Past Mathematical Biology and Ecology Seminar

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.

Actin filaments are polymers that interact with myosin motor
proteins and play important roles in cell motility, shape, and
development. Depending on its function, this dynamic network of
interacting proteins reshapes and organizes in a variety of structures,
including bundles, clusters, and contractile rings. Motivated by
observations from the reproductive system of the roundworm C. elegans,
we use an agent-based modeling framework to simulate interactions
between actin filaments and myosin motor proteins inside cells. We also
develop tools based on topological data analysis to understand
time-series data extracted from these filament network interactions. We
use these tools to compare the filament organization resulting from
myosin motors with different properties. We have also recently studied
how myosin motor regulation may regulate actin network architectures
during cell cycle progression. This work also raises questions about how
to assess the significance of topological features in common topological
summary visualizations.
 

Our society is witnessing an exponential growth of data being generated. Among the various data types being routinely collected, event logs are available in a wide variety of domains. Despite historical and structural digitalisation challenges, healthcare is an example where the analysis of event logs might bring a new revolution.

In this talk, I will present our recent efforts in analysing and exploring temporal event data sequences extracted from event logs. Our visual analytics approach is able to summarise and seamlessly explore large volumes of complex event data sequences. We are able to easily derive observations and findings that otherwise would have required significant investment of time and effort.  To facilitate the identification of findings, we use a hierarchical clustering approach to cluster sequences according to time and a novel visualisation environment.  To control the level of detail presented to the analyst, we use a hierarchical aggregation tree and an Align-Score-Simplify strategy based on an information score.   To show the benefits of this approach, I will present our results in three real world case studies: CUREd, Outpatient clinics and MIMIC-III. These will respectively cover the analysis of calls and responses of emergency services, the efficiency of operation of two outpatient clinics, and the evolution of patients with atrial fibrillation hospitalised in an acute and critical care unit. To finalise the talk, I will share our most recent work in the analysis of clinical events extracted from Electronic Health Records for the study of multimorbidity.

Natural killer (NK) cells are part of the innate immune system and are capable of killing diseased cells. As a result, NK cells are being used for adoptive cell therapies for cancer patients. The activation of NK cell stimulatory receptors leads to a cascade of intracellular phosphorylation reactions, which activates key signaling species that facilitate the secretion of cytolytic molecules required for cell killing. Strategies that maximize the activation of such intracellular species can increase the likelihood of NK cell killing upon contact with a cancer cell and thereby improve efficacy of NK cell-based therapies. However, NK cell exhaustion, a phenotype characterized by reduced effector functionality, can limit the NK cell’s capacity for cell lysis. Due to the complexity of intracellular signaling, it is difficult to deduce a priori which strategies can enhance species activation.  

To aid in the development of strategies to enhance NK cell activation and limit the NK cell exhaustion, we constructed a mechanistic model of the signaling pathways activated by stimulatory receptors in NK cells. We then extended the model to describe the dynamics of the cytolytic molecules granzyme B (GZMB) and perforin-1 (PRF1). We implemented an information-theoretic approach to perform a global sensitivity analysis and optimal control theory to investigate strategies to enhance intracellular signaling and maximize GZMB and PRF1 secretion. We recently expanded the modeling to investigate the role of NK cell heterogeneity on tumor cell killing. In total, we developed a theoretical framework that provides actionable insight into engineering robust NK cells for clinical applications.

The amazing results of DeepMind's AlphaFold2 in the last CASP experiment  caused a huge stir in both the AI and biology fields, and this was of 
course widely reported in the general media. The claim is that the  protein folding problem has finally been solved, but has it really? Not 
to spoil the ending, but of course not. In this talk I will not be  talking (much) about AlphaFold2 itself, but instead what inspiration we 
can take from it about future directions we might want to take in protein structure bioinformatics research using modern AI techniques. 
Along the way, I'll illustrate my thoughts with some recent and current  machine-learning-based projects from my own lab in the area of protein 
structure and folding.
 

The last years have seen an immense increase in high-throughput and high-resolution technologies for experimental observation as well as
high-performance techniques to simulate molecular systems at a microscopic level, resulting in vast and ever-increasing amounts of high-dimensional data.
However, experiments provide only a partial view of macromolecular processes and are limited in their temporal and spatial resolution. On the other hand,
atomistic simulations are still not able to sample the conformation space of large complexes, thus leaving significant gaps in our ability to study
molecular processes at a biologically relevant scale. We present our efforts to bridge these gaps, by exploiting the available data and using state-of-the-art
machine-learning methods to design optimal coarse models for complex macromolecular systems. We show that it is possible to define simplified
molecular models to reproduce the essential information contained both in microscopic simulation and experimental measurements.

Geometrical questions commonly arise in clinical practice: for example, what is the optimal shape for a particular medical device? or what shapes of anatomical structures are indicative of pathological events? In this talk we explore two disparate clinical applications of geometrical underpinning: (A) how to design the optimal device for kidney stone removal surgery? and (B) what blood vessel shapes are associated with biomechanical failure? (A) Flexible ureteroscopy is a minimally invasive treatment for the removal of kidney stones by irrigating dust-like stone fragments with a saline solution. Finding the optimal ureteroscope tip shape for efficient flushing of stone fragments is a pertinent but complex question. We represent the renal pelvis (the main hollow cavity within the kidney) as a 2D cavity and employ adjoint-based shape optimisation to identify tip geometries that shrink the size of recirculation zones thereby reducing stone washout times. (B) The aorta is the largest blood vessel in the body, with an archetypal arched “candy-cane” shape and is responsible for transporting blood from the heart to the rest of the body. Aortic dissection, in which the inner layer of the aorta tears, can lead to frank rupture and is often rapidly fatal. Accurate clinical assessment of dissection risk from a CT scan of a patient’s thorax is paramount to patient survival. We apply statistical shape analysis, coupled with hemodynamic simulations, to identify pathological shape features of the aortic arch and to elucidate mechanistic underpinnings of aortic dissection.

The circadian clock generates ~24h rhythms everyday via a transcriptional-translational negative feedback loop. Although this involves the daily entry of repressor molecules into the nucleus after random diffusion through a crowded cytoplasm, the period remains extremely consistent. In this talk, I will describe how we identified a key molecular mechanism for such robustness of the circadian clock against spatio-temporal noise by analyzing spatio-temporal timeseries data of clock molecules. Furthermore, I will illustrate a systemic modeling approach that can identify hidden molecular interactions from oscillatory timeseries with an example of a circadian clock and tumorigenesis system.  Finally, I will talk about a fundamental question underlying the model-based time-series analysis: “Can we always fit a model to given timeseries data as long as the number of parameters is large?”. That is, is Von Neumann's quote “With four parameters I can fit an elephant, and with five I can make him wiggle his trunk” true?

There has been a surge of interest in machine learning in the past few years, and deep learning techniques are more and more integrated into
the way we do quantitative science. A particularly exciting case for deep learning is molecular physics, where some of the "superpowers" of
machine learning can make a real difference in addressing hard and fundamental computational problems - on the other hand the rigorous
physical footing of these problems guides us in how to pose the learning problem and making the design decisions for the learning architecture.
In this lecture I will review some of our recent contributions in marrying deep learning with statistical mechanics, rare-event sampling
and quantum mechanics.

We propose a mathematical model that unifies the psychiatric concepts of drug-induced incentive salience (IST), reward prediction error

(RPE) and opponent process theory (OPT) to describe the emergence of addiction within substance abuse. The biphasic reward response (initially

positive, then negative) of the OPT is activated by a drug-induced dopamine release, and evolves according to neuro-adaptative brain

processes.  Successive drug intakes enhance the negative component of the reward response, which the user compensates for by increasing the

drug dose.  Further neuroadaptive processes ensue, creating a positive feedback between physiological changes and user-controlled drug

intake. Our drug response model can give rise to qualitatively different pathways for an initially naive user to become fully addicted.  The

path to addiction is represented by trajectories in parameter space that depend on the RPE, drug intake, and neuroadaptive changes.

We will discuss how our model can be used to guide detoxification protocols using auxiliary substances such as methadone, to mitigate withdrawal symptoms.

If this is useful here are my co-authors:
Davide Maestrini, Tom Chou, Maria R. D'Orsogna

The talk will discuss the use of mathematical models for understanding targeted cancer therapies. One area of focus is the treatment of chronic lymphocytic leukemia with tyrosine kinase inhibitors. I will explore how mathematical approaches have helped elucidate the mechanism of action of the targeted drug ibrutinib, and will discuss how evolutionary models, based on patient-specific parameters, can make individualized predictions about treatment outcomes. Another focus of the talk is the use of oncolytic viruses to kill cancer cells and drive cancers into remission. These are viruses that specifically infect cancer cells and spread throughout tumors. I will discuss mathematical models applied to experimental data that analyze virus spread in a spatially structured setting, concentrating on the interactions of the virus with innate immune mechanisms that determine the outcome of virus spread.  

Human life expectancy has been increasing steadily over the last century but this has resulted in an increasing incidence of age-related chronic diseases. Over 60% of people over the age of 65 will suffer from more than one disease at the same time (multimorbidity) and 25-50% of those over 80 years old develop frailty, defined as an accumulation of deficits and loss of reserve. Multimorbidity and frailty have complex medical needs and are strongly associated with disability and hospitalization. However, current treatments are suboptimal with problems of polypharmacy due to the fact that each disease is treated individually. Geroprotectors target fundamental mechanisms of ageing common to multiple age-related diseases and shows promise in delaying the onset of multimorbidity and frailty in animal models. However, their clinical testing in patients has been challenging due to the high level of complexity in the mode of action of geroprotectors and in the way multimorbidity and frailty develop.

 The talk will give an overview of these problems and make the case for the use of AI approaches to solve some of those complex issues with a view of designing appropriate clinical trials with geroprotectors to prevent age-related multimorbidity and frailty and extend healthspan.

Our current approach to cancer treatment has been largely driven by finding molecular targets, those patients fortunate enough to have a targetable mutation will receive a fixed treatment schedule designed to deliver the maximum tolerated dose (MTD). These therapies generally achieve impressive short-term responses, that unfortunately give way to treatment resistance and tumor relapse. The importance of evolution during both tumor progression, metastasis and treatment response is becoming more widely accepted. However, MTD treatment strategies continue to dominate the precision oncology landscape and ignore the fact that treatments drive the evolution of resistance. Here we present an integrated theoretical, experimental and clinical approach to develop treatment strategies that specifically embrace cancer evolution. We will consider the importance of using treatment response as a critical driver of subsequent treatment decisions, rather than fixed strategies that ignore it. Through the integrated application of drug treatments and drug holidays we will illustrate that, evolutionary therapy can drive either tumor control or extinction. Our results strongly indicate that the future of precision medicine shouldn’t be in the development of new drugs but rather in the smarter evolutionary application of preexisting ones.

Bacteria use intercellular signalling, or quorum sensing (QS), to share information and respond collectively to aspects of their surroundings. The autoinducers that carry this information are exposed to the external environment. Consequently, they are affected by factors such as removal through fluid flow, a ubiquitous feature of bacterial habitats ranging from the gut and lungs to lakes and oceans.

We develop and apply a general theory that identifies and quantifies the conditions required for QS activation in fluid flow by systematically linking cell- and population-level genetic and physical processes. We predict that cell-level positive feedback promotes a robust collective response, and can act as a low-pass filter at the population level in oscillatory flow, responding only to changes over slow enough timescales. Moreover, we use our model to hypothesize how bacterial populations can discern between increases in cell density and decreases in flow rate.

A major challenge in the study of biological systems is that of model discovery: turning data into reduced order models that are not just predictive, but provide insight into the nature of the underlying system that generated the data. We introduce a number of data-driven strategies for discovering nonlinear multiscale dynamical systems and their embeddings from data.  Such data-driven methods can be used in the biological sciences where rich data streams are affording new possibilities for the understanding and characterization of complex, networked systems.  In neuroscience, for instance, the integration of these various concepts (reduced-order modeling, equation-free, machine learning, sparsity, networks, multi-scale physics and adaptive control) are critical to formulating successful modeling strategies that perhaps can say something meaningful about experiments.   These methods will be demonstrated on a number of neural systems.  I will also highlight how such methods can be used to quantify cognitive and decision-making deficits arising from neurodegenerative diseases and/or traumatic brain injuries (concussions).

Genotype-phenotype associations can be results of direct effects, genetic nurturing effects and population stratification confounding (The nature of nurture: Effects of parental genotypes, Science, 2018, Deconstructing the sources of genotype-phenotype associations in humans, Science, 2019). Genotypes from parents and siblings of the proband can be used to statistically disentangle these effects. To maximize power, a comprehensive framework for utilizing various combinations of parents’ and siblings’ genotypes is introduced. Central to the approach is mendelian imputation, a method that utilizes identity by descent (IBD) information to non-linearly impute genotypes into untyped relatives using genotypes of typed individuals. Applying the method to UK Biobank probands with at least one parent or sibling genotyped, for an educational attainment (EA) polygenic score that has a R² of 5.7% with EA, its predictive power based on direct genetic effect alone is demonstrated to be only about 1.4%. For women, the EA polygenic score has a bigger estimated direct effect on age-at-first-birth than EA itself.

The puzzle-shaped cells that appear in the epidermis of many plants are a striking example of a complex cell shape. Since shape in an organism is often thought to be closely related to its function, it suggests that these unusual shapes must have some functional benefit to the plant. We 
propose that the creation of these complex shapes is an effective strategy to reduce mechanical stress in the cell wall. Although the 
formation of these shapes requires highly anisotropic and non-uniform growth at the sub-cellular level, it appears to be triggered by 
isotropic growth at the organ level. Analysis of cell shape over multiple species is consistent with the idea that the puzzle is in 
response to a developmental constraint, and that the mechanism is like to be conserved among higher plants.

 “In this talk, I shall present the past research track passing through quantum mechanical studies of small molecules to biomolecules, to proteome-wide big data analyses and computational genomics. Next, the ongoing research in our group will be presented that builds upon the expertise on different levels of information processing in life (genome, transcriptome, proteins, small molecules), to develop self-consistent “first principles” models in biology with a wide spectrum of usage. The immediate benefits and the targeted processes will be described covering different layers of the central dogma of biology, multigenic diseases and disease driver/passenger mutation predictions."

Signalling pathways can be modelled as a biochemical reaction network. When the kinetics are to follow mass-action kinetics, the resulting
mathematical model is a polynomial dynamical system. I will overview approaches to analyse these models with steady-state data using
computational algebraic geometry and statistics. Then I will present how to analyse such models with time-course data using differential
algebra and geometry for model identifiability. Finally, I will present how topological data analysis can be help distinguish models
and data.

While the pathological mechanisms in COVID-19 illness are still poorly understood, it is increasingly clear that high levels of pro-inflammatory mediators play a major role in clinical deterioration in patients with severe disease. Current evidence points to a hyperinflammatory state as the driver of respiratory compromise in severe COVID-19 disease, with a clinical trajectory resembling acute respiratory distress syndrome (ARDS) but how this “runaway train” inflammatory response emergences and is maintained is not known. In this talk, we present the first mathematical model of lung hyperinflammation due to SARS- CoV-2 infection. This model is based on a network of purported mechanistic and physiological pathways linking together five distinct biochemical species involved in the inflammatory response. Simulations of our model give rise to distinct qualitative classes of COVID-19 patients: (i) individuals who naturally clear the virus, (ii) asymptomatic carriers and (iii–v) individuals who develop a case of mild, moderate, or severe illness. These findings, supported by a comprehensive sensitivity analysis, points to potential therapeutic interventions to prevent the emergence of hyperinflammation. Specifically, we suggest that early intervention with a locally-acting anti-inflammatory agent (such as inhaled corticosteroids) may effectively blockade the pathological hyperinflammatory reaction as it emerges.

Influenza viruses infect millions of individuals each year and cause a significant amount of morbidity and mortality. Understanding how the virus spreads within the lung, how efficacious host immune control is, and how each influences acute lung injury and disease severity is critical to combat the infection. We used an integrative model-experiment exchange to establish the dynamical connections between viral loads, infected cells, CD8+ T cells, lung injury, and disease severity. Our model predicts that infection resolution is sensitive to CD8+ T cell expansion, that there is a critical T cell magnitude needed for efficient resolution, and that the rate of T cell-mediated clearance is dependent on infected cell density. 
We validated the model through a series of experiments, including CD8 depletion and whole lung histomorphometry. This showed that the infected area of the lung matches the model-predicted infected cell dynamics, and that the resolved area of the lung parallels the relative CD8 dynamics. Additional analysis revealed a nonlinear relation between disease severity, inflammation, and lung injury. These novel links between important host-pathogen kinetics and pathology enhance our ability to forecast disease progression.

Multi-modal data sets are growing rapidly in single cell genomics, as well as other fields in science and engineering. We introduce MultiMAP, an approach for dimensionality reduction and integration of multiple datasets. MultiMAP embeds multiple datasets into a shared space so as to preserve both the manifold structure of each dataset independently, in addition to the manifold structure in shared feature spaces. MultiMAP is based on the rich mathematical foundation of UMAP, generalizing it to the setting of more than one data manifold. MultiMAP can be used for visualization of multiple datasets as well as an integration approach that enables subsequent joint analyses. Compared to other integration for single cell data, MultiMAP is not restricted to a linear transformation, is extremely fast, and is able to leverage features that may not be present in all datasets. We apply MultiMAP to the integration of a variety of single-cell transcriptomics, chromatin accessibility, methylation, and spatial data, and show that it outperforms current approaches in run time, label transfer, and label consistency. On a newly generated single cell ATAC-seq and RNA-seq dataset of the human thymus, we use MultiMAP to integrate cells across pseudotime. This enables the study of chromatin accessibility and TF binding over the course of T cell differentiation.

 Inherent fluctuations may play an important role in biological and chemical systems when the copy number of some chemical species is small. This talk will present the recent work on the stochastic modeling of reaction-diffusion processes in biochemical systems. First, I will introduce several stochastic models, which describe system features at different scales of interest. Then, model reduction and coarse-graining methods will be discussed to reduce model complexity. Next, I will show multiscale algorithms for stochastic simulation of reaction-diffusion processes that couple different modeling schemes for better efficiency of the simulation. The algorithms apply to the systems whose domain is partitioned into two regions with a few molecules and a large number of molecules.

Femoral neck response to physiological loading during level walking can be better understood, if personalized muscle and bone anatomy is considered. Finite element (FE) models of in vivo cadaveric bones combined with gait data from body-matched volunteers were used in the earlier studies, which could introduce errors in the results. The aim of the current study is to report the first fully personalized multiscale model to investigate the strains predicted at the femoral neck during a full gait cycle. CT-based Finite element models (CT/FE) of the right femur were developed following a validated framework. Muscle forces estimated by the musculoskeletal model were applied to the CT/FE model. For most of the cases, two overall peaks were predicted around 15% and 50% of the gait. Maximum strains were predicted at the superior neck region in the model. Anatomical muscle variations seem to affect femur response leading to considerable variations among individuals, both in term of the strains level and the trend at the femoral neck.
 

Pattern formation emerges during development from the interplay between gene regulatory networks (GRNs) acting at the single cell level and cell movements driving tissue level morphogenetic changes. As a result, the timing of cell specification and the dynamics of morphogenesis must be tightly cross-regulated. In the developing zebrafish, mesoderm progenitors will spend varying amounts of time (from 5 to 10hrs) in the tailbud before entering the pre-somitic mesoderm (PSM) and initiating a stereotypical transcriptional trajectory towards a mesodermal fate. In contrast, when dissociated and placed in vitro, these progenitors differentiate synchronously in around 5 hours. We have used a data-driven mathematical modelling approach to reverse-engineer a GRN that is able to tune the timing of mesodermal differentiation as progenitors leave the tailbud’s signalling environment, which also explains our in vitro observations. This GRN recapitulates pattern formation at the tissue level when modelled on cell tracks obtained from live-imaging a developing PSM. Our “live-modelling” framework also allows us to simulate how perturbations to the GRN affect the emergence of pattern in zebrafish mutants. We are now extending this analysis to cichlid fishes in order to explore the regulation of developmental time in evolution.

There is a need for a new kind of maths course, to be taught, not to mathematics students, but to biologists with little or no maths background. There have been many recent calls for an upgrade to the mathematical background of biologists: undergraduate biology students need to understand the role of modeling and dynamics in understanding ecological systems, evolutionary dynamics, neuroscience, physiology, epidemiology, and the modeling that underlies the concept of climate change. They also need to understand the importance of feedback, both positive and negative, in creating dynamical systems in biology.

 Such a course is possible. The most important foundational development was the 20^th century replacement of the vague and unhelpful concept of a differential equation by the rigorous geometric concept of a vector field, a function from a multidimensional state space to its tangent space, assigning “change vectors” to every point in state space. This twentieth-century concept is not just more rigorous, but in fact makes for superior pedagogy. We also discuss the key nonlinear behaviors that biological systems display, such as switch-like behavior, robust oscillations and even chaotic behavior.

 This talk will outline such a course. It would have a significant effect on the conduct of biological research and teaching, and bring the usefulness of mathematical modeling to a wide audience.

During development, cells take on specific fates to properly build tissues and organs. These cell fates are regulated by short and long range signalling mechanisms, as well as feedback on gene expression and protein activity. Despite the high conservation of these signalling pathways, we often see different cell fate outcomes in similar tissues or related species in response to similar perturbations. How these short and long range signals work to control patterning during development, and how the same network can lead to species specific responses to perturbations, is not yet understood. Exploiting the high conservation of developmental pathways, we theoretically and experimentally explore mechanisms of cell fate patterning during development of the egg laying structure (vulva) in nematode worms. We developed differential equation models of the main signalling networks (EGF/Ras, Notch and Wnt) responsible for vulval cell fate specification, and validated them using experimental data. A complex, biologically based model identified key network components for wild type patterning, and relationships that render the network more sensitive to perturbations. Analysis of a simplified model indicated that short and long range signalling play complementary roles in developmental patterning. The rich data sets produced by these models form the basis for further analysis and increase our understanding of cell fate regulation in development.

Sudden cardiac death is the most feared complication of Hypertrophic Cardiomyopathy. This inherited heart muscle disease affects 1 in 500 people. But we are poor at identifying those who really need a potentially life-saving implantable cardioverter-defibrillator. Measuring the abnormalities believed to trigger fatal ventricular arrhythmias could guide treatment. Myocardial disarray is the hallmark feature of patients who die suddenly but is currently a post mortem finding. Through recent advances, the microstructure of the myocardium can now be examined by mapping the preferential diffusion of water molecules along fibres using Diffusion Tensor Cardiac Magnetic Resonance imaging. Fractional anisotropy calculated from the diffusion tensor, quantifies the directionality of diffusion.  Here, we show that fractional anisotropy demonstrates normal myocardial architecture and provides a novel imaging biomarker of the underlying substrate in hypertrophic cardiomyopathy which relates to ventricular arrhythmia.

Tensors are higher dimensional analogues of matrices, used to record data with multiple changing variables. Interpreting tensor data requires finding multi-linear stucture that depends on the application or context. I will describe a tensor-based clustering method for multi-dimensional data. The multi-linear structure is encoded as algebraic constraints in a linear program. I apply the method to a collection of experiments measuring the response of genetically diverse breast cancer cell lines to an array of ligands. In the second part of the talk, I will discuss low-rank decompositions of tensors that arise in statistics, focusing on two graphical models with hidden variables. I describe how the implicit semi-algebraic description of the statistical models can be used to obtain a closed form expression for the maximum likelihood estimate.

The pRED Clinical Pharmacology Disease Modelling Group (CPDMG) aims to better understand the biological basis of inter-patient variability of clinical response to drugs.  Improved understanding of how our drugs drive clinical responses informs which combination dosing regimens (“right drugs”) specific patient populations (“right patients”) are most likely to benefit from. Drug evoked responses are driven by drug-molecular-target interactions that perturb target functions. These direct, "proximal effects" (typically activation and/or inhibition of protein function) propagate across the biological processes these targets participate in via “distal effects” to drive clinical responses. Clinical Systems Pharmacology approaches are used by CPDMG to predict the mechanisms by which drug combinations evoke observed clinical responses. Over the last 5 years, CPDMG has successfully applied these approaches to inform key decisions across clinical development programs. Implementation of these approaches requires: (i) integration of prior relevant biological/clinical knowledge with large clinical and “omics” datasets; (ii) application of supervised machine learning (specifically, Artificial Neural Networks (ANNs)) to transform this knowledge/data into actionable, clinically relevant, mechanistic insights.  In this presentation, key features of these approaches will be discussed by way of clinical examples.  This will provide a framework for outlining the current limitations of these approaches and how we plan to address them in the future.

Single cell RNA-Seq data is challenging to analyse due to problems like dropout and cell type identification. We present a novel clustering 
approach that applies mixture models to learn interpretable clusters from RNA-Seq data, and demonstrate how it can be applied to publicly 
available scRNA-Seq data from the mouse brain. Having inferred groupings of the cells, we can then attempt to learn networks from the data. These 
approaches are widely applicable to single cell RNA-Seq datasets where  there is a need to identify and characterise sub-populations of cells.

Globally, almost 38 million people are living with HIV.  HPTN 071 (PopART) is the largest HIV prevention trial to date, taking place in 21 communities in Zambia and South Africa with a combined population of more than 1 million people.  As part of the trial an individual-based mathematical model was developed to help in planning the trial, to help interpret the results of the trial, and to make projections both into the future and to areas where the trial did not take place. In this talk I will outline the individual-based mathematical model used in the trial, the inference framework, and will discuss examples of how the results from the model have been used to help inform policy decisions.  

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.

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.