Wednesday, November 4, 2009

motor protein syncrony and LCM

11.04.09. The step length of a motor protein (see previous posts) is affected by external factors both deterministic, such as the force exerted by its cargo, and random, such as collisions with other particles in the cell (see, e.g., Clemen et al, Biophys J, 2005). We imagined two motor proteins with different step lengths starting at the same point on a filament, and we asked at what distance would they coincide once more? Viewing each protein as stepping along a number line, it is clear that the answer is the least common multiple (LCM) of their step sizes. Students practiced finding LCMs in the context of stepping proteins, and this led to a comparison of two very different techniques for finding the LCM: (1) listing out the multiples of each number explicitly and (2) finding the prime factorization of each number and multiplying the greatest common factor (GCF) by the unshared factors.