Protein Brownian Rotation at the Glass Transition Temperature of a Freeze-Concentrated Buffer Probed by Superparamagnetic Nanoparticles

Abstract

For applications from food science to the freeze-thawing of proteins it is important to understand the often complex freezing behavior of solutions of biomolecules. Here we use a magnetic method to monitor the Brownian rotation of a quasi-spherical cage-shaped protein, apoferritin, approaching the glass transition T_g in a freeze-concentrated buffer (Tris-HCl). The protein incorporates a synthetic magnetic nanoparticle (Co-doped Fe₃O₄ (magnetite)). We use the magnetic signal from the nanoparticles to monitor the protein orientation. As T decreases toward T_g of the buffer solution the protein’s rotational relaxation time increases exponentially, taking values in the range from a few seconds up to thousands of seconds, i.e., orders of magnitude greater than usually accessed, e.g., by NMR. The longest relaxation times measured correspond to estimated viscosities >2 MPa s. As well as being a means to study low-temperature, high-viscosity environments, our method provides evidence that, for the cooling protocol used, the following applies: 1), the concentration of the freeze-concentrated buffer at T_g is independent of its initial concentration; 2), little protein adsorption takes place at the interface between ice and buffer; and 3), the protein is free to rotate even at temperatures as low as 207 K.

Introduction

Issues such as biomolecule adsorption at the ice-liquid interface, molecular aggregation, and the temperature dependence of the solution viscosity are fundamental to understanding the freezing or vitrification of biomolecule solutions. Rotational Brownian motion gives a valuable insight into each of these phenomena, because biomolecule adsorption at the ice-liquid interface reduces the number of freely rotating molecules, aggregation increases their hydrodynamic radius, and a higher viscosity increases the characteristic relaxation time

$$\tau \propto \frac{{\zeta }_{\text{R}}}{kT},$$

where ζ_R is the rotational friction coefficient (1), and

$${\zeta }_{\text{R}}=8\pi \eta a^3,$$

where η is the viscosity experienced by the molecule and a its hydrodynamic radius (2).

Rotational Brownian motion probes the local viscosity experienced by the protein at low temperatures directly, in contrast to, e.g., specific heat spectroscopy, which probes the bulk viscosity (3). Brownian rotation may be measured experimentally by methods including fluorescence anisotropy (4) and NMR measurements (5). However, most existing methods cannot determine rotational relaxation times τ that are >∼100 ns for spherical molecules (2). One exception is fluorescence anisotropy correlation spectroscopy (6), but the presence of ice as in our study could cause problems for this technique. Here we use a, to our knowledge, new method to measure rotational relaxation times of ∼10,000 s for a representative quasi-spherical protein, ferritin, in a freeze-concentrated buffer solution, approaching its glass transition temperature T_g. Our method relies on incorporating a synthetic magnetic nanoparticle within the ferritin. Rotational relaxation can then be measured by monitoring the relaxation of the magnetic signal from the nanoparticle.

Ferritin consists of 24 subunits that assemble to form an approximately spherical shell with internal diameter ∼8 nm and external diameter ∼12 nm (7). It plays an essential role in regulating the iron content of cells whereby the central cavity stores excess iron as the mineral ferrihydrite. For this work we replaced the antiferromagnetic ferrihydrite with a synthetic magnetic nanoparticle (8) of magnetite (Fe₃O₄) doped with 2.5% Co to enable us to monitor the protein orientation via the magnetic signal (Fig. 1). In the remainder of this article we abbreviate cobalt-doped magnetite nanoparticles enclosed in ferritin as CMF.

Figure 1.

Schematic drawing of Cobalt-doped magnetite nanoparticle enclosed in ferritin (CMF).

The reason we dope the magnetite with Co is to raise the blocking temperature T_B of the nanoparticles from 18 ± 1 K to 62 ± 1 K (9). T_B is the temperature above which the direction of the magnetization vector is no longer parallel to the particle magnetic easy axis (a direction that minimizes the anisotropy energy) but instead fluctuates rapidly due to thermal energy. In other words, above T_B the direction of the magnetization vector is not fixed relative to the particle orientation. The greater the ratio T_B/T_g, the greater the extent to which we can control nanoparticle alignment magnetically close to T_g. The value of 2.5% Co is a compromise; although additional Co could raise T_B even higher, increasing the Co content also reduced the yield of the synthesis.

Materials and Methods

Synthesis and purification of Co-doped magnetite-ferritin (CMF)

CMF synthesis and purification followed modified procedures from the literature (10,11). In brief, horse spleen apoferritin (Sigma, St. Louis, MO) was suspended in HEPES-NaOH (Thermo Fisher Scientific, Waltham, MA) pH 8.6 at 65°C deaerated by N₂. Iron (Ammonium iron sulfate hexahydrate; Sigma) and cobalt (Cobalt sulfate monohydrate; Sigma) solutions were added together with hydrogen peroxide (Sigma) at a constant flow-speed to the protein solution to form the Co-doped magnetite core. After synthesis, the solution was centrifuged and passed through an ion-exchange chromatography column (ANX FF; GE Healthcare Life Sciences, Piscataway, NJ). The CMF was separated from empty or partially filled ferritin using a column filled with stainless steel in a 0.7–0.8 T magnetic field. A final size-exclusion chromatography step (Sephacryl S300; GE Healthcare Life Sciences) yielded purely magnetic, monodisperse CMF. The HEPES-NaOH buffer was exchanged by Tris-HCl (Sigma) pH 8.0 of the relevant concentration. The protein solution concentration was assessed by the Bradford assay method.

Magnetic characterization

All magnetic measurements were performed using a superconducting quantum interference device (SQUID) magnetometer (MPMS-XL; Quantum Design, San Diego, CA) with temperature and applied field controlled in the ranges 2–300 K and 0–5 T, respectively. Previous studies of the rotational relaxation of suspended nanomagnets have used optical methods or AC susceptibility (12,13), but for this work, SQUID magnetometry is more appropriate because of the longer relaxation times and lower temperatures studied.

We studied solutions with a CMF concentration of 0.9 μmol/L, to minimize the influence of dipolar interactions by ensuring an average interparticle separation before freeze concentration of at least 100 nm. Solutions of disperse CMF were placed in sealed polypropylene tubes and mounted inside a plastic drinking straw for SQUID magnetization measurements. From fits to magnetic data measured at temperatures well above T_B, the mean magnetic dipole moment m of the synthetic magnetic nanoparticles is typically 6000 μ_B (Bohr magnetons).

Dynamic light scattering

A goniometer and a laser light scattering system (BI-200SM; Brookhaven Instruments, Holtsville, NY) were used to determine the hydrodynamic radius of monodisperse CMF in solution at room temperature.

Results

Magnetic alignment of CMF

Fig. 2 shows the normalized magnetic moment M measured as a function of applied magnetic field B for the same sample of 0.9 μM CMF in 50 mM Tris-HCl solution cooled by using two different protocols. Open circles represent data obtained after cooling from room temperature to 5 K in zero applied field at 10 K/min. Solid circles represent data obtained after initially cooling the sample from room temperature to 250 K in zero applied field (to avoid field-induced agglomeration of CMF before the bulk of the water in the Tris-HCl solution freezes) and then cooling it down to 5 K in a 5 T applied field. The most important difference between the two sets of data is that the loop formed by the solid circles is much squarer than the loop formed by the open circles. This difference is caused by the magnetic easy axes of the CMF being aligned parallel to the applied field in the former case, i.e., after cooling in a 5 T applied field and randomly aligned in the latter, i.e., after cooling in zero applied field. The alignment in the applied field is not perfect, because the ratio T_B/T_g is <1/3 (14); however, it is sufficient to produce significant changes in the measured magnetic properties of the system (Fig. 2).

Figure 2.

Normalized magnetic moment curves at 5 K of a 0.9 μM solution in 50 mM Tris-HCl of unaligned CMF (open circles) and CMF aligned by cooling in a 5 T applied field (solid circles).

The applied field causes the complete CMF (i.e., protein + nanoparticle) to rotate relative to its matrix, rather than rotation of the Co-doped magnetite nanoparticle within the protein cage. To check that the observed alignment of the nanoparticle easy axes is indeed due to rotation of the complete CMF, we compared CMF crystallized into a periodic three-dimensional array (11,15) with a solution of CMF. Crystallization prevents the protein molecules from rotating without, in principle, affecting any motion of the nanoparticles within their cages. Cooling the sample in a 5 T field no longer gives a magnetization curve characteristic of aligned CMF, but such a curve is obtained again as expected when the protein molecules are freed to rotate by dissolving the CMF crystals.

CMF alignment as a function of temperature

In Fig. 3 we compare normalized M measured at constant B for unaligned (zero field-cooled) and aligned (5 T field-cooled) samples of CMF in 50 mM Tris-HCl. As T rises, thermal energy permits the magnetization of some nanoparticles in the unaligned sample to switch to an easy axis direction more nearly parallel to the applied field, increasing M. In the aligned sample, the nanoparticle magnetization is already along a favorable easy axis direction, so this increase is not observed. Above T_B, M decreases smoothly with T for both samples as the thermal energy permits greater and greater fluctuations of the nanoparticle magnetization relative to the easy axis. However, at T ∼207 K, M for the aligned sample starts to decrease more rapidly, and within a few K it is the same as for the unaligned sample. This sudden decrease in M is caused by the loss of alignment as the sample passes through T_g, the viscosity decreases, and the ferritin molecules start to undergo rotational Brownian motion.

Figure 3.

Normalized magnetic moment M measured on warming a 0.9 μM solution of CMF in 50 mM Tris-HCl in a 0.05 T applied field after cooling from 250 K to 5 K in zero (open circles) and 5 T applied field (solid circles).

Data similar to Fig. 3 are obtained for higher and lower concentrations of Tris-HCl in water. From a comparison of data for different Tris-HCl concentrations, the size of the step in M caused by the loss of alignment, which is a measure of the amount of CMF that participates in the rotational relaxation process, is approximately the same for CMF in 50 mM and 1 M Tris-HCl (Fig. 4). Even for CMF in 2.5 mM Tris-HCl there is only a small decrease in the step size and increase in the temperature for the onset of rotational relaxation. We have studied other glass-forming solutions and find similar transitions, though at different temperatures corresponding to the different T_g. For example, for 1 M glycerol-water, the temperature for the onset of rotational relaxation is ∼185 K (see Fig. S1 in the Supporting Material), which is ∼20 K above the expected T_g for freeze-concentrated glycerol (16). However, we do not find any such transition for CMF solution in pure water without the addition of a glass-former.

Figure 4.

Magnetic moment M measured upon warming 0.9 μM solutions of CMF in 1 M (open circles), 50 mM (shaded circles), and 2.5 mM (solid circles) Tris-HCl. Scans recorded in B = 0.05 T applied field after cooling from 250 K to 5 K in 5 T applied field.

Determination of the rotational relaxation time and viscosity for CMF in 50 mM Tris-HCl solution

Measuring M at constant T and B permits us to determine the characteristic relaxation time τ for Brownian rotation. Fig. 5 shows that when an initially aligned sample is allowed to relax at B = 0.05 T, M − M₀ ∝ exp − (t/τ), where M₀ is the equilibrium value of M for a particular B and T, which can be determined from a theoretical treatment such as that of Hartmann and Mende (14). Fig. 5 also shows that τ decreases rapidly with increasing temperature.

Figure 5.

Relaxation measurements at B = 0.05 T after a 5 T cool to various temperatures, with a single exponential fit. Time t = 0 is the time at which B is switched from 5 T to 0.05 T. M₀ (see text) was fixed at the appropriate value when fitting the data.

If the CMF is initially unaligned, and a magnetic field B applied to orient it, M approaches its equilibrium value M₀ such that M₀ − M ∝ exp − (t/τ) (see Fig. S2). Within error, the value of the time constant τ for CMF alignment is the same as it is for Brownian rotation, and independent of the magnitude of B for the range of B studied. This suggests that to a good approximation the magnetization dynamics for both alignment and relaxation are described by a single equation of the form

$$\frac{dM}{dt}\propto \frac{\left(M_0-M\right)}{{\zeta }_{\text{R}}}.$$

If we make the assumption that M ∝ $\langle {\cos }^2\theta \rangle$, where θ is the angle between an easy axis of the CMF and the applied field B (14), then (5)

$$\tau =\frac{{\zeta }_{\text{R}}}{6kT}.$$

Using this expression for τ, the rotational friction coefficient ζ_R changes from 4.8 (±0.1) × 10⁻¹⁸ kg m² s⁻¹ at 213 K to 1.3 (±0.1) × 10⁻¹⁶ kg m² s⁻¹ at 207 K. If our assumption that M ∝ 〈cos² θ〉 is incorrect, it will change the constant of proportionality in the equation for τ but is unlikely to affect the order of magnitude of ζ_R. Using the Stokes expression ζ_R = 8πηa³, and a value for the molecular hydrodynamic radius a = 13.5 ± 0.1 nm, measured for our CMF using dynamic light scattering at room temperature, the corresponding viscosity range is 0.08–2.2 ± 0.1 MPa s. The viscosity derived in this way is an effective microscopic viscosity experienced by the protein (17) and not the bulk viscosity of the sample, which is ill-defined as the sample is inhomogeneous, containing a large proportion of ice crystals. Although the effective viscosity values we measure are very high, substantial Brownian rotation still takes place over the timescale of the experiment because the ferritin molecule has a hydrodynamic radius of only a few nanometers.

In Fig. 6, we plot the relaxation time τ as a function of 1/T. The experimental results are described well by an exponential relationship, though we cannot exclude slightly super-Arrhenius T-dependence given the relatively small T-range (18). An exponential T-dependence of τ is typical of strong glass-formers close to T_g.

Figure 6.

Plot of rotational relaxation time τ as a function of T⁻¹ with an exponential fit (dashed line).

Discussion

On cooling the Tris-HCl solution there is extensive ice formation, which concentrates the remaining protein/Tris-HCl solution. The ice gives rise to a large endothermic peak in differential scanning calorimetry (DSC) data (see Fig. S3). DSC data also indicates that part of a 1 M Tris-HCl solution undergoes a glass transition at T ∼ 207 K, but we do not observe this transition for 50 mM Tris-HCl (see Fig. S3). Furthermore, this transition cannot be directly responsible for the exponential increase in rotational relaxation time seen in Fig. 6, because at T = 207 K, the relaxation time of Fig. 6 corresponds to a viscosity of at most a few MPa s, i.e., orders of magnitude less than the 10¹² Pa s expected of a glass. Extrapolation of the data in Fig. 6 suggests that η = 10¹² Pa s at ∼190 K, i.e., that T_g for the freeze-concentrated Tris-HCl solution surrounding the CMF is ∼190 K, which lies outside the T-range of our DSC. Note that the difference between the temperature for the onset of rotational relaxation for freeze-concentrated Tris-HCl solution and our estimate of T_g is 17 K, which is very close to the difference between the temperature for the onset of rotational relaxation for freeze-concentrated glycerol-water and the expected T_g (∼20 K) (16).

Our observations that the measured temperature for the onset of rotational relaxation of CMF (the step in Fig. 3) is different for different glass-forming solutions having different T_g (see Fig. S1) suggest that the rapid change in τ is due to changes in the solvent viscosity rather than any changes in the intrinsic protein dynamics. Furthermore, because rotation is not observed for CMF solution in pure water, even if the protein solvation shell remains mobile before undergoing a glass transition at ∼170 K (19), this is insufficient to permit the protein to rotate.

The fact that approximately the same temperature for the onset of rotational relaxation is obtained for CMF in Tris-HCl concentrations from 1 M down to 50 mM, and that even in 2.5 mM Tris-HCl the observed change is small (Fig. 4), suggests that T_g for the fluid surrounding the CMF is independent of the starting Tris-HCl concentration. Though this might seen surprising, it is to be expected if in each case ice crystallization freeze-concentrates the Tris-HCl solution to a composition close to the eutectic composition. The observed temperature for the onset of rotational relaxation would then be that which corresponds to this composition, not the starting composition.

Our observation (Fig. 4) that the size of the step in M caused by the loss of alignment of CMF is also largely independent of the starting Tris-HCl concentration and hence the amount of ice formed on freeze-concentration of the sample confirms that the ferritin segregates to the Tris-HCl rather than be incorporated in the ice crystals that form. The fact that the step in M is approximately constant also suggests that there is limited adsorption at the ice-liquid interface. Such adsorption has been postulated as a reason why some proteins aggregate on freeze-thawing (20,21). However, we cannot rule out some adsorption and denaturation, as the size of the step in M does reduce slightly when the CMF solution is warmed to above T_g and refrozen.

In the Introduction we stated that in addition to providing information on biomolecule adsorption at the ice-liquid interface, protein Brownian rotation should provide insight into whether biomolecules aggregate. For our system, although it is only a preliminary conclusion, we can state that because the data of Fig. 5 and Fig. S2 can be fitted with a single relaxation time at a given T, there is no evidence of freezing-induced aggregation. Such aggregation would give material with a larger hydrodynamic radius and hence also a larger τ.

Conclusion

Monitoring the orientation of an incorporated superparamagnetic nanoparticles has allowed us to study the rotational dynamics of a protein molecule at timescales much longer (much higher viscosities) than previously studied. Magnetic relaxation can provide information on the local viscosity, even for such highly heterogeneous systems as the freeze-concentrated solutions studied here. We expect that studies of other solvents and nanoparticles other than CMF will also yield valuable data. For example, a comparison of magnetic nanoparticles with different surface functionalizations would enable the effect of surface chemistry on nanoparticle aggregation and adsorption during freeze-concentration to be studied.