Malignant transformation of somatic tissues is an evolutionary process, driven by selection for oncogenic mutations. Understanding when these mutations occur, and how fast mutant cell clones expand can improve diagnostic schemes and therapeutic intervention. However, clonal dynamics are not directly accessible in humans, posing a need for inference approaches to reconstruct the division history in normal and malignant cell clones, and to predict their future evolution. Inspired from population genetics theory, we develop mathematical models to detect imprints of clonal selection in the variant allele frequency distribution measured in a single tissue sample of a homeostatic tissue. I will present the theoretical basis of our approach and inference results for the tissue dynamics in physiological and clonal hematopoiesis, obtained from variant allele frequencies measured by snapshot bulk whole genome sequencing of human bone marrow samples.

Unraveling the intricacies of intracellular signalling through predictive mathematical models holds great promise for advancing precision medicine and enhancing our foundational comprehension of biology. However, navigating the labyrinth of biological mechanisms governing signalling demands a delicate balance between a faithful description of the underlying biology and the practical utility of parsimonious models.
In this talk, I will present methods that enable training of large ordinary differential equation models of intracellular signalling and showcase application of such models to predict sensitivity to anti-cancer drugs. Through illustrative examples, I will demonstrate the application of these models in predicting sensitivity to anti-cancer drugs. A critical reflection on the construction of such models will be offered, exploring the perpetual question of complexity and how intricate these models should be.
Moreover, the talk will explore novel approaches that meld machine learning techniques with mathematical modelling. These approaches aim to harness the benefits of simplistic and unbiased phenomenological models while retaining the interpretability and biological fidelity inherent in mechanistic models.
 

Motile cells inside living tissues often encounter junctions, where their path branches into several alternative directions of migration. We present a theoretical model of cellular polarization for cells migrating along one-dimensional lines, exhibiting diverse migration modes. When arriving at a symmetric Y-junction and extending protrusions along the different paths that emanate from the junction. The model predicts the spontaneous emergence of deterministic oscillations between competing protrusions, whereby the cellular polarization and growth alternates between the competing protrusions. These predicted oscillations are found experimentally for two different cell types, noncancerous endothelial and cancerous glioma cells, migrating on patterned network of thin adhesive lanes with junctions. Finally we present an analysis of the migration modes of multicellular "trains" along one-dimensional tracks.

Sparse neural networks, where a substantial portion of the components are eliminated, have widely shown their versatility in model compression, robustness improvement, and overfitting mitigation. However, traditional methods for obtaining such sparse networks usually involve a fully pre-trained, dense model. As foundation models become prevailing, the cost of this pre-training step can be prohibitive. On the other hand, training intrinsic sparse neural networks from scratch usually leads to inferior performance compared to their dense counterpart. 

In this talk, I will present a series of approaches to obtain such fantastic sparse neural networks by training from scratch without the need for any dense pre-training steps, including dynamic sparse training, static sparse with random pruning, and only masking no training. First, I will introduce the concept of in-time over-parameterization (ITOP) (ICML2021) which enables training sparse neural networks from scratch (commonly known as sparse training) to attain the full accuracy of dense models. By dynamically exploring new sparse topologies during training, we avoid the costly necessity of pre-training and re-training, requiring only a single training run to obtain strong sparse neural networks. Secondly, ITOP involves additional overhead due to the frequent change in sparse topology. Our following work (ICLR2022) demonstrates that even a naïve, static sparse network produced by random pruning can be trained to achieve dense model performance as long as our model is relatively larger. Moreover, I will further discuss that we can continue to push the extreme of training efficiency by only learning masks at initialization without any weight updates, addressing the over-smoothing challenge in building deep graph neural networks (LoG2022).