fix integration bounds for the polydispersity
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2 changed files with 24 additions and 119 deletions
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@ -9,7 +9,8 @@ import math
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sys.path.append("/mntdirect/_users/semeraro/python_tools")
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sys.path.append("/mntdirect/_users/semeraro/python_tools")
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import FormFactor
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import FormFactor
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#import PLUV_POPC_RecBuf
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#import PLUV_POPC_RecBuf
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from PLUV import SDP_base_POPC_RecBuf, SDP_POPC_RecBuf, SDP_POPC_RecBuf_LogNormal
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from PLUV import SDP_POPC_RecBuf
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#from PLUV import SDP_base_POPC_RecBuf, SDP_POPC_RecBuf, SDP_POPC_RecBuf_LogNormal
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###########################################################################################
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###########################################################################################
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###########################################################################################
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###########################################################################################
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@ -167,109 +167,6 @@ def mu4(q, Z, a) :
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######### liposomes and proteoliposomes #################
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######### liposomes and proteoliposomes #################
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#########################################################
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#########################################################
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class SDP_base_POPC_RecBuf:
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##################
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def __init__(self, q, PAR) :
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self.q = q
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[self.Norm, self.nv,
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self.Rm, self.Z,
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self.n_TR, self.d_TR, self.s_TR,
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self.d_Chol, self.s_Chol, self.d_PCN, self.s_PCN, self.d_CG, self.s_CG,
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self.A_L,
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self.s_CH2, self.d_CH, self.s_CH, self.s_CH3,
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self.r_PCN, self.r_CG, self.r12, self.r32,
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self.T, self.V_BW,
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self.Con] = PAR
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Cw = CONST_p0_Cw + CONST_p1_Cw*self.T + CONST_p2_Cw*self.T**2 + CONST_p3_Cw*self.T**3
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xtris = CONST_ctris / Cw # mole fraction of free TRIS in bulk
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xEDTA = CONST_cEDTA / Cw # mole fraction of free EDTA in bulk
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# Volumes
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self.V_L = lipid_volume(self.T)
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V_HW = water_volume(self.T)
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V_HC = self.V_L - ( (1-CONST_x_PG) * CONST_V_HL_PC + CONST_x_PG * CONST_V_HL_PG )
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# Quasi-molecular volumes
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V_CH2 = V_HC / ( CONST_n_CH2 + CONST_n_CH*self.r12 + CONST_n_CH3*self.r32 ) # Volume of CH2 groups
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V_CH = V_CH2 * self.r12 # Volume of CH groups
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V_CH3 = V_CH2 * self.r32 # Volume of CH3 groups
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self.V_CG = CONST_V_HL_PC * self.r_CG # Volume of CG group
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self.V_PCN = CONST_V_HL_PC * self.r_PCN # Volume of PCN group
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self.V_Chol = CONST_V_HL_PC * (1-self.r_PCN-self.r_CG) # Volume of CholCH3 group
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V_PG1 = CONST_V_HL_PG * 0.16 # Kucerka 2012
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V_PG2 = CONST_V_HL_PG * ( 1 - 0.51 - 0.16) # Kucerka 2012
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# Calculation of mean D_C
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self.D_C = V_HC / self.A_L
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# X-ray scattering lengths (nm)
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rho_sol = ( CONST_b_HW + xtris*CONST_b_tris + xEDTA*CONST_b_EDTA ) / V_HW
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drho_Chol = ( (1-CONST_x_PG)*CONST_b_Chol/self.V_Chol + CONST_x_PG*CONST_b_PG2/V_PG2 ) - rho_sol
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drho_PCN = ( (1-CONST_x_PG)*CONST_b_PCN/self.V_PCN + CONST_x_PG*CONST_b_PG1/V_PG1 ) - rho_sol
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drho_CG = CONST_b_CG / self.V_CG - rho_sol
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drho_TR = CONST_b_tris/ CONST_V_tris - rho_sol
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drho_CH = CONST_b_CH / V_CH - rho_sol
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drho_CH2 = CONST_b_CH2 / V_CH2 - rho_sol
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drho_CH3 = CONST_b_CH3 / V_CH3 - rho_sol
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drho_HW = CONST_b_HW / self.V_BW - rho_sol
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# c-prefactors
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c_Chol = ( (1-CONST_x_PG)*self.V_Chol + CONST_x_PG*V_PG2 ) / self.A_L
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c_PCN = ( (1-CONST_x_PG)*self.V_PCN + CONST_x_PG*V_PG1 ) / self.A_L
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c_CG = self.V_CG / self.A_L
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c_TR = CONST_V_tris*self.n_TR / self.A_L
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c_CH = V_CH * CONST_n_CH / self.A_L
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c_CH3 = V_CH3 * CONST_n_CH3 / self.A_L
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# calculating scattering amplitude
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self.Am=np.zeros(q.shape[0],dtype=float)
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# Adding hydrocarbon-chain envelope
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self.Am += 2 * drho_CH2 *self.D_C * FTreal_erf(self.q, 0, 2*self.D_C, self.s_CH2)
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# Adding CH and CH3 groups
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self.Am += 2 * (drho_CH - drho_CH2) * c_CH * FTreal_gauss(self.q, self.d_CH, self.s_CH)
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self.Am += 2 * (drho_CH3 - drho_CH2) * c_CH3 * FTreal_gauss(self.q, 0, self.s_CH3)
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# Adding hydration-water envelope
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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)
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# Adding CG, PCN and CholCH3 groups
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self.Am += 2 * (drho_TR - drho_HW) * c_TR * FTreal_gauss(self.q, (self.D_C+self.d_TR/2.), self.s_TR)
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self.Am += 2 * (drho_CG - drho_HW) * c_CG * FTreal_gauss(self.q, (self.D_C+self.d_CG/2.), self.s_CG)
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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)
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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)
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##################
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def amplitude(self):
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return self.Am
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##################
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def intensity(self):
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alp = self.Rm/(self.Z+1)
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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 )
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##################
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def negative_water(self):
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self.check = 0
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z_array = np.linspace(0.,4.,81)
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CG = Gauss(z_array, self.V_CG, self.D_C+self.d_CG/2., self.s_CG, self.A_L)
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PCN = Gauss(z_array, self.V_PCN, self.D_C+self.d_CG+self.d_PCN/2., self.s_PCN, self.A_L)
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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)
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TRIS = Gauss(z_array, self.n_TR*CONST_V_tris, self.D_C+self.d_TR/2., self.s_TR, self.A_L)
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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
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for i in(BW) :
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if i <-0.001 : self.check+= 1
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return self.check
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##################################################################################################################
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##################################################################################################################
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class SDP_POPC_RecBuf:
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class SDP_POPC_RecBuf:
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##################
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##################
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@ -336,14 +233,25 @@ class SDP_POPC_RecBuf:
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drho_HW = CONST_b_HW / self.V_BW - rho_sol
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drho_HW = CONST_b_HW / self.V_BW - rho_sol
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############### D_C polydispersity
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############### D_C polydispersity
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N = 21
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# Number of integration points
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HC_array = np.linspace(self.D_C-3*self.s_D_C, self.D_C+3*self.s_D_C, N)
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N = 201
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# Parameter dependent integration bounds
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# HC_min, HC_max = self.D_C-3*self.s_D_C, self.D_C+3*self.s_D_C
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#
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# Hardcoded integration bounds for POPC, fixed T = 37, A_L in [0.598, 0.719]
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HC_min, HC_max = V_HC/0.719-0.5, V_HC/0.589+0.5
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# Minimum and maximum samples (offset by 1/2 of the integration step w.r.t integration bounds for the midpoint rule)
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integration_step = (HC_max - HC_min) / N
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HC_first, HC_last = HC_min + 0.5*integration_step, HC_max - 0.5*integration_step
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HC_array = np.linspace(HC_first, HC_last, N)
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Normal = PDF_normal(HC_array, self.D_C, self.s_D_C)
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Normal = PDF_normal(HC_array, self.D_C, self.s_D_C)
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############### calculating scattering amplitude -----------------------------------------------
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############### calculating scattering amplitude -----------------------------------------------
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self.Am = np.zeros([HC_array.shape[0],self.q.shape[0]],dtype=float)
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self.Am = np.zeros([N,self.q.shape[0]],dtype=float)
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c_CH = np.zeros(HC_array.shape[0],dtype=float)
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c_CH = np.zeros(N,dtype=float)
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c_CH3 = np.zeros(HC_array.shape[0],dtype=float)
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c_CH3 = np.zeros(N,dtype=float)
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############### c-prefactors
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############### c-prefactors
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c_Chol = ( (1-CONST_x_PG)*self.V_Chol + CONST_x_PG*CONST_V_PG2 ) / self.A_L
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c_Chol = ( (1-CONST_x_PG)*self.V_Chol + CONST_x_PG*CONST_V_PG2 ) / self.A_L
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@ -351,11 +259,11 @@ class SDP_POPC_RecBuf:
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c_CG = self.V_CG / self.A_L
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c_CG = self.V_CG / self.A_L
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c_TR = CONST_V_tris*self.n_TR / self.A_L
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c_TR = CONST_V_tris*self.n_TR / self.A_L
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for hc in range(HC_array.shape[0]):
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for hc in range(N):
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c_CH[hc] = V_CH * CONST_n_CH / (V_HC / HC_array[hc] )
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c_CH[hc] = V_CH * CONST_n_CH / (V_HC / HC_array[hc] )
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c_CH3[hc] = V_CH3 * CONST_n_CH3 / (V_HC / HC_array[hc] )
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c_CH3[hc] = V_CH3 * CONST_n_CH3 / (V_HC / HC_array[hc] )
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for hc in range(HC_array.shape[0]):
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for hc in range(N):
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# Adding hydrocarbon-chain envelope
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# Adding hydrocarbon-chain envelope
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self.Am[hc] += 2 * drho_CH2 *HC_array[hc] * FTreal_erf(self.q, 0, 2*HC_array[hc], self.s_CH2)
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self.Am[hc] += 2 * drho_CH2 *HC_array[hc] * FTreal_erf(self.q, 0, 2*HC_array[hc], self.s_CH2)
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@ -372,13 +280,9 @@ class SDP_POPC_RecBuf:
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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)
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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)
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############### Ensemble average
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############### Ensemble average
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self.I = np.zeros(self.q.shape[0], dtype=float)
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# multiply each columns of Am by Normal and sum along the columns,
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# then multiply by integration step
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for hc in range(HC_array.shape[0]):
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self.I = np.einsum('ij,i->j', self.Am**2, Normal) * integration_step
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if hc==0 or hc==N-1 : self.I+= self.Am[hc]**2 * Normal[hc] / 2
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else : self.I+= self.Am[hc]**2 * Normal[hc]
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self.I*= 6*self.s_D_C/(N-1)
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##################
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##################
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def intensity(self):
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def intensity(self):
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@ -471,7 +375,7 @@ class SDP_POPC_RecBuf_LogNormal:
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drho_HW = CONST_b_HW / self.V_BW - rho_sol
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drho_HW = CONST_b_HW / self.V_BW - rho_sol
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############### D_C polydispersity
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############### D_C polydispersity
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N = 21
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N = 200
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HC_array = np.linspace(self.D_C-3*self.s_D_C, self.D_C+3*self.s_D_C, N)
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HC_array = np.linspace(self.D_C-3*self.s_D_C, self.D_C+3*self.s_D_C, N)
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LogNormal = PDF_lognormal(HC_array, self.D_C, self.s_D_C)
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LogNormal = PDF_lognormal(HC_array, self.D_C, self.s_D_C)
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