L3

Understanding the mechanisms of mutagenesis is important for prevention and treatment of numerous diseases, most prominently cancer. Large sequencing datasets revealed a substantial number of mutational processes in recent years, many of which are poorly understood or of completely unknown aetiology. These mutational processes leave characteristic sequence patterns in the DNA, often called "mutational signatures". We use bioinformatics methods to characterise the mutational signatures with respect to different genomic features and processes in order to unravel the aetiology and mechanisms of mutagenesis. 

In this talk, I will present our results on how mutational processes might be modulated by DNA replication. We developed a linear-algebra-based method to quantify the magnitude of replication strand asymmetry of mutational signatures in individual patients, followed by detection of these signatures in early and late replicating regions. Our analysis shows that a surprisingly high proportion (more than 75 %) of mutational signatures exhibits a significant replication strand asymmetry or correlation with replication timing. However, distinct groups of signatures have distinct replication-associated properties, capturing differences in DNA repair related to replication, and how different types of DNA damage are translated into mutations during replication. These findings shed new light on the aetiology of several common but poorly explained mutational signatures, such as suggesting a novel role of replication in the mutagenesis due to 5-methylcytosine (signature 1), or supporting involvement of oxidative damage in the aetiology of a signature characteristic for oesophageal cancers (signature 17). I will conclude with our ongoing work of wet-lab validations of some of these hypotheses and usage of computational methods (such as genetic algorithms) in guiding the development of experimental protocols.

The spatial coordination of cellular differentiation enables functional organogenesis. How coordination results in specific patterns of differentiation in a robust manner is a fundamental question for all developmental systems in biology. Theoreticians such as Turing and Wolpert have proposed the importance of specific mechanisms that enable certain types of patterns to emerge, but these mechanisms are often difficult to identify in natural systems. Therefore, we have started using synthetic biology to ask whether specific mechanisms of pattern formation can be engineered into a simple cellular background. In this talk, I will show several examples of emergent spatial patterning that results from the insertion of synthetic signalling pathways and transcriptional logic into E. coli. In all cases, we use computational modelling to initially design circuits with a desired outcome, and improve the selection of biological components (DNA sub-sequences) that achieve this outcome according to a quantifiable measure. In the specific case of Turing patterns, we have yet to produce a functional system in vivo, but I will describe new analytical tools that are helping to guide the design of synthetic circuits that can produce a Turing instability.

We aim to establish and experimentally test mathematical models of embryogenesis. While the foundation of this research is based on models of isolated developmental events, the ultimate challenge is to formulate and understand dynamical systems encompassing multiple stages of development and multiple levels of regulation. These range from specific chemical reactions in single cells to coordinated dynamics of multiple cells during morphogenesis. Examples of our dynamical systems models of embryogenesis – from the events in the Drosophila egg to the early stages of gastrulation – will be presented. Each of these will demonstrate what had been learned from model analysis and model-driven experiments, and what further research directions are guided by these models.

In this talk I shall describe recent work inspired by problems in cell biology, namely how the dynamics of small G-proteins underlies polarity formation. Their dynamics is such that their active membrane bound form diffuses more slowly. Hence you might expect Turing patterns. Yet how do cells form backs and fronts or single isolated patches. In understanding these questions we shall show that the key is to identify the parameter region where Turing bifurcations are sub-critical. What emerges is a unified 2-parameter bifurcation diagram containing pinned fronts, localised spots, localised patterns. This diagram appears in many canonical models such as Schnakenberg and Brusselator, as well as biologically more realistic systems. A link is also found between theories of semi-string interaction asymptotics and so-called homoclinic snaking. I will close with some remarks about relevance to root hair formation and to the importance of subcriticality in biology. 

We find a new duality for form factors of lightlike Wilson loops in planar N=4 super-Yang-Mills theory. The duality maps a form factor involving an n-sided lightlike polygonal super-Wilson loop together with m external on-shell states, to the same type of object but with the edges of the Wilson loop and the external states swapping roles. This relation can essentially be seen graphically in Lorentz harmonic chiral (LHC) superspace where it is equivalent to planar graph duality. However there are some crucial subtleties with the cancellation of spurious poles due to the gauge fixing. They are resolved by finding the correct formulation of the Wilson loop and by careful analytic continuation from Minkowski to Euclidean space. We illustrate all of these subtleties explicitly in the simplest non-trivial NMHV-like case.

In existing techniques for model-based derivative-free optimisation, the computational cost of constructing local models and Lagrange polynomials can be high. As a result, these algorithms are not as suitable for large-scale problems as derivative-based methods. In this talk, I will introduce a derivative-free method based on exploration of random subspaces, suitable for nonlinear least-squares problems. This method has a substantially reduced computational cost (in terms of linear algebra), while still making progress using few objective evaluations.

I will talk about supersymmetric index of 4d N=1 supersymmetric theories on S^1xM_3 which counts supersymmetric states.  
In the first part, I will discuss a general formula to describe an asymptotic behaviour of the index in the limit of shrinking S^1
which we refer to as 4d (refined) supersymmetric Cardy formula. This part is based on arXiv:1611.00380 with Lorenzo Di Pietro.
In the second part, I will apply this formula to black hole physics. I will mainly focus on superconformal index of SU(N) N=4 super Yang-Mills theory
which is expected to be dual to type IIB superstring theory on AdS_5 x S^5. We will see that the index in the large-N limit reproduces the Bekenstein-Hawking entropy
of rotating charged BPS black hole on the gravity side. Our result for finite N makes a prediction to the black hole entropy with full quantum corrections.
The second part is based on arXiv:1901.08091.