Using light scattering and Atomic Force Microscopy techniques, we have studied the kinetics and equilibrium scattering intensity of collagen association, which is pertinent to the vitreous of the human eye. Specifically, we have characterized fibrillization dependence on pH, temperature, and ionic strength. At higher and lower pH, collagen triple helices remain stable in solution without fibrillization. At physiological pH, fibrillization occurs and the fibril growth is slowed upon either an increase in ionic strength or a decrease in temperature. The total light scattering with respect to ionic strength is non-monotonic in these conditions as a result of a competing dependence of fibril concentration and size on ionic strength. Fibril concentration is the highest at lower ionic strengths and rapidly decays for higher ionic strengths. On the other hand, fibril size is larger in solutions with higher ionic strength. We present a theoretical model, based on dipolar interactions in solutions, to describe the observed electrostatic nature of collagen assembly. At extreme pH values, either very low or very high, collagen triple helices carry a large net charge of the same sign preventing their assembly into fibrils. At intermediate pH values, fluctuations in the charge distribution of the collagen triple helices around roughly zero net charge lead to fibrillization. The growth kinetics of fibrils in this regime can be adequately described by dipolar interactions arising from charge fluctuations.
The structure and concentration of collagen fibrils are essential for the support of animal tissues and depend on the specifics of the self-assembly mechanism. Without the rigid collagen fibrils, the vitreous in the eye and the cartilage in the knee are primarily composed of hyaluronic acid, which is a highly swollen soft hydrogel, and would fail mechanically at an early age. It has been previously shown that the electrostatic environment affects the final structure and the kinetics of collagen fibril formation, but the extent of the contribution, such as how ionic strength and pH influence the kinetics of fibril formation and the equilibrium concentration of fibrils, remains unclear.1,2
In this paper, we address the role of electrostatics on the structure and kinetics of fibrillar assemblies of collagen type II. Out of the 28 different collagens, collagen types I, II, III, V, and XI self-assemble into fibrils in a staggered way.3–6 Protein subunits that form fibrils are triple helices, in which three peptide chains are hydrogen bonded together. Each of the collagens type I, II, III, V, and XI has a unique structure.5,7–15 Collagen type II is a triple helix with three identical left-handed helical chains that are hydrogen-bonded together in a right-handed manner. The rigid molecule is 1.5 nm in diameter and 300 nm in length. Every chain contains the repeating amino acid sequence Gly-X-Y, with Pro and Hyp mainly occupying the X and Y positions. The glycine residues are responsible for the stability of the triple helix through hydrogen bonds (N–H O=C) and are buried, facing into the triple helix axis. By contrast, the rest of the X and Y residues are highly exposed to the solvent and are responsible for maintaining the collagen fibril structure.4,14 Approximately 18% of the overall amino acid sequence is ionizable and the isoelectric point of collagen type II is at pH 8.5. Charged residues such as Lys, Glu, and Arg are asymmetrically distributed along the molecule, but about 40% of every Gly-X-Y triplet has at least three positive or negative charges at pH 7.4 (Fig. 1).16,17 Positive residues are more often found in the Y positions, and the negative residues are more often found in the X positions.16,18,19 At the ends of each collagen type II triple helix, there are globular domains. These domains are mainly responsible for covalently linking the collagen fibril assemblies together and are unnecessary for fibril formation.20
The surface charge of collagen type II triple helices is highly dependent on the pH of the solution (Fig. 1). From the theoretical titration curve based on the pKas of the charged residues, at pH below 4, the collagen triple helix surface charge density is composed entirely of positive charges, with a linear charge density of 1.15 positive charges/nm in the helical region. And at pH above 10, the collagen triple helix surface charge is negative, with a charge density of 1.08 negative charges/nm in the helical region. At intermediate pH (4 < pH < 10), the collagen type II triple helix region is decorated with both positive and negative ions. At pH 4, there are 345 positive and 324 negative ionized residues. At pH 5, there are 345 positive and 324 negative ionized residues. At pH 6-8, there are 336 positive and 324 negative residues. At pH 9, the charge density becomes negative, with 318 positive and 324 negative ionized residues.
Collagen is organized in a very specific way within the fibrils. The triple helices wind around each other in a staggered, quasi-hexagonal manner. From X-ray scattering data, Hulmes et al.,6 Ottani et al.,12 Orgel et al.,9 Holmes and Kadler,21 and Antipova and Orgel10 have deduced the radial and lateral order for collagen fibrils. Laterally, collagen triple helices associate in a staggered way. For collagen type II, Antipova and Orgel10 have found that the stagger length is 234 amino acids. Hulmes et al.6 have found that radially, the triple helices are arranged in lateral unit cells which contain five collagen triple helices in cross section. They have found a radial periodicity outward from the center that corresponds to ∼4 nm, which they attribute to the concentric organization of collagen bundles. Data by Holmes and Kadler,21 Ottani et al.12 and Hulmes et al.6 argue that collagen molecules are arranged in a helical way such that the molecules are titled obliquely in plane, oriented 30° to the fibril surface.
Collagen type II is specifically important for reinforcing the mammalian extracellular matrix. Despite its ubiquity, data describing the mechanism for collagen type II assemblies are incomplete and are limited to comparisons to a much more widely studied protein, collagen type I.4,22–24 There are substantial differences between collagen type I and collagen type II. Although both molecules share the Gly-X-Y triplet motif, each has a unique amino acid composition and surface charge density. The total number of ionizable groups for collagen type I triple-helix is 535 amino acids and for collagen type II is 669 amino acids. Collagen type I has a lower isoelectric point at pH 7.2, whereas collagen type II is net neutral at pH 8.5. Fibrillization is faster for collagen type II, suggesting that the intermolecular interactions are much stronger for this molecule than for collagen type I.23 Most significantly, collagen type II is a symmetric triple helix, made up of three hydrogen bonded peptides of the same amino acid sequence.
By observing the temperature dependence of the critical concentration for fibril formation, Kadler and Prockops20 and Cooper25 estimated both the enthalpic and entropic contributions to collagen type I fibril formation. They found that the total Gibbs free energy of fibril formation at a fairly high ionic strength of 0.2M is −13 kcal/mol, with the enthalpic contribution of 53 kcal/mol and the entropic contribution of 220 kcal/mol. While Cooper25 noticed a solubility increase of collagen type I triple helices with salt concentration, he was unable to quantify the effect due to experimental limitations. Cassel26 and Silver27 made a distinction between lateral and linear growth of collagen type I fibrils, and argued that the two growth steps have different mechanisms. The smaller microfibers assemble through electrostatic interactions and then bundle together in an entropically driven process. Both steps are essential for stabilizing collagen fibrils.
It is generally agreed upon that electrostatic interactions contribute to the fibrillization process, but the specifics of this process are unclear and are still controversial. It has been postulated that the relatively high amphiphilic charge density on the surface of collagen type I triple helices has to contribute to the intermolecular ion-pair formation.2,16,18,27–29 The large number of charged residues has made it difficult to isolate and determine specific interactions. From rheological studies at lower ionic strengths, at which there is no optical evidence of fibril formation, Cassel noted an increased viscosity at neutral pH and low NaCl concentrations relative to solutions of soluble triple helices.26 This evidence for extremely thin microfibers in non-ionic solutions suggests some ionic complexation for collagen type I. From the collagen type I amino acid sequence, Silver27 proposed a mechanism for the charged pair interactions in collagen fibers, suggesting that there are on the order of 40–150 intermolecular charge pairs in physiological conditions that can stabilize collagen assembles. By contrast, Wallace2 estimated the contribution of the charged pair interactions for collagen type I assemblies by applying a model for the total electrostatic interactions present in the assembly. He estimated that the driving force will be due to ion-pairs between two collagen molecules and that the electrostatic contribution to the overall bulk energy of formation is about −1 kcal/mol or one charged pair per triple-helix pair. Still, no such data are available for collagen type II fibrils.
To elucidate the contribution of electrostatic interactions on collagen type II fibrillization, we have studied the effects of monovalent salt concentration (0.006M–0.5M) and pH (2-10) on both the kinetics of fiber formation and the equilibrium fibril size and concentration. Using turbidity measurements in tandem with more sensitive and higher-resolution techniques such as picro-sirius red staining and dynamic light scattering (DLS), we are able to gauge the solubility of collagen for broad salt and pH ranges. We find that electrostatic interactions contribute heavily to fibril formation at intermediate pH.
II. MATERIALS AND METHODS
In all experiments, we have used purified soluble type II collagen from bovine nasal septum (EPC Elastin Products CN276). Collagen solutions were kept at 4 °C until the use and re-made on a weekly basis to avoid denaturation. Soluble triple helix solutions were prepared in 0.012M HCl. All other solutions were made using a phosphate buffer, 0.1M NaOH, and 1M NaCl. Samples contained 0.2 mM of 7.4 pH phosphate buffer to stabilize pH, which was tuned by adding 0.1M NaOH. All salts were purchased at Sigma-Aldrich.
B. Static light scattering (SLS)
Static light scattering (SLS) is used to determine the weight-averaged molecular weight , radius of gyration Rg, and the second virial coefficient A2 for soluble collagen. For dilute solutions, the scattered intensity of the solution depends on both the concentration and the structure factor.30–32 In our experiments, collagen was dissolved directly into 0.012M HCl and 0.001M NaOH with 0, 0.1, and 1M NaCl. The prepared solutions were filtered with a 0.8 μm PES filter into cleaned 10 mm diameter borosilicate glass tubes. Each sample was then placed in a xylene bath to index-match the glass. The sample was illuminated with a 2W 514.5 nm Argon laser working approximately at 400 mW, and the scattered intensity was picked up with a photo-multiplier tube attached to an ALV goniometer arm. The intensity was time averaged for 30 s at each angle (30°-120° for our experiment).
We define turbidity τ as the total scattered intensity which, according to Doty and Steiner,33 is calculated by integrating the scattered intensity over all possible directions at an angle, θ, between the beam and the scattering direction,
for an incident beam of intensity Iin, the scattered intensity Iout, distance between the scattering cross section and the detector d, and a sample of thickness ℓ.34 For long, thin fibers, Eq. (1) depends on the concentration and the mass-length ratio of the fibers.34–36
Turbidity measurements were done using a Hitachi u-3010 spectrophotometer. Each solution was pre-warmed using a water-bath heated metal sample holder before the addition of 0.01M HCl 1 mg/ml collagen stock solution at the required pH and salt concentrations. The temperature was monitored using a thermo-couple attached to the bottom of the glass sample holder. Turbidity was measured every 2 s at 600 nm.
D. Ionic strength
The ionic strength recorded for all solutions was calculated from the estimated amount of both the phosphate and the monovalent salt concentration in the solution using
where ci is the molar concentration of ionic species i, and zi is the valency of the i-type ion. The inverse Debye screening length κ depends on according to
where e is the electronic charge, ϵ0 is the permittivity of vacuum, ϵ is the dielectric constant of the solution, and kBT is the Boltzmann constant times absolute temperature. We note that we are limited on the lowest ionic strength in neutral conditions because we start with a solution of collagen in 0.012M HCl, which we neutralize with NaOH and phosphate buffer.
E. Dynamic light scattering (DLS)
Dynamic light scattering (DLS) was used to analyze collagen solutions that did not show any turbidity change. DLS was measured on the same samples as prepared for SLS. The time signal was correlated using the ALV-5000/E correlator. The intensities were correlated at an angle range of 30°–50° at 5-degree intervals, and at an angle range of 60°–90° with 10° intervals, so that the corresponding q range is 8.41 × 106–2.3 × 107 m−1.37,38 The normalized intensity correlations (g2) showed expected decays, from which relaxation times as a function of scattering wave vector were determined.
The data were analyzed using both single exponential fits and CONTIN analysis. CONTIN was used to evaluate the polydispersity in the sample by re-formulating the electric field auto-correlations (g1) as a sum of exponentials. Each exponential is multiplied by its weight,39
There are two ways to determine the decay time of g1 and therefore the decay time of the experimentally achievable g2. First is the cumulant analysis, for which we can model a single component system as , where μ2 is the variance. The second method is the CONTIN analysis, for which we take the inverse transform of Eq. (4) to calculate the function (Γ). From this, the distribution function of decay times A(b) is obtained, which we can relate to the most probable decay time.
For all Atomic Force Microscopy (AFM) imaging experiments, collagen solutions were incubated at 37 °C for 48 h to ensure that the reaction has reached completion. A 10 μL droplet of each sample was deposited on a freshly cleaved mica substrate for 10 min in a humid environment to avoid solution evaporation. The mica was then washed gently with de-ionized filtered water (Milli-q 12.8 MΩ) to avoid salt crystallization on the substrate surface. Finally the samples were air-dried. All collagen samples were imaged using Digital Instrument AFM, model Dimension-3000, with a App Nano ACT-R-W Tapping Mode Probe tip. The tip radius is <10 nm with a nominal frequency in air of about 200–400 KHz and a spring constant on an order of 25–75 N/m. The samples were imaged in a dry environment using the tapping mode.
G. Determination of fiber concentration
Spectrophotometry techniques have been used extensively for the determination of soluble collagen in solution.25,40 The concentration of soluble collagen in solution was determined using a Sirius red F3B stain (1 g/L in water) (Polysciences, Inc.). To quantify the concentration of collagen that has not formed fibrils after a 48 h incubation at a constant temperature and salt concentration, collagen fibril solutions were first centrifuged at 20 000 rpm for 15 min. During centrifugation, the fibrils are separated from the solution of soluble collagen in the supernatant. The supernatant was removed and filtered using a 0.45 μm PES Millipore filter into a solution of 0.45 ml picro-sirius red stain and 0.1 ml 0.12M HCl. Collagen precipitates as it complexes with the dye. After 20 min of incubation time at room temperature, the resulting precipitate was spun down at 20 000 RPM for 15 min. To get rid of excess dye, the precipitate was washed with 0.012M HCl and spun down again at 20 000 RPM for 15 min. Then the supernatant was removed and the precipitated collagen was solubilized using a 0.1M NaOH solution. The absorption of the basic solution is related to the concentration of collagen complexed with the dye and determined by a calibrated standard curve. For the calibration curve, solutions with an exact concentration of collagen were precipitated by the dye solution and re-dissolved in 0.1M NaOH. The fiber concentration and the concentration of soluble triple helices are assumed to be additive. Therefore to calculate the former quantity, the concentration of soluble triple helices was subtracted from the initial bulk concentration of 0.189 g/L.
A. High and low pH
Collagen type II is highly decorated with both positively and negatively ionizable amino acid groups. As shown in Fig. 1, the counterion dissociation of these groups is strongly pH dependent. At pH lower than 4, the total charge on the collagen triple helix is large and positive, and at pH greater than 9, the total charge is large and negative. Assembly becomes strongly unfavorable for homogenously charged molecules. Using DLS and SLS, we confirm that collagen triple helices are not self-associating at pH < 2 and >10, independent of the salt concentration.
We show the Zimm plot for collagen dissolved in pH 2 with 0 M added NaCl in Fig. 2(a) and tabulate the results in Table I. From the extrapolated q = 0 and c = 0 lines, = 248 000 g/mol, Rg = 81 nm, and A2 = 2 × 10−3 mL mol/g2. The molecular weight is consistent with the expected molecular weight of a collagen triple helix and is close to the theoretically predicted Rg for a rigid rod of 300 nm in length and 1.5 nm in diameter. The radius of gyration of a dense cylinder of radius r and length L is given by . For collagen type II triple helices, with a diameter of 1.5 nm, and a length of 300 nm, Rg is predicted to be 86 nm. The experimental value is consistent with this prediction.
|NaCl (M) .||Rg (nm) .||(kg/mol) .||A2 (mL mol/g2) .||D (m2/s) .||Rh (nm) .||Rg/Rh .||ℓp (nm) .|
|0||81 ± 5||248||2 × 10−3||7.9 ± 0.44 × 10−12||29 ± 2||2.8||60|
|0.1||74 ± 5||248||4 × 10−4||7.1 ± 0.56 × 10−12||32 ± 2||2.2||47|
|NaCl (M) .||Rg (nm) .||(kg/mol) .||A2 (mL mol/g2) .||D (m2/s) .||Rh (nm) .||Rg/Rh .||ℓp (nm) .|
|0||81 ± 5||248||2 × 10−3||7.9 ± 0.44 × 10−12||29 ± 2||2.8||60|
|0.1||74 ± 5||248||4 × 10−4||7.1 ± 0.56 × 10−12||32 ± 2||2.2||47|
The Zimm plot at pH 2 with 0.1M NaCl is qualitatively similar, but the added salt gives rise to a few major differences [Fig. 2(b)]. As expected, the molecular weight remains the same at 24 800 g/mol (Table I). On the other hand, both Rg and A2 decrease with added salt. At 0.1M NaCl, Rg = 74 nm, and A2 = 4 × 10−4 mL mol/g2.
Broersma41 predicted the expected Rh for this geometry as , from which the diffusion coefficient follows from the Stokes-Einstein equation. For collagen type II triple helices, the expected diffusion coefficient is 7.4 × 10−12 m2/s. DLS shows that the intensity autocorrelation at pH 2 with 0M added NaCl and with 0.1M added NaCl has a single relaxation time [Figs. 2(c) and 2(d) and Table I]. The relaxation rate is a linear function of q2, and from the slope, we determine the diffusion coefficient. D (Table I) is consistent with the predicted diffusion coefficient for rigid rods 300 nm in length and 1.5 nm in diameter. From the diffusion coefficient, we determine Rh (Table I) for collagen triple helices in pH 2 with 0M added NaCl and 0.1M added NaCl. In pH 2 solutions with 0.25M NaCl, the diffusion coefficient is slightly higher at 8.8 × 10−12 m2/s, corresponding to a slightly lower Rh of 26 nm. As expected from the charge density calculations shown in Fig. 1, collagen triple helices are soluble in pH 2 solutions, regardless of the ionic strength.
The results are consistent in the other extreme as well in pH 10 solutions. The measured diffusion coefficient is 6.4 ± 0.56 × 10−12 m2/s in solution with 0M added NaCl and increases to 8.1 and 7.9 × 10−12 m2/s in solutions with 0.1M added NaCl and 0.25M added NaCl. The determined Rh values are 36 ± 2 nm for 0M NaCl, pH 10, 28 nm for 0.1M NaCl, pH10, and 29 nm for 0.25M NaCl, pH 10.
The decrease in Rg, Rh, and A2 with added salt is consistent with a homogeneous charge on the surface of collagen triple helices [Fig. 1(b)]. In dilute conditions, the second virial coefficient is related to collagen-collagen interactions mediated by the solvent and salt molecules. For homogeneously charged proteins, repulsive charge interactions contribute to the magnitude of A2. At lower salt concentrations, as expected from Debye-Hückel theory, the repulsive charge interactions are long range, which lead to a larger positive A2. With added salt, the electrostatic interactions are screened and A2 decreases. The decrease in Rg is consistent with the polyelectrolyte effect. At low ionic strengths, the homogeneous charge density stretches the molecule out. With added salt, collagen triple helices relax. We quantify this effect by determining the persistence length (ℓp) of collagen triple helices using the Kratky-Porod equation,42
where L is the contour length of the molecule. Without salt, ℓp is equal to 60 nm, and with salt, it drops to 47 nm. These results are consistent with the shape (ρ = Rg/Rh) of collagen triple helices (Table I). In solutions without salt, ρ is equal to 2.8, which is consistent with almost rod-like extended molecules. With the addition of salt, ρ drops to 2.2, which is consistent with a less rod-like shape. Both static and dynamic light scattering results suggest that at extreme pH, the solubility of collagen triple helices is a result of a homogeneous charge density.
B. Intermediate pH
At intermediate pH (4-9), both positive and negative amino acids are ionizable, reducing the total surface charge and at the same time increasing the possibility of dipolar interactions [Fig. 1(b)]. At these conditions, collagen triple helices rapidly self-assemble into fibrils, microns in length, and hundreds of nanometers in diameter. DLS and SLS become completely unfeasible in this case because the solutions quickly become cloudy and inhomogeneous. In Fig. 3, we quantify the total scattering intensity after 48 h at 37 °C as a function of pH and ionic strength turbidimetrically. This technique measures the total scattered light from a solution at a chosen wavelength and depends on the size and concentration of the scattering species relative to a background [Eq. (2)]. Surprisingly, turbidity at 37 °C in the intermediate pH range is a non-monotonic function of ionic strength, with a peak close to the physiological salt concentration ∼150 mM. At lower ionic strengths, the turbidity is low but present. The value reaches a maximum at around ∼0.1M and decays rapidly to zero. At above 0.2M, we no longer observe an optical change in the sample. The maximum has a slight pH dependence: turbidity peaks at higher ionic strengths for lower pH solutions. For pH 7.2, at 6 mM, solution turbidity after 48 h is 0.003 ± 0.001 and peaks at 0.049 ± 0.004 in 116 mM [I]. The trends are similar for pH 6.2, 8, and 9. For pH 6.2, turbidity peaks at 0.045 ± 0.004 in 156 mM [I], and for pH 8 and pH 9, the turbidity peaks at 0.043 ± 0.004 in 116 mM [I] and 0.062 ± 0.004 in 116 mM [I], respectively. In all solutions, τ decreases for ionic strengths above 150 mM and is undetectable above 250 mM. As expected at high and low pH solutions, we do not observe any change in the scattering intensity for ionic strengths up to 0.25M NaCl.
It is striking that the maximum turbidity at 37 °C and 7.4 pH is almost at the human body ionic strength (0.15M), but since τ is a function of both concentration and size of the scattering object, it is hard to interpret the value or the origins of the non-monotonicity. To decouple the experimental parameters that are responsible for the change in τ, we measure both the concentration and size scale of collagen fibrils. In Fig. 4, we plot the AFM non-contact mode phase profiles of collagen samples deposited onto a mica substrate and rinsed with water. In neutral solutions, collagen type II assembles into fibrils for all ionic strengths below 250 mM. Even at the lowest testable ionic strengths, ∼6 mM, we observe the formation of fibrils with AFM. Although there is some evidence of a turbidity change at these conditions, the fibers are so thin that the scattering from these solutions is close to the low sensitivity range of the spectrophotometer.
The fibril thickness has a strong dependence on the ionic strength [Figs. 4 and 5(a)]. We quantify this observation by measuring the height profile distribution of collagen fibrils at each ionic strength [Fig. 5(a)]. In 6 mM [I], the fibrils are the thinnest, with an average height of 15 ± 5 nm. The diameter generally increases with salt concentration. In 116 mM [I], the average fibril diameter is 600 ± 400 nm. Above 116 mM, the diameter is relatively constant, and in 206 mM [I], the fibril diameter is on average 540 ± 200 nm. The fibril thickness can change an order of magnitude depending on the salt concentration. In Fig. 5, we summarize the structure results and compare them to the total concentration of fibrils that are formed. The diameter of collagen fibrils increases monotonically as a function of ionic strength [Fig. 5(a)]. The total concentration of fibrils however decreases [Fig. 5(b)]. The concentration of soluble collagen in solution was determined using a Sirius red F3B stain (1 g/L in water). Starting with a total collagen concentration of 0.189 g/L, at 0.06M ionic strength, 99% of collagen triple helices assemble into fibrils. In solutions with increased ionic strength, collagen fibril concentration decreases. In solutions with [I] = 250 mM and above, 0% of the initial collagen triple-helices are assembled into fibrils. The trend is independent of the temperature of the solution, but the decay of the fibril concentration as a function of ionic strength is systematically faster at lower temperatures. So while the size scale of the assembled collagen fibril structure increases systematically, the total concentration of collagen assembled into fibrils decreases.
Decoupling the fibril structure and concentration is consistent with two competing effects that contribute to the non-monotonic relationship of turbidity with ionic strength. In solutions with lower ionic strength, collagen fibril concentration is high, but the fibrils are thin. In solutions with higher ionic strengths, the fibrils are thicker, but the total fibril concentration is much lower. We illustrate this effect in Fig. 5(c). Since total light scattering intensity depends on both concentration and structure, the competition of the fibrils size and concentration as a function of ionic strength is responsible for the non-monotonicity shown in Fig. 3. We note however that we have not considered the aspect ratio and the length evolution of collagen fibrils, which could contribute to a deeper understanding of the mechanism of collagen assembly.
C. Kinetics at intermediate pH
The kinetics of collagen fibrillization are extremely sensitive to the ionic strength of the solution. In solutions with lower ionic strengths, the process is fast and rapidly slows down in higher ionic strengths. To resolve the temporal evolution of fibrillization, we monitor the turbidity of collagen solutions at 600 nm every 2 s. The resulting turbidity curves have a characteristic sigmoidal shape with three features: a lag time, a saturation turbidity, and a linear growth rate [Fig. 6(a)]. To compare the lag times and growth rates, we normalize the total curve by the saturation intensity. The growth rate is taken to be the slope of the linear portion of the curve (G). The lag time tlag is the intercept of the same linear fit [Fig. 6(a)]. The nucleation rate is inversely proportional to the lag time, Gn ∼ 1/tlag. The resulting data are an estimated extent of reaction versus time.
We find that as we increase the ionic strength of the solution from 96 to 126 mM, collagen type II fibrillization kinetics are generally slowed [Figs. 6(b) and 6(c)]. The data presented in Figs. 6(b) and 6(c) are plotted against the inverse Debye screening length, , and determine the inverse length scale below which electrostatics dominates over thermal fluctuations. By changing the ionic strength of the solution, the range of the electrostatic interactions is modified. In solutions with lower ionic strengths, with smaller κ values, electrostatic interactions are longer range than in solutions with higher ionic strengths. In an analogous way, temperature influences the strength of interactions. Thus, monitoring the growth rate and lag time as we vary both the temperature and the salt concentration reveals important information about the mechanism of collagen fiber formation.
The lag time for solutions with higher ionic strengths is dramatically longer compared to solutions with lower ionic strengths. tlag increases from 5.5 ± 1 s in 85 mM [I] (κ = 1.01 nm−1) to 350 ± 40 s in 126 mM [I] (κ = 1.11 nm−1) at 37 °C and from 230 s to 3500 s at 24 °C [Fig. 6(b)]. The increase in tlag indicates a slowing down of fibril formation in higher salt concentration solutions. The growth rate shows the same trend. G decreases by a factor of 3 from 0.0097 s−1 in 96 mM [I] (κ = 1.08 nm−1) to 0.0030 s−1 in 126 mM [I] (κ = 1.16 nm−1) at 37 °C and by a factor of 10, from 2 × 10−4 s−1 to 3.2 × 10−5 s−1 at 24 °C [Fig. 6(c)]. Increasing temperature and decreasing the ionic strength of the solution increases both the nucleation and growth rates of collagen fibrillization.
The ionic strength and pH of the solution have a direct impact on collagen type II fibril formation. First, collagen fibril formation only occurs at intermediate pH (4-9), at which both positive and negative charge residues are ionizable. On the other hand, at pH lower than 4 and at pH higher than 10, collagen triple helices have a homogeneous charge density. In these extreme pH conditions, both DLS and SLS confirm that collagen does not associate. In solutions at high and low pH with low ionic strengths (10−6M), polymer-polymer interactions are strong, corroborated by high A2 (Fig. 1), ℓp, and ρ values (Table I). In solutions with higher ionic strength (100 mM), the repulsive electrostatic interactions are shorter range and weaker, which leads to smaller A2 values and more flexible and more compact collagen triple helices.
At intermediate pH solutions with ionic strengths lower than 250 mM, collagen type II forms fibrils. In solutions with low [I], collagen fibril formation is much more favorable as indicated by a higher concentration of fibrils and faster kinetics. In solutions with higher ionic strengths, the concentration of fibrils is lower and kinetics are slowed monotonically. These results are consistent with attractive pairwise charge interactions driving collagen self-assembly in intermediate pH solutions. This requires the molecules to be close to net neural or at conditions at which both positive and negative charges are ionizable. With added salt, the attractive potential is weakened due to screening of the dipolar interactions.
The effect of ionic strength on the assembly of collagen type II is consistent with electrostatics acting as a driving force for fibril formation.2,43–45 Previously, Wallace2 modeled the electrostatic contribution to the work of bringing two collagen triple helices a distance d apart by assuming that upon association, collagen is stabilized by a number of charged pairs. In his method, the electrostatic free energy, Δfel, contributed to the bulk free energy of fibril formation, Δf = Δfel + Δfother. This free energy depends on both the distance between charges, d, and κ. In a general sense, the bulk formation energy is proportional to the work done for the assembly of a collagen type II dimer. To be more precise, we build upon Wallace’s method by directly calculating the electrostatic contribution to the work done to form a collagen dimer in different pH and salt conditions by calculating the electrostatic interactions directly from the amino acid sequence.
To calculate electrostatic contribution directly, we numerically sum up the possible extended Debye-Hückel charge interactions as a function of [I] and pH. The triple helix proteins have a stiff backbone with a persistence length in water ∼40 nm,46 with all the charges on the perimeter of the molecule, facing the solvent. The amino acid sequence for each of the three peptides that form collagen type II is the same. Following the earlier models,2,43–45 we model a collagen triple helix as a cylinder with radius a and the cylinder axis being a line charge with charges separated by a distance ℓ along the chain. In order to specify the different charges of the various amino acids in the sequence constituting the triple helix, each cylinder is imagined to be made of smaller cylinders each of length ℓ and radius a. Each such small cylinder has a smeared charge of value 0, 3, or −3, depending on the amino acid sequence.
The electrostatic potential ψ(r) due to a charge zje inside a small cylinder at a radial distance r in the plane normal to the cylinder axis is given by47
where K0 and K1 are the usual modified Bessel functions.48 The above result is obtained by solving the Debye-Hückel equation in a cylindrical coordinate system,
with the boundary conditions given as follows: (a) the electric field E(r) vanishes as r → ∞ and (b) E(a) = zje/(2πϵ0ϵℓa) at the surface of the cylinder.
The electrostatic interaction energy Δfel(r) between two subunits i and j separated by distance rij is zieψj(rij),
For large values of κrij and κa, K0 and K1 can be written as48
The overall electrostatic interaction energy for two parallel cylinders separated by d + 2a between the cylinder axes with a stagger length nℓ follows from Eq. (10) as
where L is the total length of the cylinder and
In Eq. (11), zi is the charge of value 0, 3, or −3 of coordinate i away from the start of the stagger, and is the charge on the second rod. The total pairwise electrostatic interaction will depend on the stagger number n based on the amino acid sequence of collagen type II. For some configurations, the formation energy is positive and for others it is negative. Previous wide angle x-ray scattering work by Antipova and Orgel10 has shown that in the assembled form, collagen type II triple helixes are staggered ∼67 nm or around ∼234 amino acids in the helical region. To be consistent with these results, the electrostatic interaction energy is calculated when the two parallel rods are mutually displaced by 234 residues. From these calculations, we find that for κ ranging from 0.001 to 3 (nm−1), the electrostatic contribution to the energy of formation varies in a non-monotonic way with pH [Fig. 7(c)]. Δfel is positive for pH < 4 and pH > 10. In the intermediate pH range, at pH 7, Δfel is minimum at κ = 0.01 nm−1 and decays with increased amount of salt [Fig. 7(d)]. In calculating the above results, we have used representative values for the parameters d = 1.3 nm, ℓ = 0.29 nm, and a = 0.75 nm (L = 300 nm and n = 234).
This model predicts the key experimental findings. At extreme pH, the homogeneous charge on collagen triple helices leads to a strong repulsive force preventing assembly. With added salt, the interactions are still repulsive but weaker. At intermediate pH, dipolar electrostatic interactions contribute to collagen fibril formation. At lower ionic strength, this interaction is stronger, leading to a greater concentration of collagen fibrils.
We have shown that collagen fibrillization is significantly influenced by electrostatic forces. At extreme pH, collagen is homogeneously charged and triple helices are soluble because of strong repulsive electrostatic interactions. At intermediate pH, at which both positive and negative amino acids are ionized, collagen triple helices self-assemble into fibrils. Numerical calculations show that pair-wise electrostatic interactions between parallel triple helices contribute to the collective association. Salt is directly responsible for the range of these interactions such that at lower ionic strengths, electrostatic forces are long range and collagen triple helices are strongly attractive. This results in a higher concentration of collagen fibers in solution from the bulk and faster kinetics. With the addition of salt, the interactions are screened, and the concentration of fibers is lower. Likewise the kinetics are slowed. Although electrostatic interactions are consistent with the increase in fibril concentration at neutral pH and low salt concentrations, they do not account for the size increase in solutions with higher ionic strengths. This process of fibril bundling is likely due to a separate mechanism, the origins of which are not investigated in this paper. Although the morphological features reported here are robust under the mentioned experimental conditions, how they would evolve with aging conditions is being presently pursued in our laboratory.
Acknowledgment is made to the National Science Foundation (Award No. 1504265) and Air Force Office of Scientific Research (Grant No. FA9550-17-1-0160).