Accumulation of Oncogenic Mutations During Progression from Healthy Tissue to Cancer

by Ruibo Zhang and Ivana Bozic

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Carcinogenesis is a multi-stage process in which driver gene mutations occur sequentially. Understanding the arrival times of genetically different subclones provides important insights into tumorigenesis. In this work, we establish a multi-type branching process to model the initiation of cancer that starts from a healthy tissue in homeostasis. Mutations can be either neutral or advantageous, which reflects that inactivating a single copy of a tumor suppressor gene does not directly provide a selective growth advantage. We approximate the distribution of the arrival time for each type and compare it to computer simulations of the process. The results are applied to study the initiation of colorectal cancer and chronic myeloid leukemia. 

Model illustration. The model describes an evolutionary process that starts with a large healthy population in homeostasis (blue circles). Mutations that are either neutral or advantageous occur sequentially, which causes subsequent types to be either homeostatic (yellow) or initiated (orange). The cancerous type (red) emerges only when all the required genetic alterations have taken place.

Editorial By Sara Loo

Ways to engage with SMB

This quarter’s editorial is less an editorial, and more of a spiel of a couple of ways in which you can engage with the Society and share with others in the community! We love hearing from our community and looking for ways in which to engage with one another.  As a member of SMB, you have access to our Member Forum, news items, and can share your work and interests with others through our Highlights page. If you haven't logged on for a while, now might be a good time to make sure your profile is up to date with your latest interests - click here to update and select your preferred Subgroups to receive communications from subgroup leaders.  SMB Member Forum A primary way you can do this is through the SMB Member Forum. The forum is a great platform for sharing with others in our community – be it an upcoming conference, job postings, funding opportunities, or even a call-out for like-minded members to collaborate. On the main website, recent member forum posts can be seen on the Home page, as well as through the Communications tab. If you are a member of SMB, once you are logged on to the main website, post on our Member Forum by clicking on Create Topic and including any details you want to share. Click on Subscribe to get updates on all new posts via email. You can also subscribe to a single forum post for updates to that specific post.  For any membership issues or problems with logging on to the website, contact website@smb.org

Highlights In addition to the forum, if you have a paper published in the Bulletin of Mathematical Biology that you would like to highlight, our publications team would like to hear from you! Submit the paper to the team to highlight, using the linked form in the website menu, with a brief description (max 750 words) of the highlights of your paper, along with a figure. Think of this as a brief ‘featured figure’! These get posted by the Publications Team in the News section of our website.

Bluesky Have you found yourself in the recent wave drifting over to Bluesky?  You can find us at @smbmathbiology.bsky.social where we share recent paper highlights, repost job advertisements,  and other recent news. We’ve also pulled together an SMB Starter Pack so you can follow all your favorite mathematical biologists and continue to grow our community.

Other social media Follow us on X: @SMB_MathBiology Instagram: @smbmathbio Threads: @smbmathbio Featured Figures By Thomas Woolley In this issue, we feature the work of Jana Gevertz, College of New Jersey, and Giulia Celora, University College London.  We asked Jana Gevertz to tell us a bit more about her work here: Assessing the Role of Patient Generation Techniques in Virtual Clinical Trial Outcomes Clinical trials are research studies where novel medical interventions are tested on people who volunteer to receive the treatment of interest. These studies are the primary way that researchers find out if a new treatment is safe and effective in humans. The predictions made by clinical trials are generally limited by small sample sizes and may be biased to certain demographic groups which are more inclined to enroll in these studies. Virtual clinical trials (VCTs), grounded in data-informed mathematics models, are growing in popularity as a tool for quantitatively predicting heterogeneous treatment responses across a population. They hold the promise of complementing standard clinical trials by computationally permitting the analysis of a more diverse and representative patient population. In the context of a VCT, a “plausible patient” is an instance of a mathematical model with parameter (or attribute) values chosen to reflect features of the disease and response to treatment for that particular patient. A challenging question in the design of VCTs is to determine which set of model parameterizations (that is, which “plausible patients”) should actually be included in the virtual population. The aim of our work was to rigorously quantify the impact that VCT design choices have on the heterogeneity of the virtual population, and on the predictions of a virtual clinical trial. To isolate the impact of VCT design choices, we worked with simulated patient data and a simple, toy model of tumor growth that predicted response to the treatment. In this controlled setting, we studied the impact of the following VCT design choices (see Figure): the prior distribution of each parameter that varies across patients, and the method for selecting which parameterizations are considered virtual patients and thus included in the VCT. Our analysis revealed that the prior distribution, rather than the inclusion/exclusion criteria, has a larger impact on the heterogeneity of the virtual population. Yet, the predictions of the virtual clinical trial were more sensitive to the inclusion/exclusion criteria utilized. This foundational understanding of the role of virtual clinical trial design should help inform the development of future VCTs that use more complex models and real data. We asked Giulia Celora to tell us a bit more about her work here: Characterising Cancer Cell Responses to Cyclic Hypoxia Using Mathematical Modelling In solid tumours, the presence of regions of abnormally low oxygen levels (i.e., hypoxia) is recognised as a major driver of tumour progression and therapeutic resistance. Even though in vitro models of hypoxia exist, they often fail to capture the complex and heterogeneous oxygenation dynamics of real tumours. While most experimental studies have focussed on characterising cell responses to constant hypoxic conditions, in vivo observations show that tumour oxygen levels can fluctuate on fast timescales and expose cancer cells to periodic cycles of hypoxia; a phenomenon known as cyclic hypoxia. These observations raise questions regarding the applicability of such experimental findings to the clinical understanding of hypoxia: do cyclic and constant hypoxia elicit different responses in cancer cells? If so, what features of fluctuating oxygen conditions are cancer cells sensitive to? Is the frequency of hypoxia cycles, their duration? Or both? In our recent publication, we used mechanistic mathematical modelling to quantify the impact of prolonged exposure to various cyclic hypoxia conditions on the population growth and survival of tumour cell cultures. In particular, we developed a structured stochastic individual-based cell cycle model that accounts for hypoxia-driven dysregulation of both cell cycle and cell survival. In this framework, each cell is an agent that can either proliferate or die with probabilities that depend on its internal state. The cell internal state is described by a list of categorical and continuous structure variables, that also evolve probabilistically over time. Structure variables allow us to capture the multi-layered feedback between oxygen levels, intracellular processes (such as DNA replication and repair), and cell fate – namely, proliferation and death.

Our model allows us to efficiently characterise how cancer cells respond to hypoxia cycles of varying duration and frequency. As shown in the Figure, we find that cell responses to cyclic hypoxia can be classified into four major groups depending on the extent to which population growth and cell survival are affected by periodic exposure to hypoxia. Our results highlight the multifaceted nature of cyclic hypoxia and the role of fluctuating oxygen levels in creating heterogeneous environmental conditions within tumours. You can learn more about our work and the implications of our results on the connection between cyclic hypoxia and intra-tumour heterogeneity here:

Sara Loo (Johns Hopkins University), Burcu Gürbüz (Johannes Gutenberg-University Mainz), Thomas Woolley (Cardiff University), and Olivia Chu (Bryn Mawr College).

1. News - updates from: 
   • SMB Subgroups
   • Royal Society Publishing
2. People - Interview with Dr Hao Wang, University of Alberta.
3. Editorial - Engaging with the SMB Community
4. Featured Figures - 
   • Jana Gevertz
   • Giulia Celora

To see the articles in this issue, click the links at the above items.

Contributing content

Issues of the newsletter are released four times per year in Spring, Summer, Autumn, and Winter. The newsletter serves the SMB community with news and updates, so please share it with your colleagues and contribute content to future issues.

We welcome submissions to expand the content of the newsletter.  The next issue will be released in January, so if you would like to contribute, please send an email to the editors by the start of January 2025 to discuss how your content can be included. This could include summaries of relevant conferences that you have attended, suggestions for interviews, professional development opportunities etc. Please note that job advertisements should be sent to the Member Forum rather than to the newsletter.

If you have any suggestions on how to improve the newsletter and would like to become more involved and/or contribute, please contact us at any time. We appreciate and welcome feedback and ideas from the community. The editors can be reached at newsletter@smb.org.

We hope you enjoy this issue of the newsletter!

Sara, Burcu, Thomas and Olivia
Editors, SMB Newsletter

News Section

By Olivia Chu In this issue of the News section, we highlight the updates from the SMB Subgroups and Royal Society Publishing. Read on below.

Engage in innovative mathematical biology research at the NSF-Simons National Institute for Theory and Mathematics in Biology

Random Dynamical Systems, with Applications in Biology workshop held in November 2024

The NSF-Simons National Institute for Theory and Mathematics in Biology (NITMB) was founded in 2023, with its mission being to enhance integration of research in the mathematics and biology disciplines. The overall vision of the NITMB is to understand the mathematical basis of constraints that drive biological capabilities. Achieving this goal promises to transform biological research and to inspire new mathematical discoveries. Funded by the U.S. National Science Foundation and the Simons Foundation, NITMB operates as a working partnership between Northwestern University and the University of Chicago. NITMB is located on the 35th floor of the John Hancock Center at 875 N. Michigan Avenue in downtown Chicago. It is located halfway between the Northwestern University campus in Evanston and the University of Chicago campus in Hyde Park. NITMB has a dedicated auditorium for convening activities, a dining area, temporary offices for visitors, and extensive open collaborative work spaces for research and interaction. The Institute is designed to house most of its research and convening activities, and it is readily accessible to participants from across the U.S. and the world. Researchers at the Institute generate new mathematical results and uncover the “rules of life” through theoretical studies, data-informed mathematical models, and various computational and statistical tools. The structure of NITMB-supported research allows theorists and experimentalists to collaborate on experimental design, data analysis, and modeling. NITMB also fosters the development of new mathematics that is inspired by biology. In particular, the Institute offers two forms of research support: (i) funding for research projects and (ii) funding to visit and perform research at NITMB. Scientific conferences, workshops, and long programs hosted by NITMB are organized around broad conceptual themes that are common in both mathematics and biology; they also highlight opportunities to develop new mathematics. These events are open to participants from institutions across the world and include researchers in both mathematics and biology. Stay up to date with the latest information about NITMB by visiting nitmb.org.

SMB Subgroups Updates

Population Dynamics, Ecology, and Evolution (PDEE)

The PDEE subgroup successfully launched an online journal club. We are seeking presenters and article suggestions; we are particularly interested in participation from scholars in the global South. To learn more, email subgroup chair Judith Miller at Judith.Miller@georgetown.edu.

Mathematical Epidemiology (MEPI)

The Mathematical Epidemiology (MEPI) subgroup had a wonderful time at the annual meeting in Korea. We held a session on Infectious Disease Modeling Across Time, Space, and Scale. Speakers included Soyoung Park, Edward Hill, Stacey Smith?, Folashade Agusto, Sunhwa Choi, Camelia Rose Walker, and Tin Phan.

We also wish to share that our current officers are Meredith Greer (Chair) and Prashant Kumar Srivastava (Co-Chair), along with Michael Robert (Past Chair).

Cardiovascular Modeling

• Committee membership update: we now have Mitchell Colebank at University of South Carolina joining our committee as Secretary in addition to Michael Watson and Vijay Rajagopal as President and Vice President. We will be growing our committee membership in 2025 to adequately represent our growing member community.
• We have a website which we would love to populate with CVM subgroup member stories and publications, please email one of the committee members to let us know.
• We have also created a LinkedIn page that we encourage our members to join. Get immediate access to your network of colleagues for your next collaboration, next job search or next recruit into your team.
• If you would like to get involved with our community please make sure you register your membership with CVM when you renew membership or become a new member of SMB.
• Look out for an email from us when SMB2025 opens up proposals for minisymposia.

Mathematical Oncology

• Fields Thematic Program in Mathematical Oncology, July - December 2024
  Over the past 20 years the mathematical modelling of cancer has developed from a side discipline to centre stage. Many modern treatment developments are accompanied by mathematical and computational modelling. For example, optimal radiation schedules are computed based on tumor control probabilities, glioma treatment is guided by medical image processing, and evolutionary adaptive therapies are guided by mathematical modelling. In fact, all aspects of the seminal “Hallmarks of Cancer” from Hanahan and Weinberg (2000 and 2010) have now been modelled with mathematical and computational models.  The well structured and uncompromisingly rigorous methods of mathematical modeling has a lot to offer for future developments in cancer research and treatments. Not only does it guide researchers in the right direction, it also, unceremoniously, tells us when something does not work, and why. In support of research activities in this very active area of applied mathematics, the Thematic Program in Mathematical Oncology has been hosted at the Fields Institute from July to December 2024. The thematic program has featured a large number of activities, including six workshops, two Fields postdocs, several long term visitors, and over 250 short term visitors. It has also hosted three distinguished visitors (N. Komarova, H. Byrne, T. Hillen) and offered a mathematical oncology graduate course. For details and videos of many of the talks, please see: http://www.fields.utoronto.ca/activities/24-25/oncology
• Math Oncology Interviews
  Thomas Hillen started an interview series on youtube, where he invites experts in mathematical oncology for a short interview to find out who they are, what career path they had, and what motivates them. These informal conversations are fun to watch and allow younger scientists to meet some of the leaders in the field. Check it out:  https://www.youtube.com/@MathOncologyInterviews/playlists 
• Workshop on Uncertainty Quantification
  One of your MathOnco co-chairs is also co-organizing an ICERM workshop on Uncertainty Quantification for Mathematical Biology, where many SMB members will participate. All are welcome to apply: https://icerm.brown.edu/program/topical_workshop/tw-25-uqmb

Cell and Developmental Biology

The Cell and Developmental Biology (CDEV) subgroup elected new officers this fall:

Chair: Keisha Cook (Clemson University, keisha@clemson.edu)

Secretary: Anna Nelson (Duke University, anelson@math.duke.edu)

Committee members:

• Alessandra Bonfanti (Politecnico di Milano, bonfantiale.ab@gmail.com)
• Giulia Celora (University College London, g.celora@ucl.ac.uk)
• Kelsey Gasior (University of Notre Dame, kgasior2@nd.edu)
• Qixuan Wang (University of California, Riverside qixuan.wang@ucr.edu)

Royal Society Publishing

Journal of the Royal Society Interface celebrates its 20th anniversary! On 22nd November 2004, J. R. Soc. Interface was launched to provide a home for cross-disciplinary science at the boundary of the life and physical sciences.  To mark its 20thanniversary, we are looking back on the landscape of interdisciplinary science two decades ago and looking forward to what the future may hold. As part of our celebrations, you are invited to write a Perspective on where you think this field will be in 20 years’ time, with a £1000 on offer. We also have interviews with our past and present editors, as well as a blog post with our Senior Publishing Editor, and a collection of new reviews and historic research.

Tree frog (Litoria caerulea). Credit: iStock.com / jamcgraw.

People Section By Burcu Gürbüz

Interview with Dr Hao Wang, University of Alberta, an organizer for next year's SMB Annual Meeting.

A coupled spatial-network model: A mathematical framework for applications in epidemiology

by Louis V. Kunz, Jesús J. Bosque, Mohammad Nikmaneshi, Ibrahim Chamseddine, Lance L. Munn, Jan Schuemann, Harald Paganetti, and Alejandro Bertolet

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AMBER (Agent-based fraMework of radioBiological effects of Radiotherapy) simulates tumor growth, vasculature, and radiation response by combining agent-based modeling (ABM) with Monte Carlo (MC) methods. Using a hybrid approach and voxelated geometry it tracks tumor and microenvironmental changes over time, including oxygen levels and VEGF at a mesoscopic scale, allowing for facilitated comparison with MRI and CT. The inclusion of multifactorial biological determinants allows AMBER to represent tumor growth and response to radiotherapy in a relevant manner, with for example the appearance of a necrotic core. The modular implementation of the framework allows for easy extension and refinement to specific applications. 

Evolution of the distribution of alive and necrotic cells in a central slice of a tumor grown with AMBER, along with the evolution of the vasculature, from low density in purple to high density in yellow. Third row shows the micro vessel density, with well oxygenated voxels in blue and hypoxic/anoxic voxels in orange/red. Last row shows the explicit vasculature, with only healthy vasculature in the first column and new vessels growing due to angiogenesis in the next columns.

A coupled spatial-network model: A mathematical framework for applications in epidemiology

by Hannah Kravitz, Christina Durón, and Moysey Brio

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A new compartmental modeling framework is proposed which couples population centers at the vertices, 1D travel routes on the edges, and a 2D continuum containing the rest of the population to simulate how an infection spreads through a population. The edge equations are coupled to the vertex ODEs through junction conditions, while the domain equations are coupled to the edges through boundary conditions. The model is illustrated on some example geometries, and a parameter study example is performed. The observed solutions exhibit exponential decay after a certain time has passed, and the cumulative infected population over the vertices, edges, and domain tends to a constant in time but varying in space, i.e., a steady state solution. 

Example implementation of the coupled spatial-network model.

Forecasting and Predicting Stochastic Agent-Based Model Data with Biologically-Informed Neural Networks

by John T Nardini

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Agent-based models (ABMs) are widely used to study biological systems, but heavy computational requirements limit our ability to predict their behavior. Differential equation (DE) models are often used as ABM surrogates, but they can provide poor predictions. We propose that biologically-informed neural networks (BINNs) can learn informative DE models that predict ABM behavior. We demonstrate how BINNs’ learned DE models can forecast future ABM data at new parameter values. We highlight the strong performance of this methodology in three case study ABMs that explore different rules on cell-cell interactions in collective migration. BINNs learn predictive and interpretable DE models even when other DE models are ill-posed or complex.

1) We explore several different ABM rules and summarize the ABM density over time. 2) BINN models can be trained to the ABM data. 3) We predict new ABM data by simulating the BINN's learned PDE model.

…where we talk about a paper studying who and when we should vaccinate.

After completing a DPhil in Statistics from the University of Oxford, focussing in epidemiology and phylogenetics, Matt now works as a data scientist for Italian football club Como 1907.

Matt was awarded the Lee A. Segel Prize for Best Student Paper published inThe Bulletin of Mathematical Biology for his paper Asymptotic Analysis of Optimal Vaccination Policies.

Join us to learn more about how this paper can help health professionals better assess the best way to distribute vaccines.

Find out more about Matt and his work on Linkedin:
linkedin.com/in/matthew-penn-732551232/

Find out more about SMB on: 

• Twitter: @smb_mathbiology 
• Facebook: @smb.org 
• Linkedin: @smb_mathbiology 
• The Bulletin of Mathematical Biology

Apple Link      Spotify Link     Read the full transcript

…where we talk parasites, motorbikes, and digital twins.

Professor Reinhard Laubenbacher is: the Director of Laboratory for Systems Medicine at the University of Florida, an AAAS fellow (American Association for the Advancement of Science), and a scientist interested in using math to understand human disease and more specifically fungal infections in the lungs. When not at work, Reinhard and his wife enjoy motorbiking everywhere from the swamps of Florida, to the plains of Patagonia.

Find out more about Reinhard’s work on the following websites:

https://systemsmedicine.pulmonary.medicine.ufl.edu/

https://systemsmedicine.pulmonary.medicine.ufl.edu/profile/laubenbacher-reinhard/

Find out more about SMB on: 

• Twitter: @smb_mathbiology 
• Facebook: @smb.org 
• Linkedin: @smb_mathbiology 
• The Bulletin of Mathematical Biology

Apple Link      Spotify Link     Read the full transcript

Harnessing flex point symmetry to estimate logistic tumor population growth

by Stefano Pasetto, Isha Harshe, Renee Brady-Nicholls, Robert A. Gatenby, Heiko Enderling

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Tumor growth dynamics are well-described mathematically by the S-shaped logistic function. Initially exponential growth decelerates as the tumor approaches its carrying capacity – the maximum tumor burden that can be sustained by the local and systemic (micro-)environment. The volume-to-carrying capacity ratio is a major determinant of response to (radio-)therapy; therefore, it is of high importance to estimate the carrying capacity from limited tumor volume measurements. The symmetry around the logistic growth flex point can be used to introduce ghost points symmetric to observed data points to double the available data to calibrate model parameters for an individual patient. With this approach, fewer data points are necessary to identify patient-specific carrying capacities, thereby potentiating shorter times to treatment decisions.

Relational Persistent Homology for Multispecies Data with Application to the Tumor Microenvironment

by Bernadette J. Stolz, Jagdeep Dhesi, Joshua A. Bull, Heather A. Harrington, Helen M. Byrne, Iris H. R. Yoon

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State-of-the-art data is exquisite in detail, often containing information on multiple species, e.g. cell types in imaging data. However, there are very few techniques equipped to analyse and quantify relations in such data. The paper by Stolz, Dhesi et al. proposes two topological approaches for multispecies data that can encode relations in spatial data. The authors showcase the methods on synthetic data of the tumour microenvironment which models the behaviour and interactions between tumour cells, macrophage subtypes, necrotic cells, and blood vessels. They demonstrate that relational topological features can extract biological insight, including dominant immune cell phenotype and parameter regimes of the data-generating model.

Relational persistent homology encodes spatial relations in multispecies data. We use synthetic images of the tumour microenvironment generated by an agent-based model as input to two different topological methods for encoding relations: Dowker persistent homology (top row) and multispecies witness persistent homology (bottom row). The topological features that we extract can classify the synthetic images according to dominant immune cell type and cluster qualitative behaviours of the model.