CDEV Subgroup Contributed Talks

Stephen Zhang

University of British Columbia

"Learning cell state dynamics from noisy time-series data using optimal transport"

We devise a theoretical framework and a numerical method to infer trajectories of a stochastic process from snapshots of its temporal marginals. This problem arises in the analysis of single cell RNA-sequencing data, which provide high dimensional measurements of cell states but cannot track the trajectories of the cells over time. We prove that for a class of stochastic processes it is possible to recover the ground truth trajectories from limited samples of the temporal marginals at each time-point, and provide an efficient algorithm to do so in practice. The method we develop, Global Waddington-OT (gWOT), boils down to a smooth convex optimization problem posed globally over all time-points involving entropy-regularized optimal transport. We demonstrate that this problem can be solved efficiently in practice and yields good reconstructions, as we show on several synthetic and real datasets.

Joshua Forrest

University of Melbourne

"Energy based modelling of bacterial signalling systems"

A key challenge in systems biology is creating mathematical models that can be easily and accurately combined with other models. Such models will need to share a consistent modelling framework and be easily reusable by systems biologists.One solution to this challenge is to use a physics-based approach to modelling. Bond graphs are an energy-based modelling framework that describe the rate of energy flow (power) moving through system components. By construction, bond graphs models enforce physical and thermodynamic constraints, making model components physically consistent with one another. Bond graphs also provide a graphical representation of the model and allow for easy hierarchical modelling.To demonstrate bond graph modelling applied to biological systems, we have applied this framework to Two Component Systems (TCS). TCS are a signalling mechanism found in many common bacteria such as E. coli and B. subtilis. By modelling the explicit energy dependence of TCS using bond graphs, we find new insights into the behaviour of the system in different energy contexts. A modular framework also means we can combine models together to investigate coupling dynamics of TCS. In future, we argue that such an approach could lead towards the development of a systems-wide, physically plausible whole-cell model.

Nishtha Pandey

Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology - Hyderabad, India

"Mathematical modelling of neuronal cell cycle re-entry in Alzheimer's disease"

Neurodegenerative disease (ND) is an umbrella term used to classify medical conditions associated with neuronal atrophy and gradual loss of cognitive abilities. The most common ND is Alzheimer's disease (AD). However, the approved drugs mostly treat the symptoms of AD. Therapeutic approaches targeting Amyloid beta (Aβ) aggregation fail to reverse or inhibit disease progression. These observations point towards gaps in the understanding of disease mechanisms. During development, the progenitor cells mature into neurons and they switch to a post mitotic, resting state. However, cell cycle reentry often precedes neuronal apoptosis hinting at a close interaction between the two processes. In this study we develop mathematical models of multiple pathways leading to cell cycle re-entry in neurons. These models incorporate the cross talk between cell cycle, neuronal and apoptotic signaling mechanisms. Our study shows that different self-sustaining feedback loops operate in post mitotic neurons that can make the cell cycle re-entry and transition to an apoptotic state irreversible. Important cell cycle regulators that function as hub nodes were identified. Further, we propose a combinatorial therapy targeting Aβ proteolysis as well as blocking the cell cycle feedback loop may alleviate the severity of the disease.

Domenic Germano

The University of Melbourne

"Towards a realistic 3D deformable model of dynamic tissues"

Colorectal Cancer is one of the most prevalent forms of cancer within western society. It is known to develop within the epithelia of the colon, localised to distinct invaginations within the intestinal wall, known as the crypts of Lieberkürn. While much is known about these crypts, the biomechanical process responsible for their structural maintenance remains unknown. One such process believed to be responsible for the crypts structural stability is believed to be a result of the surrounding stromal tissue.Here, we will present a 3D, multilayer, cell-centre model of tissue deformation, where cell movement is governed by the minimisation of a bending potential across the epithelium, cell-cell adhesion, and viscous effects. Using this model, we will show how the tissue is capable of maintaining a consistent structure while undergoing self renewal. We will also show how the model extends natural to describe general tissue deformations, and we hope to further extend it to describe crypt dynamic homeostasis.