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PHYSICAL SCIENCES / BIOLOGICAL SCIENCES / CHEMISTRY / BIOPHYSICS
Altered phase diagram due to a single point mutation in human 
D-crystallin
,,
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*Materials Processing Center, Department of Physics, and Center for Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139
Contributed by George B. Benedek, August 7, 2007 (received for review June 27, 2007)
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D-crystallin (HGD) is associated with cataract. We have previously investigated the solution properties of this mutant, as well as those of the closely related P23V and P23S mutants, and shown that although mutations at site 23 of HGD do not produce a significant structural change in the protein, they nevertheless profoundly alter the solubility of the protein. Remarkably, the solubility of the mutants decreases with increasing temperature, in sharp contrast to the behavior of the native protein. This inverted solubility corresponds to a strong increase in the binding energy with temperature. Here we have investigated the liquid–liquid coexistence curve and the diffusivity of the P23V mutant and find that these solution properties are unaffected by the mutation. This means that the chemical potentials in the solution phase are essentially unaltered. The apparent discrepancy between the interaction energies in the solution phase, as compared with the solid phase, is explicable in terms of highly anisotropic interprotein interactions, which are averaged out in the solution phase but are fully engaged in the solid phase.
cataract | lens | protein phase diagram | quasielastic light scattering
D-crystallin (HGD) is an important member of the -crystallin family of proteins found in the human lens. Mutations in HGD in particular have been associated with a number of childhood cataracts (1–4). Recently, the P23T mutant of HGD has been associated with coralliform, cerulean, and fasciculiform cataract phenotypes (refs. 1 and 2 and references therein). Mutation at site 23 of HGD is only one of a number of single point mutations, including the R14C, R58H, and R36S mutations, that occur on the CRGD gene and that have been linked with early-onset cataract disease (5–9). Physicochemical characterization of the mutant proteins shows why these changes result in the formation of either covalently linked aggregates in the case of R14C (5, 6) or crystals in the case of the R58H and R36S mutants (7–9). The P23T mutation results in decreased solubility of the protein, leading to protein aggregation and light scattering, and hence to lens opacity. However, the aggregates are not covalently linked, since the aggregation process is completely reversible with temperature.
Formation of protein aggregates is a common motif in many "condensation diseases," which include cataract (10), sickle-cell anemia (11, 12), and Alzheimer's disease (13, 14), as well as other amyloid diseases such as diabetes and Parkinson's disease (15, 16). These examples highlight the importance of understanding the processes that lead to the formation of condensed protein phases under physiological conditions. In particular, protein condensation diseases resulting from a single amino acid substitution provide favorable conditions for biophysical analysis because such substitutions produce a change in the interaction potential between the proteins but may not necessarily result in significant structural changes to the protein itself. The first example of a protein condensation disease being associated with a single amino acid substitution was sickle cell anemia (11). Interestingly, hemoglobin S (HbS) displays retrograde solubility in its phase diagram and also a lower consolute temperature (17). A more detailed investigation of P23T and other mutants of HGD at site 23 (i.e., P23S and P23V) has shown that unusual phase behavior is displayed by all three of these mutants, implying that the region around site 23 of HGD is important in maintaining the solubility of the protein (1). Although substituting a single amino acid residue at site 23 does not alter the regular form of the coexistence curve, it results in decreased protein solubility and remarkably inverts the form of the solubility line. The mutation responsible for the inversion of the solubility line in vivo is P23T. Unfortunately, P23T has very low solubility [<5 mg/ml; 
= 0.0035. The volume fraction = c·
sp, where c is the concentration in milligrams per milliliter and sp is the partial specific volume 7.1 x 10–4 ml/mg (18) over the temperature range investigated]. With such low solubility, many features of the phase diagram are not accessible and cannot be measured, including liquid–liquid phase separation (LLPS). We chose to focus on the more soluble P23V substitution because this mutant demonstrates the same inverse solubility as P23T but over a larger concentration range, allowing us to investigate LLPS, aggregation, and crystallization. Although we will focus our experimental efforts on the P23V mutant, it will be possible to comment on the behavior of all three mutants.
We first summarize the state of our knowledge regarding the P23V mutant of HGD. The solubility line of mutants of HGD at site 23 shows a retrograde temperature dependence. The replacement of Thr-23 with a Ser or Val residue shifts the location of the inverted solubility line to higher concentrations (1). On the other hand, LLPS for P23V appears to be the same as for HGD, and the CD, Raman, and IR spectra show that no major secondary or tertiary structural changes take place upon mutagenesis (1).
Given the unusual nature of the phase diagram, we undertook further studies of these phase separation phenomena. We have extended the data for the LLPS, confirming that it is in fact the same as for the native protein. Furthermore, we have used quasielastic light scattering (QLS) spectroscopy to probe the interactions between the proteins in the soluble region of the phase diagram. We have also produced crystals of P23V and will comment on this in relation to the phase diagram.
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without aggregation. The maximum protein concentration we could reach at a temperature of 277 K (4°C) was 
100 mg/ml ( = 0.071) before aggregation began to occur. Consequently, this was the highest concentration at which measurements of LLPS could be taken. The LLPS for the native protein is also shown for comparison. Clearly, the coexistence curves for both native and mutant proteins are the same.
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We produced crystals of P23V within a narrow section of region B on the phase diagram, when solutions were passed through 0.02-µm filters (Fig. 1). Samples at concentrations between 20 and 40 mg/ml ( = 0.014 to 0.028) were incubated at 32°C (305 K) overnight. Visual examination of the glass tubes revealed that small crystals had formed on the walls; their crystalline order was confirmed by observation of optical birefringence (Fig. 2). These crystals were of very low quality and only grew in small numbers. Many were irregularly shaped. Attempts to improve the number and quality of the crystals failed because aggregation often occurred when we tried to manipulate the samples. This further highlighted the competition between crystallization and aggregation. Protein crystals produced from a solution at a concentration of 20 mg/ml ( = 0.014) began to melt at room temperature (20°C, 293 K), as can be seen at the edges of the protein crystal in Fig. 2. To establish a point on the liquidus line, crystals are usually placed in a small volume of protein-free solvent. The protein crystals will dissolve until equilibrium has been reached. Because of the small number of crystals that grew, we determined the solubility of the protein crystal by starting from a supersaturated solution (19, 20). In solutions in which crystals grew, we lowered the temperature until melting began to occur at the edges of the crystals. We took this as the solubility. When this method is used, the surface may be poisoned by impurities or imperfections arising from improperly oriented proteins, thereby stopping further crystal growth (21, 22); however, previous work (20) has shown that in practice there is no significant difference in the results obtained using either method.
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Because aggregation occurs at low supersaturations, we found only a narrow window in the phase diagram in which aggregation could be suppressed in favor of crystallization. Essentially, we suppressed aggregation long enough to allow crystallization to occur. Given that the crystals grew only on the walls and the surface of the protein solutions, this crystal growth was by heterogeneous nucleation. Thus, knowledge of the phase diagram of this protein gave us a good indication of the conditions under which crystallization might occur (i.e., at higher temperatures).
QLS. We also carried out QLS measurements that showed that in the soluble region of the phase diagram, the diffusion coefficient of P23V is consistent with monomeric protein, and no aggregation is observed (region A in Fig. 1).
QLS and Protein Aggregation.
In region B of the phase diagram (Fig. 1), where aggregation occurs, this aggregation was in the form of isolated particles/aggregates of protein, with larger hydrodynamic radii passing through the scattering volume. These large particles always represented a very small portion of the entire sample, comprising usually <5% of the total scattering intensity (in the concentration and temperature regimes we examined). Most of the protein remained as monomer. It is important to note that there was no evidence of percolation or gelation in the light scattering data. In Fig. 3 we show QLS data for P23V at 5 mg/ml ( = 0.0035) at 42°C (315 K), just inside region B of the phase diagram. At the beginning of the measurement, only monomer is present in solution (Fig. 3 Upper). After a lag time, protein aggregates begin to form, and higher molecular weight aggregates are observed (Fig. 3 Lower). This aggregation is reversible. Once the temperature is lowered again, the aggregates dissolve, leaving only protein monomer in solution.
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= 0.0028 to 0.021) and at temperatures ranging from 20° to 35°C (293–308 K), all in region A of the phase diagram. For this range of concentrations, we would expect Dc to depend linearly on . We linearly extrapolated Dc to = 0 to determine the free-particle diffusion coefficient, D0, which we found to be 1.15 x 10–6cm2·s–1 (25°C, 298 K). This corresponds to a hydrodynamic radius of 2.1 nm by the Stokes–Einstein equation: D0 = kT/6
R, where D0 is the diffusion coefficient (in cm2/s), is the solvent viscosity, k is Boltzman's constant, and R is the hydrodynamic radius. These samples were all measured in the region of the phase diagram where aggregation and crystallization are absent and multiple scattering is not present. Our D0 for HGD is consistent with D0 for bovine B-crystallin (23). There is a high degree of sequence homology between the -crystallins and, because the molecular weights of bovine B-crystallin and P23V differ by only 350 Da, we would expect to measure very similar diffusion coefficients. Bovine B-crystallin, like HGD, exhibits LLPS and has "normal" solubility.
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, T)/D0(T) data for P23V at different temperatures. Our data show that Dc decreases with increasing protein concentration at all temperatures between 20° and 35°C (293–308 K) investigated. This behavior is expected from particles with attractive interactions because concentration fluctuations dissipate more slowly as the particle concentration increases, resulting in a smaller measured D0. Our measurements of diffusivity for P23V show that with increasing temperature, the collective diffusion coefficient for the protein particles becomes smaller (at constant ). Both the concentration and temperature dependence we find were observed by Fine et al. (23) for bovine B-crystallin. In both cases, the slope of Dc vs. is negative and of approximately the same magnitude (approximately –7.5 for bovine B-crystallin and approximately –5.0 for HGD), and the values for D0 of both proteins at 25°C (298 K) agree within 10%. Several studies have used QLS to probe interactions between proteins (23–33). According to Muschol and Rosenberger (27),
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where the static structure factor S(q = 0, ) 1 – kS and the hydrodynamic interaction term H(q = 0, ) 1 – kH. kS, kH, and kD are defined in ref. 27. We can deduce kD at each temperature from our data. These results are shown in Table 1. We also include D0 at each temperature. Examining the data, kD is negative at all temperatures. We can compare this result with the value predicted for hard spheres, kD = 1.45 [Batchelor (34)]. Clearly, our kD has the opposite sign. As the temperature increases, our value for kD becomes slightly less negative, indicating that the interactions between the protein particles become slightly less attractive (i.e., they are approaching a more hard-sphere, repulsive-type behavior). This solution behavior was not initially expected because of the strong inverted temperature dependence of the solubility. Both QLS data and LLPS data for native and mutant proteins indicate that the solution behavior is essentially the same for both proteins.
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Analysis of the Solubility Data.
We can represent the data for the liquidus line for native HGD and the solubility line of the mutant proteins in terms of the magnitude and temperature dependence of the relevant transfer chemical potential, 
µtrans, defined as
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where µC is the chemical potential of a protein molecule with 
associated water molecules in the solid phase. µC generally represents the chemical potential in the crystal phase, but in this case we use it to represent the aggregate phase (for the reasons discussed earlier in this section). µC is a negative number, larger in magnitude than the negative quantity, µ
+ µ
, which is the standard part of the chemical potential of the protein with associated water molecules. Therefore, µtrans is a positive quantity. We may use the Van't Hoff law, which states that the volume fraction, , along the solubility line is related to the transfer chemical potential, µtrans, according to (36)
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If we define X = T0/T, where T0 = 298 K, it follows that = exp – (µtrans/kT0)X. Using the solubility data for native HGD (6) and the mutants, P23V, P23S, and P23T (1), we can determine µtrans for each protein. Plotting µtrans/kT0 vs. T/T0, we find that the slope for the native protein is negative, whereas it is positive for all of the mutant proteins. Also, using Eq. 3, we observe that at volume fractions higher than 0.02, µtrans/kT0 does not depend linearly on T. It is important to determine the reason for the nonlinearity. Here we employ a more accurate form of Eq. 3, using the virial expansion:
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B2, the second virial coefficient, is the second term in the virial expansion. B2 is defined by Lomakin et al. (37):
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where 
= eff/kT, and from the LLPS, 
= 1.25 and eff/kTc = 1.27 (38). B2 then becomes
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We note that B2 has a weak temperature dependence. Using this expression for B2 in Eq. 4, we find that µtrans/kT0 vs. T/T0 is in fact linear over the temperature range studied (See Fig. 5). Defining 
= T/T0, we express this linear temperature dependence as
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where V = µtrans(T0)/kT0; S = [
(µtrans/kT0)/]=1; and = (T – T0)/T0.
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µtrans/kT0 in the Van't Hoff law, and noting that (T0/T) 
(1 – ), we find that in the low region ( < 0.02), the solubility line has the very simple form
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From Eq. 7a and 7b, we see at once that the increase or decrease of the solubility with increasing temperature is determined entirely by the sign of the quantity K = ([µtrans(T0)/kT0] – S). The value of this quantity is listed in column 4 of Table 2 for the native and mutant proteins. In each case, the magnitude of the slope S makes the dominant contribution to K. For the native protein, K is +23.8, corresponding to the observed "normal" increase in solubility with increasing temperature. On the other hand, for the P23V mutant, K is negative because of the large positive value of S for this protein. Thus, the strong increase of µtrans/kT0 with increasing temperature is responsible for the retrograde solubility line for the P23V mutant and the other mutants as well.
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, T) plane is determined by the prefactor 0 according to Eq. 7b. Indeed, the dramatic decrease in the observed solubility at T0 as one compares P23V with P23S and P23T is, in fact, the result of an increase in V, from 4.8 to 7.2. Thus, the large change in solubility and consequent opacification of the lens is due to a relatively small change of approximately µtrans(1) 2.4kT0, which appears as the exponent in Eq. 7b.
Aeolotopic Model and P23V Mutation.
The striking feature of our experimental data is the finding that although the mutations dramatically change the solubility of the protein, they have a negligible effect on the properties of the solution phase, such as the LLPS or the concentration dependence of the protein diffusivity. In effect, the mutations change the chemical potentials of the solid phase but not those of the liquid phase. This represents an inexplicable paradox if the interprotein interactions are treated using a simple isotropic model. Indeed, in such a model a change in the attractive energy as a result of the mutation must have a proportional effect on both the coexistence curve and the solubility line. In reality, however, as we have emphasized previously (37), the interprotein interactions are highly anisotropic and localized. The analysis of our data indicates that a mutation at site 23 dramatically affects the temperature dependence of the interprotein interaction. Indeed, according to the estimates above, we deduce that the energy change upon mutation in this region has a strong temperature dependence, amounting to several kT over a 30°C temperature range. This energy magnitude is small compared with the typical energy associated with crystal contacts. Interestingly, the x-ray structure of native HGD crystals (39) indicates that site 23 is not directly involved as a crystal contact. Furthermore, no crystal structure is available for the site 23 mutants. Because the solubility at T0 is nearly the same for mutant and native proteins, it is reasonable to assume that there is no significant structural change as a result of the mutation.
Our data show that a local energy change of this magnitude produces a negligible effect on the average pairwise interaction (second virial coefficient and diffusivity) and on the liquid–liquid coexistence in the solution phase. This observation finds its natural explanation in the framework of the aeolotopic model (37). In this model, we have shown that the thermodynamic properties of the liquid phase can be described by a spatial thermodynamic average of the highly anisotropic actual potential. Using the expression for the effective attractive energy given in ref. 37, suitably generalized for attractive spots with different energies and areas, it is possible to show that for a protein with >30 attractive spots, the aforementioned change of 2.4 kT0 in the energy of one spot will translate into a <0.3% change in the thermodynamically averaged effective energy in the solution phase. This corresponds to 1°C shift in the coexistence curve, which is within the level of uncertainty in the measurements of LLPS. Thus, the apparent discrepancy between the interaction energies in the solution phase vs. the solid phase is explicable in terms of highly anisotropic interprotein interactions, which are averaged out in the solution phase but are fully engaged in the solid phase.
Role of Proline 23 in HGD. The overall structure of HGD has been determined (39), and Raman, IR, and far-UV CD analyses suggest that mutations at site 23 produce no major structural changes. Therefore, the observed dramatic changes in solubility, and especially the retrograde temperature dependence in the mutant proteins, must be ascribed to local changes in the immediate vicinity of site 23. The fact that, regardless of the residue replacing proline, the solubility curve always changes to retrograde, suggests the importance of the removal of the proline. Indeed, it has been found that the addition of proline at site 24, while the Val or Thr residues are left at position 23, restores the normal temperature dependence of the solubility of the protein (1). Thus we can conclude that the presence of proline in the vicinity of site 23 contributes importantly to the binding energy, decreasing it as the temperature increases. This conclusion presents an interesting challenge to theoretical analysis using molecular dynamic simulations.
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2.4 kT. Comparison with data on other mutants (1) suggests that the underlying source of these binding energy changes is associated with the presence or absence of proline in the vicinity of position 23. |
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= c·sp, where c is the concentration in milligrams per milliliter and sp is the partial specific volume, 7.1 x 10–4 ml/mg (18). QLS. QLS was performed with an instrument built in-house, using a coherent 35-mW, 632.8-nm He-Ne laser (Coherent Radiation, Santa Clara, CA) and a PD2000DLSPLUS 256-channel correlator (Precision Detectors, Bellingham, MA). The scattering angle in all experiments was 90°. The temperature was controlled by using an external circulating water bath, with the sample temperature monitored by a thermocouple probe positioned beside the sample vial during measurements. The measured correlation functions were analyzed by the Precision Deconvolve 4.4 software method (Precision Detectors), which determines the total scattered light intensity vs. the diffusion coefficient of the sample. Protein solutions were prepared at the desired concentration in 0.1 M sodium phosphate buffer (20 mM DTT/0.02% sodium azide) and then filtered through 0.02-µm Anatop filters (Whatman, Clifton, NJ) before measurement. Cylindrical glass tubes (Kimble, Vineland, NJ) with an internal diameter of 0.4 cm were used for QLS measurements.
Measurement of LLPS.
P23V solutions, filtered through 0.22-µm PDVF filters (Millipore, Billerica, MA) of known concentration in 0.4-cm-diameter glass tubes, were placed in a cell with transparent windows, connected to an external circulating water bath. The samples were cooled to just below the solubility line (4°C) and allowed to equilibrate. There is a very narrow region, below the solubility line and above the coexistence curve, where the protein exists as a homogeneous monomeric solution. It is important to ensure that the protein is in monomeric form before the temperature is lowered to measure LLPS, so particular care was taken in this regard. The temperature inside the cell was measured by a thermocouple probe placed in an identical glass vial containing water, inside the same cooled cell. A 4-mW He-Ne laser was focused on the sample, and the transmitted light intensity was detected by a photomultiplier connected to a voltmeter. The initial light intensity value was recorded. The cell was then cooled, and the transmitted light intensity was monitored. When the light intensity fell to half of its initial value, the temperature at which this occurred was recorded. When the transmitted intensity dropped further, below 1%, the cell was heated and the temperature at which the transmitted intensity reached half the initial value again was recorded. The phase separation temperature, Tph, was taken as the average of the clouding and clearing temperatures. Interactions between -crystallins are attractive and are also characterized by a high content of free cysteine residues, which leaves these proteins susceptible to disulfide-bond formation. Here we have avoided the formation of these covalently linked aggregates with the addition of DTT (41).
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Abbreviations: HbS, hemoglobin S; HGD, human D-crystallin; LLPS, liquid–liquid phase separation; QLS, quasielastic light scattering.
¶To whom correspondence should be addressed at: Room 13-2005, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139. E-mail: benedek{at}mit.edu
Author contributions: J.J.M., J.P., and G.B.B. designed research; J.J.M., A.L., O.O., A.P., and M.B. performed research; J.J.M., A.L., and G.B.B. analyzed data; and J.J.M., A.L., and G.B.B. wrote the paper.
Present address: Department of Chemistry, University at Albany, State University of New York, 1400 Washington Avenue, Albany, NY 12222. 
The authors declare no conflict of interest.
© 2007 by The National Academy of Sciences of the USA
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ka, K, Novák, P, Rezácová, P, Ondrová, L, Filipec, M, Sedlácek, J & Elleder, M. (2000) Hum Mol Genet 9, 1779–1786.
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  G. M. Thurston Protein anisotropy turns solubility on its head PNAS, November 27, 2007; 104(48): 18877 - 18878. [Full Text] [PDF]
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(T)/kT0 vs. T/T0 for native HGD and the three mutant proteins, P23T, P23S, and P23V, as deduced by using