Monday, October 19, 2009
10.19.09. With enough external force, kinesin (see previous post) can be forced to take backwards steps as well as forward steps. In fact, the fraction of forward to backwards steps can be measured as a function of the external force applied by the optical trap (the plot shown is from Shao et al, PNAS, 2006). Forward and backward motion fit nicely with students' understanding of positive and negative numbers, and we imagined kinesin stepping along a number line. Students represented individual kinesin paths both visually as trajectories along a number line and numerically with an equation showing addition of positive and negative integers. Comparing the absolute value of all forward steps to that of all backward steps provides a quick way to determine the sign of the kinesin's net displacement.
Wednesday, October 14, 2009
10.14.09. Kinesin is a well-studied example of a "motor protein," a protein that steps along microtubules to transport cargo from one side of a cell to another (see an animation of kinesin by the Vale lab at UCSF here). Recent experiments (the plot shown is from Visscher et al, Nature, 1999) have been able to track the movement of a single kinesin molecule by attaching its cargo end to a plastic bead whose displacement is controlled by a laser beam (a so-called "optical trap"). At low (or no) cargo load, the velocity of kinesin depends on two parameters: its step size and the diffusion constant. Students practiced turning statements into equations by translating sentences such as "kinesin’s velocity is the quotient of twice the diffusion constant and the step size." Students then calculated the velocity for the approximate values D = 600 nm^2/s for the diffusion constant and L = 8 nm for the step size and compared with the slope of the plot.
10.14.09. Mr. Seymour and Mr. Mugler are back for a new year with a whole new batch of students hungry to learn! This year we'll be combining the most successful lessons from last year with new lessons to create a curriculum that is more cohesive, exciting, and beneficial to the students' understanding of seventh grade math.