"""
This module contains helper functions to obtain the signal, given certain parameters
Author: Osvaldo Burastero
Note: One could move dT outside the signal functions but the speedup was not significant.
"""
from .rates import (
eq_constant_termochem,
eq_constant_thermo
)
import numpy as np
from .fractions import (
fn_two_state_monomer,
fu_two_state_dimer,
fu_two_state_trimer,
fu_two_state_tetramer,
fi_three_state_tetramer_monomeric_intermediate,
fi_three_state_dimer_monomeric_intermediate,
fu_three_state_dimer_dimeric_intermediate,
fi_three_state_dimer_dimeric_intermediate,
fi_three_state_trimer_monomeric_intermediate,
fu_three_state_trimer_trimeric_intermediate,
fi_three_state_trimer_trimeric_intermediate,
)
from .math import shift_temperature_K
__all__ = [
"signal_two_state_tc_unfolding",
"signal_two_state_tc_unfolding_shifted",
"signal_two_state_t_unfolding",
"two_state_thermal_unfold_curve",
"two_state_thermal_unfold_curve_dimer",
"two_state_thermal_unfold_curve_trimer",
"two_state_thermal_unfold_curve_tetramer",
"unfolding_curve_monomer_monomeric_intermediate",
"unfolding_curve_dimer_monomeric_intermediate",
"unfolding_curve_trimer_monomeric_intermediate",
"unfolding_curve_tetramer_monomeric_intermediate",
"unfolding_curve_trimer_trimeric_intermediate",
"unfolding_curve_dimer_dimeric_intermediate",
"map_two_state_model_to_signal_fx",
"map_three_state_model_to_signal_fx"
]
[docs]
def signal_two_state_tc_unfolding(
T,D,DHm,Tm,Cp0,m0,m1,
p1_N, p2_N, p3_N, p4_N,
p1_U, p2_U, p3_U, p4_U,
baseline_N_fx,
baseline_U_fx,
extra_arg=None):
"""
Ref: Louise Hamborg et al., 2020. Global analysis of protein stability by temperature and chemical
denaturation
Parameters
----------
T : array-like
Temperature in Kelvin units
D : array-like
Denaturant agent concentration
DHm : float
Variation of enthalpy between the two considered states at Tm
Tm : float
Temperature at which the equilibrium constant equals one, in Kelvin units
Cp0 : float
Variation of calorific capacity between the two states
m0 : float
m-value at the reference temperature (Tref)
m1 : float
Variation of m-value with temperature
p1_N, p2_N, p3_N, p4_N : float
parameters describing the native-state baseline
p1_U, p2_U, p3_U, p4_U : float
parameters describing the unfolded-state baseline
baseline_N_fx : function
for the native-state baseline
baseline_U_fx : function
for the unfolded-state baseline
extra_arg : None, optional
Not used but present for API compatibility with oligomeric models
Returns
-------
numpy.ndarray
Signal at the given temperatures and denaturant agent concentration, given the parameters
"""
K = eq_constant_termochem(T,D,DHm,Tm,Cp0,m0,m1)
fn = fn_two_state_monomer(K)
fu = 1 - fn
dT = shift_temperature_K(T)
# Baseline signals (with quadratic dependence on temperature)
S_native = baseline_N_fx(dT,D,p1_N, p2_N, p3_N, p4_N)
S_unfolded = baseline_U_fx(dT,D,p1_U, p2_U, p3_U, p4_U)
return fn*(S_native) + fu*(S_unfolded)
[docs]
def signal_two_state_t_unfolding(
T,Tm,dHm,
p1_N, p2_N, p3_N,
p1_U, p2_U, p3_U,
baseline_N_fx,
baseline_U_fx,
Cp=0,
extra_arg=None):
"""
Two-state temperature unfolding (monomer).
Parameters
----------
T : array-like
Temperature
Tm : float
Temperature at which the equilibrium constant equals one
dHm : float
Variation of enthalpy between the two considered states at Tm
p1_N, p2_N, p3_N : float
baseline parameters for the native-state baseline
p1_U, p2_U, p3_U : float
baseline parameters for the unfolded-state baseline
baseline_N_fx : callable
function to calculate the baseline for the native state
baseline_U_fx : callable
function to calculate the baseline for the unfolded state
Cp : float, optional
Variation of heat capacity between the two states (default: 0)
extra_arg : None, optional
Not used but present for compatibility
Returns
-------
numpy.ndarray
Signal at the given temperatures, given the parameters
"""
K = eq_constant_thermo(T,dHm,Tm,Cp)
fn = fn_two_state_monomer(K)
fu = 1 - fn
dT = shift_temperature_K(T)
S_native = baseline_N_fx(dT,0,0,p1_N,p2_N,p3_N) # No denaturant dependence, that's why d=0 and den_slope = 0
S_unfolded = baseline_U_fx(dT,0,0,p1_U,p2_U,p3_U) # No denaturant dependence, that's why d=0 and den_slope = 0
return fn*(S_native) + fu*(S_unfolded)
# Oligomeric thermal unfolding signals
[docs]
def two_state_thermal_unfold_curve(
T,C,Tm,dHm,
p1_N, p2_N, p3_N,
p1_U, p2_U, p3_U,
baseline_N_fx,
baseline_U_fx,
Cp=0):
"""
Two-state temperature unfolding (monomer).
N ⇔ U
Parameters
----------
T : array-like
Temperature
C : array-like
Oligomer sample concentration - only for compatibility with oligomeric models, not used in the monomeric model
Tm : float
Temperature at which the equilibrium constant equals one
dHm : float
Variation of enthalpy between the two considered states at Tm
p1_N, p2_N, p3_N : float
baseline parameters for the native-state baseline
p1_U, p2_U, p3_U : float
baseline parameters for the unfolded-state baseline
baseline_N_fx : callable
function to calculate the baseline for the native state
baseline_U_fx : callable
function to calculate the baseline for the unfolded state
Cp : float, optional
Variation of heat capacity between the two states (default: 0)
Returns
-------
numpy.ndarray
Signal at the given temperatures, given the parameters
"""
K = eq_constant_thermo(T,dHm,Tm,Cp)
fn = fn_two_state_monomer(K)
fu = 1 - fn
dT = shift_temperature_K(T)
S_native = baseline_N_fx(dT, p1_N, p2_N, p3_N)
S_unfolded = baseline_U_fx(dT, p1_U, p2_U, p3_U)
return C * (fn * (S_native) + fu * (S_unfolded))
[docs]
def two_state_thermal_unfold_curve_dimer(
T,C,Tm,dHm,
p1_N, p2_N, p3_N,
p1_U, p2_U, p3_U,
baseline_N_fx,
baseline_U_fx,
Cp=0):
"""
Two-state temperature unfolding (dimer).
N2 ⇔ 2U C is the total concentration (M) of the protein in dimer equivalent.
Parameters
----------
T : array-like
Temperature
C : array-like
Oligomer sample concentration
Tm : float
Temperature at which the equilibrium constant equals one
dHm : float
Variation of enthalpy between the two considered states at Tm
p1_N, p2_N, p3_N : float
baseline parameters for the native-state baseline
p1_U, p2_U, p3_U : float
baseline parameters for the unfolded-state baseline
baseline_N_fx : callable
function to calculate the baseline for the native state
baseline_U_fx : callable
function to calculate the baseline for the unfolded state
Cp : float, optional
Variation of heat capacity between the two states (default: 0)
Returns
-------
numpy.ndarray
Signal at the given temperatures, given the parameters
Notes
-----
C is the total concentration (M) of the protein in dimer equivalent.
"""
K = eq_constant_thermo(T,dHm,Tm,Cp)
fu = fu_two_state_dimer(K,C)
fn = 1 - fu
dT = shift_temperature_K(T)
S_native = baseline_N_fx(dT,p1_N,p2_N,p3_N)
S_unfolded = baseline_U_fx(dT,p1_U,p2_U,p3_U)
return C * (fn * (S_native) + fu * (S_unfolded) * 2)
[docs]
def two_state_thermal_unfold_curve_trimer(
T,C,Tm,dHm,
p1_N, p2_N, p3_N,
p1_U, p2_U, p3_U,
baseline_N_fx,
baseline_U_fx,
Cp=0):
"""
Two-state temperature unfolding (trimer).
N3 ⇔ 3U
Parameters
----------
T : array-like
Temperature
C : array-like
Oligomer sample concentration
Tm : float
Temperature at which the equilibrium constant equals one
dHm : float
Variation of enthalpy between the two considered states at Tm
p1_N, p2_N, p3_N : float
baseline parameters for the native-state baseline
p1_U, p2_U, p3_U : float
baseline parameters for the unfolded-state baseline
baseline_N_fx : callable
function to calculate the baseline for the native state
baseline_U_fx : callable
function to calculate the baseline for the unfolded state
Cp : float, optional
Variation of heat capacity between the two states (default: 0)
Returns
-------
numpy.ndarray
Signal at the given temperatures, given the parameters
Notes
-----
C is the total concentration (M) of the protein in trimer equivalent.
"""
K = eq_constant_thermo(T,dHm,Tm,Cp)
fu = fu_two_state_trimer(K,C)
fn = 1 - fu
dT = shift_temperature_K(T)
S_native = baseline_N_fx(dT,p1_N,p2_N,p3_N)
S_unfolded = baseline_U_fx(dT,p1_U,p2_U,p3_U)
return C * (fn * (S_native) + fu * (S_unfolded) * 3)
[docs]
def two_state_thermal_unfold_curve_tetramer(
T,C,Tm,dHm,
p1_N, p2_N, p3_N,
p1_U, p2_U, p3_U,
baseline_N_fx,
baseline_U_fx,
Cp=0,
extra_arg=None):
"""
Two-state temperature unfolding (tetramer).
N4 ⇔ 4U
Parameters
----------
T : array-like
Temperature
C : array-like
Oligomer sample concentration
Tm : float
Temperature at which the equilibrium constant equals one
dHm : float
Variation of enthalpy between the two considered states at Tm
p1_N, p2_N, p3_N : float
baseline parameters for the native-state baseline
p1_U, p2_U, p3_U : float
baseline parameters for the unfolded-state baseline
baseline_N_fx : callable
function to calculate the baseline for the native state
baseline_U_fx : callable
function to calculate the baseline for the unfolded state
Cp : float, optional
Variation of heat capacity between the two states (default: 0)
Returns
-------
numpy.ndarray
Signal at the given temperatures, given the parameters
Notes
-----
C is the total concentration (M) of the protein in tetramer equivalent.
"""
K = eq_constant_thermo(T,dHm,Tm,Cp)
fu = fu_two_state_tetramer(K,C)
fn = 1 - fu
dT = shift_temperature_K(T)
S_native = baseline_N_fx(dT,p1_N,p2_N,p3_N)
S_unfolded = baseline_U_fx(dT,p1_U,p2_U,p3_U)
return C * (fn * (S_native) + fu * (S_unfolded) * 4)
[docs]
def map_two_state_model_to_signal_fx(model):
"""
Maps the model string to the signal type
Parameters
----------
model : str,
string representation of model type.
Returns
-------
function
signal function corresponding to the string
"""
signal_fx_map = {
'Monomer': two_state_thermal_unfold_curve,
'Dimer': two_state_thermal_unfold_curve_dimer,
'Trimer': two_state_thermal_unfold_curve_trimer,
'Tetramer': two_state_thermal_unfold_curve_tetramer
}
return signal_fx_map.get(model)
#Oligomeric thermal unfolding signals with intermediate signals
[docs]
def map_three_state_model_to_signal_fx(model):
signal_fx_map = {
'Monomer_monomeric_intermediate': unfolding_curve_monomer_monomeric_intermediate,
'Dimer_monomeric_intermediate': unfolding_curve_dimer_monomeric_intermediate,
'Dimer_dimeric_intermediate': unfolding_curve_dimer_dimeric_intermediate,
'Trimer_monomeric_intermediate': unfolding_curve_trimer_monomeric_intermediate,
'Trimer_trimeric_intermediate': unfolding_curve_trimer_trimeric_intermediate,
'Tetramer_monomeric_intermediate': unfolding_curve_tetramer_monomeric_intermediate
}
return signal_fx_map.get(model)