This is the summary of my paper "From hyperinsulinemia to cancer progression: how diminishing glucose storage capacity fuels insulin resistance." Aging and Cancer 5.3 (2024): 51-61; https://onlinelibrary.wiley.com/doi/full/10.1002/aac2.12073
I really enjoyed working on this project because it made me go back to the fundamentals of metabolism, learn about Kraft patterns and find ways to capture the emergence of insulin resistance and subsequent T2D. And then connect the whole picture to how hidden hyperinsulinemia can accelerate cancer progression.
It also was a gateway for the subsequent work on Alzheimer's disease, and thinking through emergence of dementia through the lens of metabolism.
And also, it was really fun.
This was a result of the most recent collaboration we had with my father Georgy Karev.
Two or three years ago I asked him what he's thinking about these days (as we often ask each other), and he said that he was thinking about group size selection, and the question of "what is the optimal group size". That led to a discussion of the meaning of "optimal", the mathematical formulation through the lens of game theory and then me asking "what would happen to group size selection if an element in the payoff matrix were not fixed but a function".
That overlaid with my thoughts on interplay between metabolism, emergence of T2D (see the paper on hyperinsulinemia and cancer progression) and looking at neurons in terms of group size selection, with the hypothesis that smaller groups would correspond to cognitive decline (and if the element of the payoff matrix depends on glucose concentration, could that - for T2D - eventually tip the scales from healthy more connected groups of neurons to smaller less connected ones?)
Long story slightly less long, this is the recorded summary of the resulting paper: Kareva, Irina, and Georgiy Karev. "Energy Constraints and Neural Strategy Transitions in Alzheimer's: A Game-Theoretic Model." bioRxiv (2025): 2025-05. https://www.biorxiv.org/content/10.1101/2025.05.24.655918v1
A more detailed deep dive into the biology of Alzheimer's is in the following paper (with the corresponding recording of the summary given on this page): Kareva, Irina. "The many roads to dementia: a systems view of Alzheimer's disease." arXiv preprint arXiv:2504.05441 (2025). https://arxiv.org/abs/2504.05441
And now I finally got these dementia papers out of my head. At least for now!
This is a summary of my deep dive into understanding dementia and Alzheimer's disease in particular - the background research that I ended up doing for another mathematical modeling project. I kind of went down a rabbit hole with this one over the last few years and I'm glad I did - at least I think I have a better understanding of the different types of dementia, the evidence for different hypotheses about the origin of dementia, and am comfortable with the conclusions about what I understand to be the most likely initiating events.
This paper: Kareva, Irina. "The many roads to dementia: a systems view of Alzheimer's disease." arXiv preprint arXiv:2504.05441 (2025). https://arxiv.org/abs/2504.05441
The paper, for which this was really the background research: Kareva and Karev, "Energy Constraints and Neural Strategy Transitions in Alzheimer's: A Game-Theoretic Model". https://www.biorxiv.org/content/10.1101/2025.05.24.655918v1
This is a summary of our paper with Jana Gevertz "Minimally Sufficient Experimental Design using Identifiability Analysis" (https://www.nature.com/articles/s41540-023-00325-1)
I love this project for many reasons but especially because it
1) provides a way to estimate parameters that you cannot feasibly measure experimentally
2) highlights that there is no "right" model, and that the level of detail of the model should be driven by the data. That is, the structure of a model, even for the same question, can conceivably be different but equally useful depending on the data available to identifiably parametrize it. Take that, giant models! :)
This is more of a thinking detour work on time perception in a dying brain that we did with my father Georgy Karev almost a decade ago - I think this was one of our first collaborations.
In this recording I'm giving a summary of the time perception portion of this paper: Karev, Georgy P., and I. Kareva. "Mathematical modeling of extinction of inhomogeneous populations." Bulletin of mathematical biology 78 (2016): 834-858.
A biology-centric (as opposed to math-centric) version is here: Kareva and Karev, “Possible mechanisms underlying time perception: decoupling internal and external time” (doi.org/10.48550/arXiv.2505.07712)
It was very interesting to learn about different models of time perception and to propose a mathematical formalization of how external and internal time perception can be decoupled. And working professionally with my dad is always a treat.
This is a summary of my 2022 paper "Understanding Metabolic Alterations in Cancer Cachexia through the Lens of Exercise Physiology" (PMID: 35954163; https://www.mdpi.com/2073-4409/11/15/2317)
Here I propose that systemic cancer creates a chronic resource drain on the body that results in the same metabolic adaptations and patterns of nutrient consumption that are supposed to be transient during strenuous physical activity.
I evaluate this hypothesis through modeling a very interesting set of data published by San Millan and Brooks (2018), where they describe patterns of nutrient metabolism as a function of increase in exercise intensity, and then I interpret it using the framework of ventilatory thresholds. Then I simulate the predicted pattern of relative nutrient metabolism if the simulated effort "got stuck" between the thresholds, and propose that this is consistent with what we observe in cachexia.
This is a theoretical model, so if you have any experiment supporting or disproving this hypothesis, reach out, I'd love to know more!
This is a summary of our paper with Jana Gevertz "Guiding model-driven combination dose selection using multi-objective synergy optimization" (PMID: 37415306; https://ascpt.onlinelibrary.wiley.com/doi/10.1002/psp4.12997).
Here we focus on the question of optimizing dose/schedule for two pre-selected drugs (for an amazing method on how to select those drugs in the first place, check the MuSyc method at musyc.lolab.xyz/about#overview)
We review existing metrics for quantifying synergy and show that they can be wildly inconsistent with what they predict as a synergistic vs additive vs antagonistic combination.
We then propose that this can be overcome using multi-objective optimization and the concept of Pareto optimality, and apply this approach to a published combination of pembrolizumab and bevacizumab.
We then show what you need to apply this to your own combinations. So if you run experiments where you chose doses using this approach, please, let us know!
This is a summary of our paper with Joel Brown, "Estrogen as an essential resource and the coexistence of ER+ and ER- cancer cells". (https://www.frontiersin.org/articles/10.3389/fevo.2021.673082/full)
It provides a summary of the key ideas and results:
- essential resources and Liebig's law of the minimum
- evolutionary steering through resource manipulation (with applications of our HKV method for modeling evolution of heterogeneous populations)
- a discussion of some issues with how ER+ vs ER- tumors are classified
This is a summary of the key ideas of this paper that we did with my dad Georgy Karev: "Linear rather than exponential decay: a mathematical model and underlying mechanisms" (https://arxiv.org/ftp/arxiv/papers/2004/2004.05726.pdf).
It talks about how a sub-exponential power law model can capture linear rather than exponential decay observed in red blood cells, and how this model in turn can be derived within the frameworks of frequency-dependent model of population extinction if there exists heterogeneity with respect to mortality rates such that their initial distribution is the Gamma distribution.
It's a lot of words and some math, but it's actually really cool :) And it allows capturing the decay of red blood cells using a simple ODE, which was really the goal of the whole exercise.