the construction of specific surface architectures via controlled self - assembly is a key goal in the design of nanoscale molecular electronic devices . in this respect ,
particularly , attractive candidates are guanine ( g ) and its derivatives , which are unique among the dna constituents for their propensity to form quadruplex structures , known to be stabilized through hoogsteen and watson - crick base pairing [ 1 , 2 ] .
moreover , guanine has a low ionization potential due to which it plays a key role in electrical conductivity of dna - based materials .
various research groups have recently reported on the evolution of the  art  of making surface deposited 1-dimensional ( 1d ) structures known as guanosine wires ( g - wires ) [ 312 ] . however , despite the promising experimental results , basic processes responsible for wire formation are still far from being fully understood .
two main steps are fundamental to drive the topic from a laboratory curiosity towards the technologically relevant g - wire engineering : ( a ) achieving control of self - folding and self - stimulated end - to - end fusion of the macromolecular quadruplexes in solution as a function of their molecular composition ( i.e. , base sequence ) and solution conditions , and ( b ) understanding the effect of surface interactions on material deposition from solution phase onto the solid substrate . in this work
, we report on how particular modifications of the base sequence of a g - rich oligonucleotide , which are supposed to affect the folding geometry of the quadruplex , affect its ability to form g - wires in solution phase .
the idea of wire formation is based on the previously established finding that gc  sticky ends  may be used to link quadruplexes into longer 1d aggregates .
a series of oligonucleotide sequences with one or two gc ends and central sequences of different length were designed for this purpose ( see table 1 ) .
the folding topology [ 14 , 15 ] has been previously investigated , and quadruplex formation has been recently studied by mergny et al . .
in these studies , length and nature of propeller loops were studied , but end - to - end fusion of the quadruplexes was not considered . here , we focused on end - to - end fusion of these quadruplex folds .
polyacrilamide gel electrophoresis ( page ) is a conventional tool to differentiate between macromolecular objects of different length . during migration through
an alternative noninvasive method for determining the size of macromolecular objects is dynamic light scattering ( dls ) .
this method was extensively applied to study dna molecules over a wide range of sizes [ 1721 ] .
specifically , it has been used to characterize g - quartet stacking in solutions of single guanosine molecules [ 2226 ] , and for studying formation of g - quadruplexes [ 2730 ] .
protozanova and macgregor    compared the use of dls and page on sequences with long terminal tracks .
these tracks were based on sequences such as d(a15g15 ) and d(a13g15tc ) , which form frayed wires with a g - quadruplex stem and nonguanine portions reaching out as single - stranded arms .
we investigated the formation and dimensions of the supramolecular objects formed in aqueous solution of specially designed g - rich dna sequences ( table 1 ) by combining dls and page measurements .
we studied the effects of temperature , oligonucleotide concentration , method of preparation , and base sequence to explore the basic principles of g - wire formation .
oligonucleotides ( see table 1 ) were ordered from eurogentec ( belgium ) as 40  nm desalted syntheses and reconstituted in water .  
dialysis was performed at a concentration of 100  m dna in the presence of 100  mm nacl buffered with 10  mm napi at ph 6.8 , then diluted in same concentration of buffer or h2o to specified concentrations immediately prior to measurements . where heat treatment is specified , oligonucleotides at 100  m dna in presence of 100  mm nacl , 10  mm napi ( ph 6.8 ) were heated to 93c for ten minutes and left to cool in heating block to room temperature prior to experiment . for dls measurements ,
the oligonucleotides with a 0.4  mm concentration were used . for the concentration dependence studies
gel electrophoresis experiments were performed on 15% native bis / acrylamide gels , utilising 1x tbe running buffer supplemented with 5  mm nabo2 to retain folded architectures .
oligonucleotide samples were prepared to a final concentration of 2  m dna in presence of 100  mm nacl buffered with 10  mm napi at ph 6.8 with 5% sucrose to facilitate sample loading .  
gels were run at 120  v and   4c for a maximum of 2 hours and stained with 1x sybr gold ( invitrogen , paisley , uk ) in 1x tbe buffer .   in order to compare migration rates between different oligonucleotide samples , a generuler ultra low range ( 10200  bps ) dna ladder ( fermentas , york , uk ) was used .
dynamic light scattering experiments ( dls ) were performed using a digital correlator ( alv - laser vertriebgesellschaft ) , a goniometer , and a photomultiplier detector .
the light source was a frequency doubled nd : yag laser with a wavelength of 532  nm .
the incident laser beam was linearly polarized in the direction perpendicular to the scattering plane .
the scattered light of the same polarization was detected at scattering angles 50    130. the capillary containing the sample had an inner diameter of 5  mm and was immersed in an index matching bath with a diameter of 10 cm to minimize stray light from the outer capillary wall .  
we measured the autocorrelation function g2(t ) = i(0)i(t)/i of the average scattered light intensity i .
most of the measurements were performed in a mixed regime , in which the intensity autocorrelation function is related to the field correlation function g1(t ) by the relation 
								 ( 1)g2(t)=1 + 2(1jd)jdg1(t)+jd2g12(t ) , 
							 with jd being the ratio between the intensity of the light that is scattered inelastically and the total scattered intensity .
the field correlation function g1(t ) for systems with a polydisperse size distribution can be expressed by stretch exponential functions 
								 ( 2)g1(t)=iaiexp  ( ti)i , 
							 where ai is the amplitude of the ith relaxation mode and the stretch exponent lies in the range 0  i  1 .
the average relaxation time of the ith relaxation mode is given by 
								 ( 3)i=ii(1i ) , 
							 where (1/i ) is the gamma function .
the parameter i is a measure of the width of the distribution of relaxation times .
very narrow distributions correspond to i ~ 1 , while smaller values of i indicate broader distributions .
the characteristic relaxation times of the observed dynamic modes were obtained by fitting the measured autocorrelation curves g2(t ) to ( 1 ) and ( 2 ) .   according to the polarized scattering ( so called vv scattering ) detected in our experiments ,
the translational diffusion coefficients were calculated as 
								 ( 4)di=1iq2 , 
							 where q is the scattering wave vector given as q = ( 4n/)sin  ( /2 ) with n = 1.33 being the solution refractive index ,  the laser wavelength and  the scattering angle . in most cases ,
several correlation curves were measured for every solution and averaged values of the fitting parameters were taken for further consideration .   from the translational diffusion coefficients ,
the corresponding hydrodynamic radius is calculated as 
								 ( 5)rh = kbt6d , 
							 with kb being the boltzmann constant , t the absolute temperature , and  the solvent viscosity . for dilute solutions of rod - like particles the hydrodynamic theory of tirado and garcia de la torre [ 3436 ] can be applied as long as the ratio of length to diameter p = l / d is in the range 2  p  30 . the translational diffusion coefficient in this theory is given by 
								 ( 6)d = kbt3l(ln  p+ ) , 
							 where  is the end - effect correction term given as  = 0.312 + 0.565/p  0.100/p .
knowing the diameter of the studied rod - like assembly , thus the length of the objects can be estimated .
the sequences were first investigated by page to check for folding of oligonucleotides into higher order architectures .
samples prepared by heat treatment show a lesser degree of macromolecular assembly as compared to dialysed samples for all investigated oligonucleotides ( figure 1 ) .
the band with the highest mobility in each lane corresponds to a bistranded monomeric unit .
the shortest dialysed sequences ( sequences 2 and 3 ) show only few albeit sharp bands pointing to the formation of smaller discrete stable species and a very low degree of macromolecular self - assembly .
the longer sequences 1 , 5 and 6 , on the other hand , indicate possible stepwise assembly into large aggregates .   in all investigated samples , we detected a slow diffusive mode with correlation times in the range of 110  ms ( at  = 90 ) ( figures 2 and 3 ) .
such a mode corresponds to translational motion of large globular aggregates with hydrodynamic radii in the range of micrometers .
they are usually attributed to the presence of loose multichain associates formed due to electrostatic interactions , but their nature is still not quite resolved [ 20 , 37 , 38 ] .
as these aggregates are to our opinion not connected with g - wire formation , they will not be further considered . in all heat
treated samples , only the above mentioned  slow mode  exists , so they will not be further discussed .
solely the  slow mode  is observed also in the dialysed sequence 2 ( figure 3(a ) ) , which is the only sequence containing adenine base . in dialysed sequence 3
, an additional fast diffusive mode can be faintly resolved at large scattering angles (  > 90 ) .
the corresponding diffusion coefficient calculated from ( 4 ) has a value of df = 3.0  0.3  10  m / s ( table 2 ) , which indicates fast translational motion of very small scattering objects , most probably single oligonucleotides . in dialysed sequence 4 ,
the fast mode is more profound and can be clearly resolved ( figure 3(b ) ) .
the dls autocorrelation functions of dialysed sequences containing gggg repeats ( sequences 1 , 5 , and 6 ) all show two relaxation modes .
the angular dependence of the inverse relaxation time of the fast mode ( figure 4 ) reveals quadratic dispersion as given by ( 4 ) .
the resultant diffusion coefficients df obtained for solution concentration of 0.4  mm are listed in table 2 .
the obtained values suggest that the fast mode is most probably associated with translational motion of oligonucleotides assembled into g - quadruplex structures .  
the dialysed sequence 4 at 0.4  mm dna was also used to investigate the temperature dependence of the fast diffusive mode ( figure 5 ) .
a relative amplitude of the fast mode decreased with increasing temperature and for t > 338  k the fast mode could not be resolved anymore .
to reveal possible temperature - induced structural changes of the scattering objects , the values of diffusion coefficient df obtained at different temperatures were divided by temperature t and multiplied by the corresponding solvent viscosity (t ) .
the resulting values of df(t)/t as a function of temperature are shown in figure 5 .
one can notice that they remain constant throughout the investigated temperature range , which indicates that no structural modification of the scattering objects ( quadruplexes ) takes place .
the effect of oligonucleotide concentration on the value of df was investigated for dialyzed sequence 1 ( figure 6 ) .
although it appears that the values decrease with increasing concentration , no precise conclusion can be drawn due to the large uncertainty of the measured data points . at low solution concentrations and short relaxation times
however , for dna concentrations below 1  mm , which was the case in all our measurements , the effect of electrostatic interactions on solution dynamics is usually negligible and so the solution can be considered as infinitely dilute .
both , page and dls analysis , reveal that the method of sample preparation is essential for the level of self - assembly in solution .
we observe formation of slower migrating species for all oligonucleotides in page for the dialysis treated samples .
sequences 1 , 2 , 5 , and 6 appear to form larger assemblies , whilst sequences 3 and 4 do not .
the most striking results are for sequences 2 and 6 , where one or two species of lower molecular weight were formed in the annealing treatment versus numerous larger species through dialysis .   
page comparison between sequences 2 and 3 shows that there are sequence effects in the kinetics of formation for the same topology .
when comparing dialysis , a band appearing at nominal 15  bp in sequence 3 appears only very faintly in sequence 2 , while a faster , and a slower , migrating bands appear quite distinctively in both .
the effect of  sticky ends  is also shown when comparing sequences 1 and 6 . while between nominal 10 and 35  bp they have the same number of bands appearing in approximately the same positions , their intensities vary substantially . for these particular sequences ,
the difference in the annealing treatment is greater , with sequence 6 showing a very strong fast migrating band at nominal 16  bp . in contrast ,
the fastest migrating band for seq1 is at nominal 12  bp . in general , and as expected , it is apparent that the greater the oligonucleotide length the longer the species formed .
indeed , it is apparent for the longest oligonucleotide sequence ( sequence 5 ) that the macromolecular dna objects   break into smaller units in a less discrete manner than for the other sequences .
the smear for low migrating dna in sequence 5 may thus be due to steric hindrance by the pore size of the gel .   for the shortest of the dialysed sequences , sequences 2 and 3 ,
the absence of any measurable fast dls mode for the former and the observation of a faint extremely fast mode for the latter , can be explained only by the presence of very small scattering objects , most probably single oligonucleotide molecules .
this finding is not consistent with page results ( figure 1 ) , which reveal additional slower diffusing species resulting in sharp bands , probably signifying multimers .
similar discrete bands are seen also in the picture of page for dialysed sequence 4 . for this sequence ,
the diffusion coefficient of the fast dls mode gives quadruplex length of 8.8  0.8  nm ( table 2 ) , which is considerably larger than the length of a single oligonucleotide strand ( about 4.8  nm ) .
the two dialysed intermediate - length sequences ( sequences 1 and 6 ) both exhibit the same page band attributed to fast migrating monomers and a strong band at about 35  bps ( accordingly to the reference duplex dna ladder ) .
the main difference between the two oligonucleotides is in the formation of two intermediate bands for sequence 6 , while sequence 1 forms no intermediate species .
interestingly , the two strong bands ( at 35  bps ) very well agree with the quadruplex length l estimated from the dls measurements , which is 5.0  0.4  nm for sequence 6 and 6.1  0.5 nm for sequence 1 , respectively .
the smaller apparent length of sequence 6 can be explained by the presence of the intermediate species contributing to the scattering . the diffusion coefficient measured for sequence 1 ( df = 1.06  0.037 ) is in very good agreement with the values obtained for similar folded structures by hydrodynamic modelling .
in page , the majority of the material is so slowly migrating through the gel , that just a broad smearing is observed .
dls measurements , on the other hand , reveal the presence of supramolecular assemblies with the length of 11.0  0.2  nm , which is only slightly larger than the length of a single strand .
in contrast to page , dls also reveals a relatively narrow distribution of aggregate lengths .
this is seen from the dls stretch exponent factor for the fast mode , which is in the range 0.9 < f < 1 , thus excluding a broad distribution of the dimensions of the scattering objects . also for other sequences ,
the origin of the differences between the page and the dls results is not clear . on the basis of the page results , sequences 1 , 5 , and 6
are all supposed to form some long wire - like assemblies , but dls measurements do not support this expectations .
accordingly to the dls results , the highest level of self - assembly is expected for sequence 4 , which exhibits the largest length of the scattering objects with respect to the length of the single strand .
one possible reason for the discrepancies might be quite different solution concentrations used for the two experiments .
page is usually performed with concentrations c  ~  10  m , while dls gives reasonable signals . yet for c > 100  m , this is not consistent with what we intuitively know , that is , higher concentrations tend to favour multimer formation .
another aspect arises from the slow dls mode , which signifies that in addition to wire - like assemblies there are also some other aggregate types present in solution .
these aggregates , most probably loose multipolyion associates , might correspond to the slow diffusing objects observed in page .   
dls experiments bring also information on temperature and concentration dependence of the self - assembly .
the temperature dependence ( figure 5 ) shows that up to t = 65c the length of the self - assembled objects remains constant .
nevertheless , the amplitude of the fast dls mode strongly decreases by increasing temperature , while the overall scattering intensity is only slightly reduced .
this signifies that the slow mode , which mainly contributes to the scattering intensity , is not much affected by heating .
but relatively to it , the scattering intensity related to the fast mode becomes more and more weak .
this can be explained by temperature - driven dissociation of the self - assembled structures of well - defined size into much smaller single oligonucleotides , which are practically invisible by dls .
dependence of the fast dls mode on the concentration of the solution ( figure 6 ) also supports the idea of formation of the self - assembled structures with well - defined length , which are not affected by modifications of the solution concentration . on the contrary to wire - like assemblies formed from single guanosine molecules ( gmp )
, it seems that formation of supramolecular assemblies of g - rich oligonucleotides , does not exhibit any critical solution concentration , at which the assembling would become profound .
a series of g - rich oligonucleotides was studied by page and dls to investigate the formation and dimensions of g - quadruplexes .
both methods show that thermal annealing induces much less macromolecular self - assembly than the dialysis method .
this demonstrates that not only the base sequence , but also the folding kinetics play an important role in the self - assembly process . on one hand , this makes the phenomenon very complex , but on the other hand it provides a possibility for fine tuning of the assembling features via external stimuli .
further studies are needed to find the source of the differences and how they can be modulated .  
page and dls show the best agreement on quadruplex dimensions for sequences of intermediate length ( sequences 1 , 4 and 6 ) .
the last band of sequence 4 coincides with the dls signal arising from aggregates of a 9  nm length .
the two similar sequences 1 and 6 give also aggregates of similar length 56  nm and these agree with a strong page band observed for both sequences .  
for the shortest sequences 2 and 3 , page suggest the formation of multimers not detected by dls .
the only dls signal comes from very fast diffusing objects with effective dimensions below 1  nm pointing to single oligonucleotides . for the largest sequence , on the other hand , page suggests very long aggregates giving a broad smeared band at the beginning of the lane . in dls instead , a well defined fast mode is attributed to a species with the length of about 11  nm .
because we are able to assess intermediate lengths , we are currently investigating the mechanism of self - assembly of these wires by combining both methods .
thus , the combination provides valuable information on the g - quadruplex formation towards control of its length .
 the formation and dimensions of g - wires by different short g - rich dna sequences in solution were investigated by dynamic light scattering ( dls ) and polyacrilamide gel electrophoresis ( page ) . to explore the basic principles of wire formation 
 , we studied the effects of base sequence , method of preparation , temperature , and oligonucleotide concentration . 
 both dls and page show that thermal annealing induces much less macromolecular self - assembly than dialysis . 
 the degree of assembly and consequently length of g - wires ( 5 - 6  nm ) are well resolved by both methods for dna sequences with intermediate length , while some discrepancies appear for the shortest and longest sequences . 
 as expected , the longest dna sequence gives the longest macromolecular aggregates with a length of about 11  nm as estimated by dls . 
 the quadruplex topologies show no concentration dependence in the investigated dna concentration range ( 0.1  mm0.4  mm ) and no structural change upon heating . 
1. Introduction
2. Experimental
3. Results
4. Discussion
5. Conclusions