Over the past several years, scientists have begun to understand that seemingly unrelated diseases, like Alzheimer’s, Parkinson’s, ALS, or type II diabetes, actually have a common underlying cause- protein aggregation, where groups of protein molecules stick together and form clumps, called aggregates. These clumps then grow over time, leading to cell death and organ degeneration. Though several drugs have been tested to prevent the formation or growth of these aggregates, development of effective therapies has been slow. Now, researchers from Harvard’s School of Engineering and Applied Sciences have designed a new strategy to determine the most effective treatment protocol based on mathematical modeling, drug properties, and available treatment times.

Since different drugs have widely varying properties, it is unsurprising that one treatment strategy is not universally effective. To account for these differences, the authors developed a model for how the drug interferes with the formation (or nucleation) of new protein clumps and the growth of existing ones, as most tested drugs primarily influence only one of these processes. The authors also consider drug toxicity in their model, in which the drugs can negatively affect the patient by influencing the function of other proteins and cellular pathways. By using mathematical techniques from an area of engineering called optimal control theory, they are then able to determine the best treatment protocol for a specific drug, molecular target, and amount of time available for treatment. A treatment protocol specifies what concentration of drug to use, when to begin treatment, and when to stop. Drugs that interfere with initial formation of aggregates must be administered early on to be effective, and if the disease has progressed significantly, it becomes more favorable to use inhibitors of growth. However, balancing drug efficacy and toxicity is also essential, as too large drug concentrations can make it more favorable to use no treatment at all.

The authors confirmed predicted results of their model on previously published data for aggregation in worms using two different drugs, observing that inhibitors of nucleation were more effective when administered earlier, while growth inhibitors are more effective after a delay. Certainly, this model will need to be validated on other systems, and more importantly, should be modified to include other relevant factors, such as how the body absorbs and processes drugs over time, before it can be used to plan clinical treatments. Nevertheless, such a rigorous mathematical strategy could prove to be immensely useful in optimizing treatments for numerous diseases.

Managing Correspondent: Andrew T. Sullivan

Press Articles: Using math to help treat Alzheimer’s, Parkinson’s and other diseases, Medical Xpress

Original Journal Article: “Optimal control strategies for inhibition of protein aggregation”, PNAS

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