Mathematical modeling of tumor immune interactions: the role of anti-FGFR and anti-PD-1 in the combination therapy

by Chenghang Li, Zonghang Ren, Guiyu Yang, Jinzhi Lei

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Bladder cancer is a malignant tumors of the urinary system known for its high incidence and recurrence rates. Recent studies suggest that combination therapy could improve survival outcomes for bladder cancer patients with high FGFR and PD-L1 expression. This study introduces a mathematical model that integrates the inter-regulatory network of the tumor microenvironment and the competition mechanism between the drug and the ligand-binding receptor. This model describes tumor proliferation dynamics under various treatment strategies and visualizes these process through an agent-based model. The study analyzes the tumor microenvironment dynamics, combination therapy efficacy, treatment sequencing, disease progression, and patient survival.

The protocol of data-driven mathematical model development and application.

The Distance Between: An Algorithmic Approach to Comparing Stochastic Models to Time-Series Data

by Brock D. Sherlock, Marko A.A. Boon, Maria Vlasiou, Adelle C.F. Coster

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Experimental data is often in the form of time-series data with multiple measurements taken at a number of time points. In biological datasets the number of measurements at each time point is often small. So, it can be useful to consider data from multiple experimental protocols to constrain model parameters. In this study, we identify distance metrics for the comparison of stochastic model outputs and time-evolving stochastic measurements of a system. Our distance is across three scales: that of the data at each time point of each type of experiment; a combined distance across the time course of each experiment; and a combined distance across all the experiments. The distances identified offer a means to fit a wide range of models to data.

The algorithm to produce a hierarchical distance measure over three scales: individual time points, across a time course of a single experiment, and a combined distance over all experiments. This combined distance can then be used for parameter inference, model or other comparisons.

Oscillations in a Spatial Oncolytic Virus Model

by A. Baabdulla and T. Hillen

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A viral infection of the tumor has two effects, the virus infects cells which subsequently lyse to release more virus particles, and, the virus marks cancer cells as infected and the immune system comes in to eradicate them. Both processes have to work in balance as to efficiently clear the entire tumor. The basic model for oncolytic viruses is an SIV predator-prey model, which has a Hopf bifurcation and periodic solutions. An interesting question is the spatial coupling of these oscillators as many different types of spatio-temporal patterns are possible (see Figure). The key question for clinical applications is how to manipulate the virus such that the system is in the oscillatory state. We discuss several of these approaches.

Simulation of an oncolytic virus model using Andrew Krause’s VisualPDE. C shows the cancer cells (brown is low, black is high), I the infected cancer cells (blue is low and white is high), and V the virus (blue is low and red is high).

A Role of Effector CD8+ T Cells Against Circulating Tumor Cells Cloaked with Platelets: Insights from a Mathematical Model

by Khaphetsi Joseph Mahasa, Rachid Ouifki, Lisette de Pillis, Amina Eladdadi

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Circulation of tumor cells, shed from the primary tumor into the blood stream or lymphatic circulation, posits a great threat for patients having metastatic cancers. In this study, we developed a simple mathematical model describing how the primary tumor, CTCs arrested within the circulation, activated platelets and effector CD8+ T cells all shape metastatic framework. Our simulations reveal that high number of activated platelets on CTCs exacerbate CTC’s evasion from immune surveillance. Our model suggests that the efficacy of immunotherapy, based on CD8+ T cells, can be improved by increasing the proliferation rate of CD8+ T cells, although this resolution should be weighted against the CD8+ T cell toxicity in the circulation.

A schematic diagram of the cellular interactions at the primary site, within the circulation and the secondary site.

A mathematical model for fibrous dysplasia: The role of the flow of mutant cells

by Mariia Soloviova, Juan C. Beltrán-Vargas, Luis Fernandez de Castro, Juan Belmonte-Beitia, Víctor M. Pérez-García, Magdalena Caballero

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Fibrous dysplasia (FD) is a rare mosaic, non-inheritable genetic disorder that affects the skeleton, where normal bone is replaced by weaker, fibrous tissue. This disorder is characterized by expansible lesions prone to fracture, deformity, and pain, and currently has no cure. We have developed a simple mathematical model to better understand the behavior of bone cells in FD. Our model includes the basic biological processes known to occur in FD and tracks the changes in different populations of bone cells over time. We conducted a detailed analysis of the model, examining its properties, the existence and stability of steady states, and the sensitivity of various parameters.

Representation of the bone-cell populations and interactions between them.

Evolutionary invasion analysis of modern epidemics highlights the context-dependence of virulence evolution

by Sudam Surasinghe, Ketty Kabengele, Paul E. Turner, C. Brandon Ogbunugafor

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Why do some pathogens evolve to make their hosts more sick, and others less?  This characteristic is embodied in the concept of “virulence,” a central idea in infectious diseases that describes the harm that a pathogen inflicts upon a host. Examining how virulence evolves constitutes a subfield of evolutionary theory, that attempts to make concrete predictions for how we should expect infectious diseases to evolve. In this study, we construct models of various epidemics, and apply a set of mathematical methods based on game theory that identify characteristics of mutant pathogens that render them uninvadable (that is, they cannot be invaded and replaced by a different strain of pathogen).  We demonstrate that pathogens that are spread via different routes—“directly” (as in SARS-CoV-2) or “indirectly” as in diseases like hepatitis C virus in a population of persons who inject drugs—have profoundly different expectations for how. Our findings have implications for how we analyze and prevent modern epidemics. We learn that how virulence will evolve is context-dependent. Consequently, our predictive models of the evolution of virulence should be tailor made to fit the particulars of certain infectious diseases.

A diagram of an infectious disease model with multiple evolved strains of a pathogen.

Multi-layer Bundling as a New Approach for Determining Multi-scale Correlations Within a High-Dimensional Dataset

by Mehran Fazli, Richard Bertram & Deborah Striegel

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The multi-layer bundling (MLB) method delivers a robust new approach to cluster elements of complex biological networks. Using different partitioning schemes (clustering regimes) obtained by spectral clustering on the affinity matrix, MLB provides hierarchical layers of clusters called bundles, where each bundle in a layer is formed from all elements with the same membership throughout all partitioning schemes used up to the current layer. This iterative process offers profound insights into the interconnections among data elements not apparent through a single clustering approach. For example, MLB excels in identifying critical bridge sets within interacting systems. If removed, these bridges can disrupt system compartments and halt information propagation, making their identification crucial for understanding network integrity. Moreover, MLB's unique capability to integrate bundle membership information through multiple layers with the affinity matrix significantly enhances its predictive power in network reconstruction. Compared to methods like WGCNA, MLB offers a more robust and versatile approach. Requiring fewer user-defined parameters, MLB provides a clearer view of the underlying data structures, empowering researchers with a powerful tool to decode complex datasets and uncover meaningful biological insight. Its versatility extends beyond biological networks, making it valuable for various research domains.

Impact of Resistance on Therapeutic Design: A Moran Model of Cancer Growth

by Mason Lacy & Adrianne Jenner 

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Cancers often develop resistance to standard treatments, such as chemotherapy. Understanding how the appearance of resistant cells impacts the effectiveness of treatment is an important area of study. In this work, we use a Moran model to investigate the impact of resistance on two styles of treatment administration: single high-dose injections (or maximum tolerated dose) and sustained low-dose treatments.

Experimentalists have been developing devices, such as hydrogels, that can be loaded with drug and injected close to the tumour. These devices then release the treatment slowly over time, giving a sustained (often low) dose of the therapy. Using a Moran model capturing a population of sensitive and resistant cells, we were able to show that maximum tolerated dosages are still the most effective protocols in the presence of an aggressive, resistant-prone tumour. We showed how even when the Moran model was calibrated to capture experimental data for treatment of breast cancer, the same result holds.

Caption: Schematic depicting tumour evolution over time and the fixation of a resistant clone following therapy. As a cancer grows, it is subjected to various pressures which can cause mutations to arise. Some clones may contain mutations that may be more adept at coping with treatment or provide a fitness advantage to those cells, such as faster proliferation rates, and we denote these as driver mutations. After treatment, often cells with driver mutations conferring resistance and/or fitness advantages will expand in number. In some cases, this can result in a tumour that is no longer as genetically complex. Most importantly, these tumours are often no-longer sensitive to the original therapy (Color figure online)

Alys Clark (University of Auckland), Sara Loo (Johns Hopkins University), Burcu Gürbüz (Johannes Gutenberg-University Mainz), Thomas Woolley (Cardiff University), and Olivia Chu (Dartmouth College). 

1. News – updates from: 
   • SMB Subgroups and DEI Committee
   • Upcoming Conferences and Workshops
   • Updates from Royal Society Publishing
2. People – New editor Burcu Gürbüz.
3. Editorial – on Big Moves during academic careers.
4. Featured Figure – Highlighting the research by early career researcher Veronica Ciocanel, Duke University.

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.

If you have any suggestions for content or on how to improve the newsletter, 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!

Alys, Sara, Thomas, Burcu, and Olivia

News Section

By Sara Loo and Olivia Chu

SMB Subgroups Update

Cell and Developmental Biology Subgroup

The SMB Cell and Developmental Biology (CDEV) subgroup held its first virtual mini-conference in March 2024 (picture attached), featuring about 25 speakers and panelists, with participants registering from across 5 continents! Our virtual mini-conference “Cell and Development Festival Week” consisted of 5 sessions across 4 days, each with about two hours of programming. Thank you to all who presented and participated. Our subgroup has also continued to post interviews highlighting scientists in mathematical cell and developmental biology. In our three most recent blog posts, we hear from Evan Curcio, Duncan Martinson, and Hannah Scanlon; see https://smb-celldevbio.github.io/blog/ for their interviews, as well as past interviews of other members of the CDEV community.

Immunobiology and Infection Subgroup

As a follow-up to the NIAID/SMB Workshop on Multiscale Modeling of Infectious and Immune-Mediated Diseases held at last summer’s SMB Annual Meeting, the Immunobiology and Infection Subgroup would like to highlight a paper summarizing the event that was recently published in the Bulletin of Mathematical Biology: https://doi.org/10.1007/s11538-024-01276-2 We look forward to organizing similar events/workshops in coordination with other SMB subgroups!

MathOnco Subgroup

Jason George and Harsh Jain’s terms as co-chairs are coming to an end. We are in the process of recruiting 2 co-chairs. Nominations have closed.

The subgroup is also organizing a mini-symposium at the SMB 2024 Annual Meeting in Korea - ‘Emerging Researchers in Mathematical Oncology: The ONCO Group Minisymposium’. This will feature 10 talks by exciting early-career researchers from around the world.

SMB DEI Committee

1. The DEI Committee is pleased to share a recent publication in the Bulletin of Mathematical Biology entitled “Integrating Diversity, Equity, and Inclusion into Preclinical, Clinical, and Public Health Mathematical Models”. The paper is a follow-up from the DEI-focused session and discussion at the 2023 SMB Annual Meeting held in Columbus, Ohio last year. The article presents key issues for the increased integration of DEI in mathematical modelling in biology. Such integration ensures the applicability and relevancy of mathematical models and their predictions to all.

Justin Sheen, Lee Curtin, Stacey Finley, Anna Konstorum, Reginald McGee, and Morgan Craig. “Integrating Diversity, Equity, and Inclusion into Preclinical, Clinical, and Public Health Mathematical Models”. Bull Math Biol 86, 56 (2024). https://doi.org/10.1007/s11538-024-01282-42.

The 2nd Diversity of Math Bio Summer Virtual Seminar Series starts June 4! This series aims to highlight the diversity of mathematical biology research and the diversity of researchers in the field. The talks will be held on Tuesdays at 8:00 PDT / 11:00 EDT / 17:00 CEST via zoom. See the attached flyer for more details and register at https://tinyurl.com/SMB-Diversity-Summer2024 to receive the zoom information. Please join in for an exciting summer of math bio talks!

Dates: June 4, June 18, July 16, July 30, August 30

• Confirmed Speakers:
  
• 1. June 4: Paola Vera-Licona, University of Connecticut Health Center; Omar Saucedo, Virginia Tech
  2. June 18: Punit Gandhi, Virginia Commonwealth University; Maisha Marzan, North Central College
  3. July 16: Kristina Wicke, New Jersey Institute of Technology; Celeste Vallejo, Simulations Plus
  4. July 30: Van Pham, University of South Florida; Alex Ochoa, Duke University
  5. August 13: Malena Español, Arizona State University

Upcoming Conferences and Workshops

Society for Mathematical Biology Annual Meeting

From 30^th June - 5^th July Friday 2024, the joint annual meeting of the Korean Society for Mathematical Biology and the Society for Mathematical Biology will be held at KonKuk University, Seoul, Republic of Korea. For more details check the conference website: https://smb2024.org/

Royal Society Publishing

The Royal Society's journal Proceedings of the Royal Society A welcomes submissions of research and review articles in Mathematical Biology. With a broad, international readership and a thorough, constructive review process, authors can be confident that their work published with us will have an impact.

Browse recent content including articles such as Structural identifiability analysis of linear reaction–advection–diffusion processes in mathematical biology on the website at https://royalsocietypublishing.org/journal/rspa

Proceedings A publishes review articles of interest to a wide range of scientists and the Reviews Editors welcome proposals for new reviews. All review articles are made immediately open access at no cost to the author. See https://royalsocietypublishing.org/rspa/reviews for information on proposing a Review and see some recent review articles at https://royalsocietypublishing.org/toc/rspa/2024/480/2285

People

By Thomas Woolley

We interviewed one of our two new editors Burcu Gürbüz (Johannes Gutenberg-University Mainz). Find out more here.

Editorial

By Alys Clark

Big moves

Moving institutions, or moving countries, is often talked about from the perspective of furthering an academic career. There are benefits from learning a new way of working, or from seeking a career pathway that simply isn’t available at your home institution. Across the field of mathematical biology most of us will have come across students and academics who have moved for one reason or another, and throughout an academic career opportunities may arise to further our careers further afield.

We often discuss the academic considerations around these big moves - are we going to be studying or working at a good institution, what is the reputation of our new supervisor or mentor, and are we going to be moving to a research environment where we are going to be intellectually stimulated and supported? It is really important to talk to those that you will be working with or for, and making sure that the culture of the research team and/or department you will be working for suits you and your background. Perhaps less discussed though are the everyday practicalities of such a move and these may be equally important determinants of success at your new home (be it a short or a long term stay).

I recall on my own (second) international move, for a postdoc position, I found myself in the situation of being unable to open a bank account to pay my salary into without proof of address, and being unable to move into an apartment without proof of finances (i.e. a salary). It is really stressful in your first days or weeks in a new country to be navigating these kind of situations (which are ultimately resolvable) so planning where you might live and the administrative steps you will need to take to set yourself up in advance is desirable. Luckily, there will likely be many that have been in the same situation before you, so your new workplace may be able to put you in touch with people who have recently been through the same process. For those who are moving for employment, working out whether you be eligible for retirement plans (or whether they are transferable if you move again) is also a good idea. Making friends takes time, and joining clubs and community groups can help some to establish networks, but time of life and the community to which you move can influence how long it takes to feel at home. We are all now much more used to online communication which can help you to stay connected with old friends and family. But with patience these connections in your new home build too, so it is worthwhile building those connections even if the move is short term.

There are also international contexts to research priorities and funding. Post-PhD access to research funding may be a priority for establishing a career, but in many countries funding is limited to people with citizenship or residence of the country in question. This may be worth checking before you move to avoid any surprises. In mathematical biology, local priorities may also drive research direction. Will you be able to establish good links to experimental scientists, and are there requirements for ethical approval or consultation specific to your new institution that you should be aware of?

Finally, a move between countries, or even between cities is not for everyone and there are multiple reasons that mean we are best to stay just where we are. Luckily, the thought that we must move to ensure success are fading and there are several opportunities to learn new ways of thinking and doing research from our international colleagues via short term stays or online events. This might include learning from experts in your own field of mathematical biology, or even picking up some experimental skills to complement the theory you are developing. Keep an eye on SMB subgroup news for opportunities, or keep a look out for summer schools or workshops associated with conferences you may be attending online or in person.

Featured Figure

By Sara Loo and Olivia Chu

Early Career Feature - Veronica Ciocanel, Duke University

In this issue, we feature a recent article "Parameter Identifiability in PDE Models of Fluorescence Recovery After Photobleaching", by Veronica Ciocanel, Assistant Professor of Mathematics and Biology at Duke University. We asked Veronica to tell us a bit more about her work here:

Identifying unique parameters for mathematical models describing biological data can be challenging. When studying models of macromolecular dynamics inside cells, spatial movement (characterized by diffusion, transport, and binding dynamics) can be significant and has an impact on the parameters that describe a given model. Therefore, partial differential equations (PDEs) that track the dynamics of proteins as a function of time and space are often an appropriate modeling framework. However, PDEs present challenges when trying to understand identifiability, especially since many established in vivo measurements of protein dynamics average out the spatial information.

In this work, we focus on biological data obtained from a commonly-used and versatile experimental technique for probing protein dynamics in living cells: FRAP (fluorescence recovery after photobleaching). In particular, we would like to understand what insights we can gain from FRAP data about binding protein interactions in RNA localization bodies (biomolecular condensates) in oocytes of the frog Xenopus laevis. We find that known methods of (structural and practical) parameter identifiability have certain limitations for FRAP data and for the reaction-diffusion PDEs describing the binding protein dynamics. We therefore propose a pipeline for assessing parameter identifiability and for learning parameter combinations for this model. This method recovers the protein diffusion coefficient in synthetic datasets and predicts and the relationship between binding and unbinding rates in experimental datasets. Ultimately, we would like to use these insights to understand how various protein components interact and bind with RNA in biomolecular condensates.

Figure Caption:

A) Schematic of a stage II Xenopus frog oocyte with RNA granules localizing at the bottom shown in magenta. The black square region is shown magnified on the right, with a cartoon of a FRAP (fluorescence recovery after photobleaching) experimental bleach spot. B) The amount of fluorescence in the bleach spot over time gives rise to the blue experimental FRAP curve (blue). The fit with simulated FRAP data is equally good with two sets of binding/unbinding rate parameters as indicated in panel C). C) Approximation of the likelihood landscape for the non-identifiable parameters.

You can find out more about this research here: https://link.springer.com/article/10.1007/s11538-024-01266-4 

Dimensional Dependence of Binding Kinetics

by Megan Dixon & James Keener 

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Experimentally, the strength of protein-protein interactions is typically measured in solution, and dissociation constants are traditionally reported in units of volume concentration. It is often assumed that these three-dimensional dissociation constants give direct insight into how tightly the same proteins bind when they are membrane-associated. In this article, we explore and counter this notion. We demonstrate mathematically that dissociation constants are highly dependent on dimension. In both discrete and continuous space, we present and analyze stochastic models of binding kinetics in one, two, and three dimensions. Not only do dissociation constants in two dimensions have different units and forms than dissociation constants in three dimensions, the conversion between them is quite complex and requires detailed information. We present a novel formula to convert three-dimensional dissociation constants to two-dimensional dissociation constants. This conversion allows for better understanding of protein interactions on membranes and how to appropriately model them.