Despite great advances achieved in the past decades through applications of traditional empirical pharmacokinetic (PK) and pharmacodynamics (PD) models during different stages of drug development, it is constantly challenged by low success rate. One of the main reasons is the lack of important inputs from biology in the models, be that a pathway or some other physiological process at a cell, tissue, organ, or multi-organ/whole-body level. With a focus on incorporating such underlying biology and physiological processes to quantify the response of interest to a pharmacological intervention at a systems level the emerging field of Quantitative and Systems Pharmacology (QSP) has attracted ever-increasing attention.
How can QSP be used to build better models to inform drug development? QSP researchers Dr. Ardeshir Goliaei and Dr. Helen Moore, both from AstraZeneca, shared their insights during the recent Boston QSP May event, Modeling and Simulation in Oncology. I had the honor to talk with them more after the event.
Interview with Dr. Ardeshir Goliaei
Dr. Goliaei’s talk drew our attention to the heterogeneity of protein expression in individual cancer cells, which can be the very reason leading to drug resistance. A model was built to integrate the single cell death event with the phenotypic viability. The model allows characterizing drug response and resistance development of a cell population. Furthermore, it allows simulation of in vitro viability profiles of virtual cell lines, which are currently being experimentally validated.
Scientific Writer (Jae): Compared to genetic mutations, how do non-genetic factors contribute to various cellular responses to drugs?
Ardeshir: Non-genetic variations are random fluctuations in expression levels of proteins. If a cell, by random, happens to have higher levels of a specific drug target, then that cell is going to respond differently to the treatment relative to a cell that has lower levels. Since some drugs could potentially have effects on many proteins and targets, the outcome of the treatment really depends on those rare cells that are outliers in the population.
Jae: Modeling and simulation involves assumptions to simplify the situation. How did you decide which assumption to include in your model?
Ardeshir: We tried our best to stay close to experimental data. We made assumptions that allowed us to re-generate and simulate laboratory data. As long as the outcome of the simulation is close to the experimental observation, the assumptions are safe.
Jae: The model has been tested on the in vitro cancer cell systems. How are you going to translate this model to in vivo tumor systems?
Ardeshir: Being able to use these predictions in-vivo is ideal, however, there are many differences between in-vitro and in-vivo. Doubling time is one major difference. Cells in the lab grow much faster relative to cells in a real tumor (in-vivo), so that should be addressed. Another factor is elimination and degradation of the drug in-vivo which is currently not implemented in the model. That needs to be included as well.
Interview with Dr. Helen Moore
Dr. Moore’s research focuses on improving QSP modeling through optimal control and related mathematical techniques, based on examples from oncology and virology. Her work highlights the decision-making information researchers can gain from the use of semi-mechanistic, fit-for-purpose mathematical models and optimization in drug development.
Jae: Using optimal control in drug development and combination regimens is a fairly new concept. How is it different from the traditional QSP approach?
Helen: QSP represents the model itself, while optimal control is one of the many methods we can apply to a model. Optimal control is used to compute a dosing regimen that is predicted to achieve the best possible outcome. As with any application of modeling, the results are only as good as the underlying model is. Using an optimal control method allows us to optimize the outcome not only for efficacy, but also for toxicity. Additionally, dosing constraints can be incorporated in computing the optimal regimen. Here is a paper with more information about this.
Jae: Personalized therapy has been suggested to hold the direction and future in drug development. Optimal control is aimed at understanding the drug efficacy of a particular population. Can optimal control be used to optimize individual treatments?
Helen: Optimal control can be applied for either specific individuals or a population, even if the model is a deterministic system of ordinary differential equations. In either case, we can determine key parameters through global sensitivity analysis. The other parameters in the model can be frozen to fixed values, as their values will not impact the system outcome as much. The key parameters can then be fit using nonlinear mixed effects modeling (for individuals) or sampled from feasible ranges (for a population). Running optimal control with particular sets of parameter values gives individualized recommendations, or patterns that can inform regimens for a population.
Jae: Despite a huge improvement in immuno-oncology therapies, there is still limited efficacy when it comes to solid tumors. From the standpoint of mathematical modeling, what do you think the reason might be?
Helen: From the modeling I have done and seen, it seems that response to immunotherapy depends not only on the tumor’s susceptibility, but also on characteristics of the patient’s immune system. These are both complex systems, and we still don’t have a good way to predict a patient’s likely response before they begin immunotherapy. Currently, many people are applying powerful computational techniques to large data sets, and making progress in figuring out the most important predictors of response. Good predictors of response may also provide clues for interventions that could increase efficacy.
Jae: Irina Kareva, a theoretical biologist from Germany, once described herself as a “translator” who translate biology into math and vice versa, and use these mathematical models to find therapies for cancers. Do you feel the same way?
Helen: I have enjoyed Irina’s TED talk! I like to think of mathematical models as artistic expressions of biological systems. Pablo Picasso made line drawings of animals that are easily recognizable as a dog or a bird. When we create a mathematical representation of a physical system, we can’t capture every detail, so we need to consider our goal. Will a line drawing suffice, or do I need the level of detail of Claude Monet, or of Mary Cassatt, or of a photograph? Each represents a system at a different level of detail, but none as complete as the original system. We choose the appropriate level for the question we want to address. Once we have selected and validated an appropriate model, we have the full array of mathematical and computational techniques that can be applied to analyze the system.
Jae: What advice would you give graduate students who are indecisive of which path to pursue? And how has it been working at AstraZeneca?
Helen: One of the great things about industry is the chance to more directly impact patients’ lives. To do that, you often work on someone else’s projects, but sometimes can work on a project you propose. In contrast, academic faculty have more independence in their research, but spend a lot of time teaching classes or writing grant proposals. I was not allowed to publish most of my industry work. But AstraZeneca encourages publication and working with students, which I value, as I want to share my results and help new researchers. I recommend that undecided students try an industry internship. No matter which career you choose, learning lots of math, statistics, and programming will provide opportunities to do interesting work.
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Boston QSP is a 501(c)(3) non-profit organization whose mission is to foster the sharing of QSP knowledge, challenges, solutions, and opportunities to advance the field as an interdisciplinary community in Boston.