Source code for cytocalc.helper

#! /usr/bin/env python3
# This file contains helper functions i.e. functions
# that have a one-off use and do not really fit elsewhere
# NOTE: When 3-4 functions have a similar paradigm, convert
# them into a different class/file.

import math


# For the formulae, refer to supplementary information: https://doi.org/10.15252%2Fmsb.20177796


def theoretical_cont_rate(
    motor_count, crosslinker_count, sim_params, buckling_thres, scale
):
    """Predicts the concentration rate for a given set of simulation parameters"""
    s = math.pi * (sim_params["cell_radius"]) ** 2  # Area of cell
    l = sim_params["filament"]["length"]
    f = sim_params["filament_count"]

    x = ((f * (f - 1)) * l * l) / (math.pi * s)  # number of intersections

    def _get_probability(obj, obj_count):
        """finds the probability of couple being attached to filament"""
        k_on = obj["binding_rate"]
        k_off = obj["unbinding_rate"]
        eps = obj["binding_range"]

        v2 = 4 * math.pi * x * (eps**2)
        v1 = 2 * f * l * eps - v2

        a = k_on / k_off
        avg = (
            obj_count
            * (a**2 * v2 / (2 * s))
            * (1 + a * ((v1 + v2) / s) + a * (v2**2 / (2 * s))) ** (-1)
        )

        lamda = avg / x  # not a typo - lambda shouldn't be used a var name in python

        prob = 1 - math.e ** (-lamda)
        return prob

    prob_m = _get_probability(sim_params["plus_motor"], motor_count)
    prob_c = _get_probability(sim_params["binder"], crosslinker_count)

    return scale * (prob_m) * (prob_c) * (1 - prob_c) ** (buckling_thres)