Past Mathematical Biology and Ecology Seminar

Competition between peptides for binding and presentation by MHC class I molecules decides the immune response to foreign or tumor antigens. Many previous studies have attempted to classify the immunogenicity of a peptide using machine learning algorithms to predict the affinity, or half-life, of the peptide binding to MHC. However immunopeptidome analyses have shown a poor correlation between sequence based predictions and the abundance on the cell surface of the experimentally identified peptides. Such metrics are, for instance, only comparable when the abundance of competing peptides can be accurately quantified. We have developed a model for predicting the relative presentation of competing peptides that takes into account off-rate, source protein abundance and turnover and cofactor-assisted MHC assembly with peptides. This model is mechanism based so that it can accommodate complex biology phenomena such as inflammation, up or downregulation of peptide loading complex chaperones, appearance of a mutanome. We have used aspects of the model to drive an investigation of the precise molecular mechanism of peptide selection by MHC I and its associated intracellular cofactors.

PLEASE NOTE THAT THIS SEMINAR IS CANCELLED DUE TO UNFORSEEN CIRCUMSTANCES.

Despite their tiny size, microorganisms play a huge role in many biological, medical, and engineering phenomena. For example, massive plankton blooms are an integral part of the oceanic ecosystem. Algal cells incorporate carbon dioxide, which affects global warming. In industry, microorganisms are used in bioreactors to produce food and medicines and to treat sewage. The human body hosts hundreds of microorganism species, and the number of microorganisms in the human body is roughly double the number of cells in the body. In the intestine, approximately 1 kg of enterobacteria form a unique ecosystem, called the gut flora, which plays important roles in digestion and in relation to infection. Because of the considerable influence that microorganisms have on human life, the study of their behavior and function is important.

Recent research has demonstrated the importance of biomechanics in understanding the behavior and functions of microorganisms. For example, red tides can be induced by the interplay between the background flow and swimming cells. A dense suspension of bacteria can generate a coherent structure, which strongly enhances mass transport in a suspension. These phenomena show that the physical environments around cells alter their behavior and biological functions. Such a biomechanical understanding is still lacking in microbiology, and we believe that biomechanics can provide new perspectives on future microbiology.

In this talk, we first introduce some of our studies of the behavior of individual swimming microorganisms near surfaces. We show that hydrodynamic forces can trap cells at liquid–air or liquid–solid interfaces. We then introduce interactions between a pair of swimming microorganisms, because a two-body interaction is the simplest many-body interaction. We show that our mathematical models can describe the interactions between two nearby swimming microorganisms. Collective motions formed by a group of swimming microorganisms are also introduced. We show that some collective motions of microorganisms, such as coherent structures of bacterial suspensions, can be understood in terms of fluid mechanics. We then discuss how cellular-level phenomena can change the rheological and diffusion properties of a suspension. The macroscopic properties of a suspension are strongly affected by mesoscale flow structures, which in turn are strongly affected by the interactions between cells. Hence, a bottom-up strategy, i.e., from a cellular level to a continuum suspension level, represents a natural approach to the study of a suspension of swimming microorganisms. Finally, we discuss whether our understanding of biological functions can be strengthened by the application of biomechanics, and how we can contribute to the future of microbiology.

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

Switch-like and oscillatory dynamical systems are widely observed in biology. We investigate the simplest biological switch that is composed of a single molecule that can be autocatalytically converted between two opposing activity forms. We test how this simple network can keep its switching behaviour under perturbations in the system. We show that this molecule can work as a robust bistable system, even for alterations in the reactions that drive the switching between various conformations. We propose that this single molecule system could work as a primitive biological sensor and show by steady state analysis of a mathematical model of the system that it could switch between possible states for changes in environmental signals. Particularly, we show that a single molecule phosphorylation-dephosphorylation switch could work as a nucleotide or energy sensor. We also notice that a given set of reductions in the reaction network can lead to the emergence of oscillatory behaviour. We propose that evolution could have converted this switch into a single molecule oscillator, which could have been used as a primitive timekeeper. I will discuss how the structure of the simplest known circadian clock regulatory system, found in cyanobacteria, resembles the proposed single molecule oscillator. Besides, we speculate if such minimal systems could have existed in an RNA world. I will also present how the regulatory network of the cell cycle could have emerged from this system and what are the consequences of this possible evolution from a single antagonistic kinase-phosphatase network.

Despite progress in understanding many aspects of malignancy, resistance to therapy is still a frequent occurrence. Recognised causes of this resistance include 1) intra-tumour heterogeneity resulting in selection of resistant clones, 2) redundancy and adaptability of gene signalling networks, and 3) a dynamic and protective microenvironment. I will discuss how these aspects influence each other, and then focus on the tumour microenvironment.

The tumour microenvironment comprises a heterogeneous, dynamic and highly interactive system of cancer and stromal cells. One of the key physiological and micro-environmental differences between tumour and normal tissues is the presence of hypoxia, which not only alters cell metabolism but also affects DNA damage repair and induces genomic instability. Moreover, emerging evidence is uncovering the potential role of multiple stroma cell types in protecting the tumour primary niche.

I will discuss our work on in silico cancer models, which is using genomic data from large clinical cohorts of individuals to provide new insights into the role of the tumour microenvironment in cancer progression and response to treatment. I will then discuss how this information can help to improve patient stratification and develop novel therapeutic strategies.

Computer vision approaches have made huge advances with deep learning research. These algorithms can be employed as a basis for phenotyping of biological traits from imaging modalities. This can be employed, for example, in the context of facial photographs of rare diseases as a means of aiding diagnostic pathways, or as means to large scale phenotyping in histological imaging. With any data set, inherent biases and problems in the data available for training can have a detrimental impact on your models. I will describe some examples of such data set problems and outline how to build models that are not confounded – despite biases in the training data. 

Atherosclerosis is a manifestation of cardiovascular disease consisting of the buildup of inflamed arterial plaques. Because most heart attacks are caused by the rupture of unstable "vulnerable" plaque, the characterization of plaques and their vulnerability remains an outstanding problem in medicine.

Morphoelasticity is a mathematical framework commonly employed to describe tissue growth.

Its central premise is the decomposition of the deformation gradient into the product of an elastic tensor and a growth tensor.

In this talk, I will present some recent efforts to simulate intimal thickening -- the precursor to atherosclerosis -- using morphoelasticity theory.

The arterial wall is composed of three layers: the intima, media and adventitia. 

The intima is allowed to grow isotropically while the area of the media and adventitia is approximately conserved. 

All three layers are modeled as anisotropic hyperelastic materials, reinforced by collagen fibers.

We explore idealized axisymmetric arteries as well as more general geometries that are solved using the finite element method.

Results are discussed in the context of balloon-injury experiments on animals and Glagovian remodeling in humans.

Transdifferentiation, the process of converting from one cell type to another without going through a pluripotent state, has great promise for regenerative medicine. The identification of key transcription factors for reprogramming is limited by the cost of exhaustive experimental testing of plausible sets of factors, an approach that is inefficient and unscalable. We developed a predictive system (Mogrify) that combines gene expression data with regulatory network information to predict the reprogramming factors necessary to induce cell conversion. We have applied Mogrify to 173 human cell types and 134 tissues, defining an atlas of cellular reprogramming. Mogrify correctly predicts the transcription factors used in known transdifferentiations. Furthermore, we validated several new transdifferentiations predicted by Mogrify, including both into and out of the same cell type (keratinocytes). We provide a practical and efficient mechanism for systematically implementing novel cell conversions, facilitating the generalization of reprogramming of human cells. Predictions are made available via http://mogrify.net to help rapidly further the field of cell conversion.

Ultrasound (US) imaging is one of the first steps in a continuum of pregnancy care. During the fetal period, the brain undergoes dramatic structural changes, many of which are informative of healthy maturation. The resolution of modern US machines enables us to observe and measure brain structures, as well as detect cerebral abnormalities in fetuses from as early as 18 weeks. Recent breakthroughs in machine learning techniques for image analysis introduce opportunities to  develop bespoke methods to track spatial and temporal patterns of fetal brain development. My work focuses on the design of appropriate data-driven techniques to extract developmental information from standard clinical US images of the brain.

In this talk I will discuss how computational algebraic geometry and topology can be useful for studying questions arising in systems biology. In particular I will focus on the problem of comparing models and data through the lens of computational algebraic geometry and statistics. I will provide concrete examples of biological signalling systems that are better understood with the developed methods.

Please note that this will be held at Tsuzuki Lecture Theatre, St Annes College, Oxford.

Please note that you will need to register for this event via https://www.eventbrite.co.uk/e/qbiox-colloquium-trinity-term-2018-ticke…

Cancer causing mutations must become permanently fixed within tissues. 

Please note that this will be held at Tsuzuki Lecture Theatre, St Annes College, Oxford.

Please note that you will need to register for this event via https://www.eventbrite.co.uk/e/qbiox-colloquium-trinity-term-2018-ticke…

In this talk, I will review a number of interdisciplinary collaborations in which I have been involved over the years that have coupled mathematical
modelling with experimental studies to try to advance our understanding of processes in biology and medicine. Examples will include somatic evolution in
tumours, collective cell movement in epithelial sheets, cell invasion in neural crest, and pattern formation in slime mold. These are examples where
verbal reasoning models are misleading and insufficient, while mathematical models can enhance our intuition.

Please note that this will be held at Tsuzuki Lecture Theatre, St Annes College, Oxford.

Please note that you will need to register for this event via https://www.eventbrite.co.uk/e/qbiox-colloquium-trinity-term-2018-ticke…

ATP-sensitive potassium (KATP) channels are critical for coupling changes in blood glucose to insulin secretion. Gain-of-function mutations in KATP channels cause a rare inherited form of diabetes that manifest soon after birth (neonatal diabetes). This talk shows how understanding KATP channel function has enabled many neonatal diabetes patients to switch from insulin injections to sulphonylurea drugs that block KATP channel activity, with considerable improvement in their clinical condition and quality of life.   Using a mouse model of neonatal diabetes, we also found that as little as 2 weeks of diabetes led to dramatic changes in gene expression, protein levels and metabolite concentrations. This reduced glucose-stimulated ATP production and insulin release. It also caused substantial glycogen storage and β-cell apoptosis. This may help explain why older neonatal diabetes patients with find it more difficult to transfer to drug therapy, and why the drug dose decreases with time in many patients. It also suggests that altered metabolism may underlie both the progressive impairment of insulin secretion and reduced β-cell mass in type 2 diabetes.

I will discuss some properties of delay differential equations in which the delay is not prescribed a-priori but is determined from a threshold condition. Sometimes the delay depends on the solution of the differential equation and its history. A scenario giving rise to a threshold type delay is that larval insects sometimes experience halting or slowing down of development, known as diapause, perhaps as a consequence of intra-specific competition among larvae at higher densities. Threshold delays can result in population dynamical models having some unusual properties, for example, if the model has an Allee effect then diapause may cause extinction in some parameter regimes even where the initial population is high.

Please  note that this talk is only suitable for Mathematicians.