diff --git a/Minimization/PLUV.py b/Minimization/PLUV.py index d56d7dc..47cf31a 100644 --- a/Minimization/PLUV.py +++ b/Minimization/PLUV.py @@ -11,378 +11,373 @@ 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: ############### -###################################################################################################### -###################################################################################################### -###################################################################################################### +###################################################################################################### +###################################################################################################### +###################################################################################################### +############### 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 -x_PG = 0.05 +CONST_x_PG = 0.05 -# ############## POPC and POPG ############### -# 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine -# 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoglycerol +# ############## POPC and POPG ############### +# 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine +# 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoglycerol # number of chain groups -n_CH = 2 -n_CH2 = 28 -n_CH3 = 2 +CONST_n_CH = 2 +CONST_n_CH2 = 28 +CONST_n_CH3 = 2 #X-ray scattering length chain groups (nm) -b_CH = 1.97256E-05 ; -b_CH2 = 2.25435E-05 ; -b_CH3 = 2.53615E-05 ; +CONST_b_CH = 1.97256E-05 ; +CONST_b_CH2 = 2.25435E-05 ; +CONST_b_CH3 = 2.53615E-05 ; -### POPC -# Lipid-head volume -V_HL_PC = 0.331 # 0.320 -# X-ray scattering length of head groups (nm) -b_PC = 2.73340E-04 -b_CG = 1.88802E-04 -b_PCN = 1.97256E-04 -b_Chol = 7.60844E-05 -# Lipid-volume temperature-dependencies a0 + a1*T (nm^3) -a0_V_POPC = 1.22810311835285 -a1_V_POPC = 0.000934915795086395 - -### POPG +### POPC # Lipid-head volume -V_HL_PG = 0.289 ; +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) -b_PG = 2.47979E-04 -b_PG1 = 1.32443E-04 -b_PG2 = 1.15536E-04 +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) -a0_V_POPG = 1.17881068602663 -a1_V_POPG = 0.00108364914520327 +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 -p0_VW = 0.0299218 -p1_VW = -2.25941e-06 -p2_VW = 2.5675e-07 -p3_VW = -1.69661e-09 -p4_VW = 6.52029e-12 -# polynome coefficient for T-dependency of bulk-water molar concentration (Cw) -#Units in degree Celsius -p0_Cw = 55.5052 -p1_Cw = 0.00131894 -p2_Cw = -0.000334396 -p3_Cw = 9.10861e-07 +############### 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 -b_HW = 2.8179E-05 -d_shl = 0.31 # (nm) Perkins 2001 (Hydration shell in proteins) +CONST_b_HW = 2.8179E-05 +CONST_d_shl = 0.31 # (nm) Perkins 2001 (Hydration shell in proteins) -# Composition of the Reconstitution buffer (M) -ctris = 0.02 -cEDTA = 0.002 +# Composition of the Reconstitution buffer (M) +CONST_ctris = 0.02 +CONST_cEDTA = 0.002 -### Extra molecules +### Extra molecules # TRIS buffer -b_tris = 1.860E-04 -V_tris = 0.15147 # (nm^3) +CONST_b_tris = 1.860E-04 +CONST_V_tris = 0.15147 # (nm^3) # EDTA -b_EDTA = 4.340E-04 ; -V_EDTA = 0.56430 # (nm^3) +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)) - + ######################################################### def lipid_volume(T) : - return (1-x_PG) * (a0_V_POPC +T * a1_V_POPC) + x_PG * (a0_V_POPG + T * a1_V_POPG) + 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 p0_VW + p1_VW*T + p2_VW*T**2 + p3_VW*T**3 + p4_VW*T**4 - + 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) : - return np.where(q==0, 1, np.sin(q*d/2.)/(q*d/2.) * np.exp(-(q*sig)**2/2.) * np.cos(q*mu) ) + 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) : 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) ) ) + 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 + return V * PDF_normal(x, mu, sig) / A_L -#################################### j0^2 MOMENTS (SCHULZ PDF) ######################################### -#################################### (checked!) ######################################### +#################################### 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 ) ) + 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 ######################################### +################################ SYMMETRIC VESICLE FOR X-RAY SLDs ######################################### -######################################### SDP MODELLING ######################################### -#################################### SEPARATED FORM FACTOR ######################################### +######################################## SDP MODELLING ######################################### +#################################### SEPARATED FORM FACTOR ######################################### -################################################################################################################## -################################################################################################################## +################################################################################################################## +################################################################################################################## -######################################################### -######### Symmetric POPC bilayer ######################## -######### liposomes and proteoliposomes ################# -######################################################### +######################################################### +######### Symmetric POPC bilayer ######################## +######### liposomes and proteoliposomes ################# +######################################################### class SDP_base_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_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 - - Cw = p0_Cw + p1_Cw*self.T + p2_Cw*self.T**2 + p3_Cw*self.T**3 - xtris = ctris / Cw # mole fraction of free TRIS in bulk - xEDTA = cEDTA / Cw # mole fraction of free EDTA in bulk + 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_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 - # Volumes - self.V_L = lipid_volume(self.T) - V_HW = water_volume(self.T) - V_HC = self.V_L - ( (1-x_PG) * V_HL_PC + x_PG * V_HL_PG ) + 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 - # Quasi-molecular volumes - V_CH2 = V_HC / ( n_CH2 + n_CH*self.r12 + 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 + # Volumes + 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 ) - self.V_CG = V_HL_PC * self.r_CG # Volume of CG group - self.V_PCN = V_HL_PC * self.r_PCN # Volume of PCN group - self.V_Chol = V_HL_PC * (1-self.r_PCN-self.r_CG) # Volume of CholCH3 group + # Quasi-molecular volumes + 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 - V_PG1 = V_HL_PG * 0.16 # Kucerka 2012 - V_PG2 = V_HL_PG * ( 1 - 0.51 - 0.16) # Kucerka 2012 + 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 - # Calculation of mean D_C - self.D_C = V_HC / self.A_L - - # X-ray scattering lengths (nm) - rho_sol = ( b_HW + xtris*b_tris + xEDTA*b_EDTA ) / V_HW - drho_Chol = ( (1-x_PG)*b_Chol/self.V_Chol + x_PG*b_PG2/V_PG2 ) - rho_sol - drho_PCN = ( (1-x_PG)*b_PCN/self.V_PCN + x_PG*b_PG1/V_PG1 ) - rho_sol - drho_CG = b_CG / self.V_CG - rho_sol - drho_TR = b_tris/ V_tris - rho_sol - drho_CH = b_CH / V_CH - rho_sol - drho_CH2 = b_CH2 / V_CH2 - rho_sol - drho_CH3 = b_CH3 / V_CH3 - rho_sol - drho_HW = b_HW / self.V_BW - rho_sol + V_PG1 = CONST_V_HL_PG * 0.16 # Kucerka 2012 + V_PG2 = CONST_V_HL_PG * ( 1 - 0.51 - 0.16) # Kucerka 2012 - # c-prefactors - c_Chol = ( (1-x_PG)*self.V_Chol + x_PG*V_PG2 ) / self.A_L - c_PCN = ( (1-x_PG)*self.V_PCN + x_PG*V_PG1 ) / self.A_L - c_CG = self.V_CG / self.A_L - c_TR = V_tris*self.n_TR / self.A_L - c_CH = V_CH * n_CH / self.A_L - c_CH3 = V_CH3 * n_CH3 / self.A_L + # Calculation of mean D_C + self.D_C = V_HC / self.A_L - # calculating scattering amplitude - self.Am=np.zeros(q.shape[0],dtype=float) + # X-ray scattering lengths (nm) + 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/V_PG2 ) - rho_sol + drho_PCN = ( (1-CONST_x_PG)*CONST_b_PCN/self.V_PCN + CONST_x_PG*CONST_b_PG1/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 - # Adding hydrocarbon-chain envelope - self.Am += 2 * drho_CH2 *self.D_C * FTreal_erf(self.q, 0, 2*self.D_C, self.s_CH2) - # Adding CH and CH3 groups - self.Am += 2 * (drho_CH - drho_CH2) * c_CH * FTreal_gauss(self.q, self.d_CH, self.s_CH) - self.Am += 2 * (drho_CH3 - drho_CH2) * c_CH3 * FTreal_gauss(self.q, 0, self.s_CH3) + # c-prefactors + c_Chol = ( (1-CONST_x_PG)*self.V_Chol + CONST_x_PG*V_PG2 ) / self.A_L + c_PCN = ( (1-CONST_x_PG)*self.V_PCN + CONST_x_PG*V_PG1 ) / self.A_L + c_CG = self.V_CG / self.A_L + c_TR = CONST_V_tris*self.n_TR / self.A_L + c_CH = V_CH * CONST_n_CH / self.A_L + c_CH3 = V_CH3 * CONST_n_CH3 / self.A_L - # Adding hydration-water envelope - self.Am += 4 * drho_HW * ( self.d_CG + self.d_PCN + self.d_Chol + d_shl) * FTreal_erf(self.q, (self.D_C+(self.d_CG+self.d_PCN+self.d_Chol+d_shl)/2.), (self.d_CG+self.d_PCN+self.d_Chol+d_shl), self.s_CH2) - # Adding CG, PCN and CholCH3 groups - self.Am += 2 * (drho_TR - drho_HW) * c_TR * FTreal_gauss(self.q, (self.D_C+self.d_TR/2.), self.s_TR) - self.Am += 2 * (drho_CG - drho_HW) * c_CG * FTreal_gauss(self.q, (self.D_C+self.d_CG/2.), self.s_CG) - self.Am += 2 * (drho_PCN - drho_HW) * c_PCN * FTreal_gauss(self.q, (self.D_C+self.d_CG+self.d_PCN/2.), self.s_PCN) - self.Am += 2 * (drho_Chol - drho_HW) * c_Chol * FTreal_gauss(self.q, (self.D_C+self.d_CG+self.d_PCN+self.d_Chol/2.), self.s_Chol) + # calculating scattering amplitude + self.Am=np.zeros(q.shape[0],dtype=float) -################## - def amplitude(self): - return self.Am - -################## - def intensity(self): - alp = self.Rm/(self.Z+1) - return ( self.Norm * self.nv*1e-6 ) * self.Am**2 * ( 16*np.pi**2*mu4(self.q,self.Z,alp) ) + self.Con*( 0.99*(1./(1+np.exp(-8*(self.q-1.)))) + 0.01 ) + # Adding hydrocarbon-chain envelope + self.Am += 2 * drho_CH2 *self.D_C * FTreal_erf(self.q, 0, 2*self.D_C, self.s_CH2) + # Adding CH and CH3 groups + self.Am += 2 * (drho_CH - drho_CH2) * c_CH * FTreal_gauss(self.q, self.d_CH, self.s_CH) + self.Am += 2 * (drho_CH3 - drho_CH2) * c_CH3 * FTreal_gauss(self.q, 0, self.s_CH3) -################## - def negative_water(self): + # Adding hydration-water envelope + self.Am += 4 * drho_HW * ( self.d_CG + self.d_PCN + self.d_Chol + CONST_d_shl) * FTreal_erf(self.q, (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) + # Adding CG, PCN and CholCH3 groups + self.Am += 2 * (drho_TR - drho_HW) * c_TR * FTreal_gauss(self.q, (self.D_C+self.d_TR/2.), self.s_TR) + self.Am += 2 * (drho_CG - drho_HW) * c_CG * FTreal_gauss(self.q, (self.D_C+self.d_CG/2.), self.s_CG) + self.Am += 2 * (drho_PCN - drho_HW) * c_PCN * FTreal_gauss(self.q, (self.D_C+self.d_CG+self.d_PCN/2.), self.s_PCN) + self.Am += 2 * (drho_Chol - drho_HW) * c_Chol * FTreal_gauss(self.q, (self.D_C+self.d_CG+self.d_PCN+self.d_Chol/2.), self.s_Chol) - 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*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+d_shl)/2., self.d_CG+self.d_PCN+self.d_Chol+d_shl, self.s_CH2) - CG - PCN - Chol - TRIS +################## + def amplitude(self): + return self.Am - for i in(BW) : - if i <-0.001 : self.check+= 1 +################## + def intensity(self): + alp = self.Rm/(self.Z+1) + return ( self.Norm * self.nv*1e-6 ) * self.Am**2 * ( 16*np.pi**2*mu4(self.q,self.Z,alp) ) + self.Con*( 0.99*(1./(1+np.exp(-8*(self.q-1.)))) + 0.01 ) - return self.check +################## + 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: ################## - 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 - - Cw = p0_Cw + p1_Cw*self.T + p2_Cw*self.T**2 + p3_Cw*self.T**3 - xtris = ctris / Cw # mole fraction of free TRIS in bulk - xEDTA = cEDTA / Cw # mole fraction of free EDTA in bulk + 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 - # Volumes - self.V_L = lipid_volume(self.T) - V_HW = water_volume(self.T) - V_HC = self.V_L - ( (1-x_PG) * V_HL_PC + x_PG * V_HL_PG ) + 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 - # Calculation of mean D_C - self.D_C = V_HC / self.A_L - - # Quasi-molecular volumes - V_CH2 = V_HC / ( n_CH2 + n_CH*self.r12 + 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 + # Volumes + 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 ) - self.V_CG = V_HL_PC * self.r_CG # Volume of CG group - self.V_PCN = V_HL_PC * self.r_PCN # Volume of PCN group - self.V_Chol = V_HL_PC * (1-self.r_PCN-self.r_CG) # Volume of CholCH3 group + # Calculation of mean D_C + self.D_C = V_HC / self.A_L - V_PG1 = V_HL_PG * 0.16 # Kucerka 2012 - V_PG2 = V_HL_PG * ( 1 - 0.51 - 0.16) # Kucerka 2012 + # Quasi-molecular volumes + 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 - ############### X-ray scattering lengths (nm) - rho_sol = ( b_HW + xtris*b_tris + xEDTA*b_EDTA ) / V_HW - drho_Chol = ( (1-x_PG)*b_Chol/self.V_Chol + x_PG*b_PG2/V_PG2 ) - rho_sol - drho_PCN = ( (1-x_PG)*b_PCN/self.V_PCN + x_PG*b_PG1/V_PG1 ) - rho_sol - drho_CG = b_CG / self.V_CG - rho_sol - drho_TR = b_tris/ V_tris - rho_sol - drho_CH = b_CH / V_CH - rho_sol - drho_CH2 = b_CH2 / V_CH2 - rho_sol - drho_CH3 = b_CH3 / V_CH3 - rho_sol - drho_HW = b_HW / self.V_BW - rho_sol - - ############### D_C polydispersity - N = 21 - HC_array = np.linspace(self.D_C-3*self.s_D_C, self.D_C+3*self.s_D_C, N) - Normal = PDF_normal(HC_array, self.D_C, self.s_D_C) + 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 - ############### 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-x_PG)*self.V_Chol + x_PG*V_PG2 ) / self.A_L - c_PCN = ( (1-x_PG)*self.V_PCN + x_PG*V_PG1 ) / self.A_L - c_CG = self.V_CG / self.A_L - c_TR = V_tris*self.n_TR / self.A_L + V_PG1 = CONST_V_HL_PG * 0.16 # Kucerka 2012 + V_PG2 = CONST_V_HL_PG * ( 1 - 0.51 - 0.16) # Kucerka 2012 - for hc in range(HC_array.shape[0]): - c_CH[hc] = V_CH * n_CH / (V_HC / HC_array[hc] ) - c_CH3[hc] = V_CH3 * 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) + ############### X-ray scattering lengths (nm) + 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/V_PG2 ) - rho_sol + drho_PCN = ( (1-CONST_x_PG)*CONST_b_PCN/self.V_PCN + CONST_x_PG*CONST_b_PG1/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 - # Adding hydration-water envelope - self.Am[hc] += 4 * drho_HW * ( self.d_CG + self.d_PCN + self.d_Chol + d_shl) * FTreal_erf(self.q, (HC_array[hc]+(self.d_CG+self.d_PCN+self.d_Chol+d_shl)/2.), (self.d_CG+self.d_PCN+self.d_Chol+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) + ############### D_C polydispersity + N = 21 + HC_array = np.linspace(self.D_C-3*self.s_D_C, self.D_C+3*self.s_D_C, N) + Normal = PDF_normal(HC_array, self.D_C, self.s_D_C) - ############### 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 * Normal[hc] / 2 - else : self.I+= self.Am[hc]**2 * Normal[hc] - - self.I*= 6*self.s_D_C/(N-1) + ############### 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) -################## - 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 ) + ############### c-prefactors + c_Chol = ( (1-CONST_x_PG)*self.V_Chol + CONST_x_PG*V_PG2 ) / self.A_L + c_PCN = ( (1-CONST_x_PG)*self.V_PCN + CONST_x_PG*V_PG1 ) / self.A_L + c_CG = self.V_CG / self.A_L + c_TR = CONST_V_tris*self.n_TR / self.A_L -################## - def negative_water(self): + 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] ) - 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*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+d_shl)/2., self.d_CG+self.d_PCN+self.d_Chol+d_shl, self.s_CH2) - CG - PCN - Chol - TRIS + for hc in range(HC_array.shape[0]): - for i in(BW) : - if i <-0.001 : self.check+= 1 + # 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 * Normal[hc] / 2 + else : self.I+= self.Am[hc]**2 * Normal[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 - return self.check - ################################################################################################################## ################################################################################################################## - - - - - - +# vim ts=4,sts=4,sw=4