for the solution conditions we used [@wang97a]. There are *no fit parameters;* the theoretical model uses values for bead diameter given by the manufacturer’s specification. The bumpiness in the curves reflects the statistical character of the Monte Carlo algorithm that generated them. ](bitmaps/KBT_calib.eps "fig:"){width="3.54truein"}

We also compared the experimental data in to a mathematical simulation of the bead-tether-wall system (). The excursion of the bead away from its attachment point on the microscope slide is affected by the length and stiffness of the DNA tether, the size of the bead, and the various interactions between the bead/wall, bead/tether, and wall/tether. To account for all these effects, we modified the Gaussian sampling Monte Carlo technique previously used in [@sega06a; @Nelson2006; @czap06a; @nels07a] (see [@Towles2008] for details).

Suppose first that a semiflexible polymer chain is anchored at one point in space, but is otherwise unconstrained. At the anchored point we suppose we are given a probability distribution of different possible initial orientations for the first chain segment. The distribution of positions and orientations of the other end is then a convolution of this initial distribution with a kernel representing a particular diffusion process (random walk) on the group manifold of the three-dimensional 