Entropy of water and the temperature-induced stiffening of amyloid networks
Slav A. Semerdzhiev, Saskia Lindhoud, Anja Stefanovic, Vinod Subramaniam, Paul van der Schoot, Mireille M.A.E. Claessens
EEntropy of water and the temperature-induced stiffening of amyloid networks
Slav A. Semerdzhiev, Saskia Lindhoud, Anja Stefanovic, VinodSubramaniam, Paul van der Schoot, and Mireille M.A.E. Claessens* Nanobiophysics, MESA+ Institute for Nanotechnology and MIRAInstitute for Biomedical Technology and Technical Medicine,University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands. Vrije Universiteit Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands. Theory of Polymers and Soft Matter, Eindhoven University of Technology,P.O. Box 513, 5600 MB Eindhoven, The Netherlands (Dated: November 15, 2018)In water, networks of semi-flexible fibrils of the protein α -synuclein stiffen significantly withincreasing temperature. We make plausible that this reversible stiffening is a result of hydrophobiccontacts between the fibrils that become more prominent with increasing temperature. The goodagreement of our experimentally observed temperature dependence of the storage modulus of thenetwork with a scaling theory linking network elasticity with reversible crosslinking enables us toquantify the endothermic binding enthalpy and an estimate the effective size of hydrophobic patcheson the fibril surface. INTRODUCTION
Water and oil do not mix. Even after vigorous stir-ring, these two compounds spontaneously separate intodistinct liquid phases. This is a macroscopic manifes-tation of the hydrophobic effect, a phenomenon drivenby the microscopic behavior of water in the presence ofnonpolar molecules. Ultimately, this is caused by hy-drophobic molecules and assemblies thereof being inca-pable of forming hydrogen bonds. If introduced in anaqueous environment, hydrophobic molecular units per-turb or even disrupt the dynamic hydrogen bonded net-work that is formed by the water molecules. As a result,water molecules self-organize into more strongly orderedstructures in the vicinity of the hydrophobic molecularunits. This response is entropically unfavorable, and,hence, hydrophobic solutes become sticky and tend tocluster together. The solvent-mediated interactions atplay are known as hydrophobic interactions (HIs). Adistinguishing hallmark of HIs is their non-trivial depen-dence on temperature. For small hydrophobic solutesas well as large ones characterized by small hydropho-bic patches, below, say, 1nm , HIs become stronger withincreasing temperature [1]. This characteristic feature ofHIs persists in liquid water and distinguishes HIs from allother types of non-covalent attractive interactions thatbecome effectively weaker at higher temperature.HIs play a central role in various phenomena in chem-istry and biology, from the cleaning action of detergentsand the production of micro-emulsions, to the in vivo as-sembly of biological macromolecules into complex struc-tures. HIs often facilitate proteins in attaining their func-tional form by supporting their native fold or by bind-ing to partners [2, 3]. HIs have been also implicated in promoting the self-assembly of proteins into oligomericspecies and amyloid fibrils, a process accompanying manydisease conditions [4]. Finally, HIs, in an intricate inter-play with other types of non-covalent interactions, drivethe self-assembly of virus coat proteins into virus capsids[5]. This phenomenon has inspired the field of bionan-otechnology to create novel self-assembled biosyntheticstructures [6, 7]. Apart from being a characteristic fea-ture of HIs, the unique temperature response makes thistype of non-covalent interaction a suitable tool to ma-nipulate the properties of materials that have exposedpatches of hydrophobic surface. Nevertheless, control-ling material properties through hydrophobic forces re-mains a challenge, arguably resulting from our limitedunderstanding of HIs and the lack of design principlesfor the synthesis of tunable materials, the responsivenessof which is based on HIs.Here, we make use of the neuronal protein alpha-synuclein ( α S) that under appropriate conditions self-assembles into amyloid fibrils, and take it as a modelsystem in which material properties can be controlled byharnessing HIs. This protein exhibits a complex phasebehavior and, depending on the physico-chemical condi-tions, organizes into hierarchical suprafibrillar aggregateswith varying morphologies or into isotropic semi-flexibleamyloid networks [8, 9]. We carefully choose the experi-mental conditions to steer the self-assembly into the re-gion of the phase diagram where semi-flexible networksare formed. Fibril networks are a convenient platformi) to convincingly address the hydrophobic nature of theattractive interactions that drive the self-organization of α S fibrils into larger scale structures, helping us to iden-tify the role and formation mechanism of pathologicalfibril structures such as Lewy bodies that accompany the a r X i v : . [ c ond - m a t . s o f t ] D ec progression of Parkinson’s disease, and ii) to exploit hy-drophobic interactions to tune the mechanical propertiesof a material and inspire design principles for the creationof novel temperature responsive materials. We use tem-perature as a ‘tuning knob’ to adjust the effective degreeof crosslinking in the α S fibril network and by doing sochange the viscoelastic response of the material withoutforcing any permanent structural alterations in the ma-terial. Finally, we quantitatively connect the thermallyinduced enhancement of HIs to the observed stiffening inthe viscoelastic response of the network by incorporatingthe effect of reversible crosslinking in established scalingtheory for semi-flexible networks.
RESULTS AND DISCUSSION
The polymerization of α S into amyloid fibrils is a slowprocess. Within 7 days after the initiation of polymeriza-tion, a solution of monomeric α S typically evolves into agel (Fig. S1). It takes up to 37 days until all the proteinhas polymerized into fibrils (Fig. S2) and the networkhas equilibrated (Fig. 1a). Rheologically, the networksof semi-flexible amyloid fibrils behave as viscoelastic ma-terials. Frequency sweeps of aged networks produce rela-tively featureless spectra. No cross-overs between the fre-quency dependent storage modulus G (cid:48) ( f ) and loss mod-ulus G (cid:48)(cid:48) ( f ) are observed in the probed frequency range(Fig. 1a). The amyloid network properties are domi-nated by the storage modulus, as is characteristic for vis-coelastic solids. Both G (cid:48) and G (cid:48)(cid:48) are weakly dependenton the frequency, a feature typical of cross-linked poly-meric materials. However, since the α S amyloid networksare not chemically cross-linked, this observation impliessignificant attractive inter-fibril interactions, physicallycross-link the fibrils. The presence of associative inter-fibril interactions is further supported by creep-recoveryexperiments (Fig. 1b). Applying a constant stress onan α S fibril network initially induces a time-dependentstrain response of the material. Shortly after the stressis applied, the change in the strain reaches a steady stateknown as creep. The α S fibril gel exhibits very low creep(Fig. 1b), which is again in line with the presence of(localized) attractive inter-fibril interactions. Once thestress is removed, the network shows very low levels ofplastic deformation and recovers almost completely to itsoriginal state. The same behavior is observed after ex-tending the period during which the sample is subjectedto stress (Fig. 1b).Given the triblock copolymer-like architecture of the α S monomer, consisting of an amphiphilic domain, a hy-drophobic domain and a net charged domain, it is notsurprising that this protein exhibits multiple modes of in-termolecular interactions. While the stability of the amy-loid fibrils is provided by hydrogen bonding, the drivingforce for the self-assembly into amyloid fibrils is believed
FIG. 1. Rheology on α S amyloid networks. (a) Frequencysweeps for a 7 day ( p ) and 37 days ( u ) old sample. The stor-age modulus and the loss modulus are designated with closedand open symbols respectively. (b) Creep-recovery tests for anequilibrated 300 µ M α S amyloid network. Squares designatethe measured strain and the dashed block pulses representthe loading stages characterized by their duration and theamount of stress (0.7 Pa) applied. Squares and dashed lineswith different colors are used to discern the measured strainand the duration of the applied stress respectively for the 3subsequent creep-recovery tests with increasing duration ofthe loading stage. The same sample was used for the threemeasurements. The estimate for the creep-compliance is ob-tained from the slope of the dashed line.(c) Frequency sweepsfor an equilibrated network subjected to an extended temper-ature treatment. (inset) The damping factor G (cid:48) /G (cid:48)(cid:48) (tan β ) at1 Hz as a function of temperature. The decreasing value ofthe damping factor shows an increase in the elastic portion ofthe mechanical response of the network. to be hydrophobic interactions. The latter most probablyalso play a role in inter-fibril interactions [4]. Consideringthat the α S amyloid fold results from the subtle interplaybetween electrostatic interactions between the chargeddomains, hydrogen bonding and HIs, the minimum freeenergy conformation of the protein in the fibrils does notpreclude some residual exposure of hydrophobic domainsthat can mediate HIs between fibrils [10]. The formationof α S fibril clusters after a high-temperature treatmentof fibril suspensions indicates that HIs are indeed also in-volved at the inter-fibril level [8]. Plausibly, HIs are alsoresponsible for the observed viscoelastic behavior of α Snetworks (Fig. 1a).In the right settings, HIs can be made stronger by el-evating the temperature of the system [1]. If HIs areindeed responsible for inter-fibril interactions in α S amy-loid networks, temperature should have a pronounced ef-fect on the viscoelastic response of the network to applieddeformations. Indeed, an α S network significantly stiff-ens in the temperature range from 15 o C to 85 o C, whichexpresses itself in an order of magnitude increase of thestorage modulus G (cid:48) (Fig. 1c). This temperature-inducednetwork stiffening is reversible. The value of G (cid:48) tightlyfollows the changes in the temperature even if the net-work is repeatedly subjected to temperature cycles withdifferent amplitudes (Fig. S3). This behavior is typicallynot observed in networks of semi-flexible polymers, yetdoes superficially resemble the elastic behavior of rub-bers. In the latter, the free energy cost of stretching outthe stored contour length of the crosslinked polymers be-comes much larger at elevated temperatures, an effectassociated with them being flexible rather than semi-flexible. However, α S fibrils formed at the conditionsused to prepare the amyloid gels appear to be very stiffas is evidenced by TIRF microscopy images (Fig. S4a).An end-to-end distance versus contour length analysis ofthe fibrils yields an estimate for the persistence lengthof l p ≈ µ m, which is very much larger than the meshsize expected for a 300 µ M α S fibril network (Fig. S4band S4c). It is therefore unlikely that the increased freeenergy cost of reducing the conformational freedom of anindividual fibril contributes significantly to the observedincrease in G (cid:48) with increasing temperature.A huge experimental and theoretical research effort hasbeen invested in the past few decades to better under-stand the viscoelastic properties of networks comprisedof semi-flexible polymers [11]. These efforts have resultedin theoretical frameworks that describe scaling relationsbetween quantities characterizing the properties of thesenetworks, and which have been successfully applied toa wide range of biological and synthetic materials, allfalling in the general class of semi-flexible polymer net-works [12–14]. In view of the featureless frequency sweepsand the creep recovery experiments, the α S fibril net-work seems to behave as a crosslinked network (Fig. 1a).With this in mind, we have adopted the scaling theory forcross-linked semi-flexible networks in order to interpretthe temperature behavior of the α S amyloid network. Be-cause of the relatively large persistence length of α S fib-rils compared to the mesh size, we invoke a scaling theorybased on the so-called floppy modes model, assuming aconstant strain [15]. According to this model, we have: G (cid:48) = κξ l c (1)where G (cid:48) is the plateau modulus of the network, κ is the bending stiffness of the semi-flexible chains, ξ theaverage mesh size and l c the average distance betweencrosslinks [16] (see also Fig. 2b). Note that the persis-tence length and bending stiffness are related accordingto l p = κ/k B T . The strong dependence of the plateaumodulus on the number of crosslinks (through l c ) is ap- parent. However, before focusing on this particular quan-tity, the possible contribution of the other two relevantparameters to the observed thermal stiffening in α S net-works, namely ξ and κ , needs to be considered. Largetemperature-induced stiffening of semi-flexible polymershas been observed in some synthetic systems. Drivenby the enhanced hydrophobic interactions at higher tem-peratures, synthetic polymers may bundle into filamentswith more than an order of magnitude larger rigidity [14].The enhancement of κ can in that case be large enoughto overcome the effect of the increased mesh size, whichis expected to soften the network (eq. 1) and to producean overall increase in the plateau modulus [17]. Eventhough hydrophobic interactions also seem to play animportant role at the intra- and inter-fibril level in α Snetworks, bundling is an unlikely mechanism to accountfor the experimental observations at higher temperatures.SAXS measurements do not provide any evidence for sig-nificant structural changes in the α S network at thesehigher temperatures. The size of the fibrils cross-sectionremains close to constant throughout the temperatureramps (Fig. S4d and S4e). Moreover, the SAXS curvesremain identical at the different temperatures indicatingthat there are no sizable changes in the overall structureof the network and consequently in the mesh size ξ .If bundling does not take place, then the strong tem-perature dependence of G (cid:48) might result from a drasticchange in the bending rigidity of the individual fibrilsthemselves with temperature. Since G (cid:48) ∼ κ (eq. 1), theobserved change in G (cid:48) between 5 - 80 o C would implya 13-fold increase over that temperature range. This es-timate is based solely on changes in κ without takinginto account the changes in the so-called entanglementlength l e . If the sensitivity of l e on the temperature isalso taken into account, using the known scaling relationsand assuming crosslinks can only appear at entanglementpoints l c ∼ l e ∼ l p ∼ ( κ/k b T ) , then the increase of κ with temperature would need to be even larger (eq. 1)[18]. The temperature dependence of κ is however gen-erally very moderate for semi-flexible biopolymers. Ad-ditionally the sign of the change strongly depends on thebiopolymer species. While, depending on GC contentand salt concentration, double-stranded DNA seems toexhibit a 15-20 % reduction in κ with increasing temper-ature by 30-45 o C, single-stranded DNA shows a 15% in-crease of κ over a comparable temperature range [19–21].A drastic change in the mechanical properties of individ-ual α S fibrils also seems highly unlikely. As mentionedearlier, the protein monomers in the cross β -sheets fibrilbackbone are held together by numerous intermolecularhydrogen bonds, which are the main determinant for thefibril stiffness [22]. Driven by inter- and intra-molecularHIs, α S monomers aggregate and attain a fold with op-timized internalization of apolar residues in the fibrilscore. Keeping this in mind, higher temperatures stimu-late two counteracting effects: on one hand, the breaking
FIG. 2. Hydrophobically crosslinked α S amyloid networks. (a) Stress relaxation tests of a 300 µ M α S network (2 mM Na + ) atdifferent temperatures. The stress-relaxation curves are vertically shifted for a better visualization. (B) Artist impression of ahydrophobically crosslinked α S amyloid network. The tentative hydrophobic patches on the surface of the fibrils are presentedin red. (c) Scaling of the storage modulus with temperature. The circles represent the experimental data, the red curve is thefit generated using the scaling relation derived in the main text (eq. 2 ). (cartoon insets) At higher temperature the numberof effective cross-links is significantly higher as compared to lower temperatures. of hydrogen bonds should reduce the rigidity of the fibrilsand, on the other, the enhancement of the hydrophobicinteraction could increase the stiffness. However, it is un-likely that the strength of inter-monomer HIs increasessufficiently to compensate for the loss of hydrogen bonds,and produce the dramatic net increase in κ that wouldaccount for the unusual increase in the G (cid:48) of the net-work. Indeed, other molecular assemblies that are heldtogether by hydrophobic interactions also do not showsigns of unusual stiffening, induced by an increase in tem-perature in the range comparable to the one used in thisstudy. Lipid bilayers, for example, become easier to de-form with increasing temperature [23, 24]. The filamen-tous fd virus exhibits a non-monotonic change in the per-sistence length l p = κ/k b T with temperature: at highertemperature, l p decreases, while an increase is found atthe lower temperature range [25]. This variation in l p ishowever small, amounting to no more than 30%.With changes in κ being an unlikely cause for thelarge temperature-induced increment of G (cid:48) , the onlyparameter left that could potentially account for thisphenomenon is the mean distance between crosslinks l c .Heating up the system seems to strengthen the hydropho-bic contacts between the fibrils, which ultimately resultsin a more densely crosslinked network. Results fromstress-relaxation measurements on an α S network at dif-ferent temperatures are in line with this hypothesis. In-stead of speeding up the relaxation processes, heating upthe sample actually slows down the relaxation dynamics(Fig. 2a), probably due to the enhanced inter-fibrillar contacts (Fig. 2b).To test the hypothesis that heating the amyloid net-work strengthens hydrophobic contacts between fibrils,we establish a quantitative relation between tempera-ture and the storage modulus. For this purpose, the im-pact of temperature on the effective number of crosslinksin the system is evaluated at the level of a Boltzmannequilibrium and incorporated in the scaling relations forcrosslinked semi-flexible networks (for the derivation seethe Supplemental Material). This results in the followingrelation: G (cid:48) ( T ) = G (cid:48) ( T ) e H kbT ( T − T ) (cid:32) T T (cid:33) (2 / (2)where G (cid:48) ( T ) is the temperature-dependent plateaumodulus, and G (cid:48) ( T ) the plateau modulus at the refer-ence temperature T . The value of H strongly dependson the architecture of α S fibrils. Since there is no estab-lished model for this architecture, H is left as a free pa-rameter. The reference temperature T = 288 K , whichis the lowest temperature at which the storage moduluswas measured, is used to fit equation 2 to the experimen-tal data. Equation 2 seems to describe the experimentalobservations very well indeed (Fig. 2c). The fit yieldsan endothermic value for H = 7 . k b T . From the ob-tained value for H we can estimate the apparent sizeof the hydrophobic patches using the expression for theenthalpy at the reference state of hydrophobic contacts: H = 2 h h.i. a where h h.i. is the energy cost per unit areaof exposed hydrophobic surface and a is the area [26].Taking into account that typically h h.i. ∼ k b T nm − ,the estimate for the size of the hydrophobic patches onthe fibril surface is ∼ . nm which is comparable towhat has been found previously for virus coat proteins[5, 26, 27]. CONCLUSION
In summary, α S amyloid networks exhibit remarkablethermo-responsive properties. The fibrillar gel signif-icantly stiffens at higher temperatures and completelyrecovers its original state once the temperature is low-ered again. We propose that the thermo-stiffening ofthe α S network is the consequence of enhanced inter-fibrillar hydrophobic contacts stimulated by the highertemperature. This is consistent with previously estab-lished qualitative findings, suggesting that the hydropho-bic effect plays an essential role in the interaction be-tween α S fibrils [8]. The presence of hydrophobic inter-actions between fibrils suggest that multiple hydropho-bic domains in the fibril core remain solvent exposed.At higher temperatures these hydrophobic areas becomeactivated, which effectively increases the number of con-tacts points between fibrils. An alternative explanationin which the exposure of the hydrophobic domains it-self is a temperature-induced phenomenon could also beconsidered. At higher temperature segments of the α Sfibrils may unfold and reveal the hydrophobic stretchesof the protein sequence to the solvent, which later be-come anchoring points between fibrils. Such a hypothet-ical scenario would be consistent with previous research,suggesting that at elevated temperatures the cross-betasheet structure of the fibrils starts to fall apart [28]. How-ever, the experimental findings reported here do not giveany clues supporting this interpretation. Numerous un-folding events in fibrils should have become apparent inthe SAXS cross-sectional Guinier analysis, as it changesthe effective cross-section of the fibril. We do not observethis in our SAXS data. Moreover, compromising thestructural integrity of the fibrils should also have alteredthe mechanical response of the network towards soften-ing rather than towards stiffening.Elucidating the cohe-sive forces between amyloid fibrils is crucial for obtaininga better understanding of the associated pathology andthe physiological role of such structures. A correlationbetween the exposure of hydrophobic surface in amyloidaggregates and their toxicity has been suggested by nu-merous studies [29–31]. Considering the nanoscale orga-nization of the α S fibrils it is unlikely that all hydropho-bic patches on the fibril surface are protected from con-tact with the aqueous environment by inter-fibril interac-tions. The exposure of these hydrophobic fibril patchesto the cytosol may induce interactions with other pro-teins. The accumulation of additional proteins in amy- loid deposits may therefore not be a result of preservedfunctional interactions but rather be an effect of HIs.The accumulation of amyloid fibrils might increase thetotal hydrophobic surface present in the cell and therebyinterfere with its normal functioning.Understanding the inter-fibril interactions is also im-perative for the successful utilization and manipulationof amyloid materials. Our data indicate that there areopportunities to harness these interactions and tune themechanical properties of amyloid materials. Moreover,these findings indicate that it should be possible to designamyloid fibrils or other supramolecular assemblies withengineered hydrophobic patches and synthesize materialswith imprinted temperature responsiveness. An impor-tant question remains, however. Are these interactionsgeneric for amyloids or just specific for α S? Exposure ofamyloid networks comprised of the disease-unrelated pro-tein β -lactoglobulin does not seem to provoke the sameresponse, indicating that the degree of thermo-stiffeningobserved for α S gels cannot be expected to hold for allamyloid materials [32].
ACKNOWLEDGEMENTS
This work was supported by the Nederlandse Organ-isatie voor Wetenschappelijk Onderzoek (NWO) throughNWO-CW Veni grant (722.013.013) to S.L., NWO-CWTOP program (700.58.302) to V.S., NWO-CW VIDIgrant (700.59.423) to M.M.A.E.C., and through andNanonext NL theme 8A. The authors thank Kirsten vanLeijenhorst-Groener and Nathalie Schilderink for the ex-pression and purification of - synuclein. SAXS experi-ments were performed at ESRF, BM26B (DUBBLE) ex-periment number 26-02-664. We thank Dr. G. Portale(Beamline Scientist) for his help performing SAXS ex-periments.
SUPPLEMENTAL MATERIALI. Materials and methods A. α S gel preparation
Expression of the human wild type α S was performed in
E. coli
B121 (DE3) using the pT7-7 based expression system.Details on the purification procedure for α S are described elsewhere [33]. Gels of α S amyloid fibrils were preparedin quiescent conditions. Fibril growth was seeded by 5 mol.% preformed α S seeds at a total protein concentrationof 300 µ M α S in 10 mM Tris, pH 7.4 and 10 mM NaCl (Sigma). The first 6 days samples were incubated at 37 o Cand after that the gels were stored to mature at room temperature. The gels for SAXS measurement were directlygrown in quartz capillaries (Hilgenberg GmbH, L=80, OD=1.5, Wall=0.01 mm) using the procedure described above.Samples for the TIRFM imaging were stained with the amyloid specific fluorescent dye Thioflavin T (ThT) and sealedin custom made glass chambers. B. α S gel preparation
A solution of fibrils was prepared by incubating 100 µ M of α S in 10 mM Tris (Sigma), 2 mM NaCl (Sigma), pH=7.4,37 o C and shaking at 900 RPM. Once the aggregation was completed, the fibril solution was sonicated (Branson,Sonifier 250) on ice. The solution was sonicated at the lowest power for 5 seconds and left at rest for another 55second. The cycle was repeated five times. Subsequently, the sonicated samples were tested for seeding efficiency byincubation with α S monomers.
C. SAXS
Experiments were performed at the BM26 DUBBLE (Dutch-Belgian Beamline, ESRF, Grenoble, France). Twodimensional images were collected using Pilatus 1M photon counting detector. The sample to detector distance was6.6 m. The wavelength for the incident x-ray was 0.1 nm -1 and beam cross-section with dimensions 2.5 mm x 4.5 mm.The energy of the x-rays was 12 eV. The attained q range was 0.031.5 nm -1 . The ATSAS 2.6.0 software package wasused for post-acquisition processing and analysis of the SAXS data [34]. D. Rheology
Rheology measurements were performed on an Anton Paar MCR 301 rheometer using a plate-plate geometry, witha plate diameter of 25 mm. Gel samples were carefully collected from the storage tubes using truncated pipette tipsto minimize shearing and network disruption. The gel was then carefully deposited on the rheometers stage. Mea-surements were conducted at gap size of 0.16 mm and the samples were covered with mineral oil to avoid evaporationduring the temperature runs. For each temperature step the sample was first left to equilibrated until the storagemodulus G (cid:48) measured at f = 0.5 Hz, γ = 0.5 %, attained a stationary value (usually within 1 hour). Subsequently, afrequency spectrum was recorded at γ = 1 %. Stress relaxation test were conducted by first equilibrating the sampleat a given temperature and then subjecting it to a strain γ = 3 % which is within the linear viscoelastic responseregion of the sample. Subsequently the time relaxation modulus G ( t ) was recorded. E. Total Internal Reflection Fluorescence Microscopy (TIRFM)
The TIRFM imaging was performed using a Nikon Ti-E microscopy setup coupled with an Argon laser (35-IMA-040, Melles Griot, USA). Images were acquired with a CFI Apo TIRF 100x objective (Nikon, Japan) and iXon 3DU-897 EMCCD camera (Andor, UK) using the 457 nm line of the laser for the excitation of the ThT dye. The usedfilter cubes contained a 455 nm excitation filter with 10 nm bandpass, a 458 nm long pass dichroic mirror and a 485nm emission filter with 30 nm bandpas
F. Determination of residual monomer concentration
Determination of residual monomer concentration. Samples of the S amyloid gels were centrifuged using a SorvallWX 80 ultracentrifuge (Thermo Scientific, USA) and Fiberlite F50L-24 x 1.5 fixed-angle rotor at 247 kG for 5hours. Subsequently the concentration of free α S monomers in the supernatant was determined using a UV-Visspectrophotometer (UV 2401 PC, Shimadzu). Absorbance was measured at 276 nm and an extinction coefficient of5600 M -1 .cm -1 was used to calculate the protein concentration. G. Persistence length analysis
Aliquots of a 300 µ M α S gel, 10 mM NaCl and 10mM Tris were diluted in the same buffer keeping the ionic strengthconstant. Thioflavin T (ThT) was subsequently added to a final concentration of 1 µ M in order to stain the fibrils. Asmall volume of the diluted sample was sealed between a glass slide and a cover slip. The sample was left at rest forthe fibrils to sediment on the cover slip and then imaged using Nikon Ti-E in TIRF mode (see section TIRFM). Imageswere analyzed using the MATLAB based package Easyworm [35]. Briefly, the persistence length is determined viarandom resampling using bootstrap with replacement method. A bootstrap sample of n chains is randomly selectedfrom the ensemble of all chains. For each bootstrap the average square of the end to end distance < R > is binnedat equal length intervals. Then all the data is fitted using the wormlike chain model: < R > = 2 l p L (cid:34) − l p L (cid:18) − e − Llp (cid:19)(cid:35) (S1)where L is the contour length. H. Derivation of the equation linking hydrophobic interactions to the temperature induced stiffening of α S fibril networks
Temperature seems to enhance the formation of physical crosslinks between fibrils in the α S amyloid network.Identifying the impact of temperature on the effective number of crosslinks in the system, would enable us to incor-porate the temperature effect in the scaling relations for the elastic response of crosslinked semi - flexible networks.To directly relate the enhanced hydrophobic interactions to the stiffening of the network, we introduce a two statemodel for the entanglements in the network A → B , where A and B represent the ‘free’ and ‘crosslinked’ entangle-ments respectively (Fig 4B from the main article). Assuming that hydrophobic interactions drive the crosslinking ofentanglements, the equilibrium dissociation constant can be written as [5, 36]: K = K T e H kbT ( T − T ) (S2)where K T is the equilibrium dissociation constant at a reference temperature T , and H > T for two hydrophobic surfaces coming into contact. Because H > K increaseswith T as is typically observed for hydrophobic surfaces [5]. We can calculate the fraction F of entanglements thatare in the crosslinked state by invoking Boltzmann statistics: F = K T e H kbT ( T − T ) K T e H kbT ( T − T ) (S3)Since K T is presumably small, at low T the hydrophobic interactions are known to be weak [37] so is | T − T | /T over the probed temperature range, we can approximate F making use of a Taylor expansion: F ≈ K T e H kbT ( T − T ) (S4)In a semiflexible network, contacts between filaments appear at the entanglement points. Given that i) there are nosignificant structural rearrangements in the network during the crosslinking process, ii) the maximum number bondsequals the number of entanglement points, we conclude that the distance between crosslinks l c can be related to theentanglement length l e through the fraction F : l c ∼ l e F (S5)Taking into account that ξ ∼ c − p , where c − p represents the concentration of the filament forming protein, theentanglement length reads as [38]: l e ∼ l / p ξ / ∼ (cid:16) κk b T (cid:17) (S6)where κ is the bending stiffness of the semi-flexible chains and ξ the average mesh size. We know that for a networkcomprised of semi-flexible polymers that appear stiff between entanglement points, the storage modulus scales as (seeeq. 1 and the discussion preceding it the main article): G (cid:48) = κξ l c (S7)where G (cid:48) is the plateau modulus of the network. Substituting equations eq. S4 and eq. S6 in eq.S5, inserting thelatter in eq. S7, and finally after some re-arrangements we arrive at: G (cid:48) ( T ) = G (cid:48) ( T ) e H kbT ( T − T ) (cid:32) T T (cid:33) (2 / (S8) II. Figures
FIG. S1. αS amyloid networks. (a) Self-supporting 300 µ M α S fibril network subjected to an inversion test. The gel wasformed in 10 mM NaCl, 10 mM Tris and pH=7.4. (b) Total internal reflection microscopy (TIRF) images of an α S networkformed at the same conditions confirm that the gel is comprised of a network of amyloid fibrils.The network is stained withThT (30 µ M). The scale bar is 5 µ m. FIG. S2. Absorbance spectra of the supernatant obtained after the ultracentrifugation of an 300 µ M α S gel at different timepoints of the aging process. After 7 days, only half of the monomers have been recruited in fibrils and a detectable amount offree ThT is present in the solution. At 37 days the residual level of monomeric protein is below the threshold for an accuratedetermination and no free ThT is detected. FIG. S3. Reversible temperature stiffening of α S amyloid networks. An equilibrated α S amyloid network that is repeatedlysubjected to cycles with different temperature amplitudes. Blue and red bars designate low and high temperature cyclesrespectively. Dark and light colored bars refer to G (cid:48) and G (cid:48)(cid:48) respectively . FIG. S4. Mechanical and SAXS characterization of α S fibrils. (a) TIRF image of individual α S fibrils. Scale bar is 5 µ m. (b)Traces for the set of analyzed fibrils. (c) Contour length vs mean square of the end to end distance. SAXS measurements of anetwork at different temperatures. (d) 1D SAXS curves for an 35 day old 300 µ M α S network. The sample was first measuredat 20 o C ( (cid:15) ) and subsequently heated up to 80 o C ( A ) and measured again. The final measurement was performed after thesample was cooled down to the starting temperature ( E ). (e) Cross-sectional Guinier (CG) plots. The fibril thickness seemsconstant before, during and after the temperature treatment of the equilibrated α S network. Data sets are vertically shiftedfor a better visualization. REFERENCES [1] D. Chandler, Nature , 640 (2005).[2] H. J. 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