L3

This presentation will focus on the role of mathematical modelling and predictive toxicology in the safety assessment of chemicals and consumer products. The starting point will be regulatory assessment of chemicals based on their potential for harming human health or the environment. This will set the scene for describing current practices in the development and application of mathematical and computational models. A wide variety of methodological approaches are employed, ranging from relatively simple statistical models to more advanced machine learning approaches. The modelling context also ranges from discovering the underlying mechanisms of chemical toxicity to the safe and sustainable design of chemical products. The main modelling approaches will be reviewed, along with the challenges and opportunities associated with their use.  The presentation will conclude by identifying current research needs, including progress towards a Unified Theory of Chemical Toxicology.

Many scientific questions in biology can be formulated as a direct problem:

given a biochemical system, can one deduce some of its properties? 

For example, one might be interested in deducing equilibria of a given intracellular network.  On the other hand, one might instead be interested in designing an intracellular network with specified equilibria. Such scientific tasks take the form of inverse problems:
given a property, can one design a biochemical system that displays this property? 

Given a biochemical system, can one embed additional molecular species and reactions into the original system to control some of its properties?
These questions are at the heart of the emerging field of synthetic biology, where it has recently become possible to systematically realize dynamical systems using molecules.  Furthermore, addressing these questions for man-made synthetic systems may also shed light on how evolution has overcome similar challenges for natural systems.  In this talk, I will focus on the inverse problems, and outline some of the results and challenges which are important when biochemical systems are designed and controlled.

Manipulation of the genome function is important for understanding the underlying genetics for sophisticated phenotypes and developing gene therapy. Beyond gene editing, there is a major need for high-precision and quantitative technologies that allow controlling and studying gene expression and epigenetics in the genome. Towards this goal, we develop the concept and technologies for the use of the nuclease-deactivated CRISPR-Cas (dCas) system, repurposed from the Cas nuclease, for programmable transcription regulation, epigenetic modifications, and the 3D genome organization. We combine genome engineering and mathematical modeling to understand the noncoding DNA function including ultralong-distance enhancers and repetitive elements. We actively explore new tools that allow precise manipulation of the large-scale chromatin as a novel gene therapy. In this talk, I will highlight our works at the interface between genome engineering and chromatin biology for studying the noncoding genome and related applications.

Subfactor theory provides a framework for studying modular invariant

partition functions in conformal field theory,

and candidates for exotic modular tensor categories and almost Calabi-Yau

algebras. I will survey some joint work with Terry Gannon and Mathew Pugh.