Bonds, Catch Bonds, and Statistics*

Unsurprisingly, education research shows that students engage better when an instructional storyline begins with a surprising claim about a topic important in their own lives. Today, everyone understands the importance of immune response to their lives, and most students find it surprising and paradoxical to be told that some bonds strengthen under applied pulling force. So the recent discovery of catch-bond behavior in T-cell activation is a very good starting point to motivate study of many molecular biophysics ideas. To understand the claim, we must discuss the nature of bonds, replace "strength" by the statistical notion of mean lifetime, and then introduce the notion of random walks on energy landscapes. Rather than the elaborate and technical Kramers theory, however, students can readily perform simple simulations. The results include memorable animated graphics, that students can make themselves in a platform such as Python or MATLAB, and that yield conceptual insight into bond formation and breakage, isomerization, and so on. Abstractions such as Boltzmann distribution and exponentially distributed lifetime emerge as concrete consequences of simple rules, and the origin of catch bonding behavior is clear when multiple unbinding routes are available.