  The helical kink instability of a twisted magnetic flux tube has been
suggested as a trigger mechanism for solar filament eruptions and coronal mass
ejections (CMEs). In order to investigate if estimations of the pre-eruptive
twist can be obtained from observations of writhe in such events, we
quantitatively analyze the conversion of twist into writhe in the course of the
instability, using numerical simulations. We consider the line tied,
cylindrically symmetric Gold-Hoyle flux rope model and measure the writhe using
the formulae by Berger and Prior which express the quantity as a single
integral in space. We find that the amount of twist converted into writhe does
not simply scale with the initial flux rope twist, but depends mainly on the
growth rates of the instability eigenmodes of higher longitudinal order than
the basic mode. The saturation levels of the writhe, as well as the shapes of
the kinked flux ropes, are very similar for considerable ranges of initial flux
rope twists, which essentially precludes estimations of pre-eruptive twist from
measurements of writhe. However, our simulations suggest an upper twist limit
of $\sim 6\pi$ for the majority of filaments prior to their eruption.
