356 lines
13 KiB
Julia
356 lines
13 KiB
Julia
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module PLUV
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import SpecialFunctions: erf
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######################################################################################################
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######################################################################################################
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######################################################################################################
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############### POPC/POPG 95/5 mol/mol LUVs ###############
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############### Reconstitution buffer: TRIS 20 mM, EDTA 2 mM ###############
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############### Buffer used for PLUV exp. in DESY in 2017: ###############
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######################################################################################################
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######################################################################################################
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######################################################################################################
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const parameter_names = [
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:norm, :nv, :rm, :z, :n_tr, :d_tr, :s_tr, :d_chol, :s_chol, :d_pcn, :s_pcn, :d_cg, :s_cg,
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:a_l, :s_d_c, :s_ch2, :d_ch, :s_ch, :s_ch3, :r_pcn, :r_cg, :r12, :r32, :t, :v_bw, :con
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]
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############### GLOBAL VARIABLES ###############
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# POPG molar ratio
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const CONST_x_PG = 0.05
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# ############## POPC and POPG ###############
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# 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine
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# 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoglycerol
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# number of chain groups
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const CONST_n_CH = 2
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const CONST_n_CH2 = 28
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const CONST_n_CH3 = 2
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#X-ray scattering length chain groups (nm)
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const CONST_b_CH = 1.97256E-05
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const CONST_b_CH2 = 2.25435E-05
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const CONST_b_CH3 = 2.53615E-05
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### POPC
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# Lipid-head volume
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const CONST_V_HL_PC = 0.331 # 0.320
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# X-ray scattering length of head groups (nm)
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const CONST_b_PC = 2.73340E-04
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const CONST_b_CG = 1.88802E-04
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const CONST_b_PCN = 1.97256E-04
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const CONST_b_Chol = 7.60844E-05
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# Lipid-volume temperature-dependencies a0 + a1*T (nm^3)
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const CONST_a0_V_POPC = 1.22810311835285
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const CONST_a1_V_POPC = 0.000934915795086395
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### POPG
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# Lipid-head volume
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const CONST_V_HL_PG = 0.289
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# X-ray Scattering length of head groups (nm)
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const CONST_b_PG = 2.47979E-04
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const CONST_b_PG1 = 1.32443E-04
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const CONST_b_PG2 = 1.15536E-04
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# Lipid-volume temperature-dependencies a0 + a1*T (nm^3)
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const CONST_a0_V_POPG = 1.17881068602663
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const CONST_a1_V_POPG = 0.00108364914520327
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############### Other variables ###############
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### Water
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# V_PW = 24.5e-3 #(nm^3) Perkins 2001 (Hydration shell in proteins)
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# polynome coefficient for T-dependency of bulk-water-molecule volume (V_HW)
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# Units in degree Celsius
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const CONST_p0_VW = 0.0299218
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const CONST_p1_VW = -2.25941e-06
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const CONST_p2_VW = 2.5675e-07
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const CONST_p3_VW = -1.69661e-09
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const CONST_p4_VW = 6.52029e-12
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# polynome coefficient for T-dependency of bulk-water molar concentration (Cw)
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#Units in degree Celsius
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const CONST_p0_Cw = 55.5052
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const CONST_p1_Cw = 0.00131894
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const CONST_p2_Cw = -0.000334396
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const CONST_p3_Cw = 9.10861e-07
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const CONST_b_HW = 2.8179E-05
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const CONST_d_shl = 0.31 # (nm) Perkins 2001 (Hydration shell in proteins)
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# Composition of the Reconstitution buffer (M)
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const CONST_ctris = 0.02
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const CONST_cEDTA = 0.002
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### Extra molecules
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# TRIS buffer
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const CONST_b_tris = 1.860E-04
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const CONST_V_tris = 0.15147 # (nm^3)
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# EDTA
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const CONST_b_EDTA = 4.340E-04
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const CONST_V_EDTA = 0.56430 # (nm^3)
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##################################################################################################################
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##################################################################################################################
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#########################################################
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#@njit(parallel=True)
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function PDF_normal(x, mu, sig)
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return exp(-(x - mu)^2 / (2 * sig^2)) / (sig * sqrt(2 * pi))
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end
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#########################################################
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#@njit(parallel=True)
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function PDF_lognormal(x, mu_x, sig_x)
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# https://en.wikipedia.org/wiki/Log-normal_distribution
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mu = log(mu_x^2 / sqrt(mu_x^2 + sig_x^2))
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sig = sqrt(log(1 + sig_x^2 / mu_x^2))
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return exp(-(log(x) - mu)^2 / (2 * sig^2)) / (x * sig * sqrt(2 * pi))
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end
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#########################################################
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function lipid_volume(T)
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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)
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end
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#########################################################
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function water_volume(T)
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return CONST_p0_VW + CONST_p1_VW * T + CONST_p2_VW * T^2 + CONST_p3_VW * T^3 + CONST_p4_VW * T^4
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end
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#########################################################
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#@njit(parallel=True)
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function FTreal_erf(q, mu, d, sig)
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""" FTreal_erf(q, mu, d, sig) """
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return sin(q * d / 2.0) / (q * d / 2.0) * exp(-(q * sig)^2 / 2.0) * cos(q * mu)
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end
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#########################################################
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#@njit(parallel=True)
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function FTreal_gauss(q, mu, sig)
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""" FTreal_gauss(q, mu, sig) """
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return exp(-(q * sig)^2 / 2.0) * cos(q * mu)
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end
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#########################################################
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function Slab(x, mu, L, sig)
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return 0.5 * (erf((x - (mu - L / 2.0)) / (sqrt(2) * sig)) - erf((x - (mu + L / 2)) / (sqrt(2) * sig)))
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end
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#########################################################
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function Gauss(x, V, mu, sig, A_L)
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return V * PDF_normal(x, mu, sig) / A_L
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end
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#################################### j0^2 MOMENTS (SCHULZ PDF) #########################################
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#################################### (checked!) #########################################
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#@njit(parallel=True)
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function mu4(q, Z, a)
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return a^2 * (Z + 2) * (Z + 1) * (1 - (1 + 4 * q^2 * a^2)^(-(Z + 3) / 2.0) * cos((Z + 3) * atan(2 * q * a))) / (2 * q^2)
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end
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##################################################################################################################
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##################################################################################################################
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################################ SYMMETRIC VESICLE FOR X-RAY SLDs #########################################
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######################################## SDP MODELLING #########################################
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#################################### SEPARATED FORM FACTOR #########################################
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##################################################################################################################
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##################################################################################################################
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#########################################################
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######### Symmetric POPC bilayer ########################
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######### liposomes and proteoliposomes #################
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#########################################################
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##################
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function intensity(P::NamedTuple, q)
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return intensity(Float64[P...], q)
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end
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function intensity(P::AbstractArray{Float64}, q)
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Norm, nv, Rm, Z, n_TR, d_TR, s_TR, d_Chol, s_Chol, d_PCN, s_PCN, d_CG, s_CG,
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A_L, s_D_C, s_CH2, d_CH, s_CH, s_CH3, r_PCN, r_CG, r12, r32, T, V_BW, Con = P
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# [Example 1], fixed parameters
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# Norm 1e5 # Normalization
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# n_TR 0.0 # Tris fraction
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# d_TR 1.0 # Tris width (nm)
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# s_TR 0.29 # Tris position (nm)
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# d_CH 0.90 # CH position (nm)
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# s_CH 0.305 # CH width (nm)
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# r12 0.81 # V_CH/V_CH2
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# T 37 # Temperature (°C)
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# [example 1] fixed
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Cw = CONST_p0_Cw + CONST_p1_Cw * T + CONST_p2_Cw * T^2 + CONST_p3_Cw * 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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# [example 1] fixed
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V_L = lipid_volume(T)
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V_HW = water_volume(T)
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V_HC = V_L - ((1 - CONST_x_PG) * CONST_V_HL_PC + CONST_x_PG * CONST_V_HL_PG)
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# Calculation of mean D_C
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D_C = V_HC / A_L
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# Quasi-molecular volumes
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# [example 1] r12 fixed
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V_CH2 = V_HC / (CONST_n_CH2 + CONST_n_CH * r12 + CONST_n_CH3 * r32) # Volume of CH2 groups
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V_CH = V_CH2 * r12 # Volume of CH groups
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V_CH3 = V_CH2 * r32 # Volume of CH3 groups
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V_CG = CONST_V_HL_PC * r_CG # Volume of CG group
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V_PCN = CONST_V_HL_PC * r_PCN # Volume of PCN group
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V_Chol = CONST_V_HL_PC * (1 - r_PCN - r_CG) # Volume of CholCH3 group
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# CONST
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CONST_V_PG1 = CONST_V_HL_PG * 0.16 # Kucerka 2012
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CONST_V_PG2 = CONST_V_HL_PG * (1 - 0.51 - 0.16) # Kucerka 2012
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############### X-ray scattering lengths (nm)
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# [example 1] rho_sol fixed
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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 / V_Chol + CONST_x_PG * CONST_b_PG2 / CONST_V_PG2) - rho_sol
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drho_PCN = ((1 - CONST_x_PG) * CONST_b_PCN / V_PCN + CONST_x_PG * CONST_b_PG1 / CONST_V_PG1) - rho_sol
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drho_CG = CONST_b_CG / 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 / V_BW - rho_sol
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############### D_C polydispersity
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# Number of integration points
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N = 201
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# Parameter dependent integration bounds
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# HC_min, HC_max = D_C-3*s_D_C, D_C+3*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 = range(HC_first, HC_last, length=N)
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Normal = PDF_normal.(HC_array, D_C, s_D_C)
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############### c-prefactors
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c_Chol = ((1 - CONST_x_PG) * V_Chol + CONST_x_PG * CONST_V_PG2) / A_L
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c_PCN = ((1 - CONST_x_PG) * V_PCN + CONST_x_PG * CONST_V_PG1) / A_L
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c_CG = V_CG / A_L
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c_TR = CONST_V_tris * n_TR / A_L
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c_CH = V_CH * CONST_n_CH / V_HC * HC_array
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c_CH3 = V_CH3 * CONST_n_CH3 / V_HC * HC_array
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d_comp = d_CG + d_PCN + d_Chol + CONST_d_shl
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############### calculating scattering amplitude -----------------------------------------------
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Am = zeros(size(q, 1), N)
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for i in 1:N
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# Adding hydrocarbon-chain envelope
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Am[:, i] += 2 * drho_CH2 * HC_array[i] * FTreal_erf.(q, 0, 2 * HC_array[i], s_CH2)
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# Adding CH and CH3 groups
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Am[:, i] += 2 * (drho_CH - drho_CH2) * c_CH[i] * FTreal_gauss.(q, d_CH, s_CH)
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Am[:, i] += 2 * (drho_CH3 - drho_CH2) * c_CH3[i] * FTreal_gauss.(q, 0, s_CH3)
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# Adding hydration-water envelope
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Am[:, i] += 4 * drho_HW * d_comp * FTreal_erf.(q, (HC_array[i] + d_comp / 2.0), d_comp, s_CH2)
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# Adding CG, PCN and CholCH3 groups
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Am[:, i] += 2 * (drho_TR - drho_HW) * c_TR * FTreal_gauss.(q, (HC_array[i] + d_TR / 2.0), s_TR)
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Am[:, i] += 2 * (drho_CG - drho_HW) * c_CG * FTreal_gauss.(q, (HC_array[i] + d_CG / 2.0), s_CG)
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Am[:, i] += 2 * (drho_PCN - drho_HW) * c_PCN * FTreal_gauss.(q, (HC_array[i] + d_CG + d_PCN / 2.0), s_PCN)
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Am[:, i] += 2 * (drho_Chol - drho_HW) * c_Chol * FTreal_gauss.(q, (HC_array[i] + d_CG + d_PCN + d_Chol / 2.0), s_Chol)
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############### Ensemble average
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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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I = vec(sum(Am .^ 2 .* Normal'; dims=2)) * integration_step
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alp = Rm / (Z + 1)
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return @. (Norm * nv * 1e-6) * I * (16 * pi^2 * mu4(q, Z, alp)) + Con * (0.99 * (1.0 / (1 + exp(-8 * (q - 1.0)))) + 0.01)
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end
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end
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##################
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function negative_water(P::NamedTuple)
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return negative_water([P...])
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end
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function negative_water(P::AbstractArray{Float64})
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_, _, _, _, n_TR, d_TR, s_TR, d_Chol, s_Chol, d_PCN, s_PCN, d_CG, s_CG,
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A_L, _, s_CH2, _, _, _, r_PCN, r_CG, _, _, T, _, _ = P
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# Volumes
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V_L = lipid_volume(T)
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V_HC = V_L - ((1 - CONST_x_PG) * CONST_V_HL_PC + CONST_x_PG * CONST_V_HL_PG)
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|
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# Calculation of mean D_C
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|
D_C = V_HC / A_L
|
||
|
|
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||
|
|
# Quasi-molecular volumes
|
||
|
|
V_CG = CONST_V_HL_PC * r_CG # Volume of CG group
|
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|
|
V_PCN = CONST_V_HL_PC * r_PCN # Volume of PCN group
|
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|
|
V_Chol = CONST_V_HL_PC * (1 - r_PCN - r_CG) # Volume of CholCH3 group
|
||
|
|
|
||
|
|
check = 0
|
||
|
|
z_array = range(0.0, 4.0, length=81)
|
||
|
|
|
||
|
|
CG = Gauss.(z_array, V_CG, D_C + d_CG / 2.0, s_CG, A_L)
|
||
|
|
PCN = Gauss.(z_array, V_PCN, D_C + d_CG + d_PCN / 2.0, s_PCN, A_L)
|
||
|
|
Chol = Gauss.(z_array, V_Chol, D_C + d_CG + d_PCN + d_Chol / 2.0, s_Chol, A_L)
|
||
|
|
TRIS = Gauss.(z_array, n_TR * CONST_V_tris, D_C + d_TR / 2.0, s_TR, A_L)
|
||
|
|
BW = Slab.(z_array, D_C + (d_CG + d_PCN + d_Chol + CONST_d_shl) / 2.0, d_CG + d_PCN + d_Chol + CONST_d_shl, s_CH2) - CG - PCN - Chol - TRIS
|
||
|
|
|
||
|
|
for i in (BW)
|
||
|
|
if i < -1e-3
|
||
|
|
check += 1
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
return check
|
||
|
|
end
|
||
|
|
|
||
|
|
function get_free_parameters_idx(metadata::Dict)
|
||
|
|
m = metadata["parameters"]
|
||
|
|
return filter(i -> !m[i]["fixed"], eachindex(m))
|
||
|
|
end
|
||
|
|
|
||
|
|
function reduce_to_free_parameters(metadata::Dict, params_init::NamedTuple, lb, ub, q)
|
||
|
|
default_params = Float64[params_init...]
|
||
|
|
free_idx = get_free_parameters_idx(metadata)
|
||
|
|
P_reduced = view(default_params, free_idx)
|
||
|
|
lb_reduced = lb[free_idx]
|
||
|
|
ub_reduced = ub[free_idx]
|
||
|
|
function reduced(P::AbstractArray{Float64})
|
||
|
|
P_reduced .= P
|
||
|
|
return intensity(default_params, q)
|
||
|
|
end
|
||
|
|
return reduced, P_reduced, lb_reduced, ub_reduced
|
||
|
|
end
|
||
|
|
|
||
|
|
function reduce_to_free_parameters(metadata::Dict, params::Vector{Float64})
|
||
|
|
free_idx = get_free_parameters_idx(metadata)
|
||
|
|
return params[free_idx]
|
||
|
|
end
|
||
|
|
|
||
|
|
end # module PLUV
|
||
|
|
|
||
|
|
# vim ts=4,sts=4,sw=4
|