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ABOUT CATARINA AMORIMI was a scientist for many years(immunology/autoimmunity) atOxford University until I decidedto move into scientificjournalism and publicunderstanding of science. I amstill an academic at Oxford...Full Bio

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Evolutionary Game Theory: A New Approach For CancerTreatmentBy Catarina Amorim | August 31st 2009 06:06 AM | Print | E-mail | Track Comments

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A new paradigm in the way we look at cancerwith important implications on how we treat itis about to be published in the British Journalof Cancer by Portuguese, Belgian andAmerican researchers. The group use amathematical approach to reveal how - bychanging the dynamics of interaction betweenthe cancer cells and those of the affectedtissue – it is possible to control and even

potentially cure the disease.

Even more interesting is the fact that this new approach can be usedin any number of pathologies where different cells interact. Thework has the potential to revolutionise the way we look into thetreatment of disease and demonstrates the relevance ofmathematical models, not only to improve our understanding ofbiological systems, but also to find more effective ways for dealingwith problems in them.

In cancer, the apparently same disease and/or treatment can have radically distinct outcomes indifferent patients, and while it is easy to understand that the interactions between the cancer cellsand the individual specificities have a major role determining the final outcome, how this happensand, consequently, how to control it is a major issue in medicine and one very far from being clear.

Trying to address the problem, D. Dingli from the Mayo Clinic in Rochester, J.M. Pacheco from theUniversity of Lisbon in Portugal and colleagues used evolutionary game theory – a mathematicalapproach that studies biological entities and predicts their behaviour based on the costs and gains ofthe different participants – to look at the specific case of Multiple Myeloma (MM), an incurable cancerof the antibody-producing cells. The idea was to develop a mathematical model that could describeand help to understand the system/disease behaviour, and consequently learn how to control it whennecessary.

In MM the cancerous cells of the immune system multiply abnormally in the bone marrow occupyingall the available space and stopping other (immune) cells of growing what eventually leads toimmunocompromised patients. But the most visible aspect of the disease is in the bones wheretumours grow leading to fractures, widespread bone thinning (osteoporosis) and generalised pain.MM affects about 750,000 people worldwide and, although quite a few treatments are available, itremains incurable with an average rate of survival of only three years.

In the work justpublished Dingli, Pacheco and colleagues focused on the interactions between MM

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cells and those from the affected tissue - in this case osteoblasts or OB (the cells that form the bone)and osteoclasts or OC (the cells that destroy the bone). In fact, during normal bone homeostasis aconstant balance between bone formation and destruction allows the renewal and maintenance of thehealthy bone, which the MM cells disrupt. The hypothesis was that the key to control cancer cells’growth could be in the manipulation of the dynamics between the three populations.

The research starts with the construction of a matrix/table describing the biochemical interactionsbetween the three populations. In fact, MM cells are known to negatively affect OB growth whilestimulating OC, while OC stimulate both MM cells and OB, and OB stimulate OC but have no effect onMM cells. All populations are considered to have no effect on itself and this appears in the table aszero. The remaining interactions are unknown variables and, as such, are represented by a letter(from “a” to “e” since there are 5 different types of interactions – MM cells affecting OB, MM cellsaffecting OC, etc – when we take out the “no effect”/zeros).

From this table, and using the tools of game theory , a series of equations are deduced and asimplified formula to describe the system is obtained, which – and here is the beauty of the wholething – has only two unknown variables: Beta and delta. Beta is described as the net effect of MM cellson OC, while Delta is the net effect of MM cells on OB cells. Again, the effect of a population on itselfis zero, but this time the effect of OB on OC or vice versa is 1.

With this much simpler formula it is now possible to (almost intuitively) understand (and predict) thebehaviour of the system/disease, which depends on the values of delta and beta determining the finalequilibrium between the three populations.

Their first observations reveal that only when beta is smaller than 1 - so when the effect of MM cellson OC is smaller than that of OB on OC (which in the simplified formula is 1) - are MM cells totallyeradicated and OB:OC balance restored. Unfortunately various experiments suggest that beta smallerthan 1 is extremely rare in nature. But the model also shows that the bigger the beta, the fastershould be tumour progression and bone destruction.

In the same way, the second variable, delta – which is the negative net effect of MM cells on OB – isdemonstrated to be particularly important for disease severity, with the model predicting that, for afixed beta, higher deltas lead to considerable bone loss, even when there is only a small number ofMM cells.

This means that therapies that decrease beta should reduce lesions and disease speed, while thosereducing delta reduce the toxicity of the myeloma, slow the progression of the disease and improvebone mass. Ultimately, both improve the patients’ quality of life, but it is the reduction of beta thatcan effectively stop disease progression (in starkly contrast with current therapies where relapses areinevitable).

And in fact, experiments that blocked some of the proteins produced by MM to stimulate OC (soexperiments were beta is reduced) were shown to stop bone destruction in a mouse model ofmyeloma and slow disease progression in humans. The work now published explains why and how.

In the same way the model can also analyse – something the team does in the article - how changesin different parameters modify the efficiency of current MM treatments, as well as how to improvethem.

The applications are many, but most importantly, the research gives us a new paradigm to look intodisease (including cancer) and its treatment. Current approaches to disease imply, most of the time, ageneralised “attack” on what is, by large, a black box of unknown mechanisms. This new approachprovides a mathematical anatomy of disease that converts complex biochemical interactions into cellfitness, which ultimately affects the populations’ frequency. In this way the model not only helps toexplain how things works but – by giving us beta and delta – provides us with an effective way ofcontrolling disease evolution.

In conclusion, Dingli and colleagues’ new work predicts that by altering the relative fitness of one celltype with respect to the others, one may effectively change disease evolution. In this way, instead oftrying to kill cancer cells, therapies should aim at changing delta and beta allowing the normal cells ofthe body to out-compete and eliminate the malignant cancer cells.

In practical terms, Dingli and Pacheco’s work tells us where we should invest resources in order tocontrol, not only MM, but also cancer in general; the answer is in drugs capable of diminishing the

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fitness of the malignant cells. These have the additional advantage of working by allowing the body torestore its own balance, a much more natural and less toxic approach to treat illness. This isespecially important in cases like cancer, where current treatments can be life-threatening. The factthat the model applies to any number of diseases where different populations of cells interact is anadded bonus.

The work here described for now remains on the scope of trying to change delta and beta directionsbut, once science is capable of determine their real values, Dingli and colleagues’ research is,ultimately, the first step for what Pacheco calls “the holy grail of medicine” - personalised therapy.

Reference: “Cancer phenotype as the outcome of an evolutionary game between normal andmalignant cells”, British Journal of Cancer – September 2009 Online Early Editiondoi:10.1038/sj.bjc.6605288

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evolutionary game theory a new approach for cancer treatment...

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