L3

Tensors are higher dimensional analogues of matrices; they are used to record data with multiple changing variables. Interpreting tensor data requires finding low rank structure, and the structure depends on the application or context. Often tensors of interest define semi-algebraic sets, given by polynomial equations and inequalities. I'll give a characterization of the set of tensors of real rank two, and answer questions about statistical models using probability tensors and semi-algebraic statistics. I will also describe work on learning a path from its three-dimensional signature tensor. This talk is based on joint work with Guido Montúfar, Max Pfeffer, and Bernd Sturmfels.

In biological cells, genomic DNA is complexed with proteins, forming so-called chromatin structure, and packed into the nucleus. Not only the nucleotide (A, T, G, C) sequence of DNA but also the 3D structure affects the genomic function. For example, certain regions of DNA are tightly packed with proteins (heterochromatin), which inhibits expression of genes coded there. The structure sometimes changes drastically depending on the state (e.g. cell cycle or developmental stage) of the cell. Hence, the structural dynamics of chromatin is now attracting attention in cell biology and medicine. However, it is difficult to experimentally observe the motion of the entire structure in detail. To combine and interpret data from different modes of observation (such as live imaging and electron micrograph) and predict the behavior, structural models of chromatin are needed. Although we can use molecular dynamics simulation at a microscopic level (~ kilo base-pairs) and for a short time (~ microseconds), we cannot reproduce long-term behavior of the entire nucleus. Mesoscopic models are wanted for that purpose, however hard to develop (there are fundamental difficulties).

In this seminar, I will introduce our recent theoretical/computational studies of chromatin structure, either microscopic (molecular dynamics of DNA or single nucleosomes) or abstract (polymer models and reaction-diffusion processes), toward development of such a mesoscopic model including local "states" of DNA and binding proteins.

References:

T. Kameda, A. Awazu, Y. Togashi, "Histone Tail Dynamics in Partially Disassembled Nucleosomes During Chromatin Remodeling", Front. Mol. Biosci., in press (2019).

Y. Togashi, "Modeling of Nanomachine/Micromachine Crowds: Interplay between the Internal State and Surroundings", J. Phys. Chem. B 123, 1481-1490 (2019).

E. Rolls, Y. Togashi, R. Erban, "Varying the Resolution of the Rouse Model on Temporal and Spatial Scales: Application to Multiscale Modelling of DNA Dynamics", Multiscale Model. Simul. 15, 1672-1693 (2017).

S. Shinkai, T. Nozaki, K. Maeshima, Y. Togashi, "Dynamic Nucleosome Movement Provides Structural Information of Topological Chromatin Domains in Living Human Cells", PLoS Comput. Biol. 12, e1005136 (2016).

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The Weak Gravity Conjecture holds that in any consistent theory of quantum gravity, gravity must be the weakest force. This simple proposition has surprisingly nontrivial physical consequences, which in the case of supersymmetric string/M-theory compactifications lead to nontrivial geometric consequences for Calabi-Yau manifolds. In this talk we will describe these conjectured geometric consequences in detail and show how they are realized in concrete examples, deriving new results about 5d supersymmetric black holes in the process.

In the first part of the talk, I will describe surface colonization strategies of the motile bacteria Pseudomonas aeruginosa. During early stages of biofilm formation, the majority of cells that land on a surface eventually detach. After a prolonged lag time, cells begin to cover the surface rapidly. Reversible attachments provide cells and their descendants with multigenerational memory of the surface that primes the planktonic population for colonization. Two different strains use different surface sensing machinery and show different colonization strategies. We use theoretical modelling to investigate how the hydrodynamics of type IV pili and flagella activity lead to increased detachment rates and show that the contribution from this hydrodynamic effect plays a role in the different colonization strategies observed in the two strains.

In the second part of the talk, I will show that when cells migrate through constricting pores, there is an increase in DNA damage and mutations. Experimental observations show that this breakage is not due to mechanical stress. I present an elastic-fluid model of the cell nucleus, coupled to kinetics of DNA breakage and repair proposing a mechanism by which nuclear deformation can lead to DNA damage. I show that segregation of soluble repair factors from the chromatin during migration leads to a decrease in the repair rate and an accumulation of damage that is sufficient to account for the extent of DNA damage observed experimentally.

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.