Braess’s Paradox

In 1990, New York City closed 42nd Street in observance of Earth Day (1).

The 42nd Street is a major thoroughfare, and its closure was expected by many to be a disaster. Manhattan’s traffic is bad enough on an ordinary day: surely the closure of a major artery could only make it worse.

To everyone’s surprise, except certain mathematicians, the closure significantly improved traffic that day.

This, and other examples in cities around the world such as London and Stuttgart, are examples of Braess’s Paradox. The paradox says that in a network such as a road network, that more routes can slow down the entire system, and that fewer roads can speed it up.

The reason for this is complicated, and a good explanation can be found on Wikipedia and on YouTube, but put simply, additional roads allow too many cars to try to switch around to take the shortcuts, rather than forcing some cars to take slightly slower routes. When every tries to take the shortcuts, the shortcuts get overloaded.

The relevance of this paradox to drug development is that biological systems are networks. Many processes such as cancer cell proliferation and coagulation cascade rely on a network of enzymes and signals that control what the cells and body do.

There have been many attempts to control the biological networks (typically by blocking an enzyme) and it is fair to say that there are more failures than successes. In some cases, it is because the drug is not very selective, can’t get into the cell, or deficient in some other way. In some cases, it is because there are redundant pathways. In some cases, it is because we biologists fail to consider that the best way to control networks is to target the feedback signals rather than the primary network.

In other cases, it is because we mistake mutations that de-activate a gene for a mutation that activates a gene such as may be the case with protein kinase c and gamma secretase.

However, it may be that in some cases, blocking a pathway may paradoxically increase the signal rather than attenuate it. Braess’s Paradox is applicable generally to any network where there are independent moving entities, which would include most or many biological systems. In chemical reaction network theory, an extremely important field for drug development, modeling indicates that Braess’s Paradox can happen. This paradox is not widely appreciated, so it has not been well studied in biology, but it is possible that it may be widespread.

(1) Kolata, Gina (1990-12-25). “What if They Closed 42d Street and Nobody Noticed?”. New York Times. Retrieved 2008-11-16.

 

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