Three mechanisms of dark selection for ruxolitinib resistance

Last week I returned from the 6th annual IMO Workshop at the Moffitt Cancer Center in Tampa, Florida. As I’ve sketched in an earlier post, my team worked on understanding ruxolitinib resistance in chronic myelomonocytic leukemia (CMML). We developed a suite of integrated multi-scale models for uncovering how resistance arises in CMML with no apparent strong selective pressures, no changes in tumour burden, and no genetic changes in the clonal architecture of the tumour. On the morning of Friday, November 11th, we were the final group of five to present. Eric Padron shared the clinical background, Andriy Marusyk set up our paradox of resistance, and I sketched six of our mathematical models, the experiments they define, and how we plan to go forward with the $50k pilot grant that was the prize of this competition.

imo2016_participants

You can look through our whole slide deck. But in this post, I will concentrate on the four models that make up the core of our approach. Three models at the level of cells corresponding to different mechanisms of dark selection, and a model at the level of receptors to justify them. The goal is to show that these models lead to qualitatively different dynamics that are sufficiently different that the models could be distinguished between by experiments with realistic levels of noise.

For us, the most striking feature of patient response to ruxolitinib was that various symptoms associated with the disease are drastically improved but, in the bone, Merlevede et al. (2016) observe no change in the tumour burden. Thus, the patient’s eventual relapse — their symptoms returning even though they are still on ruxolitinib — cannot be explained by the traditional model of a susceptible cancer population quickly dying off and leaving the bone to be repopulated by the clonal expansion of few (existing or de novo) resistant mutants.[1]

Hidden Darwinian selection

But drastic total population changes aren’t necessary for evolution. Evolutionary game theorists are more than comfortable thinking about evolution in constant sized populations, and Darwinian evolution itself emerged in the context of a species competing at carrying capacity. As such, the proper null model for us is selection at carrying capacity: a hidden Darwinian selection.

During the week, Nara Yoon and Lin Liu concentrated on building this model of hidden Darwinian selection. They introduced selection through a highly reduced cell turnover. The hypothesis is that as the tumour fills up the bone, it pushes the extra daughter cells out into the peripheral blood; these accumulate in the spleen and cause its drastic enlargement. As therapy takes effects, the division rate of sensitive cells is greatly reduced, enough that much fewer cells are pushed into the periphery, but not low enough that the tumour burden decreases. Fewer excess cells are made, but the made cells are still excess.

With this model of hidden selection, it is possible to recapitulate the dynamics of the spleen shrinking and relapsing. However, there are tensions with our microdynamical knowledge in the bone. Merlevede et al. (2016) observed no changes in the clonal architecture of the tumour, meaning that this hidden selection would have to be epigenetic. They also don’t see large changes in proliferation rate, which would be required for this model. In future experiments, we’d need to measure the variance in proliferation rates carefully to rule out hidden selection.[2]

hiddendarwin

Lamarkian and non-cell autonomous selection

Since we are forced to move from the genetic to the epigenetic level of description, it becomes important to suggest a plausible mechanism for heritable epigenetic effects. We need to find a stochastic ratcheted phenotypic switch among the pathways of the CMML cells. Here, the Koppikar et al. (2012) study of the microdynamical basis of roxlitinib resistance becomes very valuable. In the untreated cancer cell, two JAX2 attach to a receptor, cross-phosphorylate each other, and then active a STAT. Roxlitinib blocks the ability of the JAX2 pair to do this, shutting down the JAX-STAT pathway. Koppikar et al. (2012) showed that some CMML cells find a way around this by having JAX2 heterodimerize with JAX1 or TYK2 instead of another copy of JAX2. Once the cell finds this alternative pathway, it is able to maintain it and start over-producing cytokines as it did before. With enough cells discovering this bypass pathway, global cytokine levels can become elevated again, leading to a return of symptoms.[3]

Mathematically, this allows us to think of the discovery of the heterodimerization bypass as a therapy-induced mutation. The central question becomes if this mutation rate is constant or dependent on the local concentration of cytokines.[4] If it is constant then we have a standard Lamarkian model and if it increases with cytokine concentration then our process is non-cell autonomous. This is represented in the figure below, with the Lamarkian process in the red panel and non-cell autonomous in the blue. On the left of each panel is the CMML cell in drug, with the standard pathway blocked. For the Lamarkian process, their rate of discovery of the heterodimerization bypass is independent of the number of cytokines around them, for the non-cell autonomous it is low with few cytokines and high with many.

processes

These two processes result in drastically different relapse curves. Consider, for example, the figure below. In red is the Lamarkian process, and in blue is the non-cell autonomous. Both have the same average mutation rate, but for the former it is constant through time while the latter scales with the amount of cytokines and thus increases over time. The result is that the relapse curve for blue is much more convex and has a higher variance.

processcurves

With qualitative different curves like the ones above, we can hope to distinguish between the models with the sort of noisy data that one can expect from biological experiments. In particular, we hope to use proximity ligation of JAK-TYK to see which cells have discovered the bypass in bone histologies of mice. By taking bone histologies from mice sacrificed at 10 different time points, we can build up a time series of acquisition of resistance to test our models against.

Overall, our presentation was well received, and the judges awarded us first place and a $50k pilot grant to take this project further. We are currently working out the details of our budget and designing the experiments that will be most informative for discriminating between our models. I look forward to updating you on our progress, dear reader.

imo2016_teamorange_awardphoto

Notes and References

  1. In many ways, our case study of CMML and roxlitinib feels unique and very specific, as if it wouldn’t generalize to other drugs and cancer. It was certainly very different from the treatments/cancers considered by the other four teams during the workshop. We had thought this lack of generality a potential weakness of our system. However, after we were finished the presentations, Andriy raised a good suggestion: does our model system seem so unique due to the drug approval process rather than biology?

    One of the central metrics for approval of new cancer drugs is the effect on tumour burden. If there is not a large reduction in tumour burden then the drug is unlikely to be approved. Since resistance is usually studied for approved (or near the end of the pipeline) drugs, most cases end up following the traditional trajectory of the sudden death of a sensitive population (the approval criteria) followed by the recovery of the population from small numbers by a resistant clonal expansion. Thus, the approval process selects for drugs that don’t follow our alternative non-traditional process of resistance.

    However, reduction in tumour burden is not the only metric we could use for drug approval. And in the future, especially as more effort is devoted to prevention and management of tumours rather than an exclusive focus on ‘cures’, it is foreseeable that more drugs will be approved on measures other than the reduction in tumour burden. If resistance arises to these therapies — as it has for roxlitinib — then it is going to be of a non-traditional type, and our research would provide the groundwork for understanding this process. Even if our systems seems unusual now, it might be due to the approval process. It might become a more commonly encountered case as the approval criteria develop.

  2. Finally, there might be a pathway-based intuition against the null model. Shutting down the JAX-STAT pathway by treatment leads to less production of STAT, but STAT is usually associated with cell survival. With less production of STAT in the sensitive cells, it doesn’t necessarily make sense for the turnover to decrease.
  3. One hypothesis is that this JAX-TYK bypass is heritable. This could be achieved, for example, by the up-regulation of TYK2 following successful discovery and then Poisson variation in the inheritance of the protein among the two daughter cells. Receptors can be divided in a similar way, probably even more uniformly due to the even division of the cytoplasm. And since daughter cells occupy area close to where their mother cell used to be, local extracellular cytokine concentration are also inherited.
  4. For the dependence of the JAX-TYK bypass discovery rate on the levels of cytokines in the non-cell autonomous model, it is again good to turn to models at the levels of receptors. Depending on the sort of feedback loops possible within the cell’s internal signaling, it is possible to get different functional forms for the mutation rate. To avoid testing against any possible mutation function, it is best to consider the functional form that comes out of biologically reasonable assumptions of the cellular pathways. We started working on this during the workshop, with Robert Vander Velde throwing together a Gellispie simulation of some candidate pathways. However, there is a lot still to be done here.

    Depending on the sort of data available to us, it might be worth considering adapting recent techniques like Lever et al. (2016) for inferring the form of the minimal signaling pathway from standard molecular and systems biology experiments.

Merlevede, J., Droin, N., Qin, T., Meldi, K., Yoshida, K., Morabito, M., Chautard, E., Auboeuf, D., Fenaux, P., Braun, T., Itzykson, R., de Botton, S., Quesnel, B., Commes, T., Jourdan, E., Vainchenker, W., Bernard, O., Pata-Merci, N., Solier, S., Gayevskiy, V., Dinger, M.E., Cowley, M.J., Selimoglu-Buet, D., Meyer, V., Artiguenave, F., Deleuze, J.F., Preudhomme, C., Stratton, M.R., Alexandrov, L.B., Padron, E., Ogawa, S., Koscielny, S., Figueroa, M., & Solary, E. (2016). Mutation allele burden remains unchanged in chronic myelomonocytic leukaemia responding to hypomethylating agents. Nature Communications, 7 PMID: 26908133

Koppikar, P., Bhagwat, N., Kilpivaara, O., Manshouri, T., Adli, M., Hricik, T., … & Leung, L. (2012). Heterodimeric JAK-STAT activation as a mechanism of persistence to JAK2 inhibitor therapy. Nature, 489(7414), 155-159.

Lever, M., Lim, H. S., Kruger, P., Nguyen, J., Trendel, N., Abu-Shah, E., … & Dushek, O. (2016). Architecture of a minimal signaling pathway explains the T-cell response to a 1 million-fold variation in antigen affinity and dose. Proceedings of the National Academy of Sciences, 201608820.

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About Artem Kaznatcheev
From the Department of Computer Science at Oxford University and Department of Translational Hematology & Oncology Research at Cleveland Clinic, I marvel at the world through algorithmic lenses. My mind is drawn to evolutionary dynamics, theoretical computer science, mathematical oncology, computational learning theory, and philosophy of science. Previously I was at the Department of Integrated Mathematical Oncology at Moffitt Cancer Center, and the School of Computer Science and Department of Psychology at McGill University. In a past life, I worried about quantum queries at the Institute for Quantum Computing and Department of Combinatorics & Optimization at University of Waterloo and as a visitor to the Centre for Quantum Technologies at National University of Singapore. Meander with me on Google+ and Twitter.

4 Responses to Three mechanisms of dark selection for ruxolitinib resistance

  1. Rob Noble says:

    Interesting stuff, and congratulations for winning the funding! One quick question: is JAX synonymous with JAK (Janus kinase)? If so, why the ‘X’?

    • You are absolutely correct. I keep pronouncing JAK as ‘JAX’ in my head and made that error while typing up this post (along with some other errors that I should correct in a big comment or follow up post when I get the time). Sorry for that.

      Thank you. Too bad you couldn’t make it to the workshop this year, but you were still present in person through references to your Box-Einstein surface. Next time!

      • Rob Noble says:

        Easily done. Incidentally, Wikipedia explains an interesting etymology:

        ‘They were initially named “just another kinase” 1 and 2 … but were ultimately published as “Janus kinase”. The name is taken from the two-faced Roman god of beginnings and endings, Janus, because the JAKs possess two near-identical phosphate-transferring domains. One domain exhibits the kinase activity, while the other negatively regulates the kinase activity of the first.’

        See also etymology (or backronyms) of JAVA and Yahoo!.

  2. Pingback: Cataloging a year of cancer blogging: double goods, measuring games & resistance | Theory, Evolution, and Games Group

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