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Hydration Dynamics of Hyaluronan and Dextran
Johannes Hunger,*,‡ Anja Bernecker,† Huib J. Bakker,* Mischa Bonn,*,‡ Ralf P.
*Fundamenteel Onderzoek der Materie (FOM) Institute AMOLF, Amsterdam, The Netherlands ‡Max Planck Institute for Polymer Research, Mainz, Germany †Center for Cooperative Research in Biosciences (CIC biomaGUNE), San Sebasti´an, Spain §Max Planck Institute for Intelligent Systems, Stuttgart, Germany Supporting Material
Hyaluronic acid sodium salt (hyaluronan, HA) from rooster comb (molecular weight 1 to 4 · 106 g mol−1)and dextran from Leuconostoc mesenteroides (analytic standard grade, molecular weight 1.4 · 106 g mol−1, ∼ 5 % branched) were purchased from Sigma Aldrich and used without further purification. Sampleswith different weight fractions, w, (g of polysaccharide / g of solution ) were prepared using an analyticalbalance. Dextran was dissolved in ultrapure water at the desired concentrations and shaken for 2 h at roomtemperature. HA was dissolved in ultrapure water and shaken overnight at 40 °C. The hyaluronic acidsalt samples were centrifuged several times for 10 min at 10000 rpm to obtain a homogeneous solution.
For femtosecond-infrared experiments a small amount (∼ 4 % (w/w)) deuterium oxide (99.97 %D fromEuriso-top, Saint-Aubin, France) was added to the ultrapure water before dissolving dextran or HA. Due tofast isotopic exchange, we obtain the equilibrium distribution of deuterium atoms among all acidic protons.
Therefore the dominant isotopically labeled species are HOD molecules.
For analysis of the Terahertz (THz) experiments, molar concentrations (in mol L−1) of water, cH2O, in the sample are required. These were calculated from the weight fractions, w, using solution densities, ρ,interpolated from literature (ρ(dextran) = (997.05 + 410 · w) g L−1; ρ(HA) = (997.05 + 440 · w) g L−1)[1, 2, 3].
Polarization-resolved femtosecond-infrared spectroscopy Femtosecond infrared pump and probe pulses were generated via a sequence of nonlinear optical conver-sion processes that are pumped by a commercial Ti:sapphire regenerative amplified laser system (Spectra-Physics Hurricane, USA). This system delivers pulses at 800 nm with a duration of 100 fs at a repetitionrate of 1 kHz (1 mJ per pulse). Approximately 0.7 mJ of pulse energy is used to pump an optical parametricamplifier based on a β-barium borate crystal. The optical parametric amplifier is used to generate idlerpulses at ∼ 2 µm, which are subsequently frequency-doubled in a second β-barium borate crystal, yieldingpulses at ∼ 1 µm. In a second parametric amplification process in a lithium niobate crystal the 1 µm pulsesare used as a seed and the remaining 800 nm pulses (0.3 mJ) as a pump to generate mid-infrared pulses witha duration of ∼ 150 fs and an energy of ∼ 6 µJ. The frequency of these pulses is centered at 2500 cm−1,which coincides with the absorption of the O-D stretching vibration of HOD molecules (Note that the N-Dstretch vibration, which is formed via isotopic exchange with HOD absorbs at similar wavenumbers. Itscontribution to our experiments, however, is negligible [4]).
A CaF2 wedged window is used to split the mid-infrared pulses into a pump (∼ 92 %), a probe (∼ 4 %), and a reference (∼ 4 %) pulse. The polarization of the pump pulse is rotated by 45 ° with respectto the probe and the reference polarization using a λ/2 plate. The time delay of the probe pulses withrespect to the pump is varied via a variable path-length delay line. The pump pulse is modulated using an optical chopper. The three pulses are focused into the sample with an off-axis parabolic mirror. Inthe sample, which is held between two CaF2 windows, the foci of the probe and pump-pulse overlap.
After passing a polarizer that allows us to select the parallel or perpendicular (with respect to the pump)polarization components, the probe and reference beams are sent into a spectrometer dispersing the beamson a liquid-nitrogen-cooled mercury-cadmium telluride detector. The probe pulse is used to measure the(pump-induced) transient absorption in the sample parallel (∆α∥(ω, t)) and perpendicular (∆α⊥(ω, t)) tothe pump polarization as a function of delay time, t, and wavenumber, ω. The reference pulse is used for aspectrally resolved correction of the pulse to pulse energy fluctuations [5].
From the measured absorption changes ∆α∥(ω, t) and ∆α⊥(ω, t) we construct the isotropic signal: ∆α∥(ω, t) + 2∆α⊥(ω, t) The isotropic signal is independent of reorientation processes and is dominated by the vibrational relaxationof the excitation and by the dynamics of any consecutive processes. At short delays the isotropic signalis dominated by the vibrational excitation of the OD oscillators. The vibrational energy relaxes to anintermediate state (i.e. intermediate energy levels) and eventually leads to heating of the sample by a fewdegrees (low energy levels) [6, 7, 8]. At long delay times (t > 20 ps) this heating effect prevails. Toobtain the anisotropy dynamics, R(t) of the excited OD-stretch transition dipoles, we correct the measuredsignals ∆α∥(ω, t) and ∆α⊥(ω, t) for this time-dependent thermalization of the sample. The evolution ofthe thermalization is obtained via detailed analysis of ∆αiso(ω, t) following the route described in detailin Ref. [10]. To briefly summarize, we fit a kinetic model to the isotropic data. In this model the pumppulse generates a population in the first vibrational excited state. This excitation transiently populates anintermediate state with a characteristic time constant of ∼ 1.7 ps. For the present samples this time isvirtually constant at all concentrations of polysaccharide. The intermediate state has the same absorptionspectrum as the vibrational ground state (i.e. the transient absorption equals zero). The intermediate statefurther relaxes to the final thermal state with a characteristic time constant of ∼ 1 ps for solutions of 8 %HOD in H2O. For the present samples this equilibration time is increasing smoothly as the concentrationof polysaccharide increases. At the highest concentration (20 % (w/w)) of polysaccharide the equilibrationoccurs on a ∼ 1.5 ps timescale. This slow-down of the equilibration indicates a slower equilibration of thesamples to the thermal disturbance and/or the appearance of additional intermediate energy levels.
From this analysis, the spectral signature and the temporal evolution of the thermalization is obtained, which is subsequently subtracted from the raw transient spectra (∆α∥(ω, t) and ∆α⊥(ω, t)). The thusobtained corrected transient spectra, ∆α′∥(ω, t) and ∆α′⊥(ω, t) solely reflect the signal originating from From the corrected signals we construct the anisotropy parameter R(t): ∆α′∥(ω, t) − ∆α′⊥(ω, t) ∆α′∥(ω, t) + 2∆α′⊥(ω, t) R(t) directly corresponds to the second order rotational correlation time of the excited OD oscillators [9].
R(t) decays are averaged over frequencies ranging from 2460 cm−1 to 2540 cm−1 as it is independent ofabsorption frequency [10].
The thus obtained anisotropies are inconsistent with all water molecules having the same rotational dynamics (as for neat water [7]), which is described by a single exponential decay of R(t) (see Figure S1).
Hence, we model the experimental anisotropies with a double exponential decay (eq 1), which excellentlydescribes the observed rotational dynamics of the HOD molecules (see Figures 1 & S1). From these fitswe obtain a rotational correlation time of τs,IR ≫ 10 ps at all concentrations, if all parameters of eq 1 areallowed to vary. This means that the rotational dynamics of the slow subensemble of water molecules areessentially static on the 5 ps time-scale of our experiment. To reduce the number of free parameters, we fixthe rotation times of the slowed down subensemble of water to τs,IR ≈ ∞ (t/τs,IR ≈ 0).
Terahertz pulses are generated in a ZnTe (110) nonlinear crystal [11] from 800 nm pulses with a durationof ∼ 150 fs from a Ti:Sapphire laser (Coherent Legend Elite, USA). The generated THz pulses have aduration of ∼ 1 ps. The time-dependent electric field of the THz pulse is measured via its electro-opticeffect on a variably delayed 800 nm laser pulse in a second ZnTe crystal. A frequency domain analysisof the THz pulse transmitted through an empty cell and the THz pulse transmitted through a filled samplecell yields the frequency dependent complex index of refraction (ˆ n(ν) = n(ν) − ik(ν)) as function of field frequency, ν (ranging from 0.4 to 1.2 THz). In analysing the data, all (multiple) reflection and transmissioncoefficients for all transitions (air-window-sample-window-air) were taken into account [12]. To minimizethe effect of fluctuations in the THz intensity, a rotating sample cell with two separate sample compartmentsis used to position the sample and a pure water reference alternatingly in the focus of the THz beam. Thesample is held between two Polychlorotrifluoroethylene windows separated by a teflon spacer (thickness∼ 100 µm). The neat water data were used to calibrate the spectra of the samples.
Complex refractive index spectra were converted to complex permittivity spectra, ˆ ε(ν) is dominated by an intense relaxation mode at ∼ 20 GHz that can be well described with a Debye equation (i.e. a single exponential decay of the orientational polarization of the sample in thetime-domain) [13]. This relaxation originates from the partial alignment of the (dipolar) water moleculesto the external electric field. For neat water a characteristic collective first-order orientational relaxationtime of τ1 = 8.3 ps is observed at ambient temperature [13]. Its amplitude is found to be S1 = 72. Further,a weak Debye-type high-frequency mode centered at ∼ 0.5 THz is observed with an amplitude S2 ≈ 1.3and relaxation time τ2 ≈ 200 fs. Thus, we model the experimental spectra with a superposition of twoDebye-type relaxation modes: where ε∞ represents the high-frequency limit of the permittivity. ε∞ subsumes all electronic and in-tramolecular polarizations at infrared and optical frequencies. Following previous work [14], τ1 was fixedto the value obtained from the reference sample (pure water) using the known static permittivity of water,ε = S1 + S2 + ε∞ = 78.368 [15]. τ2, S1, S2, and ε∞ are the independent fit parameters. The thus ob-tained amplitude S1 can be converted to the molar concentration of unaffected (bulk-like) water molecules,cb using the Cavell equation [16, 17]: where NA and kB are the Avogadro and Boltzmann constant, respectively and T is the thermodynamictemperature. µeff is the effective dipole moment of water in solution. µeff was assumed to be constant andthe same as for neat water µeff = 3.8 D (1 D = 3.33564 × 10−30 Cm) [13, 18].
Figure S1: Anisotropy parameter, R(t), for the OD stretch vibration for solutions of 20 % hyaluronan (a)and 20 % dextran (b) in isotopically diluted water (8 % HOD in H2O). Dashed red lines correspond tofits of a single exponential decay to the experimental data. Solid blue lines show the fits with a doubleexponential decay (eq 1).
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