Different Effects of Albumin and Hydroxyethyl Starch on Low Molecular-Weight Solute Permeation Through Sodium Hyaluronic Acid Solution

polymers

Article Different Effects of Albumin and Hydroxyethyl Starch on Low Molecular-Weight Solute Permeation through Sodium Hyaluronic Acid Solution

Tsuneo Tatara

Department of Anesthesiology and Pain Medicine, Hyogo College of Medicine, 1-1 Mukogawa-cho, Nishinomiya, Hyogo 663-8501, Japan; [email protected]

Abstract: Hyaluronic acid (HA), a high-molecular-weight linear polysaccharide, restricts solute transport through the interstitial space. Albumin and hydroxyethyl starch (HES) solutions are used to correct the decrease of blood volume during surgery, but may leak into the interstitial space under inﬂammation conditions. Given the possibility that the structure of HA may be affected by adjacent macromolecules, this study tested whether albumin and HES (Mw 130,000) exert different effects 6 on solute permeation through sodium hyaluronic acid (NaHA: Mw 1.3 × 10 ) solution. To this end, permeation of Orange G, a synthetic azo dye (Mw 452), into NaHA solutions containing albumin or HES over time was assessed. The amount of time it took for the relative absorbance of Orange G to

reach 0.3 (T0.3) was determined in each NaHA solution relative to the reference solution (i.e., colloid solution without NaHA). Relative T0.3 values of albumin were larger than those of HES for 0.1% NaHA solution (3.33 ± 0.69 vs. 1.16 ± 0.08, p = 0.006, n = 3) and 0.2% NaHA solution (1.95 ± 0.32 vs.

0.92 ± 0.27, p = 0.013, n = 3). This ﬁnding may help in the selection of an appropriate colloid solution to control drug delivery into the interstitial space of cancer tissue under inﬂammation conditions.

Citation: Tatara, T. Different Effects of Albumin and Hydroxyethyl Starch Keywords: hyaluronic acid; permeation; hydroxyethyl starch; inflammation on Low Molecular-Weight Solute Permeation through Sodium Hyaluronic Acid Solution. Polymers 2021, 13, 514. https://doi.org/ 1. Introduction 10.3390/polym13040514 Hyaluronic acid (HA), a glycosaminoglycan found in the interstitial space [1,2], is a high-molecular-weight linear polysaccharide polymer consisting of repeating disaccharide Academic Editor: Karin units of β-D-glucuronic acid and N-acetyl-β-D-glucosamine [3]. HA plays a major role in Stana Kleinschek many biological processes including cell signaling, wound healing, and matrix organiza- Received: 2 January 2021 tion [4]. HA forms a fibrous gel-like network at semidiluted concentrations (approximately Accepted: 5 February 2021 0.6 mg/mL) [5]. Since the concentration of HA in the interstitial space is in the range of Published: 9 February 2021 1–10 mg/mL, HA is presumed to exist in a physically entangled state in the interstitial space [1,2], which restricts solute transport [6,7]. This is a clinically important aspect, as dif- Publisher’s Note: MDPI stays neutral fusion properties of solutes in the interstitial space influence the inflammatory process [8] with regard to jurisdictional claims in and drug delivery in diseases such as cancer [9]. published maps and institutional affil- iations. In cancer patients undergoing major surgery, adequate fluid administration using colloid solutions is essential for correcting the decrease of blood volume due to ongoing hemorrhage and inflammation during surgery. Albumin solution, which is prepared from pooled human plasma, is suitable for this purpose, but its limited availability and high cost are major issues. Accordingly, hydroxyethyl starch (HES) solution, a synthetic Copyright: © 2021 by the author. colloid solution modified from waxy maize starch largely composed of highly branched Licensee MDPI, Basel, Switzerland. amylopectin, is now widely used as an alternative to albumin solution [10]. Nevertheless, as This article is an open access article inflammation caused by surgical injury increases capillary permeability to macromolecules, distributed under the terms and conditions of the Creative Commons intravenously infused colloids may leak into the interstitial space [11]. It is thus necessary Attribution (CC BY) license (https:// to investigate whether leakage of albumin and HES into the interstitial space could modify creativecommons.org/licenses/by/ the structure of HA and thereby affect interstitial solute transport. 4.0/).

Polymers 2021, 13, 514. https://doi.org/10.3390/polym13040514 https://www.mdpi.com/journal/polymers Polymers 2021, 13, 514 2 of 12

Albumin stabilizes HA structure by binding to HA via weak electrostatic forces and hydrogen bonding [12,13]. In a recent study, HES, but not albumin, was found to decrease the intrinsic viscosity of sodium hyaluronic acid (NaHA), suggesting that HES may locally restrict NaHA diffusion via hydrogen bonding with NaHA chains [14]. However, as the intrinsic viscosity of NaHA is obtained by extrapolating reduced viscosity of NaHA solution to zero concentration of NaHA, the effects of albumin and HES on the physical properties of semidiluted NaHA solution, in which the interaction of NaHA chains among themselves cannot be neglected, must be investigated. On this basis, the present study hypothesized that albumin and HES exert different effects on NaHA diffusion and thus on the permeation of small solutes through NaHA solution at physiological concentration. Since HES causes the formation of clusters of NaHA chain segments by restricting the spreading of NaHA chains, the resultant decrease of friction force between NaHA chains and the permeating solute might accelerate solute permeation into NaHA solution compared to albumin [15]. To test this, the present study examined how albumin and HES affect small solute permeation into NaHA solution. Moreover, to characterize the diffusion properties of NaHA, the osmotic swelling pressure, hydraulic permeability coefficient, and dynamic shear moduli of NaHA solution in the presence of albumin and HES were measured. The finding that albumin restricted low molecular-weight solute permeation through NaHA solution to a greater degree than HES may help in the selection of an appropriate colloid solution to control drug delivery into the interstitial space of cancer tissue under inflammation conditions.

2. Materials and Methods 2.1. Materials This study used a bovine serum albumin solution and a commercially available 6% (w/v) HES solution of weight-average Mw 130,000 (waxy maize starch-based HES: ® molar substitution, 0.41; C2/C6 ratio, 9:1; Voluven , Fresenius Kabi, Bad Homburg, Ger- many) [10]. These colloid solutions were diluted to desired concentrations with phosphate buffered saline (PBS) (pH 7.4). 6 NaHA from Streptococcus equil (Mw 1.3 × 10 )[14] and bovine serum albumin (Mw 66,000) were purchased from Sigma-Aldrich (St. Louis, MO, USA). Orange G, a synthetic azo dye (Mw 452), was purchased from FUJIFILM Wako Pure Chemical (Osaka, Japan). Chemical structures of NaHA, albumin, HES, and Orange G are shown in Supplementary Figure S1. All reactions were carried out using purified water from a Millipore Milli-Q purification system (Merck Millipore, Burlington, MA, USA). Colloid solutions were filtered through a 0.45-µm membrane prior to analysis.

2.2. Permeation of Orange G into NaHA Solutions NaHA was dissolved in albumin or HES solution and left for 24 h to solidify with gentle stirring at room temperature (25 ◦C). NaHA solutions were prepared at the following concentrations: (i) 0.1% (w/w) NaHA in 1.1% (w/v) albumin or HES solution; (ii) 0.2% (w/w) NaHA in 1% (w/v) albumin or HES solution; and (iii) 0.4% (w/w) NaHA in 0.8% (w/v) albumin or HES solution. In all solutions, the total concentration of solutes (i.e., NaHA plus colloids) was kept constant so as to minimize the effects of speciﬁc gravity of the solution on solute permeation. Colloid solutions without NaHA (1.2% (w/v) albumin/HES) were used as references. These NaHA concentrations fall within the range observed in the interstitial space (i.e., 0.1–1%) [1,2]. A HES concentration of 1% was chosen because this concentration falls within the range of plasma concentration in clinical settings (i.e., 1–2%) [10]. PBS solution containing 0.1 mL 0.01% (w/v) Orange G was gently poured over 1.4 mL NaHA solution in a semimicro ultraviolet (UV) cuvette (12.5 mm square; inner width, 4 mm; height, 45 mm; path length, 10 mm) (Figure1). The amount of Orange G that permeated into NaHA solution was determined every 6 min for 20 h by measuring absorbance at 478 nm using a UV spectrometer (Model UV-1850; Shimadzu, Kyoto, Japan) (Figure1). The Polymers 2021, 13, x FOR PEER REVIEW 3 of 12

PBS solution containing 0.1 mL 0.01% (w/v) Orange G was gently poured over 1.4 mL NaHA solution in a semimicro ultraviolet (UV) cuvette (12.5 mm square; inner width, 4 mm; height, 45 mm; path length, 10 mm) (Figure 1). The amount of Orange G that per- Polymers 2021, 13, 514 meated into NaHA solution was determined every 6 min for 20 h by measuring absorb-3 of 12 ance at 478 nm using a UV spectrometer (Model UV-1850; Shimadzu, Kyoto, Japan) (Figure 1). The temperature of the UV cuvette was maintained at 37 °C with a temperature control unit (Model TCC-100; Shimadzu, Kyoto, Japan). The top of the UV cuvette temperature of the UV cuvette was maintained at 37 ◦C with a temperature control unit was sealed with laboratory film (Parafilm®, Bemis Flexible packaging, Chicago, IL, USA) (Model TCC-100; Shimadzu, Kyoto, Japan). The top of the UV cuvette was sealed with to prevent sample evaporation. Experiments were carried out at least in triplicate. Re- laboratory ﬁlm (Paraﬁlm®, Bemis Flexible packaging, Chicago, IL, USA) to prevent sample sults were expressed as relative absorbance (i.e., relative to the absorbance value calcu- evaporation. Experiments were carried out at least in triplicate. Results were expressed as lated assuming that Orange G is uniformly distributed into NaHA solution in the cu- relative absorbance (i.e., relative to the absorbance value calculated assuming that Orange vette). G is uniformly distributed into NaHA solution in the cuvette).

FigureFigure 1. 1.ExperimentalExperimental set-up set-up for forthe themeasurement measurement of solute of solute permeation permeation intointo sodium sodium hyaluronic hyaluronic acidacid (NaHA) (NaHA) solution. solution. A solution A solution containing containing Orange Orange G (0.1 G (0.1 mL) mL) was was poured poured over over NaHA NaHA solution solution containingcontaining colloid colloid (i.e., (i.e., albu albuminmin or orhydroxyethyl hydroxyethyl starch) starch) in inan an ultraviolet ultraviolet (UV) (UV) cuvette. cuvette.

ForFor the the quantitative quantitative analysisanalysis ofof Orange Orange G permeationG permeation into into NaHA NaHA solution, solution, the amount the amountof time of it tooktime forit took the relativefor the absorbancerelative absorbance of Orange of G Orange to reach G 0.3 to( reachT0.3 in 0.3 h) was(T0.3 determinedin h) was determinedin each NaHA in each solution NaHA relativesolution to relative the reference to the reference solution solution (i.e., colloid (i.e., colloid solution solution without withoutNaHA). NaHA). Results Results were compared were compared between be NaHAtween solutionsNaHA solutions containing containing albumin albumin and those andcontaining those containing HES with HES the with unpaired the unpairedt-test. t-test. 2.3. Effects of Albumin and HES on Osmotic Swelling Pressure of NaHA Solution 2.3. Effects of Albumin and HES on Osmotic Swelling Pressure of NaHA Solution NaHA was dissolved in PBS to prepare a 1% (w/w) solution and left for 24 h to solidify NaHA was dissolved in PBS to prepare a 1% (w/w) solution and left for 24 h to so- with gentle stirring at room temperature. The osmotic swelling pressure of 1% NaHA lidify with gentle stirring at room temperature. The osmotic swelling pressure of 1% solution was measured using an osmotic flow cell as previously reported [16,17]. The basic NaHA solution was measured using an osmotic flow cell as previously reported [16,17]. principle of the osmotic flow cell is as follows: two fluid chambers are separated by a The basic principle of the osmotic flow cell is as follows: two fluid chambers are sepa- semipermeable membrane (molecular weight cut-off, 300,000; ultrafiltration membrane rated by a semipermeable membrane (molecular weight cut-off, 300,000; ultrafiltration disk PBMK; Merck Millipore, Burlington, MA, USA) (Figure2), with one of the chambers membraneserving as disk the PBMK; sample Merck chamber Millipore, (filled with Burlington, 0.5 mL 1%MA, NaHA USA) in(Figure PBS) and2), with the otherone of as thethe chambers reference serving chamber as the (filled sample with chamber PBS, 2% ((filledw/v) albumin,with 0.5 mL or 2%1% (NaHAw/v) HES), in PBS) which and is theconnected other as viathe areference narrow channelchamber (0.5 (filled mm with diameter) PBS, to2% a ( manometricw/v) albumin, chamber or 2% fitted(w/v) HES), with an whichelectronic is connected pressure via transducer a narrow (PGM-02KG, channel (0.5 Kyowa, mm diameter) Tokyo, Japan). to a manometric The volume chamber of colloid- fitteddiffusing with fluidan electronic space (i.e., pressure reference transduc and manometricer (PGM-02KG, chambers, Kyowa, and the Tokyo, channel Japan). connecting The volumethem) isof 1.5colloid-diffusing mL. Fluid movement fluid space from the(i.e., reference reference chamber and manometric toward the chambers, sample chamber and due to the osmotic swelling force of NaHA solution creates a negative hydrostatic pressure in the reference chamber, which equals the osmotic swelling pressure of NaHA solution against test colloid solutions. Hydrostatic pressure in the reference chamber was recorded every 10 s for 20 h using LabVIEW® (National Instruments, Austin, TX, USA). Experiments were repeated four times at room temperature. Polymers 2021, 13, x FOR PEER REVIEW 4 of 12

the channel connecting them) is 1.5 mL. Fluid movement from the reference chamber toward the sample chamber due to the osmotic swelling force of NaHA solution creates a negative hydrostatic pressure in the reference chamber, which equals the osmotic swelling pressure of NaHA solution against test colloid solutions. Hydrostatic pressure in the reference chamber was recorded every 10 s for 20 h using LabVIEW® (National In- struments, Austin, TX, USA). Experiments were repeated four times at room temperature. Values of hydrostatic pressure in the reference chamber at 2 h, 5 h, 10 h, 15 h, and 20 h Polymers 2021, 13, 514 were compared between PBS, albumin, and HES by one-way analysis of variance4 of 12 (ANOVA).

FigureFigure 2. Schematic 2. Schematic of an of anosmotic osmotic flow flow cell. cell. Fluid Fluid flow flowss from from the thereference reference chamber chamber to the to sample the sample chamberchamber due due to osmotic to osmotic swelling swelling of sodium of sodium hyalur hyaluroniconic acid acid (NaHA) (NaHA) in phosphate in phosphate buffered buffered saline saline (PBS).(PBS). The The sample sample chamber chamber was was filled filled with with 0.5 0.5 mL mL 1% 1% NaHA NaHA solution, solution, and and the reference chamberchamber was wasfilled filled with with PBS, PBS, 2% 2% albumin, albumin, or or 2% 2% hydroxyethyl hydroxyethyl starch starch solution solution (HES). (HES). A semipermeable A semipermeable membrane membranewith a molecular with a molecular weight cut-off weight of cut-off 300,000 of was 300,000 used. was used.

2.4. EffectsValues of Albumin of hydrostatic and HES pressure on Darcy’s in Permeability the reference Coefficient chamber of at NaHA 2 h, 5 Solution h, 10 h, 15 h, and 20NaHA h were was compared dissolved between in PBS PBS, to prepare albumin, 0.1% and (w HES/w), 0.3% by one-way (w/w), and analysis 0.5% of(w/ variancew) solutions(ANOVA). and left for 24 h to solidify with gentle stirring at room temperature. Darcy’s permeability coefficient (K) of each NaHA solution was measured using the ultra-fast 2.4. Effects of Albumin and HES on Darcy’s Permeability Coefficient of NaHA Solution double-sided reusable sample dialyzerTM (outer diameter 2.5 cm, chamber volume 500 µL: 7404-5001D,NaHA Harvard was dissolved Apparatus, in PBSHolliston, to prepare MA, 0.1%USA) ( w(Figure/w), 0.3% 3). The (w/ systemw), and interposed 0.5% (w/w ) 0.5solutions mL of NaHA and leftsolution for 24 between h to solidify two precut with gentle cellulose stirring acetate at roomdialysis temperature. membranes Darcy’s(mo- lecularpermeability weight cut-off coefficient 300 kDa: (K) of7403-CA300K each NaHA, Harvard solution Apparatus, was measured Holliston, using MA, the ultra-fast USA). TM PBSdouble-sided or 2% (w/v) reusablecolloid (i.e., sample albumin, dialyzer HES)(outer solution diameter was infused 2.5 cm, into chamber the dialysis volume cham- 500 µL: ber7404-5001D, containing HarvardNaHA solution Apparatus, via a Holliston, connectin MA,g tube USA) with (Figure an automatic3). The system infusion interposed pump (FP-2200,0.5 mL ofMELQUEST, NaHA solution Toyama, between Japan) two precutat a constant cellulose acetaterate (Q dialysis) ranging membranes from 1 to (molec- 20 µL/minular weight (Figure cut-off 3). 300 kDa: 7403-CA300K, Harvard Apparatus, Holliston, MA, USA). PBS or 2% (w/v) colloid (i.e., albumin, HES) solution was infused into the dialysis chamber containing NaHA solution via a connecting tube with an automatic infusion pump (FP-2200, MELQUEST, Toyama, Japan) at a constant rate (Q) ranging from 1 to 20 µL/min (Figure3). The pressure tube was connected to a manometric chamber fitted with an electronic pressure transducer (PGM-1KG, Kyowa, Tokyo, Japan). Hydrostatic pressure in the pressure tube was continuously recorded every 50 s using LabVIEW® (National Instruments, Austin, TX, USA), which was found to steeply increase with time and then reach a plateau over 1–40 h, depending on NaHA concentration. The value of K (cm2) was calculated according to Darcy’s law, as follows [2]:

l η K = · , (1) A (∆P/∆Q)

where A is the membrane surface area available for fluid filtration (0.752 × 3.14 = 1.77 cm2), l is the thickness of NaHA solution in the dialysis chamber (0.28 cm, calculated as 0.5/A), η is the viscosity of infused fluid, and P is the hydrostatic pressure in the pressure tube at plateau. Values of ∆P/∆Q were obtained by the linear fitting procedure for P values plotted against Q values using GraphPad Prism 5® software (GraphPad Software Inc., San Diego, CA, USA). Values of η at 25 ◦C (mPa·s) for PBS, 2% albumin, and 2% HES were 0.95, 0.99, and 1.39, respectively, which were measured using a vibrational viscometer (Model SV-1A; A&D, Inc., Tokyo, Japan) equipped with a temperature controller (Model NCB-1200; EYELA, Tokyo, Japan) kept at 25 ◦C. Polymers 2021, 13, x FOR PEER REVIEW 5 of 12 Polymers 2021, 13, 514 5 of 12

FigureFigure 3. 3.ExperimentalExperimental set-up set-up for for the the measurement measurement of ofDarcy’s Darcy’s permeability permeability coefficient coefﬁcient of sodium of sodium hyaluronichyaluronic acid acid (NaHA) (NaHA) solution. solution. The The fluid ﬂuid (i.e., (i.e., phosphate phosphate buffered buffered saline saline or or colloid colloid solution) solution) was was infusedinfused into into the the dialysis dialysis chamber chamber containing containing NaHA NaHA solution solution at a atconstant a constant rate, rate,and hydrostatic and hydrostatic pressurepressure in in the the pressure pressure tube tube was was continuously continuously recorded. recorded.

2.5.The Effects pressure of Albumin tube andwas HES connected on Dynamic to a mano Shearmetric Moduli chamber of NaHA fitted Solution with an electronic pressureNaHA transducer was dissolved (PGM-1KG, in PBS toKyowa, prepare To 0.5%kyo, ( wJapan)./w) solution Hydrostatic with or pressure without 3%in (wthe/v ) pressureand 6% tube (w/v )was albumin continuously or HES, recorded and left forevery 24 h50 to s solidifyusing LabVIEW with gentle® (National stirring atInstru- room ments,temperature. Austin, TX, Dynamic USA), shearwhich moduli was found of each to steeply NaHA increase solution with were time measured and then by reach small a amplitudeplateau over oscillatory 1–40 h, depending shear experiments on NaHA overconcentration. the frequency range of 0.1–10 Hz with a rotationalThe value rheometer of K (cm (HAAKE2) was calculated Viscotester according iQ Air, Thermo to Darcy’s Fisher law, Scientific, as follows Waltham, [2]: MA, USA) equipped with a Peltier temperature control module kept at 37 ◦C. The software l η HAAKE RheoWin (ver. 4.86, ThermoK Fisher= ⋅ Scientific,, Waltham, MA, USA) was used(1) to determine storage (G0) and loss (G”) shearA moduli()ΔP / ΔQ of NaHA solution at each frequency. Cone geometry with a diameter of 6 cm and core angle of 2◦ was used. Prior to frequency where A is the membrane surface area available for fluid filtration (0.752 × 3.14 = 1.77 sweep experiments, strain amplitude was confirmed by strain sweep experiments to be cm2), l is the thickness of NaHA solution in the dialysis chamber (0.28 cm, calculated as sufficiently small to provide a linear material response at all investigated frequencies. A 0.5/A), η is the viscosity of infused fluid, and P is the hydrostatic pressure in the pressure solvent trap was used to avoid evaporation of samples during experiments. Experiments tube at plateau. Values of ΔP/ΔQ were obtained by the linear fitting procedure for P were carried out at least six times. values plotted against Q values using GraphPad Prism 5® software (GraphPad Software Inc.,2.6. San Statistical Diego, Analysis CA, USA). Values of η at 25 °C (mPa·s) for PBS, 2% albumin, and 2% HES were 0.95, 0.99, and 1.39, respectively, which were measured using a vibrational Statistical analyses were performed using SigmaPlot 13 (Systat Software Inc., Chicago, viscometer (Model SV-1A; A&D, Inc., Tokyo, Japan) equipped with a temperature con- IL, USA) software. p < 0.05 was considered statistically significant. troller (Model NCB-1200; EYELA, Tokyo, Japan) kept at 25 °C. 3. Results 2.5.3.1. Effects Permeation of Albumin of Orange and HES G into on NaHA Dynamic Solution Shear Moduli of NaHA Solution NaHADirect was visualization dissolved ofin NaHAPBS to solutionprepare in0.5% the ( UVw/w) cuvette solution showed with or that without Orange 3% G (wpermeated/v) and 6% into (w/ NaHAv) albumin in HES or HES, solution and rapidly left forcompared 24 h to solidify to NaHA with in gentle albumin stirring solution at room(Supplementary temperature. Figure Dynamic S2). Theshear presence moduli of of albumin each NaHA significantly solution decreased were measured permeation by smallof Orange amplitude G into oscillatory NaHA solution shear experiment almost bys half over compared the frequency to the reference,range of 0.1–10 regardless Hz withof NaHA a rotational concentration rheometer (Figure (HAAKE4a). On Viscotester the other iQ hand, Air, theThermo presence Fisher of Scientific, HES decreased Wal- tham,permeation MA, USA) of Orange equipped G into with NaHA a Peltier solution temperature at 0.4%,but control not at module 0.1% or kept 0.2%, at compared 37 °C. The to softwarethe reference HAAKE (Figure RheoWin4b). (ver. 4.86, Thermo Fisher Scientific, Waltham, MA, USA) was used to determine storage (G′) and loss (G″) shear moduli of NaHA solution at each frequency. Cone geometry with a diameter of 6 cm and core angle of 2° was used. Prior

Polymers 2021, 13, x FOR PEER REVIEW 6 of 12

to frequency sweep experiments, strain amplitude was confirmed by strain sweep experiments to be sufficiently small to provide a linear material response at all investigated frequencies. A solvent trap was used to avoid evaporation of samples during experiments. Experiments were carried out at least six times.

2.6. Statistical Analysis Statistical analyses were performed using SigmaPlot 13 (Systat Software Inc., Chi- cago, IL, USA) software. p < 0.05 was considered statistically significant.

3. Results 3.1. Permeation of Orange G into NaHA Solution Direct visualization of NaHA solution in the UV cuvette showed that Orange G permeated into NaHA in HES solution rapidly compared to NaHA in albumin solution (Supplementary Figure S2). The presence of albumin significantly decreased permeation of Orange G into NaHA solution almost by half compared to the reference, regardless of NaHA concentration (Figure 4a). On the other hand, the presence of HES decreased Polymers 2021, 13, 514 6 of 12 permeation of Orange G into NaHA solution at 0.4%, but not at 0.1% or 0.2%, compared to the reference (Figure 4b).

Figure 4. TimeTime course of relative absorbance of Orange G permeati permeatingng into different concentrationsconcentrations of sodium hyaluronic acidacid (NaHA) solutionsolution containing containing (a ()a albumin) albumin or or (b )(b hydroxyethyl) hydroxyethyl starch starch (HES). (HES). Relative Relative absorbance absorbance of Orange of Orange G is expressed G is ex- pressedas a value as relativea value torelative that calculated to that calculated assuming assuming that Orange that G Orange is uniformly G is uniformly distributed distributed into NaHA into solution NaHA in solution the ultraviolet in the ultravioletcuvette. Experiments cuvette. Experiments were carried were out atcarried least inout triplicate. at least in For triplicate. simplicity, For values simplicity, are presented values are as meanpresented and standard as mean errorand standardfor every error 2 h. The for dottedevery 2 horizontal h. The dotted line horizontal indicates a line relative indicates absorbance a relative of 0.3.absorbance of 0.3.

RelativeRelative TT0.30.3 valuesvalues of of albumin albumin were were significantly signiﬁcantly larger larger than than those those of of HES HES for for the 0.1%0.1% and 0.2%0.2% NaHANaHA solutions, solutions, but but did did not not signiﬁcantly significantly differ differ between between albumin albumin and HESand HESfor the for 0.4% the 0.4% NaHA NaHA solution solution (Table (Table1). 1).

TableTable 1. RelativeRelative time time 1 1atat which which relative relative Orange Orange G absorbance G absorbance reached reached 0.3 0.3as it as permeated it permeated into into sodiumsodium hyaluronic hyaluronic acid acid solution solution (NaHA) (NaHA) contai containingning albumin or hydroxyethyl starch (HES). Colloid Colloid 2 Test SolutionTest Solution p Valuep Value2 AlbuminAlbumin HES HES 0.1%0.1% NaHA NaHA in 1.1% in colloid 1.1% colloid 3.33 ± 0.69 3.33 ± 0.69 1.16 ± 0.08 1.16 ± 0.08 0.006 0.006 0.2%0.2% NaHA NaHA in 1% colloidin 1% colloid 1.95 ± 0.32 1.95 ± 0.32 0.92 ± 0.27 0.92 ± 0.27 0.013 0.013 0.4%0.4% NaHA NaHA in 0.8% in colloid 0.8% colloid 3.19 ± 1.33 3.19 ± 1.33 1.58 ± 0.03 1.58 ± 0.03 0.11 0.11 11 TimeTime relativerelative to to reference reference (1.2% (1.2% colloid). colloid).2 Albumin 2 Albumin versus HES.versus Values HES. are Values shown asare mean shown± standard as mean deviation ± standard(n = 3). deviation (n = 3).

3.2. Effects of Albumin and HES on Osmotic Swelling Pressure of NaHA Solution Hydrostatic pressure of PBS, 2% albumin, and 2% HES solutions measured in the

reference chamber steeply decreased within 30 min, and thereafter gradually decreased until equilibrium was reached at roughly 15 h (Figure5). HES had a higher hydrostatic pressure in the reference chamber at 2 h compared to PBS (p = 0.022) and albumin (p = 0.021) and at 5 h compared to PBS (p = 0.029). No signiﬁcant difference in hydrostatic pressure was noted between PBS, albumin, and HES at other time points. PolymersPolymers 2021 2021, 13, ,13 x ,FOR x FOR PEER PEER REVIEW REVIEW 7 of7 of12 12

3.2.3.2. Effects Effects of ofAlbumin Albumin and and HES HES on on Os Osmoticmotic Swelling Swelling Pressure Pressure of ofNaHA NaHA Solution Solution HydrostaticHydrostatic pressure pressure of of PBS, PBS, 2% 2% albumin, albumin, and and 2% 2% HES HES solutions solutions measured measured in in the the referencereference chamber chamber steeply steeply decreased decreased within within 30 30 min, min, and and thereafter thereafter gradually gradually decreased decreased untiluntil equilibrium equilibrium was was reached reached at atroughly roughly 15 15 h h(Figure (Figure 5). 5). HES HES had had a highera higher hydrostatic hydrostatic pressurepressure in in the the reference reference chamber chamber at at2 h2 hcompared compared to to PBS PBS (p (=p 0.022)= 0.022) and and albumin albumin (p (=p = Polymers 2021, 13, 514 0.021)0.021) and and at at5 5h hcompared compared to to PBS PBS (p (p= =0.029). 0.029). No No significant significant difference difference in in hydrostatic hydrostatic7 of 12 pressurepressure was was noted noted between between PBS, PBS, albumin, albumin, and and HES HES at atother other time time points. points.

FigureFigureFigure 5. 5.5.Comparison Comparison of ofchanges changes over over time time of ofhydrosta hydrostatichydrostatictic pressure pressure in inthe the reference reference chamber chamber of ofthe the osmoticosmoticosmotic flow flowflow cell cell for for 1% 1% sodium sodium hyaluronic hyaluronic hyaluronic acid acid acid solution solution solution (i.e., (i.e., (i.e., osmotic osmotic osmotic swelling swelling swelling pressure) pressure) pressure) against against against phosphatephosphatephosphate buffered buffered saline saline (PBS), (PBS), 2% 2% albumin, albumin, an andand 2%d 2% hydroxyethyl hydroxyethyl starch starch (HES) (HES) solution. solution. solution. Ex- Ex- Experi- perimentsmentsperiments were were were carried carried carried out out at out 25at at25◦C. 25 °C. For °C. For simplicity, For simplicit simplicit valuesy, valuesy, values are are presented are presented presented as meanas asmean mean and and standard and standard standard deviation deviationdeviation for for every every 5 h5 (hn (=n 4).= 4). *: significantly*: significantly different different from from PBS PBS and and albumin albumin at atthe the same same time time for every 5 h (n = 4). *: significantly different from PBS and albumin at the same time point; #: point;point; #: #:significantly significantly different different fr omfrom PBS PBS at atthe the same same time time point. point. significantly different from PBS at the same time point.

3.3.3.3.3.3. Effects Effects of ofAlbumin Albumin and and HES HES on on Darcy’s Darcy’s Permeability PermeabilityPermeability Coefficient CoefficientCoefficient of of ofNaHA NaHANaHA Solution SolutionSolution FluidFluid infusion infusioninfusion into intointo NaHA NaHA NaHA solution solution solution increa increased increasedsed the the hydrostatichydrostatic hydrostatic pressurepr pressureessure in in thein the the pressure pres- pres- suretubesure tube overtube over time,over time, reachingtime, reaching reaching a plateau a plateaua plateau (Figure (Figure (Figure6a). It 6a). was 6a). It thus Itwas was confirmed thus thus confirmed confirmed that the that flow–pressurethat the the flow– flow– pressurerelationshippressure relationship relationship obeyed obeyed Darcy’s obeyed Darcy’s law. Darcy’sP valueslaw. law. P atPvalues plateauvalues at atplateau were plateau plotted were were againstplotted plotted Qagainst againstvalues Q to Q valuesobtainvalues to ∆to obtainP /obtain∆Q Δvalues PΔ/PΔ/QΔ usingQvalues values a linearusing using a fitting lineara linear procedure, fitting fitting procedure, procedure, which were which which then were usedwere then tothen determine used used to to determineKdeterminevalues ofK Kvalues NaHA values of solutions of NaHA NaHA solutions (Figure solutions6b). (Figure (Figure 6b). 6b).

FigureFigureFigure 6. 6.6.(a ()(a aTime)) TimeTime course course course of of ofchanges changes changes in in inhydrostatic hydrostatic hydrostatic pressure pressure pressure in in inth the eth pressuree pressure tubetube tube forfor for 0.3%0.3% 0.3% sodiumso sodiumdium hyaluronic hyaluronic hyaluronic acid acid acid solution solu- solu- tion(NaHA)tion (NaHA) (NaHA) at different at atdifferent different infusion infusion infusion rates rates of rates phosphate of ofphosphate phosphate buffered buffe buffe salineredred saline (PBS) saline in(PBS) the(PBS) measurementin inthe the measurement measurement of Darcy’s of of permeabilityDarcy’s Darcy’s permeability permeability coefﬁcient coefficientofcoefficient NaHA of solution. ofNaHA NaHA Experimentssolution. solution. Experiments Experiments were carried were were out carried at carried 25 ◦ C.out out For at simplicity,at25 25 °C. °C. For For valuessimplicity, simplicity, are presented values values are asare presented mean presented and as standard asmean mean and error and standardforstandard every error 2error h. for (b for) Relationshipevery every 2 h.2 h.(b between)( bRelationship) Relationship infusion between between rates ofinfusion PBSinfusion and rates hydrostaticrates of ofPB PBS andS pressure and hydrostatic hydrostatic in the pressure pressu pressure tube rein inthe at the plateaupressure pressure for tubetube at atplateau plateau for for different different concentrations concentrations of ofNaHA NaHA solu solutiontion fitted fitted with with linear linear regr regressionession lines lines (dashed (dashed lines). lines). different concentrations of NaHA solution ﬁtted with linear regression lines (dashed lines).

K values decreased as the concentration of NaHA increased for both PBS and colloid solutions. K values of colloid solutions were lower than those of PBS solution at all concentrations of NaHA. Compared to albumin, higher K values were observed for HES at 0.1% NaHA, while values were lower at 0.3% and 0.5% NaHA (Figure7). As a result, the slope of K values against NaHA concentrations was steeper for HES than that for albumin. PolymersPolymers 2021 2021, ,13 13, ,x x FOR FOR PEER PEER REVIEW REVIEW 88 of of 12 12

KK valuesvalues decreaseddecreased asas thethe concentrationconcentration ofof NaHANaHA increasedincreased forfor bothboth PBSPBS andand col-col- loidloid solutions.solutions. KK valuesvalues ofof colloidcolloid solutionssolutions werewere lowerlower thanthan thosethose ofof PBSPBS solutionsolution atat allall concentrationsconcentrations ofof NaHA.NaHA. ComparedCompared toto albumin,albumin, higherhigher KK valuesvalues werewere observedobserved forfor HESHES atat 0.1%0.1% NaHA,NaHA, whilewhile valuesvalues werewere lowerlower atat 0.3%0.3% andand 0.5%0.5% NaHANaHA (Figure(Figure 7).7). AsAs aa result,result, Polymers 2021, 13, 514 8 of 12 thethe slopeslope ofof KK valuesvalues againstagainst NaHANaHA concentrationsconcentrations waswas steepersteeper forfor HESHES thanthan thatthat forfor albumin.albumin.

FigureFigureFigure 7. 7. 7. Comparison ComparisonComparison of of of Darcy’s Darcy’s Darcy’s permeability permeability permeability coefficients coefficients coefﬁcients ( (KK) () Kof of) ofsodium sodium sodium hyaluronic hyaluronic hyaluronic acid acid acid (NaHA) (NaHA) (NaHA) solutionsolutionsolution when when when phosphate phosphate phosphate buffered buffered buffered saline saline (PBS) (PBS) or or 2% 2% colloid colloid solution solutionsolution (i.e., (i.e.,(i.e., albumin albuminalbumin or or hydroxy- hydroxyethylhydroxy- ethyl starch (HES)) was infused. Solid line denotes K values calculated by Equation (4) according ethylstarch starch (HES)) (HES)) was was infused. infused. Solid Solid line line denotes denotesK values K values calculated calculated by Equationby Equation (4) according(4) according tothe toto the the hydrodynamic hydrodynamic model model of of hyaluronic hyaluronic acid acid polymer polymer networks. networks. Dotted Dotted lines lines denote denote linear linear re- re- hydrodynamic model of hyaluronic acid polymer networks. Dotted lines denote linear regression gressiongression lines lines between between logarithmic logarithmic values values of of NaHA NaHA concentrations concentrations and and K K. . lines between logarithmic values of NaHA concentrations and K.

3.4.3.4.3.4. EffectsEffects Effects ofof of AlbuminAlbumin Albumin andand and HESHES HES onon on DynamicDynamic Dynamic ShearShear Shear ModuliModuli Moduli ofof of NaHANaHA NaHA SolutionSolution Solution WhileWhileWhile thethe the presencepresence presence ofof of 3%3% 3% albuminalbumin albumin inin in NaHANaHA solutionsolution significantlysignificantly signiﬁcantly increasedincreased increased GG′ ′0 andandand GGG″″ ” ofof of NaHANaHA NaHA solutionsolution solution relativerelative relative toto to PBSPBS PBS atat at lowlow low frequencyfrequency (i.e.,(i.e., <1<1 Hz),Hz), Hz), GGG′ ′0 andandand GGG″″” ofof of NaHANaHA NaHA solutionsolutionsolution werewere were similarsimilar similar forfor for PBSPBS PBS andand and 3%3% 3% HESHES HES (Figure(Figure (Figure 8a).88a).a). Nevertheless, Nevertheless, the the increase increase in in HES HESHES concentrationconcentrationconcentration from from 3%3% tototo 6% 6%6% signiﬁcantly significantlysignificantly increased increasedincreasedG0 GandG′ ′ andandG” ofGG″″NaHA ofof NaHANaHA solution, solution,solution, resulting re-re- sultingsultingin larger inin G largerlarger0 and GG”′ ′ and ofand NaHA GG″″ ofofsolution NaHANaHA solution comparedsolution comparedcompared to PBS and toto 6% PBSPBS albumin andand 6%6% at albuminalbumin all frequencies atat allall frequenciesfrequenciesexamined (Figure examinedexamined8b). (Figure(Figure 8b).8b).

0 FigureFigureFigure 8. 8. 8. ( (a(aa)) ) ComparisonComparison Comparison ofof of storage storage storage ((G (GG′)′) ) andand and lossloss loss ((G (GG″″)”)) shearshear shear modulimoduli moduli ofof of 0.5%0.5% 0.5% sodiumsodium sodium hyalhyal hyaluronicuronicuronic acidacid acid (NaHA)(NaHA) (NaHA) dissolved dissolved dissolved in in in 0 phosphatephosphatephosphate bufferedbuffered saline saline (PBS) (PBS)(PBS) or or 3%3% colloidcolloid solutionsolutisolutionon (i.e., (i.e.,(i.e., albumin albuminalbumin or oror hydroxyethyl hydroxyethylhydroxyethyl starch starchstarch (HES)). (HES)).(HES)). (b ()(bb Comparison)) ComparisonComparison of ofofG GGand′ ′ andandG ” GG of″″ ofof 0.5% 0.5%0.5% NaHA NaHANaHA dissolved dissolveddissolved in in PBSin PBSPBS or or 6%or 6%6% colloid colloidcolloid solution solutionsolution (i.e., (i.e.,(i.e., albumin albuminalbumin or HES).oror HES).HES). Values ValuesValues are are expressedare expressedexpressed as mean asas meanmean and andandstandard standard standard deviation deviation deviation (n = ( (n 6n = or= 6 6 7).or or 7). 7).

4. Discussion 4.1. Permeation of Orange G into NaHA Solution

This study demonstrated that albumin and HES exerted different effects on the permeation of Orange G into NaHA solution. The presence of albumin signiﬁcantly decreased Orange G permeation at ≥0.1% NaHA (Figure4a), while the presence of HES did not signiﬁcantly affect Orange G permeation into NaHA solution at concentrations up to 0.2% Polymers 2021, 13, 514 9 of 12

(Figure4b). According to Ogston’s theory on the distribution of spaces in a uniform random suspension of ﬁbers [18], the pore radius of NaHA solution (rp) is expressed as follows [19]: p rp = (rf/4) π/ϕf, (2)

where rf and ϕf are the radius and volume fraction of NaHA, respectively, and

ϕf = c · ν, (3)

where c and ν are the concentration (g/cm3) and partial specific volume of NaHA (0.653 cm3/g in 0.2 M NaCl solution [2]), respectively. The reported rf value of NaHA is 0.55 nm [2]. Therefore, the pore radii of 0.1%, 0.2%, and 0.4% NaHA solutions according to Equa- tions (2) and (3) are 9.5 nm, 6.7 nm, and 4.8 nm, respectively. Given that the Stokes–Einstein radii of albumin and HES molecules are reported to be 3.5 nm [20] and 6.1 nm [21], respectively, albumin can permeate through the pores of NaHA solution at all three concentrations, whereas HES molecules can permeate through the pores of NaHA solution at 0.1% and 0.2%, but not 0.4%. The partitioning of albumin into NaHA pores explains its obstructive effect, and hence, the restriction of Orange G permeation into NaHA solution [22]. As for HES, despite the assumption that HES can partition into the hydrodynamic pores of NaHA solution at concentrations of 0.1% and 0.2%, no restriction of Orange G permeation into NaHA solution was observed. One possible explanation for this discrepancy is the difference between the global structure of albumin and HES. First, the spherical structure of albumin may retard Orange G diffusion compared to the linear polymer structure of HES by increasing frictional resistance between Orange G and albumin. Second, the electrostatic interaction of positively charged amino acid residues of albumin with negatively charged Orange G could slow Orange G diffusion compared to electrically neutral HES (Figure S1). Finally, the inhomogeneous structure of NaHA solution may have contributed at least in part to the observed discrepancy. The uneven distribution of NaHA chain segments creates regions of low NaHA concentration and high NaHA concentration (i.e., clusters) due to the entanglement of NaHA chain segments [15]. Given that HES accelerates this uneven NaHA chain segment distribution by restricting NaHA diffusion, the resultant decrease of friction force between NaHA chains and permeating solute [15] might have cancelled out the obstructive effect of HES.

4.2. Effects of Albumin and HES on Osmotic Swelling Pressure and Darcy’s Permeability Coefficient of NaHA Solution The mean osmotic pressure (i.e., decrease of hydrostatic pressure in the reference chamber at 20 h from baseline) of 1% NaHA in PBS was 0.69 kPa, which is comparable to 6 that of 1% HA (Mw 1.5 × 10 ) in PBS (pH 7.6) reported previously (0.69 kPa) [23], demon- strating the acceptable accuracy of the measuring system. The significantly smaller osmotic swelling pressure (i.e., decrease of hydrostatic pressure in the reference chamber from baseline) of 1% NaHA against HES at 2 h compared to albumin suggests that HES slows osmotic swelling of NaHA arising from the collective diffusion of NaHA (Figure5)[15]. According to the hydrodynamic modeling of HA polymer network, K (Darcy’s permeability coefficient, cm2) is expressed as follows [24]:

ln(1/c) − 0.18 K = 5.4 × 10−16 · , (4) c

where c is the concentration (g/cm3) of NaHA. Consistent with a previous study, which measured ﬂow rates at given pressure drops (i.e., up to 10 kPa) across HA solutions of 0.05–1.5% (w/w)[24], the K values obtained in the present study were comparable with those calculated by Equation (4) for 0.3% NaHA in PBS (8.1 cm2 vs. 10.1 cm2) and 0.5% NaHA in PBS (4.4 cm2 vs. 5.5 cm2) (Figure7). The K value for 0.1% NaHA in PBS, which was two-fold smaller than that calculated by Equation (4) (17 cm2 vs. 36 cm2), may not Polymers 2021, 13, 514 10 of 12

be unreasonable given that the contribution of dialysis membranes to the overall K value is not negligible compared to the K value for 0.1% NaHA in PBS. The steep slope of K values against NaHA concentrations for HES compared to albumin (Figure7) suggests that frictional resistance between HES and NaHA chains increased with increasing NaHA concentration to a larger extent compared to albumin. Collective diffusion is determined by the balance between the thermodynamic force, which drives spreading of solute particles and the frictional force, which resists the spreading [15]: n ∂Π D (n) = · , (5) c ξ ∂n

where Dc(n) is the collective diffusion constant of solute, n is the particle density, ξ is the friction coefﬁcient, and ∂Π/∂n is the osmotic pressure. Given that HES increases frictional resistance, as reﬂected by the steep slope of K values against NaHA concentrations (i.e., larger ξ), HES might have restricted the collective diffusion of NaHA as shown by slowed osmotic swelling of NaHA by HES aforementioned, thereby accelerating the uneven distribution of NaHA chain segments.

4.3. Effects of Albumin and HES on Dynamic Shear Moduli of NaHA Solution G0 and G” of NaHA solution were significantly increased in the presence of 6% HES compared to PBS or 6% albumin (Figure8b). HA chain segments are considered to exist in a continuous equilibrium between stiff and flexible states, and their local conformational ordering is maintained by continuous forming and breaking of hydrogen bonds [25]. In particular, hydrogen bonds between adjacent saccharides largely contribute to the intrinsic stiffness of HA under physiological electrolyte concentrations and pH conditions [26]. HES-induced increases in G0 and G” of NaHA solution were consistent with sugar- induced increases in G0 and G” of HA previously reported, and likely resulted from the increase of bond angle restriction and the creation of new hydrogen bonds [25]. As G0 and G” of NaHA solution at frequency <100 Hz reflect the orientational dynamics of NaHA chains [27], 6% HES might increase the number of elastically active NaHA chains to a greater extent than 6% albumin by strengthening the transient NaHA network. HES at 6% exceeds the plasma HES concentration used in clinical settings (1–2%). Nevertheless, it is possible that the viscoelastic property of NaHA at lower concentrations (e.g., 0.2%) is readily affected by lower concentrations of HES (e.g., 2%), although the rotational rheometer used in the present study could not examine dynamic shear moduli of NaHA solution of lower concentrations due to minimum torque constraints.

4.4. Implications The present study demonstrated that albumin restricted Orange G permeation through NaHA solution to a greater degree than HES. The different effects of albumin and HES may be related to the uneven NaHA chain segment distribution arising from the restriction of NaHA diffusion by HES. Since the molecular weights of antibiotics, anti-inflammatory drugs, and anticancer drugs range from hundreds to thousands [28–30], i.e., comparable with that of Orange G, this finding may help in selecting an optimal colloid solution for effective drug delivery in the treatment of cancer patients undergoing major surgery. If the treatment requires rapid onset of drugs, HES solution may allow for their rapid distribution in the interstitial space. In contrast, given that anticancer drugs must remain in the interstitial space for an extended period, albumin solution may be preferable because it may delay the transport of the drugs from the interstitial space to lymphatic vessels by restricting diffusion through the interstitial space. As interstitial resistance to solute permeation is influenced not only by finer fibrous molecules such as HA, but also coarse fixed elements such as collagen fibrils [2], these scenarios warrant further investigation in in vivo studies. Studies on the contribution of hydrogen bonding of colloids with NaHA chains to solute permeation properties are also warranted. Polymers 2021, 13, 514 11 of 12

Supplementary Materials: The following are available online at https://www.mdpi.com/2073-436 0/13/4/514/s1, Figure S1: Chemical structures, Figure S2: Visualization for dye permeation. Funding: This work was supported by JSPS KAKENHI [grant numbers 15K10549, 19K09363]. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author. Conﬂicts of Interest: The author declares no conﬂict of interest.

References 1. Comper, W.D.; Laurent, T.C. Physiological function of connective tissue polysaccharides. Physiol. Rev. 1978, 58, 255–315. [CrossRef] 2. Levick, J.R. Flow through interstitium and other fibrous matrices. Q. J. Exp. Physiol. 1987, 72, 409–437. [CrossRef] 3. Cowman, M.K.; Matsuoka, S. Experimental approaches to hyaluronan structure. Carbohydr. Res. 2005, 340, 791–809. [CrossRef] 4. Fallacara, A.; Baldini, E.; Manfredini, S.; Vertuani, S. Hyaluronic acid in the third millennium. Polymers 2018, 10, 701. [CrossRef] [PubMed] 5. Fouissac, E.; Milas, M.; Rinaudo, M. Shear-rate, concentration, molecular weight, and temperature viscosity dependences of hyaluronate, a wormlike polyelectrolyte. Macromolecules 1993, 26, 6945–6951. [CrossRef] 6. Laurent, T.C. In Vitro studies on the transport of macromolecules through the connective tissue. Fed. Proc. 1966, 25, 1128–1134. [PubMed] 7. Laurent, T.C. Structure of the extracellular matrix and the biology of hyaluronan. In Interstitium, Connective Tissue and Lymphatics; Reed, R.K., McHale, N.G., Bert, J.L., Winlove, C.P., Laine, G.A., Eds.; Portland Press: London, UK, 1995; pp. 1–12. 8. Chen, W.Y.; Abatangelo, G. Functions of hyaluronan in wound repair. Wound Repair Regen. 1999, 7, 79–89. [CrossRef][PubMed] 9. Jain, R.K. Transport of molecules in the tumor interstitium: A review. Cancer Res. 1987, 47, 3039–3051. 10. Westphal, M.; James, M.F.M.; Kozek-Langenecker, S.; Stocker, R.; Guidet, B.; Van Aken, H. Hydroxyethyl starches: Different products—Different effects. Anesthesiology 2009, 111, 187–202. [CrossRef] 11. Woodcock, T.E.; Woodcock, T.M. Revised Starling equation and the glycocalyx model of transvascular fluid exchange: An improved paradigm for prescribing intravenous fluid therapy. Br. J. Anaesth. 2012, 108, 384–394. [CrossRef] 12. Xu, S.; Yamanaka, J.; Sato, S.; Miyama, I.; Yonese, M. Characteristics of complexes composed of sodium hyaluronate and bovine serum albumin. Chem. Pharm. Bull. 2000, 48, 779–783. [CrossRef][PubMed] 13. Grymonpré, K.R.; Staggemeier, B.A.; Dubin, P.L.; Mattison, K.W. Identification by integrated computer modeling and light scattering studies of an electrostatic serum albumin-hyaluronic acid binding site. Biomacromolecules 2001, 2, 422–429. [CrossRef] [PubMed] 14. Tatara, T. Contrasting effects of albumin and hydroxyethyl starch solutions on physical properties of sodium hyaluronate solution. Carbohydr. Polym. 2018, 201, 60–64. [CrossRef][PubMed] 15. Doi, M. Soft Matter Physics; Oxford University Press: New York, NY, USA, 2018. 16. Tatara, T. The contribution of solute-solvent exchange at the membrane surface to the reduction by albumin of the hydraulic permeability coefficient of an artificial semipermeable membrane. Anesth. Analg. 2003, 97, 1137–1142. [CrossRef] 17. Tatara, T.; Tashiro, C. Analysis using a linear viscoelastic model of the In Vitro osmotic kinetics of polydisperse synthetic colloids. Biomacromolecules 2005, 6, 1732–1738. [CrossRef] 18. Ogston, A.G. The spaces in a uniform random suspension of fibres. Trans. Faraday Soc. 1958, 54, 1754–1757. [CrossRef] 19. White, J.A.; Deen, W.M. Agarose-dextran gels as synthetic analogs of glomerular basement membrane: Water permeability. Biophys. J. 2002, 82, 2081–2089. [CrossRef] 20. Armstrong, J.K.; Wenby, R.B.; Meiselman, H.J.; Fisher, T.C. The hydrodynamic radii of macromolecules and their effect on red blood cell aggregation. Biophys. J. 2004, 87, 4259–4270. [CrossRef] 21. Sakai, H.; Sato, A.; Takeoka, S.; Tsuchida, E. Mechanism of flocculate formation of highly concentrated phospholipid vesicles suspended in a series of water-soluble biopolymers. Biomacromolecules 2009, 10, 2344–2350. [CrossRef] 22. Masaro, L.; Zhu, X.X. Physical models of diffusion for polymer solutions, gels, and solids. Prog. Polym. Sci. 1999, 24, 731–775. [CrossRef] 23. Laurent, T.C.; Ogston, A.G. The interaction between polysaccharides and other macromolecules. 4. The osmotic pressure of mixtures of serum albumin and hyaluronic acid. Biochem. J. 1963, 89, 249–253. [CrossRef] 24. Jackson, G.W.; James, D.F. The hydrodynamic resistance of hyaluronic acid and its contribution to tissue permeability. Biorheology 1982, 19, 317–330. [CrossRef] 25. Kobayashi, Y.; Okamoto, A.; Nishinari, K. Viscoelasticity of hyaluronic acid with different molecular weights. Biorheology 1994, 31, 235–244. [CrossRef] Polymers 2021, 13, 514 12 of 12

26. Gribbon, P.; Heng, B.C.; Hardingham, T.E. The molecular basis of the solution properties of hyaluronan investigated by confocal fluorescence recovery after photobleaching. Biophys. J. 1999, 77, 2210–2216. [CrossRef] 27. Nijenhuis, N.; Mizuno, D.; Spaan, J.A.E.; Schmidt, C.F. Viscoelastic response of a model endothelial glycocalyx. Phys. Biol. 2009, 6, 025014. [CrossRef][PubMed] 28. Altman, S. Antibiotics present and future. FEBS Lett. 2014, 588, 1–2. [CrossRef][PubMed] 29. Bartzatt, R. Anti-inflammatory drugs and prediction of new structures by comparative analysis. Antiinflamm. Antiallergy Agents Med. Chem. 2012, 11, 151–160. [CrossRef][PubMed] 30. Swabb, E.A.; Wei, J.; Gullino, P.M. Diffusion and convection in normal and neoplastic tissues. Cancer Res. 1974, 34, 2814–2822.