Figure 5.
Estimated torsional spring constants, waiting times for thermal pivoting, and transverse forces for antiparallel alignment. (A) The SPB–microtubule interface was assumed to behave as a Hookean spring (red), whose angular deflection, θ = τ/κ, varies linearly with applied torque, τ, where κ represents the torsional spring constant. (B) The waiting time for thermal pivoting to bring microtubules from adjacent SPBs into contact was estimated from the first-passage time for deflection to θ = 17°, the minimum angle needed to bring the tips of two microtubules of length L = 250 nm, separated laterally by distance s = 150 nm, into contact. (C) The transverse force required for deflection to θ = 90° was estimated by assuming a force acting perpendicularly to the microtubule at distance s = 150 nm from its pivot point (Ftrans, orange arrow). Values of L and s were chosen to match the physiological arrangement of SPBs when they are tethered together by a bridge (purple), after duplication and insertion into the nuclear envelope (O’Toole et al., 1999). (D) Torsional spring constants, κ, and transverse forces required to bring microtubules from adjacent, side-by-side SPBs into antiparallel alignment, Ftrans, estimated from the measured angular deviations, <σ>. Approximate waiting times for thermal pivoting to bring microtubules from adjacent SPBs into initial contact, tK, were estimated using Kramer’s rate theory (Howard, 2001). See Materials and methods for details.