Axonemal bending stiffness of $Chlamydomonas$ cilia implies single-motor forces above $5\mathrm{p}\mathrm{N}$

The regular bending waves of cilia and flagella provide an iconic model system for the collective dynamics of molecular motors. The known regular arrangement of dynein motors in a cilium’s axoneme allows us to connect mesoscopic cilia properties, such as axonemal bending stiffness, to microscopic motor properties, such as the force exerted by an individual motor. We estimate the active force generated by the collection of dynein molecular motors in $Chlamydomonas$ axonemes using previous estimates of its bending stiffness. Divided by the maximal possible number of active motor heads, this provides a lower bound of $>10\mathrm{p}\mathrm{N}$ for the peak force generated by a motor head, which exceeds typical stall forces $<5\mathrm{p}\mathrm{N}$ of molecular motors. This discrepancy suggests that either the bending stiffness of microtubules and axonemes was previously overestimated, or that collective force generation in dense motor arrays can surpass the sum of expected contributions of individual motors.