Determination of the Refractive Index Increment (dn/dc) of

molecule and macromolecule solutions by Surface Plasmon

Resonance

Tathyana Tumolo 1, Lucio Angnes 2 and Mauricio S. Baptista1*

1 Departamento de Bioquímica, Instituto de Química, Universidade de São

Paulo, Brazil

2 Departamento de Química Fundamental, Instituto de Química, Universidade

de São Paulo, Brazil

to whom correspondence should be addressed: e-mail:baptista@iq.usp.br;

Fax: (xx5511)3815-5579

Abbreviations used: SPR, surface plasmon resonanse; FIG, flow injection

gradient; MC, mixing chamber.

Category: Physical Techniques

ABSTRACT

An automated method for dn/dc determination using a surface plasmon

resonance equipament in tandem with a flow injection gradient system (FIG-

SPR) is proposed. dn/dc determinations of small molecule and biomolecule,

surfactant, polymer and biopolymer solutions with precision around 1-2% and

good accuracy were performed utilizing this method. dn/dc measurements

were also carried out manually on a conventional SPR equipment with similar

accuracy and precision. The FIG-SPR instrument is inexpensive and could be

easily coupled to commercially available SPR and liquid chromatography

equipments in order to obtain several properties of the solutions, which are

based on measurements of refractive index.

2

INTRODUCTION

The change in refractive index of solutions as a function of solute

concentration (dn/dc, also called refractive index increment) is an essential

parameter to several physical and analytical techniques that are based in

optical measurements (1). For example, it is necessary to know dn/dc in order

to: i) characterize the sizes, shapes, molecular weights, and the virial

coefficients of polymers, macromolecules and surfactant aggregates through

light scattering methods (2), ii) calculate solute concentration based in

refractive index measurements in any kind of column chromatography (3), and

iii) obtain concentration and kinetics of molecules adsorbing on surfaces

through optical methods like Surface Plasmon Resonance (SPR) and

ellipsometry (4).

dn/dc corresponds to the slope of the dependence of the refractive

index (n) of a solution as a function of the solute concentration (c). The search

for refractometers with high precision (1x10-6 refractive index units, RIU) and

the capability of measuring dn/dc led to the development of the differential

refractometers (DR) (5,6). In fact, most of the dn/dc values reported in the

literature were measured using DR, including low molecular weight

compounds (7) block copolymers (8), agarose (9), poly(thiocarbonate)s and

poly(carbonate)s (10), and surfactants (11). Other refractometers like the

Zeiss interferometer and the Mach-Zehnder interferometer (6) have also been

used to obtain dn/dc of segmented poly(ester urethane)s

polymethylmethacrylate (PMMA) in different solvents (12).

SPR is a surface sensitive method that measures the reflectance

intensity as a function of incident angle θ of a light beam incident on a thin

3

metal film. It has been extensively used to evaluate properties of thin films

self-assembled on gold, to study the adsorption of molecules at surfaces and

to characterize intermolecular interactions in general (13). The application of

SPR to study intermolecular interactions in high throughput screening essays

using combinatorial libraries opened a wide window for its application in

mutation detections, genomics, proteomics and drug development (14).

In order to obtain the concentration of molecules adsorbing over

surfaces (C) by the response of a SPR instrument (∆θ, where θ is the SPR

angle) in the linear regime (small refractive index variations) (15) it is

necessary to know the instrument calibration constant (X) and refractive index

increment of the ligand (dn/dc)ligand (16)

[1] C

Xligand dndC ligand

=∆θ

.( )

Accurate values of dn/dc were not fundamental in many SPR

applications because most of the studies were done with compounds that

have similar dn/dc values (17). However, it becomes extremely important in

the combinatorial libraries investigations where a wide range of different

compounds is tested, whose values of dn/dc can vary from 0.1 to 0.3 cm3g-1 ,

thus affecting directly the interpretation of the results (7). Accurate values of

dn/dc for ligands are also important when studying the interactions of common

molecules (like DNA-protein interactions) with stoichiometries different than

1:1 (7,18). It also enables for the calculation of bulk refractive index of

compounds (n), which is necessary in order to estimate film thickness and

surface coverage (16,19).

4

Because the SPR technique measures refractive index variations that

occur up to 400nm above the dielectric thin film (usually gold or silver thin

films), its signal is sensitive to the adsorption of molecules at the gold surface

(functionalized or not) and to the presence and concentration of molecules in

the liquid above the interface (13,16). In theory the value of dn/dc of ligand

solutions could be estimated from any equation fitting a SPR angle versus

reflection data (16). However, parameter compensation during the fitting

prevents accurate calculation of all other parameters, and it is usually

necessary to obtain the value of dn/dc from one of the independent

techniques cited above, which increases severely the time of the

measurements and hinders the more extensive application of SPR to high

through screening techniques. Therefore, it is desirable to develop a method

in which the dn/dc values of ligands could be calculated directly using the

SPR equipment. Also, this method should be easily automated to facilitate its

use in high through screening assays.

The variation of the SPR signal as a function of solute concentration in

the regime of small refractive index variations provides directly the ratio of

∆n/∆c, where ∆n is the difference of refractive indexes related with a

difference in solute concentration (∆c) (1,2). This is also true for the case in

which there is the formation of a thin film at the interface, below the fluid in

which the dn/dc determination is being performed, as far as the thickness of

this film is small (<50nm) compared with the decay length of the evanescent

field (~360nm in our instrument) (16). In fact, in order to calculate precisely

adsorption and desorption of surfactants in functionalized gold films, Sigal at

5

al were able to successfully calculate values of dn/dc of surfactant solutions

using SPR (20).

In this work we set up an instrument in which the SPR chip is

connected to a flow injection gradient (FIG) system (21,22).1 With the FIG

technique, a mixing chamber (MC) is used as a device to generate

reproducible concentration gradients whose refractive indexes are monitored

continuously in the SPR chip. The obtained concentration profiles not only can

replace the manual preparation and the measurement of several solutions

with different concentrations of the reactants but also can increase the

velocity keeping the high precision and accuracy of the determinations (21-

23). The dn/dc determination of several compounds was performed using

clean gold film with and without a mixing chamber. Therefore, we describe an

automated method to obtain the dn/dc of polymer, surfactant, macromolecule

and small molecule solutions using a SPR instrument.

1

1 Patent application under consideration

6

Experimental Section

Samples

All reagents used were at least of analytical grade. Solutions of Alanine

(Aldrich), Bovine Serum Albumin (BSA) (Acros Organics),

Cetyltrimethylammonium bromide (CTAB, Acros Organics), DNA sodium salt

Type I from calf Thymus (Sigma), Guanidine (Sigma), Heparin (Sigma), 3-(N-

Hexadecyl-N,N-dimethylammonium)propanesulfonate (HPS, Sigma), Lactose

(J.T. Baker), glucose (Vetec, Brazil), maltose (Merck), Poly(ethylene glycol)

4000 (PEG 4000, Polysciences Inc.), Poly(ethylene glycol) 6000 (PEG 6000,

Fluka), Polyvinylpirrolidone (PVP K90) (Acros Organics), Sodium Chloride

(Synth, Brazil), Sodium dodecyl sulfate (SDS, Merck), Spermine (Acros

Organics), Sucrose (Synth, Brazil), Tartaric acid (Aldrich) Urea (Cinética

Química, Brazil), were prepared with Milli-Q water. SDS, HPS, sodium

chloride, CTAB and Urea solutions were stirred for 5 minutes, heparin for 1

hour and PEG 4000 and 6000 for 3 hours. PVP was dried in oven for 3 days

previously to weighting and its aqueous solution was left mixing for 2 days.

BSA solution was warmed at 32 oC for better solubilization and left mixing for

10 minutes.

To determine dn/dc without the mixing chamber, solutions were

prepared with different concentrations in g.cm-3: BSA (0.005, 0.010, 0.015,

0.020, 0.025, 0.030, 0.035, 0.040, 0.045, 0.050), CTAB (0.006, 0.009, 0.012,

0.015, 0.018, 0.021, 0.024, 0.027), Heparin (0.005, 0.010, 0.015, 0.020,

0.025, 0.030, 0.035, 0.040, 0.045), HPS (0.00391, 0.00587, 0.00783,

0.00979, 0.01175, 0.01566, 0.01762, 0.01958), PEG 4000 (0.0040, 0.0081,

0.0121, 0.0161, 0.0201, 0.0242, 0.0282, 0.0322, 0.0363, 0.0403), SDS

7

(0.0053, 0.0064, 0.0073, 0.0079, 0.0087, 0.0116, 0.0131, 0.0145), Sucrose

(0.0104, 0.0207, 0.0415, 0.0518, 0.0622, 0.0726, 0.0830, 0.1037).

To determine the dn/dc with the mixing chamber, the concentrations

(g.cm-3) of the stock solutions used were: Alanine (0.1354), BSA (0.0100),

CTAB (0.01795), DNA (0.00329), Glucose (0.0117), Guanidine (0.01785),

Heparin (0.0206), HPS (0.0085), Lactose (0.0111), Maltose (0.0097), PEG

4000 (0.0504), PEG 6000 (0.0405), PVP (0.0448), SDS (0.0183), spermine

(0.0043), Sucrose (0.0718), Tartaric acid (0.0119) Urea (0.1201).

In the case of surfactant solutions, the value of concentration used in

the dn/dc determination was expressed as the total surfactant concentration

minus the critical micelle concentration (cmc), because we aimed to

determine the value of dn/dc of micellized surfactant solutions (11). This

correction was performed both when using and when not using the mixing

chamber.

Instrumentation

Refractive index values were obtained with a miniature integrated SPR

sensing system (Spreeta Sensor, Texas Instruments), which uses a near-

infrared light emitting diode (840 nm) to excite surface plasmon in a 50 nm

thickness gold film. This sensor is interfaced with a 8-Bit Interface Box (I/F

Box). The data acquisition and instrument control was performed by a

Pentium 2 microcomputer. The flow cell was constituted by a Teflon piece

fixed over the SPR device. Between these two parts was positioned a Teflon

spacer defining the volume of the flow cell (25 µL). The solutions were

propelled by a peristaltic pump ( Isco Inc. Model Tris, USA) utilizing a flow rate

8

of 2.7 cm3.min-1. With this equipment one can expect detection limits of in the

order of 10-6 R.I.U, which is equivalent to the best classical methods available

(5,6). dn/dc determinations were carried out in two different ways: i) under

steady state conditions, in which each stock solution with known

concentration was injected in triplicate and the refractive indexes were

measured independently; ii) using FIG line with a home-made MC with an

internal volume of 1.50 cm3 and magnetic stirrer. The value of θSPR (angle of

minimum reflectance) was obtained by fitting the data with the polynomial

method. All analyses were performed in a thermostatized room (23±1 oC).

<FIGURE 1>

Before beginning the analysis, the gold surface of the sensor was

cleaned with isopropyl alcohol and Kodak lens cleaning paper, rinsed with

Milli-Q water and calibrated in air (n=1) and in water (n=1,3330) To clean-up

the sensor surface after each analysis a 50mM SDS solution was injected in

the cell, followed by an excess of water sufficient to obtain the value of n

measured previously for pure water.

RESULTS AND DISCUSSION dn/dc determination without the mixing chamber

The plots of n as a function of c for sucrose and micellized HPS are

shown in Figure 2. It can be observed an excellent linearity of both curves

(r>0.999), in agreement with the assumption that at these low concentration

conditions there is a linear relationchip between n and c. The slope of this

curve is the value of dn/dc in cm3.g-1.

<FIGURE 2>

9

<TABLE 1>

Table 1 shows the dn/dc values for several compounds obtained by

SPR and the literature values. Standard deviations around 1 to 2% in dn/dc

were obtained for this series of compounds attesting the good precision of the

method. The comparison of the dn/dc values obtained by SPR and those from

the literature shows differences smaller than 10% indicating that the accuracy

of these measurements is also good. The main causes of divergences among

the values obtained by SPR and those from the literature are likely to be the

different experimental conditions, such as differences in wavelength,

temperature and reagent purity.

dn/dc determination with the FIG-SPR instrument

In order to calculate the dn/dc with this method it is necessary to

generate curves of refractive index as a function of solute concentration. This

can be done by using a calibrated MC, as in the conventional flow gradient

technique (21,22). In the MC occurs the rapid dilution of the stock solutions,

and a gradient of solute concentrations is generated. Initially a curve of

refractive index as a function of time after injecting a specific solution in the

MC is obtained. The concentration as a function of time profile of the injected

compound was obtained by calibrating the system with sucrose. Both curves

n versus t e c versus t were used to plot the n versus c curve allowing the

dn/dc calculation.

The refractive index versus time curves of sucrose, urea and SDS are

shown in Figure 3A, 4A and 5A, respectively. Note that after the injection of

stock solutions in the MC, an increase is observed in the value of n. For

10

sucrose and urea there is a continuous increase while for SDS there is a

small bump around 10s after injection that is likely to be due to surfactant

adsorption on gold and self-aggregation (Figure 5A, inset). This phenomenon

will be further discussed in this manuscript. Refractive index reaches a

constant value ~200 seconds after the injection. The increase in solute

concentration in the SPR flow cell reflects an increase in the refractive index,

and the flat region indicates that the concentration of solute in the mixing

chamber is equal to the solute concentration in the stock solution. 600

seconds after the injection, water or buffer instead of solute was injected in

the MC and a dilution profile was observed with the respective decrease in the

refractive index. In the case of SDS there is an evident bump in the dilution

gradient. The concentration onset of this bump is ~ 7mM, which is exactly the

value of the cmc of SDS (27). We are investigating whether or not these

refractive indexes changes from linearity can be used to study surfactant-

polymer interactions and adsorption processes in general.

By using a molecule whose relationship between refractive index and

concentration is well established, one can transform the refractive index

versus time curve into concentration versus time curve, i.e. to calibrate the

MC. Sucrose was chosen as standard, because its dn/dc is well known, its

solutions are easy to prepare accurately and it does not adsorb on the gold

film. Figure 3B shows the concentration versus time curve of sucrose,

indicating that its concentration increases, flats up and decreases as

mentioned before. The numeric values of these sucrose concentrations are

dependent on both the concentration of the injected stock solution and the

instrument characteristics. In order to calculate a parameter that is

11

independent from the concentration of the stock solution, the dilution factor

(DF), which is the calculated concentration at specific times after injection

divided by the concentration of stock solution, was calculated by Eq. [2]

(Figure 3C). Note that after the stock solution is injected, DF increases from

zero to one, showing that the concentration increases and reaches the same

concentration as the stock solution (DF=1) (Figure 3C). We have previously

established that by injecting the stock solution for 200 seconds in the MC

previously filled with water, is enough to obtain the same value n as by

injecting the stock solution directly in the SPR cell.

DF tC tCSTOCK

( )( )

= [2]

Where: DF(t) is the dilution factor, C(t) is the solute concentration monitored

as a function of time, CSTOCK is the concentration of the stock solution.

As far as the speed of the peristaltic pump and the volume of the MC

are unchanged this temporal DF profile will be the same for all compounds

injected. Therefore, one can easily obtain the concentration at specific times

after injection in the MC for any molecule simply by multiplying the

concentration of the stock solution by DF, as it is shown for urea and SDS in

Figures 4B and 5B, respectively. Consequently, one can convert the refractive

index versus time curves into refractive index versus concentration curves

(Figures 4C and 5C) with the dn/dc values being the slopes of these curves.

The increasing concentration portion of the curve was chosen for these

calculations, although the decreasing portions also works well. Therefore, it is

12

possible to calculate dn/dc without the cumbersome work of manually

preparing a series of solutions with different concentrations.

Note that in the case of urea, the refractive index versus concentration

curve (Figure 4C) is linear in all concentration profile, facilitating the dn/dc

determination. This is due to the fact that urea does not have the tendency to

adsorb on the gold thin film. However, in the case of SDS, the curve was not

linear at low concentrations (Figure 5C). This effect was observed for all

molecules that have the tendency to adsorb on the interface (surfactants and

polymers). In order to calculate dn/dc in these cases, we first obtained the

derivative graph of the refractive index versus concentration curve, observed

in which concentration range the derivative is linear, and then obtained the

dn/dc considering this range. Because the thickness of the self-assembled

film of surfactants or biopolymers is extremely thin (<20nm) the SPR response

is still linear as a function of solute concentration.

<FIGURE 3>

<FIGURE 4>

<FIGURE 5>

The dn/dc values of an extended list of substances was obtained and

they are shown in table 2. Note that the values of dn/dc vary almost 100%

among the compounds tested (compare Spermine and Guanidine with SDS

and Tartaric acid), demonstrating the necessity of obtaining accurate values

of dn/dc in order to correctly exploit SPR data.

As observed in the continuous injection method, the results obtained

with FIG-SPR are also in agreement with the literature values of dn/dc.

Differences smaller than 5% are observed when compared to literature data.

13

This difference is ascribed to the different experimental conditions related to

temperature, wavelength and reagent purity. Note that in the case of Heparin

and HPS, whose conditions are the same as ours, the difference in the dn/dc

is smaller.

Compared to the continuous injection method (Table 1) the automated

FIG technique presented similar accuracy and precision, with the advantage

of being less time-consuming. This is in accordance with the conclusions of

Shank-Retzlaff and Sliger that studied protein-protein interactions, by using an

HPLC pump coupled to an home made SPR device (23). Linear concentration

gradients were generated and used to calculate equilibrium constants and

kinetic data of these interactions. The authors attested that several limitations

of usual SPR devices, i.e. long-time analysis and need for surface

regeneration, were relaxed in their instrument.

Conclusions

The elaboration of the method of dn/dc determination with the

concentration gradient eliminated the stage of preparing several samples with

different concentrations. Using only one stock solution it is possible to obtain

hundreds of refractive index versus concentration data points, allowing the

precise and accurate calculation of dn/dc. The MC is a simple and

inexpensive apparatus that could be included in commercially available SPR

instruments. Also, a SPR chip could be used in any kind of polymer

chromatography methodology, replacing more expensive refractomers, to

obtain refractive index and dn/dc on line. When compared to other SPR

14

methods, the present FIG-SPR technique may also be of advantage to

characterize intermolecular interactions of biomolecules.

ACKNOWLEDGEMENTS: The authors would like to thank FAPESP, CNPq and

PRP-USP for financial support and D. Briotto for technical assistance. We also

would like to thank M.J.Politi and E.Barbieri for helpful discussions. T.T. is a

graduate student supported by FAPESP fellowship.

15

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13. (a) M. Malmqvist, Biospecific interaction analysis using biosensor technology, Nature 361 (1993) 186-187. (b) A.G. Frutos, R.M. Corn, SPR of Ultrathin Organic Films, Anal. Chem. 70 (1998) 449A-455A. 14. (a) E. Lopez-Crapez, T. Livache, J. Marchand, J. Grenier, K-ras mutation detection by hybridization to a polypyrrole DNA chip, Clin. Chem. 47 (2001) 186-194. (b) M.A. Cooper, Label-free screening of bio-molecular interactions, Anal. Bioanal. Chem. 377 (2003) 834-842. (c) E.H. Kerns, L. Di, Pharmaceutical profiling in drug discovery, Drug Discov. Today 8 (2003) 316-323. (d) D. Nedelkov, R.W. Nelson, Trends Biotechnol. 21 (2003) 301-305. 15. B. Liedberg, I. Lundstrom, E. Stenberg, Principles of Biosensing with an extended coupling matrix and surface-plasmon resonance, Sens. Actuators B 11 (1993) 63-72. 16. L.S. Jung, C.T. Campbell, T.M. Chinowsky, Mimi N. Mar, S.S. Yee, Quantitative interpretation of the response of surface plasmon resonance sensors to adsorbed films, Langmuir 14 (1998) 5636-5648. 17. (a) E.-M. Erb, X. Chen, S. Allen, C.J. Roberts, S.J.B. Tendler, M.C. Davies, S. Forsén, Characterization of the surfaces generated by liposome binding to the modified dextran matrix of a surface plasmon resonance sensor chip,. Anal. Biochem. 280 (2000) 29-35. (b) M.A. Cooper, A. Hansson, S. Löfås, D.H. Williams, A vesicle capture sensor chip for kinetic analysis of interactions with membrane-bound receptors, Anal. Biochem. 277 (2000), 196-205. 18. L. Wang, C. Bailly, K. Arvind, D. Ding, M. Bajic, D.W. Boykin, W.D. Wilson Specific molecular recognition of mixed nucleic acid sequences: An aromatic dication that binds in the DNA minor groove as a dimer, Proc. Natl. Acad. Sci. USA 97 (2000) 12-16. 19. E. Stenberg, B. Persson, H. Roos, C. Urbaniczky, Quantitative Determination of Surface Concentration of Protein with Surface Plasmon Resonance Using Radiolabeled Proteins, J. Coll. Interf. Sci. 143 (1991) 513-526. 20. G. B. Sigal, M. Mrksich, G. M. Whitesides, Using Surface Plasmon Resonance to measure the association of detergents with self-assembled monolayers of hexadecanethiolate on gold, Langmuir 13 (1997) 2749-2755. 21. C.D. Tran, M.S. Baptista, T. Tomooka, Determination of binding constants by flow injection gradient technique, Langmuir 14 (1998) 6886-6892. 22. M.E. Georgiou, C.A. Georgiou, M.A. Koupparis, Flow injection gradient technique in spectrophotometric determination of formation constants of macromolecule-cyclodextrin complexes, Anal. Chem. 67(1) (1995) 114-123.

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23. M.L. Shank-Retzlaff, S.G. Sligar, Analyte gradient-surface plasmon resonance: a one-step method for determining kinetic rates and macromolecules binding affinities, Anal. Chem. 72 (2000) 4212-4220. 24. E.M. Furst, E.S. Pagac, R.D. Tilton, Coadsorption of polylysine and the cationic surfactant cetyltrimethylammonium bromide on silica, Ind. Eng. Chem. Res. 35(5) (1996) 1566-1574 25. J.E. Knobloch, P.N. Shaklee, Absolute Molecular Weight Distribution of Low-Molecular-Weight Heparins by Size-Exclusion Chromatography with Multiangle Laser Light Scattering Detection, Anal. Biochem. 245 (1997) 231-241. 26. R.C. Weast, M.J. Astle (Eds.) CRC Handbook of Chemistry and Physics, 61st ed., CRC Press, Florida, 1980, pp. D229-D274. 27. Junqueira, H.C.; Severino, D.; Dias, L.G. ; Gugliotti, M. ; Baptista, M.S., Modulation of the Methylene Blue Photochemical Properties Based on the Adsorption at Aqueous Micelle Interfaces, Phys. Chem. Chem. Phys. 4 (2002) 2320-2328.

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FIGURE CAPTION Figure 1 – Schematic diagram of the FIG-SPR instrument: A, water; B, sample; C, peristaltic pump; D, steady state line, E, FIG line, F mixing chamber (MC);G, magnetic stirrer; H, SPR sensor; I, interface box; J, waste; L, computer. Figure 2 – Refractive index as a function of sucrose concentration (A) and HPS concentration minus cmc (cmcHPS=1x10-4M) (B) using the steady state line. Figure 3 – Refractive index (A), sucrose concentration (B) and Dilution factor (C) as a function of time after injecting a 0.07184 g.cm-3 sucrose stock solution, obtained in the FIG line. Figure 4 – Refractive index (A) and urea concentration (B) as a function of time after injecting a 0.1202 g.cm-3 urea stock solution. (C) Refractive index as a function of urea concentration, obtained in the FIG line. Figure 5 – Refractive index (A) and SDS concentration (B) as a function of time after injecting a 0.01826 g.cm-3 SDS stock solution. Inset A is an amplification of the main figure. (C) Refractive index as a function of SDS concentration minus cmc (cmcSDS=7x10-3M), obtained in the FIG line.

19

TABLE 1

dn/dc values obtained by SPR and found in the literature.

______________________________________________________________

Sample dn/dc (cm3.g-1) a ± δ b dn/dc (cm3.g-1) difference (%)

by SPR literature

______________________________________________________________

CTAB 0.151 ± 0.007 0.150 c 0.6

Heparin 0.122 ± 0.003 0.129 d 5.4

HPS 0.162 ± 0.003 0.162 e 0.0

PEG 4000 0.128± 0.002 0.134 f 3.0

SDS 0.100 ± 0.003 0.108 g 8.0

Sucrose 0.147 ± 0.001 0.144 h 2.1

______________________________________________________________ a water, λ=840 nm, T=23oC; b standard deviations obtained with three independent measurements; c water, λ=632.8 nm (24); d Dalteparin sodium, a low-molecular weight heparin, in buffer pH 7, λ=690 nm, T=25oC (25); e λ=632.8 nm, T=25oC (18); f water, λ=589 nm, T=25 oC (1); g buffer PBS (20); h

water, λ=589.3nm, T=20 oC (26).

20

TABLE 2

dn/dc values obtained by SPR (flow gradient) and found in the literature.

______________________________________________________________

Sample dn/dc (cm3.g-1) a ± δ b dn/dc (cm3.g-1) difference c (%)

by SPR literature

______________________________________________________________

Alanina 0.192 ± 0.001 -----d ------

BSA 0.190 ± 0.002 0.183 e 3.8

CTAB 0.143 ± 0.010 0.150 f 4.6

DNA 0.183 ± 0.006 0.180 g 1.6

Espermine 0.221 ± 0.005 ----- d ------

Glucose 0.145 ± 0.005 0.142 h 2.1

Guanidine 0.220 ± 0.001 ----- d ------

Heparin 0.130 ± 0.008 0.129 i 0.8

HPS 0.164 ± 0.003 0.162 j 1.2

Lactose 0.153 ± 0.003 0.150 k 2.0

Maltose 0.152 ± 0.003 0.146 l 4.1

PEG 4000 0.128 ± 0.002 0.134 m 4.5

PEG 6000 0.131 ± 0.001 0.134 n 2.2

PVP 0.166 ± 0.005 0.175 o 5.1

SDS 0.110 ± 0.007 0.108 p 2.6

Tartaric ac. 0.127 ± 0.002 0.120 q 5.8

Urea 0.143 ± 0.001 0.143 r 0.0

______________________________________________________________ a water, λ=840 nm, T=23oC; b standard deviations obtained with three independent measurements; c percentual difference between dn/dc obtained by SPR and those obtained in the literature; d dn/dc not available; e water, λ=589.3nm, T=25oC (1); f water, λ=632.8 nm (24); g

0.2M NaCl I=0.005, λ=436nm, T=25oC (1); h water, λ=589.3nm, T=20oC (25); i Dalteparin sodium, a low-molecular weight heparin, in buffer pH 7, λ=690 nm, T=25oC (25); j λ=632.8 nm, T=25oC (18); k water, λ=589.3nm, T=20oC (26); l water, λ=589.3nm, T=20oC (26); m water, λ=589.3nm, T=25oC (1); n water, λ=589.3nm, T=20oC (1); o water, λ=578nm, T=25oC (1); p buffer PBS (20); q

water, λ=589.3nm, T=20oC (26); r water, λ=589.3nm, T=20oC (26).

21

L

A

B

E F

I

J

D

H

G C

FIGURE 1

22

B

A

0 .0 0 2 0 .0 0 4 0 .0 0 6 0 .0 0 8 0 .0 1 0

1 .3 3 4

1 .3 3 4

1 .3 3 4

1 .3 3 5

1 .3 3 5

n

[ S u c r o s e ] ( g .c m - 3 )

0 .0 0 5 0 .0 1 0 0 . 0 1 5 0 .0 2 0

1 .3 3 4

1 .3 3 5

1 .3 3 6

1 .3 3 6

1 .3 3 7

1 .3 3 7

n

[ H P S - c m c ] ( g .c m - 3 )

FIGURE 2

23

0 200 400 600 800

0.0

0.2

0.4

0.6

0.8

1.0

DF

Time (s)0 200 400 600 800

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

[Suc

rose

] (g.

cm-3)

Time (s)

0 200 400 600 800 10001.332

1.334

1.336

1.338

1.340

1.342

1.344

n

Time (s)

CBA

FIGURE 3

24

[ U r

e a

] (

g .

cm

-3 )

CBA

0.00 0.02 0.04 0.06 0.08 0.10

1.332

1.334

1.336

1.338

1.340

1.342

1.344

1.346

1.348

n

[Urea] (g.cm-3)-100 0 100 200 300 400 500 600 700 800

1.332

1.336

1.340

1.344

1.348

n

Time (s)-100 0 100 200 300 400 500 600 700

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Time (s)

FIGURE 4

25

[ S

D S

] (g

.cm

-3)

0 10 20 30 40 50

1.333

1.334

n

Time (s)

CB

A

-0.004 0.000 0.004 0.008 0.012 0.016

1.333

1.333

1.334

1.334

1.335

1.335

cmc

n

[SDS-cmc] (g.cm-3)

0 200 400 600 800

0.000

0.004

0.008

0.012

0.016

0.020

Time (s)0 200 400 600 800

1.333

1.333

1.334

1.334

1.335

1.335

n

Time (s)

FIGURE 5

26