On the Distribution of Protein Refractive Index Increments

Abstract

The protein refractive index increment, dn/dc, is an important parameter underlying the concentration determination and the biophysical characterization of proteins and protein complexes in many techniques. In this study, we examine the widely used assumption that most proteins have dn/dc values in a very narrow range, and reappraise the prediction of dn/dc of unmodified proteins based on their amino acid composition. Applying this approach in large scale to the entire set of known and predicted human proteins, we obtain, for the first time, to our knowledge, an estimate of the full distribution of protein dn/dc values. The distribution is close to Gaussian with a mean of 0.190 ml/g (for unmodified proteins at 589 nm) and a standard deviation of 0.003 ml/g. However, small proteins <10 kDa exhibit a larger spread, and almost 3000 proteins have values deviating by more than two standard deviations from the mean. Due to the widespread availability of protein sequences and the potential for outliers, the compositional prediction should be convenient and provide greater accuracy than an average consensus value for all proteins. We discuss how this approach should be particularly valuable for certain protein classes where a high dn/dc is coincidental to structural features, or may be functionally relevant such as in proteins of the eye.

Introduction

The question of what is the refractive index increment of proteins, and whether it is a constant, dates back more than a century (1–3). The knowledge of this parameter is important in many biophysical techniques. This includes the refractometric measurement of protein concentrations in analytical ultracentrifugation (AUC), surface plasmon resonance and other label-free optical biosensors, and the determination of protein molecular mass from the intensity of scattered light (4–8). The protein refractive index is also a key parameter in various types of optical imaging. Furthermore, knowing the molecular refractive index contribution of macromolecular components is crucial for understanding the optical properties, structure, and function of different tissues in the eye.

It is widely recognized that unmodified proteins, in the absence of significant solvation effects and ligand binding, generally do not have very different refractive index increments, and that a consensus value may be used in a good approximation. For example, a consensus value (in green or yellow light) of 0.185 ml/g (±2%) was proposed by Barer and Josephs (9), reporting extreme values for the proteins tested of 0.181 and 0.188 ml/g. Similarly, a value of 0.186 ml/g in phosphate buffered saline at 633 nm was proposed by Wen and colleagues (10,11) (which would translate to 0.188 ml/g at 580 nm after a wavelength correction following reference (12)). The ability to use such a consensus value is convenient and very important because the absolute experimental determination of a protein refractive index increment is not only very cumbersome, but also requires tens of milligrams of highly pure soluble protein for accurate dry weight measurements, which would be prohibitive for many or most proteins.

Physically, the refractive index of particles in the visible spectrum of light is a result of the local polarizability of the atoms and chemical groups due to deformation of the electron configuration about nuclei, and therefore insensitive to the long-range structure of macromolecules (6), and long known to be to a good approximation additive toward macromolecular refractivity (3,13,14). As a consequence, the protein amino acid composition represents the major determinant for the protein refractive index increment, dn/dc (3). In the 1960s, McMeekin and colleagues (15,16) determined the refractivities of amino acids (Table 1), and proposed protein dn/dc values to be estimated from their amino acid composition. This approach compared very well with experimental protein dn/dc data (7,15). For the proteins tested at the time, this reaffirmed the conclusion that protein dn/dc values fall within a narrow range of values (within 0.18–0.19 ml/g), such that, in the absence of sequence data or sufficient material for dn/dc determination, a consensus value should yield a good approximation to within 2–3% (7).

Table 1.

Refractive index properties of amino acids

Amino acid	Molar residue refractivity∗ (cm3)	$\overline{v}$ (ml/g)†	dn/dc(ml/g)‡
Arg	39.47	0.70	0.206
His	34.62	0.67	0.219
Lys	34.10	0.82	0.181
Asp	26.06	0.60	0.197
Glu	30.07	0.66	0.183
Ser	19.16	0.63	0.170
Thr	23.82	0.70	0.172
Asn	26.09	0.62	0.192
Gln	30.37	0.67	0.186
Cys	48.58	0.63	0.206
Gly	12.81	0.64	0.175
Pro	23.74	0.76	0.165
Ala	17.15	0.74	0.167
Ile	31.87	0.90	0.179
Leu	31.59	0.90	0.173
Met	34.45	0.75	0.204
Phe	42.21	0.77	0.244
Trp	55.24	0.74	0.277
Tyr	44.34	0.71	0.240
Val	26.73	0.86	0.172

^∗From McMeekin et al. (16) (measured experimentally as molar refraction of amino acid from which residue molar refraction was calculated).

^†From Cohn et al. (34).

^‡Predicted at 589 nm for hypothetical polypeptide in water with 150 mM NaCl, as described in Materials and Methods.

Unfortunately, the quality of this consensus value approximation has not been entirely clear. A recent compilation of experimentally measured dn/dc values (17) shows values largely consistent with this view. However, the literature also contains experimental values ranging from at least 0.168 ml/g for β-lactoglobulin A (18) (in phosphate buffered saline after wavelength correction) to 0.203 ml/g for bovine γ-crystallin (19) (in phosphate buffer at pH 7.0). Furthermore, because the number of experimentally measured values for unmodified proteins is quite limited, it is questionable whether they are representative for the entire set of human proteins, in particular, when considering that the molar residue refraction values of amino acids span more than a fourfold range (Table 1). This topic is of some importance because errors may be further amplified; for example, due to the square dependence of the intensity of scattered light on dn/dc (4), and a much larger error amplification could potentially occur in methods that use multisignal approaches, for example, to calculate the extent of protein derivatization (10,20), the degree of detergent-binding (21), or the stoichiometry of protein complexes (22,23).

While the knowledge of protein amino acid sequences was extremely sparse in the 1960s, this is usually not a limitation anymore for contemporary studies. Strengthening the strategy of a compositional prediction are modern ab initio computations of the mean polarizabilities of amino acids, which were found to be in good agreement with the tabulated data of McMeekin and colleagues (24–26). Thus, where dn/dc cannot be experimentally measured for practical reasons, it might be valuable to obtain an estimate from the compositional prediction rather than using an average value for all proteins. For the protein partial-specific volumes, quite analogous compositional predictions are highly useful and a current practice in the field of AUC (27–30)—with all their caveats and limitations (31,32). Accordingly, for this work we have embedded a dn/dc calculator function into the software SEDFIT (33).

Furthermore, the modern availability of large-scale protein sequence data bases allows us to reexamine more thoroughly than previously possible the question of how much the protein dn/dc value can possibly deviate from the standard expectation. To this end, in the current work we have embarked on using the composition-based prediction of dn/dc in a bioinformatics approach to the set of predicted proteins from the genome of humans and other species, with the aim to determine the complete distribution of dn/dc values. Finally, we have experimentally probed the range of predicted dn/dc values with synthetic peptides of high and low dn/dc.

Materials and Methods

Prediction of protein dn/dc based on amino acid composition

The prediction of the protein refractive index increment follows the method outlined by McMeekin and colleagues (15,16). In brief, we can write the refraction per gram R_P of the protein as the weight average of the contributions from the individual amino acids R_a (enumerated with the index a):

$$R_p=\frac{\sum _a{R}_a{M}_a}{\sum _a{M}_a},$$ (1)

where M_a is the residue molecular mass. Similarly, the protein partial specific volume, ${\overline{v}}_p$, may be estimated based on the amino acid composition as the weight average

$${\overline{v}}_p=\frac{\sum _a{\overline{v}}_a{M}_a}{\sum _a{M}_a},$$ (2)

with ${\overline{v}}_a$ denoting the residue partial specific volume (27,34). Using the Lorentz-Lorenz formula $R=\overline{v}\left(n^2-1\right)/\left(n^2+2\right)$, the refractive index of the protein is

$$n_p=\sqrt{\frac{2R_p+{\overline{v}}_p}{{\overline{v}}_p-R_p}}.$$ (3)

Based on the Wiener equation for dilute solutions (35) (Eq. 17 in reference (36)), the refractive index increment then follows as

$$\frac{dn}{dc}=\frac{3}{2}{\overline{v}}_p{n}_0\frac{n_p^2-n_0^2}{n_p^2+2n_0^2},$$ (4)

with solvent refractive index n₀.

The wavelength dependence of several proteins has been examined by Perlmann and Longsworth (12). It was found to follow a Cauchy relation, and the formula

$${\left(\frac{dn}{dc}\right)}_{\lambda }={\left(\frac{dn}{dc}\right)}_{578\text{nm}}\times \left(0.940+\frac{20,000{\text{nm}}^2}{{\lambda }^2}\right)$$ (5)

was proposed for the approximate wavelength correction (with the wavelength λ measured in nm). By the same authors, a small temperature dependence was measured, which we can approximately describe by a factor (1 + (25-t) × 0.0025/30°C), with t denoting the temperature in °C, in the range approximately between 10 and 25°C. Further corrections could be applied, in principle, for contributions from charge, preferential solvation, and known posttranslational modifications (5,10,12,37–39).

We implemented in the software SEDFIT version >12.2 (33) the prediction of dn/dc from a user-supplied amino acid sequence in single letter format, with wavelength and temperature corrections, using the tabulated experimental values for the amino acid refraction per gram from McMeekin and colleagues (16) for sodium light at a wavelength of 589.3 nm and a temperature of 25°C (Table 1), in combination with the tables for the amino acid partial-specific volumes determined by Cohn and Edsall (34). Unless otherwise mentioned in the following, we assume a reference solvent refractive index n₀ of 1.3340, corresponding to water at 25°C with 150 mM sodium chloride. For convenience, also implemented are the approximate corrections for temperature and wavelength dependence, the transformation of dn/dc into a fringe increment for interference optical AUC, and the compositional prediction of the protein extinction properties (40).

Experimental determination of dn/dc and dry weight measurement

The peptides were purchased from the Keck Biotechnology Resource Laboratory (New Haven, CT). The dry weight concentration was determined with modifications of the method outlined by Kupke and Dorrier (41). Stocks of both peptides and a control solution consisting of 5 mM NaCl were prepared by exhaustive dialysis against 5 mM NaCl. A gravimetrically recorded quantity (∼3 ml) of filtered stocks, control solution, and dialysate were transferred (in triplicate) into preweighed pyrex weighing bottles. These samples, as well as three empty preweighed bottles, were placed under vacuum (at a pressure of 90 mbar) overnight at 45°C, with caps unaffixed. For the next 3.5 days, the temperature was raised to 105°C while remaining under vacuum. Following the drying session, the samples were placed within an evacuated pyrex desiccator (containing calcium sulfate as a desiccant) at room temperature. The mass of all bottles was measured using an XP-26 microbalance (Mettler Toledo, Columbus, OH). To this end, the apparent mass was recorded in 1 min intervals up to 15 min, and a second degree polynomial fit was used to determine by extrapolation the mass at a time immediately following breakage of the vacuum seal on the desiccators. The mass values obtained were corrected for atmospheric buoyancy due to small temporal variations in local temperature, humidity, and barometric pressure. The bottles were subjected to three more rounds of overnight incubation at 105°C under vacuum, overnight incubation in desiccator, and mass measurements to ensure no further loss of water. For dialysate and control solutions, the wt% of NaCl was determined from the quotient of water mass evaporated to mass of material remaining dried in the bottle. For the peptide samples, the mass of protein was determined as the difference between the total dry mass remaining and the mass of the sodium chloride.

The total solution volume was calculated based on the tabulated density of the 5 mM NaCl solution at 20°C, corrected for the volume occupied by the peptide (predicted using the partial-specific volume based on amino acid composition). Peptide concentrations were then determined from quotient of peptide dry weight and total solution volume. The concentrations were (5.400 ± 0.007) mg/ml and (3.828 ± 0.007) mg/ml for both peptides, respectively.

Experimental dn/dc measurements were conducted from the same dialysis stock immediately after start of the dry weight determination. For each peptide, six sample solutions were prepared, with 10%, 20%, 40%, 60%, 80%, and 100% concentration of the stock. The refractive index of the solutions were determined with an Optilab ReX (Wyatt Technology, Santa Barbara, CA), at a wavelength of 690 nm. The protein refractive index increment was determined from the slope of the linear relationship between refractive index and concentration. The Cauchy wavelength corrections were applied (12).

Results

Table 1 shows the molar residue refractivities of the different amino acids from McMeekin and colleagues, and the calculated dn/dc for hypothetical polypeptides from each. Clearly, there are considerable differences in the refractive properties of the amino acids, ranging from dn/dc of 0.165 ml/g for proline to 0.277 ml/g for tryptophan. Amino acids with high polarizability and refractive index increment are those containing aromatic rings, sulfur, or double-bonds in the R-group, the highest ones being tryptophan, phenylalanine, tyrosine, histidine, cysteine, arginine, and methionine (Table 1).

The compositional approach for predicting protein refractive index increments has been compared in the literature with the values measured for naturally occurring mid-sized proteins, where difference from the constituent amino acids can be expected to have averaged out. In a different strategy, we aimed to experimentally demonstrate the sequence dependence of dn/dc and the range of possible values by constructing two short peptides that would be predicted to exhibit very high and very low values, respectively. To this end, a peptide A was created by concatenating two repeats of the solubility tag PEEASVTSTEETLTPAQEAAY, whereas peptide B was created as a concatenation of the tag with HHMHHMHHMHHMHHMHHMHH. (This sequence represented a compromise between a high predicted dn/dc value, the expected solubility, and the possibility for synthesis and purification.) The peptides were dialyzed in 5 mM NaCl and their concentration determined by careful dry weight measurement. By sedimentation velocity, both peptides were essentially monomeric with a large frictional ratio, consistent with the circular dichroism spectra containing significant contributions from the spectral signature of unordered peptides. Refractive index measurements of each peptide at different dilutions are shown in Fig. 1. The data show excellent linearity, with very different slopes corresponding to dn/dc values of 0.179 ± 0.003 ml/g and 0.194 ± 0.003 ml/g for peptide A and B, respectively. Within error, the values obtained are identical or very close to the theoretically predicted ones of 0.178 ml/g and 0.199 ml/g, respectively. Likely contributing factors to the small deviation are solvation and errors propagated from the tabulated amino acid partial specific volumes (see Discussion). This close agreement clearly confirms the amino acid composition dependence of the refractive index increment and the large range in principle available for proteins.

Figure 1.

Differential refractometry of peptides A (triangles) and B (circles). Concentrations were measured by dry weight determination. After wavelength correction to 589 nm, the slopes correspond to dn/dc values of 0.179 ± 0.003 ml/g (solid line) and 0.194 ± 0.003 ml/g (dashed line).

Next, we computed the dn/dc values for all 62,378 predicted protein sequences obtained from the University of California Santa Cruz (UCSC) genome browser for the human Feb. 2009 (GRCh37/hg19) assembly (Fig. 2). Interestingly, their distribution is very close to Gaussian, as if the refractive index of each residue were an independent random variable. Clearly, the considerable differences of the refractive properties of the amino acids average out for most natural protein sequences to an average of 0.1899 ml/g. The small standard deviation of 0.0030 ml/g confirms the expected similarity of refractive indices among most proteins. Similar distributions were obtained from the genome of different organisms that had mean values differing by less than the standard deviation of the distributions (Table 2). We observed that the predicted dn/dc value correlates well with the fraction of residues being Arg, Asp, Cys, His, Met, Phe, Trp, or Tyr, which are those with the highest eight values (Fig. 3). This correlation indicates that high dn/dc values are predominantly determined by the presence of these amino acids. This may be useful for a quick assessment of whether a protein with a given sequence should be expected to have unusually high or low values. (Many low dn/dc residues have refractivities closer to the average, and therefore individually do not contribute as much to the overall dn/dc.)

Figure 2.

Histogram of calculated dn/dc values for the 62,378 predicted proteins from the UCSC human genome browser for the human Feb. 2009 (GRCh37/hg19) assembly. The best-fit Gaussian is indicated as a black solid line, with mean of 0.1899 ml/g and standard deviation of 0.0030 ml/g.

Table 2.

Distributions of refractive index increments for different organisms and different classes of proteins

Species	Mean dn/dc value(ml/g)	Standard deviation (ml/g)	Mean $\overline{v}$ value (ml/g)	Standard deviation (ml/g)
Human∗	0.1899	0.0030	0.735	0.010
Zebrafish†	0.1904	0.0030	0.735	0.010
Yeast‡	0.1907	0.0030	0.739	0.011
C. elegans§	0.1911	0.0033	0.737	0.012
Methanosarcina acetivorans C2A	0.1904	0.0034	0.744	0.011
E. coli K-12¶	0.1902	0.0032	0.742	0.012
Membrane proteins‖	0.1916	0.0034
Membrane proteome∗∗	0.1908	0.0037
Intrinsically unstructured proteins††	0.1888	0.0033
Crystallins‖	0.1930	0.0055
Fatty acid hydroxylases‖	0.1971	0.0029
Reflectins‖	0.2097	0.0046

^∗Assembly Feb 2009 (GRCh37/hg19).

^†Dec 2008 (Zv8/danRer6).

^‡June 2008 (SGD/scaCer2).

^§May 2008 (WS190/ce6).

^¶Protein sequences available in NCBI for E. coli K-12.

^‖NCBI search results with this key word.

^∗∗Almén et al. (48).

^††Dunker et al. (49).

Figure 3.

Two-dimensional histogram of proteins from Fig. 2 and their dn/dc value as a function of the fraction of amino acid residues being either Arg, Asp, Cys, His, Met, Phe, Trp, or Tyr (this fraction being termed high dn/dc aa index in the axis label).

There are a significant number of proteins with dn/dc values more than two standard deviations from the mean. For the human proteins in the database, at the low end there are 1388 proteins with dn/dc < 0.1838 ml/g, the lowest one with 0.173 ml/g; and at the high end there are 1444 proteins with dn/dc > 0.1976 ml/g, the highest one being a keratin-associated protein with 0.215 ml/g. Prominent examples of more extreme values include titin, with a predicted dn/dc 0.177 ml/g, and γ-crystallins with values in excess of 0.199 ml/g. Furthermore, the shape of the dn/dc distribution depends significantly on the protein size (Fig. 4). For small proteins with molecular mass below 10 kDa the standard deviation of the distribution is 0.0053 ml/g, more than twice the number of 0.0025 ml/g obtained for large proteins with molecular mass in excess of 100 kDa. This suggests that shorter sequences are not averaging out as much the differences in the residue refractivities.

Figure 4.

Histogram of dn/dc values from known human proteins with molecular mass below 10 kDa (top) and above 100 kDa (bottom), respectively. The solid line is the best-fit Gaussian, with a mean of 0.1902 ml/g and standard deviation of 0.0053 ml/g for small proteins, and a mean of 0.1888 ml/g and a standard deviation of 0.0025 ml/g for the large proteins.

In addition to the molar refractivity, the molecular volume is an important quantity determining the refractive index increment. Therefore, we also determined the distribution of predicted protein partial-specific volumes. To this end, the established approach of Eq. 2 was applied across all predicted human proteins. The distribution obtained was close to Gaussian, with a mean of 0.735 ml/g and standard deviation of 0.010 ml/g. This is within error consistent with the consensus average value of 0.724 (± 0.024) ml/g calculated on the basis of 141 proteins by Attri and Minton (42). Fig. 5 shows a two-dimensional histogram of dn/dc and the partial-specific volume of each protein, suggesting the absence of a cross correlation between dn/dc and the partial-specific volume. (Potential confusion on this topic could arise from work by Scholte on the relationship between density increments and refractive increments of polymers (43); however, this work is concerned with the compounds of given refractive index. In Eq. 4, the protein partial-specific volume and dn/dc are indeed closely related for the given n_P. However, n_P itself is determined by the particle refractivity and partial-specific volume (Eq. 3), which are both amino acid composition-dependent for proteins and properties independent of each other (Eqs. 1 and 2). Table 1, for example, shows that arginine and threonine have the same residue partial-specific volume, but the latter has only half the refractivity. This can be understood by considering that the molecular polarizability depends on how strong electrons are localized in the outer shells of its atoms and chemical bonds, not necessarily related to the molecular volume.)

Figure 5.

Two-dimensional histogram of the human proteins from Fig. 2 sorted according to protein dn/dc and the partial-specific volume.

Discussion

In this work, we have reappraised the compositional prediction of the refractive index increment of proteins. Clearly, though very useful, the compositional estimate in the current form is imperfect. For example, it does not account for contributions from preferential interactions with solvent components (37,38), such as charge effects and ion binding (12), which can lead to different experimental dn/dc values at different pH and buffer conditions and for folded or unfolded proteins. Other factors that are not captured are the contributions of prosthetic groups and chemical modifications, although corrections for glycosylation (like other conjugation) should be possible as a weighted average of predicted amino acid and carbodydrate component (20).

These limitations should be very similar to those of the compositional prediction of the partial-specific volume, which is widely applied in the fields of small angle scattering and AUC for protein samples that do not lend themselves to dialysis and densimetry. As predicted by the Lorentz-Lorenz formula (Eq. 2), errors in the protein partial-specific volume will always also propagate into errors of dn/dc, and the tabulated amino acid partial-specific volumes probably represent the largest source of possible systematic error for the computation of a protein dn/dc. In fact, because the residue refractivities are known with great confidence experimentally and computationally from first principles, the ability to predict correct refractive indices is an indirect method to verify the tabulated protein partial-specific volumes. In this regard, we found the data tables by Cohn and Edsall (34) clearly superior to those from Zamyatnin (44), consistent with the observation of Durchschlag and Zipper (45) and Perkins (28).

Despite these limitations and potential sources of systematic error, as the experience from the widespread use of compositional partial specific volumes in the fields of small angle scattering and AUC shows, the amino acid composition will still be the dominant factor in many practical studies where proteins are not extremely charged, studied in simple buffers without osmolytes. Because sequences of the proteins under study are usually easily available, replacing the prediction from a postulated consensus value with a compositional prediction is easily possible and should present a better approximation.

Applying this approach to the entire space of predicted human proteins has shed new light on the idea of consensus dn/dc values. Although these are computed rather than experimental values, this improves on the surprisingly thin data basis of only a few dozen proteins, at best, on which the historic studies proposing the constancy of protein refractive indices were based (7,9). Of importance, the width of the calculated distribution is qualitatively consistent with some of the previous estimates. The large differences in amino acid refractivity usually average out, in particular, for large proteins.

On the other hand, the dn/dc distributions obtained also show that this averaging of amino acid refractivity is less effective for small proteins <10 kDa. It is certainly not negligible that we found close to 3000 human proteins that differ from the mean dn/dc of the distribution by more than two standard deviations. Furthermore, the span of dn/dc values of (predicted) human proteins ranging from 0.173 ml/g to 0.215 ml/g is much larger than previously thought (9). These aspects suggest caution against indiscriminately using a consensus dn/dc value that could potentially involve a maximum error of up to ∼10%.

An illustration for possible outliers offers the distribution obtained from a search of the National Center for Biotechnology Information (NCBI) for fatty acid hydroxylases (Fig. 6, top). In these enzymes, the high refractive index increment (0.1971 ± 0.0029 ml/g) arises from the consistently higher than average content of aromatic amino acids, some of them possibly aiding in substrate binding (e.g., in CYP120A1 (46)). However, generally it is not straightforward to identify entire protein families that would have consistently and significantly different dn/dc, because examples for amino acids with both high and low dn/dc can be found among all subsets that have either basic, acidic, charged, or hydrophobic properties. For example, although clusters of aromatic amino acids are a common motif of protein-membrane interactions (47), we have not observed significant deviations in the dn/dc distribution of membrane proteins from that of most other proteins (0.1916 ± 0.0034 ml/g for the 6717 sequences in the human membrane proteome (48) and 0.1908 ± 0.0037 ml/g for all 382,577 results searching NCBI for membrane protein (interestingly, though, a significantly higher average partial-specific volume of 0.753 ml/g than the average for all human proteins of 0.735 ml/g was calculated). Likewise, intrinsically unstructured proteins (49) do not seem to systematically deviate very much from the average dn/dc (0.1888 ± 0.0033 ml/g). Conspicuous is the observation of a much broader dn/dc distribution of proteins classified as crystallins (0.1930 ± 0.0055 ml/g), with many high dn/dc members and values up to ∼10% above average (Fig. 6, bottom). Extremely high values are also found in the proteins termed reflectins recently discovered in squid tissues (50).

Figure 6.

(Top panel) Histogram of the computed dn/dc values of all 6306 proteins obtained searching the NCBI protein sequence database for fatty acid hydroxylase. The solid line is the best-fit Gaussian, with a mean of 0.1971 ml/g and standard deviation of 0.0029 ml/g. As a visual reference, the Gaussian distribution from the analysis of all known and predicted human proteins is shown as a dotted line. (Bottom panel) Histogram of the computed dn/dc values of the 1514 proteins in NCBI classified as crystallins.

Whether or not the distribution of dn/dc values reported here is narrow enough to be considered consistent with uniform dn/dc values of proteins will certainly depend on the specific application and the level of accuracy needed. Often in biophysical studies characterizing protein interactions, the protein refractive index increment is needed solely to measure protein concentration, or in biosensing a surface layer thickness. Small errors should usually be tolerable, considering that binding isotherms typically result in statistical errors of the equilibrium binding constants values far greater than a few percent. However, error amplification can occur in the measurement of molecular mass from light scattering, to the extent that the incorrect assumption of a consensus value for one of the proteins in the tail of the distribution might make the discrimination between higher oligomers ambiguous. Error amplification in molecular mass determined by light scattering will be avoided if the protein concentration is measured refractometrically (51,52); nevertheless, accurate knowledge of the dn/dc parameter was found to be the limiting factor in the accuracy of peptide molecular mass determination by size-exclusion chromatography with multiangle laser light scattering (52). Errors in dn/dc would translate into even larger relative errors for some multisignal approaches, for example, where the excess refractive index signal is interpreted in terms of ligand binding, detergent binding, or protein modification. More accuracy in dn/dc could potentially be a significant improvement.

The availability of accurate protein refractive indices is also crucial for understanding the biophysics of eyes. For example, dn/dc enters as a key parameter in models for light transmission and scattering in the cornea (53–55). Similarly, lens protein concentrations are often estimated from measured lens refractive indices on the basis of assumed crystallin dn/dc values (56). In fact, crystallin concentrations in the lens are among the highest of any tissue, in some species reaching up to 500–1000 mg/ml (57). The thermodynamic phase behavior of such highly concentrated protein solutions close to the highest possible packing density is still an active area of research and very important for understanding the formation of cataract (58,59). However, it is clear that the strong nonideality under such crowded conditions will create highly nonlinear concentration dependence of thermodynamic parameters, such as chemical activity and osmotic pressure. Consequently, the accurate measurement of lenticular concentrations will be critical to understand actual intracellular conditions.

In this context, Pierscionek and colleagues (19) have concluded from their study of eye lens crystallins that the paradigm of constancy of refractive index increments is false and reported measurement of lens crystallin dn/dc resulting in values of 0.190 ml/g for bovine α-crystallin and 0.203 ml/g for bovine γ-crystallin. This correlates with the predominant spatial location of these crystallin species in the lens, as well as the well-known refractive index gradient from the cortex to the nucleus the lens (19,60,61). Recently, Kappé and co-workers (62) have similarly speculated that a high dn/dc value of γ-crystallins may be a result of sulfur-containing residues (e.g., amounting to 21.2% in lip shark γM1-crystallin) and be functionally relevant. To study the evolution of crystallins from this perspective, Kappé and co-workers (62) proposed the measurement of refractive index increments of crystallins from different clades. Although such experiments seem to pose insurmountable practical difficulties, the sequence-based computational approach can accomplish this task. In a forthcoming communication, we show by systematic sequence analysis of crystallins of different members of the βγ-crystallin family that lens (but not nonlens) γ-crystallins have indeed specifically evolved toward an elevated refractive index increment (H. Zhao, P. H. Brown, M. T. Magone, and P. Schuck, unpublished). Thus, this method represents what we believe to be a useful new bioinformatics tool for the prediction of potential protein function based on amino acid sequences from proteomic data bases.