Thermodynamics of Polypeptide Supramolecular Assembly in the

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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 J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.7b00229 • Publication Date (Web): 10 Oct 2017 Downloaded from http://pubs.acs.org on October 17, 2017

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Journal of the American Chemical Society

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, Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA, Department for Molecular Microbiology and Biotechnology, University of Tel Aviv, Tel Aviv, and Institute of Physical Biology, University of D¨ usseldorf, D¨ usseldorf E-mail: [email protected]; [email protected]

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. This dipeptide forms the central motif of the Aβ polypeptides 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 diphenylalanine in aqueous solution, and we evaluate these findings in the context of the aggregation free energies of longer ∗

To whom correspondence should be addressed University of Cambridge ‡ Harvard University ¶ University of Tel Aviv § University of D¨ usseldorf †

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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 crystallisation theories reveals that the transition state from solution to crystalline aggregates is enthalpically unfavourable and entropically favourable, 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 behaviour.

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 peptide and the structural and functional properties of the resulting assemblies, 10,11 surprisingly little is known about the fundamental physico-chemical 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, in order to select for sequences with a higher tendency to self-assemble. 12 A more quantitative understanding of the forces at work in such systems would be desirable, as it can help optimise computational screening approaches that 2 ACS Paragon Plus Environment

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have been used to identify those parts of sequence space that are able to assemble 13 as well as facilitate the optimisation 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 at atomic detail with currently available computational resources. Such combined experimental and computational studies can act as important benchmarks on the way towards the description of more complex, biologically relevant assembling peptide systems. Here, we establish the thermodynamic parameters of the self-assembly of diphenylalanine, the paradigmatic system of short peptide assembly, that is able to form a well-defined crystalline phase from aqueous solution. 1,6 Distinctly from some of its simple derivatives, such as Boc-FF 9 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 condiditions. 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 based on their amphiphilicity. 19 Within this framework, a molecule such as FF, that does not form fibrils but only crystals is characterised 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 was 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 Based on 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



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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 the ones 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 depolymerisation studies and analysed via the linear polymerisation 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 Diphenylalanine displays 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 the energetics of the transition state of the assembly reaction that governs its kinetics is dominated by an enthalpically unfavourable barrier that is partly compensated by a favourable entropy of activation, similar to what has been observed for longer, amyloid-forming sequences. 28

Results and discussion We first aimed to determine the critical concentration, i.e. 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 crystallisation being ∆G = −RT log ccs , where c is the FF concentration. We established the critical concentration of FF in pure water through ultracentrifugation of aggregated samples (represented by the green line in Figure 1 a). We then determined the concentration of soluble peptide as a function of total peptide concentration. Figure 1 a


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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 behaviour 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. In order to obtain additional support for the absence of significant quantities of pre-critical clusters, we performed dynamic light scattering (DLS) experiments (see supplementary results Figure 1) of suband 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 sub-critical 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 supports the absence of significant quantities of large pre-nucleation clusters or micelles. Such species would be expected to be populated to a much more significant extent at supercritical concentrations, 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 that have been reported to yield the formation of a range of clusters from dimers to octamers 17 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.



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Figure 1: The 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 behaviour, from linear with slope 1 to independent, at a concentration 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 crystallisation as a function of temperature, derived from the solubility data and the van’t Hoff relation in c).


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The critical concentration of FF assembly Next, in order to obtain further insight into the thermodynamics of aggregation of the FF system, we investigated the dependence of the critical concentration on temperature (Figure 1 b and c). Solubilities at the tested temperatures (4 to 68◦ C) range from 0.5 to 1.8 g/L, with a minimum close to 10◦ C. The variation of the solubility with temperature allows the enthalpy change on crystallisation to be derived from the van’t Hoff relation R d(logd K1cryst ) = −∆Hcryst . Figure 1 d shows that the ∆Hcryst is temperature dependent, and (T ) therefore confirms the existence of a heat capacity of crystallisation, ∆Ccryst , which decreases in magnitude with increasing temperature. The minimum of the van’t Hoff plot in Figure 1 c represents a point of zero enthalpic change upon crystallisation, ∆Gcryst being solely determined by the favourable entropy of the crystallisation process at this temperature. Despite the large changes in ∆Hcryst and ∆Scryst across the measured temperature range (Figure 1 d), the process of FF crystallisation in water is heavily compensated, i.e. 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 unfolding 30 and aggregation, 28 but a final agreement has not yet been reached whether this type of compensation is an intrinsic physico-chemical property of such systems, or whether it is just a manifestation of experimental bias. 31 In the case of diphenylalanine, a favourable enthalpy of assembly will arise from a number of different interactions in the crystal- the aromatic substituents are engaged in an extended πstacked 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 non-polar 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 7 ACS Paragon Plus Environment


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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 crystallisation 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, based on 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 In order to gain insight into this factor, we also measured the critical concentration at room temperature at different pH values (see supplementary results Figure 2). We find that the critical concentration has a minimum around pH 5-6, which corresponds to the pH of a solution of lyophilised 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 before 7,35 and can be rationalised based on the relatively weak absolute values of the driving forces for assembly, that are not able to overcome strongly unfavourable electrostatic interactions between peptides carrying a net charge. While, therefore, the peptide molecules have to be globally neutral in order to incorporate into the crystal, they still carry a positive and a negative charge, which, as suggested by the crystal structure, 6 are involved in salt bridges. In order to test whether these charges influence the assembly behaviour of FF, we performed crystallisation experiments at varying concentrations of NaCl, ranging from 1 mM to 2 M (see supplementary results 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 benzene 36 or of proteins, 37 and that favourable electrostatic interactions, such as the ones observed in the case of KFFE 20 either play no significant role, or are too close range and


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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 for its solubility. Interestingly, crystal morphology is also affected at high NaCl concentrations, suggesting a higher nucleation rate at high NaCl concentrations (see supplementary materials for a detailed discussion).

Comparison of FF assembly thermodynamics with longer chain amyloidogenic species The critical concentration of diphenylalanine can be directly compared with 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 long-standing question 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 depolymerisation curves, using a denaturant such as GndHCl combined with data analysis in the framework of linear polymerisation theory. 23,25 Such experiments have been performed 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 ∆Gel N

= 0 + 1 N γ . In order to test whether this relationship holds for the diphenylalanine

system, the relevant values were computed for FF and the entire dataset evaluated with this additional data point in Figure 2 a (N = 2, ∆Gel /N = 7.35 kJ/mol at 298 K). We find that diphenylalanine 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 peptide 23 (GNNQQNY at N = 7) suggest reasons for the deviation arising from the amino acid composition of the fragments. GNNQQNY 9 ACS Paragon Plus Environment


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−50 102

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Figure 2: Peptide assembly thermodynamics and the limit of short sequences. a) Data from 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 non-polar solvent-accessible surface area (NPSASA) of the studied 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 ˚ A2 and only through those data with NPSASA > 2000˚ A2 . The very different slopes in the latter two groups suggest that the peptides fall into two regimes.


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is unusually hydrophilic and deviates in the opposite direction from the overall scaling law, 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 diphenylalanine were compared to the predictions above. We found that glycylglycine had a small positive ∆G/N of 0.51 kJ/mol/peptide, while GF displays ∆G/N of -2.50 kJ/mol/peptide for the equilibrium between monomer and crystals of fine needle-like habit. In this case the free energy of aggregation shows a nonlinear dependence on non-polar surface area - the F2G substitution results in nearly twice the energy change of the first substitution. In Figure 2 b, we have plotted the free energy of monomer addition (onto crystals or amyloid fibrils) as a function of the logarithm of the non-polar 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 of the short peptides, the free energy of association appears to become nearly independent of the NPSASA within the group of longer sequences (NPSASA > 2000 ˚ A); this is confirmed by performing two independent fits of the parts of the data set above and below a NPSASA of 2000˚ A2 . This is likely to be due to the fact that the simple calculation used here for non-polar solvent accessible surface area (based on accessible side chain area for each amino acid in a Gly-X-Gly tripeptide 40 ) 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 was discussed in, 23 with the prediction of a different scaling exponent (γ = − 12 ) arising from the application of the cen-



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tral 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 stabilise 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 ∆NPSASA. It is interesting to compare the thermodynamic data from this study with that obtained from chromatographic techniques, that have been specifically designed for the estimation of interactions between R-groups of amino acids. A study in which the stationary phase was designed to mimic the R-group 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 ∆Gcryst observed here for diphenylalanine (-15.3 kJ/mol).

The nature and height of the kinetic barrier of FF self-assembly The aggregation behaviour 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 never observed to aggregate 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 behaviour of ensembles of protein aggregates has been recorded, as it is challenging to observe the growth of individual protein aggregates in real time, given their often nano-scale 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 microscopy 48–50 12 ACS Paragon Plus Environment

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and total internal reflection fluorescence (TIRF) microscopy. 51,52 The supersaturations relative to the fibrillar state are very high in typical experiments with amyloid fibrils of longer sequences compared to the supersaturations 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 sub-micromolar 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 supersaturation, which amounts to neglecting the fibril dissociation rate. It was 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 unfavourable enthalpic contribution, i.e. amyloid fibril growth is a thermally activated process. 28 In order 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 Methods section and 14 ), at a constant concentration of soluble FF of 1.2 g/L. The results of these measurements are shown in Figure 3 a. 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 distinctly from amyloid fibrils. In particular, we have found that the growth rate data can be fitted to an expression of the form Rg = kn σ nc , 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 3 c and



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14

). This finding is in agreement with a crystal growth mechanism that is either limited

by the formation and subsequent spreading of two-dimensional 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 normalise 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)/σ nc (nc = 1.9; see supplementary materials for a discussion of the temperature dependence of the scaling exponent). If we carry out this normalisation and if we plot the natural logarithm of kn against inverse absolute temperature, we obtain 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 3 b). The slope of the Arrhenius-plot corresponds to the Arrhenius activation energy, EA that we identify here with the enthalpy of activation, ∆H‡ . We determine a value of EA = 55 kJ/mol. Interestingly, this value is very close to that of the full length amyloid β (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 in order to reach the transition state. This similarity could indicate that the FF moiety of the amyloid β-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. In order to proceed further with the analysis of the energy barriers of FF crystal growth, and in particular in order to compare the behaviour 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 3 c for FF and two amyloid systems as a function of 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 = v 1/3 is


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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 one order of magnitude smaller than that of insulin. This comparison shows that the ratio of diffusional to reactive flux is comparable between 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 peptide 45,47 or taking them into account 53 (see supplementary materials). However, due to 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 in order to determine the free energy and hence also the entropic barrier. We have performed such an analysis (see supplementary materials for details) and the results are presented in Figure 3 d, where for comparison, we include an analysis of FF in both the diffusive 53 and the crystal growth framework (see supplementary materials). 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 favourable 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 entropic barriers depends on the choice of pre-factor, as is discussed in detail in the supplementary materials. Similarly to what has been found for a range of amyloid fibrils 28 the entropy of activation is favourable for the FF assembly reaction. In order to obtain insight into the magnitude of the unfavourable contribution from the association of a soluble FF molecule with the crystal face, we have estimated the entropy loss of the FF



2,200

1.2

2,000

1.1

a)

9.5

1,400 0.7 1,200 0.6 1,000

9

ln(k+)

0.8

Growth rate R g (μm/s)

0.9

1,600 Addition rate (s -1)

b)

1

1,800

0.5

8.5

8

800 0.4 ln(φ/σ1.9) Best fit, ln(k+)= -7120 K+31.4, R2=0.971

Addition rate of FF molecules per lattice site

600

Best fit line (linear)

0.3

7.5

400 290

c)

295

300

305 310 Temperature (K)

315

320

3.10·10−3

325

107

usion

FF diff

3.15·10−3

3.20·10−3 3.25·10−3 3.30·10−3 Inverse temperature (K -1)

d)

limit

106

80

60

105

w) r la

10

3

10

Aβ (1-40)

sion li diffu

102

Insulin

mit

on lim

diffusi

it

107

3x104

103

106 105

101

104

100

inear)

10−1

n

itio

dd

a FF

we po e( rat

Energy (kJ/mol)

4

Rates (/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Aβ (1-40)

= Slope

103

(l n rate additio

n Insuli

add

ear) te (lin ition ra

1.9

102 101

Exponential fit- 1750σ1.9 0.4

0.6

0.8

1

Enthalpy, ΔH‡ Entropy, T ΔS‡ Free energy, ΔG‡

80

60

40

40

20

20

0

0

−20

−20

−40

−40

−60

−60

−80 0.1

3.40·10−3

1

10−2 0.01

3.35·10−3

10

Mass concentration (mg/ml)

(Aβ1-42) FF diffusive diffusive crystal pre-factor pre-factor pre-factor

FF

−80

Figure 3: The barriers of FF self-assembly in relationship to those of amyloid fibril growth. a) Relationship between growth rate and temperature for FF for the five temperatures tested. b) Arrhenius plot of FF crystal growth; the growth rate data from panel a) has been corrected for the supersaturation dependence of the rate. c) Log-log graph comparing the aggregate growth rates of two amyloid systems (insulin 47 and Aβ(1-40) 57 ) with those of FF. 14 All concentrations are given in [mg/ml]. 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 rate 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 between FF (computed with two different kinetic pre-factors, see supplementary material) and Aβ(1-42). 28 Note that FF is compared with Aβ(1-40) in c) and with Aβ(1-42) in d), due to the fact that concentration-dependence data has been measured for Aβ(1-40) 57 and a complete barrier analysis has been performed for Aβ(1-42). 28


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molecule due to the restriction of its translation and internal motion in the transition state (lower bound -21 kJ/mol at 300 K, see supplementary material). 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 favourable 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 crystallisation 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 crystallisation is most appropriate for the analysis of FF kinetic data, as well as the multi-step nature of the crystallisation 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.

Conclusions In this study we have performed a detailed characterisation of the thermodynamic stability and the kinetic barriers of the self-assembly 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 favourable 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



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dipeptide. We have also analysed and decomposed the free energy barrier and have found that, if the appropriate kinetic models are used for amyloid fibril growth and FF crystal growth, respectively, that the thermodynamic signatures of the free energy barriers are qualitatively similar, with an unfavourable enthalpy of activation, partly compensated by a favourable entropy of activation, due to the desolvation of hydrophobic molecular surface area.

Experimental 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 minutes 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 one 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 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 vacuum filtration and washed on the filter with 2 ml 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 18 ACS Paragon Plus Environment

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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 lysophilised 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, differently from previous studies, 6 in the present study we relied entirely on the UV absorption measurements. To investigate potential sub-critical association in water and hence the validity of the crystallisation model (which assumes no long-lived association below the critical concentration, and nucleation-dependent association thereafter), solutions at concentrations 0.10 to 1.00 g/L were prepared by dilution of 1.00 g/L stock. These were allowed to stand for one hour, and then ultracentrifuged for one hour at 62,000 g. The absorption above a zero (300 nm) at 258 nm was plotted against concentration. To ascertain critical concentrations (solubility) as a function of temperature, quantities of diphenylalanine 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 website was used to record a series of



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spectra between 230 and 300 nm following stirring for 80 minutes at a number of temperatures between 8 and 68◦ C. The uncertainty in the FF concentrations, ∆cs , was determined from repeated measurements. From the uncertainties in the concentration measurements at different temperatures, we determined the uncertainty in the enthalpy of crystallisation, ∆∆H, by using the van’t Hoff equation, according to ∆∆H =

RT 2 ∂cs ∆cs . c2s ∂T

The error in

the entropy of crystallisation was 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 performed 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 25µm thick layer of SU-8 3025 photoresist was spin-coated onto a silicon wafer, exposed to UV-light 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, USA), 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 3x1 inch 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/hr, corresponding to velocities on the order of millimetres per second in the channel centre, by means of a NemeSys syringe pump (Cetoni, Korbussen, Germany). Temperature was controlled using a microscope heating stage. Measurements of lengths of growing microcrystals 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, USA). The axial growth rates were computed as the mean ± standard deviation of the five fastest 20 ACS Paragon Plus Environment

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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, 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 supplementary materials for details of the analysis).

Dynamic light scattering DLS experiments where 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 filtered through a 220 nm pore size syringe filter and measured in disposable small volume sizing cuvettes at different temperatures and dilution factors. The data was plotted as scattering intensity weighted size distribution.

Acknowledgement We thank the Newman Foundation (TOM, TPJK), the Biotechnology and Biological Sciences Research Council (TPJK), the Israeli National Nanotechnology Initiative (EG), the Helmsley Charitable Trust (EG), the Leverhulme Trust (AKB), Magdalene College, Cambridge (AKB), the Alzheimer Forschung Initiative (AKB), the Federation of European Biochemical Societies (AL), the Swiss National Science Foundation (TCTM) and Peterhouse College, Cambridge (TCTM) for financial support.

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Graphical TOC Entry 80

2

Enthalpy, ΔH‡ Temp./entropy, TΔS‡ Free energy, ΔG‡

Critical concentration, g/L 60

80

60

40

40

20

20

0

0

1.5

Energy (kJ/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Concentration (g/L)

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1

−20

−20

−40 0.5

−60 0

10

20

30

40

Temperature (oC)

50

60

70

−80

−40

FF

FF

(Aβ1-42) crystal diffusive diffusive pre-factor pre-factor pre-factor


−60

−80

Thermodynamics of Polypeptide Supramolecular Assembly in the

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