that deals with these two polarities. The model is applied to the biological process of gastrulation, of neural tube formation, and to mimic the dynamics of branching tubes seen in the growth of lungs or kidneys.

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Modern network science has greatly contributed to our understanding of many processes in diverse fields of science. Arguably, contagion dynamics -including network epidemiology- is where network concepts have had a bigger practical impact. Nowadays, we can model how diseases unfold and spread with unprecedented precision, making it possible to analyze other spreading-like processes, such as social contagion. In this talk, we revise this area of research by discussing how the modeling of spreading processes has evolved in the last two decades. We start by analyzing contagion dynamics in single populations described by different network topologies. Next, we discuss cases in which a multilayer approach is needed. Finally, we discuss the recent COVID-19 pandemic using tools that combine theoretical models with data-driven simulations and network science tools. We conclude the talk by discussing the challenges that remain for the future.

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Cellular systems - enzymes, motors, allosteric proteins, genes, ion channels, receptors, etc - are often described by the functional dependence of some output property on the concentrations of input factors, with the system itself described as a Markov process. Such input-output functions are calculated by a variety of methods with apparently few common features. In fact, this typical biological heterogeneity conceals a remarkable underlying mathematical unity. All such input-output functions are rational functions of their inputs, whose coefficients are themselves rational functions of the Markov transition rates. There is a uniform procedure for calculating each function in terms of the linear-framework graph associated to the Markov process. Furthermore, input-output functions exhibit a Hopfield barrier: if the Markov process can reach thermodynamic equilibrium, then the degree of the rational function depends only on the numbers of input binding sites and is otherwise model independent. Hopfield barriers offer a powerful method for assessing energy expenditure in cellular systems, which does not require fitting models to data.

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Heterogeneity in cancer is an observed fact, both genetically and phenotypically. Cell-to-cell variation is seen in all aspects of cancer, from early development to invasion and subsequent metastasis. This heterogeneity is also at the heart of why many cancer treatments fail, as it facilitates the emergence of drug resistance. The complex spatial and temporal process by which tumors initiate, grow and evolve is a major focus of the oncology community and one that requires the integration of multiple disciplines. Tumor heterogeneity at the tissue scale is largely due to ecological variations in
terms of the tumor habitat driven by spatially heterogeneous vascularity, which is
readily observed on cross sectional imaging. Molecular techniques have
historically averaged genomic signals from large numbers of cells obtained in a
single biopsy site, thus smoothing and potentially hiding underlying spatial
variations. The complex dialogue between tumor cells and
environment that produces intra- and inter-tumoral heterogeneity is
fundamentally governed by Darwinian dynamics. That is, local microenvironmental conditions select phenotypic clones that are best adapted to
survive and proliferate and, conversely, the phenotypic properties of the cells affect the
environmental properties. While these complex interactions have enormous
clinical implications because they promote resistance to therapy, the dynamics
are impossible to fully capture via experimentation alone. Here we present an integrated theoretical/experimental approach to develop dynamical models of the complex multiscale interactions that manifest as temporal and spatial heterogeneity in cancers and ultimately govern tumor response and resistance to therapy. Specifically, we examine the impact of microenvironmental modulation on cancer evolution both in silico, using a hybrid multiscale mathematical model, and in vivo, using three different spontaneous murine cancers. These models allow the tumor to be steered into a less invasive pathway through the application of small but selective biological force. Our long term goal is explicitly translational as we focus our integrated approach on an emerging cancer treatment paradigm that actively harnesses evolutionary dynamics to improve patient outcomes.

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Biological systems exhibit a high degree of hierarchical organisation, where individual elements come together to form more complex and unique entities, which integrate into tissues, organs, organisms, and entire communities. The interactions within these systems are highly combinatorial, leading to the emergence of holistic processes such as development, immune response, and ageing. These systems are dynamic, composed of densely packed components and shaped by intricate interactions that range from cooperative behaviours to competitive conflicts. Such interactions, driven by the unique roles of individual elements, can significantly influence the stability and functionality of the entire system.

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How can tissue shapes and patterns emerge reproducibly and robustly in multicellular systems like animals?  Despite more than 100 years of embryology, it still remains unclear how gene networks, forces and mechanical properties and the metabolic state of the cells integrate together to self-organize complex structures. This is due to our inability to disentangle the combined action of these factors (biophysical properties, gene networks and metabolic activity) within populations of genetically equivalent cells. In our work we focus on understanding the interplay of these factors within the context of the establishment of body axes in metazoans. We take advantage of aggregates of embryonic stem cells (ESCs) that recapitulate hallmarks of early embryonic development in vitro and probe the first symmetry breaking event that establishes anteroposterior polarity in those aggregates. We aim to understand how gene expression controls tissue rheology which can then dictate spatial segregation of cell types, while the metabolic activity of the cells in the background influences signalling and cell fate decisions. In the long term we aspire to generate a theoretical framework that can capture these processes occurring at different time scales and the feedbacks that together generate a robust pattern in multicellular systems. 

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Large quantities of heterogeneous, interconnected, systems-level, molecular (multi-omic) data are increasingly becoming available. They provide complementary information about cells, tissues and diseases. We need to utilize them to better stratify patients into risk groups, discover new biomarkers and targets, re-purpose known and discover new drugs to personalize medical treatment. This is nontrivial, because of computational intractability of many underlying problems on large interconnected data (networks, or graphs), necessitating the development of new algorithms for finding approximate solutions (heuristics).

We develop a versatile data fusion artificial intelligence (AI) framework, that also utilizes the state-of-the-art network science methods, to address key challenges in precision medicine from the multi-omics data: better stratification of patients, prediction of biomarkers and targets, and re-purposing of approved drugs to particular patient groups, applied to different types of cancer, Covid-19, Parkinson’s and other diseases. Our new methods stem from graph-regularized non-negative matrix tri-factorization (NMTF), a machine learning technique for dimensionality reduction, inference and co-clustering of heterogeneous datasets, coupled with novel network science algorithms. We utilize our new frameworks to develop methodologies for improving the understanding the molecular organization and diseases from the omics data embedding spaces.

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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.

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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.