Effects of Protein Unfolding on Aggregation and Gelation In

biomolecules

Article Eﬀects of Protein Unfolding on Aggregation and Gelation in Lysozyme Solutions

Shakiba Nikfarjam 1, Elena V. Jouravleva 2, Mikhail A. Anisimov 1,2,* and Taylor J. Woehl 1

1 Department of Chemical and Biomolecular Engineering, University of Maryland, College Park, MD 20742, USA; [email protected] (S.N.); [email protected] (T.J.W.) 2 Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA; [email protected] * Correspondence: [email protected]

Received: 10 August 2020; Accepted: 29 August 2020; Published: 2 September 2020

Abstract: In this work, we investigate the role of folding/unfolding equilibrium in protein aggregation and formation of a gel network. Near the neutral pH and at a low buﬀer ionic strength, the formation of the gel network around unfolding conditions prevents investigations of protein aggregation. In this study, by deploying the fact that in lysozyme solutions the time of folding/unfolding is much shorter than the characteristic time of gelation, we have prevented gelation by rapidly heating the solution up to the unfolding temperature (~80 ◦C) for a short time (~30 min.) followed by fast cooling to the room temperature. Dynamic light scattering measurements show that if the gelation is prevented, nanosized irreversible aggregates (about 10–15 nm radius) form over a time scale of 10 days. These small aggregates persist and aggregate further into larger aggregates over several weeks. If gelation is not prevented, the nanosized aggregates become the building blocks for the gel network and deﬁne its mesh length scale. These results support our previously published conclusion on the nature of mesoscopic aggregates commonly observed in solutions of lysozyme, namely that aggregates do not form from lysozyme monomers in their native folded state. Only with the emergence of a small fraction of unfolded proteins molecules will the aggregates start to appear and grow.

Keywords: lysozyme; aggregation; gelation; protein folding/unfolding

1. Introduction Aggregation of proteins and peptides is a broad and complex phenomenon with several subsets, each progressing via a distinct mechanism [1]. Neurodegenerative diseases such as Alzheimer’s disease and Parkinson’s disease, caused by misfolding and aggregation of proteins followed by precipitation of these aggregates in the central nerves system, are examples of indigenous protein aggregation [2]. Detailed understanding of the aggregation mechanism would help to gain insight into the origin of diseases and their prevention [3]. Because some of the amyloidogenic proteins have a three-dimensional folded structure [4], studying the difference between the driving forces for aggregation of finely folded and partially unfolded proteins would help to elucidate the aggregation mechanisms of pathogenic proteins responsible for amyloid diseases. In biopharmaceuticals protein-based drug formulations may undergo reversible or irreversible aggregation at high concentrations, which negatively affects their therapeutic efficiency and consequently introduces challenges in their production and clinical administration [5]. The increase in the number of protein drugs and the obstacles, caused by aggregation, in production and shelf-life of these drugs is another motivation for studying the aggregation mechanisms [3]. There are several known mechanisms of aggregation in proteins [6]. Depending on the degree of protein folding in the aggregate, the aggregates can be formed either reversible or irreversible [6].

Biomolecules 2020, 10, 1262; doi:10.3390/biom10091262 www.mdpi.com/journal/biomolecules Biomolecules 2020, 10, 1262 2 of 14

While primary and secondary structures of a protein are internal factors affecting the aggregation propensity of a protein, external factors such as the temperature, pH, ionic strength, shear stress and concentration can also affect the aggregation of proteins in solutions [7–9]. The reversible protein oligomers arise from monomers in their native states [10]. As a next step, these oligomers can form irreversible aggregates if the interactions in an oligomeric state favor the conformational change of the monomers towards an aggregate prone state [5,11]. In aggregation through another mechanism, originated from non-native contacts, alteration in conformation of proteins due to heat or physical stress may lead to the formation of irreversible aggregates [6,12,13]. Depending on the pH and ionic strength of solution and at high enough protein concentrations [14,15], by prolong heating, the aggregates associate and eventually can form a gel network [16–18]. A clear mechanism of interplay between protein aggregation, phase separation and gelation, is difficult to establish for several reasons—proteins show unique behavior depending on their amino acid content and function. Additionally, aggregation comprises multiple steps depending on the environment. Finally, detection of smaller aggregates with a short lifetime is experimentally nontrivial. Lysozyme is a popular model protein, due to its structural and functional simplicity, extensive documentation and commercial availability. However, there are several unresolved issues regarding lysozyme aggregation. In particular, the nature of its folding/unfolding intermediates, transient oligomerization and the role of gelation. Several publications of lysozyme solutions mentioned the presence of mesoscopic aggregates or so called “mesoscopic protein-rich clusters” [19,20]. It was found that these aggregates typically had 4 a diameter between 60–200 nm and a fraction of ~10− of total soluble protein [21]. The aggregates were commonly thought to be reversible [22], undergoing dynamic molecular exchange with protein in solution [23]. In our previous study [24] on the nature of mesoscopic aggregates in solutions of lysozyme, we investigated the effects of concentration, filtration and temperature on the sizes and relative amount of mesoscopic aggregates in solutions of lysozyme. We showed that systematic filtration through 20 nm filters completely removed the aggregates from solution. Moreover, the aggregates did not reemerge. This indicates that the aggregates of lysozyme are unlikely to be a result of reversible self-assembly of unfolded lysozyme molecules. Therefore, the aggregates do not form from lysozyme monomers in their native, biologically active folded state. However, the origin of the main driving forces of aggregation in lysozyme solutions at moderate and low temperatures remain elusive. In this work we investigate a connection between the formation of lysozyme aggregates and protein unfolding triggered by heating. In particular, we clarify the effect of heating duration on the formation and growth of lysozyme aggregates and a gel network. Formation of the gel network at a nearly neutral pH and low ionic strength occurs in concentrated solutions of lysozyme at about the same temperature as protein denaturation, which prevents direct studies of protein aggregation without being affected by gelation. To block the formation of a gel, we used rapid heating to the protein melting temperature following by quenching to the room temperature. This protocol enabled us to monitor in real time the step-by-step formation of small aggregates, which originate from a certain fraction of unfolded protein molecules, acting as nucleus of amyloid aggregates, by forming amorphous nanoscale aggregates first. If gelation is prevented, nanoscale aggregates (about 10–15 nm radius) are formed. At room temperature, when the samples are monitored for weeks, these clusters persist and can further form larger aggregates. If gelation is not prevented, these clusters become the building blocks of the gel network and define its mesh size.

2. Materials and Methods

Lyophilized powder of lysozyme (Mw = 14 kDa) was obtained from ThermoFisher Scientific (20,000 units/mg solid). HEPES buffer (Sodium salt of 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid, >99%) was supplied as a solid powder from VWR. All lysozyme samples for dynamic light Biomolecules 2020, 10, 1262 3 of 14 scattering (DLS) studies were prepared in a 20 mM HEPES buffer at pH 7.8 and filtered through 100 nm and 20 nm pore filters, according to the procedure explained in our previous work [24]. By DLS, we studied three concentrations of lysozyme, 18, 30 and 60 mg/mL. The concentration of protein samples were measured by using the absorbance at 280 nm. The details the DLS techniques and measurements are described in our previous work [24]. The lyophilized lysozyme powder was directly dissolved in the buffer for the preparation of the concentrated stock solution. The concentrations were measured after filtration with 200 nm filters. The samples with the desired concentrations were then prepared by dilution. DLS measurements were taken using a multi-angle dynamic light scattering complex from Photocor. Autocorrelation functions were generated for 600 s at each specific angle and temperature. HEPES buffer has a temperature coefficient equal to 0.14, increasing the temperature − to 80 ◦C would decrease the pH less than by 10%, which that should not affect the aggregation. Additionally, a sodium dodecyl sulfate–polyacrylamide gel electrophoresis (SDS-PAGE) gel analysis on both heated and unheated 30 mg/mL samples was performed to investigate the possibility of protein’s degradation. The unheated samples and the sample heated to 80 ◦C for 30 min were incubated at room temperature for three weeks prior to running the SDS-PAGE gel. Also, the heated and unheated samples were additionally incubated at 95 ◦C for 5 min right before running the gel.

3. Results

3.1. Apparent Monomer Size Primarily, DLS measures the scattering intensity autocorrelation function, exponentially decaying with the diffusive relaxation rate of optical inhomogeneities that exhibit Brownian motion in solution [25], Γ = Dq2, (1) where D is the diffusion coefficient and q = (4π/λ)n sin(θ/2) is the scattering wave number (with λ being the wavelength of light, n the refractive index, θ the scattering angle). The hydrodynamic radius of inhomogeneities, such as the protein molecules or aggregates, is obtained by assuming the validity of the Stokes-Einstein equation that relates the diffusion coefficient (D), viscosity of the solvent (η) and hydrodynamic radius R [25]:

k T D = B , (2) 6πηR where kB is Boltzmann’s constant and T is the temperature. This assumption is fully justified only for dilute solutions of presumably spherical, noninteracting inhomogeneities. Formal application of the Stokes-Einstein equation to semi-dilute and concentrated protein (or, generally, polymer) solutions, results in obtaining a so-called “apparent” hydrodynamic radius that is smaller than the actual hydrodynamic radius of noninteracting individual molecules (moreover, decreasing with the increase of polymer concentration) [26]. The apparent hydrodynamic radius as a function of lysozyme concentration, obtained in our new DLS measurements for three concentrations of lysozyme, is in good agreement with our data reported previously [24]. As demonstrated in Figure1, the apparent radius corresponds to the actual size of individual molecules (“monomers”) only in dilute solutions of lysozyme (<10 mg/mL). One of the goals in making this chart (Figure1) was to track changes in sample concentrations using the apparent hydrodynamic radius of lysozyme monomers. During the three weeks of measurements, no change in hydrodynamic radius of lysozyme monomers where observed. This observation confirms that crystal growth and sedimentation did not affect the solution concentrations. This assumption is in agree with the reported phase diagram of lysozyme phase separation and crystallization in 20 mM HEPES and pH of 7.8 reported in Reference [21]. Biomolecules 2020, 10, 1262 4 of 14 Biomolecules 2020, 10, x FOR PEER REVIEW 4 of 14

FigureFigure 1.1. Apparent hydrodynamic radius of of lysozyme lysozyme mo monomers,nomers, obtained obtained by by DLS, DLS, as as a afunction function of ofconcentration concentration at at25 25 °C◦C[ [10].10]. In In dilute dilute solutions solutions (<10 (<10 mg/mL) mg/mL) it it represents represents the actual sizesize ofof thethe lysozymelysozyme monomers. monomers. UponUpon thethe increaseincrease ofof concentration,concentration, thethe apparentapparent radiusradius (blue(blue crosses)crosses) sharply sharply decreasesdecreases becausebecause ofof thethe interactionsinteractions betweenbetween lysozymelysozyme molecules.molecules. RedRed circlescircles areare thethe resultsresults ofof ourour newnew measurements.measurements. It is important to note that the Stokes-Einstein equation remains valid for mesoscopic lysozyme It is important to note that the Stokes-Einstein equation remains valid for mesoscopic lysozyme aggregates even in concentrated solutions. This is because the number of the aggregates are relatively aggregates even in concentrated solutions. This is because the number of the aggregates are relatively small. Therefore, with respects to the aggregates, the concentrated solution of lysozyme can be regarded small. Therefore, with respects to the aggregates, the concentrated solution of lysozyme can be as dilute. The hydrodynamic radius of the aggregates thus characterizes their actual size, provided regarded as dilute. The hydrodynamic radius of the aggregates thus characterizes their actual size, that the actual viscosity of the solution is used in the equation. provided that the actual viscosity of the solution is used in the equation. 3.2. Continuous Heating 3.2. Continuous Heating We ﬁrst studied an 18 mg/mL lysozyme solution heated from 25 ◦C to 62.5 ◦C. Using the protocol We first studied an 18 mg/mL lysozyme solution heated from 25 °C to 62.5 °C. Using the protocol outlined in Figure2a. After holding the solution for 8 h at 55 ◦C, we observed a change in the outlined in Figure 2a. After holding the solution for 8 h at 55 °C, we observed a change in the DLS DLS autocorrelation function (g2), presented in Figure2b, which marks the onset of aggregation. Twoautocorrelation characteristic function sizes of the( g2 aggregates,), presented of in the Figure order of2b, ~30 which and ~100marks nm, the were onset detected. of aggregation. After further Two heatingcharacteristic and holding sizes of the the sample aggregates, for about of the 60 order h at 62.5 of ~30◦C, asand shown ~100 innm, Figure were2 b,detected. the autocorrelation After further functionheating and demonstrated holding the a dramaticsample for shift about from 60 ah doubleat 62.5 exponential°C, as shown to in a Figure broader 2b, spectrum the autocorrelation of the size distributionfunction demonstrated (Figure2c). The a dramatic distribution shift reveals from a three double characteristic exponential length to a broader scales, one spectrum corresponding of the size to apparentdistribution size (Figure of lysozyme 2c). The monomers distribution ~1.5 nm,reveals another three one characteristic to small number length of scales, ~100 nmone aggregates corresponding and ato third apparent to inhomogeneities size of lysozyme with monomers a length scale ~1.5 ofnm, about another 15 nm one in to size, small which number are dominant. of ~100 nm Cooling aggregates the sampleand a third back to theinhomogeneities room temperature with dida length not change scale of the about DLS characteristics15 nm in size, ofwhich the sample. are dominant. Visual observationCooling the showedsample thatback the to samplethe room was temperatur in the gel state.e did Therefore,not change we the interpret DLS characteristics the length scale of the of aboutsample. 15 nmVisual as theobservation gelation meshshowed size. that the sample was in the gel state. Therefore, we interpret the length scale of about 15 nm as the gelation mesh size. Biomolecules 2020, 10, 1262 5 of 14 Biomolecules 2020, 10, x FOR PEER REVIEW 5 of 14

(a) (b)

(c)

Figure 2. Heating protocol (a) and DLS analysis (b) and (c) demonstrating the process of aggregation and Figuregelation 2. inHeating the 18 mgprotocol/mL lysozyme (a) and DLS solution, analysis gradually (b) and heated(c) demonstrating to 62.5 ◦C and the kept process at this of aggregation temperature b = c andfor 60gelation h. ( ) DLS in the autocorrelation 18 mg/mL functionlysozyme (θ solution,45◦) before gradually and after heated gel formation;to 62.5 °C ( and) size kept distribution at this of the apparent inhomogeneities before and after gelation.  temperature for 60 h. (b) DLS autocorrelation function (θ = 45 ) before and after gel formation; (c) sizeWe distribution performed of another the apparent experiment inhomogeneities on a lysozyme before and solution after gelation. of about the same concentration (20 mg/mL) but with a diﬀerent protocol. The sample was heated to 60 ◦C and the DLS correlation functionWe performed was measured another after experiment 18, 42 and 90on h a while lysozyme held atsolution this temperature. of about the The same results concentration are presented (20 mg/mL)in Figure but3. We with observe a different the formation protocol. of inhomogeneitiesThe sample was ofheated a radius to growing60 °C and from the ~17 DLS nm correlation after 18 h function(with a signiﬁcant was measured dominance after 18, of 42 the and nano-sized 90 h while monomers held at this and temperature. oligomers) to The ~40 results nm after are 42 presented h and to in Figure 3. We observe the formation of inhomogeneities of a radius growing from ~17 nm after 18 80–90 nm after 90 h. Remarkably, after 90 h at 60 ◦C, a meso-size (~20–25 nm) reemerges, while the size hdistribution (with a significant of the larger dominance aggregates of the becomes nano-sized narrower. monomers Qualitatively, and oligomers) this experiment to ~40 nm shares after 42 features h and towith 80–90 the nm results after presented 90 h. Remarkably, in Figure2 after; the growth90 h at 60 of °C, aggregates a meso-size (a faster (~20–25 process) nm) startsreemerges, before while gelation the size(a slower distribution process of of the formation larger aggregates of network become with a meshs narrower. size of aboutQualitatively, 15–25 nm). this experiment shares features with the results presented in Figure 2; the growth of aggregates (a faster process) starts before gelation (a slower process of formation of network with a mesh size of about 15–25 nm). BiomoleculesBiomolecules 20202020,, 1010,, 1262x FOR PEER REVIEW 66 ofof 1414 Biomolecules 2020, 10, x FOR PEER REVIEW 6 of 14

(a) (b) (a) (b) Figure 3. DLS analysis in the 20 mg/mL lysozyme solution gradually heated to 60 °C and kept at this Figure 3. DLSDLS analysis analysis in in the the 20 20 mg/mL mg/mL lysozyme lysozyme solution solution gradually gradually heated heated to 60 to °C 60 and◦C andkept kept at this at  thistemperature temperature for 18, for 42 18, and 42 and90 h. 90 (a h.) DLS (a) DLSautocorrelation autocorrelation function function (θ = (θ90= )90 before) before and and after after gel temperature for 18, 42 and 90 h. (a) DLS autocorrelation function (θ = 90 ) before◦ and after gel gelformation; formation; (b) (bsize) size distribution distribution of ofthe the apparent apparent inhomogeneities. inhomogeneities. Note Note an an increase increase in apparentapparent formation; (b) size distribution of the apparent inhomogeneities. Note an increase in apparent monomermonomer sizesize duedue toto oligomerization.oligomerization. monomer size due to oligomerization. WeWe havehave also found that, that, for for this this sample, sample, despite despite gelation gelation occurring occurring after after 90 h 90 of h incubation, of incubation, the We have also found that, for this sample, despite gelation occurring after2 90 h of incubation, the thedecay decay rates rates for forthe theboth both inhomogeneities, inhomogeneities, 20–25 20–25 and and 80–90 80–90 nm, nm, exhibit exhibit a q a2 qlinearlinear dependence dependence that that is decay rates for the both inhomogeneities, 20–25 and 80–90 nm, exhibit a q2 linear dependence that is ischaracteristic characteristic for for diffusive diﬀusive relaxation relaxation (Figure (Figure 4).4). characteristic for diffusive relaxation (Figure 4).

Figure 4. Wave number dependence for three scattering angles (30 , 60 and 90 , q sin(θ/2) of ◦ ◦ ◦ ∝ Figure 4. Wave number dependence for three scattering angles (30°, 60° and 90°, q ∝ sin()θ / 2 theFigure two 4. decay Wave rates number in the dependence 20 mg/mL samplefor three after scattering 90 h of angles holding (30°, at 60 60°◦C and (see 90°, Figure q ∝3b).sin Blue()θ line:/ 2 fastof the mode two (smallerdecay rates aggregates), in the 20 mg/mL orange line:sample slow after mode 90 h (larger of holding aggregates). at 60 °C (see Figure 3b). Blue line: of the two decay rates in the 20 mg/mL sample after 90 h of holding at 60 °C (see Figure 3b). Blue line: fast mode (smaller aggregates), orange line: slow mode (larger aggregates). 3.3. Preventingfast mode (smaller Gelation aggregates), and Long-Time orange Monitoring line: slow mode (larger aggregates). 3.3. PreventingOur other Gelation heating experimentsand Long-Time included Monitoring the rapid heating of two lysozyme samples (18 mg/mL 3.3. Preventing Gelation and Long-Time Monitoring and 30 mg/mL) to the projected unfolding temperature, 80 C. We explored the ﬁnding that the Our other heating experiments included the rapid heating◦ of two lysozyme samples (18 mg/mL emergenceOur other and growthheating ofexperiments aggregates isincluded signiﬁcantly the rapid faster heating that the of time two of lysozyme gelation. samples To prevent (18 gelation, mg/mL and 30 mg/mL) to the projected unfolding temperature, 80 °C. We explored the finding that the theand sample 30 mg/mL) was keptto the at thisprojected temperature unfolding for atemperature, short period 80 of time°C. We (30 explored min) following the finding fast cooling that the to emergence and growth of aggregates is significantly faster that the time of gelation. To prevent roomemergence temperature. and growth The samples of aggregates were then is keptsignificantl at roomy temperaturefaster that the and time monitored of gelation. with DLS To forprevent over gelation, the sample was kept at this temperature for a short period of time (30 min) following fast twogelation, weeks. the The sample DLS was results kept are at shown this temperature in Figures5 foandr a6 .short period of time (30 min) following fast cooling to room temperature. The samples were then kept at room temperature and monitored with cooling to room temperature. The samples were then kept at room temperature and monitored with DLS for over two weeks. The DLS results are shown in Figures 5 and 6. DLS for over two weeks. The DLS results are shown in Figures 5 and 6. Biomolecules 2020, 10, x FOR PEER REVIEW 7 of 14 Biomolecules 2020, 10, 1262 7 of 14 Biomolecules 2020, 10, x FOR PEER REVIEW 7 of 14 0.7 Before heating 0.7 Right after heating 0.6 BeforeDay 1 heating RightDay 2 after heating 0.6 DayDay 13 0.5 DayDay 26 DayDay 316 0.5 Day 6 0.4 Day 16

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0.1 0 100 101 0 Hydrodynamic radius (nm) 100 101 Hydrodynamic radius (nm) Figure 5. Long-term monitoring of the 18 mg/mL lysozyme solution via DLS. Solution was rapidly Figureheated 5. toLong-term the unfolding monitoring temperature of the of 18 80 mg °C/mL and lysozyme held there solution for 30 min via at DLS. this Solution temperature was rapidlyto trigger Figure 5. Long-term monitoring of the 18 mg/mL lysozyme solution via DLS. Solution was rapidly heatedaggregation. to the unfolding temperature of 80 ◦C and held there for 30 min at this temperature to heated to the unfolding temperature of 80 °C and held there for 30 min at this temperature to trigger trigger aggregation. aggregation. 0.35 Before heating 0.35 Right after heating BeforeDay 1 heating 0.3 RightDay 2 after heating DayDay 15 0.3 DayDay 215 Day 21 0.25 Day 5 Day 15 Day 21 0.25 0.2

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0.05 0 100 101 102 0 Hydrodynamic radius (nm) 100 101 102 Figure 6. Long-term monitoring of the 30Hydrodynamic mg/mL lysozyme radius solution (nm) via DLS. The solution rapidly Figure 6. Long-term monitoring of the 30 mg/mL lysozyme solution via DLS. The solution rapidly heated to the unfolding temperature of 80 ◦C and held there for 30 min at this temperature to heated to the unfolding temperature of 80 °C and held there for 30 min at this temperature to trigger triggerFigure aggregation. 6. Long-term monitoring of the 30 mg/mL lysozyme solution via DLS. The solution rapidly aggregation. heated to the unfolding temperature of 80 °C and held there for 30 min at this temperature to trigger In these figures the sequence of the line colors corresponds the sequence of monitoring days. aggregation. One canIn see these the formationfigures the of sequence polydisperse of the nanoscale line colors aggregates corresponds with gradual the sequence increase of of monitoring the contribution days. ofOne aggregates Incan these see with figuresthe the formation sizethe ofsequence 10–15 of nm.polydisperse of Notethe line that colorsnanosc this value correspondsale isaggregates close to the the sequencewith length gradual scale of thatmonitoring increase we interpret ofdays. the asOnecontribution a mesh can sizesee ofthe theaggregates formation gel network. with of thepolydisperse size of 10–15 nanosc nm. aleNote aggregates that this value with isgradual close to increasethe length of scale the contributionthatThe we averageinterpret of aggregates size as a of mesh aggregates with size theoffor the size the gel of 18 network. 10–15 mg/mL nm (Sample. Note that 1)and this 30value mg/ mLis close (Sample to the 2) length lysozyme scale solutionsthat we heatedinterpret for as 30 a minmesh in size 80 ◦ C,of cooledthe gel downnetwork. and monitored at room temperature as a function of Biomolecules 2020, 10, 1262 8 of 14 the monitoring time is presented in Figure7. The results are well described by the di ffusion-limited aggregation law [27,28]: R = R + At1/d f Biomolecules 2020, 10, x FOR PEER REVIEW 0 ,8 of (3) 14 where R0 is the initial radius of aggregates/monomers (1.6 and 1.5 nm, respectively), t is time, A is The average size of aggregates for the 18 mg/mL (Sample 1) and 30 mg/mL (Sample 2) lysozyme a constant and d f is the fractal dimension of aggregates (Table1). For both samples Equation (3) was fittedsolutions to the heated experimental for 30 min data in on80 °C, the cooled aggregate down size and as monitored a function ofat time,room withtemperature using the as MATLABa function of the monitoring time is presented in Figure 7. The results are well described by the diffusion-limited Levenberg-Marquardt algorithm. The data are consistent with the maximum fractal dimension, d f = 3, indicatingaggregation that law the [27,28]: lysozyme aggregates can be viewed as relatively compact spherical objects [29]. We find it not surprising that the ratio A2/A1 = =+1.65 is almost1/d f equal to the sample concentration ratio, R RAt0 , (3) namely 1.66.

18 mg/mL 2 30 mg/mL

0 0 5 10 15 20 days FigureFigure 7.7. Average hydrodynamic radius radius of of lysozyme lysozyme ag aggregatesgregates in in solutions solutions of of 18 18 mg/mL mg/mL and and 30 30mg/mL mg/mL samples, samples, as as a afunction function of of time. time. The The solid solid curves curves are are approximations approximations with with Equation Equation (3). (3).

Table 1. Fitting parameters in the diﬀusion-limited aggregation law, with d f = 3. where R0 is the initial radius of aggregates/monomers (1.6 and 1.5 nm, respectively), t is time, A is Concentration (mg/mL) Amplitude (A) Standard Deviation a constant and d is the fractal dimension of aggregates (Table 1). For both samples Equation (3) f 18 3.68 0.37 ± was fitted to the experimental30 data on the aggreg 6.07ate size as a function0.36 of time, with using the ± MATLAB Levenberg-Marquardt algorithm. The data are consistent with the maximum fractal = 3.4.dimension, Formation d off Polydisperse3 , indicating Aggregates that the lysozyme aggregates can be viewed as relatively compact

sphericalWe used objects the same[29]. We protocol find it of not measurements surprising that for athe more ratio concentrated 𝐴/𝐴 =1.65 solution, is almost 60 mgequal/mL to but the observedsample concentration a diﬀerent pattern ratio, of namely aggregation 1.66. phenomena. In addition to monomeric-like and mesoscopic (~10 nm) inhomogeneities, the sample reveals of formation of a broader spectrum of large aggregates Table 1. Fitting parameters in the diffusion-limited aggregation law, with = . growing from 200 nm to almost a micron (Figure8). However, these aggregates ared sof large3 that their growth is accompanied by gradual sedimentation, thus, upon a time, resulting in decreasing their Concentration (mg/mL) Amplitude (A) Standard Deviation contribution in the DLS correlation function. 18 3.68 ±0.37 30 6.07 ±0.36

3.4. Formation of Polydisperse Aggregates We used the same protocol of measurements for a more concentrated solution, 60 mg/mL but observed a different pattern of aggregation phenomena. In addition to monomeric-like and mesoscopic (~10 nm) inhomogeneities, the sample reveals of formation of a broader spectrum of large aggregates growing from 200 nm to almost a micron (Figure 8). However, these aggregates are so large that their growth is accompanied by gradual sedimentation, thus, upon a time, resulting in decreasing their contribution in the DLS correlation function. Biomolecules 2020, 10, 1262 9 of 14 Biomolecules 2020, 10, x FOR PEER REVIEW 9 of 14

0.7 Before heating Biomolecules 2020, 10, x FOR PEER REVIEW 9 of 14 0.6 Right after heating Day 1 0.7 Day3 0.5 DayBefore 7 heating 0.6 DayRight 24 after heating Day 1 0.4 Day3 0.5 Day 7 Day 24 0.3 0.4 Intensity (a.u)

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0 0.1 100 101 102 103 0 Hydrodynamic radius (nm) 100 101 102 103 FigureFigure 8. 8.DLS DLS size size distribution distribution analysis analysis of ofHydrodynamic a a 60 60 mg mg/mL/mL lysozyme lyradiussozyme (nm) sample sample heated heated for for 30 30 min min at at 80 80◦ C°C to to trigger aggregation and monitored for 24 days. triggerFigure aggregation 8. DLS sizeand distribution monitored analysis for 24 days. of a 60 mg/mL lysozyme sample heated for 30 min at 80 °C to Proteinstrigger may undergoaggregation oxidative and monitored or enzymatic for 24 days. degradation over a long time of incubation. This is an Proteins may undergo oxidative or enzymatic degradation over a long time of incubation. This important issue that we have considered seriously. Indeed, according to the work of Avanti et al. [30], is an importantProteins issue may that undergo we have oxidative considered or enzymatic seriously. degr adationIndeed, over according a long time to the of incubation.work of Avanti This et a heat stressed lysozyme loses about 60% of its activity after 3 weeks of incubation due to degradation. al. [30],is aan heat important stressed issue lysozyme that we have loses considered about 60% seri ofously. its activity Indeed, afteraccording 3 weeks to the of work incubation of Avanti due et to While it is certainly probable that our samples undergo degradation, while being kept at room degradation.al. [30], Whilea heat itstressed is certainly lysozyme probable loses about that our60% samples of its activity undergo after degradation,3 weeks of incubation while being due to kept temperature during a long period of time, we tried to minimize this effect by filtering samples by at roomdegradation. temperature While during it is acertainly long period probable of time, that ourwe triedsamples to minimizeundergo degradation, this effect by while filtering being samples kept a 20 nmat pore room size temperature filter to remove during a any long bacteria period of from time, thewe tried solution. to minimize Buffers this were effect degassed by filtering prior samples to use, by a 20 nm pore size filter to remove any bacteria from the solution. Buffers were degassed prior to so the amountby a 20 ofnm oxygen pore size in thefilter solution to remove was any minimized. bacteria from However, the solution. some Buffers degradation were degassed was still prior possible. to use, so the amount of oxygen in the solution was minimized. However, some degradation was still Therefore,use, to so test the theamount effect of ofoxygen lysozyme’s in the solution degradation was minimized. on the aggregation, However, some a 60 degradation mg/mL sample was still was possible.possible. Therefore, Therefore, to test to testthe theeffect effect of oflysozyme’s lysozyme’s degradation degradation on thethe aggregation, aggregation, a 60a 60mg/mL mg/mL kept at 80 ◦C for 10 min, quickly cooled down to room temperature and was monitored over three samplesample was kept was atkept 80 at°C 80 for °C 10for min, 10 min, quickly quickly cooled cooled down down to to roomroom temperaturetemperature and and was was monitored monitored weeks. The amount of aggregates formed during that period, was so small that was hardly detectable over threeover weeks.three weeks. The amountThe amount of aggregates of aggregates formed formed during during that that period, was was so so small small that that was was hardly hardly (Figure9). Additionally, an SDS-PAGE gel analysis (illustrated in Figure 10) on both heated and detectabledetectable (Figure (Figure 9). Additionally, 9). Additionally, an anSDS-PAGE SDS-PAGE gel gel analysisanalysis (illustrated in in Figure Figure 10) 10) on onboth both unheated 30 mg/mL samples confirmed the absence of protein’s degradation during the experiments, heatedheated and unheated and unheated 30 mg/mL 30 mg/mL samples samples confirmed confirmed the the absence absence of protein’s degradation degradation during during the the as no lower molecular weight fragments was observed, while some protein dimers and trimers were experiments,experiments, as no as lower no lower molecular molecular weight weight fragments fragments was was observed, observed, whilewhile some some protein protein dimers dimers and and detected in heated samples. We conclude that the aggregation mechanism in our study is insignificantly trimerstrimers were detectedwere detected in heated in heated samples. samples. We We conclude conclude that that the the aggregationaggregation mechanism mechanism in ourin our study study affectedis by insignificantly lysozyme degradation. affected by lysozyme degradation. is insignificantly affected by lysozyme degradation.

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0.1 0.2

0 0.1 100 101 102 Hydrodynamic radius (nm)

0 Figure 9. DLS distribution analysis100 of a 60 mg/mL10 lysozyme1 sample10 heated2 for 10 min at 80 ◦C to Figure 9. DLS distribution analysis ofHydrodynamic a 60 mg/mL radius lysozyme (nm) sample heated for 10 min at 80 ℃ to screen thescreen eﬀect the of effect heating of heating on the on aggregation the aggregation process. process. Figure 9. DLS distribution analysis of a 60 mg/mL lysozyme sample heated for 10 min at 80 ℃ to screen the effect of heating on the aggregation process. Biomolecules 2020, 10, 1262 10 of 14 Biomolecules 2020, 10, x FOR PEER REVIEW 10 of 14

Figure 10. SDS-PAGEFigure 10. SDS-PAGE gel image gel image for Lysozyme for Lysozyme (30 (30 mg/mL) mg/mL) incubated incubated at room at temperature room temperature for three for three weeks priorweeks running prior therunning gel. the Left gel. Left to right:to right: 1.1. Ladd Ladderer (From (From the bottom the bottom10, 15, 20, 10,25, 37, 15, 50 20,kDa). 25, 2. 37, 50 kDa). Sample unheated. 3. Sample heated to 80 °C. 4. Sample unheated, then incubated at 95 °C for 5 min 2. Sample unheated.prior running 3. Samplethe gel. 5. heatedSample heated to 80 to◦ C.80 °C, 4. th Sampleen incubated unheated, at 95 °C for then 5 min incubated prior running at 95the ◦C for 5 min prior runninggel. the gel. 5. Sample heated to 80 ◦C, then incubated at 95 ◦C for 5 min prior running the gel. 4. Discussion 4. Discussion Globular proteins may undergo structural changes due to partial unfolding when being exposed to a higher temperature, even below its true denaturation point. As a result, normally buried Globularhydrophobic proteins residues may undergo may act as structural a crosslinker changes for intermolecular due to partialbeta-sheet unfolding structures and when lead beingto exposed to a higherformation temperature, of aggregates even of below different its shapes, true glob denaturationular or amyloid point. like, depending As a result,on the solution normally buried conditions [16,31,32]. Continuous heating leads to association of aggregates and subsequent hydrophobic residues may act as a crosslinker for intermolecular beta-sheet structures and lead to formation of a gel network [16–18,32,33]. formation of aggregatesBased on our of findings, different we shapes,can qualitatively globular suggest or amyloida mechanism like, of aggregation depending that onwe the solution conditions [16observed,31,32]. in Continuouslysozyme samples heating treated leads under to diff associationerent heating of protocols. aggregates Lysozyme and at subsequent low ionic formation strength (20 mM) and nearly neutral pH unfolds at a temperature around 80 ℃ [22]. of a gel network [16–18,32,33]. We estimate the fraction of unfolded lysozyme molecules, φ , as a function of temperature Based on our findings, we can qualitativelyΔ suggest a mechanism of aggregation that we observed through the enthalpy of folding/unfolding, H0 (kJ/mol), at the “melting” temperatureT0 , defined in lysozyme samplesto be the temperature treated under at which di fftheerent fraction heating of fold protocols.ed and unfolded Lysozyme lysozymeat is lowequal. ionic In the strength first (20 mM) and nearly neutralapproximation, pH unfolds we obtain: at a temperature around 80 ◦C[22]. We estimate the fraction of unfoldedΔ lysozyme molecules,φ φ, as a function of temperature through H0 11 −=ln . (4) the enthalpy of folding/unfolding, ∆H0 (kJ/mol), at the “melting”−φ temperature T0, defined to be the kTTB 0 1 temperature at which the fraction of folded and unfolded lysozyme is equal. In the first approximation, According to References [22,34,35], the enthalpy of lysozyme unfolding varies between 200 and we obtain: ! 600 kJ/mol, depending on experiment∆Hal techniques1 1 and buffer φconditions. In Figure 11 we present the fraction of unfolded lysozyme, calculated0 from= lnEquation .(4), with adopted values of (4) Δ=H 540 kJ/mol and TC = 80 kB T − T0 1 φ 00 [34]. In this adoption− we neglect a dependence of Δ AccordingH00 to and References T on lysozyme [22 concentration.,34,35], the enthalpy of lysozyme unfolding varies between 200 and 600 kJ/mol, depending on experimental techniques and buffer conditions. In Figure 11 we present the fraction of unfolded lysozyme, calculated from Equation (4), with adopted values of ∆H0 = 540 kJ/mol and T0 = 80 ◦C [34]. In this adoption we neglect a dependence of ∆H0 and T0 on lysozyme concentration.Biomolecules 2020, 10, x FOR PEER REVIEW 11 of 14

Figure 11.FigureFraction 11. Fraction of unfolded of unfolded lysozyme lysozyme as as a function a function of temperature. of temperature.

In the hierarchy of times scales, the lysozyme interconversion rate is fastest (overall folding time is of the order of 1 s) [36,37], while characteristic times of the motion of molecular segments could be of the order of 1 𝜇𝑠 [38]. Then a relatively lower rate of aggregation follows. The rate of gelation is the slowest and strongly depends on concentration and temperature. Our experiments on a 20 mg/mL sample showed that at 60 °C it took up to 90 h to observe a distinct gel state. The lower the temperature, the smaller the fraction of unfolded lysozyme molecules, the smaller the probability of aggregation and larger the time of gelation. As estimated with Equation (4), the fraction of the unfolded molecules at 60 °C could be as small as 210%. Nevertheless, these molecules serve as seeds of nucleation to form growing aggregates and eventually a gel network. We must note that even an extremely small number of mesoscopic aggregates could make a significant contribution to the DLS correlation function because light scattering intensity strongly depends on the size, especially at small scattering angles. The reaction coordinate, the fraction of unfolded protein molecules, exhibit thermal fluctuations around its “chemical reaction” equilibrium value. The average amplitude and lifetime of these fluctuations depend on the thermodynamic conditions and can be found by statistical thermodynamics. However, because the distribution of the fluctuations in space and time is Gaussian, occasionally, during a long observation time, the deviations in concentration of the unfolded protein from the equilibrium value, could become significant and hence initiate the gelation process. The analysis of the correlation function of gel formed by heating lysozyme solutions ~20 °C below the melting temperature over a long period of time indicates the presence of diffusion relaxation in the gel. In this work we did not address the interesting dynamic properties of gels, which would require a more detailed DLS experiments and analysis. We just note that the correlation function of density/concentration fluctuations in gel can exhibit a compressed exponential decay [16,33]. The observed relaxation modes can be attributed to concentration fluctuations of the aggregates which are not a part of gel network, branching points, segments and restructuring of the gel [31,32,39]. In case of the extremely fragile lysozyme gel, the diffusive inhomogeneities with the sizes ~15–20 and ~100 nm (Figure 2c, red curves), could be interpreted as a branch/mesh pattern forming the gel network (smaller size) and separate aggregates (larger size) diffusing across the network. Biomolecules 2020, 10, 1262 11 of 14

In the hierarchy of times scales, the lysozyme interconversion rate is fastest (overall folding time is of the order of 1 s) [36,37], while characteristic times of the motion of molecular segments could be of the order of 1 µs [38]. Then a relatively lower rate of aggregation follows. The rate of gelation is the slowest and strongly depends on concentration and temperature. Our experiments on a 20 mg/mL sample showed that at 60 ◦C it took up to 90 h to observe a distinct gel state. The lower the temperature, the smaller the fraction of unfolded lysozyme molecules, the smaller the probability of aggregation and larger the time of gelation. As estimated with Equation (4), the fraction of the unfolded molecules at 60 C could be as small as 2 10 3%. Nevertheless, these molecules serve as seeds of nucleation to ◦ × − form growing aggregates and eventually a gel network. We must note that even an extremely small number of mesoscopic aggregates could make a significant contribution to the DLS correlation function because light scattering intensity strongly depends on the size, especially at small scattering angles. The reaction coordinate, the fraction of unfolded protein molecules, exhibit thermal fluctuations around its “chemical reaction” equilibrium value. The average amplitude and lifetime of these fluctuations depend on the thermodynamic conditions and can be found by statistical thermodynamics. However, because the distribution of the fluctuations in space and time is Gaussian, occasionally, during a long observation time, the deviations in concentration of the unfolded protein from the equilibrium value, could become significant and hence initiate the gelation process. The analysis of the correlation function of gel formed by heating lysozyme solutions ~20 ◦C below the melting temperature over a long period of time indicates the presence of diffusion relaxation in the gel. In this work we did not address the interesting dynamic properties of gels, which would require a more detailed DLS experiments and analysis. We just note that the correlation function of density/concentration fluctuations in gel can exhibit a compressed exponential decay [16,33]. The observed relaxation modes can be attributed to concentration fluctuations of the aggregates which are not a part of gel network, branching points, segments and restructuring of the gel [31,32,39]. In case of the extremely fragile lysozyme gel, the diffusive inhomogeneities with the sizes ~15–20 and ~100 nm (Figure2c, red curves), could be interpreted as a branch /mesh pattern forming the gel network (smaller size) and separate aggregates (larger size) diffusing across the network.

5. Conclusions In this work, the role of equilibrium unfolding as the main driving force for protein aggregation at elevated temperatures is clarified. While monomeric lysozyme molecules do not have a propensity to form detectable aggregates for a long period of time [24], increasing the temperature and shifting the equilibrium to marginally unfolded protein leads to the emergence of aggregate seeds. These seeds can either rapidly grow if heated continuously or undergo a slow diffusion limited aggregation over a long time of monitoring. Our results resonate with the observations of previous investigators on aggregation phenomena in lysozyme solutions. The importance of driving forces for aggregation at physiological temperatures was emphasized in the work of Vekilov et al. [23], where the presence of transient dimers of lysozyme was found. Also, according to Strander et al. [10], at the same ionic strength and pH, the presence of short-range attractions and long-range repulsions leads to the formation of dense liquid phases in lysozyme solutions. The reported clusters have an aggregation number between 2–7 monomers per cluster at the range of concentrations of 50–100 mg/mL. DLS was not able to detect the presence of such clusters. The lack of DLS ability for the detection of these clusters can be because of the short lifetime of the clusters and/or their small population. However, although these clusters have a very small population, they may be involved in the formation of larger observed aggregates. According to References [40–42], amyloid aggregates can eventually form a viscoelastic gel solution. Since the time scale of gel formation is much longer than the folding/unfolding interconversion and aggregation, the aggregation is a required step for the gel formation. A fundamental, yet unexplored problem that could be addressed in further experimental and theoretical studies, would be a possible role of fluctuations of unfolded molecular states near the interconversion equilibrium. Protein molecules Biomolecules 2020, 10, 1262 12 of 14 can fluctuate between their alternative states and eventually bind to each other and form aggregates. Fluctuation-induced aggregation [43] and, more recently, fluctuation-induced phase transitions [44] have been discussed with respect to the phase behavior of classical colloids. It would be interesting to investigate this effect with respect to aggregation of proteins.

Author Contributions: S.N. performed sample preparation, a part of dynamic light scattering measurements, analyzed the data, and wrote the manuscript. E.V.J. performed the dynamic light scattering measurements. M.A.A. conceived the project and wrote the manuscript. T.J.W. wrote the manuscript. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by American Chemical Society Petroleum Research Fund, Grant no. 59 434-ND6. M.A.A. acknowledges the National Science Foundation, award number 1856479, for the support of his research. T.J.W. acknowledges partial funding from the Maryland Industrial Partnerships program. Acknowledgments: The authors thank Peter Vekilov (University of Houston) and Irina Nesmelova (University of North Carolina, Charlotte) for discussions and advising on the issue of mesoscopic aggregation in lysozyme solutions. The authors are also indebted to Venkatesh Ranjan (University of North Carolina, Charlotte) for running the SDS-PAGE gel and Louis Coplan (University of Maryland, College Park) for reading the manuscript and making useful suggestions. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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