BioSANS2020.propagation.deterministic.lna_function_of_time

This module is the lna_function_of_time module

This module performs numerical propagation of linear noise approxi-

mation or LNA by exploiting the following relationship.

dC/dt = AC + CA.T + BB

where A is defined as d(S*f)/dx where S is the stoichiometric matrix, f are the propensities or fluxes, and x are the components or species. The flux is a function of species x and rate constant k. BB is the diffusion matrix equivalent to S*diag(f)*S.T where diag(f) is a square matrix with zero non-diagonal elements and f[i] in each diagonal elements. C is the covariance matrix and t is time.

The following are the list of function for this module.

Module Contents

Functions

lna_ode_model(zlist, t_var, sp_comp, ks_dict, r_dict, p_dict, stch_var, molar=False)

This function returns the derivative of components with respect

lna_cov_model(a_jac, b_diff, cov)

Returns the evaluated dC/dt at a particular instant based on the

lna_non_steady_state(conc, t_var, sp_comp, ks_dict, r_dict, p_dict, stch_var, molar=True, rfile='', del_coef=10)

This function returns covariance trajectoy based on LNA

lna_non_steady_state2(conc, t_var, sp_comp, ks_dict, r_dict, p_dict, stch_var, molar=True, rfile='', del_coef=10)

This function returns Fan-factor trajectoy based on LNA
BioSANS2020.propagation.deterministic.lna_function_of_time.lna_ode_model(zlist, t_var, sp_comp, ks_dict, r_dict, p_dict, stch_var, molar=False)

This function returns the derivative of components with respect to time at a particular state of the system based on the inputs.

Args:

zlist (list): list of components or species amounts sp_comp (dict): dictionary of appearance or position of species

or component in the reaction tag of BioSANS topology file.

For example;

#REACTIONS A => B, -kf1 # negative means to be estimated B => C, kf2

The value of sp_comp is

sp_comp = {‘A’: {0}, ‘B’: {0, 1}, ‘C’: {1}}

A appears in first reaction with index 0 B appears in first and second reaction with index 0, 1 C appears in second reaction with index 1

ks_dict (dict): dictionary of rate constant that appear in each

reactions.

For example;

#REACTIONS A => B , 0.3 # first reaction B <=> C, 0.1, 0.2 # second reaction

The value of ks_dict is

ks_dict = {

0 : [0.3], # first reaction 1 : [0.1, 0.2] # second reaction

}

r_dict (dict): dictionary of reactant stoichiometry. For example

r_dict = {

0: {‘A’: 1}, # first reaction, coefficient of A is 1 1: {‘B’: 1} # second reaction, coefficient of B is 1

}

p_dict (dict): dictionary of product stoichiometry. For example

p_dict = {

0: {‘B’: 1}, # first reaction, coefficient of B is 1 1: {‘C’: 1} # second reaction, coefficient of C is 1

}

stch_var (np.ndarray): stoichiometric matrix molar (boolean) : if yes, uses macroscopic propensities else

uses microscopic propensities

Returns:

np.ndarray: derivative of species with respect to time.d(S*f)/dt

BioSANS2020.propagation.deterministic.lna_function_of_time.lna_cov_model(a_jac, b_diff, cov)

Returns the evaluated dC/dt at a particular instant based on the current state of a_jac, b_diff, cov

Args:
a_jac (np.ndarray): d(S*f)/dx or jacobian of ODE with respect

to components or species

b_diff (np.ndarray): diffusuin matrix cov (np.ndarray): covariance matrix

Returns:

[type]: [description]

BioSANS2020.propagation.deterministic.lna_function_of_time.lna_non_steady_state(conc, t_var, sp_comp, ks_dict, r_dict, p_dict, stch_var, molar=True, rfile='', del_coef=10)

This function returns covariance trajectoy based on LNA

Args:

conc (dict): dictionary of initial concentration.

For example;

{‘A’: 100.0, ‘B’: -1.0, ‘C’: 0.0} negative means unknown or for estimation

t_var (list): time stamp of trajectories sp_comp (dict): dictionary of appearance or position of species

or component in the reaction tag of BioSANS topology file.

For example;

#REACTIONS A => B, -kf1 # negative means to be estimated B => C, kf2

The value of sp_comp is

sp_comp = {‘A’: {0}, ‘B’: {0, 1}, ‘C’: {1}}

A appears in first reaction with index 0 B appears in first and second reaction with index 0, 1 C appears in second reaction with index 1

ks_dict (dict): dictionary of rate constant that appear in each

reactions.

For example;

#REACTIONS A => B , 0.3 # first reaction B <=> C, 0.1, 0.2 # second reaction

The value of ks_dict is

ks_dict = {

0 : [0.3], # first reaction 1 : [0.1, 0.2] # second reaction

}

r_dict (dict): dictionary of reactant stoichiometry. For example

r_dict = {

0: {‘A’: 1}, # first reaction, coefficient of A is 1 1: {‘B’: 1} # second reaction, coefficient of B is 1

}

p_dict (dict): dictionary of product stoichiometry. For example

p_dict = {

0: {‘B’: 1}, # first reaction, coefficient of B is 1 1: {‘C’: 1} # second reaction, coefficient of C is 1

}

stch_var (np.ndarray): stoichiometric matrix molar : True if conc. is in molar otherwise False rfile (str): file name of BioSANS topology file. del_coef (float, optional): factor for modifying time steps used

in the integration/propagation of ODE. Defaults to 10.

Returns:

list: [covariance, labels, time]

BioSANS2020.propagation.deterministic.lna_function_of_time.lna_non_steady_state2(conc, t_var, sp_comp, ks_dict, r_dict, p_dict, stch_var, molar=True, rfile='', del_coef=10)

This function returns Fan-factor trajectoy based on LNA

Args:

conc (dict): dictionary of initial concentration.

For example;

{‘A’: 100.0, ‘B’: -1.0, ‘C’: 0.0} negative means unknown or for estimation

t_var (list): time stamp of trajectories sp_comp (dict): dictionary of appearance or position of species

or component in the reaction tag of BioSANS topology file.

For example;

#REACTIONS A => B, -kf1 # negative means to be estimated B => C, kf2

The value of sp_comp is

sp_comp = {‘A’: {0}, ‘B’: {0, 1}, ‘C’: {1}}

A appears in first reaction with index 0 B appears in first and second reaction with index 0, 1 C appears in second reaction with index 1

ks_dict (dict): dictionary of rate constant that appear in each

reactions.

For example;

#REACTIONS A => B , 0.3 # first reaction B <=> C, 0.1, 0.2 # second reaction

The value of ks_dict is

ks_dict = {

0 : [0.3], # first reaction 1 : [0.1, 0.2] # second reaction

}

r_dict (dict): dictionary of reactant stoichiometry. For example

r_dict = {

0: {‘A’: 1}, # first reaction, coefficient of A is 1 1: {‘B’: 1} # second reaction, coefficient of B is 1

}

p_dict (dict): dictionary of product stoichiometry. For example

p_dict = {

0: {‘B’: 1}, # first reaction, coefficient of B is 1 1: {‘C’: 1} # second reaction, coefficient of C is 1

}

stch_var (np.ndarray): stoichiometric matrix molar : True if conc. is in molar otherwise False rfile (str): file name of BioSANS topology file. del_coef (float, optional): factor for modifying time steps used

in the integration/propagation of ODE. Defaults to 10.

Returns:

list: [fanp_factor, labels, time]