Comment on "Elasticity model of a supercoiled DNA molecule".

C om m ent on \E lasticity M odelofa Supercoiled D N A M olecule" B ouchi at and M ezard [ 1]have proposed a \worm-l i ke rod chai n m odel " to descri berecentexperi m entson D N A m echani cs [ 2]. T hei r m odelcan be sol ved usi ng an analogy w i th quantum m echani cs,thanks to the l ocalnature ofthe eecti ve H am i l toni an. T he l etter concl uded that thi s m odelhas excepti onalphysi calbehavi or: T he con-ti nuum l i m i t i s si ngul ar and l i near response theory can not be used i n the absence ofa cut-o to cal cul ate the experi m entalcurves:Forexam pl ethecurvesofextensi on versus torsi on atten i n the conti nuum l i m i t. T he w ri the,W r = C W =2,ofa chai n i s gi ven by the C al ug areanu-W hi te form ul a [ 3] C W = 1 2 ZZ L 0 r(s) r(s 0) j r(s) r(s 0)j 3 dr(s) ds dr(s 0) ds dsds 0 ; (1) w here r(s)= R s 0 t(s 0)ds 0 i sthe posi ti on i n space and L i s thel ength ofthechai n.Ful l ershowed thati fwerepresent the tangent vector t by a poi nt on the uni t sphere the area, F W ,encl osed by t(s)on the sphere [ 4] ,i si n certai n casesequalto C W. T he generalrel ati on between Ful l er' s and C al ug areanu' sform ul as i s expressed by: F W C W m od:4: (2) Ful l er' s resul t,expressed as a l ocali ntegral ,was used i n [ 1] .T he authorsjusti fy the use of F W to i nterpretexper-i m ents on open chai nsw i th a topol ogi calm odi cati on of the sphere [ 5]and nd that the probabi l i ty di stri buti on p(F W) vari es as 1= F W 2 for l arge F W due to w i ndi ng oftrajectori esabout the south pol e ofthe sphere. W e have perform ed a si m ul ati ons to di rectl y com pare the …