Pavol Balgavý

Pavol Balgavý
Comenius University Bratislava · Faculty of Pharmacy

PhD
Professor Emeritus

About

188
Publications
11,994
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
2,793
Citations

Publications

Publications (188)
Article
Full-text available
The thermodynamic and structural behaviors of lamellar dimyristoylphosphatidylcholine-alkanol (abbreviation DMPC-CnOH, n = 8-18 is the even number of carbons in the alkyl chain) systems were studied by using DSC and SAXD/WAXD methods at a 0-0.8 CnOH : DMPC molar ratio range. Up to n≤ 10 a significant biphasic effect depending on the main transition...
Article
The location of n-decane molecules within the model biological membrane consisting of dioleoyl-phosphocholine (DOPC) bilayers has been investigated via small angle neutron diffraction (SAND) method and molecular dynamics (MD) simulations. Diffraction patterns of the samples containing varied amounts of labeled and unlabeled n-decane have been obtai...
Article
Full-text available
Dispersion of multilamellar liposomes of dimyristoylphosphatidylcholine (DMPC) and cholesterol (CHOL) were studied by vibrational densitometer for the CHOL mole fractions X = 0−0.54 in the temperature range 18−50 °C, both below and above the main phase transition. DMPC-CHOL bilayers served as a simple model for lipidic part of biological membrane....
Article
Full-text available
The effect of general anaesthetics alkan-1-ols (CnOH, where n = 10, 12, 14, 16 and 18 is the number of carbon atoms in the molecule) on the structure of dioleoylphosphatidylcholine (DOPC) model membrane was studied by small-angle neutron scattering (SANS) and small-angle neutron diffraction (SAND). Fluid bilayers were prepared at CnOH:DOPC = 0.3 mo...
Article
The structural polymorphism and parameters of lyotropic phases formed in the mixed dioleoylphosphatidylcholine-dioleoylphosphatidylethanolamine (DOPC-DOPE) system upon heating and varying DOPC:DOPE composition were studied by means of small-angle X-ray diffraction (SAXD). In the temperature range 5–80 °C a sequence of fluid lamellar Lα – inverse he...
Article
The mixtures of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) and 1,2-dioleoyl-sn-glycero-3-phospho-l-serine (DOPS) in bilayers of multilamellar vesicles were studied by method of densitometry. In the range of DOPS molar fraction 0-100%, specific volumes of mixtures of lipids coincide with theoretical values in the case of ideal mixing of lipids....
Article
Small- and wide-angle X-ray diffraction was used to study the effect of 1-alkanols, as simple models of general anesthetics, (abbreviation CnOH, n = 8-18 is the even number of carbons in the aliphatic chain) on the lamellar to hexagonal Lα → HII phase transition in the dioleoylphosphatidylethanolamine-dioleoylphosphatidylcholine = 3 : 1 mol/mol (DO...
Article
The volumetric properties of fluid bilayers formed of dioleoylphosphatidylcholine (DOPC) with incorporated N ,N -dimethyl-N -alkylamine N -oxides (Cn NO, n = 6, 10–18 is the even number of carbons in alkyl chain) were studied by vibrating tube densitometry in the temperature interval from 20 °C to 50 °C. It was found that the DOPC and Cn NO mixed i...
Article
Full-text available
Small-angle neutron scattering data were collected from aqueous dispersions of unilamellar vesicles (ULVs) consisting of mixtures of 1,2-dioleoyl-sn-glycero-3-phosphatidylcholine and a homologous series of N,N-dimethyl-N-alkylamine-N-oxides (CnNO, n = 12, 14, 16, and 18, where n is the number of carbon atoms in the alkyl chain). A modeling approach...
Article
Full-text available
In our paper, we demonstrate several possibilities of using neutrons in pharmaceutical research with the help of examples of scientific results achieved at our University. In this first part, basic properties of neutrons and elementary principles of elastic scattering of thermal neutrons are described. Results of contrast variation neutron diffract...
Article
Full-text available
In this paper, we demonstrate several possibilities of using neutron scattering in pharmaceutical research based on examples of scientific results achieved at our University. In this second part, elementary principles of small-angle neutron scattering and simple methods of scattering data evaluation are described. Results of scattering on bilayers...
Article
Full-text available
The effect of N-dodecyl-N,N-dimethylamine N-oxide (C12NO) on the unilamellar liposomes prepared from egg yolk phosphatidylcholine (EYPC) was studied using turbidimetric and fluorescence spectroscopic methods. The concentrations of C12NO causing saturation and total solubilization of membrane were evaluated turbidimetrically. Liposomes filled with h...
Article
The excimer 1,2-dipyrenedecanoyl-sn-glycero-3-phosphatidylcholine (dipy10PC) fluorescence probe was used to determine effects of aliphatic alcohols (CnH2n+1OH, n = 12-18 is the even number of carbons in alkyl chain) on fluid dioleoylphosphatidylcholine (DOPC) +dioleoylphosphatidylserine (DOPS) bilayers in multilamellar vesicles at molar ratio DOPC/...
Article
Full-text available
The structure of aggregates formed due to DNA interaction with dipalmitoylphosphatidylcholine (DPPC) in presence of Ca2+ and Zn2+ is examined using small-angle synchrotron X-ray diffraction (SAXD) and small-angle neutron scattering (SANS). SAXD detected two structures: LC - condensed lamellar phase and LX - lamellar phase with DNA strands intercala...
Article
Full-text available
The influence of cholesterol and β-sitosterol on egg yolk phosphatidylcholine (EYPC) bilayers is compared. Different interactions of these sterols with EYPC bilayers were observed using X-ray diffraction. Cholesterol was miscible with EYPC in the studied concentration range (0-50 mol%), but crystallization of β-sitosterol in EYPC bilayers was obser...
Article
We studied the effect of divalent alkaline earth metal cations Ca²⁺, Mg²⁺ and transition metals Co²⁺, Ni²⁺, Cu²⁺ and Zn²⁺ on DNA condensation and its protection against thermal denaturation in presence of dioleoylphosphatidylcholine liposomes (DOPC). Experimental results have shown that Ca²⁺ and Mg²⁺ as well as Zn²⁺ mediate DNA condensation. Cu²⁺ c...
Article
Small-angle neutron scattering and coarse-grained molecular dynamics simulations have been used to determine the structural parameters (bilayer thickness D, polar region thickness D(H), interfacial lateral area of the unit cell A(UC) and alcohol partial interfacial area A(CnOH)) of fluid dioleoylphosphatidylcholine:dioleoylphosphatidylserine (PCPS,...
Article
Lamellar phases composed of fluid dioleoylphosphatidylcholine (DOPC) bilayers containing alkan-1-ols (CnOH, n = 8, 10, 14, 16, 18 is the number of carbon atoms) at CnOH : DOPC = 0.3 molar ratio and hydrated with heavy water at 20.2 ≥ D2O : DOPC ≥ 14.4 molar ratio were studied by neutron diffraction. The bilayer thickness d(L) and the bilayer surfac...
Article
The influence of cholesterol on the structural parameters of phosphatidylcholine bilayers is studied by small-angle neutron scattering on unilamellar liposomes. Monounsaturated diacylphosphatidylcholines diCn:1PC with the length of acyl chains n=14, 18 and 22 carbons are used. We confirm that the bilayer thickness increases with increasing concentr...
Article
Full-text available
We have studied the structural properties of lipid bilayers made up of monounsaturated phosphatidylcholines (i.e. diCn:1PC, where n=14, 16, 18, 20, 22 and 24). High-resolution x-ray scattering data were analyzed in conjunction with contrast varied neutron scattering data, using the recently developed technique by Kucerka et al. [Biophys. J. 95, 235...
Article
Full-text available
The structures of DMPC and DPPC bilayers in unilamellar liposomes, in the presence of 33.3 mol% cholesterol or the plant sterol β-sitosterol, have been studied by small-angle neutron scattering. The bilayer thickness d(L) increases in a similar way for both sterols. The repeat distance in multilamellar liposomes, as determined by small-angle X-ray...
Article
The volumetric properties of fluid bilayers consisting of dioleoylphosphatidylcholine (DOPC, 96wt%) and dioleoylphosphatidylserine (DOPS, 4wt%) with incorporated saturated n-alkanols (CnOH, n=10-16 is the even number of carbons in alkyl chain) were studied by vibrating tube densitometry. The mixing of DOPC and DOPS was found to be ideal and the mol...
Article
The effect of 1-alkanols (abbreviation CnOH, n = 8-18 is the even number of alkyl carbons) on the transition from lamellar Lalpha to inverted hexagonal HII phase of multilamellar dioleylphosphatidylcholine (DOPC)+dioleylphosphatidylethanolamine (DOPE) vesicles at full hydration was studied using small angle X-ray diffraction. For DOPC:DOPE = 1:9 mo...
Article
The microstructure of DNA - dioleoylphosphatidylethanolamine (DOPE) - propane-1,3-diyl-bis(dodecyldimethylammonium bromide) (C3GS12) aggregates as a function of the C3GS12:DOPE molar ratio and temperature was investigated using small angle X-ray diffraction. At 20° C, we observe a condensed lamellar phase (Lαc) with the lattice parameter d∼6.8-6.2...
Article
We have studied the structural properties of monounsaturated diacylphosphatidylcholine lipid bilayers (i.e., diCn:1PC, where n = 14, 16, 18, 20, 22, and 24 is the number of acyl chain carbons). High-resolution x-ray scattering data were analyzed in conjunction with contrast-varied neutron scattering data using a technique we recently developed. Ana...
Article
Full-text available
We examine the structure of aggregates formed due to DNA interaction with dipalmitoylphosphatidylcholine (DPPC) in presence of Ca2+ and Zn2+ using small-angle synchrotron X-ray diffraction (SAXD) and neutron scattering (SANS). SAXD shows structural heterogeneity as a function of the cation concentration and temperature: At low cation concentration...
Article
The effect of alkane-1-ols (CnOH, n = 8, 12, 16 is the number of carbons in alkyl chain) on lamellar (La)., inverse hexagonal (HII) phase transition temperature of egg yolk phosphatidylethanolamine (EYPE) was studied using turbidimetry and 31P-NMR at 0.1: 1 CnOH: EYPE mole ratio. The transition showed a characteristic temperature dependenceof turbi...
Article
The influence of a mammalian sterol cholesterol and a plant sterol beta-sitosterol on the structural parameters and hydration of bilayers in unilamellar vesicles made of monounsaturated diacylphosphatidylcholines (diCn:1PC, n=14-22 is the even number of acyl chain carbons) was studied at 30 degrees C using small-angle neutron scattering (SANS). Rec...
Article
Small-angle neutron scattering (SANS) curves of unilamellar dipalmitoylphosphatidylcholine (DPPC) vesicles in 1-60mM CaCl2 were analyzed using a strip-function model of the phospholipid bilayer. The fraction of Ca2+ ions bound in the DPPC polar head group region was determined using Langmuir adsorption isotherm. In the gel phase, at 20 degrees C, t...
Article
Full-text available
Solubilization of large unilamellar 1,2-dioleoylphosphatidylcholine (DOPC) vesicles by N-dodecyl-N,N-dimethylamine-N-oxide (LDAO) was studied using turbidimetry. From turbidity data, the LDAO partition coefficient between the aqueous phase and DOPC bilayers was obtained. Using this partition coefficient, the LDAO:DOPC molar ratio in the bilayer was...
Article
We investigate the structure of aggregates formed due to DNA interaction with saturated neutral phosphatidylcholines [dipalmitoylphosphatidylcholine (DPPC) and dimyristoylphosphatidylcholine] in presence of Ca2+ and Mg2+ cations using simultaneous synchrotron small- and wide-angle X-ray diffractions. For DPPC:DNA = 3:1 mol/base and in the range of...
Article
The specific volumes of six 1,2-diacylphosphatidylcholines with monounsaturated acyl chains (diCn:1PC, n=14-24 is the even number of acyl chain carbons) in fluid bilayers in multilamellar vesicles dispersed in H(2)O were determined by the vibrating tube densitometry as a function of temperature. From the data obtained with diCn:1PC (n=14-22) vesicl...
Article
The tri-headed anionic dendritic amphiphile, 4-(2-carboxyethyl)-4-[(icosyloxycarbonyl)amino]heptanedioic acid (3CCb20), forms mixed aggregates with dipalmitoylphosphatidylcholine (DPPC) in excess water at 3CCb20:DPPC = 0.91:1 molar ratio. On heating, these mixed aggregates transform into fluid bilayers stacked in the liquid crystalline lamellar L(a...
Article
Full-text available
Dipalmitoylphosphatidylcholine (DPPC) was hydrated in 0.2–60 mM solution of CaCl2 in heavy water and thoroughly homogenized by freezing-thawing process. Small-angle neutron scattering (SANS) shows formation of unilamellar vesicles in the range 1–60 mM of CaCl2. From the Kratky–Porod plot ln [I(Q)Q2] vs. Q2 of SANS intensity I(Q) in the range of sca...
Article
The structure of hydrated mixtures of primary alifatic alcohols (CnOH, n = 8-18 is the even number of carbon atoms in the alcohol aliphatic chain) with dipalmitoylphosphatidylcholine (DPPC) at molar ratios of CnOH:DPPC = 0,4:1 and H 2O:DPPC = 20:1 was studied by the synchrotron radiation small- (SAX) and wide- (WAX) angle diffraction. From diffract...
Article
Full-text available
Pycnogenol (PYC), a procyanidin-rich extract of French maritime pine bark (Pinus pinaster) has strong antioxidant potential and promotes cellular health. The aim of this study was to investigate a possible cooperation of natural antioxidant PYC with synthetic antioxidants ascorbic acid and trolox in the model system of lipid peroxidation determined...
Article
Sarcoplasmic reticulum Ca-transporting ATPase (EC 3.6.1.38) was isolated from rabbit white muscle, purified and reconstituted into vesicles of synthetic diacylphosphatidylcholines with monounsaturated acyl chains using the cholate dilution method. In fluid bilayers at 37 degrees C, the specific activity of ATPase displays a maximum (31.5+/-0.8 IU/m...
Article
The structure of aggregates formed due to DNA interaction with dioleoylphosphatidylcholine (DOPC) vesicles in presence of Ca(2+) and Mg(2+) cations was investigated using synchrotron small-angle X-ray diffraction. For DOPC/DNA=1:1 mol/base and in the range of concentration of the cation(2+) 0-76.5 mM, the diffractograms show the coexistence of two...
Article
The size and structure of aggregates formed by interaction of DNA with homologous series of cationic gemini surfactants butane-1,4-diyl-bis(alkyldimethylammonium bromide) (CnGS, n=10-16 is the number of alkyl carbons) were investigated using UV-vis turbidity, dynamic light scattering and small-angle synchrotron X-ray (SAX) diffraction. The detailed...
Article
Full-text available
N-alkyl-N,N-dimethylamine-N-oxides (CnNO, n = 10-20 is the number of alkyl carbon atoms) stimulate the skeletal sarcoplasmic reticulum (SR) Ca(2+)-transporting ATPase activity at low concentrations and inhibit it at high concentrations. The minimum concentration (cmin), at which CnNO inhibits the ATPase, continuously decreases up to n = 16-18 and t...
Article
Solubilization of unilamellar egg yolk phosphatidylcholine (EYPC) liposomes induced by N-dodecyl-N, N-dimethylamine N-oxide (C12NO) was studied using turbidimetry and static light scattering. The liposomes were prepared by extrusion through membrane filters with pores having 25 nm, 50 nm and 100 nm radii. The solubilizing concentration of C12NO (cs...
Article
Full-text available
The structure of aggregates formed by interaction of DNA with unilamellar dilauroylphosphatidylcholine (DLPC) vesicles (DNA:DLPC=1:1 base/mol) in the presence of gemini surfactant butane-1,4-diyl-bis(dodecyldimethylammonium bromide) (C12GS) was investigated using synchrotron small angle X-ray diffraction. In the concentration range C12GS+:DLPC< or...
Article
Small-angle neutron scattering on extruded unilamellar vesicles in water was used to study bilayer thickness when cholesterol (CHOL) was added at 44.4 mol% to 1,2-dimyristoleoylphosphatidylcholine (diC14:1PC) and 1,2-dierucoylphosphatidylcholine (diC22:1PC) bilayers. Using the (1)H(2)O/(2)H(2)O contrast variation and the small-angle form of Kratky-...
Article
Full-text available
Equoral oral solution is a novel drug delivery system for cyclosporine consisting mainly of non-ionic surfactants, polyglycerol esters and polyoxyethylated fatty acids aggregates, and gives microdispersions in the aqueous enviroment. To simulate dispergation, Equoral was mixed with varying amounts of water. Changes in the structure of the prepared...
Article
Full-text available
Small-angle neutron scattering (SANS) experiments were performed on unilamellar 1,2-dimyristoylphosphatidylcholine (DMPC) vesicles prepared in heavy water by extrusion through polycarbonate filters with 500 A pores. The data obtained at 30+/-0.1 degrees C were evaluated using a five-strip function model of the bilayer coherent neutron scattering le...
Article
The thickness of the lipid bilayer in extruded unilamellar vesicles prepared from synthetic 1,2-diacyl-sn-glycero-3-phosphorylcholines with monounsaturated acyl chains (diCn:1PC, n=14-22) was studied at 30°C in the small-angle neutron scattering (SANS) experiment. Several contrasts of the neutron scattering length density between the aqueous phase...
Article
Full-text available
Small-angle scattering has been employed to study the structure of lipid bilayers in unilamellar vesicles. This paper evaluates the use of a model approach for the analysis of such data. A long molecular dynamics simulation of a dipalmitoylphosphatidylcholine bilayer in the L(alpha) phase provides detailed structural information from which scatteri...
Article
The phase preferences of egg yolk phosphatidylcholine (EYPC) have been examined in the presence of tertiary amine anesthetics [2-(propyloxy)phenyl]-2-(1-piperidinyl)ethyl ester of carbamic acid (C3A) and [2-(heptyloxy)phenyl]-2-(1-piperidinyl)ethyl ester of carbamic acid (C7A, heptacaine). Using the synchrotron small-angle X-ray diffraction (SAXD),...
Article
Effects of non-ionic surfactants N-alkyl-N,N-dimethylamine-N-oxides (C(n)NO, n is the number of alkyl carbons) on the structure of egg yolk phosphatidylcholine (EYPC) bilayers in the lamellar fluid phase was studied by small-angle X-ray diffraction as a function of H(2)O:EYPC and C(n)NO:EYPC molar ratios. The bilayer thickness d(L) and the lipid su...
Article
The influence of 1,4-butanediamonium-N,N'-dialkyl-N,N,N',N'-tetramethyl dibromides (CmA, m = 7-16 is the number of alkyl carbons) on the egg yolk phosphatidylcholine (EYPC) bilayer thickness and lipid surface area at the bilayer-aqueous phase interface is studied using X-ray diffraction on fluid lamellar CmA + EYPC + H2O phases as a function of CmA...
Article
Full-text available
Small-angle neutron scattering on extruded unilamellar vesicles in water was used to study bilayer thickness when cholesterol (CHOL) was added to dilauroylphosphatidylcholine (DLPC) and dioleoylphosphatidylcholine (DOPC) bilayers in molar fraction 0.44. Using the H2O/2H2O contrast variation and the small-angle form of Kratky-Porod approximation, th...
Article
The solubilization of extruded (100 nm) unilamellar egg yolk phosphatidylcholine (EYPC) liposomes by a series of N-alkyl-N,N-dimethylamine N-oxides (CnNO, n = 10-14 carbon atoms in the alkyl substituent) was studied using turbidimetry. The solubilizing concentration of CnNO (cS) was estimated as the CnNO concentration causing the half-maximum decre...
Article
Previous X-ray diffraction studies on fully hydrated fluid lamellar egg phosphatidylcholine phases indicated a approximately 10 A increase of bilayer thickness in the presence of excess n-decane [Biochim. Biophys. Acta 597 (1980) 455], while the small-angle neutron scattering (SANS) on unilamellar extruded dioleoylphosphatidylcholine (DOPC) vesicle...
Article
We report on a small-angle synchrotron X-ray diffraction study of dilauroylphosphatidylcholine (DLPC) liposomes aggregated with high molecular DNA in the presence of 1,4-butanediammonium-N,N'-dilauryl-N,N,N',N'-tetramethyl gemini surfactant cations (C12GS). The aggregates prepared at the DLPC/C12GS/DNA phosphate group=2:1:1.6 molar ratio in 0.0015...
Article
The effect of cholesterol (CHOL) on the rate of autoperoxidation of chromatographically pure phosphatidylcholine from hen egg yolks (EYPC) in aerated multilamellar liposomes was examined at eight CHOL:EYPC molar ratios from 0.1 up to 1.0 at 45 degrees C. Autoperoxidation was measured as conjugated diene (CD) formation by UV-VIS spectrophotometry. I...
Article
Lipid peroxidation of aerated multilamellar liposomes composed of egg yolk phosphatidylcholine (EYPC) and cholesterol (CHOL) at molar ratios CHOL:EYPC = 0, 0.1, 0.2, 0.3, 0.4, 0.6 and 1.0 was studied during autooxidation and during Fe2+/H2O2-induced peroxidation by following the formation of conjugated diene and thiobarbituric acid reactive substan...
Article
Full-text available
The lipid bilayer thickness d L and the surface area A L in fluid lyotropic lamellar L α phases of dipalmitoylphosphatidylcholine (DPPC) containing amphiphilic monohydrochiorides of [2-(alkyloxy)phenyl]-2-(1-piperidinyl)ethyl esters of carbamic acid (C n A, n =number of alkyloxy chain carbons) at DPPC:C n A=1:1 and H 2 O:DPPC· 20:1 molar ratios hav...
Article
The interaction of n-decane (C10) with phospholipid bilayers in the lamellar fluid L á phase of chromatographically pure egg phosphatidylcholine (EYPC) has been studied by the use of x-ray diffraction at 20 °C and molar ratios H 2O: EYPC ≈ 20 and C10: EYPC ≤ 2,13. The surface area A L per one EYPC molecule at the bilayer - aqueous phase interface d...
Article
Full-text available
Mixtures of N-dodecyl-N,N-dimethylamine N-oxide (DDAO) and 1,2-dioleoylphosphatidyl choline (DOPC) in chloroform/methanol were evaporated, dried and hydrated in excess 2H2O. Aqueous dispersions thus prepared were extruded through polycarbonate filter with pores of diameter 500A. These samples were studied using small-angle neutron scattering. DDAO...
Article
Small-angle neutron scattering (SANS) experiments have been performed on large unilamellar liposomes prepared from 1,2-dilauroylphosphatidylcholine (DLPC), 1,2-dimyristoyl-phosphatidylcholine (DMPC) and 1,2-distearoylphosphatidylcholine (DSPC) in heavy water by extrusion through polycarbonate filters with 500 A pores. The neutron scattering intensi...
Article
Conjugated dienes (CD) and thiobarbituric acid reactive substances (TBARS) have been estimated during the autoperoxidation of chromatographically pure phosphatidylcholine from hen eggs (EYPC) in multilamellar liposomes by UV-VIS spectrophotometry. During the propagation phase of autoperoxidation reaction, n-decane (C10) and n-octadecane (C18) gradu...
Article
Computer simulated small-angle neutron scattering (SANS) curves of spherical polydisperse extruded unilamellar liposomes from saturated 1,2-diacylphosphatidylcholines in the aqueous phase are evaluated by using a multishell model, which divides the lipid bilayer of liposomes into the polar head group region, and the nonpolar hydrocarbon region cons...
Article
Full-text available
The lipid bilayer thickness d(L), the transbilayer distance of lipid phosphate groups d(pp/inf> and the lipid surface area A(L) of fluid hydrated bilayers of lamellar phases of egg phosphatidylcholine or dipalmitoylphosphatidylcholine containing N-alkyl-N,N-dimethylamine N-oxides (CnNO), 1,4-butanedi-ammonium-N,N'-dialkyl-N,N,N',N'-tetramethyl dibr...
Article
Dioleoylphosphatidylcholine (DOPC) and n-decane were mixed and hydrated afterwards in an excess of heavy water at 1 wt.% of DOPC. From this dispersion, unilamellar liposomes were prepared by extrusion through polycarbonate filter with 500-A pores. Small-angle neutron scattering (SANS) was conducted on these liposomes. From the Kratky-Porod plot ln[...
Article
Full-text available
Using the small-angle neutron scattering and the Kratky-Porod plot, the bilayer thickness d L = 41.7 ± 0.3Å has been determined in unilamellar egg yolk phosphatidylcholine liposomes dispersed in heavy water and prepared by extrusion through 500Å pores in polycarbonate filters. The peak-peak distance across the bilayer obtained from the data of smal...