hydrotropic solubilization , the technique whereby the addition of one solute significantly promotes the solubility of another , has been widely applied to this end [ 35 ] . yet , the nature and mechanisms of hydrotropic solubilization remain elusive and a topic of debate , especially with regard to the structural diversity of hydrotropic agents ( has ) and the apparent drug - hydrotrope selectivity [ 79 ] .
this situation , in combination with the compelling application needs , demands more structure - specific understanding of the hydrotropic effect .
in fact , dating back to almost the beginning of the discovery of hydrotropy , neuberg   already noted that the hydrotropic agents consisted generally of an anionic ( hydrophilic ) group and a hydrophobic aromatic ring or ring system , where the type of anion or metal ion appeared to have a minor effect .
the aromatic ring , on the other hand , appeared to be critical to the hydrotropic effect .
molecular orbital calculation later suggested that the aromatic ring or ring system may facilitate a -donor -acceptor interaction [ 10 , 11 ] , a potential mechanism once widely believed to account for the hydrotropic effect of nicotinamide and other heteroaromatic hydrotropic agents .
.   also showed that aromatic ring systems may promote the stacking of molecules and , as a result , enhanced drug aqueous solubility more effectively than the aliphatic amides ( e.g. , urea and its derivatives ) .
these evidences were in support of the classical molecular complexation mechanism , whereby the aromaticity of hydrotropic agents apparently played a critical role . nevertheless , experimental findings inconsistent with this potential mechanism were also reported .
for example , nicotinamide was shown to solubilize drugs in the absence of a -donor -acceptor interaction .
it was also found that the hydrophobicity , rather than the aromaticity , of hydrotropic agents is the determinant of their solubilization ability [ 7 , 14 , 15 ] .
clearly , these seemingly contradictory observations are essential in clarifying the mechanism of hydrotropy and therefore warrant further investigation . in the light of this situation
, we initiated a series of studies using molecular dynamics ( md ) simulation , a technique with an atomic - level resolution , to probe hydrotropic solubilization . in an earlier study
, we successfully modeled the solubilization of a poorly water - soluble anti - hiv compound , pg-300995 , by the hydrotropic agent nicotinamide .
the study clearly showed that the solubilization was driven by the restoration of normal water structure that was disrupted by the dispersion of solutes .
this process was accompanied by significant molecular aggregation of nicotinamide and the drug in an aqueous solution . the -donor -acceptor interaction and the so - induced molecular complexation
were not the determinant of the solubilization . in a second study   on the solubilization of riboflavin in the presence of caffeine , the parallel stacking of the solutes
was found . despite that the solute clusters present different appearances for these two systems , the driving forces are the same : the restoration of normal water structure . with these interesting findings
, the current study attempted to further expand the md simulation to aliphatic amides , another group of hydrotropic agents .
the purposes of this study are to elucidate the hydrotropic solubilization mechanism of aliphatic amides and , in combination with our earlier reports , to provide a more comprehensive understanding to the mechanism of hydrotropy .
the study employed model systems consisting of nifedipine ( nf ) , a poorlysoluble antihypertension drug , solubilized by a series of urea analogues in an aqueous environment .
hydrotropic solubilization of nf was previously reported   in the presence of urea ( ur ) , methylurea ( mu ) , ethylurea ( eu ) , and butylurea ( bu ) , respectively , with the solubilization effect ranked as bu > eu > mu > ur ( see figure 1 for chemical structures of nf and butylurea ) . a similar progressive solubilization effect correlated with increasing hydrophobicity
therefore , studying such model systems may also help elucidate the role of hydrophobicity in hydrotropic solubilization .
the solubility of nf ( mw 346.3 ) in water ( ph 7 ) is approximately 5 - 6  g / ml , or approximately 0.17  10  m. it was reported that the solubility of nf had approximately 3- , 15- , 65- , and 65-folds increase in the presence of ur ( 4  m ) , mu ( 4  m ) , eu ( 4  m ) , and bu ( 1.2  m ) , respectively ( estimated from figure  6 of ) .
these results translate to nf solubilities below 0.2  :  1000 ( nf  :  water , molar ratio ) in the presence of these has , whose concentrations are approximately 72  :  1000 ( ha  :  water ) for ur , mu , and eu ( 4  m ) , or 22  :  1000 for bu ( 1.2  m ) . given these experimental results and bearing in mind the limited computation resource ,
four primary models were constructed containing ( 1 ) one nf and 72  ur in 1000 water ( nf + ur + water system ) ( 2 ) one nf and 72  mu in 1000 water ( nf + mu + water system ) ( 3 ) one nf and 72  eu in 1000 water ( nf + eu + water system ) and ( 4 ) one nf and 37  bu in 1000 water ( nf + bu + water system ) . as such
, the concentrations for has were 4  m for ur , mu , and eu and 2  m for bu ( all in solution state based on experimental solubility data ) .
the bu concentration in the nf + bu + water system was adjusted to approximately 2  m from 1.2  m in the experimental system .
the nf was supersaturated in these models but was accepted as this study was designed to elucidate the qualitative mechanism rather than to quantify the solubility . to study behaviors of
has in aqueous solutions in the absence of nf , four additional models were built : ( 1 ) 72  ur in 1000 water ( ur + water system ) ( 2 ) 72  mu in 1000 water ( mu + water system ) ( 3 ) 72  eu in 1000 water ( eu + water system ) and ( 4 ) 37  bu in 1000 water ( bu + water system ) .
furthermore , several additional model systems were constructed in the same manner to assist the analysis of energetic and dynamic changes upon hydrotropic solubilization .
solutes were randomly dispersed in the solvent ( 1000 water molecules ) and all molecules were treated unionized in accordance to the experimental condition of ph 7 .
model systems were set up using the amorphous cell module of the material studio ( ms ) 4.3 software package .
cubic simulation boxes with periodic boundary conditions in all directions were constructed with a density of 1  g / cm , followed by the geometric optimization of molecular configurations utilizing compass force field .
compass is a class ii ab initio force field designed for use with organic molecules and optimized for the simulation of condensed phases ( see [ 1921 ] for the parameterization and validation of this force field ) .
the md simulations were then carried out under npt conditions in the forcite module of ms , with pressure and temperature held at 100  kpa and 298  k , respectively , by employing nose thermostat and berendsen barostat .
the compass force field was used to calculate both van der waals and electrostatic interactions .
charge groups were applied with cutoff distances of 14   for both interactions ( among the eight models given above , the smallest simulation box size after md runs is > 33   . a box containing 1000 water molecules
the time step was 1  fs , and the simulation time was at least 3  ns . for most models
, simulations were run up to 4  ns , and successful equilibration was confirmed . for further details of the simulation method ,
readers are referred to the work of sellner et al .   and the references therein .
data analysis was performed using the forcite analysis function . for calculating radial distribution functions ( rdfs ) ,
the amide carbon atom was selected to represent ha molecules as the amide group is shared by all has .
the oxygen atom was chosen for water molecules as this is the only heavy atom in water . the calculation cutoff distance and step size
the rdfs at the starting time were calculated by averaging over the first 100  ps of the simulations and denoted as t = 0  ns in the text , while those of the ending time were averaged over the last 1  ns of the runs and denoted as t = 3  ns . for hydrogen bond calculations ,
a cutoff distance of 2.5   was applied . the total number and the average length of hbs in the systems
were averaged over the first five ( 5  ps ) and the last 20 ( 20  ps ) frames with a step size of 1  ps .
since the initial states of the systems equilibrated rapidly , the total number of hbs was constantly increasing , which led to large variations in the averaged values even in the first 20  ps .
thus , only the first 5  ps were used to calculate the initial states . in calculating mean square displacements ,
molecular centroids were defined , and the calculation was conducted with a step size of 1  ps and a calculation length of 500  ps over the last 1  ns period .
the representativeness of these snapshots was checked by examining the last 0.5  ns of each running trajectory .
both nf + ur + water and ur + water systems in figure 2 appeared to be homogeneous solutions after the 3  ns simulation , with little structural changes perceived visually .
clearly , these two systems were still one - phase systems after the npt runs .
the nf + mu + water and mu + water systems , on the other hand , demonstrated significant aggregation of solute molecules after 3  ns as shown in figures 3(a)-3(b ) and figure 3(e ) , respectively .
furthermore , in comparing frames captured at 3 ( figures 3(a ) , 3(b ) , and 3(e ) ) and 4  ns ( figures 3(c ) , 3(d ) , and 3(f ) ) from the same perspectives , drastic changes in the shape of aggregates were observed for both nf + mu + water and mu + water systems over the period of 1  ns , indicating that the aggregates were rather fluidic . while clearly in the aggregation mode , the translational movement of mu molecules swept across the whole simulation box in 1  ns , showing clearly a single - phase liquid system .
similar to the mu systems , significant aggregation of solutes was also observed in the nf + eu + water ( figures 4(a)-4(b ) ) and the nf + bu + water ( figures 4(c)-4(d ) ) .
the snapshots of the eu + water and bu + water systems were omitted due to their resemblance to figure 4 .
when comparing frames of the eu and bu systems at 3 ( figures 4(a ) and 4(c ) ) and 4  ns ( figures 4(b ) and 4(d ) ) , morphological changes of aggregates were also evident , albeit that solutes in these systems appeared to be in a more clearly defined  aggregation  mode constantly in 1  ns , in contrast to the ur and mu systems .
consequently , for the bu and eu systems , it is difficult to tell by visual inspection in 1  ns period whether the aggregates are still in a single phase with aqueous medium or phase - separated . finally , in all models simulated , the aggregation was found nonstoichiometric , and little parallel stacking was perceived among the solute molecules .
the observation above supplies an interesting insight to the potential of phase separation . in the case of mu systems in particular , snapshots at 3 or 4  ns alone all show clearly the aggregates .
it is difficult to tell just by the snapshots at a certain time point whether the systems are phase - separated . combining together the snapshots of multiple time points , that is , 3 and 4  ns ,
however , it is clear that the aggregates are quite volatile and are actively mixing with the solvent medium , indicating that these aggregates are still miscible with the solvent . in other words ,
the ha molecules appear as aggregates when the observation time is short , that is , in fs , while they are miscible solutions when observed over a much longer time frame .
this hints that , by a conventional experimental observation , whose time frame is typically 1100  s , these aggregates could be perceived visually as miscible with the solvent media ( as one - phase solutions ) . therefore , it seems that the potential phase separation issue may be attributed to the drastically different observation times between simulation studies and conventional experimental observations .
note that although the same conclusion is not as readily drawn for the eu and bu systems , the short simulation time ( between 3 and 4  ns ) relative to slower dynamics of eu and bu is likely to account for this vagueness .
we further examined structural evolutions of the simulated solutions by inspecting radial distribution functions ( rdfs ) within and between each type of molecules .  
figure 5 depicts rdfs between nf and four hydrotropic agents as averaged over the periods of 0100  ps ( t = 0 ) and 2 - 3  ns ( t = 3  ns ) , respectively .
the nf - ur rdfs in figure 5(a ) show that the peak shifted to a shorter distance and was slightly strengthened after the simulation , indicating a weak but positive aggregation of the nf and ur molecules .
this effect was too minor to be visually perceived from the snapshots in figure 2 .
additionally , figures 5(b)5(d ) record clear and significant peak strengthening towards closer distances for the remaining three hydrotropic solutions after 3  ns . furthermore , the nf - water rdfs for the four hydrotropic solutions are given in figure 6 .
except for the nf + ur + water system ( figure 5(a ) ) , which exhibits a fairly minor change , the remaining three ( figures 5(b)5(d ) ) all show significant declines in water concentration in the neighborhood of the nf molecule after 3  ns , suggesting that the aggregation reduces the exposure of nf to the solvent .
this is consistent with the visual observations presented earlier and confirms that significant aggregations took place in these solutions .
the comparison between the structures of the hydrotropic solutions with and without nf was conducted via the ha - ha and ha - h2o rdfs as shown in figures 7 and 8 , respectively .
again , the ur - ur ( figure 7(a ) ) and ur - h2o ( figure 8(a ) ) rdfs in both nf + ur + water and ur + water systems exhibited little changes after the simulations , while substantial increases in ha concentrations and decreases in water concentration near the ha molecules were revealed for the remaining six systems ( figures 7(b)7(d ) and 8(b)8(d ) ) .
more importantly , the ha - ha and the ha - h2o rdfs of the four hydrotropic solutions ( with nf ) resemble closely their respective counterparts of the four ha solutions ( without nf ) , suggesting that structurally the systems in the presence of nf correlate closely with their counterparts in the absence of nf .
this advocates that the self - aggregation of has may be a prerequisite in enabling the incorporation of the drug into the ha aggregates .
interestingly , earlier reports [ 2325 ] indicated that hydrotropic agents often tend to self - aggregate in aqueous solutions , which is consistent with the results above . 

figure 9 compares various rdfs across the four hydrotropic solutions ( with nf ) at t = 3  ns .
it can be seen from figures 9(a)9(c ) that the aggregation in these systems can be approximately ranked as bu > eu > mu > ur , indicating that the growing hydrophobicity of the has enhances their aggregation and reduces the water concentration in the neighborhood of the nf and ha molecule .
this result is expected and can be readily accounted for by our current understanding on hydrophobic interactions . from the methodology perspective , it supplies a solid evidence validating the simulation approach adopted .
it is worth further noting that the urea derivatives in the study vividly show a gradual transition from a true homogeneous solution to a state with solutes clustered together while it has yet been phase - separated .
typically , solutions at concentrations lower than the compound solubility are in homogeneous state , while those at concentrations higher than the solubility are often phase - separated , either in experimental or in simulated studies .
while their aggregation protects hydrophobic solutes from water , and therefore , the degree of aggregation correlates with the solubilization effect of these has ( i.e. , bu > eu > mu > ur ) , refraining from phase - separation is crucial to maintain a single - phase liquid state .
a second note is that the ha - h2o rdfs in figure 9(d ) show that the declines in water concentration near ha molecules are ranked as eu > bu > mu > ur , with the maximum decline claimed by eu instead of bu .
it was suspected that as the hydrophobic alkyl chains grow and the molecule elongates , the amide carbon atom sitting at the hydrophilic end of the molecule may become less representative for the whole ha in the rdf calculation .
this was proved by the eu - h2o and bu - h2o rdfs recalculated using alternative carbons c2 and c3 ( see figure 1 for the numbering of carbons of bu .
eu used the same numbering sequence ) of eu and bu , which are illustrated in figure 10 .
it is evident that water concentration near the alkyl chain ( represented by c2 and c3 ) of bu is lower than that of eu .
hence , the results in general are consistent with those above and support that the degree of aggregation correlates positively with the growing hydrophobicity of has .
the above finding hints that the distribution of water may be heterogeneous along the elongated ha molecules . to demonstrate this
, time evolutions of rdfs between water and various carbons along bu are compared in figure 11 .
it is clearly seen that while the water concentration around the amide carbon ( c1 ) still tops the rest after 3  ns , those of c5 and c2 switch their places upon simulations with c5 becoming the one with least surrounding water .
this evidence shows that during aggregation , bu molecules reorient themselves with their hydrophobic alkyl chains shying away from water , an effect similar to the micelle formation of amphiphilic agents in water .
the difference is , though , that no apparent self - assembling of bu molecules is observed as witnessed in figure 4 .
it , therefore , suggests that aside from micelle formation the solute aggregation may be another effect driven also by hydrophobic interactions and functioning similarly to micelles in promoting the solubility of hydrophobic compounds .
a similar comparison ( data not shown ) between the water concentrations surrounding c2 and c3 of eu indicates that the water concentration around c3 is still slightly higher than that of c2 .
this can be attributed to the insufficient length of the alkyl chain of eu , whose hydrophobicity is not strong enough to drive the alkyl chain away from water .
overall , hydrophobic interactions appear to account for the aggregation of urea derivatives . to confirm the role of hydrophobic interactions , we analyzed changes in hydrogen bonds ( hbs ) in these systems upon simulations .
a few observations are in order ( 1 ) all eight systems are dominated by h2o - h2o hbs ( approximately 8293% of the total hbs ) both before and after simulations , followed by ha - h2o ( approximately 417% of the total hbs ) and ha - ha hbs ( approximately 0.15% of the total hbs ) .
the hbs sponsored by nf , that is , nf - ha and nf - h2o hbs , are trivial ( < 0.3% of the total hbs ) ; ( 2 ) upon simulations , the numbers of h2o - h2o and ha - ha hbs increase in all systems , while those of ha - h2o hbs decrease except in the ur + water system ( see figure 12 ) .
again , changes in nf - ha and nf - h2o hbs are negligible , despite that nf - ha hbs consistently present slight increases as a result of the inclusion of nf in aggregations . the total numbers of hbs , however , exhibit appreciable increases in conjunction with the declines in hb bond length in all systems ( see table 1 ) , indicating that hb interactions in these systems are strengthened upon simulations .
overall , these changes , that is , gains in h2o - h2o and ha - ha hbs in exchange of losses in ha - h2o hbs , are in agreement with the aggregations observed , whereby the partitioning of solutes and water should promote hb interactions between water molecules as well as between solute molecules but demote hbs across water and solutes .
these exchanges result in significant net gains in the number and strength of hbs , which are obviously energetically favorable ; ( 3 ) from the water structure perspective , it is interesting to compare the hbs in pure water with those in the eight solution systems in study . to this end ,
a system containing 1000 water molecules only ( the water system ) was constructed and subjected to a 3  ns npt run in the same manner as described in section 2 .
table 1 lists the number of h2o - h2o hbs of the water system after simulation , which is appreciably higher than that of the eight solution systems in study . additionally , the average hb bond length in the water system is the shortest compared to that of the eight systems , indicating that h2o - h2o hbs are stronger than other types of hbs in these solutions .
the evidences demonstrate that homogeneous dispersion of urea derivatives in water disrupts the water structure and reduces substantially the h2o - h2o hbs , while aggregations of solutes promote the energetically more favorable h2o - h2o hbs in these systems via a partial restoration of the normal water structure .
on this basis , we may attribute the restoration of the water structure , and thereby the aggregation of solutes , to hydrophobic interactions ; ( 4 ) further analysis across various types of hbs shows ( see figure 12 ) that ha - h2o hbs score the largest changes ( declines ) upon simulations in all cases , while h2o - h2o hbs present slightly lower changes ( increases ) .
the changes in ha - h2o and h2o - h2o hbs are close in magnitude in some cases ( e.g. , the nf + mu + water and nf + eu + water systems ) , but opposite in direction .
the ha - ha hbs , on the other hand , show some smaller but solid gains except in the two ur - containing systems ( i.e. , the ur + water and nf + ur + water systems ) .
this result may suggest that self - interactions between urea derivatives may also play a role to the aggregation . especially in cases where the declines in ha - h2o hbs are in magnitude comparable to the increases of the h2o - h2o hbs
even if hydrophobic interactions alone may induce ha aggregations , which set the stage for ha self - interactions , they do not guarantee enhanced ha - ha hbs between ha molecules .
thus , the current results seem to suggest that the aggregations of urea derivatives can be accounted for by the coordinated effects of hydrophobic interactions and the self - interactions between hydrotropic agents . the mean square displacements ( msds ) of the ha molecules
were calculated for the eight systems in study in the last 1  ns of the runs and are plotted in figure 13 .
it is evident that the slopes of msd - time curves are ranked as ur > mu > eu > bu . no plateau is observed for any system . the diffusion coefficients ( d ) derived from slopes of the curves via d = slope/6 are given in table 2 , which indicates clearly that the dynamics of the aggregates slow progressively as the ha hydrophobicity grows .
the diffusion coefficients range from 0.31 to 2.1 ( 10  m / s ) , falling in the typical range of diffusion coefficients in liquids ( the bulk data of diffusion coefficients in liquids appear in the magnitude of 10 10  m / s ) [ 2628 ] .
this indicates that the aggregates in these systems are still in liquid state , a result consistent with the active dynamics discussed earlier . to differentiate these liquid states from pure amorphous phases of the has ,
diffusion coefficients of has in amorphous state were estimated under the same temperature and pressure .
to do so , four amorphous systems containing 300  ur , mu , eu , and bu molecules , respectively , were constructed and subsequently subjected to npt runs of 3  ns .
the smallest box size ( 300  urs ) of the four systems is 31   .
the diffusion coefficients were then calculated in the same manner as shown above and are listed in table 2 .
it is readily seen that the diffusion coefficients of has in amorphous state are about two orders of magnitude lower than the ones in aggregates , indicating that the aggregates are much more active dynamically than the amorphous phase of the respective has .
this evidence is in favor of the case that the aggregates are not amorphous / liquid phases of has separated from water medium .
more likely , as suggested earlier , the active dynamics of ha molecules may keep the aggregates from being phase - separated .
it should be noted that the presence of the nf molecule seems to reduce consistently slopes of msd - time curves for all four has ( see figure 13 and table 2 ) , signifying that the addition of nf hinders the mobility of has in the aggregates .
this is certainly different from the nicotinamide hydrotropic solution reported earlier , where virtually no impact on the mobility of the hydrotropic agent ( nicotinamide ) was found following the addition of the drug .
it is somewhat surprising that one nf molecule can effectively slow the mobility of much large numbers of ha molecules , which apparently can not be accounted for by just a handful of hydrogen bonds formed between the nf and ha molecules ( see table 1 ) .
we have not found an explanation for this observation . to verify our simulation results , diffusion coefficients of has in dilute aqueous solutions
were estimated by the wilke and chang method [ 26 , 27 ] , and the results are provided in table 2 .
the estimated diffusion coefficients are of the same order of magnitude but about 13-folds higher than the values obtained from the simulations .
since the wilke and chang method only applies to dilute solutions , where solute - solute interactions are negligible , it is understandable that diffusion coefficients estimated by this method are somewhat higher than those in concentrated solutions .
furthermore , a clear trend is observed in table 2 that the discrepancy between these two groups of diffusion coefficients grows larger as ur < mu < eu < bu , a trend correlating positively to the increasing degree of aggregation of the has .
thus , it seems reasonable to attribute the discrepancy in diffusion coefficient from these two sources to the impediment of molecular diffusion by the increasing degree of ha aggregation .
overall , the simulated diffusion coefficients in solutions appear reasonable relative to the empirically estimated values . to explore energy changes upon aggregation
, another system was built containing one nf in 1000 water ( pg + water system ) and was subjected to a 3  ns npt run under the same conditions as described above .
the average total energy of this system during the last 1  ns was normalized to per mole of water and is listed in table 3 , together with that of eight systems in study and of the water system ( 1000 water molecules ) . applying the formula proposed by sellner et al . , the energy gain of the hydrotropic solubilization , that is , of incorporating the nf into the ha aggregates , can be estimated as esolubilization = ( enf+ha+water  eha+water)(enf+water  ewater ) .
the two brackets on the right side of the equation represent sequentially energy changes upon the addition of nf to the ha + water and to the water systems .
the difference between these two energy changes , esolubilization , is negative when the solubility of nf in the ha + water systems is higher than that in the water system , provided the changes in entropy and volume upon adding one nf are comparable between the two systems .
table 3 shows that esolubilization for various has are all negative , that is , 0.500 ( ua ) , 0.517 ( mu ) , 0.596 ( eu ) , and 0.607 ( bu )  kj / mol water , indicating that hydrotropic solubilization is energetically favored in all four ha solutions .
the magnitudes of esolubilization are ranked as bu > eu > mu > ua , corresponding to the solubilization effects measured experimentally on these systems ( i.e. , approximately 3- , 15- , 65- , and 65-folds increase in nf solubility in ur [ 4  m ] , mu [ 4  m ] , eu [ 4  m ] , and bu [ 1.2  m ] solutions ) .
note that the bu concentration was raised to 2  m in our simulations , and thereby a higher degree of solubilization in the bu solution was expected , which seemed to be reflected in the highest esolubilization value of the bu system .
nevertheless , given the large standard deviations of these average total system energies as listed in table 3 , the differences in esolubilization between various ha systems are by no means statistically significant .
the large standard deviation is an inherent weakness of this calculation procedure , where relatively large values ( average total system energies ) are subtracted leaving the results ( differences ) submerged in the background noises ( standard deviations ) . to conduct an accurate calculation ,
significantly longer simulations are required to reduce noises ( e.g. ,   employed simulations of 30  ns ) .
we extended the simulations to 4  ns and found that the improvements were minimal .
restricted by computation resources and considering also that the goal of this study is more of mechanistic elucidation than of quantitative energy calculation , further extension of simulations was not pursued . setting aside the specific ranking , the negative esolubilization values indeed show that the hydrotropic solubilization of nf is energetically favored in all urea derivative solutions .
to summarize , the study finds nonstoichiometric molecular aggregation of urea derivatives in their aqueous solutions .
further analysis shows that partial restoration of normal water structure drives the nonstoichiometric molecular aggregation , despite that self - interactions between ha molecules have also contributed to this process .
furthermore , energetic data support that the hydrotropic solubilization of nf is favored in the presence of urea derivatives in aqueous solutions .
it is particularly interesting to note that urea derivatives demonstrate a gradual transition from a homogeneous solution to a highly aggregated state .
these transition states feature active solute dynamic movements , which give rise to a single - phase liquid state in spite of a varying degree of solute aggregation .
we speculate that this characteristic could be the key for certain agents to display hydrotropic solubilization effects in aqueous solutions . in the spirit of the discussion above
, we may reflect on the size of aggregates and the aggregation number . historically , the aggregation ( or complexation ) number , the number of molecules involved in one aggregate , was a critical parameter . based upon the molecular complexation hypothesis
[ 13 , 29 , 30 ] , or alternatively , upon the molecular aggregation hypothesis [ 6 , 31 ] , this number was often estimated by fitting the experimental solubility data to appropriate kinetic functions and was used in return to support the respective hypothesis . in either way , the value obtained was low , with the maximum reported value of 4.37 .
this is obviously inconsistent with our observations in simulation studies , which appeared far beyond a handful . yet , as shown in the case of mu , the aggregates are completely miscible with solvent media if given sufficient observation time .
that is , despite that the ha molecules are in aggregated mode within a short period of time , for example , 1  ps , the active translational movements render the aggregates very volatile and of very short shelf lives .
therefore , with one aggregate constantly re - dispersed / restructured in the solvent medium , the number of solute molecules incorporated in such an  aggregate  is not set , and thereby the aggregation number or the size of the aggregate under the classical view of an  aggregate  may not be relevant , unless the observation time is shorter than the life span of these dynamic  aggregates . 
this study finds a varying level of nonstoichiometric molecular aggregation of urea derivatives in their aqueous solutions .
structural and dynamic evidences show that the degree of aggregation correlates positively with the hydrophobicity of urea derivatives .
analysis of hb changes upon simulations provides insights that strengthening hb interactions as a result of the restoration of normal water structure facilitates the aggregation and solubilization of the model drug .
this study , in combination with our earlier reports [ 16 , 17 ] , demonstrates that the restoration of normal water structure is the ultimate driving force for hydrotropic solubilization , despite that solute clusters may take different formats .
this mechanism is in accordance with hydrophobic interactions , the underlying driving force for the micelle formation of amphiphilic solutes .
hence , maybe it is fair to say that solutes may cluster , as a result of hydrophobic interactions , into various states including aggregates , parallel stacks , and micelles .
all these clusters may have the potential to incorporate hydrophobic solutes and consequently increase their solubility in water . hence , despite that hydrotropic agents do not undergo self - assembly as surfactants in solutions , hydrophobicity still plays a fundamental role in inducing hydrophobic interactions and , therefore , is critical to the solubilization effects .
aromatic ring structures , on the other hand , induce the same effect of hydrophobic interactions , as shown in our earlier reports [ 16 , 17 ] , without involving the hydrophobic alkyl chains . in other words , the underlying driving forces for urea derivatives , nicotinamide , and caffeine are the same , despite their different structural characteristics .
 hydrotropy is a phenomenon where the presence of a large quantity of one solute enhances the solubility of another solute . 
 the mechanism of this phenomenon remains a topic of debate . 
 this study employed molecular dynamics simulation to investigate the hydrotropic mechanism of a series of urea derivatives , that is , urea ( ur ) , methylurea ( mu ) , ethylurea ( eu ) , and butylurea ( bu ) . 
 a poorly water - soluble compound , nifedipine ( nf ) , was used as the model solute that was solubilized . 
 structural , dynamic , and energetic changes upon equilibration were analyzed to supply insights to the solubilization mechanism . 
 the study demonstrated that nf and urea derivatives underwent significant nonstoichiometric molecular aggregation in the aqueous solution , a result consistent with the self - aggregation of urea derivatives under the same conditions . 
 the analysis of hydrogen bonding and energy changes revealed that the aggregation was driven by the partial restoration of normal water structure . 
 the energetic data also suggested that the promoted solubilization of nf is favored in the presence of urea derivatives . 
 while the solutes aggregated to a varying degree , the systems were still in single - phase liquid state as attested by their active dynamics . 
1. Introduction
2. Computational Method
3. Results and Discussion
4. Conclusion