helixmc.fitfxn.wlc_bouchiat_impl

helixmc.fitfxn.wlc_bouchiat_impl(A, L, S, z, F, kT=41.164043971999995)

Implicit worm-like chain formula described in Bouchiat et al. 1999 paper. Comparison is done in log10(F) space instead (more robust in practice). An extensive rod factor is added for fitting force-extension curve at high-force.

Parameters:

A : float

Bending persistence length, in Å.

L : float

Contour length, in Å.

S : float

Stretch modulus, in pN.

z : float or 1D ndarray

Average Z-extension of the helix, 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:

zero : float or 1D ndarray

Difference value, should approach zero at perfect fit.

See also

wlc_bouchiat

Worm-like chain fitting formula described in Bouchiat et al.

f_wlc_bouchiat_impl

Approximately solve the force from implicit wlc model by grid search.

Notes

The fitting function (see wlc_bouchiat for reference) is

\[\log_{10} \left[ \frac{kT}{A} \left( \frac{1}{4(1-l)^2} - \frac{1}{4} + l + \sum \limits_{i=2}^{i \le 7}{\alpha_i l^i} \right) \right] - \log_{10} (F) = 0\]

With \(l = z / L - F / S\)