As an M.Sc. student, I worked on a model describing the early stages of
type 1 diabetes. Type 1 diabetes occurs when the immune system attacks and destroys the insulin producing beta-cells in the pancreas. Our
experimental collaborator had observed that macrophages (a part of the immune system that clears away dead cells from tissues) from mice susceptible to type 1 diabetes were less efficient than macrophages from healthy mice. It was also observed that not every mouse susceptible to the disease developed it. Based on these observations, we developed a model to answer two questions:
1. Can the difference in macrophage efficiency account for the differences observed between healthy and susceptible mice?
2. Can a naturally occurring wave of beta-cell death associated with normal development in all mice be a triggering event that leads to type 1 diabetes in susceptible mice?
Within our modeling framework, the healthy state corresponds to a steady-state solution representing no inflammation, while the diseased state corresponds to a steady-state solution representing chronic inflammation. It is then assumed that during the chronic inflammation state the immune system will become primed to attack and kill the pancreatic beta-cells. Since not all susceptible mice develop type 1 diabetes, the healthy state should exist and be stable for both strains of mice being modeled. In addition, the steady state corresponding to chronic inflammation should exist and be stable for the susceptible mice. Through the use of dynamical systems approaches (especially phase-plane analysis) we determined that the initial model could not satisfy these requirements for biologically reasonable parameter values. The model was then expanded to include additional cell populations as well as the toxic effect of harmful cytokines released by the macrophages. This expanded model, shown below, demonstrated that differences in macrophage efficiency could explain the difference between healthy and susceptible mice.
To answer the second question, the wave of beta-cell death was incorporated into the model. The model demonstrated that for healthy mice the temporary inflammation quickly died down, and the model returned to the non-inflamed steady state. In the case of the susceptible mice, the wave of beta-cell death was sufficient to push the system to chronic inflammation, suggesting that the naturally occurring cell death could indeed be a triggering stimulus for the development of type 1 diabetes.
For more details, read the full paper here.
I recently attended the Sanofi – MSISB Mount Sinai Systems Pharmacology Symposium. This one day meeting focused on the ways quantitative systems pharmacology approaches can be used throughout the drug development process and how these approaches can gain larger prominence within the industry. Speakers from academia, industry, and the FDA presented their success stories and vision for the future. In this short post, I will share what I took away from the meeting.
With greater availability of data, advances in computing, and the previous successes of quantitative approaches, mechanistic modelling is gaining prominence under the label “quantitative systems pharmacology” (QSP). Many of the speakers at the symposium discussed the benefits of QSP. A QSP approach quantifies the mental model and assumptions that the research team is working from, and provides a framework for integrating data and making predictions. A QSP model also provides insight when it fails to fit the data; highlighting gaps in knowledge that can in turn suggest new experiments and prioritize future studies.
The standard modeling approach that is used within the pharmaceutical industry is a data-driven, empirical approach. This brute-force approach requires many experimental tests and statistical analysis to obtain a set of equations that can reproduce the observed behavior. These models are relatively inexpensive to produce, but are problem specific and only valid within the range of experimentally observed data. On the other hand, QSP models take much longer to develop but the extra cost can be worthwhile since QSP models are not restricted to a “range of validity” and so can be used to extrapolate from observed values to make predictions. These predictions can be used to translate observations from one system to another, allowing researchers to make predictions in human populations based on animal models for example.
Another advantage of QSP models is that they are not “single-use” products, and can be used during the drug development process for many compounds that affect the system covered by the model. During some of the informal discussions it came out that this aspect of QSP was the foundation of the business plan for companies like Rosa & Co. and Applied BioMath, who develop large models based on basic biology (described as “pre-competitive” models) and then incorporate the client company’s proprietary data to create a system-specific model for the compound under investigation. I have also come across the company DILIsym, that has created a mechanistic model of drug induced liver injury that they license to companies to support risk-assessment and decision making related to new compounds.
Perhaps the biggest take-away for me was a renewed appreciation for the power of mathematical modeling that I discovered as a student. The speakers presented concrete examples of how mathematical modeling contributed to advances in care for people with heart arrhythmia, kidney disease, TB, and other conditions. These examples demonstrate the powerful role mathematics can play, and are a preview of the changes to come within the pharmaceutical industry as quantitative systems pharmacology approaches gain more traction.