Using physics, math and models to fight cancer drug resistance

Despite the increasing effectiveness of breast cancer treatments over the last 50 years, tumors often become resistent to the drugs used. While drug combinations could be part of the solution to this problem, their development is very challenging. In this blog post Jorge Zanudo explains how it is possible to combine physical and mathemathical models with clinical and biological data to determine which drug combinations would be most effective in breast cancer therapy.

Each year breast cancer takes the lives of several hundred thousand women and millions of new cases are diagnosed. Although the number of breast cancer deaths has steadily decreased over the last 50 years, the emergence of resistance of the tumor to drug treatments is one of the main obstacles in the ability of clinicians to manage and control breast cancer. In other words, even when clinicians have the best drug to treat a tumor and the tumor responds to the drug treatment, the tumor will often become resistant to the treatment and grow back.

Given that resistance to drug treatment is unavoidable, the question is then how to address it. Lessons from cancer types where curative drug treatments have been identified (e.g. certain leukemia subtypes) suggests that carefully designed drugs combinations are an important part of the solution. Unfortunately, designing drug combinations is challenging because of the large number of possible combinations and because of the complicated molecular network of genes and signaling molecules on which drugs act, particularly targeted drug treatments (drugs that, unlike chemotherapeutic drugs, target specific proteins or molecules, e.g. hormonal therapies like fulvestrant).

Given that resistance to drug treatment is unavoidable, the question is then how to address it.

How do we then design drug combinations? In our work, we provide a methodology to tackle this problem and argue that it requires the combination of physical and mathematical modeling with the clinical and biological knowledge of the underlying molecular network. To be more precise, we do a comprehensive review of the literature of targeted therapies in breast cancer (with a focus on estrogen receptor positive, HER2 negative, PIK3CA-mutant breast cancer) to identify the key molecular players and the interactions among them, build a mathematical model that simulates how biological signals propagate throughout the molecular network, and use it to identify alterations that cause drug resistance and effective drug combinations.

Network model of oncogenic signal transduction in ER+ breast cancer (Zenudo et al. 2017)

The type of mathematical model we use is called a discrete dynamic model and its main characteristic is that the state of each molecular species in the model is described by a discrete value (e.g. active or inactive). This simplified (or coarse-grained) description of the states of the molecular species allows us to include the large number of signaling molecules and genes needed to describe the breast cancer molecular network without making its analysis intractable. This type of model also allows us to focus on how the regulatory interactions of the network result in beneficial or unwanted outcome under the presence of an alteration (e.g. a mutation), without having to know quantitative details such as biochemical parameters and protein abundances.

The model is able to recapitulate how activating or inactivating certain proteins can make breast cancer cells resistant or sensitive to PI3K inhibitors, a type of targeted therapy currently in clinical trials.

The breast cancer model is built based only on information and assumptions about the direct effect of interactions, yet it is able to reproduce network-level outcomes such as the effect of a drug or a mutation on cell death or proliferation. For example, the model is able to recapitulate how activating or inactivating certain proteins can make breast cancer cells resistant or sensitive to PI3K inhibitors, a type of targeted therapy currently in clinical trials. The model also predicts that drugs that downregulate directly or indirectly certain cell death proteins (namely, MCL1 or BCL2) can be combined with PI3K inhibitors to enhance their therapeutic effect.

The model we present, just like any model, needs to be empirically tested and this is what the multi-institution translational research team we are part of is doing. By testing the predicted drug combinations or protein alterations in laboratory cancer models and exploring the genetic information of tumor biopsies of patients treated with PI3K inhibitors, we expect to find confirmations and contradictions of the model’s predictions. These tests will lead us to re-evaluate the model and lead to new predictions, thus completing the experiment/model cycle necessary for any model. The result will be an experimentally tested mathematical model of key components of the breast cancer molecular network that can make robust predictions of the effect of drug combinations and activating/inactivating proteins.

In the future, we expect that experimentally and clinically validated mathematical models of cancer subtypes, similar to the one presented in our work, will become an integral part of identifying effective drug combination therapies that can overcome tumor resistance and lead to treatments that provide a durable control of cancer.

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