def dot_g_r(self, gamma_a, lambd):
""" Differential for ribosome protein species Supp Eq (3)
"""
c_r = self.species_values['c_r']
n_r = self.params['n_r']
k_b = self.params['k_b']
k_u = self.params['k_u']
g_r = self.species_values['g_r']
nu_r = funcs.nu_x(c_r, n_r, gamma_a)
sum_c_mrna = 0
for c in self.c_mrna_species:
c_x = self.species_values[c]
n_x_param = 'n_' + '_'.join(c.split('_')[1:])
n_x = self.params[n_x_param]
nu_x = funcs.nu_x(c_x, n_x, gamma_a)
# mRNA species for x
m_x = self.species_values['m_' + '_'.join(c.split('_')[1:])]
sum_c_mrna += nu_x - (k_b * g_r * m_x) + (k_u * c_x)
dot_r = nu_r - lambd * g_r + sum_c_mrna
return dot_r
def dot_g_x(self, g_x, c_x, n_x, gamma_a, lambd):
""" Differential for translation of non ribosome protein species Supp Eq (4)
"""
nu_x = funcs.nu_x(c_x, n_x, gamma_a)
dot_g_x = nu_x - lambd * g_x
return dot_g_x
def dot_m_x(self, m_x, c_x, n_x, w_x, theta_x, gamma_a, lambd):
""" Differential for transcription of an m_RNA species Supp Eq (5)
"""
g_r = self.species_values['g_r']
a = self.species_values['a']
d_m = self.params['d_m']
k_b = self.params['k_b']
k_u = self.params['k_u']
omega_x = funcs.omega_x(w_x, theta_x, a)
nu_x = funcs.nu_x(c_x, n_x, gamma_a)
dot_m_x = omega_x - (lambd +
d_m) * m_x + nu_x - k_b * g_r * m_x + k_u * c_x
return dot_m_x
def dot_a(self, nu_cat, gamma_a, lambd):
""" Differential for energy species Supp Eq (2)
"""
n_s = self.params['n_s']
a = self.species_values['a']
sum_translation_costs = 0
for c in self.c_mrna_species:
c_x = self.species_values[c]
n_x_param = 'n_' + '_'.join(c.split('_')[1:])
n_x = self.params[n_x_param]
sum_translation_costs += funcs.nu_x(c_x, n_x, gamma_a) * n_x
dot_a = n_s * nu_cat - sum_translation_costs - lambd * a
return dot_a
def dot_c_x(self, m_x, c_x, n_x, gamma_a, lambd):
""" Differential for a mRNA transcript undergoing translation Supp Eq (6)
@param m_x mRNA species value
@param c_x mRNA-ribosome complex species value
@param n_x protein length
@param gamma_a
@param lambd
@return dot_c_x is the derivative for a particular mRNA-ribosome complex species
"""
g_r = self.species_values['g_r']
k_b = self.params['k_b']
k_u = self.params['k_u']
nu_x = funcs.nu_x(c_x, n_x, gamma_a)
dot_c_x = -(lambd * c_x) + k_b * g_r * m_x - k_u * c_x - nu_x
return dot_c_x