dna - functionalized gold nanoparticles are an interesting 
 system with applications ranging from biological sensors to the construction of 
 self - assembled materials .   experiments are based on attaching single - stranded 
 dna molecules via thiol - gold bonds to the surface of au nanoparticles and a 
 subsequent self - assembly process of these conjugates by making use of base 
 pairing of complementary dna molecules [ 15 ] . for example , by employing au - dna conjugates , 
 several groups have developed schemes to detect target dna sequences   and to assemble nanoparticles 
 into macroscopic materials [ 7 , 8 ] . dna - functionalized au nanoparticles are the building blocks for the above - mentioned experiments . 
 therefore , it is of great interest to investigate the properties of these 
 conjugates in detail . due to the high affinity of thiol groups to gold surfaces , thiol - modified dna molecules can be directly bound to the surface of citrate- or phosphine - stabilized au nanoparticles [ 9 , 10 ] . although commonly a random 
 number of dna molecules are attached per au nanoparticle , also particles with an 
 exactly defined number of one , two , or three attached dna molecules per 
 nanoparticles can be obtained [ 1115 ] . certainly , several 
 parameters have significant influence on the properties of au - dna conjugates , 
 such as coverage of the au surface with dna , configuration of the attached dna 
 molecules , and hybridization efficiency of dna attached to au surfaces . the degree of dna coverage will influence 
 the dna conformation , which , in turn , will affect the hybridization efficiency . a body of experiments investigating these parameters has been 
 reported for dna attached to flat au surfaces using different techniques such 
 as atomic force microscopy ( afm ) [ 1618 ] , surface plasmon resonance 
 ( spr ) spectroscopy [ 1921 ] , radioisotopic techniques [ 22 , 23 ] , ellipsometry , and x - ray photoelectron 
 spectroscopy ( xps ) . these experiments allow for 
 a detailed picture of dna bound to planar gold surfaces and the results have 
 clarified the binding mechanism , the surface coverage , the hybridization 
 efficiency , and the role of nonspecific adsorption , all in dependence of the 
 length of the dna . since the effect of surface curvature has to be taken into 
 account , the results obtained for 
 planar au surfaces may be transferred to spherical au nanoparticles only under 
 certain restrictions . the surface coverage of au nanoparticles with dna has 
 been investigated using the displacement of fluorescence - labeled dna molecules 
 with mercaptoethanol   and by gel electrophoresis . also , the conformation of 
 bound dna [ 27 , 28 ] , hybridization , and the role of nonspecific 
 adsorption [ 26 , 28 , 30 ] have been investigated for au 
 nanoparticles . in this report , we present a detailed study of electrophoretic 
 mobility of au - dna conjugates . with this study , we want to determine the 
 possibilities and limitations of this technique . besides our own previous work [ 27 , 31 ] , also other groups [ 28 , 32 , 33 ] have recently reported about 
 the possibility to extract effective diameters for bioconjugated colloidal 
 nanoparticles from electrophoretic mobilities . the aim of this study is , in 
 particular , to investigate the limitations of this analysis . citrate - coated gold nanoparticles of 5 , 10 , and 20  nm 
 diameter were purchased from bbi / ted pella ( redding , calif , usa ) . in order to 
 improve their stability in buffer solution , the adsorbed citrate molecules were 
 replaced by a phosphine ( bis(p - sulfonatophenil)phenylphosphine dehydrate , 
 dipotassium salt ) . the concentration of the au 
 nanoparticles was determined by uv / vis spectroscopy by using the molecular 
 extinction coefficient of their absorption at the plasmon peak . thiol- and cy5-modified and unmodified single - stranded dna were purchased from idt ( coralville , 
 iowa , usa ) or metabion ( mnchen , germany ) . all sequences can be found in the supplementary material ( available   online at doi : 10.1155/2007/26796 ) . the concentration of the dna was determined by uv / vis spectroscopy by using the molecular extinctions coefficient of their absorption at 260 nm . the thiol - modified and plain dna were added to the phosphine - coated au nanoparticles at ph = 7.3 , c ( nacl ) = 50 mm , and samples were incubated for some hours up to several days [ 11 , 27 ] . generally , in such 
 experiments , dna is always added in large excess , thus that the number of 
 attached molecules is related but not fully controlled by the stoichiometry of 
 dna : au - np because of the rather low 
 binding yield . the resulting au - dna conjugates were loaded on 0.5%6% 
 agarose gels ( agarose : gibco brl , number 15510 - 027 ; 0.5  tbe buffer , ph 9 ) and 
 run for one hour at 100  v [ 11 , 27 ] . ( since 6% gels can be 
 inhomogeneous due to their high viscosity , the data obtained with these gels 
 have to be interpreted with care . ) as reference , always unconjugated au 
 nanoparticles of the same diameter were run on the same gel . in addition , gels 
 with unconjugated au nanoparticles of different diameter and free dna of 
 different length were run . the bands of the plain and dna - conjugated au 
 nanoparticles were directly visible by the red color of the au colloid and the 
 free dna was visualized by an attached fluorescence label ( fluorescein , cy3 , or 
 cy5 ) . the bands of the gels were photographed using a digital camera system 
 ( eagle eye iii , stratagene ) . the mobility of each sample was determined by 
 measuring the position of each band referring to the start position where the 
 samples had been loaded . this resulted in a comprehensive set of data which 
 relates the mobility of au - dna conjugates to the diameter of the au particles , where the relation between the amount 
 and the length of the attached dna , nonspecific versus specific attachment 
 via thiol - gold bonds , and the gel percentage was studied . since mobility is not an illustrative quantity , we have attempted 
 to convert the mobilities of au - dna conjugates in effective diameters . the 
 evaluation of the gels in which plain au - nanoparticles of known diameter were 
 run yielded a calibration curve in which the mobility is plotted versus the diameter . 
 by using this calibration curve , the mobility of the au - dna conjugates could be 
 directly converted into effective diameters . alternatively , the mobility 
 of au - dna conjugates at different agarose concentrations was used to obtain 
 ferguson plots   and fits of the ferguson 
 plots yielded the retardation coefficients . first , ferguson plots were 
 made for plain au - nanoparticles of known diameter and a calibration curve in 
 which the retardation coefficients were plotted versus the particle diameter 
 was obtained . by using this calibration 
 curve , the effective diameters of au - dna conjugates could be derived from the 
 retardation coefficients derived from the ferguson plots of the au - dna 
 conjugates . we have also quantified the maximum number of dna molecules that 
 can be attached per gold nanoparticle for particles with 5  nm and 10  nm 
 diameter and single - stranded dna with 8 and 43 bases . for this purpose , single - stranded dna that had been modified with a thiol group on the 3 ' and a cy5 dye on the 5 ' end 
 has been attached via formation of thiol - au bonds to the surface of au particles . dna was added in different dna to au ratios and the conjugates were run on an agarose gel . the more dna bound per au nanoparticle , the more the 
 band of this conjugate was retarded on the gel . at a certain amount of added 
 dna , the retardation of the band of the conjugates did not further increase , 
 which indicates that the au surface is fully saturated with dna . the bands were extracted from the gel by cutting out the agarose piece that contained the band and 
 immersing it into 0.5  tbe buffer solution . after two days , the au - dna 
 conjugates had diffused out of the gel into the buffer . the extraction procedure ensures that all dna is really attached to the au particles , since free dna migrates in a much faster band . uv / vis spectra were recorded of the 
 extracted au - dna conjugates . for each of the conjugates , the dna concentration 
 was determined by the cy5 absorption and the au concentration was determined by 
 the absorption at the plasmon peak and from both concentrations the number of 
 attached dna molecules per particles was derived . as we quantified the number 
 of attached cy5 molecules only with absorption and not with fluorescence 
 measurements , the effect that the fluorescence of cy5 close to au surfaces is 
 quenched all methods and additional experiments can be found in detail 
 in the supplementary material . the attachment of dna to au nanoparticles can be clearly observed by gel electrophoresis [ 9 , 11 , 13 , 2628 , 3638 ] . the mobility of particles on the gel depends on two factors : size and charge . the bigger the size , the slower and the higher the charge , the faster 
 particles will migrate . in the case of negatively charged au particles ( e.g. , 
 with citrate or phosphine molecules adsorbed to the particles ) , the attachment 
 of negatively charged dna molecules causes in first place an increase of size 
 that can be seen as a retardation of the band of the gel . if the change in charge 
 dominated , then the mobility of the au particles should be increased ( addition 
 of negative charge ) or drastically decreased ( addition of positive charge ) up 
 to change in the direction of migration . although this effect has been observed 
 for different systems [ 31 , 39 ] , it has not been observed for the au - dna conjugates used in this study . upon attachment of dna , therefore , in 
 agreement with previous reports , we assume throughout this manuscript that 
 attachment of dna to au nanoparticles in first order increases the effective 
 diameter of the conjugates which can be directly seen in the retardation of the 
 band of the conjugates in gel electrophoresis experiments [ 9 , 11 , 2628 , 3638 ] . one aim of this study was to obtain calibration curves in 
 which measured electrophoretic mobilities m can be related to effective diameters deff . by running phosphine - stabilized au particles of known diameter ( the overall diameter of phosphine - coated au np was assumed 
 as the core diameter plus two times 0.5 nm for the thickness of the phosphine layer and the smallest nanoparticle size used for calibration was 6 nm ) on gels , by measuring their mobility , by fitting the data empirically with an exponential function , and by using the inverse of the fit function , we obtained a function in which the effective diameter of au particles and au - dna conjugates can be directly calculated from their electrophoretic mobility : 
 ( 1)deff(m)=ty*ln((m / m10  nm , y)/ay)+6  nm . 
 the parameters for y = 0.5% , 1% , 2% , 3% , 4% , 5% , and 6% 
 agarose gels are enlisted in table 1 . in order to enhance the accuracy by 
 making relative instead of absolute measurements , we always normalized the mobilities m to the mobilities m10 nm , y of plain phosphine - stabilized au particles of 10 nm core diameter on the same gel . therefore , although the primary data of all electrophoresis measurements are electrophoretic mobilities , 
 we are discussing the experimental results in terms of effective diameters . the diameters have been obtained with the above - described formula from the mobility data . since obviously the effective diameter of au - dna conjugates 
 is a fixed physical property , it should not depend on the form of measurement 
 and analysis . we , therefore , compared the effective diameters derived from 1% , 
 2% , 3% gels via the respective mobility - diameter calibration curves and from 
 ferguson plots . for the ferguson plots , the determined   effective diameters for au - dna conjugates for 
 au particles saturated with dna and for au particles with only few dna strands 
 attached per particle are plotted in figures 1 and 2 for dna of different 
 length . in all cases , regardless the length of the dna , whether dna was 
 attached by specific thiol - gold linkage or by nonspecific adsorption , or 
 whether only a few or a many as possible dna molecules were bound per au 
 nanoparticles , the effective diameters derived with the mobility - diameter 
 calibration curves are different for different gel percentages . though most of 
 the times the effective diameters derived from gels with higher percentage were 
 found to be larger than the ones obtained from gels with lower percentage , also 
 the opposite effect was observed within the experimental error bars ( see , e.g. , 
 figure 2 ) . the effective diameters derived from ferguson plots were always 
 smaller than the ones derived from the mobility - diameter calibration curves . if always the effective diameters derived from 
 the gels of higher percentage were smaller than the one derived from gels with 
 lower percentage , one could have argued that the soft dna shell around the 
 rigid au cores would be squeezed or compressed more while migrating through the 
 gel of higher agarose concentration , which would lead to smaller effective diameters . however , since no clear correlation between the gel concentration and the 
 derived effective diameters was observed , we have to consider the difference 
 between the effective diameters that have been obtained from gels of different 
 concentrations as error bars . the bigger the au particles become due to 
 attachment of dna , the bigger the error in deriving their effective diameter 
 from electrophoretic mobilities becomes . for example , according to figure 1 , 
 the effective diameters of 10  nm au particles saturated with 100 bases dna that 
 is specifically linked via thiol - au bonds are 66.3  nm , 69.5  nm , and 58.5  nm as 
 determined from 1% , 2% , and 3% gels . we believe that from these data we can 
 assume that the effective diameter of these conjugates is around 60  nm with an error bar of 
 around 10  nm . from these and additional similar data ( not shown ) , we conclude 
 that deriving absolute effective diameters from electrophoretic mobilities via 
 mobility - diameter calibration curves is possible only under certain 
 restrictions . it is not sufficient to extract the data just from gels of one 
 percentage . only by using gels of different percentage an average value for the 
 effective diameter and an estimate about the error can be obtained . part of 
 this limitation might be due to our principal assumption that in the case of phosphine - stabilized 
 au particles conjugated with dna , the electrophoretic mobility is in first 
 order only 
 determined by the size of the conjugates . for other systems in which charge 
 effects certainly will play a more important role , it might be even impossible 
 to derive effective diameters from electrophoretic mobilities with the here - reported 
 mobility - diameter calibration curves . it also has to be pointed out that the 
 possible application of the here - reported calibration curves is limited to 
 relatively rigid objects similar in nature to au nanoparticles . as these 
 objects were used in first order to obtain the experimental data on which the 
 calibration functions are based , the calibration functions certainly will not 
 describe the diameters of soft objects , such as dna , very well . a likely 
 explanation for the deviation in the effective diameters obtained for the 
 dna - au conjugates with the calibration functions for the gels of different 
 percentage can be seen in the fact that the calibration functions are directly 
 only applicable for au particle - like rigid objects . attaching soft objects as 
 dna to the au particle surface changes their electrophoretic behavior so that 
 the calibration curves can be only applied in a restricted way . we have also evaluated the possibility to obtain effective 
 diameters of au - dna conjugates via ferguson plots , as had already suggested by 
 the group of hamad - schifferli . from figures 1 and 2 , it is 
 evident that the effective diameters obtained from ferguson plots are always 
 significantly smaller than the ones obtained from mobility - diameter calibration 
 curves . it has to be pointed out that both evaluation methods are based on the 
 same set of experimentally obtained mobilities . in a classical ferguson plot , 
 for example for free dna , however , in the case of au and au - dna conjugates , this linearity 
 holds no longer true , in particular for gels of higher percentage . we , therefore , had to 
 restrict our analysis to gels from 1% to 3% although in some cases data for 4% 
 to 6% had also been available . though theories for nonlinear , convex ferguson plots exist 
 [ 40 , 41 ] , we did not try to apply them 
 here . due to the significant deviation from the data obtained with the ferguson 
 plots to the data obtained with mobility - diameter calibration curves and due to 
 the above - mentioned limitations , we conclude that the linear ferguson analysis 
 is less suited to obtain absolute effective diameters . however , relative 
 increases in size due to binding of molecules can be observed with sufficient 
 resolution with ferguson analysis . our data clearly indicate that there is also nonspecific 
 adsorption of dna to the surface of au particles in case the particles are 
 exposed to many dna molecules , see figure 1 . it is important to point out that 
 in figure 1 , the data of au particles that have been exposed to as much dna as 
 possible and that are , therefore , saturated with dna are described . this is 
 different from the case in which the au particles are exposed to only to a few 
 strands of dna as in figure 2 , where no nonspecific adsorption could be 
 observed , as already reported by zanchet et al . . nonspecific adsorption of 
 dna to au particles is significantly lower compared to specific thiol - au bond - mediated 
 attachment and thus can only be observed in case of exposure of the particles 
 to very high dna concentrations . although the absolute numbers derived for effective diameters 
 for au - dna conjugates are afflicted with significant error bars as described 
 above , these data nevertheless contain valuable information about the binding 
 of dna to au particles . any attachment of dna leads to an increase in the effective 
 diameter , dependent on the nature of attachment , the amount of bound dna , and 
 the length of each dna molecule , see figure 1 . with very simple models , we can 
 assume that dna attached to the surface of au particles can adopt two basic 
 types of conformation . in the first case , the 
 confirmation of dna is not effected by the presence of the au particles and it 
 will form a random coil . in the second case , dna has to compete for the binding 
 places at the gold surface and thus , in order to bind as many dna molecules per 
 area as possible , the dna has 
 to be stretched . in figure 1 , the effective diameters for the different models ( randomly coiled dna , fully stretched dna , and dna that is stretched for the first 30 bases and randomly coiled for the 
 rest of the bases ) are plotted versus the dna length for au particles that are 
 saturated with dna . clearly , thiol - gold - bond specific attachment can be 
 distinguished from nonspecific adsorption of dna . similar observations have 
 been reported also before by sandstrm et al . [ 26 , 37 ] . first , the increase in the 
 effective diameter tells that also dna without thiol modification can be 
 adsorbed to the surface of phosphine - stabilized au nanoparticles . second , a 
 comparison with the effective diameters of the theoretical models clearly 
 proves that nonspecifically adsorbed dna does not exist in a stretched 
 configuration perpendicular to the au surface . the data rather indicate that 
 even when the particle surface is saturated with nonspecifically attached dna , 
 only parts of the dna molecules will be randomly coiled , as the experimentally 
 obtained effective diameters are smaller than the diameter of conjugates in 
 which the adsorbed dna is randomly coiled . from this , one can conclude that due 
 to nonspecific au - dna interaction , the adsorbed dna is at least partly wrapped 
 around the surface of the au particles , which is in agreement with other 
 studies . in case of au surfaces 
 saturated with thiol - modified dna , the effective diameters are significantly 
 bigger compared to nonspecifically adsorbed dna , see figure 1 . by comparison 
 with basic models , we conclude in agreement to our previous study that 
 specifically bound dna adopts a stretched configuration so that as many dna 
 molecules as possible can bind to the au surface . due to the spherical geometry , 
 dna longer than around 30 bases only needs to be stretched due to this space 
 limitation within around the first 30 bases , whereas the parts of the dna 
 molecules further away from the au particle are not affected by space 
 limitation and thus can be randomly coiled . these results again show the 
 possibilities and limitations of the here - described method . though it is 
 complicated to derive accurate absolute effective diameters of au - dna 
 conjugates , the binding of dna molecules can be clearly seen as an increase in 
 the effective diameters and a comparison with theoretical models can give 
 indications about the conformation of the attached dna . these types of binding 
 assays via gel electrophoresis are an attractive complementary method compared 
 to other techniques , such as light scattering . presumably a combination of 
 gel electrophoresis , light scattering , and zeta potential measurements of identical samples would give the most accurate analysis about au - dna conjugates . it 
 remains to note that although electrophoresis of free dna is well studied both experimentally 
 and theoretically , the case of au - dna conjugates is more complex because 
 several properties ( total charge , charge density , and elasticity ) are not 
 constant but depend all at the same time on the binding of dna to the au 
 nanoparticles . a theoretical model for gel electrophoresis of such conjugates would be helpful for data 
 analysis . when organic fluorophores are attached to au - dna conjugates 
 at the free end of the dna , which is pointing towards solution , then energy 
 transfer between the fluorophore and the au nanoparticle can be observed . this effect can be , for 
 example , employed for dna sensors . since energy transfer 
 depends on the distance between the organic fluorophore and the au surface [ 35 , 47 ] , certainly the configuration 
 of the bound fluorophore - modified dna is important for this process . in case of 
 nonspecific adsorption of the fluorophore to the au surface , the distance 
 between the fluorophore and the au would be much smaller than for the case in 
 which the dna is linked with its thiol - modified end , see figure 3 . in this study , we have shown that the attachment of cy5 to the free end of thiol - modified dna does not change the 
 effective diameter in the case of au particles saturated with dna , see figure 3 . these results demonstrate that the direct adsorption of cy5 to the au surface 
 is much less probable than the formation of thiol - au bonds and that , therefore , 
 the dye points towards the solution . the number of bound dna molecules per au particle has already 
 been determined with several methods [ 25 , 26 , 48 ] . in comparison to methods in 
 which the number of dna molecules is quantified by the fluorescence of attached 
 fluorophores , the counting of dna via absorption measurements ( as reported in 
 this study ) is not affected by photobleaching and quenching effects . extracting 
 the au - dna conjugates from the gel also helps that no unbound excess dna is 
 present in the solution , as it still might be possible in the case of 
 purification with filter membranes . the results of this study are summarized in 
 figure 4 and are in the same range as the results obtained by other groups [ 25 , 26 , 48 ] though our determined dna 
 densities are rather lower than the ones determined by other groups . this might 
 be due to the fact that the phosphine stabilization is harder to be displaced by dna than citrate stabilization and in particular due to the fact that our incubation was 
 performed at lower nacl concentrations . in our measurements , we 
 could not find any effect of the different curvature between 5  nm and 10  nm 
 gold particles on the density of attached dna molecules . this can be understood 
 as the surface curvature difference between both types of particles is not very 
 high and dna attachment to both types of particles was done under the same 
 buffer conditions . recently , qin and yung have instead demonstrated that the most relevant 
 parameter for the maximum number of attached dna molecules per particle is the 
 salt concentration under which the attachment was performed . high salt concentrations 
 reduce electrostatic repulsion und thus allow for higher dna surface densities . as already reported in earlier publications , gel electrophoresis allows for a separation of au - dna conjugates with 0 , 1 , 2 ,  dna molecules attached per particle [ 9 , 11 ] . in figures 2 and 5 , the 
 effective diameters of such conjugates as determined from their electrophoretic 
 mobilities are presented . the dependence of dna length and au core diameter on 
 the effective diameter is as expected . the longer the dna , the more the 
 effective diameter of au - dna conjugates upon which attachment of another dna molecule to one 
 gold particle is increased ( see figure 2 ) . the more long dna strands are 
 attached per individual gold particle , the fewer the effective diameter of the au - dna 
 conjugated depends on the initial diameter of the au core ( see figure 5 ) . although no simple model for au - dna conjugates is available that could predict 
 the exact mobility in gel electrophoresis , the bands of particles with a 
 defined number of dna strands can be identified with their structure by 
 relative ( qualitative ) comparison and control experiments that include hybridization . so far , we are not aware of another separation technique ( such as hplc ) that 
 can resolve au particles with an individual number of attached dna molecules as 
 it is possible with gel electrophoresis . the concept of separating conjugates 
 of particles with a discrete number of attached molecules by gel 
 electrophoresis could be also be generalized and used besides for au - dna conjugates for other 
 systems . because of their defined 
 composition , we think that such conjugates of particles with a defined number 
 of linked molecules are very interesting model systems and several applications 
 have been already demonstrated [ 50 , 51 ] .
gold - dna conjugates were investigated in detail by a comprehensive gel electrophoresis study based on 1200 gels . 
 a controlled number of single - stranded dna of different length was attached specifically via thiol - au bonds to phosphine - stabilized colloidal gold nanoparticles . 
 alternatively , the surface of the gold particles was saturated with single stranded dna of different length either specifically via thiol - au bonds or by nonspecific adsorption . from the experimentally determined electrophoretic mobilities , estimates for the effective diameters of the gold - dna conjugates were derived by applying two different data treatment approaches . 
 the first method is based on making a calibration curve for the relation between effective diameters and mobilities with gold nanoparticles of known diameter . 
 the second method is based on ferguson analysis which uses gold nanoparticles of known diameter as reference database . 
 our study shows that effective diameters derived from gel electrophoresis measurements are affected with a high error bar as the determined values strongly depend on the method of evaluation , though relative changes in size upon binding of molecules can be detected with high precision . 
 furthermore , in this study , the specific attachment of dna via gold - thiol bonds to au nanoparticles is compared to nonspecific adsorption of dna . 
 also , the maximum number of dna molecules that can be bound per particle was determined .