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tsa_saxs/Minimization/PLUV.py

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#!/usr/bin/python
import sys
import os.path
import re
import time
import numpy as np
from scipy.stats import norm , gamma
from scipy import special
from scipy import signal
from scipy import ndimage
#from numba import njit, prange
######################################################################################################
######################################################################################################
######################################################################################################
############### POPC/POPG 95/5 mol/mol LUVs ###############
############### Reconstitution buffer: TRIS 20 mM, EDTA 2 mM ###############
############### Buffer used for PLUV exp. in DESY in 2017: ###############
######################################################################################################
######################################################################################################
######################################################################################################
############### GLOBAL VARIABLES ###############
# POPG molar ratio
CONST_x_PG = 0.05
# ############## POPC and POPG ###############
# 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine
# 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoglycerol
# number of chain groups
CONST_n_CH = 2
CONST_n_CH2 = 28
CONST_n_CH3 = 2
#X-ray scattering length chain groups (nm)
CONST_b_CH = 1.97256E-05 ;
CONST_b_CH2 = 2.25435E-05 ;
CONST_b_CH3 = 2.53615E-05 ;
### POPC
# Lipid-head volume
CONST_V_HL_PC = 0.331 # 0.320
# X-ray scattering length of head groups (nm)
CONST_b_PC = 2.73340E-04
CONST_b_CG = 1.88802E-04
CONST_b_PCN = 1.97256E-04
CONST_b_Chol = 7.60844E-05
# Lipid-volume temperature-dependencies a0 + a1*T (nm^3)
CONST_a0_V_POPC = 1.22810311835285
CONST_a1_V_POPC = 0.000934915795086395
### POPG
# Lipid-head volume
CONST_V_HL_PG = 0.289 ;
# X-ray Scattering length of head groups (nm)
CONST_b_PG = 2.47979E-04
CONST_b_PG1 = 1.32443E-04
CONST_b_PG2 = 1.15536E-04
# Lipid-volume temperature-dependencies a0 + a1*T (nm^3)
CONST_a0_V_POPG = 1.17881068602663
CONST_a1_V_POPG = 0.00108364914520327
############### Other variables ###############
### Water
# V_PW = 24.5e-3 #(nm^3) Perkins 2001 (Hydration shell in proteins)
# polynome coefficient for T-dependency of bulk-water-molecule volume (V_HW)
# Units in degree Celsius
CONST_p0_VW = 0.0299218
CONST_p1_VW = -2.25941e-06
CONST_p2_VW = 2.5675e-07
CONST_p3_VW = -1.69661e-09
CONST_p4_VW = 6.52029e-12
# polynome coefficient for T-dependency of bulk-water molar concentration (Cw)
#Units in degree Celsius
CONST_p0_Cw = 55.5052
CONST_p1_Cw = 0.00131894
CONST_p2_Cw = -0.000334396
CONST_p3_Cw = 9.10861e-07
CONST_b_HW = 2.8179E-05
CONST_d_shl = 0.31 # (nm) Perkins 2001 (Hydration shell in proteins)
# Composition of the Reconstitution buffer (M)
CONST_ctris = 0.02
CONST_cEDTA = 0.002
### Extra molecules
# TRIS buffer
CONST_b_tris = 1.860E-04
CONST_V_tris = 0.15147 # (nm^3)
# EDTA
CONST_b_EDTA = 4.340E-04 ;
CONST_V_EDTA = 0.56430 # (nm^3)
##################################################################################################################
##################################################################################################################
#########################################################
#@njit(parallel=True)
def PDF_normal(x, mu, sig) :
return np.exp(-(x-mu)**2 / (2*sig**2) ) /( sig*np.sqrt(2*np.pi))
#########################################################
#@njit(parallel=True)
def PDF_lognormal(x, mu_x, sig_x) :
# https://en.wikipedia.org/wiki/Log-normal_distribution
mu = np.log(mu_x**2 / np.sqrt(mu_x**2 + sig_x**2))
sig = np.sqrt(np.log(1 + sig_x**2 / mu_x**2))
return np.exp(-(np.log(x)-mu)**2 / (2*sig**2) ) /( x*sig*np.sqrt(2*np.pi))
#########################################################
def lipid_volume(T) :
return (1-CONST_x_PG) * (CONST_a0_V_POPC +T * CONST_a1_V_POPC) + CONST_x_PG * (CONST_a0_V_POPG + T * CONST_a1_V_POPG)
#########################################################
def water_volume(T) :
return CONST_p0_VW + CONST_p1_VW*T + CONST_p2_VW*T**2 + CONST_p3_VW*T**3 + CONST_p4_VW*T**4
#########################################################
#@njit(parallel=True)
def FTreal_erf(q, mu, d, sig) :
""" FTreal_erf(q, mu, d, sig) """
return np.where(q==0, 1, np.sin(q*d/2.)/(q*d/2.) * np.exp(-(q*sig)**2/2.) * np.cos(q*mu) )
#########################################################
#@njit(parallel=True)
def FTreal_gauss(q, mu, sig) :
""" FTreal_gauss(q, mu, sig) """
return np.exp(-(q*sig)**2/2.) * np.cos(q*mu)
#########################################################
def Slab(x, mu, L, sig) :
return 0.5 * ( special.erf( (x - (mu-L/2.))/(np.sqrt(2)*sig) ) - special.erf( (x - (mu+L/2))/(np.sqrt(2)*sig) ) )
#########################################################
def Gauss( x, V, mu, sig, A_L ) :
return V * PDF_normal(x, mu, sig) / A_L
#################################### j0^2 MOMENTS (SCHULZ PDF) #########################################
#################################### (checked!) #########################################
#@njit(parallel=True)
def mu4(q, Z, a) :
return np.where(q==0, a**4*(Z+1)*(Z+2)*(Z+3)*(Z+3), a**2 * (Z+2)*(Z+1) * ( 1 - (1+4*q*q*a*a)**(-(Z+3)/2.) * np.cos((Z+3)*np.arctan(2*q*a)) ) / ( 2*q**2 ) )
##################################################################################################################
##################################################################################################################
################################ SYMMETRIC VESICLE FOR X-RAY SLDs #########################################
######################################## SDP MODELLING #########################################
#################################### SEPARATED FORM FACTOR #########################################
##################################################################################################################
##################################################################################################################
#########################################################
######### Symmetric POPC bilayer ########################
######### liposomes and proteoliposomes #################
#########################################################
class SDP_POPC_RecBuf:
##################
def __init__(self, q, PAR) :
self.q = q
[self.Norm, self.nv,
self.Rm, self.Z,
self.n_TR, self.d_TR, self.s_TR,
self.d_Chol, self.s_Chol, self.d_PCN, self.s_PCN, self.d_CG, self.s_CG,
self.A_L, self.s_D_C,
self.s_CH2, self.d_CH, self.s_CH, self.s_CH3,
self.r_PCN, self.r_CG, self.r12, self.r32,
self.T, self.V_BW,
self.Con] = PAR
# [Example 1], fixed parameters:
# Norm 1e5 # Normalization
# n_TR 0.0 # Tris fraction
# d_TR 1.0 # Tris width (nm)
# s_TR 0.29 # Tris position (nm)
# d_CH 0.90 # CH position (nm)
# s_CH 0.305 # CH width (nm)
# r12 0.81 # V_CH/V_CH2
# T 37 # Temperature (°C)
# [example 1] fixed
Cw = CONST_p0_Cw + CONST_p1_Cw*self.T + CONST_p2_Cw*self.T**2 + CONST_p3_Cw*self.T**3
xtris = CONST_ctris / Cw # mole fraction of free TRIS in bulk
xEDTA = CONST_cEDTA / Cw # mole fraction of free EDTA in bulk
# Volumes
# [example 1] fixed
self.V_L = lipid_volume(self.T)
V_HW = water_volume(self.T)
V_HC = self.V_L - ( (1-CONST_x_PG) * CONST_V_HL_PC + CONST_x_PG * CONST_V_HL_PG )
# Calculation of mean D_C
self.D_C = V_HC / self.A_L
# Quasi-molecular volumes
# [example 1] r12 fixed
V_CH2 = V_HC / ( CONST_n_CH2 + CONST_n_CH*self.r12 + CONST_n_CH3*self.r32 ) # Volume of CH2 groups
V_CH = V_CH2 * self.r12 # Volume of CH groups
V_CH3 = V_CH2 * self.r32 # Volume of CH3 groups
self.V_CG = CONST_V_HL_PC * self.r_CG # Volume of CG group
self.V_PCN = CONST_V_HL_PC * self.r_PCN # Volume of PCN group
self.V_Chol = CONST_V_HL_PC * (1-self.r_PCN-self.r_CG) # Volume of CholCH3 group
# CONST
CONST_V_PG1 = CONST_V_HL_PG * 0.16 # Kucerka 2012
CONST_V_PG2 = CONST_V_HL_PG * ( 1 - 0.51 - 0.16) # Kucerka 2012
############### X-ray scattering lengths (nm)
# [example 1] rho_sol fixed
rho_sol = ( CONST_b_HW + xtris*CONST_b_tris + xEDTA*CONST_b_EDTA ) / V_HW
drho_Chol = ( (1-CONST_x_PG)*CONST_b_Chol/self.V_Chol + CONST_x_PG*CONST_b_PG2/CONST_V_PG2 ) - rho_sol
drho_PCN = ( (1-CONST_x_PG)*CONST_b_PCN/self.V_PCN + CONST_x_PG*CONST_b_PG1/CONST_V_PG1 ) - rho_sol
drho_CG = CONST_b_CG / self.V_CG - rho_sol
drho_TR = CONST_b_tris/ CONST_V_tris - rho_sol
drho_CH = CONST_b_CH / V_CH - rho_sol
drho_CH2 = CONST_b_CH2 / V_CH2 - rho_sol
drho_CH3 = CONST_b_CH3 / V_CH3 - rho_sol
drho_HW = CONST_b_HW / self.V_BW - rho_sol
############### D_C polydispersity
# Number of integration points
N = 201
# Parameter dependent integration bounds
# HC_min, HC_max = self.D_C-3*self.s_D_C, self.D_C+3*self.s_D_C
#
# Hardcoded integration bounds for POPC, fixed T = 37, A_L in [0.598, 0.719]
HC_min, HC_max = V_HC/0.719-0.5, V_HC/0.589+0.5
# Minimum and maximum samples (offset by 1/2 of the integration step w.r.t integration bounds for the midpoint rule)
integration_step = (HC_max - HC_min) / N
HC_first, HC_last = HC_min + 0.5*integration_step, HC_max - 0.5*integration_step
HC_array = np.linspace(HC_first, HC_last, N)
Normal = PDF_normal(HC_array, self.D_C, self.s_D_C)
############### calculating scattering amplitude -----------------------------------------------
self.Am = np.zeros([N,self.q.shape[0]],dtype=float)
c_CH = np.zeros(N,dtype=float)
c_CH3 = np.zeros(N,dtype=float)
############### c-prefactors
c_Chol = ( (1-CONST_x_PG)*self.V_Chol + CONST_x_PG*CONST_V_PG2 ) / self.A_L
c_PCN = ( (1-CONST_x_PG)*self.V_PCN + CONST_x_PG*CONST_V_PG1 ) / self.A_L
c_CG = self.V_CG / self.A_L
c_TR = CONST_V_tris*self.n_TR / self.A_L
for hc in range(N):
c_CH[hc] = V_CH * CONST_n_CH / (V_HC / HC_array[hc] )
c_CH3[hc] = V_CH3 * CONST_n_CH3 / (V_HC / HC_array[hc] )
for hc in range(N):
# Adding hydrocarbon-chain envelope
self.Am[hc] += 2 * drho_CH2 *HC_array[hc] * FTreal_erf(self.q, 0, 2*HC_array[hc], self.s_CH2)
# Adding CH and CH3 groups
self.Am[hc] += 2 * (drho_CH - drho_CH2) * c_CH[hc] * FTreal_gauss(self.q, self.d_CH, self.s_CH)
self.Am[hc] += 2 * (drho_CH3 - drho_CH2) * c_CH3[hc] * FTreal_gauss(self.q, 0, self.s_CH3)
# Adding hydration-water envelope
self.Am[hc] += 4 * drho_HW * ( self.d_CG + self.d_PCN + self.d_Chol + CONST_d_shl) * FTreal_erf(self.q, (HC_array[hc]+(self.d_CG+self.d_PCN+self.d_Chol+CONST_d_shl)/2.), (self.d_CG+self.d_PCN+self.d_Chol+CONST_d_shl), self.s_CH2)
# Adding CG, PCN and CholCH3 groups
self.Am[hc] += 2 * (drho_TR - drho_HW) * c_TR * FTreal_gauss(self.q, (HC_array[hc]+self.d_TR/2.), self.s_TR)
self.Am[hc] += 2 * (drho_CG - drho_HW) * c_CG * FTreal_gauss(self.q, (HC_array[hc]+self.d_CG/2.), self.s_CG)
self.Am[hc] += 2 * (drho_PCN - drho_HW) * c_PCN * FTreal_gauss(self.q, (HC_array[hc]+self.d_CG+self.d_PCN/2.), self.s_PCN)
self.Am[hc] += 2 * (drho_Chol - drho_HW) * c_Chol * FTreal_gauss(self.q, (HC_array[hc]+self.d_CG+self.d_PCN+self.d_Chol/2.), self.s_Chol)
############### Ensemble average
# multiply each columns of Am by Normal and sum along the columns,
# then multiply by integration step
self.I = np.einsum('ij,i->j', self.Am**2, Normal) * integration_step
##################
def intensity(self):
alp = self.Rm/(self.Z+1)
return ( self.Norm * self.nv*1e-6 ) * self.I * ( 16*np.pi**2*mu4(self.q,self.Z,alp) ) + self.Con*( 0.99*(1./(1+np.exp(-8*(self.q-1.)))) + 0.01 )
##################
def negative_water(self):
self.check = 0
z_array = np.linspace(0.,4.,81)
CG = Gauss(z_array, self.V_CG, self.D_C+self.d_CG/2., self.s_CG, self.A_L)
PCN = Gauss(z_array, self.V_PCN, self.D_C+self.d_CG+self.d_PCN/2., self.s_PCN, self.A_L)
Chol = Gauss(z_array, self.V_Chol, self.D_C+self.d_CG+self.d_PCN+self.d_Chol/2., self.s_Chol, self.A_L)
TRIS = Gauss(z_array, self.n_TR*CONST_V_tris, self.D_C+self.d_TR/2., self.s_TR, self.A_L)
BW = Slab(z_array, self.D_C+(self.d_CG+self.d_PCN+self.d_Chol+CONST_d_shl)/2., self.d_CG+self.d_PCN+self.d_Chol+CONST_d_shl, self.s_CH2) - CG - PCN - Chol - TRIS
for i in(BW) :
if i <-0.001 : self.check+= 1
return self.check
##################################################################################################################
##################################################################################################################
class SDP_POPC_RecBuf_LogNormal:
##################
def __init__(self, q, PAR) :
self.q = q
[self.Norm, self.nv,
self.Rm, self.Z,
self.n_TR, self.d_TR, self.s_TR,
self.d_Chol, self.s_Chol, self.d_PCN, self.s_PCN, self.d_CG, self.s_CG,
self.A_L, self.s_D_C,
self.s_CH2, self.d_CH, self.s_CH, self.s_CH3,
self.r_PCN, self.r_CG, self.r12, self.r32,
self.T, self.V_BW,
self.Con] = PAR
# [Example 1], fixed parameters:
# Norm 1e5 # Normalization
# n_TR 0.0 # Tris fraction
# d_TR 1.0 # Tris width (nm)
# s_TR 0.29 # Tris position (nm)
# d_CH 0.90 # CH position (nm)
# s_CH 0.305 # CH width (nm)
# r12 0.81 # V_CH/V_CH2
# T 37 # Temperature (°C)
# [example 1] fixed
Cw = CONST_p0_Cw + CONST_p1_Cw*self.T + CONST_p2_Cw*self.T**2 + CONST_p3_Cw*self.T**3
xtris = CONST_ctris / Cw # mole fraction of free TRIS in bulk
xEDTA = CONST_cEDTA / Cw # mole fraction of free EDTA in bulk
# Volumes
# [example 1] fixed
self.V_L = lipid_volume(self.T)
V_HW = water_volume(self.T)
V_HC = self.V_L - ( (1-CONST_x_PG) * CONST_V_HL_PC + CONST_x_PG * CONST_V_HL_PG )
# Calculation of mean D_C
self.D_C = V_HC / self.A_L
# Quasi-molecular volumes
# [example 1] r12 fixed
V_CH2 = V_HC / ( CONST_n_CH2 + CONST_n_CH*self.r12 + CONST_n_CH3*self.r32 ) # Volume of CH2 groups
V_CH = V_CH2 * self.r12 # Volume of CH groups
V_CH3 = V_CH2 * self.r32 # Volume of CH3 groups
self.V_CG = CONST_V_HL_PC * self.r_CG # Volume of CG group
self.V_PCN = CONST_V_HL_PC * self.r_PCN # Volume of PCN group
self.V_Chol = CONST_V_HL_PC * (1-self.r_PCN-self.r_CG) # Volume of CholCH3 group
# CONST
CONST_V_PG1 = CONST_V_HL_PG * 0.16 # Kucerka 2012
CONST_V_PG2 = CONST_V_HL_PG * ( 1 - 0.51 - 0.16) # Kucerka 2012
############### X-ray scattering lengths (nm)
# [example 1] rho_sol fixed
rho_sol = ( CONST_b_HW + xtris*CONST_b_tris + xEDTA*CONST_b_EDTA ) / V_HW
drho_Chol = ( (1-CONST_x_PG)*CONST_b_Chol/self.V_Chol + CONST_x_PG*CONST_b_PG2/CONST_V_PG2 ) - rho_sol
drho_PCN = ( (1-CONST_x_PG)*CONST_b_PCN/self.V_PCN + CONST_x_PG*CONST_b_PG1/CONST_V_PG1 ) - rho_sol
drho_CG = CONST_b_CG / self.V_CG - rho_sol
drho_TR = CONST_b_tris/ CONST_V_tris - rho_sol
drho_CH = CONST_b_CH / V_CH - rho_sol
drho_CH2 = CONST_b_CH2 / V_CH2 - rho_sol
drho_CH3 = CONST_b_CH3 / V_CH3 - rho_sol
drho_HW = CONST_b_HW / self.V_BW - rho_sol
############### D_C polydispersity
N = 200
HC_array = np.linspace(self.D_C-3*self.s_D_C, self.D_C+3*self.s_D_C, N)
LogNormal = PDF_lognormal(HC_array, self.D_C, self.s_D_C)
############### calculating scattering amplitude -----------------------------------------------
self.Am = np.zeros([HC_array.shape[0],self.q.shape[0]],dtype=float)
c_CH = np.zeros(HC_array.shape[0],dtype=float)
c_CH3 = np.zeros(HC_array.shape[0],dtype=float)
############### c-prefactors
c_Chol = ( (1-CONST_x_PG)*self.V_Chol + CONST_x_PG*CONST_V_PG2 ) / self.A_L
c_PCN = ( (1-CONST_x_PG)*self.V_PCN + CONST_x_PG*CONST_V_PG1 ) / self.A_L
c_CG = self.V_CG / self.A_L
c_TR = CONST_V_tris*self.n_TR / self.A_L
for hc in range(HC_array.shape[0]):
c_CH[hc] = V_CH * CONST_n_CH / (V_HC / HC_array[hc] )
c_CH3[hc] = V_CH3 * CONST_n_CH3 / (V_HC / HC_array[hc] )
for hc in range(HC_array.shape[0]):
# Adding hydrocarbon-chain envelope
self.Am[hc] += 2 * drho_CH2 *HC_array[hc] * FTreal_erf(self.q, 0, 2*HC_array[hc], self.s_CH2)
# Adding CH and CH3 groups
self.Am[hc] += 2 * (drho_CH - drho_CH2) * c_CH[hc] * FTreal_gauss(self.q, self.d_CH, self.s_CH)
self.Am[hc] += 2 * (drho_CH3 - drho_CH2) * c_CH3[hc] * FTreal_gauss(self.q, 0, self.s_CH3)
# Adding hydration-water envelope
self.Am[hc] += 4 * drho_HW * ( self.d_CG + self.d_PCN + self.d_Chol + CONST_d_shl) * FTreal_erf(self.q, (HC_array[hc]+(self.d_CG+self.d_PCN+self.d_Chol+CONST_d_shl)/2.), (self.d_CG+self.d_PCN+self.d_Chol+CONST_d_shl), self.s_CH2)
# Adding CG, PCN and CholCH3 groups
self.Am[hc] += 2 * (drho_TR - drho_HW) * c_TR * FTreal_gauss(self.q, (HC_array[hc]+self.d_TR/2.), self.s_TR)
self.Am[hc] += 2 * (drho_CG - drho_HW) * c_CG * FTreal_gauss(self.q, (HC_array[hc]+self.d_CG/2.), self.s_CG)
self.Am[hc] += 2 * (drho_PCN - drho_HW) * c_PCN * FTreal_gauss(self.q, (HC_array[hc]+self.d_CG+self.d_PCN/2.), self.s_PCN)
self.Am[hc] += 2 * (drho_Chol - drho_HW) * c_Chol * FTreal_gauss(self.q, (HC_array[hc]+self.d_CG+self.d_PCN+self.d_Chol/2.), self.s_Chol)
############### Ensemble average
self.I = np.zeros(self.q.shape[0], dtype=float)
for hc in range(HC_array.shape[0]):
if hc==0 or hc==N-1 : self.I+= self.Am[hc]**2 * LogNormal[hc] / 2
else : self.I+= self.Am[hc]**2 * LogNormal[hc]
self.I*= 6*self.s_D_C/(N-1)
##################
def intensity(self):
alp = self.Rm/(self.Z+1)
return ( self.Norm * self.nv*1e-6 ) * self.I * ( 16*np.pi**2*mu4(self.q,self.Z,alp) ) + self.Con*( 0.99*(1./(1+np.exp(-8*(self.q-1.)))) + 0.01 )
##################
def negative_water(self):
self.check = 0
z_array = np.linspace(0.,4.,81)
CG = Gauss(z_array, self.V_CG, self.D_C+self.d_CG/2., self.s_CG, self.A_L)
PCN = Gauss(z_array, self.V_PCN, self.D_C+self.d_CG+self.d_PCN/2., self.s_PCN, self.A_L)
Chol = Gauss(z_array, self.V_Chol, self.D_C+self.d_CG+self.d_PCN+self.d_Chol/2., self.s_Chol, self.A_L)
TRIS = Gauss(z_array, self.n_TR*CONST_V_tris, self.D_C+self.d_TR/2., self.s_TR, self.A_L)
BW = Slab(z_array, self.D_C+(self.d_CG+self.d_PCN+self.d_Chol+CONST_d_shl)/2., self.d_CG+self.d_PCN+self.d_Chol+CONST_d_shl, self.s_CH2) - CG - PCN - Chol - TRIS
for i in(BW) :
if i <-0.001 : self.check+= 1
return self.check
##################################################################################################################
##################################################################################################################
# vim ts=4,sts=4,sw=4
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