Arginine end-functionalized poly (L-lysine) dendrigrafts for the stabilization and controlled release of insulin

Arginine end-functionalized poly (L-lysine) dendrigrafts for the stabilization and controlled release of insulin
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  See discussions, stats, and author profiles for this publication at: Arginine end-functionalized poly(L-lysine)dendrigrafts for the stabilization and controlledrelease of insulin  Article   in  Journal of Colloid and Interface Science · November 2010 DOI: 10.1016/j.jcis.2010.07.072 · Source: PubMed CITATIONS 22 READS 52 7 authors , including:Zili SideratouNational Center for Scientific Research Demo… 58   PUBLICATIONS   1,342   CITATIONS   SEE PROFILE Leto TzivelekaNational Center for Scientific Research Demo… 35   PUBLICATIONS   888   CITATIONS   SEE PROFILE Angelos ThanassoulasNational Center for Scientific Research Demo… 20   PUBLICATIONS   104   CITATIONS   SEE PROFILE Constantinos PaleosNational Center for Scientific Research Demo… 166   PUBLICATIONS   3,924   CITATIONS   SEE PROFILE All content following this page was uploaded by Angelos Thanassoulas on 19 December 2013. The user has requested enhancement of the downloaded file.  Arginine end-functionalized poly( L  -lysine) dendrigrafts for the stabilization andcontrolled release of insulin Zili Sideratou a , Nikoletta Sterioti a , Dimitris Tsiourvas a, ⇑ , Leto-Aikaterini Tziveleka a ,Angelos Thanassoulas b , George Nounesis b , Constantinos M. Paleos a a Institute of Physical Chemistry, NCSR ‘‘Demokritos ” , 15310 Aghia Paraskevi, Attiki, Greece b Biomolecular Physics Laboratory, IRRP, NCSR ‘‘Demokritos ” , 15310 Aghia Paraskevi, Attiki, Greece a r t i c l e i n f o  Article history: Received 17 June 2010Accepted 30 July 2010Available online 4 August 2010 Keywords: InsulinBiodegradable polymersDendrigraftsProtein–polymer interaction a b s t r a c t Second generation biodegradable poly( L  -lysine) dendrigrafts functionalized with 12–48 arginine end-groups interact, at physiological pH, with insulin affording dendrigraft/insulin complexes as establishedby dynamic light scattering,  f -potential, circular dichroism and isothermal titration calorimetry. Bindingoccurs in two steps; at low dendrigraft/insulin molar ratios ( 6 0.07) interaction is accompanied with theendothermic dissociation of insulin dimers, while at higher molar ratios, complexation of insulin mono-mers with dendrigraft derivatives occurs exothermically. High levels of insulin complexation efficiencies(>99%) were determined for all derivatives. Stabilization of complexed insulin against enzymatic degra-dation by trypsin and  a -chymotrypsin is observed especially for the highly arginine end-functionalizeddendrigrafts. Insulinreleaseratesinsimulatedintestinalfluidarebeingcontrolledbythenumberofargi-nine end-groups and released insulin retains its conformation.   2010 Elsevier Inc. All rights reserved. 1. Introduction The delivery of peptides and proteins including insulin to sys-temic circulation through oral administration is hindered by sev-eral obstacles such as proteolytic enzymes, sharp pH gradientsand low epithelial permeability. Since insulin oral administrationis more attractive compared to injection, extensive work has beenconducted for addressing these problems and this research efforthas been recently reviewed [1–8]. Thus, as it is the case with otherpeptideandproteindrugs,severalapproacheshavebeenemployedin order to attain an effective insulin oral delivery system. Theseinclude the utilization of absorption enhancers [9,10], proteaseinhibitors [11,12] and cell penetrating peptides [13,14] or the attachment of poly(ethylene glycol) chains [15,16] and the use of drug delivery systems such as liposomes [17,18], PLGA micro-spheres[19,20], nanoparticles[21,22], hydrogels[23,24], andpoly- mericmicellesoramphiphilicpolymerswhichspontaneouslyformnano-complexes in aqueous environment [25]. In this context, itshould be noted that directly functionalized insulin may loose itsbioactivity and, therefore, a strategy in which insulin remains in-tact or at least non-covalently conjugatedis preferred. In the lattercase, it is the carriers that are functionalized instead of insulin.Examples of this strategy are the coating of liposomes withpoly(ethylene glycol) chains (PEG) or with the sugar chain portionof mucin [26]. In both cases, enhanced resistance against emulsifi-cationbybilesalts andincreasedstabilityintheGI tract havebeenobserved [26]. Additionally, protein delivery systems relying oncomplexationandassemblyofproteinswithamphiphilicpolymerscould providean alternative approach. These polymers formnano-scale complexes with proteins through electrostatic and van derWaalsinteractions,protectingthemagainstlossofbiologicalactiv-ity while increasing their transmucosal uptake. Several polymerssuch as chitosan [27,28], block-copolymers [29,30], or branched polyesters [31,32] have been proposed for insulin delivery.Previous studies demonstrated that arginine-rich peptides im-prove the permeability of poorly taken up molecules through cellmembranes in a diversity of cells [33]. Actually, the so-called cellpenetrating peptides (CPPs) including the Tat peptides, arginine-rich peptides as well as oligoarginines, when covalently bound tovarious molecules, proteins or nanoparticles are taken up effi-ciently by cells [34–37]. This is attributed to the interaction be-tween the positively charged arginine and the negatively chargedcellmembrane-associatedproteoglycans.Inthiscontext,enhancedintestinal insulin absorption has been reported for insulin–Tatconjugates [13]. The intestinal absorption efficiency on Caco-2 cellmonolayers was 6–8 times higher compared to normal insulin.Insulin–Tat transportation was suggested to take place through 0021-9797/$ - see front matter    2010 Elsevier Inc. All rights reserved.doi:10.1016/j.jcis.2010.07.072 ⇑ Corresponding author. Address: Institute of Physical Chemistry, NCSR ‘‘Dem-okritos”,PartriarchouGregoriou&Neapoleos,15310AghiaParaskevi,Attiki,Greece.Fax: +30 210 6511766. E-mail address: (D. Tsiourvas). Journal of Colloid and Interface Science 351 (2010) 433–441 Contents lists available at ScienceDirect  Journal of Colloid and Interface Science  an active and transcytosis-like mechanism. On the other hand,CPPsandinparticularoctaarginine,havebeenreportedtoimproveintestinalabsorptioninratsfollowingco-administrationwithinsu-lin, without causing detectable damage on the intestinal mucosa[14]. Further studies [38,39] suggested that oligoarginine attach- ment to proteoglycans and energy-dependent endocytosis are in-volved in its permeation through the ileal epithelial membrane.It was further emphasized that electrostatic interaction betweenthe peptide and octaarginine or  L  -penetratin is related to theenhancing effect of intestinal absorption of insulin. Even if theirinteraction results in the formation of aggregates, insulin absorp-tionisenhanced,sincetheaggregatesarebrokendowninthepres-ence of intestinal degradation enzymes.Inthe present work, wereport the complexationof insulinwithbiodegradable arginine end-functionalized poly( L  -lysine) dendri-grafts at physiological p H   values. Specifically, a second generationpoly( L  -lysine) dendrigraft with48end-groups has beenpartiallyorfully guanidinylated affording four derivatives bearing 12, 24, 36and 48 arginine end-groups (Scheme 1). The negatively chargedinsulin interacts with the positively charged moieties located atthe surface of the dendrigraft poly( L  -lysine) derivatives formingthe corresponding dendrigraft/insulin complexes. Their formationwas studied by dynamic light scattering (DLS),  f -potential and iso-thermaltitrationcalorimetry(ITC). Thecomplexformationprocessis reversibleandtheredissolvedinsulinretainsitsconformationasrevealed by circular dichroism (CD) studies. Stabilization of com-plexed insulin against enzymatic degradation by trypsin and a -chymotrypsin, as well as its release in enzyme-free simulatedintestinal fluid will be presented. 2. Materials and methods  2.1. Materials Second generation poly( L  -lysine) dendrigraft (DL,  M  w  =8600,DPn=48, polydispersity=1.3) bearing 48 amino groups at theexternal surface was kindly donated by ColcomSARL (Montpellier,France). 1 H  -pyrazole-1-carboxamidine hydrochloride (99%), and N  , N  -diisopropylethylamine (DIPEA) were purchased from Sigma–Aldrich Co. (St. Louis, MO, USA). Human insulin was kindly pro-vided by Novo Nordisk (Denmark). Trypsin and  a -chymotrypsinwere also purchased from Sigma–Aldrich Co.  2.2. Synthesis of guanidinylated poly( L -lysine) dendrigrafts A series of partially guanidinylated poly( L  -lysine) dendrigraftsof the second generation with 12, 24, 36 guanidinium groups andthe fully functionalized dendrigraft with 48 guanidinium groupswasprepared(Scheme1)byamethodanalogoustoonepreviouslyreported [40]. Thus, to 0.05mmol poly( L  -lysine) dendrigraft dis-solved in dry DMF (20mL), a DMF solution (10mL) containing0.66, 1.32, 1.98 or 2.64mmol 1 H  -pyrazole-1-carboxamidinehydrochloride and 0.66, 1.32, 1.98 or 2.64mmol DIPEA, respec-tively, was added dropwise. The mixture was allowed to react for24h under argon. Subsequently, the solution was concentratedby solvent distillation under reduced pressure and the productwas precipitated with diethyl ether. The crude product was dis-solved in water and was subjected to dialysis (mol. weight cut-off: 1200) to remove by-products. Lyophilization afforded the final NHHNNHHNONHOHNNHOHNNHHNONHOHNNHHNONHOHNOOHH 2 NNHHNONH 2 H 2 NO NH 2 NHOH 2 N OH 2 NNHHNO NH 2 H 2 NONH 2 NHOH 2 NONH 2 NHHNONH 2 H 2 NONH 2 NHONH 2 ONH 2 NHHNNHONH 2 OH 2 NNH 2 OH 2 NHNONH 2 OH 2 NNHHNNHONH 2 OH 2 NNH 2 OH 2 NHN ONH 2 ONH 2 HNNHOH 2 NNH 2 OH 2 NHNONH 2 OH 2 NHNNHOH 2 NNH 2 OH 2 N HNONH 2 ONH 2 HNNHHNOH 2 NONH 2 H 2 NONH 2 NHOH 2 NONHH 2 NHNNHHNOH 2 NOH 2 NNH 2 OH 2 NNHOH 2 NO DL DL 48NHNH 2 NH 2+ Cl - DIPEANNNH 2+ H 2 NCl - DL-G1, n=12DL-G2, n=24DL-G3, n=36DL-G4, n=48 ONH 2 NH 2  nONH 2 48-nONH 2 NH 2 Scheme 1.  Schematic representation of second generation of poly( L  -lysine) dendrigraft (DL) and the reaction scheme affording dendrigraft derivatives functionalized with12–48 arginine end-groups.434  Z. Sideratou et al./Journal of Colloid and Interface Science 351 (2010) 433–441  products (DL-G1, DL-G2, DL-G3 and DL-G4). The structures of gua-nidinylated poly( L  -lysine) dendrigrafts were established by  1 H and 13 C NMR. The degree of substitution was determined by inverse-gated  13 C NMR. 1 H NMR (500MHz, D 2 O and DMSO-d 6 ):  d  =7.80–8.00 (broad s,N H   of guanidinium group), 6.90–7.10 (broad d, N H  þ 2 ), 4.30 (broads, NHC H  CO), 4.05 (s, NHC H  COOH), 3.35 (s, NH 2 C H  CO), 3.00–3.20(m, C H  2 NHC ð NH 2 Þ þ 2 ), 2.90 (m, NH 2 C H  2 ), 1.50–1.85 (m,  b  and  d -C H  2  of lysine), 1.10–1.50 (m,  c -C H  2  of lysine).  13 C NMR (125.1MHz, D 2 O)  d  =174.0 ( C  O), 157.0 (NH C  ð NH 2 Þ þ 2 ), 52.7–54.7( a - C  H of lysine), 41.5 ( C  H 2 NHC ð NH 2 Þ þ 2 ), 39.5 (NH 2 C  H 2 ), 31.1 ( d -C H  2  of lysine), 27.7 ( C  H 2 CH 2 NHC ð NH 2 Þ þ 2 ), 26.6 ( b - C  H 2  of lysine),22.5 ( c - C  H 2  of lysine).  2.3. Interaction of insulin with arginine end-functionalized poly( L -lysine) dendrigraft derivatives and determination of insulincomplexation efficiency Stocksolutionsofinsulin(0.36mM,2mgmL   1 )andpoly( L  -lysine)dendrigraft derivatives (1mM, 4–5mgmL   1 ) in 10mM Tris bufferp H   =7.4 were prepared. Insulin was allowed to interact with thenon-functionalized dendrigraft DL, as well as with the guanidiny-lated derivatives DL-G1, DL-G2, DL-G3, and DL-G4 after additionof dendrigraft stock solutions to insulin solution at several dendri-graft/insulin molar ratios under rigorous stirring. The spontane-ously precipitating complexes were separated from aqueousphase by centrifugation at 6000  g   for 20min at 4  C. The precipi-tatedcomplexeswerewashedtwotimeswithTrisbufferanddriedundervacuumfor24h.Thesupernatantcontainingnon-associatedinsulinwas collectedandtheamount of freeinsulinwas measuredby reversed phase high performance liquid chromatography(HPLC) [41]. A DionexHPLC systemconsistingof a heliumout-gas-ser, a gradient pumpGP 50, a LC30 oven equipped with auto injec-tion port, 25 l L loop, a 218MR54 column (4.6  250mm, 5 l mparticle size, C18, Vydac, USA) and a PDA 100 photodiode arrayUV detector set at 218nm was employed. The mobile phase con-sisted of 0.05%v/v TFA in deionized water (A) and 0.05%v/v TFAin HPLC grade acetonitrile (B). The gradient conditions were 27%B for 4min, 27–36% B within the next 11min and back to 27% Bfor 5min, at a flowrate of 1mLmin  1 at 27  C. Under these condi-tions, the retention time of insulin was 12.7min. Insulin concen-tration in the aqueous solutions was determined from acalibration curve prepared from various standard solutions(2–100 l gmL   1 ,  R  =0.9994). Insulin complexation efficiency wascalculated for complexes obtained at a dendrigraft/insulin molarratio of 0.1, according to the equation [42]. % Complexationefficiency ¼ Totalamountof insulin  FreeinsulinTotalamountof insulin  100 All samples were measured in triplicate.  2.4. Characterization techniques Interaction between functionalized dendrigraft derivatives andinsulinwasinvestigatedbydynamiclightscattering(DLS),isother-mal titration calorimetry (ITC),  f -potential measurements andNear-UV circular dichroism (NUV-CD). The obtained aggregateswere redissolved by the addition of 500mM phosphate buffer(p H   =7.4). This process was followed by DLS and Far-UV circulardichroism (FUV-CD).Dynamic light scattering studies were performed employing anAXIOS-150/EX (Triton Hellas) apparatus with a 30mW lasersource, and an Avalanche photodiode detector at an angle of 90  .For these experiments, 40 l L dispersion of the various dendri-graft/insulin complexes obtained as described above, were dilutedwith various quantities of Tris buffer (0.2–1.5mL). No size differ-ences were observed upon dilution. Ten scattering measurementswere collected for each dispersion, and the results were averaged. f -Potential measurements were conducted using a ZetaPlus of BrookhavenInstrumentsCorp.Inatypicalexperiment,apolymericsolution (1mM) was progressively added to insulin solution(0.36mM, 2mgmL   1 , 10mMTris buffer, p H   =7.4). Followingeachaddition the mixtures were quickly agitated and introduced intothe instrument cell. Ten  f -potential measurements were collectedfor each dispersion, and the results were averaged.In order to measure the thermodynamic parameters of insulinbinding to poly( L  -lysine) dendrigrafts, ITC experiments were car-ried out in a MCS-ITC calorimeter (Microcal, Northampton, USA)at 25  C in Tris–HCl (10mM, p H   =7.4) buffer. This power-compen-sation differential instrument was previously described [43]. In atypical experiment, a dendrigraft solution (1mM) was loaded intothe 250 l L injection syringe, while an insulin solution (0.50mM)was placed in the 1.334mL sample cell of the calorimeter. In thiscase, a small increase in insulin concentration employed(0.50mM instead of 0.36mM) was necessary to improve signalto noise ratio. To avoidair bubble formation, all solutions were de-gassed under vacuum for 5min immediately before measure-ments. The dendrigraft was titrated into the sample cell at asequence of 30 or 60 injections of 8 or 4 l l aliquots, respectively.The intervals between successive injections were 450s to assurethat chemical equilibrium is reached in the cell before the nextaddition. The contents of the sample cell were stirred throughoutthe experiment at 400rpm to ensure thorough mixing. Raw datawereobtainedasaplotofheat( l  J)againstinjectionnumber.Theseraw data were then integrated to obtain a plot of observed enthal-py change per mole of injectant ( D H  , kcalmol  1 ) against molar ra-tio. Enthalpies of dilution of both host and guest molecules weredetermined in separate experiments and subtracted from the cor-responding experimental curves prior to the analysis. These dilu-tion enthalpies were subtracted from the apparent enthalpyobtained in each titration run and all the net titration enthalpycurves were processed with the Origin  5.0 software with embed-ded calorimetric fitting routines.Near UV CD spectra were recorded during titration of insulinsolutions with poly( L  -lysine) dendrigraft derivatives as describedabove for ITCexperiments employing a Jasco J-715 circular dichro-ismspectrophotometer coupledwitha Peltier temperature controlsystem (Jasco PTC-348Wi). Near-UV CD spectra were recorded at25  C using a 0.1-cm path length cell at 250–350nm with a stepsize of 0.2nm, a bandwidth of 1.0nm. Experiments were run intriplicate and 30 scans for each spectrum were signal averaged.For investigating whether insulin retains its conformation aftercomplexation, phosphate buffer (0.5mL, 500mM, p H   =7.4) wasadded to dendrigraft/insulin (0.1molar ratio) precipitated com-plexes containing 2mg of insulin. Insulin complexes were thusredissolvedandtheresultingclearsolutionsweredilutedwithbuf-fertoafinalvolumeof10mL.FUVCDspectraoftheseclearinsulinsolutions were recorded at 25  C using a 0.1-cmpath length cell at200–250nm with a step size of 0.2nm, a bandwidth of 1.0nm. Toeliminate possible contributions frombuffer or dendrigraft deriva-tives that were also present in solution, their CD spectra were re-corded and subtracted from the spectra of the redissolvedsolutions. Experiments were run in triplicate and 10 scans for eachspectrum were signal averaged.  2.5. Insulin in vitro release studies For determining insulin  in vitro  release profiles in enzyme-freesimulatedintestinal fluids, complexespreparedasdescribedaboveat 0.1 dendrigraft/insulin molar ratio, were incubated in 10mL of   Z. Sideratou et al./Journal of Colloid and Interface Science 351 (2010) 433–441  435  simulated intestinal fluid (p H   =6.8) without pancreatin (preparedaccording to USP31-NF26) for 6h at 37  C in a Stuart Orbital incu-bator SI500 at 200rpm. Aliquots were collected at predeterminedtime intervals and replaced by equal volumes of fresh incubationmedium. For the determination of insulin released from com-plexes, samples were centrifuged at 7000  g   for 15min, and 25 l L of supernatant was analyzed by HPLC.  In vitro  release studies werecarried out in triplicate.  2.6. Enzymatic degradation A stock solution of trypsin (4.0mgmL   1 ) was prepared in10mMTris–HClbuffer, p H   =8.0(the optimal operatingp H   of tryp-sin). Dendrigraft/insulin complexes were obtained at a molar ratioequal to 0.1 (2mg insulin) as described above. Subsequently, com-plexes, or free insulin (2.0mg) as control, were incubated at 37  Cin 1.0mL of 10mMTris buffer, p H   8.0 in the presence of trypsin ata molar enzyme/insulinratio of 1:255 [44]. Aliquots (100 l L) werewithdrawn at various time intervals and transferred into ice-coldvials containing 300 l L Tris buffer and 100 l L trifluoroacetic acidto stop enzymatic activity (p H   =2.5); subsequently, 500 l L  tert  -butanolwerealsoaddedtocompletelydissolvethecomplexes.Experimentswereperformedintriplicateandnon-degradedinsulinwasdeterminedbyreversedphaseHPLCasdescribedabove.An analogous study was performed using  a -chymotrypsin. Spe-cifically, a stock solution of   a - chymotrypsin (0.1mgmL   1 ) wasprepared in 1mM HCl containing CaCl 2  (2mM). Dendrigraft/insu-lin complexes or free insulin (2.0mg) were incubated at 37  C in1.0mLof10mMTrisbuffer,p H   =7.8,10mMCaCl 2 ,inthepresenceof   a -chymotrypsin at a molar enzyme/insulin ratio of 1:215. Ali-quots (100 l L) were withdrawn at various time intervals and trea-ted as described above. 3. Results and discussion  3.1. Synthesis of guanidinylated poly( L -lysine) dendrigrafts A series of partially guanidinylated poly( L  -lysine) dendrigraftsof the second generation with 12, 24, 36 guanidinium groups, aswell as, the fully functionalized dendrigraft with 48 guanidiniumgroups was prepared. Thus, the primary amino groups of secondgeneration poly( L  -lysine) dendrigraft reacted with 1 H  -pyrazole-1-carboxamidine hydrochloride and  N  , N  -diisopropylethylamine,affording the guanidinylated derivatives and their structures wereestablished by  1 H and  13 C NMR spectroscopy. Specifically, a newtriplet appearing at   3.10ppm is attributed to the  a -CH 2  relativeto the guanidinium group, and the peaks at   7.00 and  7.90ppmareattributedtotheguanidiniummoieties.Inaddition,in  13 C NMR spectra the guanidinylation of primary amines is dem-onstrated by the appearance of a new peak at 41.5ppm corre-sponding to the  a  carbon relative to the guanidinium group. Alsothe carbon of the guanidinium moieties is observed at157.0ppm. Furthermore, the degree of substitution was deter-mined by inverse-gated  13 C NMR. The average number of guanidi-nium moieties for each dendrigraft derivative was determinedfrom the integration of the peaks at 41.5ppm and at 39.5ppmattributed to the  a  carbon relative to guanidinium and remainingprimary amino groups, respectively. It was thus found that 12.3,24.0, and 36.1 guanidinium groups were introduced to DL-G1,DL-G2 and DL-G3, respectively. In the case of DL-G4 derivativeno peak at 39.5ppm could be detected denoting the complete,within NMR accuracy, functionalization of the 48 primary aminoend-groups to guanidinium groups.  3.2. Dendrigraft/insulin interaction experiments. DLS and insulincomplexation efficiency The interaction of the negatively charged insulin with the pos-itively charged poly( L  -lysine) derivatives was followed by DLS.Association of insulin with dendrimers occurred spontaneously,leading to the formation of particles in the nanometer scale whenlow dendrigraft/insulin molar ratios were employed. As shown inFig. 1, when DL and DL-G1 were allowed to interact with insulinat molar ratios less than 0.01, nanoparticles of about 150nm radiiwere detected by DLS. DL-G2, DL-G3 and DL-G4 derivatives lead tothe formation of larger nanoparticles of about 300–600nm radii,respectively, even at molar ratios as low as 0.005. As the dendri-graft/insulin molar ratio increased, a plateau region was observedat ca. 0.02–0.03molar ratio (Fig. 1). However, further addition of dendrigrafts resulted in a rather abrupt increase in size. This in-crease was observedat the same molar ratiorange that conversionof insulin hexamers or dimers to insulin monomers was estab-lishedbyITC,CDand f -potentialexperiments(seebelow).Thecon-version increases the number of available insulin interacting siteswith dendrigrafts and this possibly promotes the observed aggre-gation to larger particles. The non-guanidinylated DL and thederivative having low degree of guanidinylation, DL-G1, form par-ticlesthatincreasetheirsizeuptoca1 l matabout0.05–0.06den-drigraft/insulinmolarratio,whilederivativeswithmediumtohighnumber of guanidinium end-groups form aggregates of this size ateven lower molar ratios.Ideally, a successful insulin delivery system should have a highprotein loading capacity. It has been established [45,46] that theelectrostatic interactions between the acidic groups of insulinand positively charged groups of dendritic polymers play a domi-nantroleintheassociationofinsulintothepolymericdeliverysys-tems. Insulin complexation efficiency expresses the amount of proteinentrapped by the dendritic polymers. Highlevels of insulincomplexation efficiencies were determined for all poly( L  -lysine)derivativesrangingfrom99.3%to99.7%at therelativelylowmolarratio of 0.1, corresponding to 0.16–0.18mg of dendrigraft deriva-tives per 1mg of insulin. Therefore, this molar ratio was used forenzymatic degradation and release studies.More importantly, the process is reversible since dendrigraft/insulin complexes obtained can be dissociated and redissolved byadding 500mM phosphate buffer, p H   7.4. The process was moni- 0.00 0.01 0.02 0.03 0.04 0.05 0.060200400600800100012001400160018002000    R    h    (  n  m   ) Dendrigraft / insulin molar ratio Fig. 1.  Mean hydrodynamic radii (nm) of dendrigraft/insulin complexes followinginteraction of insulin with DL (open circles), DL-G1 (up triangles), DL-G2 (downtriangles), DL-G3 (squares), and DL-G4 (solid circles) in 10mM Tris buffer, p H   7.4.436  Z. Sideratou et al./Journal of Colloid and Interface Science 351 (2010) 433–441
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