we have a loading rate
-.. math:: df/dt = df/dx dx/dt = kv \;,
+.. math:: df/dt = df/dx dx/dt = kv \\;,
so
-.. math:: f = kvt + f_0 \;.
+.. math:: f = kvt + f_0 \\;.
With an unfolding rate constant :math:`K`, the population follows
.. math::
dp/dt = Kp
- p(t) = exp(-tK) = exp(-(f-f_0)K/kv) = p(f) \;.
+ p(t) = exp(-tK) = exp(-(f-f_0)K/kv) = p(f) \\;.
Therefore, a histogram of unfolding vs. force :math:`p(f)` normalized
to :math:`p(0)=1` should follow
def probability_distribution(x, params):
"""Exponential decay decay probability distribution.
- .. math:: 1/\\tau \cdot exp(-x/\\tau)
+ .. math:: 1/\\tau \\cdot exp(-x/\\tau)
"""
p = params # convenient alias
p[0] = abs(p[0]) # cannot normalize negative tau.
Notes
-----
- .. math:: y \\propto \cdot e^{-t/\tau}
+ .. math:: y \\propto \\cdot e^{-t/\\tau}
"""
self._model_data.counts = (
self.info['binwidth']*self.info['N']*probability_distribution(