Article Cite This: J. Am. Chem. Soc. 2017, 139, 16134-16142
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Thermodynamics of Polypeptide Supramolecular Assembly in the Short-Chain Limit Thomas O. Mason,† Thomas C. T. Michaels,†,‡ Aviad Levin,† Christopher M. Dobson,† Ehud Gazit,§ Tuomas P. J. Knowles,*,† and Alexander K. Buell*,∥ †
Department of Chemistry, University of Cambridge, Cambridge CB2 1TN, United Kingdom Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States § Department for Molecular Microbiology and Biotechnology, University of Tel Aviv, Tel Aviv 6997801, Israel ∥ Institute of Physical Biology, University of Düsseldorf, Düsseldorf 40225, Germany
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‡
S Supporting Information *
ABSTRACT: The self-assembly of peptides into ordered supramolecular structures, such as fibrils and crystals, is of relevance in such diverse areas as molecular medicine and materials science. However, little information is available about the fundamental thermodynamic driving forces of these types of self-assembly processes. Here, we investigate in detail the thermodynamics of assembly of diphenylalanine (FF). This dipeptide forms the central motif of the Aβ peptides, which are associated with Alzheimer’s disease through their presence in amyloid plaques in the nervous systems of affected individuals. We identify the molecular origins of the self-assembly of FF in aqueous solution, and we evaluate these findings in the context of the aggregation free energies of longer peptides that are able to form amyloid fibrils. We find that the thermodynamics of FF assembly displays the typical characteristics of hydrophobic desolvation processes, and detailed analysis of the temperature dependence of the kinetics of assembly within the framework of crystallization theories reveals that the transition state from solution to crystalline aggregates is enthalpically unfavorable and entropically favorable, qualitatively similar to what has been found for longer sequences. This quantitative comparison of aggregating peptides of very different lengths is the basis of an in-depth understanding of the relationship between sequence and assembly behavior.
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select for those with higher tendencies to self-assemble.12 A more quantitative understanding of the forces at work in such systems would be desirable, as it can help optimize computational screening approaches that have been used to identify those parts of sequence space that are able to assemble13 as well as facilitate the optimization of synthesis conditions and enable novel types of synthesis platforms to be employed, such as those based on microfluidic flow reactors.14,15 Furthermore, accurate and quantitative experimental data on the kinetics and thermodynamics of the assembly of simple model peptides will be able to guide molecular dynamics simulations of these systems,15−17 which are of a size that can be tackled in atomic detail with currently available computational resources. Such combined experimental and computational studies can act as important benchmarks on the way toward the description of more complex, biologically relevant self-assembling peptide systems. Here, we establish the thermodynamic parameters of the selfassembly of diphenylalanine, the paradigmatic system of short peptide assembly, which is able to form a well-defined
INTRODUCTION The self-assembly of polypeptides into ordered structures has been the subject of extensive investigations in recent years, due to the role of these processes in certain human disorders, as well as the hope that these types of processes and the resulting functional assemblies can be systematically exploited. In particular, also very short peptides have been investigated in this respect, and it has been shown that an astonishing diversity of structures, such as crystals,1 fibrils,2 rods,3 spheres,4 and tubes,5 can be created from simple building blocks, by varying the solution conditions,6 or through small chemical modifications of the peptides, such as omission of the final deprotection steps after peptide synthesis.7−9 Despite an increasing understanding of the relationship between the chemical properties of the monomeric peptides and the structural and functional properties of the resulting assemblies, 10,11 surprisingly little is known about the fundamental physicochemical driving forces that determine the kinetics and thermodynamics of the self-assembly processes of different peptide sequences. It has been recently shown that the differences in self-assembly kinetics and thermodynamics between different sequences can be exploited in a dynamic setting where sequences can be exchanged and modified, to © 2017 American Chemical Society
Received: January 8, 2017 Published: October 10, 2017 16134
DOI: 10.1021/jacs.7b00229 J. Am. Chem. Soc. 2017, 139, 16134−16142
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Journal of the American Chemical Society
Figure 1. Thermodynamics of FF assembly. (a) Supernatant concentrations, following centrifugation of samples equilibrated at 293 K, are plotted as a function of varying initial peptide concentration. The abrupt change in behavior, from linear with slope 1 to independent of initial concentration, at a value of 0.58 g/L demonstrates the absence of association below the critical concentration. (b) Solubility of FF in water as a function of temperature from 4 to 68 °C. (c) van’t Hoff plot derived from the solubility data in (b). (d) Overall thermodynamics of FF crystallization as a function of temperature, derived from the solubility data and the van’t Hoff relation in (c).
crystalline phase from aqueous solution.1,6 Distinct from some of its simple derivatives, such as Boc-FF9 and Fmoc-FF,7,18 FF is not observed to form fibrillar gels, but only crystalline structures with dimensions and aspect ratios that can be adjusted by varying the assembly conditions.3,6,14 Recently, a theoretical framework has been presented that is able to explain the tendency of peptides and other “low molecular weight gelators” to form crystalline or fibrillar structures on the basis of their amphiphilicity.19 Within this framework, a molecule such as FF, which does not form fibrils but only crystals, is characterized by the absence of a well-defined solvophilic face; however, it is not straightforward to link the simplified geometrical representation of this model to the shape and solvophilic properties of FF. We compare the thermodynamic stability of FF assemblies with those determined for longer peptides (≥7 amino acids) that mostly form amyloid fibrils, rather than crystals. Indeed, it has been found that polypeptides as short as tetrapeptides (KFFE, KVVE) are capable of forming amyloid-like fibrils,20 and peptides below 10 residues in length are often capable of forming both crystals and amyloid fibrils.21 On the basis of theoretical arguments, it has been proposed that the longer the
peptide sequence, the less likely it is to be able to form crystals, due to the increasing potential energy imposed by the crystal structure that does not allow the peptide chain to adopt its natural twist.22 It is therefore of particular interest to compare the thermodynamic signatures of crystalline peptide assemblies, such as those investigated in the present work, with those of amyloid fibrils. In a previous study, we have investigated the dependence of the free energy of amyloid fibril formation on the length of the polypeptide.23 The free energy was established by equilibrium depolymerization studies and analyzed via the linear polymerization model of Oosawa,24,25 where the equilibrium constant for the addition to aggregates of all lengths is postulated to reduce to that between fibril ends and monomers. We found that the data followed an empirical power-law relationship governed by contact area between chains.23 FF displays a markedly greater average nonpolar side chain surface area per amino acid than typical biologically relevant polypeptides, and the π-stacking and hydrophobic interactions can be expected to represent a significant portion of the side chain interaction energy.26,27 We find that the aromatic character of the FF peptide can explain the thermodynamic signature of its assembly, and that the 16135
DOI: 10.1021/jacs.7b00229 J. Am. Chem. Soc. 2017, 139, 16134−16142
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with a minimum close to 10 °C. The variation of the solubility with temperature allows the enthalpy change on crystallization to be derived from the van’t Hoff relation
energetics of the transition state of the assembly reaction, that governs its kinetics is dominated by an enthalpically unfavorable barrier that is partly compensated for by a favorable entropy of activation, similar to the situation observed for longer, amyloid-forming sequences.28
R
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d
( T1 )
= −ΔHcryst . Figure 1d shows that the ΔHcryst is
temperature dependent, and therefore confirms the existence of a heat capacity of crystallization, ΔCcryst, which decreases in magnitude with increasing temperature. The minimum of the van’t Hoff plot in Figure 1c represents a point of zero enthalpic change upon crystallization, ΔGcryst being solely determined by the favorable entropy of the crystallization process at this temperature. Despite the large changes in ΔHcryst and ΔScryst across the measured temperature range (Figure 1d), the process of FF crystallization in water is heavily compensated; that is, the free energy is practically invariant. Enthalpy− entropy compensation is a common feature of many reactions, especially those of complex systems in aqueous solution, such as protein unfolding30 and aggregation,28 but a final agreement has not yet been reached whether this type of compensation is an intrinsic physicochemical property of such systems, or whether it is just a manifestation of experimental bias.31 In the case of FF, a favorable enthalpy of assembly will arise from a number of different interactions in the crystal: the aromatic substituents are engaged in an extended π-stacked structure and hydrogen bonding, and salt bridges are present in addition.6 However, these types of interactions have only a moderate temperature dependence. Instead, the temperature dependence most likely stems from the contribution of the hydrophobic effect of the aromatic side chains. Indeed, the temperature profile of the stability of the FF assemblies resembles closely that of the enthalpy of dehydration of nonpolar residues upon protein folding,32 with the driving force at room temperature being mostly entropic, whereas it becomes enthalpic at higher temperatures. The hydrophobic effect reflects the complex interactions of water with itself and with hydrophobic surfaces, and depends on temperature, as well as on the size of the surface area of the hydrophobic moiety.33,34 Despite the fact that the free energy of crystallization of FF displays the typical signature of the hydrophobic effect, electrostatic effects can be expected to play an important role as well. It has, for example, been proposed, on the basis of molecular dynamics simulations, that “electrostatic steering” plays an important role in establishing the structure of the crystal during structural rearrangements of disordered precursor structures.17 To gain insight into this factor, we also measured the critical concentration at room temperature at different pH values (see Supporting Information Figure 2). We find that the critical concentration has a minimum around pH 5−6, which corresponds to the pH of a solution of lyophilized peptide in pure water. The solubility changes only weakly in the pH range where FF can be expected to be mostly a globally neutral zwitterion, but at pH values above or below that range, the solubility increases steeply, suggesting that it is the globally neutral species that incorporates into the crystal. Strong effects of pH on the self-assembly of N-terminal derivatives of FF have been reported before7,35 and can be rationalized on the basis of the relatively weak absolute values of the driving forces for assembly, which are not able to overcome strongly unfavorable electrostatic interactions between peptides carrying a net charge. While, therefore, the peptide molecules have to be globally neutral to incorporate into the crystal, they still carry a positive
RESULTS AND DISCUSSION We first aimed to determine the critical concentration, that is, the equilibrium concentration between monomer and aggregates, below which no aggregation is observed. The critical concentration or solubility, cs, is the concentration at which the chemical potentials of FF in solution and in the (infinitely sized) crystal are equal, the driving force for the
( ), where c is the FF
crystallization being ΔG = −RT log
d(log K cryst)
c cs
concentration. We established the critical concentration of FF in pure water through ultracentrifugation of aggregated samples (represented by the green line in Figure 1a). We then determined the concentration of soluble peptide as a function of total peptide concentration. Figure 1a shows how peak absorption varies with concentration in samples above and below the critical concentration at room temperature. The absence of significant curvature to the plot implies the absence of subcritical aggregation and indicates the criticality behavior of classical nucleation theory,29 with a large critical nucleus. This conclusion is supported experimentally by the ease with which highly supersaturated solutions can be prepared through cooling, which indicates a large barrier against nucleation. Solutions of 4.5 g/L (14.5 mM) can be prepared close to the boiling point of water and can be metastable for extended time periods at room temperature, where the critical concentration is 0.58 g/L. To obtain additional support for the absence of significant quantities of precritical clusters, we performed dynamic light scattering (DLS) experiments (see Supporting Information Figure 1) with sub- and strongly supercritical solutions in water, where we found that in all cases the scattering signal was dominated by small species with a diffusion coefficient corresponding to an equivalent size of ca. 1 nm. As a reference, we also measured a strongly subcritical solution in methanol, which is a much better solvent for FF than water,6 and we obtained a very similar result. Even though DLS does not have a sufficient resolution to decide whether the detected species in this case correspond to FF monomers or to small oligomers, we conclude that the DLS data also support the absence of significant quantities of large prenucleation clusters or micelles. Such species would be expected to be populated to a much more significant extent at supercritical concentrations, as compared to subcritical ones, and the similarity of the DLS data under these different conditions is strongly indicative for the absence of significant subcritical structures. It is worth noting that molecular dynamics simulations of FF, which have been reported to yield the formation of a range of clusters from dimers to octamers17 and large-scale micellar structures,16 have been performed at concentrations 1−2 orders of magnitude higher than the ones we have examined experimentally, and therefore these results are difficult to compare. Critical Concentration of FF Assembly. Next, to obtain further insight into the thermodynamics of aggregation of the FF system, we investigated the dependence of the critical concentration on temperature (Figure 1b and c). Solubilities at the tested temperatures (4−68 °C) range from 0.5 to 1.8 g/L, 16136
DOI: 10.1021/jacs.7b00229 J. Am. Chem. Soc. 2017, 139, 16134−16142
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Figure 2. Peptide assembly thermodynamics and the limit of short sequences. (a) Data from ref 23 with addition of the dipeptides FF, AF, FV, AA, and GF (all from this study), GG,38 and PL.39 (b) Chart displaying the relationship between the nonpolar solvent-accessible surface area (NPSASA) of the polypeptides and the free energy of monomer addition. Shown are linear fits of the free energies as a function of the logarithm of the NPSASA through the entire data set, only through those data points from peptides with NPSASA < 2000 Å2, and only through those data with NPSASA > 2000 Å2. The very different slopes in the latter two groups suggest that the peptides fall into two regimes.
critical concentration of FF can be directly compared to the concentration of soluble polypeptides and proteins in equilibrium with amyloid fibrils.23 This is in particular interesting because the FF peptide is a central motif in the amino acid sequence of the Aβ peptide, and it has been a longstanding question as to how important this motif, and aromatic moieties in general, are for amyloid fibril formation.26,27 For amyloid peptides, thermodynamic measurements are challenging due to the often very low critical concentration, but can be performed more easily, albeit indirectly, through analysis of aggregate depolymerization curves, using a denaturant such as GndHCl combined with data analysis in the framework of linear polymerization theory.23,25 Such experiments have been performed previously for a range of amyloid fibril forming peptides of lengths ranging from 7 to 174 residues, and a power law relationship has been proposed between the free energy of monomer addition to the aggregate, per peptide, and the peptide length (i.e., the number of amino acids): 23 ΔGel = ε0 + ε1N γ . To test whether this relationship holds for N the diphenylalanine system, the relevant values were computed for FF, and the entire data set was evaluated with this additional
and a negative charge, which, as suggested by the crystal structure,6 are involved in salt bridges. To test whether these charges influence the assembly behavior of FF, we performed crystallization experiments at varying concentrations of NaCl, ranging from 1 mM to 2 M (see Supporting Information Figure 3). We find that the critical concentration is constant over a large range of NaCl concentrations and decreases only at concentrations of 1 M and above. This result suggests that the effect of the NaCl is related to the well-established “salting-out” of hydrophobic molecules, such as benzene36, or of proteins,37 and that favorable electrostatic interactions, such as those observed in the case of KFFE,20 either play no significant role, or are of too short range and buried inside the crystal to be screened by ions. The observed “salting out” supports the conclusion that the hydrophobic and aromatic character of FF plays an important role in its solubility. Interestingly, crystal morphology is also affected at high NaCl concentrations, suggesting a higher nucleation rateunder these conditions (see the Supporting Information for a detailed discussion). Comparison of FF Assembly Thermodynamics with those of Longer Chain Amyloidogenic Species. The 16137
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Figure 3. Barriers of FF self-assembly in relationship to those of amyloid fibril growth. (a) Relationship between axial growth rate of FF crystals and temperature for the five temperatures tested. (b) Arrhenius plot of FF crystal growth; the growth rate data from panel (a) have been corrected for the supersaturation dependence of the rate. (c) Log−log graph comparing the aggregate growth rates of two amyloid systems (insulin47 and Aβ(1− 40)57) with those of FF.14 . The solid lines represent the diffusional fluxes of monomers into a reaction volume on the end of the aggregate and correspond to the theoretical maximum rates. Inset: Comparison of the measured incorporation rates as a function of solution supersaturation with the diffusional flux into a reaction volume of the size of an FF molecule. The reaction order of the growth rate with respect to the supersaturation σ is determined from the fit to be 1.9. (d) Comparison of free energy barriers and their entropic and enthalpic contributions at room temperature between FF (computed with two different kinetic prefactors; see the Supporting Information) and Aβ(1−42).28 Note that FF is compared to Aβ(1− 40) in c) and to Aβ(1−42) in (d), due to the fact that concentration-dependence data have been measured for Aβ(1−40)57 and a complete barrier analysis has been performed for Aβ(1−42).28
data point in Figure 2a (N = 2, ΔGel/N = 7.35 kJ/mol at 298 K). We find that FF displays a greater free energy of aggregation and hence a lower free concentration than the extrapolation of the curve to N = 2 would predict. Inspection of the shortest previously investigated peptide23 (GNNQQNY at N = 7) suggests reasons for the deviation arising from the amino acid composition of the fragments. GNNQQNY is unusually hydrophilic and deviates in the opposite direction from the
overall scaling law, as compared to the hydrophobic FF peptide. As the sequences become longer, such deviations due to predominance of hydrophobic or hydrophilic peptides “average out”. The solubilities of glycylglycine (GG)38 and glycylphenylalanine (GF) were also determined, and together with that of FF were compared to the predictions above. We found that GG had a small positive ΔG/N of 0.51 kJ/mol/peptide, while GF displays ΔG/N of −2.50 kJ/mol/peptide for the equilibrium between monomer and crystals of fine needle-like 16138
DOI: 10.1021/jacs.7b00229 J. Am. Chem. Soc. 2017, 139, 16134−16142
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recorded, as it is challenging to observe the growth of individual protein aggregates in real time, given their often nanoscale dimensions. However, due to advances in experimental methods in recent years, this has been achieved in a range of studies, using techniques such as atomic force microscopy48−50 and total internal reflection fluorescence (TIRF) microscopy.51,52 The degrees of supersaturation relative to the fibrillar state are very high in typical experiments with amyloid fibrils of longer sequences as compared to the supersaturation in the FF system. For example, in the case of insulin, a protein concentration of 1 mg/mL (174 μM) corresponds to a supersaturation of the order of 103−104, due to the very low critical concentration of this system in the submicromolar range.23 It is therefore common to neglect the critical concentration in such systems and to quantify the driving force for aggregate growth directly through the absolute monomer concentration rather than the degree of supersaturation, which amounts to neglecting the fibril dissociation rate. It has been found for amyloid fibrils in bulk experiments that their growth rate is a linear function of the monomer concentration, transitioning to a sublinear relationship at higher concentrations;53 this is thought to be due to saturation of available growth sites due to the finite time required for monomer incorporation at a fibril end to produce a new growth site.53 A detailed analysis of the temperature dependence of the rates of growth of various types of amyloid fibrils has revealed that the overall free energy barriers have in all cases a significant unfavorable enthalpic contribution; that is, amyloid fibril growth is a thermally activated process.28 To be able to compare the nature of the energy barriers for the self-assembly of longer peptides with that of FF, we measured the absolute growth rates of FF crystals at different temperatures in microfluidic flow reactors (see Experimental Section and ref 14), at a constant concentration of soluble FF of 1.2 g/L. The results of these measurements are shown in Figure 3a. Interestingly, the net growth rate decreases with increasing temperature. However, this result does not imply that the growth of FF crystals is not a thermally activated process. In fact, we have shown previously that the growth rate, Rg, of FF crystals depends in a higher than linear manner on the concentration of soluble FF,14 distinct from amyloid fibrils. In particular, we have found that the growth rate data can be fitted to an expression of the form Rg = knσnc, where kn is the growth rate constant, σ is the supersaturation, and nc is the reaction order with respect to soluble FF, and we have determined nc to be 1.9 at 22 °C (Figure 3c and ref 14). This finding is consistent with a crystal growth mechanism that is either limited by the formation and subsequent spreading of twodimensional nuclei on the growth face or by the incorporation of FF molecules into the kink sites along edges, for example, of screw dislocations.14,54 We therefore need to normalize the growth rate at each temperature by the actual supersaturation at which the crystals were allowed to grow, raised to the power of nc, as kn = Rg(T)/σnc (nc = 1.9; see the Supporting Information for a discussion of the temperature dependence of the scaling exponent). When we carried out this normalization and plotted the natural logarithm of kn against inverse absolute temperature, we obtained a conventional Arrhenius plot that indicates a positive temperature dependence of the crystal growth rate constant, and hence suggests that FF crystal growth is a thermally activated process (Figure 3b). The slope of the Arrhenius plot corresponds to the Arrhenius activation energy,
habit. In this case, the free energy of aggregation shows a nonlinear dependence on nonpolar surface area; the F2G substitution results in nearly twice the energy change of the first substitution. In Figure 2b, we have plotted the free energy of monomer addition (onto crystals or amyloid fibrils) as a function of the logarithm of the nonpolar solvent accessible surface area (NPSASA), and we have fitted the entire data set with a linear function (red dashed line). We find that while a linear function represents a good fit of the data for the short peptides, the free energy of association appears to become nearly independent of the NPSASA within the group of longer sequences (NPSASA > 2000 Å); this was confirmed by performing two independent fits of the parts of the data set above and below a NPSASA of 2000 Å2. This is likely to be due to the fact that the simple calculation used here for nonpolar solvent accessible surface area (based on accessible side chain area for each amino acid in a GXG tripeptide40) will be a less accurate approximation in longer chains, many of which display defined tertiary structure in the soluble states, which will 'bury' hydrophobic residues in solvent-inaccessible areas, therefore leading to a considerably smaller overall change in SASA upon self-assembly. Furthermore, in the amyloid forms of the longer chain proteins, there exists a close-packed 'core' region,41 where the packing model will be valid, and less structured regions outside the β-sheet core that are not close-packed.42 The inability of a long chain to adopt conformations in which all contacts are optimal has been discussed in ref 23, with the prediction of a different scaling 1 exponent (γ = − 2 ) arising from the application of the central limit theorem. Additional structural complexity of the close packed regions in amyloid fibrils, such as the stacking of several protofilaments into mature fibrils,43 will increase the number of close contacts per residue and stabilize the fibril. The lack of detailed structural information for most amyloid systems, however, precludes a more detailed and quantitative correlation of aggregate stability data with ΔNPSASA. It is interesting to compare the thermodynamic data from this study with those obtained from chromatographic techniques, which have been specifically designed for the estimation of interactions between side chains of amino acids. A study in which the stationary phase was designed to mimic the side chain of phenylalanine and a phenylalanine derivative was eluted is particularly relevant to the present work.44 It was found that the free energy of this interaction was at least −5.0 kJ/mol, a significant proportion of the ΔGcryst observed here for FF (−15.3 kJ/mol). Nature and Height of the Kinetic Barrier of FF SelfAssembly. The aggregation behavior of peptides in vitro and in vivo is mostly determined by kinetics rather than thermodynamics. The latter dictates that the aggregated state represents the free energy minimum at all but very low concentrations,23 but still many polypeptides are not observed to aggregate at detectable rates under physiological conditions, despite being expressed at concentrations above their critical concentration for aggregation.23 It is therefore important to understand the magnitudes, nature, and origin of the barriers that separate the soluble from the aggregated state of a peptide. In particular, the energy barriers of aggregate growth have been studied in detail with a range of techniques, such as light scattering,45 Thioflavin-T fluorescence,46 and surface-based biosensing.28,47 In most experiments so far, the average kinetic growth behavior of ensembles of protein aggregates has been 16139
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Journal of the American Chemical Society EA, that we identify here with the enthalpy of activation, ΔH⧧. We determine a value of EA = 55 kJ/mol. Interestingly, this value is very close to that of the full length Aβ(1−42) peptide that was determined by QCM (66.1 kJ/mol,28), suggesting that a similar net number of bonds needs to be broken to reach the transition state. This similarity could indicate that the FF moiety of the Aβ peptide ('Aβ (19−20)') plays a crucial role in the establishment of the initial contacts that define the transition state ensemble, which involve significant desolvation of the aromatic moieties. To proceed further with the analysis of the energy barriers of FF crystal growth, and in particular to compare the behavior of FF with that of amyloid fibrils of longer sequences, it is instructive to compare the rate of diffusional arrival of peptide molecules into a reaction volume of size comparable to the molecule itself, corresponding to the end of an amyloid fibril or to a lattice site on the crystal face, respectively. Such a comparison between the observed growth rate and the diffusional arrival rate is shown in Figure 3c for FF and two amyloid systems as a function of the absolute peptide concentration, as well as, for FF only, as a function of supersaturation σ (see inset). The diffusional flux into a reaction volume v is given by Drc, where D is the translational diffusion coefficient, r = v1/3 is the characteristic dimension of the reaction volume v, and c is the molar concentration.45 For the computation of the diffusional fluxes, we used DIns = 1.1 × 10−10 m2/s,55 vIns = 10−27 m3,47 DAβ = 1.1 × 10−10 m2/s (based on the very similar molecular weight of Aβ and insulin), vAβ = 10−27 m3,45 DFF = 4.2 × 10−10 m2/s,56 and vFF = 2 × 10−28 m3, where the latter volume is a rough estimate based on the molecular weight of FF, which is approximately an order of magnitude smaller than that of insulin. This comparison shows that the ratio of diffusional to reactive flux is comparable in FF and amyloid fibrils, while the main difference between the systems is the strong concentration dependence of this factor in the case of FF. In the case of amyloid fibrils, the difference between diffusive and reactive fluxes can be directly translated into a free energy barrier, either neglecting internal degrees of freedom of the peptide45,47 or taking them into account53 (see the Supporting Information). However, because of the very different assembly mechanism of FF crystals, a detailed analysis of the growth kinetics within the framework of classical crystal growth theory is more appropriate to determine the free energy and hence also the entropic barrier. We have performed such an analysis (see the Supporting Information for details), and the results are presented in Figure 3 d, where, for comparison, we include an analysis of FF in both the diffusive53 and the crystal growth framework (see the Supporting Information). The comparison between amyloid fibrils and FF shows that, independently of the theoretical framework used for the analysis, the thermodynamic signatures of their free energy barriers are qualitatively similar, with a significant enthalpic barrier that is partly compensated by a favorable entropy of activation to yield a free energy barrier smaller in magnitude than the enthalpy of activation. The exact magnitude of the free energy and hence also of the entropic barriers depends on the choice of prefactor, as is discussed in detail in the Supporting Information. Similar to what has been found for a range of amyloid fibrils,28 the entropy of activation is favorable for the FF assembly reaction. To obtain insight into the magnitude of the unfavorable contribution from the association of a soluble FF molecule with the crystal face, we have estimated the entropy loss of the FF molecule due to the restriction of its
translation and internal motion in the transition state (lower bound −21 kJ/mol at 300 K; see the Supporting Information). Together with the fact that the overall entropy of activation is positive (lower bound 14 kJ/mol at 300 K), regardless of what model is used to define it, this estimate gives an idea about the magnitude of the favorable contribution to the entropy of activation, a lower bound of which is 35 kJ/mol. The latter might stem from desolvation of the hydrophobic FF molecule upon reaching the transition state, similar to the case of amyloid fibril growth.28 This conclusion is consistent with hydrophobicity also being the major driving force for the crystallization process itself (see above) and leads to the picture that the most appropriate reaction coordinate for the incorporation of an FF molecule into a crystal involves significant contributions of solvent degrees of freedom. However, due to the ambiguity as to what model of crystallization is most appropriate for the analysis of FF kinetic data, as well as the multistep nature of the crystallization process, leading to the free energy of activation being composed of multiple individual contributions, care needs to be taken in interpreting the values of the individual contributions to the free energy barrier.
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CONCLUSIONS In this study, we have performed a detailed characterization of the thermodynamic stability and the kinetic barriers of the selfassembly of diphenylalanine. This aromatic dipeptide is the central motif in the amino acid sequence of the Aβ peptides, the aggregation of which is associated with Alzheimer’s disease. We find that the thermodynamics of the self-assembly of the FF peptide displays the typical signature expected for the burial of hydrophobic residues: the driving force for assembly is entropic in nature at low temperatures and becomes enthalpic at higher temperatures. Furthermore, even though the free energy of assembly is more favorable than expected from a general scaling law relationship derived for longer sequences, the deviation can be explained through the strong sequence bias of this aromatic dipeptide. We have also analyzed and decomposed the free energy barrier for self-assembly and have found that, if the appropriate kinetic models are used for amyloid fibril growth and FF crystal growth, respectively, the thermodynamic signatures of the free energy barriers are qualitatively similar, with an unfavorable enthalpy of activation, partly compensated by a favorable entropy of activation, due to the desolvation of hydrophobic molecular surface area.
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EXPERIMENTAL SECTION
Reagents and Solutions. Solutions of FF were prepared by the suspension of diphenylalanine (Bachem, Basel, Switzerland) in distilled water (18.2 Ω/m) followed by ultrasonication in a sonic bath until the suspension was homogeneous and heating to 80−100 °C. Following 30 min at ∼100 °C, no visible aggregates were observable for concentrations up to and including 4.5 g/L (14.5 mM). Seed solutions for growth experiments were prepared by the sonication (via ultrasonic bath) at room temperature of 2 g/L water solutions that had been allowed to aggregate and left standing for at least 1 day. FF was used as received without further purification, while the sample of GF as obtained required further purification. A solution of crude GF was prepared from 692 mg GF (PeptaNova, Sandhausen, Germany) and 13 mL of distilled water at 100 °C. On cooling, GF precipitated as fine, needle-like crystals with a habit similar to FF (yield 312 mg). These crystals were removed from the mother liquor by 16140
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Journal of the American Chemical Society vacuum filtration and washed on the filter with 2 mL of cold distilled water. Concentration Measurements. The dipeptide concentrations were determined by UV spectrophotometry using a Cary 400 spectrophotometer, instrument version 8.01. Spectra were recorded between 300 and 230 nanometres with a reading every 0.4 nm. Spectral bandwidth was 2 nm. The spectrophotometer was fitted with a variable temperature stage (Peltier thermocouple system). Glass cuvettes of path length 2 mm or 4 mm were used depending on the volume of solution available for the test. Concentration was taken to be proportional to the absorption value at 258 nm, using a molar absorption coefficient of 390 M−1 cm−1, calculated from the molar absorption coefficient of phenylalanine. The change in peak absorbance with temperature was found by heating a solution of 0.5 g/L concentration from 4 to 70 °C, and this was used to correct readings at each temperature. From repeated preparations of FF solutions from as-received lysophilized peptide of different batches, we found that FF concentrations (as determined from the absorption at 258 nm) were reproducibly ca. 25% lower than predicted from weighing the peptide.6 The majority, but not all, of this difference can be attributed to the water content of the received peptide, as determined by thermogravimetric analysis (data not shown). Therefore, unlike previous studies,6 in the present study we relied entirely on the UV absorption measurements. To investigate potential subcritical association in water and hence the validity of the crystallization model (which assumes no long-lived association below the critical concentration, and nucleation-dependent association thereafter), solutions at concentrations 0.10−1.00 g/L were prepared by dilution of 1.00 g/L stock. These were allowed to stand for 1 h, and then ultracentrifuged for 1 h at 62 000g. The absorption above zero (set at 300 nm) at 258 nm was plotted against concentration. To ascertain critical concentrations (solubility) as a function of temperature, quantities of FF at a range of concentrations were prepared and allowed to equilibrate slowly in quiescent conditions to room temperature and then held at 4 °C overnight in the presence of a number of macroscopic crystals. The temperature controlled stage of the spectrophotometer was set to the starting temperature (either 4 or 8 °C) and the program “Wavelength Scans at Temperature Increments”, from the Agilent Web site, was used to record a series of spectra between 230 and 300 nm following stirring for 80 min at a number of temperatures between 8 and 68 °C. The uncertainty in the FF concentrations, Δcs, was determined from repeated measurements. From the uncertainties in the concentration measurements at different temperatures, we determined the uncertainty in the enthalpy of crystallization, ΔΔH, by using the van’t Hoff equation, according to ΔΔH =
RT 2 ∂cs Δcs . cs2 ∂T
were made every 5 s using time lapse photography, using a Zeiss Axio Observer A1 microscope (Carl Zeiss, Jena, Germany) and a CoolSNAP-MYO camera (Photometrics, Tucson, AZ). The axial growth rates were computed as the mean ± standard deviation of the five fastest growing structures.14 We measured the axial growth rates at a FF concentration of 1.2 g/L at different temperatures (22, 28, 38, 44, and 48 °C), and used the data on the temperature dependence of the critical concentration to correct for the fact that the driving force for aggregate growth decreases at higher temperatures (see the Supporting Information for details of the analysis). Dynamic Light Scattering. DLS experiments were performed with a Zetasizer ZSP Instrument (Malvern, UK), using a scattering angle of 173° (forward scattering). Concentrated stock solutions were prepared at elevated temperatures, and then the solutions were passed through a 220 nm pore size syringe filter and measured in disposable small volume sizing cuvettes at different temperatures and dilution factors. The data were plotted as size distributions weighted by scattering intensity.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.7b00229. Dynamic light scattering of subcritical and supercritical solutions of FF, pH-dependence of FF assembly, NaCl concentration-dependence of FF assembly, calculation of the free energy barrier of FF crystal growth, nucleation and spread model, integration rate control, comparison with the free energy barriers for amyloid fibril growth, estimate of the loss of entropy of FF upon formation of the transition state, entropy associated with internal degrees of freedom, translational entropy, entropy associated with overall rotation of the molecule, total entropy loss, temperature-dependence of FF crystal morphology, and references (PDF)
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AUTHOR INFORMATION
Corresponding Authors
*
[email protected] *
[email protected] ORCID
Tuomas P. J. Knowles: 0000-0002-7879-0140 Alexander K. Buell: 0000-0003-1161-3622
The error in the entropy of crystallization was
Notes
The authors declare no competing financial interest.
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taken to be the sum of the errors of the free energy and enthalpy. Microfluidics. The microfluidic measurements of the growth kinetics of the FF crystals were carried out as described previously,14 except that here the measurements were performed at different temperatures. The flow reactors were microfluidic devices constructed from polydimethylsiloxane (PDMS):58,59 a 25 μm thick layer of SU-8 3025 photoresist was spin-coated onto a silicon wafer, exposed to UVlight through a mask in which the device design was printed, then manufactured in 1-methoxy-2-propyl acetate (PGMEA). The microfluidic device was fabricated from Sylgard 184 PDMS elastomer (DowCorning, Midland, MI), using 1 h curing at 65 °C. After cutting the device, punching the holes for inlets and outlets, and activation via plasma treatment with a Femto plasma bonder (Diener Electronic, Ebhausen, Germany), the microfluidic device was bonded to a 3 × 1 in. microscope slide. A suspension of seed crystals was passed through the device, and once sufficient crystals had settled in the central chamber, a flow of FF solution was initiated at a rate of 800 μL/h, corresponding to velocities on the order of millimeters per second in the channel center, by means of a NemeSys syringe pump (Cetoni, Korbussen, Germany). Temperature was controlled using a microscope heating stage. Measurements of lengths of growing microcrystals
ACKNOWLEDGMENTS We thank the Newman Foundation (T.O.M., T.P.J.K.), the Biotechnology and Biological Sciences Research Council (T.P.J.K.), the Cambridge Centre for Misfolding Diseases (CMD, TPJK), the Israeli National Nanotechnology Initiative (E.G.), the Helmsley Charitable Trust (E.G.), the Leverhulme Trust (A.K.B.), Magdalene College, Cambridge (A.K.B.), the Alzheimer Forschung Initiative (A.K.B.), the Deutsche Forschungsgemeinschaft (AKB), the Federation of European Biochemical Societies (A.L.), the Swiss National Science Foundation (T.C.T.M.) and Peterhouse College, Cambridge (T.C.T.M.), for financial support.
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