Abstract: Akshay Venkatesh and his coauthors (Galatius, Harris, Prasanna) have recently introduced a derived Hecke algebra and a derived Galois deformation ring acting on the homology of an arithmetic group, say with p-adic coefficients. These actions account for the presence of the same system of eigenvalues simultaneously in various degrees. They have also formulated a conjecture describing a finer action of a motivic group which should preserve the rational structure $H^i(\Gamma,\Q)$. In this lecture we focus in the setting of classical modular forms of weight one, where the same systems of eigenvalues appear both in degree 0 and 1 of coherent cohomology of a modular curve, and the motivic group referred to above is generated by a Stark unit. In joint work with Darmon, Harris and Venkatesh, we exploit the Theta correspondence and higher Eisenstein elements to prove the conjecture for dihedral forms.

The mechanisms underlying the initiation and perpetuation of cardiac arrhythmias are inherently multi-scale: whereas arrhythmias are intrinsically tissue-level phenomena, they have a significant dependence cellular electrophysiological factors. Spontaneous sub-cellular calcium release events (SCRE), such as calcium waves, are a exemplars of the multi-scale nature of cardiac arrhythmias: stochastic dynamics at the nanometre-scale can influence tissue excitation  patterns at the centimetre scale, as triggered action potentials may elicit focal excitations. This latter mechanism has been long proposed to underlie, in particular, the initiation of rapid arrhythmias such as tachycardia and fibrillation, yet systematic analysis of this mechanism has yet to be fully explored. Moreover, potential bi-directional coupling has been seldom explored even in concept.

A major challenge of dissecting the role and importance of SCRE in cardiac arrhythmias is that of simultaneously exploring sub-cellular and tissue function experimentally. Computational modelling provides a potential approach to perform such analysis, but requires new techniques to be employed to practically simulate sub-cellular stochastic events in tissue-scale models comprising thousands or millions of coupled cells.

This presentation will outline the novel techniques developed to achieve this aim, and explore preliminary studies investigating the mechanisms and importance of SCRE in tissue-scale arrhythmia: How do independent, small-scale sub-cellular events overcome electrotonic load and manifest as a focal excitation? How can SCRE focal (and non-focal) dynamics lead to re-entrant excitation? How does long-term re-entrant excitation interact with SCRE to perpetuate and degenerate arrhythmia?

Computational nucleic acid devices show great potential for enabling a broad range of biotechnology applications, including smart probes for molecular biology research, in vitro assembly of complex compounds, high-precision in vitro disease diagnosis and, ultimately, computational therapeutics inside living cells. This diversity of applications is supported by a range of implementation strategies, including nucleic acid strand displacement, localisation to substrates, and the use of enzymes with polymerase, nickase and exonuclease functionality. However, existing computational design tools are unable to account for these different strategies in a unified manner. This talk presents a programming language that allows a broad range of computational nucleic acid systems to be designed and analysed. We also demonstrate how similar approaches can be incorporated into a programming language for designing genetic devices that are inserted into cells to reprogram their behaviour. The language is used to characterise the genetic components for programming populations of cells that communicate and self-organise into spatial patterns. More generally, we anticipate that languages and software for programming molecular and genetic devices will accelerate the development of future biotechnology applications.

There is great interest in the molecular characterisation of intestinal metaplasia, such as Barrett’s esophagus (BE), to understand the basic biology of metaplastic development from a tissue of origin. BE is asymptomatic, so it is not generally known how long a patient has lived with this precursor of esophageal adenocarcinoma (EAC) when initially diagnosed in the clinic. We previously constructed a BE clock model using patient-specific methylation data to estimate BE onset times using Bayesian inference techniques, and thus obtain the biological age of BE tissue (Curtius et al. 2016). We find such epigenetic drift to be widely evident in BE tissue (Luebeck et al. 2017) and the corresponding tissue ages show large inter-individual heterogeneity in two patient populations.               

From a basic biological mechanism standpoint, it is not fully understood how the Barrett’s tissue first forms in the human esophagus because this process is never observed in vivo, yet such information is critical to inform biomarkers of risk based on temporal features (e.g., growth rates, tissue age) reflecting the evolution toward cancer. We analysed multi-region samples from 17 BE patients to

1) measure the spatial heterogeneity in biological tissue ages, and 2) use these ages to calibrate mathematical models (agent-based and continuum) of the mechanisms for formation of the segment itself. Most importantly, we found that tissue must be regenerated nearer to the stomach, perhaps driven by wound healing caused by exposure to reflux, implying a gastric tissue of origin for the lesions observed in BE. Combining bioinformatics and mechanistic modelling allowed us to infer evolutionary processes that cannot be clinically observed and we believe there is great translational promise to develop such hybrid methods to better understand multiscale cancer data.

References:

Curtius K, Wong C, Hazelton WD, Kaz AM, Chak A, et al. (2016) A Molecular Clock Infers Heterogeneous Tissue Age Among Patients with Barrett's Esophagus. PLoS Comput Biol 12(5): e1004919

Luebeck EG, Curtius K, Hazelton WD, Made S, Yu M, et al. (2017) Identification of a key role of epigenetic drift in Barrett’s esophagus and esophageal adenocarcinoma. J Clin Epigenet 9:113

Genome replication is a stochastic process whereby each cell exhibits different patterns of origin activation and replication fork movement.  Despite this heterogeneity, replication is a remarkably stable process that works quickly and correctly over hundreds of thousands of iterations. Existing methods for measuring replication dynamics largely focus on how a population of cells behave on average, which precludes the detection of low probability errors that may have occurred in individual cells.  These errors can have a severe impact on genome integrity, yet existing single-molecule methods, such as DNA combing, are too costly, low-throughput, and low-resolution to effectively detect them.  We have created a method that uses Oxford Nanopore sequencing to create high-throughput genome-wide maps of DNA replication dynamics in single molecules.  I will discuss the informatics approach that our software uses, our use of mathematical modelling to explain the patterns that we observe, and questions in DNA replication and genome stability that our method is uniquely positioned to answer.

In this work we will attempt, via virtual models, to interpret how structure and body positioning impact upon the outcomes of Multi-Breath-Washout tests. 

By extrapolating data from CT images, a virtual reduced dimensional airway/vascualr network will be constructed. Using this network both airway and blood flow profiles will be calculated. These profiles will then be used to model gas transport within the lungs. The models will allow us to investigate the role of airway restriction, body position during testing and washout gas choice have on MBW measures. 
 

In this talk I will show the nature, the properties and the features of the Pareto Optimality in a diverse set of phenomena modeled as complex networks.
I will present a composite design methodology for multi-objective modeling and optimization of complex networks.  The method is based on the synergy of different algorithms and computational techniques for the analysis and modeling of natural systems (e.g., metabolic pathways in prokaryotic and eukaryotic cells) and artificial systems (e.g., traffic networks, analog circuits and solar cells).

“Pareto Optimality in Multilayer Network Growth”
G. Nicosia et al, Phys. Rev. Lett., 2018