multivalent 
 drug - polymer conjugates , in which multiple copies of 
 a drug are covalently attached to a polymeric scaffold either directly 
 or through linker chemistry , are a highly studied pathway to improve 
 therapeutic index .
in particular , conjugation of methotrexate ( mtx ) to poly(amidoamine ) 
 ( pamam ) dendrimer has been extensively studied , with over 100 related 
 publications since 2002 .
acetylated , neutral g5 pamam has been of particular interest as 
 a drug delivery vector because of its narrow polydispersity index 
 ( pdi ) , low toxicity and immunogenicity , and molecular weight ( mw ) 
 of about 30 kda that allows it to solubilize multiple hydrophobic 
 ligands while still being small enough to diffuse through tissue for 
 cell - level targeting .
mtx is a structural 
 derivative and competitive inhibitor of folic acid ( fa ) ; therefore , it was proposed that mtx conjugates 
 may also be able to provide increased binding and uptake when multivalently 
 displayed on a polymer scaffold .
has 
 shown that multivalent g5 pamam folic acid conjugates ( g5-(cog - fa)n ) bind to fbp via a slow onset , tight - binding 
 interaction in which fa first binds , the protein structure rearranges , and then polymer  protein van der waals forces provide the 
 final tight - binding interaction ( figure 1a ) .
in other words , the tight - binding of polymer 
 conjugate does not arise from multiple fa - protein interactions , and 
 a single fa - fbp interaction suffices to initiate the polymer 
interaction by licata and tkachenko , wherein fa serves as a strong 
 key to unlock van der waals polymer / protein interactions . for such protein
 ligand polymer interactions , 
 a particularly interesting aspect to explore is key strength .
when 
 interacting with fbp , mtx is a  weak key  as compared 
 to fa .
as measured by surface plasmon resonance , the kd of mtx to fbp is 2 times greater than that of 
 fa .
this difference arises from a 40% decrease in ka coupled with a 30% increase in kd .
however , several orders of 
 magnitude in higher concentrations of mtx are required to trigger 
 the observed conformational change of the fbp .
mechanism 
 of binding for ( a ) g5-(cog - fa ) conjugates to fbp mimics 
 slow , tight binding .
( b ) g5-(cog - mtx ) conjugates cause less protein 
 conformational change to the polymer and do not irreversibly bind . 

abbreviations : 
 cog = cyclooct-1-yn-3-glycolic acid , c = polymer conjugate , p = protein .
( 1 ) do the g5 pamam mtx conjugates interact with fbp via 
 the slow - onset , tight binding mechanism ? ( 2 ) can the weaker mtx still 
 initiate the strong polymer 
protein van der waals interactions ? 
 ( 3 ) can greater polymer size ( i.e. , dimer g5 with mw of 60  000 
 da vs monomer g5 mw of 30  000 da ) give rise to increased 
 total polymer 
( 4 ) does the weaker binding of mtx 
 allow g5-mtxn to achieve multivalent binding , 
 as previously proposed ? ( 5 ) what is the impact of tuning  key strength  by 
 varying the linker connecting the key to the polymer ?
in this 
 work , we examine the individual and combined impacts of 
 vector size variation , linker chemistry , and dendrimer valency by 
 synthesizing monomeric and dimeric g5 conjugates with well - defined 
 numbers of mtx attached to the dendrimer through two linker systems . 

recent protocols developed to isolate precise ratio ligand - to - dendrimer 
 conjugates from stochastic distributions were employed to create conjugates with 
 narrow , well - defined populations .
surface plasmon resonance ( spr ) 
 and isothermal titration calorimetry ( itc ) were employed to measure 
 the impact of these parameters on g5-mtxn to fbp binding .
all 
 chemicals and materials were purchased 
 from sigma - aldrich or fisher scientific and used as received unless 
 otherwise specified .
ethylene diamine ( eda ) core g5 pamam dendrimer 
 was purchased from dendritech and purified into monomer ( g5 ; average 
 molecular weight of 27.7 kda by gpc , with a range of 2630 
 kda as determined by mass spectrometry ) and dimer ( d ; average molecular 
 weight of 53 kda by gpc ) samples as previously described .
click - easy mfco - n - hydroxysuccinimide 
 was purchased from berry & associates synthetic medicinal chemistry . 

conjugates were prepared 
 using g5 via edc - nhs coupling . in brief , 
 240.4 mg of amine - terminated monomer g5 was dissolved to 0.16 m 
 in deionized water ( di ) .
a total of 12.0 mg of cog ligand was activated 
 by dissolving to 10.5 m in acetonitrile with 2.65 equiv of 
 edc and 2.78 equiv of n - hydroxysuccinimide and stirring 
 for 2 h. the activated cog solution was added dropwise via syringe 
 pump ( 0.33 ml / min ) to the dendrimer solution and allowed to 
 stir overnight .
the product was purified using amicon ultra centrifugal 
 units , 10 kda cutoff membranes , 2 pbs washes , and 4 di washes .
the material 
 was fully acetylated ( 100% of remaining primary amines converted to 
 acetyl groups , henceforth termed  ac  ) by redissolving 
 in anhydrous methanol ( 0.19 m ) , adding 450 equiv of triethylamine 
 and 360 equiv of acetic anhydride , and stirring for 4 h. the product 
 mixture was purified by centrifugation and isolated by lyophillization . 

g5-cog4.7(avg ) was characterized by rp - uplc and h nmr ( supporting information figures 
 s4s5 ) .
click - easy 
 mfco - n - hydroxysuccinimide was activated by dissolving 
 to 10.5 m in acetonitrile and added dropwise via syringe pump 
 ( 0.33 ml / min ) to the dendrimer solution .
the product was purified using amicon ultra centrifugal 
 units , 10 kda cutoff membranes , two pbs washes , and four di washes . 

g5-mfco2.0(avg ) was characterized 
 by rp - uplc and h nmr ( supporting information figures s6s7 ) .  
g5-g5 
 dimer cog conjugates were prepared using edc / nhs coupling according 
 to the procedures outlined for g5 pamam monomer .
a total of 100.8 
 mg of dimer and 5 equiv of cog ligand were employed .
d - cog4.8(avg ) was characterized by rp - uplc and h nmr ( supporting information figures s8s9 ) .  
g5 pamam 
 dimer mfco conjugates were prepared using click - easy mfco - n - hydroxysuccinimide according to the procedures outlined 
 for g5 pamam monomer .
a total of 115.5 mg of dimer and 6.4 equiv of 
 mfco ligand were employed .
d - mfco6.2(avg ) was characterized 
 by rp - uplc and h nmr ( supporting information figures s10s11 ) .  
g5 pamam monomer 
 and dimer dendrimers with precise ratios 
 of cog or mfco ligands per dendrimer were isolated via rp - hplc according 
 to modified literature procedures .
briefly , 
 multiple injections of the stochastic conjugate containing an average 
 ligand / dendrimer ratio were performed with a c18 column and a water / acetonitrile 
 gradient with 0.1% tfa .
eluted fractions were collected and combined 
 to obtain g5 pamam monomer samples with precise cog / dendrimer ratio 
 of 05 ( g5-cogx , x = 15 ) or precise mfco / dendrimer ratio of 04 ( g5-mfcox , x = 14 , 5 + ) .
g5 
 pamam dimer samples with precise cog / dimer ratio of 02 ( d - cogx , x = 12 , 3 + ) were 
 also obtained .
products were purified using pd-10 desalting protocols 
 with di as the equilibration buffer , dissolved in 10 pbs , and 
 then lyophilized to dry .
curve fitting of uplcs by igor pro was performed to 
 provide yield , purity , and hplc mfco and cog averages .
( left ) rp - hplc traces 
 and fractions collected from average conjugations 
 of ( a ) g5-cogx , ( b ) d - cogx , ( c ) g5-mfcox , and ( d ) 
 d - mfcox.(right ) rp - uplc traces of average 
 conjugation ( black ) and each collected fraction . dendrimers with defined numbers of covalently 
 bound methotrexates were synthesized via click reaction of precise 
 ratio g5-cogn , g5-mfcon , d - cogn , or d - mfcon conjugates and -azido - mtx .
briefly , dendrimer 
 conjugates were dissolved in dmso to 40 mm with respect to the click 
 ligand , and a 10-fold excess of -azido - mtx ( 40 mm in dmso ) 
 was added .
solutions were agitated for 48 h , then diluted to 2.5 ml 
 with 10 pbs and purified using pd-10 desalting columns ( gravity 
 protocols ) .
further purification was performed via 10 kda cutoff dialysis 
 against di with 16 media changes .
curve fitting of uplc 
 chromatograms provided yield , purity , and mtx averages ( supporting information figures s12s16 ) .
isolation of 
 precise ligand / dendrimer ratio conjugates was achieved using a waters 
 600 controller , waters 2707 autosampler , and waters 2998 photodiode 
 array running empower 2 software , additionally equipped with a waters 
 fraction collector iii on a phenomenex jupiter 300  c18 prep 
 column ( 21.2  150 mm , 5 m particles ) . the weak solvent 
 ( solvent a ) was hplc grade water with 0.1% tfa , and the strong solvent 
 ( solvent b ) was hplc grade acetonitrile with 0.1% tfa .
the gradient 
 employed at 16 ml / min was as follows : 2.1 min load step at 95%a/5%b , 
 3.9 min gradient to 80%a/20%b , 15 min gradient to 65%a/35%b , 5 min 
 gradient to 55%a/45%b , followed by 3 min was at 20%a/80%b , then equilibrating 
 at starting conditions for 5 min before next injection .
the stochastically 
 synthesized dendrimer conjugates were dissolved to 20 mg / ml concentration 
 and 910 l injections were used .
five - second fractions were 
 collected starting at 9 min 30 s into each run for a total of 120 
 fractions .
analytical chromatograms were collected on a waters acquity 
 uplc equipped with a scaled method using a phenomenex jupiter 4.6  
 100 mm column .
uplc chromatograms 
 were fit with gaussian 
 peaks using igor pro version 6.0.3.1 software .
h nmr spectra were obtained used 10 s preacquisition delays 
 and a total of 64 scans .
all sample solutions were set to a dendrimer 
 concentration of 5 mg / ml in deuterium oxide .
all experiments were 
 performed on a nano itc standard volume from ta instruments ( lindon , 
 ut ) .
g5-(mfco - mtx)4.0(avg ) ( 70 , 200 , 400 m with 
 respect to mtx ) , g5-(mfco - mtx)4 + ( 313.3 m with respect 
 to mtx ) , free mtx ( 200 m ) , and fbp ( 4 m ) solutions were 
 prepared in ph 7.4 pbs buffer and then degassed for 25 min . before 
 loading ,
the reference cell of the itc was refilled with degassed , 
 nanopure water every 2 days . after flushing the sample cell with buffer
, 
 the syringe was filled with the mtx solution and the sample cell was 
 filled with the fbp solution .
using itcrun software the parameters 
 of the itc were set ( stir rate , 250 rpm ; injection interval , 1000 
 s ; injection volume , 12 l ; injections , 20 ; temperature , 25 
 c ) and the instrument was allowed to auto equilibrate before 
 starting the titrations .
controls were performed by injecting the 
 same concentration of mtx conjugates into pbs buffer .
these control 
 runs were then subtracted from the experimental runs to account for 
 heat from mixing or dilution and were analyzed using ta nanoanalyze 
 software ( ver 2.4.1 ) .
the area under each peak was integrated and 
 the resulting data was modeled using an independent model fit with 
 variables h , binding stoichiometry ( n ) , and ka .
spr experiments were conducted 
 in a biacore x instrument ( pharmacia biosensor ab ) .
an immobilized 
 folate binding protein ( fbp ) chip was prepared following the instrument 
 prompted protocols , using a solution of 0.2 m edc and 0.05 m nhs as 
 an activating solution , 1 mg / ml fbp solution as the immobilization 
 solution , and ethanolamine as the deactivation solution .
the chip 
 was characterized using free fa and methotrexate solutions ranging 
 from 0.1 to 2 mm .
conjugate samples were dissolved in fresh ph 7.4 
 hbs - ep buffer ( fisher scientific ) at 60 m and serially diluted 
 to 10 , 5 , 2.5 , and 1.25 m in buffer .
the system was allowed to equilibrate 
 at the beginning of each run for no less than 300 s , followed by a 
 2 min , 30 l ( 50555 via bubble method ) 
 injection .
the system was monitored for no less than 500 s per injection . 
 between each run ,
the chip was washed with a 5 l injection 
 of ph 1.5 buffer to remove bound materials followed by a prime step 
 prior to the next injection .
isolation of 
 precise ligand / dendrimer ratio conjugates was achieved using a waters 
 600 controller , waters 2707 autosampler , and waters 2998 photodiode 
 array running empower 2 software , additionally equipped with a waters 
 fraction collector iii on a phenomenex jupiter 300  c18 prep 
 column ( 21.2  150 mm , 5 m particles ) .
the weak solvent 
 ( solvent a ) was hplc grade water with 0.1% tfa , and the strong solvent 
 ( solvent b ) was hplc grade acetonitrile with 0.1% tfa . the gradient 
 employed at 16 ml / min was as follows : 2.1 min load step at 95%a/5%b , 
 3.9 min gradient to 80%a/20%b , 15 min gradient to 65%a/35%b , 5 min 
 gradient to 55%a/45%b , followed by 3 min was at 20%a/80%b , then equilibrating 
 at starting conditions for 5 min before next injection .
the stochastically 
 synthesized dendrimer conjugates were dissolved to 20 mg / ml concentration 
 and 910 l injections were used .
five - second fractions were 
 collected starting at 9 min 30 s into each run for a total of 120 
 fractions .
analytical chromatograms were collected on a waters acquity 
 uplc equipped with a scaled method using a phenomenex jupiter 4.6  
 100 mm column .
uplc chromatograms 
 were fit with gaussian 
 peaks using igor pro version 6.0.3.1 software .
h nmr spectra were obtained used 10 s preacquisition delays 
 and a total of 64 scans .
all sample solutions were set to a dendrimer 
 concentration of 5 mg / ml in deuterium oxide .
all experiments were 
 performed on a nano itc standard volume from ta instruments ( lindon , 
 ut ) .
g5-(mfco - mtx)4.0(avg ) ( 70 , 200 , 400 m with 
 respect to mtx ) , g5-(mfco - mtx)4 + ( 313.3 m with respect 
 to mtx ) , free mtx ( 200 m ) , and fbp ( 4 m ) solutions were 
 prepared in ph 7.4 pbs buffer and then degassed for 25 min . before 
 loading , the syringe and cell were each rinsed with degassed pbs buffer 
 three times .
the reference cell of the itc was refilled with degassed , 
 nanopure water every 2 days . after flushing the sample cell with buffer
, 
 the syringe was filled with the mtx solution and the sample cell was 
 filled with the fbp solution .
using itcrun software the parameters 
 of the itc were set ( stir rate , 250 rpm ; injection interval , 1000 
 s ; injection volume , 12 l ; injections , 20 ; temperature , 25 
 c ) and the instrument was allowed to auto equilibrate before 
 starting the titrations .
controls were performed by injecting the 
 same concentration of mtx conjugates into pbs buffer .
these control 
 runs were then subtracted from the experimental runs to account for 
 heat from mixing or dilution and were analyzed using ta nanoanalyze 
 software ( ver 2.4.1 ) .
the area under each peak was integrated and 
 the resulting data was modeled using an independent model fit with 
 variables h , binding stoichiometry ( n ) , and ka .
spr experiments were conducted 
 in a biacore x instrument ( pharmacia biosensor ab ) .
an immobilized 
 folate binding protein ( fbp ) chip was prepared following the instrument 
 prompted protocols , using a solution of 0.2 m edc and 0.05 m nhs as 
 an activating solution , 1 mg / ml fbp solution as the immobilization 
 solution , and ethanolamine as the deactivation solution . the chip 
 was characterized using free fa and methotrexate solutions ranging 
 from 0.1 to 2 mm .
conjugate samples were dissolved in fresh ph 7.4 
 hbs - ep buffer ( fisher scientific ) at 60 m and serially diluted 
 to 10 , 5 , 2.5 , and 1.25 m in buffer .
the system was allowed to equilibrate 
 at the beginning of each run for no less than 300 s , followed by a 
 2 min , 30 l ( 50555 via bubble method ) 
 injection .
the system was monitored for no less than 500 s per injection . 
 between each run ,
the chip was washed with a 5 l injection 
 of ph 1.5 buffer to remove bound materials followed by a prime step 
 prior to the next injection .
a major challenge to detailed scientific understanding of multivalent 
 dendrimer binding mechanisms has been the presence of trailing generations 
 ( g1g4 ) and oligomers ( dimers , trimers , etc . ) in the dendrimer 
 conjugates studied .
recently , we have developed methods for gram - scale 
 isolation of pamam materials as a function of dendrimer size and milligram - scale isolation as a function 
 of conjugate valency .
these methods create an opportunity to improve valency 
 control of multivalent conjugates and improve the ability to analyze 
 the binding mechanism of previously developed multicomponent mixtures . 
 here , we directly compare pamam monomer and dimer mtx conjugates using 
 spr- and itc - based measurements of binding characteristics .
these 
 experiments probe the effect of vector size both as a design principle 
 for its own sake and to attribute binding behaviors to monomer and 
 dimer , which were present in the materials employed in previous spr 
 studies .
in addition to valency , the influence of 
 linker length / flexibility / hydrophobicity for the system was also explored .
g5 pamam dendrimer monomer ( g5 ) and dimer 
 ( d ) were isolated from commercially available material as previously 
 described .
stochastic conjugations to 
 fluorinated ( mfco ) and nonfluorinated ( cog ) ring strain promoted click 
 chemistry ligands were performed via amide coupling reactions resulting 
 in materials containing a distribution of ligand / dendrimer ratios 
 ranging from 0 to 13 covalently attached ligands per dendrimer .
peak fitting 
 of rp - uplc chromatograms was employed to determine the average ligand - to - dendrimer 
 ratio for each sample .
these stochastic mixtures were then isolated by semipreparative 
 rp - hplc following previously reported protocols .
the purity of the isolated , precise ratio ligand - to - dendrimer 
 conjugates range from 90 to 100% ( as defined by ligand / dendrimer ratio 
 dispersity ) .
in addition to the precise ligand / dendrimer ratio materials , 
 samples containing a high average number of mfco 
 ligands ( g5-mfco6.6(avg ) and d - mfco5.3(avg ) ) 
 and a high average of cog ligands ( d - cog6.2(avg ) ) were 
 also obtained .
importantly , these samples contain no unfunctionalized 
 ( x = 0 ) or monofunctional ( x = 1 ) 
 materials , making them good controls for the observation of multivalent 
 ( e.g. , chelation or statistical rebinding ) effects . a summary of all 
 isolated materials can be found in table 1 . 

these rp - hplc methods are versatile and have been successfully employed 
 to isolate precise ratio ligand / dendrimer conjugates for both monomer 
 and dimer pamam and using three different ligands to date .
the presumed 
 mechanism allowing this isolation protocol is a favorable interaction 
 between the conjugated , hydrophobic ligand and the reverse - phase c18 
 column .
the mfco ligand , which contains a longer carbon chain in addition 
 to the fluorine on the cyclooctyne , results in significantly higher 
 resolution than the shorter cog ligand .
this is illustrated in figure 2 , panels a and c , where g5-mfco2.0(avg ) has baseline resolution between n = 0 and 1 , and n = 1 and 2 samples ( figure 2c ) , 
 whereas g5-cog4.7(avg ) has peak overlap for all peaks , 
 even n = 0 and n = 1 ( figure 2a ) .
the difference between the x = 1 and x = 2 peak centers is 0.64 min for the 
 g5-cog conjugates compared to 1.02 min for the mfco conjugates .
the 
 improved resolution likely arises from the greater hydrophobicity 
 of the longer chain resulting in greater interaction with the c18 
 stationary phase , leading to increased retention as a function of 
 number of ligands .
the increased resolution is repeated in the dimer 
 conjugates ; however , the resolution of both dimer species is less 
 than the corresponding monomer . as the time difference in peak centers 
 for x
= 1 , 2 is nearly identical between the monomer 
 and dimer for both ligands ( 0.59 and 1.04 min for dimer conjugated 
 to cog and mfco , respectively ) , the reduced resolution is the result 
 of the increased peak width of the dimer species ( arising from a broader 
 mw distribution of branching defects ) . 

better rp - hplc resolution allows for the isolation of higher ratio 
 materials , increased yield of all conjugates , and increased purity 
 of resulting samples .
the conjugate 
 samples , containing g5 monomer or 
 dimer conjugated to precise numbers ( x = 03 ) 
 or high average ( 3 + or 4 + ) numbers of cog or mfco , were then allowed 
 to react with -azido - mtx .
a detailed analysis 
 of each sample s fractional composition is summarized in table 2 .
click efficiencies were approximately equal for 
 monomer and dimer conjugates and for mfco and cog .
because of undesired 
 interactions of the mfco conjugates with the spr surface ( vide infra ) , 
 the binding of g5-(mfco - mtx)n conjugates 
 to fbp was measured by itc .
the stochastically conjugated monomer 
 g5-(mfco - mtx)4(avg ) sample displayed endothermic binding 
 ( supporting information figure s1a ) .
this 
 indicates that binding between the conjugate and protein can occur , 
 but there is an energetic cost . by way of contrast
, there was no observable 
 binding between the isolated high average g5-(mfco - mtx)4.4 sample , which contains only dendrimer clicked to 3 or more mtx . 

one interpretation of these results would be that the flexibility 
 and hydrophobicity of the mfco linker cause it to fold into the interior 
 regions of the g5 dendrimer .
consequently , the energetic penalty to 
 hydrate the ligand and allow for mtx / protein interaction is significantly 
 higher , which negatively impacts the enthalpy of binding . because 
 the lower average sample shows some interaction with the protein , 
 it is possible that there is cooperativity within the mfco linkers 
 that further block the mtx from interacting with the protein in the 
 higher average sample .
weak , reversible 
 binding for g5-(cog - mtx)n ( n = 0.9 , 1.9 , 2.9 ) to surface 
 immobilized fbp was observed at all concentrations tested .
the control 
 samples ( fully acetylated monomer and dimer with no mtx ) had similar 
 binding to both chips , which when subtracted gave relatively flat 
 chromatograms ( figure 3a and e ) . by way of 
 contrast , all three tested valencies for the monomer show both a dendrimer 
 and total mtx concentration dependent binding with the fbp surface . 

figure 4 reveals that g5-(cog - mtx)n exhibits greater association phase binding ( i.e. , 
 higher signal ) as valency increases ( figure 4a ) .
for all injections , the signal initially rose sharply at the 
 beginning of the injection and quickly reached equilibrium between 
 association and dissociation .
in other words , in figure 1b ka and kd are both 
 large and rapid as compared to k2 , and 
 strong irreversible binding does not occur . at the end of the injection , 

all chromatograms quickly return to baseline , confirming the fast 
 dissociation of all bound species .
this indicates that even the divalent 
 ( 66% ) and trivalent species ( 13% ) in the g5-(cog - mtx)2.9 experience only monovalent binding to the fbp surface .
there is 
 no multivalency effect for increasing the mtx valency ( n ) for g5-(cog - mtx)n .
the data were fit 
 to the expression r = rmax[c]/([c ] + kd ) to yield the apparent kd values of 6.3  0.4  10 m , 7.4  0.7  10 m , and 8.6  
 1.1  10 m for g5-(cog - mtx)0.9 , g5-(cog - mtx)1.9 , and g5-(cog - mtx)2.9 , respectively 
 ( all fits used a common rmax value of 
 67 , see below ) .
however , when the data is plotted as a function of 
 total mtx concentration it fits well to a single binding isotherm 
 ( figure 4b ) . fitting the concentration dependent 
 data for all three samples to
a single expression resulted in an rmax value of 67  8 and a kd value of 7.6  1.8  10 m. spr results of all click products .
color gradients represent least 
 concentrated ( light ) to most concentrated ( dark ) injections .
( a ) g5 
 ( acetylated control ) , ( b ) g5-(cog - mtx)0.9 , ( c ) g5-(cog - mtx)1.9 , ( d ) g5-(cog - mtx)2.9 , ( e ) d ( acetylated control ) , 
 ( f ) d-(cog - mtx)1.1 , ( g ) d-(cog - mtx)2.0 , ( h ) 
 d-(cog - mtx)6.0 .
saturation of spr signal during the binding phase as a function 
 of ( a ) conjugate concentration for monomer samples , ( b ) total mtx 
 concentration for monomer samples , ( c ) conjugate concentration for 
 dimer samples , and ( d ) total mtx concentration for dimer samples . 
 the data in panels a and b is fit to the expression r = rmax[c]/([c ] + kd ) for an a + b  c equilibrium .
total concentration of mtx does not explain the trend in the 
 binding phase ( figure 4d ) and a higher average 
 number of mtx ligands per dendrimer actually show less surface binding 
 for a given concentration of mtx . however , there is a binding phase 
 signal dependence based on dendrimer concentration ( figure 4c ) .
the data indicate that at the concentrations 
 tested , d-(cog - mtx)n with an mtx valency 
 of at least n = 1 , an association / dissociation equilibrium 
 ( ka and kd as represented schematically in figure 1c ) 
 is not reached during sample injection ( figure 3f  h ) . at equilibrium , higher mtx valencies would be expected 
 to have more total binding due to statistical rebinding effects
. however , 
 at these concentrations a single mtx / fbp interaction ( figure 3e  f ) is sufficient to establish the van der 
 waals interaction ( k2 in figure 1 ) between the dimer and protein .
the amount of binding 
 observed is therefore approximately equal for equivalent dendrimer 
 concentrations ( figure 4c ) . with a stronger 
 binder , such as fa ( figure 1a ) , equilibrium 

is established at lower concentrations and the total binding becomes 
 dependent on total ligand concentration ( vide infra , figures 56 ) .
therefore , a dependence on mtx valency can not be established for 
 the d-(cog - mtx)n case .
the higher concentrations 
 ( to achieve equilibrium during the injection ) that would have allowed 
 full exploration of the likely sigmoidal functional response were 
 not tested due to conjugate solubility .
quantitative fits of the type 
 shown for figure 4a and b are not possible . 

however , it can be concluded that the interaction must be  keyed  
 by conjugated mtx , as there is negligible accumulation observed in 
 the acetylated control ( d ) sample ( figure 3e ) . in this case ,
possible mtx valency dependent effects on binding , 
 including statistical rebinding and chelation , do not lead to the 
 observed greater overall conjugate binding .
comparison of the spr 
 sensograms of a d-(cog - mtx)6.0 sample to two different 
 g5-(cog - fa)n samples , with total signal 
 normalized .
amount of bound material 
 d-(cog - mtx)n after 500 s of dissociation 
 is dependent on absolute mtx concentration 
 and fbp density , not mtx valency .
as indicated by supporting information figure s3 , both g5-(mfco - mtx)n and d-(mfco - mtx)n have a negative overall signal in injection / association 
 phase as a result of nonspecific interactions with the chip surface 
 in the control flow cell ( fc2 ) .
the mtx conjugate data described above can be compared 
 to a study 
 of monomeric g5-(cog - fa)n ( n = 0 , 1 , 1.2 , 1.9 , 2.7 ) conjugates by van dongen , banaszak holl et 
 al .
that indicated greatly increased avidity via spr with a significant 
 portion of bound material not dissociating over the time scale of 
 the experiment .
because this observation 
 held true for even a purely monovalent ( folic acid - to - dendrimer ratio 
 of 1 ) sample , it was concluded that the observation of increased avidity 
 was due to the sum of weak van der waals interactions between the 
 dendrimer and protein surface ( figure 1a ) . 

this interaction is initiated by an interaction between a conjugated 
 fa and the fbp , which causes a conformational change in the protein 
 exposing a more hydrophilic surface to interact with the dendrimer 
 ( schematically represented as a color change in figure 1 ) .
mtx , as a structurally modified competitive inhibitor of 
 fa , may undergo a similar interaction with the fbp .
however , although 
 the experiments here were performed on surfaces with both higher protein 
 densities and higher conjugate concentrations , a similar avidity increase 
 for monomer g5-(cog - mtx)n conjugates was 
 not observed at even the highest valency tested ( n = 3 ) .
previous studies indicated only a 2 fold increased 
 binding of free fa as compared to free mtx ; therefore , the significant reduction in binding strength of g5-(cog - mtx)n compared to g5-(cog - fa)n is most likely due to a reduction in polymer / protein interactions . 

mtx is a  weak  key to the fbp  lock  , 
 and the structural rearrangement of the protein is not large enough 
 to establish van der waals interactions for a polymer of the same 
 size . for the mtx case ,
there are indications of enhanced avidity 
 for the dimer samples ( d-(cog - mtx)n ) . 

however , when comparing the overall shape of the g5-(cog - fa)n and d-(cog - mtx)6.0(avg ) sensograms 
 ( figure 5 ) it becomes clear that there are 
 some fundamental differences .
for the g5-(cog - fa)n samples , nearly all materials that bound ( to a protein 
 density dependent saturation point ) remained permanently attached 
 to the surface . by contrast
, a large percentage of the d-(cog - mtx)n material quickly dissociates after the conjugate 
 flow has stopped .
this indicates that kd is much larger for the mtx conjugates as compared to the fa conjugates , 
 that k2 is much smaller ( figure 1a and c ) , or that for some binding sites steric 
 contraints prevent achieving the magnitude of polymer / protein interaction 
 that leads to irreversible binding .
the d-(cog - mtx)n conjugates 
 show a dendrimer concentration , not mtx concentration , dependent association 
 to the protein surface ( figure 4c ) .
the absolute 
 signal , when compared to that of the monomer / mtx conjugates , is approximately 
 10 higher in the dimer species at equivalent molar concentrations . 

a 2-fold increase may be expected by this technique due to doubling 
 in mass .
this leads to a qualitative assumption that more binding 
 occurs in dimer samples as compared to monomer samples for equivalent 
 total mtx concentrations .
association signal is likely caused by the larger mass and radius 
 of the dimer increasing the van der waals 
 interactions between the dendrimer / fbp ( i.e. , an increase in k2 from negligible in the monomer data to contributing 
 for dimer conjugates ) .
chelate - type binding between multiple mtx and 
 one or more fbp is not observed , in even the high - valency dimer samples . 

figure 6 indicates that the amount of irreversibly 
 bound material ( defined as the portion of signal remaining after 500 
 s of dissociation ) is dependent only on the absolute mtx concentration 
 in solution and not on conjugate valency .
if chelate binding was responsible 
 for the irreversible binding , the bivalent and high valent samples 
 would be expected to have enhanced binding as compared to the monovalent 
 samples at similar mtx concentrations . instead , the amount of strongly 
 bound material has a linear dependence on mtx concentration prior 
 to reaching a saturation at 120 response units .
previous 
 spr studies on pamam - cog - mtx conjugates ( containing mixtures 
 of dimer and monomer ) indicated both monovalent and multivalent binding 
 occurred for stochastic valencies of n = 5 and n = 10 .
the present work indicates 
 that the origin of the portion of binding assigned as  multivalent  
 arose from the presence of dimers conjugated to 3 or more mtx .
the 
 dendrimer material in previous studies contained 14% dimer and assuming a poisson distribution , the  multivalent  

portion of the n = 5 and 10 samples would be 13% 
 and 14% , respectively .
new chromatographic 
 methods have enabled the examination of vector 
 molecular weight effects ( monomer vs dimer ) , linker system effects 
 ( cog vs mfco ) , and valency effects on the highly studied drug delivery 
 system of pamam dendrimer conjugated to methotrexate . the answers 
 to the questions posed at the start of the paper
can now be addressed : 
 ( 1 ) the monomer g5 pamam - mtx conjugates show none of the irreversible 
 binding previously attributed to multivalency for stochastic conjugate 
 synthesized using commercial dendrimer containing oligomers of g5 . 

the dimer g5 pamam - mtx conjugates do show irreversible binding , including 
 d - mtx1 , which can not bind via a multivalent mtx mechanism . 

the slow - onset , tight - binding mechanism is consistent with these observations . 

( 2 and 3 ) although the weaker mtx does not initiate sufficient structural 
 change for the irreversible binding to occur between fbp and monomer 
 g5 , the larger dimer of g5 interacting with the protein is able to 
 generate a large enough interaction for irreversible binding . ( 4 ) 
 it has been suggested that weaker linkers could provide longer surface 
 diffusion times and , thus , potentially allow multivalent ligand binding .
( 5 ) we attempted to tune key strength by varying the 
 linker ; however , this resulted in a number of changes including differential 
 solution binding enthalpy likely related to hydrophobicity and undesired 
 binding to control surfaces . in summary
, the preparation of 
 controlled valency monomer g5 and 
 dimer g5g5 conjugates , demonstrate that multivalency is not 
 an active binding mechanism for these conjugates and a slow , onset 
tight 
 binding mechanism is proposed that is consistent with mechanistic 
 hypotheses for the analogous fa conjugates and the mechanistic proposals of licata and tkachenko .
 generation 
 5 poly(amidoamine ) ( g5 pamam ) methotrexate ( mtx ) conjugates 
 employing two small molecular linkers , g5-(cog - mtx)n , g5-(mfco - mtx)n were prepared along with the conjugates of the g5-g5 ( d ) 
 dimer , d-(cog - mtx)n , d-(mfco - mtx)n . 
 the monomer g5-(cog - mtx)n conjugates exhibited only a weak , rapidly reversible binding 
 to folate binding protein ( fbp ) consistent with monovalent mtx binding . 
 
 the d-(cog - mtx)n conjugates exhibited 
 a slow onset , tight - binding mechanism in which the mtx first binds 
 to the fbp , inducing protein structural rearrangement , followed by 
 polymer  protein van der waals interactions leading to tight - binding . 
 
 the extent of irreversible binding is dependent on total mtx concentration 
 and no evidence of multivalent mtx binding was observed . 
Introduction
Experimental Section
Methods
Results and Discussion
Conclusions