mythos.observables.wlc

Utility functions for computing worm-like chain (WLC) fit.

Functions

coth(→ mythos.utils.types.ARR_OR_SCALAR)	Hyperbolic cotangent function.
calculate_extension(→ mythos.utils.types.ARR_OR_SCALAR)	Computes the extension under a specified force under the wormlike chain (WLC) model.
loss(→ jax.numpy.ndarray)	An objective function for the WLC model compatible with JAX solvers.
fit_wlc(→ jax.numpy.ndarray)	Fit the WLC model via nonlinear least squares given a set of forces and measured extensions.

Module Contents

mythos.observables.wlc.coth(x: mythos.utils.types.ARR_OR_SCALAR) → mythos.utils.types.ARR_OR_SCALAR

Hyperbolic cotangent function.

mythos.observables.wlc.calculate_extension(force: mythos.utils.types.ARR_OR_SCALAR, l0: mythos.utils.types.ARR_OR_SCALAR, lp: mythos.utils.types.ARR_OR_SCALAR, k: mythos.utils.types.ARR_OR_SCALAR, kT: float) → mythos.utils.types.ARR_OR_SCALAR

Computes the extension under a specified force under the wormlike chain (WLC) model.

Via the model of Odijk, the extension of an extensible wormlike chain (WLC) under a force F can be computed as

\[x = L_0 \left (1 + \frac{F}{K} - \frac{kT}{2F} [1 + y\coth y] \right)\]

where

\[y = \left( \frac{FL_0^2}{L_p kT} \right)^{1/2}\]

where L_0 is the contour length and L_p is the persistence length. This function computes implements this model for computing the extension.

Parameters:

• force (jd_types.ARR_OR_SCALAR) – the force applied to the duplex

• l0 (jd_types.ARR_OR_SCALAR) – the contour length

• lp (jd_types.ARR_OR_SCALAR) – the persistence length

• k (jd_types.ARR_OR_SCALAR) – the extensional modulus

• kT (float) – the temperature

Returns:

the predicted extension

Return type:

jd_types.ARR_OR_SCALAR

mythos.observables.wlc.loss(coeffs: jax.numpy.ndarray, extensions: jax.numpy.ndarray, forces: jax.numpy.ndarray, kT: float) → jax.numpy.ndarray

An objective function for the WLC model compatible with JAX solvers.

Parameters:

• coeffs (jnp.ndarray) – The parameters of the WLC model, ordered as [L_0, L_p, K]

• extensions (jnp.ndarray) – The measured extensions (via simulation) to which we are fitting the model

• forces (jnp.ndarray) – The forces under which the extensions were measured

• kT (float) – the temperature

Returns:

the residual for each measured extension

Return type:

jnp.ndarray

mythos.observables.wlc.fit_wlc(extensions: jax.numpy.ndarray, forces: jax.numpy.ndarray, init_guess: jax.numpy.ndarray, kT: float, *, implicit_diff: bool = True) → jax.numpy.ndarray

Fit the WLC model via nonlinear least squares given a set of forces and measured extensions.

Parameters:

• extensions (jnp.ndarray) – The measured extensions (via simulation) to which we are fitting the model

• forces (jnp.ndarray) – The forces under which the extensions were measured

• init_guess (jnp.ndarray) – An initial guess for the parameters of the WLC model, ordered as [L_0, L_p, K]

• kT (float) – the temperature

• implicit_diff (bool) – Whether or not to use implicit differentiation for the numerical solver

Returns:

the fit parameters of the WLC model, ordered as [L_0, L_p, K]

Return type:

jnp.ndarray