Equations against cancer: Using math to predict a tumor's path

Hassan Fathallah-Shaykh, M.D., Ph.D., believes that math can transform medicine, and he has the numbers to prove it.

In the clinic, this UAB neurologist specializes in treating brain tumors. In his lab at the Comprehensive Cancer Center, Fathallah-Shaykh, who is also a professor of mathematics at UAB, wields equations as well as petri dishes. His mathematical models of cancer behavior are offering new insights on tumor growth. Eventually, they could be used to personalize treatment based on the unique characteristics of each patient’s cancer cells and anatomy.

Fathallah-Shaykh is one of a growing number of researchers worldwide exploring the field of mathematical biology, which “uses mathematical tools to generate models of biological problems,” he said. Building mathematical models based on the current understanding of a disease, for example, allows researchers to “test whether the assumptions are accurate,” Fathallah-Shaykh said.

Hassan Fathallah-Shaykh

Models can also be used “to test a treatment strategy, understand why it fails or works, and optimize therapy,” he added. The results of these tests can also generate new insights and hypotheses that can be investigated in the laboratory. “None of these goals can be achieved by traditional methods,” Fathallah-Shaykh said.

Model Behavior

Working with colleagues at the University of Bordeaux, and UAB graduate student Elizabeth Scribner, Fathallah-Shaykh has created an elegant model of the aggressive brain cancer glioblastoma multiforme (GBM). It produces simulations on the scale of clinical MRI scans, so that its predictions can be tested directly against patient data. In a paper published on Dec. 15 in PLOS ONE, the researchers demonstrated that their model can reproduce the typical GBM growth patterns seen on patient scans. They also revealed its value as a research tool.

The model predicted a previously unknown pattern of tumor growth in patients with recurrent GBM treated with the anti-angiogenesis drug bevacizumab. This growth, powered by a cycle of proliferation and brain invasion, is characterized by an expanding area of invasive cells and dead cells known as necrosis, the researchers say. A subsequent search of 70 patient MRI scans by the researchers turned up the same pattern in 11 cases.

“We hope to tailor radiation therapy, chemotherapy and other treatments based on a personalized model of a patient’s tumor.”

That pattern explains the disappointing results of recent Phase III clinical trials of anti-angiogenesis therapies against GBM, the researchers say. Anti-angiogenesis drugs attempt to kill tumors by preventing them from growing new blood vessels. But the model demonstrated how GBM cells can flee from the oxygen-depleted treatment area — and quickly begin expanding again as soon as therapy stops or the tumor becomes resistant to the drugs. (For more on the model and these findings, see “SimTumor,” below.)

“We’ve shown that we can predict new insights on cancer behavior,” Fathallah-Shaykh said. The results have already spurred Fathallah-Shaykh to pursue new therapies in his lab to limit tumor mobility. Ultimately, the researchers hope to use their model to personalize therapy to the unique characteristics of a patient’s tumor. They could do that by analyzing the existing growth pattern of a tumor and building that into the model’s parameters. Then they could simulate its future behavior on a virtual MRI slice that reproduces the unique anatomy of the patient’s brain. “We hope to tailor radiation therapy, chemotherapy and other treatments based on a personalized model of a patient’s tumor,” said Fathallah-Shaykh.

Advancing Mathematical Biology Research Hassan Fathallah-Shaykh, M.D., Ph.D., is a perfect ambassador for the highly interdisciplinary field of mathematical biology. In addition to his faculty positions in the departments of Neurology, Mathematics and Cell, Developmental and Integrative Biology, he holds an appointment in the School of Engineering. That breadth of expertise has enabled him to establish collaborations with researchers at UAB and at several international universities, and he is working to interest more colleagues in mathematical biology. This spring, Fathallah-Shaykh helped organize a symposium on the topic as part of the College of Arts and Sciences’ Interdisciplinary Innovation Forum series. The meeting attracted some of the mathematical biology’s most famous names. Meanwhile, he is helping to attract new talent to the discipline by teaching undergraduate and graduate courses on Mathematical Biology in the math department. “It is quite clear that the next great advances in medicine cannot happen without math,” Fathallah-Shaykh said. “These are exciting times.”

From Flies to Colon Cancer

Since he joined the UAB faculty in 2008, Fathallah-Shaykh has been developing ever more advanced models to predict the behavior of biological networks. He began by building a model of the molecular clock in a fruit fly’s brain. Despite the fly’s tiny size, it’s a challenging puzzle. The clock is a tangled web of positive and negative feedback loops, with five different genes producing proteins that inhibit and activate one another (as well as themselves, in some cases) in a regular cycle.

First, Fathallah-Shaykh and his collaborators “showed we can replicate everything the clock is known to do,” he said. Then they proved it was a useful research tool, answering a perplexing question about the fruit-fly gene Clockwork Orange that had stumped biologists for years.

The researchers next adapted their model to track the developing neural networks in fruit-fly embryos. To do this, they utilized the Kalman filter, a mathematical technique to analyze and predict changes that helps track planes in flight. Now, “we’re using the model to study molecular networks in colon cancer,” Fathallah-Shaykh said.

Coping with an Information Explosion

Fathallah-Shaykh has always been fascinated with math. “It’s like a symphony; it’s beautiful,” he said. “But it’s also very applicable.” He cemented the connection between medicine and math as a neurologist at Rush University Medical Center in Chicago when he enrolled in a doctoral program in mathematics at the nearby University of Illinois–Chicago. “I would go to class in between patients,” he said.

Math is essential to making progress against the toughest questions in medicine, Fathallah-Shaykh contends. To illustrate the problems that researchers face, he points to a chart of all the known molecular pathways involved in Alzheimer’s disease. It’s a mass of interlocking loops and tangles that fills an entire page. Researchers specialize in tiny sections of this wiring diagram, but understanding how it all works together is another problem entirely. Even worse, these networks are intertwined in such a way that multiple paths can lead to the same destination. That may help explain why treatments that work beautifully in isolated cell lines in a lab so often fail when they encounter the complex networks of the body.

There’s another wrinkle. “Cells migrate, they communicate, they interact with one another over time,” said Fathallah-Shaykh. The waves of mutations, which are a hallmark of cancer, make the problem particularly complex, he noted. “Whole pathways are deleted and new connections start turning up.” It’s a perfect example of a nonlinear dynamic system, like the weather or the stock market, in which slight changes in one parameter can lead to wildly diverging outcomes.

The good news, said Fathallah-Shaykh, is that “mathematics has very rich tools” to model just these types of systems, as he has demonstrated with his cancer simulations. But this work has another exciting element for Fathallah-Shaykh as a mathematician: It opens new horizons in math theory. “Equations have already been developed from biological problems,” he said, “and there is very strong evidence that they will produce spectacular advances in mathematics.”

SimTumor

At the heart of Hassan Fathallah-Shaykh’s new mathematical model of glioblastoma multiforme (GBM) are 10 partial differential equations. Here’s how it works — and what it has revealed about GBM behavior.

Formula 10

Equations track each of four different cell types, with unique rules of behavior.

Proliferative GBM cells (P), which make up the bulk of the tumor, divide but don’t move.

Invasive GBM cells (I), found on the fringes of the tumor, move but don’t divide.

Healthy brain cells (B) neither divide nor move, although they are displaced by the growing tumor.

Cells in the center of the tumor, cut off from nourishing blood vessels, are starved of oxygen (hypoxia) and die, becoming necrotic cells (N).

The remaining six equations track angiogenesis (new blood vessel formation), oxygen levels, and rates of necrosis and cell division.

Built for Speed

Fathallah-Shaykh’s first GBM model, published in August 2014 in the Bulletin of Mathematical Biology, consisted of many more equations. It required a supercomputer, and several days, to run. The model published in PLOS ONE can run in 50 seconds on a typical desktop computer.

And They’re Off!

The simulation begins with a tiny clump of tumor cells surrounded by healthy brain. As the program continues over several virtual weeks, this mass expands in the characteristic manner seen on patient MRIs, with a dark region of necrotic cells in the center, surrounded by a large group of proliferative cells and an outer rim of invasive cells.

Grow or Go

The model’s main assumption is that proliferative cells can turn into invasive cells in hypoxic conditions. This is in keeping with the “grow or go” hypothesis of GBM behavior, which says that low oxygen levels spur GBM cells to flee the dying core of the tumor. When these new invasive cells reach healthy, oxygenated areas of brain, they switch back into proliferative mode and start growing again.

How GBM Escapes Anti-Angiogenesis Therapy

As tumors grow, cells at the core lose contact with nourishing blood vessels and die.

To get around this problem, tumors release VEGF (vascular endothelial growth factor), which induces the body to create new blood vessels (a process known as angiogenesis). In fact, the well-known Folkman Hypothesis states that tumors must be able to induce blood vessel growth in order to keep growing.

Clinicians had high hopes that anti-angiogenesis medications such as bevacizumab (Avastin), could keep tumor growth in check. But two high-profile Phase III clinical trials, which released results in early 2014, found that bevacizumab therapy did not prolong overall survival in patients with recurrent GBM, although it did extend progression-free survival and patient quality of life.

Fathallah-Shaykh’s model, programmed to simulate the effects of anti-angiogenesis therapy, reveals an explanation for this “unusual clinical finding.” When bevacizumab therapy causes oxygen levels to drop, proliferative cells turn into invasive cells and flee the scene. When they reach an area with sufficient oxygen, they convert back into proliferative cells and begin a new cycle of growth. This sets up the tumor for rapid “rebound” growth as soon as it becomes resistant to bevacizumab or therapy is discontinued. That explains why patients treated with bevacizumab in the recent trials didn’t experience any increase in overall survival rates over those who were not treated.

Toward New Treatment Approaches

The model underlines the importance of better understanding the molecular mechanisms of brain cell invasion, particularly the active transport of invasive cells toward healthy brain regions, says Fathallah-Shaykh.

There are currently no available biomarkers to identify the quantity of invasive cells in a patient’s tumor. But finding such a biomarker, and drugs that can target these cells to prevent tumor migration, is a current research focus in Fathallah-Shaykh’s lab. “If we’re going to kill these tumors,” he said, “we have to target the cells that are invading.”

Exploring new frontiers in personalized cancer care

Personalized medicine is turning medical care on its head, and cancer treatment is at the forefront of that revolution. The UAB Comprehensive Cancer Center’s 17th Annual Research Retreat introduced this cutting-edge work to an audience of nearly 400 clinicians and researchers. The topic was timely after this summer’s announcement of major initiatives in genomics and personalized medicine at UAB, including a research consortium between the Cancer Center and Huntsville’s HudsonAlpha Institute for Biotechnology.

“Personalized medicine is the future of cancer care,” noted Eddy Yang, M.D., Ph.D., associate professor in the UAB Department of Radiation Oncology, who organized this year’s symposium. “This is certainly a glimpse of what is to come for the Cancer Center and UAB as a whole.”

The Future: Cancer as a Chronic Disease

“Oncology has been a first mover for personalized medicine,” said invited speaker Mark Boguski, M.D., Ph.D., founder of Genome Health Solutions and a faculty member at Harvard Medical School.

Boguski shared his remarkable vision. With the use of personalized medicine, he said, we can now begin to reimagine cancer as a manageable chronic disease. Subsequent speakers amplified that theme, describing advances, challenges and roadblocks to delivering personalized cancer care to patients across the United States.

Boguski began with three patient case histories.

The first was a patient in 2010 with adenocarcinoma that was EGFR-positive (that is, it contained mutations that activated the EGFR pathway). When treatment with the usual drug failed, genomic and transcriptomic analysis showed why — metastases from the original cancer were no longer EGFR-positive. But biomarkers on those cancer cells successfully identified a target for a different drug that was effective.

The second case was a metastatic squamous cell carcinoma. Genomic analysis showed, surprisingly, that it could be treated with a hematological cancer drug.

“You wouldn’t guess to use that on a solid tumor,” Boguski said.

Similarly, in a case of advanced lymphoblastic leukemia, genomic analysis unexpectedly pointed to using a renal cell carcinoma drug. With this sea change in the way that oncologists can make their treatment decisions, cancer patients are beginning to ask that their genomes be analyzed, Boguski said.

The UAB Cancer Center’s Molecular Tumor Board, initiated last year, identifies patients who could benefit from DNA sequencing of their tumors, said Yang. These tests, usually conducted in patients with rare tumors or tumors that do not respond to typical treatment, can identify off-label uses for cancer drugs. For example, BRAF inhibitors, which are approved for melanoma, have been used to treat patients with other tumor types that nevertheless harbor the BRAF V600E mutation, Yang said. In another important consideration, “treating physicians have been successful in getting third-party payers to pay for these drugs outside the ‘approved’ indications using the profiling results,” he explained.

Cancer Center Honors Research Excellence In addition to talks by leading investigators, the Cancer Center’s research retreat also features the work of a new generation of cancer researchers. Graduate students, postdoctoral fellows and junior faculty members took part in the annual poster competition; the 131 presentations emphasize the breadth of studies ongoing in the Cancer Center, from cancer prevention to bioinformatics. See the award winners here.

But roadblocks prevent the widespread delivery of such personalized, targeted care, Boguski noted in his talk, because:

• 80 percent of cancer care is delivered away from the top 50 cancer centers.
• Most doctors suffer from a knowledge gap; they need accelerated genome training to understand the top molecular biomarkers and how these markers can guide patient therapy.
• Pathologists — who are a key link to alter the delivery of care — need to know not only tissue pathology but also how to test for and report the molecular drivers of cancer.

Genomics Identifies Actionable Targets

Mark Kris, M.D., an attending physician at the Memorial Sloan Kettering Cancer Center and professor at the Weill Cornell Medical College, showed how genomics and personalized care can be harnessed to improve lung cancer survival.

Working with 11 cancer centers, Kris and colleagues tested 1,000 patients who had stage IV lung cancer. While tissue pathology confirmed adenocarcinoma, the cancers also underwent mutational analysis to probe for oncogenic drivers, and these findings were shared with physicians.

Two-thirds of the patients had at least one of 10 known oncogenic drivers. These drivers are “actionable targets” that helped to guide treatment choices, leading to increased median survival for these advanced cancer patients.

The French medical system, Kris noted, has provided genotyping to every lung cancer patient since 2011, at a rate of 20,000 patients a year. This equity of access to innovation does not exist in the United States, Kris said, even though the National Comprehensive Cancer Network clinical practice guidelines for non-small-cell lung cancer already list a set of molecular drivers that should be looked to to classify and guide treatment.

Needed: A New Kind of Trial

Another roadblock is the need for new ways to perform clinical trials of investigational drugs, said Donald Berry, Ph.D., professor of biostatistics at the M.D. Anderson Cancer Center and a co-founder of Berry Consultants.

Berry described how the use of Bayesian biostatistics in an adaptive platform trial can lower the numbers of patients needed for the trial, while simultaneously investigating multiple drugs and targets. He focused on a current study, I-SPY2, which is investigating treatments for breast cancer. (Berry noted that UAB is one of the largest contributors of patients to the trial.)

Data obtained during trials such as I-SPY2 are used to guide changes in the studies midstream, Berry explained. The result is nimble, lean studies that yield a more dependable estimate of the chance that a particular drug will succeed in its subsequent Phase III trial. Such information is crucial, given the cost and the failure rates of conventional Phase III trials.

Predicting Patient Response With Avatars

The final outside speaker, Paul Haluska Jr., M.D., Ph.D., associate professor of oncology at the Mayo Clinic, described an “Ovarian Avatar” model to personalize ovarian cancer treatment. The avatar is created by implanting live cancer tissue from the cancer patient into a mouse within two hours of surgery.

Haluska shared several definitions involved in this model:
• “Xenograft” is a tumor taken from one species and implanted in another;
• “Orthotopic” means the implant is placed in the natural body location for that type of tumor;
• “Patient-derived Xenograft” is a direct implant from the patient into the other species, without any intermediate in vitro growth or manipulation; and
• “Avatar” is thus an orthotopic, treatment-naïve, patient-derived xenograft.

Mayo implanted its first model in March 2010. Through this September, 404 models have been injected and 294 of them successfully engrafted. The avatar responses to a drug, Haluska said, appeared to mirror the patient responses to treatment with the same drug, and the avatars are being used for drug development.

The next step will be to actually use a particular patient’s avatar to direct her therapy. “It will be the first ovarian cancer with xenograft-directed therapy,” Haluska said. “The best predictor of response is response.”

Oncogenic Drivers and Racial Disparities

UAB has its own xenografts that are derived from glioblastoma multiforme tumors, said Christopher Willey, M.D., Ph.D., an associate professor in the Department of Radiation Oncology and director of the UAB Kinome Core (pronounced “k-eye-nome”). But these personal avatars have a problem — they take too much time to establish compared to the rapid and fatal course of glioblastomas. So Willey hopes instead to use “kinomic” profiles of established avatars from other patients to guide the treatment for a new patient; glioblastoma tissue removed from the new patient during surgery can quickly be kinomically profiled.

Kinomics uses substrate arrays to identify which kinase enzymes — often found to be key oncogenic drivers — are active in the cancer cells. This can help select among about 30 cancer chemotherapeutic agents that target kinases.

The other UAB speaker, Phillip Buckhaults, Ph.D., associate professor in the UAB Division of Hematology and Oncology, described his search for genetic mechanisms that lead to earlier onset and higher incidence of breast and colon cancers in African-Americans, as compared to Caucasian-Americans. His trail began with the discovery of a point-mutant variant of the TP53 tumor suppressor gene in African-Americans, and it has led to the variant’s effect on the PRDM1 chromatin-silencing gene.

Translating research insights from the laboratory to the clinic is a major focus of the UAB-HudsonAlpha cancer consortium, noted Cancer Center director Edward Partridge, M.D. “We’re not at the point yet where we can routinely apply genomics information from the tumor to treatment; but we’re clearly learning, and learning at a rapid pace,” Partridge said. “The goal of the consortium is to accelerate that, and we’re excited about what it means for the care we can bring to our patients.”

— Jeff Hansen

Unique gene machine opens new pathways to personalized medicine

In the UAB Nanostring Laboratory, researchers such as Eddy Yang are taking advantage of the nCounter Analysis System's novel digital profiling technology to examine specific signaling pathways in cancer and other diseases. That work could lead to new insights to improve diagnosis and treatment decisions.

Cancer is a devious enemy. In lab tests, researchers have identified plenty of exciting genetic targets — weak links that should allow them to destroy tumors by halting production of a crucial enzyme, for example, or blocking a signal the cell needs to keep growing. All too often, however, these promising findings fizzle out in further testing.

That is because cancer cells can take advantage of multiple, redundant signaling pathways to avoid areas that come under attack. “Tumor cells will just figure out a way to bypass them,” said Eddy Yang, M.D., Ph.D., an associate scientist in the UAB Comprehensive Cancer Center and associate professor in the UAB Department of Radiation Oncology.

Mapping out the complex pathways involved in cancer and other diseases is a crucial step in finding better treatments — and identifying the best treatments for individual patients. If you know all the routes a tumor can use to evade attack, you can find therapies — or combinations of therapies — to block them all. Indeed, tracing cancer-related signaling pathways, and finding ways to use these insights to improve diagnosis and treatment decisions, is a major focus of research at the Cancer Center, Yang says. But spotting these pathways amid the information overload of a genomewide screening test can be extremely complex and time-consuming.

nCounter: In Focus 48-800 genes can be studied simultaneously Applications include gene expression analysis, microRNA and lncRNA analysis, copy number variation analysis, ChIP-String analysis and leukemia fusion gene analysis The system's novel digital technology is based on direct multiplexed quantification of nucleic acids; it provides highly reproducible data over 5 logs of dynamic range Preconstructed panels include: PanCancer Pathways Panel, Human Kinase Panel, Human Immunology Panel, microRNA Panels, Cancer Copy Number Variation Assay See the UAB Nanostring Laboratory site for more information and a schedule of fees and services

Targeting Crucial Pathways

Now, UAB researchers and clinicians have a new tool to investigate signaling pathways — and to translate their discoveries into clinic-ready diagnostic tests. The unique nCounter Analysis System, produced by Nanostring Laboratories, “is a platform to measure the expression of genes in a targeted manner,” Yang said. “Instead of looking at the whole genome, you can investigate anywhere from 48-800 genes at a time.” Researchers can zero in on certain pathways that they are studying, Yang explains, or they can use preset panels of previously identified cancer networks.

Yang directs the new UAB Nanostring Laboratory, which is open to investigators across campus. He is using the nCounter to pursue his own research in experimental treatments for breast, prostate, and head and neck cancers. “I’m very interested in understanding the pathways that make a tumor tick,” Yang said. “I want to know which ones make it resistant to therapy and which ones could actually make it more sensitive to treatment.” With the nCounter, Yang said, “we can look from a 10,000-foot perspective rather than from sea level. It’s an exciting technology.”

Another advantage of the nCounter is that, unlike other technologies, which may require whole molecules of high-quality RNA or amplification for analysis, the nCounter can gather information from small pieces of RNA. That means researchers can use it to look at pathways in tissue that is up to several decades old, retroactively verifying new patterns they have found instead of having to collect new samples for analysis. The nCounter can also perform a range of other tests, Yang says, including analysis of microRNAs, gene fusions and gene amplifications.

From Concept to Clinic

The nCounter is more than a research tool. It can run new diagnostic tests such as the ProSigna Assay, which gives clinicians an estimate of a patient’s likelihood of tumor recurrence based on which pathways are active in that patient. It is an excellent example of personalized medicine in action, Yang says. He envisions UAB researchers using the nCounter to develop novel tests to inform treatment decisions in cancer and other diseases. UAB is one of the first institutions nationwide with the ability to do both laboratory and clinical testing using the nCounter.

“We hope to use the pattern of the pathway of genes to help guide therapy,” Yang said. “That’s the personalized medicine approach.”

Yang and collaborator Andres Forero, M.D., senior scientist at the UAB Cancer Center, will use the nCounter as part of a clinical trial testing a new treatment approach against triple-negative breast cancer. The trial, which recently began enrolling patients, is testing two different drugs — a PARP inhibitor and an EGFR inhibitor — to block two different pathways used by these tumors.

“By blocking PARP, you block the ability of the tumors to repair DNA damage,” which should eventually result in cell death, Yang explains. But the tumors can take advantage of an alternate backup pathway to repair that damage, meaning PARP inhibitors alone are often ineffective. “By blocking EGFR, we will block that backup pathway,” Yang said. [To learn more about this study, call (205) 934-0309; visit the Clinical Trials section of the Comprehensive Cancer Center's website to see all current studies.]

Using the nCounter, the researchers will compare the pathways altered in patients who respond to the therapy with those in patients who aren’t helped by the combination. In the future, that could let them identify the most appropriate patients for this treatment with a simple test. “We hope to use the pattern of the pathway of genes to help guide therapy,” Yang said. “That’s the personalized medicine approach.”

Superfoods and breast cancer: Study takes a closer look at broccoli and green tea

Could a combination of broccoli sprouts and green tea offer protection against breast cancer — and transform hard-to-treat breast tumors into a type that responds to medication?

A series of studies in the lab of UAB biologist Trygve Tollefsbol, Ph.D., D.O., have generated encouraging findings. Tollefsbol, who is also a senior scientist in the UAB Comprehensive Cancer Center, has shown that mice given sprouts in their chow and green tea polyphenols in their water are protected against tumor development. Intriguingly, he has also shown in animal studies that the combination can change estrogen receptor-negative (ER-) tumors, which have few treatment options, into estrogen receptor-positive (ER+) tumors, which can be treated with the anti-estrogen drug tamoxifen.

Now, Tollefsbol has received a $1.5-million, five-year grant from the National Institutes of Health to pinpoint the molecular mechanisms behind these effects. "We already have a lot of preliminary data showing that this combination works," Tollefsbol says. "The grant will allow us to extend that research and explore the effects genome-wide."

The immortality enzyme? Telomerase fights aging, fuels cancer

In a lab in the heart of Campbell Hall, UAB biologist Trygve Tollefsbol, Ph.D., D.O., stores the secret to immortality—but you may not want it.

Trygve Tollefsbol is a renowned expert on telomerase, an enzyme that
plays crucial roles in determining our lifespans and fueling cancer growth.

Telomerase, the enzyme in question, is a quirky character. Even though it is dormant most of the time, it appears to play a key role in all three of Tollefsbol’s main research interests: aging, cancer, and epigenetics.

Telomerase’s job is to lengthen telomeres, little caps at the end of our chromosomes that keep the chromosomes from becoming unstable during cell division. (They’re kind of like the plastic cylinders on the ends of shoelaces, Tollefsbol says.) But a little bit gets shaved off with each cycle of division. Eventually, there is very little protective telomere left, and cells age and stop dividing.