Module bussilab.lohman

Module implementing Lohman model for helicases.

Functions

def lohman(t, ku: float, kd: float, n: int = 1, boundaries: Tuple[float, float] = (0.0, 1.0)) ‑> float | numpy.ndarray

Expand source code

def lohman(t,
           ku: float,
           kd: float,
           n: int = 1,
           boundaries: Tuple[float, float] = (0.0, 1.0)
          ) -> Union[float, np.ndarray]:
    """Lohman model for helicases.

       Compute the fraction of unwound helices as a function of time.
       See [Lucius et al, Biophys J 2003](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1303449/).

       Parameters
       ----------
       t: float or sequence or np.ndarray
           Time. If a sequence or np.ndarray is provided, the function is computed
           for all values and an array is returned.

       ku: float
           Unwinding rate.

       kd: float
           Dissociation rate.

       n: int, optional
           Step size

       boundaries: tuple with 2 elements
           Result is mapped to this range.

       Returns
       -------

       float or np.ndarray
           The fraction of unfolded helices at a given time `t`. If an array is provided for `t`,
           an array is returned containing the fractions at all the times.
           If `boundaries` is provided, the fraction is linearly mapped into the
           `boundaries[0], boundaries[1]` range.

    """
    if isinstance(t, Sequence):
        t = np.array(t, dtype=float)
    kobs = ku+kd
    # processivity
    P = ku/kobs
    f = 0*t
    fact = 1
    for r in range(n):
        f += (kobs*t)**r/fact
        fact *= r+1
    f *= np.exp(-kobs*t)
    f = P**n*(1-f)
    return boundaries[0] + (boundaries[1]-boundaries[0]) * f

Lohman model for helicases.

Compute the fraction of unwound helices as a function of time. See Lucius et al, Biophys J 2003.

Parameters

t : float or sequence or np.ndarray

Time. If a sequence or np.ndarray is provided, the function is computed for all values and an array is returned.

ku : float

Unwinding rate.

kd : float

Dissociation rate.

n : int, optional

Step size

boundaries : tuple with 2 elements

Result is mapped to this range.

Returns

float or np.ndarray

The fraction of unfolded helices at a given time t. If an array is provided for t, an array is returned containing the fractions at all the times. If boundaries is provided, the fraction is linearly mapped into the boundaries[0], boundaries[1] range.