## Light Scattering and Size Exclusion Chromatography

Fundamental properties of hyaluronan, such as viscoelasticity and flow behavior primarily depend on the MWD, size, and conformation of the macromolecules. A primary method in estimating the molecular weight and the size of macromolecules is LS. LS and a few other methods such as osmometry, sedimentation, and mass spectrometry are absolute techniques. However, only the LS technique can be used online to a SEC system in obtaining the whole

Figure 7 Agarose gel electrophoresis of nearly monodisperse hyaluronan standards and commercial hyaluronan. Gel was 0.7% agarose in Tris-acetate-EDTA (minigel format), stained with Stains-All by the method of Lee and Cowman (61). S: a mixture of 5 different monodisperse SelectHA preparations with indicated Mw determined by SEC-MALS; C and C0: commercial hyaluronan samples; D: DNA standards, Bioline Hyperladder 1, containing DNA of 10, 8, 6, 5, 4, 3, 2.5, 2, 1.5 kb; D0: DNA standards, BioRad 1 Kilobase Ruler, containing DNA of 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2 kb. Figure kindly provided by P DeAngelis and W Jing.

Figure 7 Agarose gel electrophoresis of nearly monodisperse hyaluronan standards and commercial hyaluronan. Gel was 0.7% agarose in Tris-acetate-EDTA (minigel format), stained with Stains-All by the method of Lee and Cowman (61). S: a mixture of 5 different monodisperse SelectHA preparations with indicated Mw determined by SEC-MALS; C and C0: commercial hyaluronan samples; D: DNA standards, Bioline Hyperladder 1, containing DNA of 10, 8, 6, 5, 4, 3, 2.5, 2, 1.5 kb; D0: DNA standards, BioRad 1 Kilobase Ruler, containing DNA of 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2 kb. Figure kindly provided by P DeAngelis and W Jing.

MWD. As a consequence, LS is a fundamental method for the characterization of hyaluronan.

LS concerns the interaction of light with matter in the specific case with macromolecules in solution. The interaction of light with matter is a very complex topic. Depending on the type of scattering analyzed (elastic, quasi-elastic, Raman, etc.) different information may be obtained. For the characterization of macromolecules (molecular weight and size) only elastic and quasi-elastic LS are of interest. In an elastic LS experiment (also known as static or total intensity or Rayleigh scattering) we measure the intensity of the scattering. In this case, we assume that the scattered light has the same wavelength and polarization of the incident light. On the contrary, in a quasi-elastic LS experiment (also known as dynamic or photon correlation spectroscopy) we measure the fluctuations of the intensity of the scattering due to the Brownian movement of the macromolecules.

Following Zimm (67) the intensity of the scattering of a solution of macromolecules is related to the molecular weight M of the sample by the following equation Kc 1

where AR(ff) is the scattering excess (Rayleigh factor) at angle U of the solution with regard to the pure solvent, U the angle between the incident light and the detector, c the concentration, A2 the second virial coefficient, P(U) the form factor, K = (4p2n2(dn/dc)2)/(NaA4) an optical constant, n0 the refractive index of the solvent, dn/dc the refractive index increment of the polymer, A0 the wavelength of light in a vacuum, NA the Avagadro's number.

Modern LS photometer uses coherent light, that is a laser (often a He-Ne laser with wavelength A = 632.8 nm), and vertical polarization. The constant K puts together all the physical and optical parameters. All the parameters of the K optical constant are known, only the dn/dc of the polymer is unknown. Often the dn/dc of the polymer may be found in the literature, otherwise the value must be measured, generally by an offline refractometer at the same wavelength, solvent and temperature of the LS experiment. The dn/dc value for hyaluronan is well known: 0.15 mL/g, in 0.15 M NaCl solvent, at 25 °C and A = 632.8 nm. However, other than A, dn/dc also depends a little on the solvent (salt, buffer) used and in general it is better to measure it. The fundamental parameter of interest in obtaining the molecular weight and the size of macromolecules is the intensity of the scattering R(U) that depends on the angle U and on the concentration c. Specifically, we need R(U) at zero angle, U = 0°, and infinite dilution, c = 0. The condition of infinite dilution, that is an isolated macromolecule, could be obtained quite easily by measuring R(U) at decreasing finite concentrations (3-5) followed by an extrapolation to zero concentration. In this way, other than the molecular weight it is also possible to estimate the fundamental thermodynamic parameter of macromolecules in solution A2. Very complex is the estimation of R(U) at zero angle (68,69). In fact, R(d) at zero angle is not experimentally measurable as a consequence of the interference with the intense primary incident light. In measuring R(U) at zero angle we can use two different strategies corresponding with two different LS instrument: low-angle LS (LALS) and multi-angle LS (MALS). A LALS photometer measures R(U) at a scattering angle as low as possible and assumes that this value corresponds to R(U) at zero angle. Considering the experimental physical limit this means U about 4 - 6° for LALS. On the contrary, a MALS photometer measures R(d) in a wide range of angles, by means of an array of photodiodes, and R(U) at zero angle is calculated by an extrapolation. Both LALS and MALS photometers are commercially available. In the case of MALS there are several instruments with 2, 3, 18, and recently also 7 angles. All the LS photometers could be used both offline, batch mode, and online to a SEC/ HPLC system.

Quite complex is the definition of the form factor P(d). A macromolecule could not be considered as a single point of scattering. Hence, the light scattered from two different points of the same macromolecules will be not in phase and the total intensity of the scattering for large molecules is lower as a consequence of the destructive interference. The interference depends on the angle of measure of the intensity of the scattering. The interference is absent at 0° angle, highest at 180°. The interference depends on the shape and on the dimension of the molecules. Therefore a form factor P(d) has been introduced that quantifies the interference. P(d) is defined as the ratio between R(d) in the presence of interference, U > 0°, and R(ff) in the absence of interference, U = 0°. Thus, by definition

A direct consequence of the previous equation is that P(U) — 1 for U = 0° independent of the size of the molecules, P(d) < 1 for U > 0° when the size of the molecules is comparable with the wavelength A. Debye (70) found that P(U) could be expressed independently of the shape and of the conformation of the macromolecules. Considering the reciprocal of P(d), that is P(d)2\ Debye found the following equation

where m — 4p/A sin(U/2) and A — A0/n0 is the wavelength of the light in the solvent. Fortunately, the presence of the destructive interference is not only a problem, because from P(U) it is possible to measure the size of the macromolecules. Indeed, it is evident that combining Eqs. 9 and 11 from the initial slope of P(d) versus sin2(U/2) plot we can estimate the radius of gyration (s2)1/2 of the macromolecules. Obviously, this fact is true only for the MALS photometer in which R(U) is measured at different angles. In a LALS photometer where R(U) is measured only at low angle, we assume P(d) — 1 and the information on the size of the macromolecules is completely lost.

Regarding the size of the macromolecules from elastic LS two additional considerations are of interest. First, the size of the macromolecules is expressed in terms of the radius of gyration. Rg is defined as the mass average of the distance r from the center of gravity of the repeating units (segment) of mass mt (Eq. 12). In other word, Rg is an equilibrium parameter, distribution of masses with regard to the center of gravity of the molecule and it is different from the hydrodynamic radius RH obtained in a quasi-elastic LS experiment. Secondly, Rg is obtained from the angular variation of the scattering. If the macromolecules are smaller in size, the angular variation of the scattering is not experimentally measurable and the size is not obtained with accuracy. Practically, using an elastic MALS photometer the lower measurable Rg is about 10 nm. This is an other important difference between elastic and quasi-elastic LS. In fact, the lower measurable

Rh by quasi-elastic LS is about 1-2 nm

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