Optimization of Polyplex Formation between DNA Oligonucleotide and Poly(L-Lysine)

15 Pages·2017·4.42 MB·English

International Journal o f
Molecular Sciences
Article
Optimization of Polyplex Formation between
DNA Oligonucleotide and Poly(L-Lysine):
Experimental Study and Modeling Approach
TudorVasiliu1,CorneliuCojocaru2,AlexandruRotaru1,GabrielaPricope1,MarianaPinteala1
andLiliaClima1,*
1 CenterofAdvancedResearchinBionanocojugatesandbiopolymers,“PetruPoni”Instituteof
MacromolecularChemistry,Iasi,RomaniaAleeaGrigoreGhicaVoda41A,70487Iasi,Romania;
[email protected](T.V.);[email protected](A.R.);
[email protected](G.P.);[email protected](M.P.)
2 DepartmentofInorganicPolymers,“PetruPoni”InstituteofMacromolecularChemistry,Iasi,
RomaniaAleeaGrigoreGhicaVoda41A,70487Iasi,Romania;[email protected]
* Correspondence:[email protected];Tel.:[phone]
Received:11May2017;Accepted:13June2017;Published:17June2017
Abstract: Thepolyplexesformedbynucleicacidsandpolycationshavereceivedagreatattention
owingtotheirpotentialapplicationingenetherapy. Inourstudy,wereportexperimentalresultsand
modelingoutcomesregardingtheoptimizationofpolyplexformationbetweenthedouble-stranded
DNA(dsDNA)andpoly(L-Lysine)(PLL).Thequantificationofthebindingefficiencyduringpolyplex
formationwasperformedbyprocessingoftheimagescapturedfromthegelelectrophoresisassays.
The design of experiments (DoE) and response surface methodology (RSM) were employed to
investigate the coupling effect of key factors (pH and N/P ratio) affecting the binding efficiency.
Accordingtotheexperimentalobservationsandresponsesurfaceanalysis,theN/Pratioshoweda
majorinfluenceonbindingefficiencycomparedtopH.Model-basedoptimizationcalculationsalong
withtheexperimentalconfirmationrunsunveiledthemaximalbindingefficiency(99.4%)achieved
at pH 5.4 and N/P ratio 125. To support the experimental data and reveal insights of molecular
mechanismresponsibleforthepolyplexformationbetweendsDNAandPLL,moleculardynamics
simulationswereperformedatpH5.4and7.4.
Keywords: DNA;modeling;optimization;poly(L-Lysine)
1. Introduction
Genetherapyisamedicalprocedurethatinvolvestheinsertionofnucleicacidsintocells,thus
alteringthegeneexpressioninordertocorrectgenedefects[1]. Therearemainlytwoapproaches
to gene therapy: one that uses viral vectors as means of transporting the genetic material [2–4]
and one that uses cationic non-viral vectors [5,6]. In fact, ~70% of gene therapy clinical trials
carriedoutsofarhaveusedmodifiedvirusessuchasretroviruses, lentiviruses, adenovirusesand
adeno-associatedviruses(AAVs)todelivergenes;howevertheuseofvirusesforgenetherapyhasa
setofdisadvantagesrelatedtotheinactivationandtheirmodification[7]. Non-viralDNAdelivery
systems, on the other side, have attracted considerable attention in the last decade not only for
fundamentalresearchinterestsbutalsoforapplicationsinclinicaltrials[7]. Thecommonadvantages
of non-viral vectors are the inferior specific immune responses, and they are generally safer and
easier to design and synthesize, with more flexible structures and chemical properties for various
purposes[8–11]. Themainproblemfortheclinicaluseofnon-viralvectorsistheirlowtransfection
efficacy[12]. Often,thesyntheticpathwayofnon-viralvectorsneedstobeadjustedandoptimizedin
Int.J.Mol.Sci.2017,18,1291;doi:10.3390/ijms18061291 www.mdpi.com/journal/ijms
Int.J.Mol.Sci.2017,18,1291 2of15
ordertoobtaintheneededgenedeliveryproperties. Cationicpolymersarefrequentlyusedforthe
preparationofnon-viralvectorsduetotheircapacitytoeasilyinteractandbindnucleicacids.Themost
studied polymers for the preparation of non-viral vectors are linear or branched poly (ethylene
imine) (PEI) and polypeptide-type poly(L-Lysine) (PLL) [11,13]. PEI, depending on its structure,
constitutesahighconcentrationofpositivelychargedaminegroups(primary,secondary,tertiary),
whichenableseffectiveelectrostaticbindingandcondensationofnegativelychargedDNA[14]and
possessesbufferingcapacityandpolymerswellingattheacidicpHoftheendosomes[10]. Inthecase
ofPLL,thepolymerchemicalstructureconsistsofonlyprimaryaminesinthesidechains,whichtake
partinbindingDNA.AbsenceoftheprotonspongeabilityofPLL,togetherwiththeaggregationand
precipitationofthePLL-DNAcomplexesathighNaClconcentrations[15],considerablydiminishgene
transfectionatthecellularlevelandmakesPLLinferiorcandidatewhencomparedtoPEI.Eventhough
thePLLexpresseslowergenetransfection,itstillhasexcellentcharacteristicsasagenecarrierand
provedtobemoreadvantageousincomparisontoPEIintermsofcytotoxicity[16]. Itisstillunclear
ifthedifferencesintransfectionefficiencyofpolyplexesformedfromnucleicacidsandPEIorPLL
are caused by dissimilarities in their affinities to double-stranded DNA (dsDNA), their chemical
structureorpolyplexstructures. Revealingthesestructure–activityrelationshipsisveryimportantfor
controllingthefunctionalityofnovelbiomaterialstobeusedforgenetherapy.
Ziebarth et al. have performed theoretical molecular dynamics (MD) simulations of the short
DNAduplexinthepresenceofPEIorPLLtoshedlightonthespecificatomicinteractionthatresults
intheformationofpolyplexes[17]. Itwasfoundthat,incomparisonwithPLL,PEIisabletobetter
neutralizethechargeofdsDNA.Inanotherstudy,anexperimentalsteptowardsunderstandingthe
mechanismsofdsDNAcomplexationbehaviorofPEIandPLLwasperformedbyKetolaetal.[18].
TheauthorsinvestigatedthePEIanddsDNAandPLLanddsDNA(dsDNA/PLL)complexformationat
differentpHvaluesusingatime-resolvedspectroscopicmethod.ItwasobservedthatpHandN/Pratio
(expressedbynitrogen/phosphorusratio,whereNrepresentsthecontentofnitrogeninonepolymeric
unitofcationicpolymer(PEIorPLL)andPrepresentscontentofphosphateswithintheDNAbackbone)
haveacleareffectonthemechanismofpolyplexformationforthestudiedpolymers,theseparameters
determiningtheindependentorcooperativetypesofthebindingmechanisms.SincepHisanimportant
factorinbothbindinganddissociationoftheformedpolyplexes,itiscrucialtoexploreindepththe
interactionofvariouscationicmacromoleculeswithnucleicacidsatthephysiologicalpHrange(5.0–7.4).
Recently, we have studied the optimization of polyplex formation between short dsDNA
oligonucleotideandbranchedPEIatdifferentpHvalues[19]. Adesignofexperimentswasadoptedto
investigatethebindingefficiencyofDNAandbranchedPEIundervariousconditionsofcomponents
ratioandthepHofthesolution. Additionally,themoleculardynamicsimulationoftheinvestigated
complexation process at pH = 7.4, in order to unveil the mechanism of polycomplex formation at
atomic-scalewasperformed.
In the present study, we continue to investigate the mechanisms of polyplex formation by
optimizingtheshortdsDNAcomplexationbyPLLatdifferentphysiologicalpHvaluesandperforming
MDsimulationofthecomplexationprocessattwodifferentpHvalues(pH=5.4and7.4). Inrecent
years,severalresearchgroupshavealsoaddressedtheMDsimulationsofdsDNA/PLLcomplexes
usingaDrew–Dickersondodecamerd(CGCGAATTCGCG) asthemodelfortheshortDNAhelix[20].
2
BesidestheworkofZiebarthetal.[17],whoinvestigatedthemoleculardynamicssimulationsofDNA
duplexinthepresenceofPLLatpH=7.4,noadditionaldynamicsimulationsofPLLwithnucleic
acidswereperformedinordertocompareresultsatvariouspHvalues.
Inthisstudy,theoptimizationofthepolyplexformationprocessbetweenPLLanddsDNAwas
accomplishedbykeepingconstanttheDNAconcentrationandvaryingtheamountofPLLandpH
value.Experimentswereperformedutilizinggelelectrophoresisdataasreadoutresults. Weemployed
thedesignofexperiments(DoE)andresponsesurfacemethodology(RSM)forprocessmodelingand
optimization.Thesestatisticaltoolshavebeenwidelyacceptedandappliedforinvestigation,modeling
andoptimizationofvariousbiotechnologicalprocesses[21–26].
Int.J.Mol.Sci.2017,18,1291 3of15
2. ResultsandDiscussions
2.1. Data-DrivenModelingandOptimizationofthePolyplexFormationProcess
Thepolyplexformationhasasetofoptimumreactionconditionsinwhichtheefficiencyisata
maximumvalue,and,inordertodeterminetheexactvaluesoftheseconditions,theresponsesurface
methodology(RSM)[27–31]canbeused. Inthisstudy, thedesignofexperiments(DoE)andRSM
wasusedtoquantitativelydeterminethecomplexationbetweendsDNAandPLL,usingtwoinput
variables,i.e.,pHofthesolutionandN/Pratio. Tofacilitatethemodelingprocess,theinputvariables
wereconvertedtocodedvariables: −1fortheminimumlevel,+1forthemaximumleveland0forthe
centrallevel(Table1).
Table1.DesignvariablesandtheircodedandrealvaluesusedfordeterminationofthedsDNA/PLL
complexationprocess.
RealValuesofCodedLevels
DesignVariables(Factors) CodedVariables
−1 0 +1
InitialpHofsolution x 5.4 6.4 7.4
1
N/Pratio,r x 25 75 125
2
This conversion scheme was done to simplify the use of variables and to apply the same
non-dimensional scale for all of the factors [27–31]. The actual values of these coded variables
are summarized in Table 1. Likewise, the faced-centered experimental design used to study the
complexationprocessispresentedinTable2. Inproposedexperiments,theconcentrationofdsDNA
inthesamplewaskeptconstant(26.28µM),andthedesiredN/Pratiowasachievedbyvaryingthe
amountofPLLinthesample. PolyplexeswithN/Pratioof25,75and125werepreparedatthree
different pH values 5.4, 6.4 and 7.4. An agarose gel electrophoresis retardation assay was used to
evaluatethebindingbetweenPLLanddsDNAsequenceatdifferentpHvaluesandvariousN/Pratios
(Figure1andFiguresS1–S3). Table2summarizes11gelelectrophoresisexperimentalruns,comprising
factorial(F1–F4),axial(A1–A4)andcentralpoints(C1–C3)accordingtoDoEterminology.
Table2.Faced-centeredexperimentaldesignusedfortheinvestigationofthecondensationprocess
betweendsDNAandPLLandtheexperimentalresult(bindingefficiency)determinedforeachrun.
DesignVariables BindingEfficiency
RunNr Typea pHSolution N/PRatio (Experimental)
pH(Actual) x (Coded) r(Actual) x (Coded) Y(%)
1 2
1 F1 5.4 −1 25 −1 25.58
2 F2 7.4 +1 25 −1 17.97
3 F3 5.4 −1 125 +1 99.40
4 F4 7.4 +1 125 +1 99.21
5 A1 5.4 −1 75 0 86.28
6 A2 7.4 +1 75 0 61.97
7 A3 6.4 0 25 −1 22.87
8 A4 6.4 0 125 +1 99.30
9 C1 6.4 0 75 0 64.58
10 C2 6.4 0 75 0 62.63
11 C3 6.4 0 75 0 66.53
F:Factorialvalue;A:Axialvalue;C:Centralvalue.
Notethat,centralpoints(C1–C3)werecarriedouttotestthereproducibilityofthemethodunder
thesameexperimentalconditions. Figure1illustratesanexampleofthegelelectrophoresisassay
determinedforthecentralpoints(C1–C3),i.e.,atpH6.4andN/Pratioof75. AsshowninFigure1,
Int.J.Mol.Sci.2017,18,1291 4of15
the gel electrophoresis assay indicated a partial complexation under these conditions disclosing a
binding efficiency between 62.63% and 66.53%. According to data given in Table 2, the observed
Int. J. Mol. Sci. 2017, 18, 1291 4 of 15
bindingefficiencybetweenPLLanddsDNArangedfrom17.97%to99.4%dependingonthelevelsof
pHoaf npdH Nan/dP Nra/Pti ora.tOiov. Oervaellr,atlhl, ethceo cnocnluclsuiosinono fotf htheep peerrffoorrmmeedd ooppttiimmiizzaattiioonn eexxppeerirmimenent wtwasa tshtaht awtiwthi th
thethine cirnecarseeasoef othf tehpe oploylpylpelxexN N//PPr raattiioo,, DDNNAA bbiinnddiinngg ppeerrffoorrmmaannccee wwasa salaslos oinicnrceraesainsign. g.

FigFuigreur1e. 1E. xEaxmamplpeleo fofg eglele leelcetcrtoropphhoorreessiiss rruunn ppeerrffoorrmmeedd aatt cceennttrraal lppooinint t(p(pHH 6.64.)4 )usuinsign gGeGl eQluQaunat nt
ExpErxepsrsessso sfotwftwaraere(v (veresrisoionn,,M Maannuuffaaccttuurreerr,, CCiittyy,, UUSS SStattaet eababbrbevre. vif. aipfpalpicpalbiclea,b Cleo,uCntoruyn). tLryan).esL Can1,e Cs2C 1,
C2aanndd CC3 3inidnidcaictae tleoalodaedd esdamsapmlesp wleisthw Nit/hP N= 7/5P; b=ri7g5h;tb braingdhst ibna tnhde swienllt h(teopw) ecollr(rteospp)oncodr troe sthpeo fnodrmtoedth e
forpmoelydppleoxly, palnedx ,tahned lothweelro wmeigrrmatiegdr abteadndbsa n(bdost(tbomot)t ocmor)rceosprroensdp otnod thtoe tuhnebuonubnodu nddsDdNsDAN. ALa.nLea nCe* C*
reprreepsreenstesnatsr ae freerfeenrecnecde sdDsDNNAAs asmampplelew witihtha anna assssoocciiaatteedd ssiiggnnaall iinntteennssiittyy ooff 110000%%. .
On the basis of collected data, a response surface model was developed in terms of two coded
Onthebasisofcollecteddata,aresponsesurfacemodelwasdevelopedintermsoftwocoded
variables (x1 and x2) by using the multivariate regression method. The fitted model in terms of coded
variables(x andx )byusingthemultivariateregressionmethod. Thefittedmodelintermsofcoded
variables 1is given2 as:
variablesisgivenas:
Yˆ =66.704−5.351x +38.581x +4.234x2 −8.805x2 +1.855x x (1)
1 2 1 2 1 2
Yˆ =66.704−5.351x +38.581x +4.234x2−8.805x2+1.855x x (1)
1 2 1 2 1 2
subject to: (cid:3398)1(cid:3409)(cid:1876) (cid:3409)(cid:3397)1,∀(cid:1861)(cid:3404)1(cid:3364)(cid:3364),(cid:3364)2(cid:3364)
(cid:3036)
subjectto: −1≤ x ≤ +1, ∀i =1,2
i
The coefficients in (Equation 1) are significant ones according to a Student’s t-test [32,33]. The
deTvheleopceode fmficoideenlt swians v(Ealqiduaatteiodn by1 )thaer eansaiglynsiifis coafn vtaorinaenscea c(AcoNrdOiVnAg)t omeathSotdu d[3e0n]t.’ sOut-ttceosmt e[3s 2o,3f 3].
TheAdNeOvVelAop setadtimstiocdale ltewsta asrve adleidtaaitleedd ibny Ttahbelea n3a. lysisofvariance(ANOVA)method[30]. Outcomesof
ANOVAstatisticaltestaredetailedinTable3.
Table 3. Analysis of variance (ANOVA) for the significance of the multivariate regression model.
Table3.Analysisofvariance(ANOVA)forthesignificanceofthemultivariateregressionmodel.
Source DF (a) SS (b) MS(c) F-value(d) p-value(e) R2 (f) Radj2 (g)
Model 5 9.323 × 103 1.865 × 103 44.148 0.000387 0.978 0.956
Source DF(a) SS(b) MS(c) F-Value(d) p-Value(e) R2(f) R 2(g)
Residual 5 211.174 42.235 ad j
MoTdoteall 5 10 9.3239×.53140 ×3 103 1.865× 103 44 .148 0.0 00387 0 .978 0.9 56
Resi(da)u Daelgree o5f freedom;2 (b1) 1S.u17m4 of squares4; 2(c). 2m35ean square; (d) ratio between mean square; (e) probability
Tootaf lrandom1n0ess; (f) co9e.5ff3ic4ie×nt1 o0f3 determination; (g) adjusted coefficient of determination.
(a) Degree of freedom; (b) Sum of squares; (c) mean square; (d) ratio between mean square; (e) probability of
The significance of the statistical model is given by the fact that the p-value (probability of
randomness;(f)coefficientofdetermination;(g)adjustedcoefficientofdetermination.
randomness) is quite low (i.e., p-value = 0.000387). In addition, the value of R2 coefficient (coefficient
of determination) shows a good accuracy of the model that is able to explain more than 97% of the
data variation. The ability of the model to predict the observed binding efficiency is displayed in a
Int.J.Mol.Sci.2017,18,1291 5of15
The significance of the statistical model is given by the fact that the p-value (probability of
randomness)isquitelow(i.e.,p-value=0.000387). Inaddition,thevalueofR2coefficient(coefficient
ofdeteIrntm. J.i Mnaolt. iSocin. 2)01s7h, 1o8w, 12s9a1 goodaccuracyofthemodelthatisabletoexplainmorethan957 o%f 15o fthe
datavariation. Theabilityofthemodeltopredicttheobservedbindingefficiencyisdisplayedina
goodness-of-fit graph (Figure 2), highlighting the agreement between predicted and experimental
goodness-of-fitgraph(Figure2),highlightingtheagreementbetweenpredictedandexperimentaldata.
data.
Int. J. Mol. Sci. 2017, 18, 1291 5 of 15
goodness-of-fit graph (Figure 2), highlighting the agreement between predicted and experimental
data.

Figure 2. Goodness-of-fit analysis: agreement between experimental observations and calculated
Figure 2. Goodness-of-fit analysis: agreement between experimental observations and calculated
predictions(right);residualerrorsversusfittedvalue(left).
predictions (right); residual errors versus fitted value (left).
According to Figure 2, the data points are close to the bisector accounting for a good accuracy in
AccordFiniggurteo 2F. iGgouordene2s,s-tohf-efitd aantaalypsios:i natgsreaemreenctl obseetwteoent heexpbeirsimecentotarl aocbcseoruvantitoinnsg afnodr caalcguolaotded accuracyin
predictpirnegditchptirenedgbi ictnthioedn ibsn i(ngridgeihnftfig); creiefesfiindccuieyanl cYeˆyrr (oŶ%r s( )%v.e)rB.s uoBsto hftihttt ehtdhe ev AaAluNNe OO(leVVftAA). tteesst t(T(Tabalbel 3e) 3a)nadn tdhet hgoeogdonoesdsn-oefs-fsi-t opfl-ofit tplot
(Figure 2) suggested a statistical valid model that can be used to explore (by simulation) the designed
(Figure2)suggestedastatisticalvalidmodelthatcanbeusedtoexplore(bysimulation)thedesigned
factoriAalc csopradcien gd etosc Friigbuinrge 2t,h teh ec odmatpal pexoaintitos na rper colocesses t.o T toh ed beivseeclotopr tahcec oduanttai-ndgr ifvoer na gmooodde al cicnu rtearcmy isn o f
factoriaaclptsruepadla ivcctaeirnidgae btshlecesr ,bi abin isdnuigbnsgtt hietfeufitccioioenmn ctepyc lŶhen x(i%aqtu)i. eoB nwotaphs r taohpec peAlsiNse.dO TaVonAdd tteehsvete (flTionapabll eteh q3eu) aadtniaodtn at h-wde argsio vgoeidvnneenms sao-so:d f-eflit ipnlotte rmsof
actualv(aFriigaubrlee 2s), saugsugebsstetidt ua tsitoantistteiccahl nvaiqliud emwodaesl tahpapt cliaend bea nudsedth teo efixnpalolreeq (buya stiimonulwatiaosng) tihvee dneasisg:ned
Yfˆac=to2ri1a4l .s5p2ac2e− d6e2sc.r3i3bi5npg Hthe+ 1co.0m6p2lerx+at4io.2n 3p4ropcHes2s.− T3o. 5d2ev2e×lo1p0 −th3re 2d+at3a.-7d1ri×ve1n0 −m2opdHel ×inr t erm(2s) of
aYcˆtu=al 2v1a4ri.a5b2l2es−, a 6s2u.b3s3ti5tuptHion+ te1c.h0n6i2qure+ w4a.s2 a3p4pplHied2 a−nd3 .t5h2e2 fi×nal1 e0q−u3art2io+n w3.a7s1 g×ive1n0 a−s2: pH×r (2)
Subject to:25(cid:3409)(cid:1870)(cid:3409)125; 5.4 (cid:3409)(cid:1868)(cid:1834)(cid:3409)7.4
Yˆ =214.522−62.335pH +1.062r+4.234pH2−3.522×10−3r2+3.71×10−2pH×r (2)

Subjectto:25≤r ≤125; 5.4 ≤ pH ≤7.4
On the basis of the empirical model (Equation 2), we were able to generate the response surface
Subject to:25(cid:3409)(cid:1870)(cid:3409)125; 5.4 (cid:3409)(cid:1868)(cid:1834)(cid:3409)7.4
Opnlotht eanbda sthise ocfonthtoeuerm-linpeisr imcaalpm (Foidgeulre(E 3q) ushaotiwoning2 )t,hwe esywneerrgeeatibc lienftlouegnecnee orfa ttehet hinepruets pvaorniasbelessu rface
(factors) on the binding response (Ŷ).
plot and the contour-lines map (Figure 3) showing the synergetic influence of the input variables
On the basis of the empirical model (Equation 2), we were able to generate the response surface
(factors)polont tahned bthine dcoinngtoruers-lpinoens smea(pYˆ )(.Figure 3) showing the synergetic influence of the input variables
(factors) on the binding response (Ŷ).
Yˆ =214.522−62.335pH +1.062r+4.234pH2−3.522×10−3r2+3.71×10−2pH×r

FigYˆur=e 23.1 R4e.5sp2o2n−se6 s2u.r3fa3c5e ppHlot+ (l1e.f0t)6 a2nrd+ co4n.2to3u4r-pliHne2 m−a3p. 5(r2ig2h×t)1 d0e−p3ric2ti+ng3 .t7he1 ×ef1fe0c−t2s pofH p×H ran d
N/P ratio (r) factors on the binding efficiency Ŷ (%).
Figure3F.iRguersep 3o.n Rseespsuonrfsaec seuprflaocte (pleloftt )(laenftd) acnodn tcoonutro-ulirn-leinme ampap(r i(rgihght)t)d deeppiiccttiinngg tthhee eefffefectcst sofo pfHpH anadn dN/P
ratio(rA)Nfna/acPlt yroazrtisinoog (n rt) htfhaece tdobaristn aod nfi rntohgme eb fiFnfiidgciiunegrne ce fy3fi,cY ˆwie(ne%c yo) .bŶs (e%rv).e d that the N/P ratio (r) has the most significant
effect on the binding efficiency. The second factor (pH) played a more diminished role in the
complAexnaatliyozni npgr othcees ds actoam frpoamre Fdi gtuor eN 3/P, wraet ioob. sDerevcerde atshiantg t hoef Nth/eP prHati ov a(lru) eh afrso tmhe 7m.4o stot s5ig.4n ilfeidca tnot a
Amneaofldfyeezcrtia ntogen i tmhtheper dobavitneadmfinreongm t eoffFf itichgieeun brceiyn.3 d,Tinwhgee esofefbcicosienerdnv ceyfad, cbttouhrta , (toptvHheer) aNplll,/a tyhPeedr ia natci orme(morr)eehn tad osimft htihneeis mhNeo/dPs trrasotiligeo n ianinfi dtcha tenh et effect
onthedbeciconrmdeaipnsleegx oaeft fpifioHnc i fepanrcoctcoyer.s rsTe hscuoemltsepedac rionend td hteof eaNnch/tPoa rnrac(itpnioHg. o)Dfpe tclhareey abesidinndgai nomgf ortehrseep pdoHnims evi a(nŶliu)se.h Tfehrdoism rfo a7cl.et4 c itanon t 5bh.e4e alcettodrmi btoup talee dx ation
procestsom ctohodem ecrpoaamter peimldeptetro opvrNeomt/oenPnatt roiaoft ntih ooe.f btihDnede ipcnrrgiem eafasfiricnyi geanmcoyifn, bethu gter, oopuvHpersa vliln,a tlPhuLee Lin facrtro elmmowen7etr. 4 opfH ttoh ve5 aN.l4u/Pel .er Nadtoiott eoa ntahda tmth teoh ed erate
decrease of pH factor resulted in the enhancing of the binding response (Ŷ). This fact can be attributed
improv ementofthebindingefficiency,but,overall,theincrementoftheN/Pratioandthedecrease
to the complete protonation of the primary amine groups in PLL at lower pH value. Note that the
Int.J.Mol.Sci.2017,18,1291 6of15
of pH factor resulted in the enhancing of the binding response (Yˆ). This fact can be attributed to
the complete protonation of the primary amine groups in PLL at lower pH value. Note that the
interactioneffectbetweenfactors(randpH)isaminorone. Predictionsprovidedbytheresponse
surfacemodelwereinreasonableagreementwithexperimentaldatacollectedfromtheagarosegel
electrophoresisassays.
Theprocessoptimizationwasdonebymeansofthegeneticalgorithmmethodimplementedin
SciLAB(version5.5.2,ScilabEnterprises,RungisComplexe,France)forscientificcalculations. Tothis
end, Equation 2 was used as objective function for the model-based optimization considering the
boundaryconstraintsfortheinputvariables. Thefoundoptimalsolutionconvergedtox =−1and
1
x =1(codedvariables)and,intermsofactualfactors,theoptimalconditionswerepH5.4andN/P
2
ratio of 125. The predicted response for optimal conditions was equal to Yˆ = 104.21. In turn, the
observedbindingefficiency(experimentalconfirmation)wasfoundatitsmaximalvalueofY=99.40%.
Thedifferencebetweenthepredictedandobservedresponsesisinthelimitsoftheresidualerror.
The obtained maximum values and the observed tendencies in the above experiments are in
accordance to the previously reported investigations on PLL/DNA interactions [17–19] and are
veryimportantintermsofpolyplexformation. Theoptimumconditionsforpolyplexpreparation,
definedbyKangetal[34]as“extracellularmedium”,mightsignificantlyinfluencethesubsequent
invitro transfection experiments. This extracellular medium used for laboratory cell cultures can
be modulated by adding or removing various components and by adjusting the pH to fit specific
purposes. The exact and optimized data obtained invitro could be further used when applying
for invivo experiments where extracellular environments are specific, predominantly affected by
pathologicaldifferences[35,36]. Itisdifficulttopredictweathertheoptimumconditionsforpolyplex
formationwillgreatlyinfluencethetransfectionresultsduetothefactthatthepHenvironmentaffects
characteristicsofpolymers,polyplexes,andcells[34]. Weanticipatethatunderstandingtheeffects
ofpHvaluesandN/Pratiooptimizationonpolyplexpreparationmaystimulatenewstrategiesfor
determiningeffectiveandsafepolymericgenecarriers.
2.2. MolecularDynamicsSimulationofdsDNA/PLLPolyplexFormation
To shed light on dsDNA/PLL molecular interactions at the atomistic level, we performed
moleculardynamics(MD)simulations[33]byconsideringtheexplicitsolventenvironment. Forthis
purpose,themodeleddsDNAmimickedthesamenucleotidesequenceastheonethatweusedin
theexperiments.
From the beginning, we should mention the following aspects adopted for the simulation:
accordingtopartialPLLaminogroupprotonationinphysiologicalenvironmentduetotheneighboring
groupeffect[37]andourexperimentalobservationsgiveninTable2,thebindingefficiencywasgreater
tosomeextentatpH5.4thanatpH7.4,especiallyforN/Pratioequalto75orlower.Thisfactsuggested
thatprotonationdegreesofPLLatpH5.4and7.4mightdifferinthestatisticalsense. Becausethe
isoelectricpointofPLLisaround9.0[38],atpH7.4,thismacromoleculeobviouslycarriesanetpositive
charge. Therefore,atpH7.4,weassumedformodelingpurposes,aprotonationdegreeofPLLequalto
50%toexplorebysimulationthelowextentofprotonationinthestatisticalmean. Inturn,forpH5.4,
weadoptedthefullprotonationdegreeofPLL(i.e.,100%). Hence,thehalfprotonation(50%)ofPLL
(atpH7.4)ismoreorlessamodelingartifactadoptedonlyforinsilicoanalysisinordertosurveyby
simulationtheextremelimitofpolyplexformation.
Figure4depictstheinitialsnapshot(t=0ns)ofthemodeledsystemshowinginanexplicitfashion
allmoleculesandatoms,i.e.,dsDNAandPLLsurroundedbywatermolecules. Themacromolecules
(dsDNAandPLL)wereseparatedatthestartpointbyadistanceof40Åbetweentheircentersof
geometry(COGdistance).
Figures5and6showtypicalprogresssnapshotsofmoleculardynamicssimulationsperformedat
differentpHvalues,i.e.,pH5.4andpH7.4,respectively. AccordingtoMDsimulationresults,thepH
factorhadacentralroleonthecomplexationrate(tempo)betweendsDNAandPLL.Forinstance,at
Int.J.Mol.Sci.2017,18,1291 7of15
pH5.4,thecomplexationprocesswasalmostcompletefort=2ns(Figure5B).Inturn,atpH7.4,the
polyplexformationwasincompleteevenafter20ns(Figure6C).Thisdifferenceisattributedtothe
adopteddegreeofprotonationofPLLatdifferentpHvalues. BecausePLLwasfullyprotonatedatpH
Int. J. Mol. Sci. 2017, 18, 1291 7 of 15
5.4,themInto. Jl. eMcoul. lSeci.s 2h0o17w, 1e8,d 12a91h ighpositivechargeuniformlydistributedacrosstheentiremo7l eofc 1u5l e. Asa
consequmenolceec,utlhe.e Aesn ati rceonPsLeqLumenocele, cthuel eenwtiarse aPlLigLn medolenceualer twhaes dasliDgnNedA nienara tphae rdaslDleNlfAa sihn iao npa(rFailgleul re5B).
mfasohleiocunl e(F. iAgus rea 5cBo)n. sequence, the entire PLL molecule was aligned near the dsDNA in a parallel
fashion (Figure 5B).

Figure 4F.iguRree n4d. eRreinndgeroinfgi noif tiianlitieaql ueqiluibilirbartaetedd ssttrruuccttuurrees soof fmmacarocmroomlecoulleecsu dlesDsNdAsD aNndA PaLnL dinP aL L in a
simulatiFsoiimnguubrloea txi4o.wn R ibteohnxd ewexripitnhlgi ec xiotpf wliicnaiittt weiarla tmeeqro umlieloicbluercaluetelseds( s(sostorluvlvceetnunrtt)e),,s a atot tft =m= 0a 0ncsrno. sm.olecules dsDNA and PLL in a
simulation box with explicit water molecules (solvent), at t = 0 ns.

Figure 5. Snapshots from the simulation showing the formation of the polyplex between dsDNA and
Figure5FP.iLgLSu nraeta a5p .p sSHhno avptasslhufoer toosm ff 5ro.4tm ha ett hdseifi fmseimruenulatl atstiiimoonnu lsashthoioownwi tniigmn teghse:t (hfAoe)r mtf o=a rt1im onnsa ;o t(ifBo t)hn te = op 2fo nltyshp; e(lCepx) otb =ley t1wp0e lneesnx; (dbDseD) ttNw =A e3 e5a nnnsdd. sDNA
PLL at a pH value of 5.4 at different simulation times: (A) t = 1 ns; (B) t = 2 ns; (C) t = 10 ns; (D) t = 35 ns.
andPLLatapHvalueof5.4atdifferentsimulationtimes: (A)t=1ns; (B)t=2ns; (C)t=10ns;
(D) t=35ns.
Int.J.Mol.Sci.2017,18,1291 8of15
Int. J. Mol. Sci. 2017, 18, 1291 8 of 15

Figure 6. Snapshots showing the interactions between PLL and dsDNA at a pH value of 7.4 with the
Figure6.SnapshotsshowingtheinteractionsbetweenPLLanddsDNAatapHvalueof7.4withthe
formation of a polyplex. The time intervals are: (A) t = 5 ns; (B) t =10 ns; (C) t = 20 ns; (D) t = 35 ns.
formationofapolyplex.Thetimeintervalsare:(A)t=5ns;(B)t=10ns;(C)t=20ns;(D)t=35ns.
Once the first contacts between oligomers emerged at pH 5.4, macromolecules remained in the
Opnrcoexitmhietyfi frosrt tchoe netnaticrtes pbeeritowde oefn thoel isgimomulaetrisone mwiethrg ae mdiantimpaHl v5a.r4ia,nmcea corf oCmOoGl edcisutalenscer e(Fmigauirnee 5d). inthe
proximBiyt ycofnotrrathste, aetn ptHire 7p.4e, roinoldy ao fptahrte osfi mPLuLl a(ttoiopn siwdei)t hhaas minitneriamctaeldv waritiha ndcseDoNfAC (OFiGgudreis 6t)a. nTcheis( Fcaignu re5).
be attributed to the fact that, at pH 7.4, only 50% of the amine groups were considered protonated in
Bycontrast,atpH7.4,onlyapartofPLL(topside)hasinteractedwithdsDNA(Figure6). Thiscan
our simulation. Thus, simulation results revealed that, even if a lower protonation degree (50%) of
beattributedtothefactthat,atpH7.4,only50%oftheaminegroupswereconsideredprotonatedin
PLL was considered, the dsDNA/PLL polyplex was still formed, but more time was required for its
oursimulation. Thus,simulationresultsrevealedthat,evenifalowerprotonationdegree(50%)of
stabilization compared to a full (100%) protonation case.
PLLwascoFingsuirdee 7re ddi,spthlaeysd sthDeN hAist/oPryL L(i.ep.o, leyvpolluetxiown ains sttimillef) oorfm theed ,mbouletcmuloarr einttiemraectwioans dreesqcuriiprteodrs forits
stabilizbaettwioenenc odmsDpNaAre adndto PLaLf uthllat( 1w0e0r%e r)ecporrodteodn iant tihoen ccoausrese. of MD simulations. Hence, Figure 7A shows
Fitgheu erveo7ludtioisnp olfa tyhse tChOeGh disisttoarnyce( bi.eet.w,eeevno tlhuet imoancrionmtoimleceu)leosf att hbeothm ionvleecsutiglaartedin pteHr avcatluioens. Adse scacnri ptors
betweeben sdesenD NfroAm aFnigdurPeL 7LAt, hthaet wdisetraencree cdoercdreeadsedin vtehrye cfaosut rast epoHf 5M.4 D(frsoimm u40la Åti oant st .=H 0 ennsc teo, 1F8i gaut r e 7A
t = 2 ns), and then stabilized at a value of ~16 Å after 5 ns. In the case of pH 7.4, the polyplex formation
showstheevolutionoftheCOGdistancebetweenthemacromoleculesatbothinvestigatedpHvalues.
followed a different pathway due to the fact that only the top part of the PLL molecule interacted
AscanbeseenfromFigure7A,thedistancedecreasedveryfastatpH5.4(from40Åatt=0nsto
closely with the dsDNA. This led to an initial increase of the COG distance between the
18att=2ns),andthenstabilizedatavalueof~16Åafter5ns. InthecaseofpH7.4,thepolyplex
macromolecules (at 3.5 ns the distance was about 50 Å, compared to the 40 Å fixed at the start). After
formationfollowedadifferentpathwayduetothefactthatonlythetoppartofthePLLmolecule
4.5 ns, the distance began to fluctuate with an overall slow descending trend, attaining a value of 16
interacÅte adftecrl o3s2e nlys. wFigituhret h7Be idnsdDicNateAs .thTeh nisumlebdert oofa inntienraittioamliicn ccorenatascetso tfhatht eemCeOrgGedd biesttwaneecne dbseDtwNAee nthe
macroamndo lPeLcuL lmesac(raotm3o.5lecnusletsh feord biosttha nofc ethwe caasseasb (poHut 55.40 aÅnd, 7c.o4m). Ipna craesde otfo ptHh eof4 50.4Å, thfie xfierdst acotntthacet start).
After4o.c5cunrsr,etdh jeusdt ibsetafonrcee thbee 2g anns mtoarflku acntdu tahteenw thieth nuamnboevr eorfa clolnstlaocwts idncersecaesnedd irnapgidtrlye ntod m,aotrtea tihnainn g50a0 value
at 5 ns. After that, the number of contacts fluctuated as the macromolecules repositioned themselves.
of 16 Å after 32 ns. Figure 7B indicates the number of interatomic contacts that emerged between
However, the general trend was an upward one until 18.5 ns, when a peak was reached (816 contacts).
dsDNAandPLLmacromoleculesforbothofthecases(pH5.4and7.4). IncaseofpHof5.4,thefirst
contac toccurredjustbeforethe2nsmarkandthenthenumberofcontactsincreasedrapidlytomore
than500at5ns. Afterthat,thenumberofcontactsfluctuatedasthemacromoleculesrepositioned
themselves. However,thegeneraltrendwasanupwardoneuntil18.5ns,whenapeakwasreached
(816contacts). From18.5to35ns,thenumberofcontactsfluctuatedintotheintervalrangingfrom650
Int. J. Mol. Sci. 2017, 18, 1291 9 of 15
Int.J.Mol.Sci.2017,18,1291 9of15
From 18.5 to 35 ns, the number of contacts fluctuated into the interval ranging from 650 to 800. The
observed fast closing of the gap between the PLL molecules and the dsDNA is similar to the data
to800. TheobservedfastclosingofthegapbetweenthePLLmoleculesandthedsDNAissimilarto
reported by Ziebarth et al [17], in which the PLL was considered fully protonated.
thedatareportedbyZiebarthetal[17],inwhichthePLLwasconsideredfullyprotonated.

Figure 7. Plots, for dsDNA and PLL, as a function of time at different pH values (red line—pH
Figure 7. Plots, for dsDNA and PLL, as a function of time at different pH values (red line—pH 5.4;
5.4; blueline—pH7.4)of(A)thedistancebetweenthecentersofgeometryand(B)thenumberof
blue line—pH 7.4) of (A) the distance between the centers of geometry and (B) the number of
intermolecularcontactswithacutoffradiusof4Å,(C)numberoftotalhydrogenbondsand(D)total
intermolecular contacts with a cutoff radius of 4 Å, (C) number of total hydrogen bonds and (D) total
energyofhydrogenbondsformed.
energy of hydrogen bonds formed.
DuetothefactthatthesimulatedcomplexationratewasdeceleratedatpH7.4,thefirstcontact
Due to the fact that the simulated complexation rate was decelerated at pH 7.4, the first contact
betweenthemoleculeswasobservedonlyat5ns. Forthiscase(pH7.4),theincreaseofintermolecular
between the molecules was observed only at 5 ns. For this case (pH 7.4), the increase of intermolecular
contactswasmuchslower. Moreprecisely,at18.5ns,thenumberofcontactswasabout285anda
contacts was much slower. More precisely, at 18.5 ns, the number of contacts was about 285 and a
maximumof700contactswasattainedonlyatthefinalstage,i.e.,att=35ns.
maximum of 700 contacts was attained only at the final stage, i.e., at t = 35 ns.
Accordingtosimulationoutcomes,thestabilityofthepolyplexwasalsoinfluencedbythenumber
According to simulation outcomes, the stability of the polyplex was also influenced by the
ofhydrogenbondsthatformedbetweendsDNAandPLLmacromolecules. Figure7C–Dhighlightthe
number of hydrogen bonds that formed between dsDNA and PLL macromolecules. Figure 7C–D
nuhmigbhelirgohft hthyed nrougmenbebro onfd hsyadnrdogthenei brotontdasl eannedr gthyeairg taointaslt etnheersgiym auglaatiinosnt tthime esi.mAuslsahtioown ntimineF. iAgus rseho7Cw,n
thine fiFirgsutrhey 7dCro, gtheen fbirosnt dhsydforormgeend broanpdids lfyoramndedi nraapigdrleya atenrdn iunm a bgerreaattepr Hnu5m.4becro mat ppaHre 5d.4t ocopmHpa7r.4e.d
Thtois pmHa y7.b4e. Texhpisl aminaeyd bbye tehxepldaiifnfeerde nbtyp rthoeto ndaiftfieornendte gprreoetoonfaPtiLoLn’ sdneigtrreoeg eonf aPtoLmL’ss cnointrsoidgeenre datfoomrs
sicmonuslaidtieornesd. fTohr esinmuumlabteiornosf. hTyhde rnougmenbebro onfd hsy(dFrigogueren 7bCon)dans d(Ftiogtuarlee 7nCe)r gaineds tooftHal -ebnoenrdgise(sF oigf uHr-ebo7Dnd)s
un(Fviegiulerde 7sDim) iulanrvaesilceedn dsiimngilatrre ansdcsenadsitnigm tereenladpss aesd .timOev eerlaalpl,sethde. Odivfeferraelln, cteheb edtiwffeereenntchee btewtwoeceans ethse
cotwnsoid cearseedsm coignhstidbeereexdp mlaiingehdt bbye tehxepflaacitntehda tb,ya ttphHe f7a.4ct, tthheaht,y adtr opgHe n7.b4o, ntdhes, hfoyrdmroedgebne tbwoenednsd, sfDorNmAed
anbdetPwLeLe,nw derseDlNesAs inanndu mPbLeLr,a nwderwee aleksesr ,iwn hnicuhmlebdert oaantdo tawlleyadkeifrf,e rwenhticcohn fleodrm taot ioan tooftathlley codmiffpelreexnt
cocmonpfaorremdattoiotnh eofc athsee ocfompHpl5e.x4 .compared to the case of pH 5.4.
ImImpoprotratnanttd desecsrcirpiptotrosrsu usesdedf ofrort htehec hcahraarcatcetreirziaztaitoinono fofa am macarcormomoloelceuculeled deaelawl witihtht hteher ardaiduisuso fof
gygryartaiotinon(R (gR)ga)n adntdh ethroeo tr-omoet-amn-esaqnu-asqreu-adreev-idaetivoinat(iRonM S(RDM)oSfDa)t oomf iactpoomsiitci opnoss.iStiuocnhs.d eSsuccrhip tdoersscdriepttaoilrs
chdaentagiels cthhaantgaepsp tehaarti napthpeeacro ninfo trhme actoionnfoorfmaamtioacnr oomf ao lmecauclreoomroblieocmuolel eocru lbeiopmroovliedciunlge cpluroevsirdeilnatge dclutoes
itsreblaehteadv itoor iatns dbfeuhnacvtiioorn a[3n9d] .fTuhnectRiognm [e3a9s]u. rTehset hReg rmooeta-msueraens -sthqeu arroeodt-imstaenance-soqfucahraei ndissetgamnceen tosf fcrohmain
thseeigrmceennttesr forofmth ethmeiars cse.nTtheru os,f Rthgei smaamsse. Tanhiunsg, fRugl ims aa cmroemanoilnegcfuulal rmdaecsrcormipotolerctuhlaatr gdievsecsriapstoenr stheaotf gtihvees
Int.J.Mol.Sci.2017,18,1291 10of15
sizeoftheoligomer/(bio)polymercoil. Inturn,theseconddescriptor(RMSD)comparesthecurrent
conformationofasimulatedmacromoleculewiththeconformationofatargetstructure. Inthisstudy,
weconsideredasthetargetedstructuretheinitialequilibratedgeometryofthemacromoleculeattime
zero(t=0ns). FigureS4reportsthevariationofconformationaldescriptors(R andRMSD)during
g
thesimulationprogress. AsshowninFigureS4A,B,theR valuedroppedimmediatelyinbothpH
g
conditionsandforeachmacromolecule(i.e.,from26Åto24ÅfordsDNA,andfrom24Åto21Åfor
PLL).Aftertheinitialdrop,R fluctuatedaroundasteadyvalueforeachmacromolecule. Hence,both
g
macromolecules(PLLanddsDNA)wereinaslightlycompactedstatesduringsimulationcompared
totheirinitialequilibratedgeometries. FordsDNA,thevaluesofR fluctuatedaround24Åforboth
g
pHconditions(FigureS4B).Bycontrast,theR fluctuateddependingonpHlevelinthecaseofPLL.
g
More detailed, it has oscillated around 21 Å (at pH 5.4). In turn, at pH 7.4, the radius of gyration
associatedwithPLLdroppedtoavalueof18Å(after20ns)andfluctuatedfurthernearthisvalue
(seeFigureS4A).
FigureS4C,DhighlightsthehistoryofRMSDvaluesasthesimulationtimeelapsed. Accordingto
FigureS4C,theRMSDvaluesforPLLvariedintothelimitsof5–7Å(atpH5.4)and5–13Å(atpH7.4).
AsfordsDNA(FigureS4D),theRMSDvaluesvariedbetween4and6Å(atpH5.4)and5–8Å(at
pH7.4).
ItiswellknownthatiftheRMSDvalueisgreaterthan3Å,thenthemolecularconformationis
differentfromthetargetedstructure. Inourcase,itisclearthatbothmoleculessufferedconformational
changes during the complexation process. It should be pointed out that the conformation of PLL
macromolecule suffered the most when only 50% of the amine nitrogen atoms were considered
protonated. Asaconsequence, PLLmacromoleculewastwistedandbendedatagreaterextentin
ordertointeractwiththephosphategroupsfromdsDNA.
BycombiningtheinformationobtainedfromR andRMSDplots,onemayobservethatboth
g
dsDNAandPLLareflexiblemacromolecules,changingtheirconformationsduringthecomplexation
process. However,dsDNAstillmaintaineditsB-formattheendofthesimulation. Theseoutcomes
fallinlinewiththeresultsreportedbyOuyangetal.[40],withthedifferencethatvariousprotonated
statesofthePLLwerecorrelatedwiththechanginginpH.
3. MaterialsandMethods
3.1. Materials
Poly(L-Lysine) (PLL) in 0.1% w/v solution with an average molecular weight 150–300 kDa
and used without additional dilution, ethidium bromide, tris (hydroxymethyl)aminomethane,
Ethylenediaminetetraacetic acid (EDTA), glacial acetic acid and sucrose were purchased from
Sigma-Aldrich (Munich, Germany). Agarose for gel electrophoresis was provided by AppliChem
GmbH(Darmstadt,Germany). HPLCpurifiedDNAsequenceswerepurchasedfromMetabionAG
(Planegg/Steinkirchen,Germany),dilutedtotheconcentrationof100µMandusedasastocksolution.
The sense strand was 5(cid:48)-CAAGCCCTTAACGAACTTCAACGTA-3(cid:48) and the antisense strand was
5(cid:48)-TACGTTGAAGTTCGTTAAGGGCTTG-3(cid:48).
3.2. PolyplexPreparationandAgaroseGelElectrophoresisAssay
dsDNA stock solution was prepared by annealing sense and antisense DNA strands in
Tris-acetate-EDTA (TAE) buffer at the correspondingly adjusted pH values i.e., 50 µL DNA sense
strand,50µLDNAantisensestrand,37.5µL10×TAE(40mMTris,2mMaceticacidand1mMEDTA)
and18.8µLNaCl1M.TheexperimentalpHvaluesofsolutionswerechosenaspH5.4,6.4and7.4.
Polyplex preparation: for the calculation of N/P ratio, it was considered that 1 µg of dsDNA
contains3nmolofphosphate[41],andnitrogencontentwasdeterminedfromtheamountofadded
PLL,consideringthatMWofapolymericunitwas128g·mol−1.Thus,forthepreparationofpolyplexes,
thefollowingprocedurewasperformed: 24.6µLofDNAstocksolutionwasmixedwithsolutionof