Forthcoming events in this series


Thu, 22 Feb 2024

12:00 - 13:00
L3

OCIAM-WCMB SEMINAR Structural identifiability analysis: An important tool in systems modelling

Professor Michael Chappell
(Dept of Mathematics University of Warwick)
Abstract

 

For many systems (certainly those in biology, medicine and pharmacology) the mathematical models that are generated invariably include state variables that cannot be directly measured and associated model parameters, many of which may be unknown, and which also cannot be measured.  For such systems there is also often limited access for inputs or perturbations. These limitations can cause immense problems when investigating the existence of hidden pathways or attempting to estimate unknown parameters and this can severely hinder model validation. It is therefore highly desirable to have a formal approach to determine what additional inputs and/or measurements are necessary in order to reduce or remove these limitations and permit the derivation of models that can be used for practical purposes with greater confidence.

Structural identifiability arises in the inverse problem of inferring from the known, or assumed, properties of a biomedical or biological system a suitable model structure and estimates for the corresponding rate constants and other model parameters.  Structural identifiability analysis considers the uniqueness of the unknown model parameters from the input-output structure corresponding to proposed experiments to collect data for parameter estimation (under an assumption of the availability of continuous, noise-free observations).  This is an important, but often overlooked, theoretical prerequisite to experiment design, system identification and parameter estimation, since estimates for unidentifiable parameters are effectively meaningless.  If parameter estimates are to be used to inform about intervention or inhibition strategies, or other critical decisions, then it is essential that the parameters be uniquely identifiable. 

Numerous techniques for performing a structural identifiability analysis on linear parametric models exist and this is a well-understood topic.  In comparison, there are relatively few techniques available for nonlinear systems (the Taylor series approach, similarity transformation-based approaches, differential algebra techniques and the more recent observable normal form approach and symmetries approaches) and significant (symbolic) computational problems can arise, even for relatively simple models in applying these techniques.

In this talk an introduction to structural identifiability analysis will be provided demonstrating the application of the techniques available to both linear and nonlinear parameterised systems and to models of (nonlinear mixed effects) population nature.

Fri, 16 Feb 2024

14:00 - 15:00
L3

Active surfaces in biology

Professor Alex Mietke
(Dept of Physics University of Oxford)
Abstract

The ability of biological matter to move and deform itself is facilitated by microscopic out-of-equilibrium processes that convert chemical energy into mechanical work. In many cases, this mechano-chemical activity takes place on effectively two-dimensional domains formed by, for example, multicellular structures like epithelial tissues or the outer surface of eukaryotic cells, the so-called actomyosin cortex.
We will show in the first part of the talk, that the large-scale dynamics and self-organisation of such structures can be captured by the theory of active fluids. Specifically, using a minimal model of active isotropic fluids, we can rationalize the emergence of asymmetric epithelial tissue flows in the flower beetle during early development, and explain cell rotations in the context of active chiral flows and left-right symmetry breaking that occurs as the model organism C. elegans sets up its body plan.
To develop a more general understanding of such processes, specifically the role of geometry, curvature and interactions with the environment, we introduce in the second part a theory of active fluid surfaces and discuss analytical and numerical tools to solve the corresponding momentum balance equations of curved and deforming surfaces. By considering mechanical interactions with the environment and the fully self-organized shape dynamics of active surfaces, these tools reveal novel mechanisms of symmetry breaking and pattern formation in active matter.

Mon, 12 Feb 2024

16:30 - 17:30
L5

OxPDE-WCMB seminar - From individual-based models to continuum descriptions: Modelling and analysis of interactions between different populations.

Dr Mariya Ptashnyk
(Dept of Maths Herriot Watt University)
Abstract

First we will show that the continuum counterpart of the discrete individual-based mechanical model that describes the dynamics of two contiguous cell populations is given by a free-boundary problem for the cell densities.  Then, in addition to interactions, we will consider the microscopic movement of cells and derive a fractional cross-diffusion system as the many-particle limit of a multi-species system of moderately interacting particles.

Fri, 02 Feb 2024

14:00 - 15:00
L3

Quantifying clonal selection and drift from a single bulk tissue sample

Dr Verena Korber
(Nuffield Division of Clinical Laboratory Sciences University of Oxford)
Abstract

Malignant transformation of somatic tissues is an evolutionary process, driven by selection for oncogenic mutations. Understanding when these mutations occur, and how fast mutant cell clones expand can improve diagnostic schemes and therapeutic intervention. However, clonal dynamics are not directly accessible in humans, posing a need for inference approaches to reconstruct the division history in normal and malignant cell clones, and to predict their future evolution. Inspired from population genetics theory, we develop mathematical models to detect imprints of clonal selection in the variant allele frequency distribution measured in a single tissue sample of a homeostatic tissue. I will present the theoretical basis of our approach and inference results for the tissue dynamics in physiological and clonal hematopoiesis, obtained from variant allele frequencies measured by snapshot bulk whole genome sequencing of human bone marrow samples.

Fri, 26 Jan 2024

14:00 - 15:00
L3

The hitchhiker's guide to complex models of intracellular signalling

Professor Fabian Frohli
(The Francis Crick Institute London)
Abstract

Unraveling the intricacies of intracellular signalling through predictive mathematical models holds great promise for advancing precision medicine and enhancing our foundational comprehension of biology. However, navigating the labyrinth of biological mechanisms governing signalling demands a delicate balance between a faithful description of the underlying biology and the practical utility of parsimonious models.
In this talk, I will present methods that enable training of large ordinary differential equation models of intracellular signalling and showcase application of such models to predict sensitivity to anti-cancer drugs. Through illustrative examples, I will demonstrate the application of these models in predicting sensitivity to anti-cancer drugs. A critical reflection on the construction of such models will be offered, exploring the perpetual question of complexity and how intricate these models should be.
Moreover, the talk will explore novel approaches that meld machine learning techniques with mathematical modelling. These approaches aim to harness the benefits of simplistic and unbiased phenomenological models while retaining the interpretability and biological fidelity inherent in mechanistic models.
 

Fri, 19 Jan 2024

14:00 - 15:00
L3

Modelling cells in one-dimension: diverse migration modes, emergent oscillations on junctions and multicellular "trains"

Professor Nir Gov
(Department of Chemical and Biological Physics Weizmann Institute of Science)
Abstract

Motile cells inside living tissues often encounter junctions, where their path branches into several alternative directions of migration. We present a theoretical model of cellular polarization for cells migrating along one-dimensional lines, exhibiting diverse migration modes. When arriving at a symmetric Y-junction and extending protrusions along the different paths that emanate from the junction. The model predicts the spontaneous emergence of deterministic oscillations between competing protrusions, whereby the cellular polarization and growth alternates between the competing protrusions. These predicted oscillations are found experimentally for two different cell types, noncancerous endothelial and cancerous glioma cells, migrating on patterned network of thin adhesive lanes with junctions. Finally we present an analysis of the migration modes of multicellular "trains" along one-dimensional tracks.

Fri, 01 Dec 2023

14:00 - 15:00
Virtual

Sequence models in biomedicine: from predicting disease progression to genome editing outcomes

Professor Michael Krauthammer
(Department of Quantitative Biomedicine University of Zurich)
Abstract

Sequential biomedical data is ubiquitous, from time-resolved data about patient encounters in the clinical realm to DNA sequences in the biological domain.  The talk will review our latest work in representation learning from longitudinal data, with a particular focus on finding optimal representations for complex and sparse healthcare data. We show how these representations are useful for comparing patient journeys and finding patients with similar health outcomes. We will also venture into the field of genome engineering, where we build models that work on DNA sequences for predicting editing outcomes for base and prime editors. 

Fri, 24 Nov 2023

14:00 - 15:00
L3

Using virtual clinical trials to improve our understanding of diseases

Professor Adrianne Jenner
(Queensland University of Technology)
Abstract

Mathematical and computational techniques can improve our understanding of diseases. In this talk, I’ll present ways in which data from cancer patients can be combined with mathematical modelling and used to improve cancer treatments.

Given the variability in individual responses to cancer treatments, agent-based modelling has been a useful technique for accurately capturing cellular behaviours that may lead to stochasticity in patient outcomes. Using a hybrid agent-based model and partial differential equation system, we developed a model for brain cancer (glioblastoma) growth informed by ex-vivo patient samples. Extending the model to capture patient treatment with an oncolytic virus rQNestin, we used our model to propose reasons for treatment failure, which was later confirmed with further patient samples. More recently, we extended this model to investigate the effectiveness of combination treatments (chemotherapy, virotherapy and immunotherapy) informed by individual patient imaging mass cytometry.

This talk hopes to provide examples of ways mathematical and computational modelling can be used to run “virtual” clinical trials with the goal of obtaining more effective treatments for diseases.  

Fri, 17 Nov 2023

14:00 - 15:00
Virtual

The generalist medical AI will see you now

Professor Pranav Rajpurkar
(Department of Biomedical Informatics Harvard Medical School Boston)
Abstract

Accurate interpretation of medical images is crucial for disease diagnosis and treatment, and AI has the potential to minimize errors, reduce delays, and improve accessibility. The focal point of this presentation lies in a grand ambition: the development of 'Generalist Medical AI' systems that can closely resemble doctors in their ability to reason through a wide range of medical tasks, incorporate multiple data modalities, and communicate in natural language. Starting with pioneering algorithms that have already demonstrated their potential in diagnosing diseases from chest X-rays or electrocardiograms, matching the proficiency of expert radiologists and cardiologists, I will delve into the core challenges and advancements in the field. The discussion will navigate towards the topic of label-efficient AI models: with a scarcity of meticulously annotated data in healthcare, the development of AI systems capable of learning effectively from limited labels has become a key concern. In this vein, I'll delve into how the innovative use of self-supervision and pre-training methods has led to algorithmic advancements that can perform high-level diagnostic tasks using significantly less annotated data. Additionally, I will talk about initiatives in data curation, human-AI collaboration, and the creation of open benchmarks to evaluate the generalizability of medical AI algorithms. In sum, this talk aims to deliver a comprehensive picture of the state of 'Generalist Medical AI,' the advancements made, the challenges faced, and the prospects lying ahead.

Fri, 10 Nov 2023

14:00 - 15:00
L3

Mathematical modelling identifies serum hepatitis B RNA as an informative biomarker of anti-viral treatment efficacy

Dr Tyler Cassidy
(School of Mathematics University of Leeds)
Abstract

Chronic hepatitis B virus (HBV) infection leads to liver damage that increases the risk of hepatocellular carcinoma and liver cirrhosis. Individuals with chronic HBV infection are often either treated with interferon alpha or nucleoside reverse transcriptase inhibitors (NTRL). While these NTRLs inhibit de novo DNA synthesis, they do not represent a functional cure for chronic HBV infection and so must be taken indefinitely. The resulting life-long treatment leads to an increased risk of selection for treatment resistant strains of HBV. Consequently, there is increased interest in a novel treatment modality, capsid protein allosteric modulators (CPAMs), that blocks a crucial step in the viral life cycle. I'll discuss recent work that identifies HBV serum RNA as an informative biomarker of CPAM treatment efficacy, evaluates CPAMs as a potential functional cure for HBV infection, and illustrates the role of mechanistic modelling in trial design using an age structured, multi-scale mathematical model. 

Fri, 03 Nov 2023

14:00 - 15:00
L3

Leader, follower, and cheater in collective cancer invasion

Professor Yi Jiang
(College of Arts and Science Georgia State University)
Abstract

A major reason for the failure of cancer treatment and disease progression is the heterogeneous composition of tumor cells at the genetic, epigenetic, and phenotypic levels. Despite extensive efforts to characterize the makeup of individual cells, there is still much to be learned about the interactions between heterogeneous cancer cells and between cancer cells and the microenvironment in the context of cancer invasion. Clinical studies and in vivo models have shown that cancer invasion predominantly occurs through collective invasion packs, which invade more aggressively and result in worse outcomes. In vitro experiments on non-small cell lung cancer spheroids have demonstrated that the invasion packs consist of leaders and followers who engage in mutualistic social interactions during collective invasion. Many fundamental questions remain unanswered: What is the division of labor within the heterogeneous invasion pack? How does the leader phenotype emerge? Are the phenotypes plastic? What's the role of the individual "cheaters"? How does the invasion pack interact with the stroma? Can the social interaction network be exploited to devise novel treatment strategies? I will discuss recent modeling efforts to address these questions and hope to convince you that identifying and perturbing the "weak links" within the social interaction network can disrupt collective invasion and potentially prevent the malignant progression of cancer. 

Fri, 27 Oct 2023

14:00 - 15:00
L3

Mathematical modelling throughout infectious disease outbreaks

Dr Robin Thompson
(Dept of Maths University of Oxford)
Abstract

Mathematical models are useful tools for guiding infectious disease outbreak control measures. Before a pathogen has even entered a host population, models can be used to determine the locations that are most at risk of outbreaks, allowing limited surveillance resources to be deployed effectively. Early in an outbreak, key questions for policy advisors include whether initial cases will lead on to a major epidemic or fade out as a minor outbreak. When a major epidemic is ongoing, models can be applied to track pathogen transmissibility and inform interventions. And towards the end of (or after) an outbreak, models can be used to estimate the probability that the outbreak is over and that no cases will be detected in future, with implications for when interventions can be lifted safely. In this talk, I will summarise the work done by my research group on modelling different stages of infectious disease outbreaks. This includes: i) Before an outbreak: Projections of the locations at-risk from vector-borne pathogens towards the end of the 21st century under a changing climate; ii) Early in an outbreak: Methods for estimating the risk that introduced cases will lead to a major epidemic; and iii) During a major epidemic: A novel approach for inferring the time-dependent reproduction number during outbreaks when disease incidence time series are aggregated temporally (e.g. weekly case numbers are reported rather than daily case numbers). In addition to discussing this work, I will suggest areas for further research that will allow effective interventions to be planned during future infectious disease outbreaks.

Fri, 20 Oct 2023

15:00 - 16:00
Virtual

Machine learning for identifying translatable biomarkers and targets

Professor Daphne Koller
(Department of Computer Science Stanford University)
Abstract

Modern medicine has given us effective tools to treat some of the most significant and burdensome diseases. At the same time, it is becoming consistently more challenging and more expensive to develop new therapeutics. A key factor in this trend is that we simply don't understand the underlying biology of disease, and which interventions might meaningfully modulate clinical outcomes and in which patients. To achieve this goal, we are bringing together large amounts of high content data, taken both from humans and from human-derived cellular systems generated in our own lab. Those are then used to learn a meaningful representation of biological states via cutting edge machine learning methods, which enable us to make predictions about novel targets, coherent patient segments, and the clinical effect of molecules. Our ultimate goal is to develop a new approach to drug development that uses high-quality data and ML models to design novel, safe, and effective therapies that help more people, faster, and at a lower cost. 

Fri, 13 Oct 2023

14:00 - 15:00
L3

Agent-based, vertex-based, and continuum modeling of cell behavior in biological patterns

Prof Alexandria Volkening
(Department of Mathematics Weldon School of Biomedical Engineering)
Abstract

Many natural and social phenomena involve individual agents coming together to create group dynamics, whether the agents are drivers in a traffic jam, cells in a developing tissue, or locusts in a swarm. Here I will focus on two examples of such emergent behavior in biology, specifically cell interactions during pattern formation in zebrafish skin and gametophyte development in ferns. Different modeling approaches provide complementary insights into these systems and face different challenges. For example, vertex-based models describe cell shape, while more efficient agent-based models treat cells as particles. Continuum models, which track the evolution of cell densities, are more amenable to analysis, but it is often difficult to relate their few parameters to specific cell interactions. In this talk, I will overview our models of cell behavior in biological patterns and discuss our ongoing work on quantitatively relating different types of models using topological data analysis and data-driven techniques.

Thu, 21 Sep 2023

11:00 - 12:00
L4

Efficient prediction, estimation and identifiability analysis with mechanistic mathematical models

Professor Matthew Simpson
(QUT)
Abstract

Interpreting data using mechanistic mathematical models provides a foundation for discovery and decision-making in all areas of science and engineering. Key steps in using mechanistic mathematical models to interpret data include: (i) identifiability analysis; (ii) parameter estimation; and (iii) model prediction. Here we present a systematic, computationally efficient likelihood-based workflow that addresses all three steps in a unified way. Recently developed methods for constructing profile-wise prediction intervals enable this workflow and provide the central linkage between different workflow components. These methods propagate profile-likelihood-based confidence sets for model parameters to predictions in a way that isolates how different parameter combinations affect model predictions. We show how to extend these profile-wise prediction intervals to two-dimensional interest parameters, and then combine profile-wise prediction confidence sets to give an overall prediction confidence set that approximates the full likelihood-based prediction confidence set well.  We apply our methods to a range of synthetic data and real-world ecological data describing re-growth of coral reefs on the Great Barrier Reef after some external disturbance, such as a tropical cyclone or coral bleaching event.
 

Fri, 16 Jun 2023

14:00 - 15:00
L3

Positional information theory

Prof Karen Page
(Department of Mathematics University College London)
Abstract

We study the positional information conferred by the morphogens Sonic Hedgehog and BMP in neural tube patterning. We use the mathematics of information theory to quantify the information that cells use to decide their fate. We study the encoding, recoding and decoding that take place as the morphogen gradient is formed, triggers a nuclear response and determines cell fates using a gene regulatory network.

Fri, 09 Jun 2023

14:00 - 15:00
L3

Recent and past results on stochastically-modelled biochemical reaction networks

Professor Jinsu Kim
(POSTECH Pohang)
Abstract

When a biological system is modelled using a mathematical process, the next step is often to estimate the system parameters. Although computational and statistical techniques have been developed to estimate parameters for complex systems, this can be a difficult task. As a result, researchers have focused on revealing parameter-independent dynamical properties of a system. In this talk, we will discuss the study of qualitative behaviors of stochastic biochemical systems using reaction networks, which are graphical configurations of biochemical systems. The goal of this talk is to (1) introduce the basic modelling aspects of stochastically-modelled reaction networks and (2) discuss important results in this literature, including the random time representation, relationships between stochastic and deterministic models, and derivation of stability via network structures.

Fri, 26 May 2023

14:00 - 15:00
L3

Modelling the viral dynamics of the SARS-CoV-2 Delta and Omicron variants in different cell types

Dr Ada Yan
(Dept of Infectious Disease Imperial College London)
Abstract

The Omicron BA.1 variant of SARS-CoV-2 was more transmissible and less severe than the preceding Delta variant, including in hosts without previous infection or vaccination.  To investigate why this was the case, we conducted in vitro replication experiments in human nasal and lung cells, then constructed and fitted ODE models of varying levels of complexity to the data, using Markov chain Monte Carlo methods.  Our results fitting a simple model suggest that the basic reproduction number and growth rate are higher for Omicron in nasal cells, and higher for Delta in lung cells. As growth in nasal cells is thought to correspond to transmissibility and growth in lung cells is thought to correspond to severity, these results are consistent with epidemiological and clinical observations.  We then fitted a more complex model, including different virus entry pathways and the immune response, to the data, to understand the mechanisms leading to higher infectivity for Omicron in nasal cells. This work paves the way for using within-host mathematical models to analyse experimental data and understand the transmission potential of future variants. 

While presenting the results of this study, I will use them to open a wider discussion on common problems in mathematical biology, such as the situations in which complex models are preferable to simpler models; when it is appropriate to fix model parameters; and how to present results which are contingent on unidentifiable parameters.

Fri, 19 May 2023

14:00 - 15:00
Virtual

Mapping and navigating biology and chemistry with genome-scale imaging

Dr Imran Haque
(Recursion Pharmaceuticals)
Abstract

 

Image-based readouts of biology are information-rich and inexpensive. Yet historically, bespoke data collection methods and the intrinsically unstructured nature of image data have made these assays difficult to work with at scale. This presentation will discuss advances made at Recursion to industrialise the use of cellular imaging to decode biology and drive drug discovery. First, the use of deep learning allows the transformation of unstructured images into biologically meaningful representations, enabling a 'map of biology' relating genetic and chemical perturbations to scale drug discovery. Second, building such a map at whole-genome scale led to the discovery of a "proximity bias" globally confounding CRISPR-Cas9-based functional genomics screens. Finally, I will discuss how publicly-shared resources from Recursion, including the RxRx3 dataset and MolRec application, enable downstream research both on cellular images themselves and on deep learning-derived embeddings, making advanced image analysis more accessible to researchers worldwide.

Fri, 05 May 2023

14:00 - 15:00
Virtual

Data-driven protein design and molecular latent space simulators

Professor Andrew Ferguson
(Pritzker School of Molecular Engineering University of Chicago)
Abstract

Data-driven modeling and deep learning present powerful tools that are opening up new paradigms and opportunities in the understanding, discovery, and design of soft and biological materials. I will describe our recent applications of deep representational learning to expose the sequence-function relationship within homologous protein families and to use these principles for the data-driven design and experimental testing of synthetic proteins with elevated function. I will then describe an approach based on latent space simulators to learn ultra-fast surrogate models of protein folding and biomolecular assembly by stacking three specialized deep learning networks to (i) encode a molecular system into a slow latent space, (ii) propagate dynamics in this latent space, and (iii) generatively decode a synthetic molecular trajectory.

Fri, 28 Apr 2023

14:00 - 15:00
L3

Stochastic modeling of neurotransmission dynamics

Dr Stefanie Winkelmann
(Zuse Institute Berlin)
Abstract

Abstract: Neurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance of the vesicle to the calcium channels determines the fusion probability and consequently the postsynaptic signal. After a fusion event, both the release site and the vesicle undergo a recovery process before becoming available for reuse again. For all these process components, stochastic effects are widely recognized to play an important role. In this talk, I will present our recent efforts on how to describe and structurally understand neurotransmission dynamics using stochastic modeling approaches. Starting with a linear reaction scheme, a method to directly compute the exact first- and second-order moments of the filtered output signal is proposedFor a modification of the model including explicit recovery steps, the stochastic dynamics are compared to the mean-field approximation in terms of reaction rate equations. Finally, we reflect on spatial extensions of the model, as well as on their approximation by hybrid methods.

References:

A. Ernst, C. Schütte, S. Sigrist, S. Winkelmann. Mathematical Biosciences343, 108760, 2022.

- A. Ernst, N. Unger, C. Schütte, A. Walter, S. Winkelmann. Under Review. https://arxiv.org/abs/2302.01635

 

Fri, 10 Mar 2023

14:00 - 15:00
Virtual

CRISPR-based decoding of disease-associated genomic variants

Prof Richard Sherwood
(Brigham and Womens Hospital Harvard Medical School)
Abstract

The overall goal of the Sherwood lab is to advance genomic and precision medicine applications through high-throughput, multi-disciplinary science. In a shortened talk this past autumn, I described our recent efforts using combined analysis of rare coding variants from the UK Biobank and genome-scale CRISPR-Cas9 knockout and activation screening to improve the identification of genes, coding variants, and non-coding variants whose alteration impacts serum LDL cholesterol (LDL-C) levels.

In this talk, I will discuss our emerging efforts to optimize and employ precision CRISPR techniques such as base editing and prime editing to better understand the impacts of coding and non-coding variation on serum LDL-C levels and coronary artery disease risk. This work involves the development of novel high-throughput screening platforms and computational analysis approaches that have wide applicability in dissecting complex human disease genetics.

Fri, 03 Mar 2023

14:00 - 15:00
Virtual

An agent-based model of the tumour microenvironment

Dr Cicely Macnamara
(School of Mathematics and Statistics University of Glasgow)
Abstract

The term cancer covers a multitude of bodily diseases, broadly categorised by having cells which do not behave normally. Cancer cells can arise from any type of cell in the body; cancers can grow in or around any tissue or organ making the disease highly complex. My research is focused on understanding the specific mechanisms that occur in the tumour microenvironment via mathematical and computational modelling. In this talk I shall present a 3D individual-based force-based model for tumour growth and development in which we simulate the behaviour of, and spatio-temporal interactions between, cells, extracellular matrix fibres and blood vessels. Each agent is fully realised, for example, cells are described as viscoelastic sphere with radius and centre given within the off-lattice model. Interactions are primarily governed by mechanical forces between elements. However, as well as he mechanical interactions we also consider chemical interactions, by coupling the code to a finite element solver to model the diffusion of oxygen from blood vessels to cells, as well as intercellular aspects such as cell phenotypes.