Math can help uncover cancer's secrets | Irina Kareva

Summary

The speaker explains their role as a translator between biology and mathematics, using mathematical modeling to understand complex biological systems. They illustrate how predator-prey equations can describe both ecological interactions, like foxes and rabbits, and cellular dynamics, such as immune cells targeting cancer. By identifying key elements, formulating assumptions, and translating them into equations, modelers can simulate interventions, test hypotheses, and uncover gaps in knowledge. The approach highlights the power of mathematical models to explore ecosystems like tumors, optimize therapies, and advance personalized medicine—all safely, rigorously, and cost-effectively—ultimately aiming to improve human health and save lives.

Takeaways

• 😀 Mathematical modeling bridges biology and mathematics, helping translate biological mechanisms into mathematical equations.
• 🧑‍🔬 Modeling focuses on what biological elements *do* (interactions and behaviors), not what they *are* (e.g., cell types, species).
• 🔬 Mathematical models can describe complex biological processes, such as predator-prey interactions in both ecology and cancer research.
• 🦊 Foxes and immune cells share a predator-prey relationship with rabbits and cancer cells, respectively, which can be modeled mathematically.
• 🧫 Tumor microenvironment modeling reveals that nutrient competition (e.g., glucose) affects immune cell function and cancer progression.
• 🌱 Cancer can be viewed as an ecosystem, where different cell populations compete and interact for resources and space.
• ⚖️ Targeting the tumor microenvironment (rather than the cancer directly) may prove to be a more effective therapeutic approach.
• 💻 Mathematical modeling provides a rigorous framework for testing biological hypotheses, simulating interventions, and filling knowledge gaps.
• ⏱️ Models can zoom in on various timescales (seconds to years), allowing simulations of rapid or slow processes that may be difficult to observe experimentally.
• 💡 The collaboration between mathematicians and biologists is key, requiring translation from one domain to another for successful outcomes.
• 🧬 Mathematical modeling is essential for advancing personalized medicine by providing tailored predictions for individual health and therapeutic strategies.

Q & A

What is the main role of a mathematical modeler in biology according to the transcript?

A mathematical modeler acts as a translator between biology and mathematics, formulating biological mechanisms as mathematical equations, analyzing them, and then interpreting the results back into biological understanding.

What is the first step in developing a mathematical model of a biological system?

The first step is to identify the key elements that drive the behavior of the biological system over time.

How are assumptions used in mathematical modeling?

Assumptions are formulated about how elements interact with each other and their environment, and these assumptions are then translated into mathematical equations.

What type of equations does the speaker primarily use to model biological mechanisms?

The speaker primarily uses systems of differential equations to describe dynamic interactions within biological mechanisms.

How can predator-prey models be applied in biology beyond ecological systems?

Predator-prey models can describe interactions between immune cells and cancer cells, where immune cells act as predators and cancer cells as prey, using the same mathematical framework as for foxes and rabbits.

What role does resource competition play in tumor modeling?

Resource competition, such as for glucose, can influence the ability of immune cells to combat cancer cells, and modeling these shared resources helps understand tumor-immune dynamics and potential therapeutic interventions.

Why is mathematical modeling useful for simulating biological interventions?

It allows researchers to test hypotheses, simulate therapeutic interventions, and predict outcomes safely, efficiently, and at low cost without directly experimenting on living organisms.

What happens if a model’s predictions do not match experimental observations?

Discrepancies indicate that some assumptions are incorrect, allowing modelers to identify gaps in understanding and refine the model iteratively using both theoretical and experimental approaches.

How does mathematical modeling handle processes that occur on different timescales?

Mathematical models can zoom in on any subsystem and simulate effects over any timescale, from seconds to years, even when experimental measurements are difficult or impossible.

What is the ultimate goal of mathematical modeling in the context of the transcript?

The ultimate goal is to advance research, reduce the cost of experimentation, guide drug development, and ultimately save lives by improving understanding of biological systems and enabling personalized medicine.

Why does the speaker emphasize thinking about 'what things do' rather than 'what things are'?

Focusing on behaviors and interactions allows modelers to formalize relationships mathematically, which is crucial for predicting system dynamics and understanding underlying mechanisms.

How does the concept of ecosystems relate to cancer modeling?

Cancer can be modeled as an ecosystem where heterogeneous cell populations compete for resources, interact with predators like immune cells, and migrate, which allows researchers to target the tumor microenvironment strategically.