Many cells divide via a contractile ring Fig a A toy model o

Many cells divide via a contractile ring (Fig. a). A toy model of the ring is that it consists of a single actin filament wound into a circle. The filament is then pulled into a tighter and tighter radius over time to close down the space between the cells (Fig. b). Express the energy required to bend a filament into a single loop of radius R as a function of the persistence length the temperature T, and Boltzmann\'s constant k_B. Given a filament of length L, how many loops around the ring will it form as a function of the radius R of the contractile ring? the number of loops need not be an integer. From your answers in (a) and (b), how does the total energy stored in the ring scale with the ring radius R?

Solution

(b) if the radius is R then the circumference is 2*pi*R

given the filament length=L

no of loops= (2*pi*R/L)