BioSANS2020.propagation.deterministic.lna_approx¶
This is the lna_approx module
This module performs numerical linear noise approximation or LNA by
exploiting the following relationship.
AC + CA.T + BB = 0
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 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.
The following are the list of function for this module.
rem_rowcol_zero
lna_ss_jacobian
lna_model_ss
lna_steady_state
Module Contents¶
Functions¶
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This function removes rows and columns without non-zero entries. |
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This function calculataes the jacobian of the model ODE with |
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This function returns the derivative of components with respect |
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[summary] |
- BioSANS2020.propagation.deterministic.lna_approx.rem_rowcol_zero(a_mat)¶
This function removes rows and columns without non-zero entries.
- Args:
- a_mat (np.ndarray): numpy matrix of A or d(S*f)/dx as described
in the module docstring.
- Returns:
- np.ndarray: numpy matrix with no rows and columns without non-
zero entries.
- BioSANS2020.propagation.deterministic.lna_approx.lna_ss_jacobian(model, zlist, sp_comp, stch_var, ks_dict, r_dict, p_dict)¶
This function calculataes the jacobian of the model ODE with respect to the list of species concentration zlist.
- Args:
- model (function): the ODE model returning derivative of species
or components as a function of time
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
stch_var (np.ndarray): stoichiometric matrix 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
}
- Returns:
np.ndarray: jacobian matrix or d(S*f)/dx or A
- BioSANS2020.propagation.deterministic.lna_approx.lna_model_ss(zlist, sp_comp, ks_dict, r_dict, p_dict, stch_var)¶
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
- Returns:
np.ndarray: derivative of species with respect to time.d(S*f)/dt
- BioSANS2020.propagation.deterministic.lna_approx.lna_steady_state(t_var, sp_comp, ks_dict, conc, r_dict, p_dict, stch_var, items=None)¶
[summary]
- Args:
t_var (list): time stamp 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
}
conc (dict): dictionary of initial concentration.
For example;
{‘A’: 100.0, ‘B’: -1.0, ‘C’: 0.0} negative means unknown or for estimation
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
items (tuplel): (canvas, scroll_x, scroll_y). Defaults to None.
- Returns:
[type]: [description]