helixmc.fitfxn.moroz_3rd

helixmc.fitfxn.moroz_3rd(A, C, F, kT=41.164043971999995)

3rd order Moroz-Nelson function for effective torsional persistence.

Parameters:

A : float

Bending persistence length, in Å.

C : float

Torsional persistence length, in Å.

F : float or 1D ndarray

Z-direction stretching force, in pN.

kT : float, optional

Temperature times Boltzmann constant, in pN.Å. Default is 298.15 K.

Returns:

Ceff : float or 1D ndarray

Effective torsional persistence length in Å. Ceff = L / Var(Lk).

See also

moroz_1st

1st order Moroz-Nelson function for effective torsional persistence.

Notes

The fitting function, orginally proposed in reference [1] [2], and summarized in [3], is

\[C_{eff} = C \left( 1-\frac{M}{4K_0} + \frac{M^2-2M}{16{K_0}^2} - \frac{4M^3-16M^2+21M}{256{K_0}^3} \right )\]

With

\[M = \frac{C}{A}, \quad K_0=\sqrt{ \frac{A F}{kT} }\]

References

[1]	Moroz JD, Nelson P (1997) Torsional directed walks, entropic elasticity, and DNA twist stiffness. PNAS 94: 14418-14422.

[2]	Moroz JD, Nelson P (1998) Entropic Elasticity of Twist-Storing Polymers. Macromolecules 31: 6333-6347.

[3]	Lipfert J, Wiggin M, Kerssemakers JWJ, Pedaci F, Dekker NH (2011) Freely orbiting magnetic tweezers to directly monitor changes in the twist of nucleic acids. Nat. Comm. 2: 439.