conceptual methods for the correlation 
 of binding affinities with 
 drug structure ( 3d - qsars ) are vital to the drug development process . 
 the approaches include receptor - based methods , e.g. , free energy perturbation , the 
 linear response method , and the mining minima approach , and ligand - based methods for unknown 
 receptors , e.g. , comparative molecular field analysis ( comfa ) .
the methods have been developed and perform 
 satisfactorily for the binding data measured with isolated macromolecules . 

unfortunately , binding affinities for isolated macromolecules are 
 often unavailable because the receptors have not yet been identified , 
 can not be isolated without denaturation or dissociation , or do not 
 work in aqueous solutions . in such situations , more complex assays 

are used , deploying receptors reconstituted in lipid vesicles as the 
 simplest system or utilizing intact cells , tissues , organs , or organisms .
the effective concentrations of the drugs in the receptor surroundings 
 vary among the studied compounds because of interactions with nonreceptor 
 assay constituents .
drug disposition has often been neglected in modeling 
 the bioactivities measured in complex systems . at best ,
the 1-octanol / water 
 partition coefficients and their squares , and sometimes the dissociation constants , as properties affecting the disposition , have been included in simplified 
 linear forms .
in many cell - level studies , 3d - qsar methods have been 
 applied without any correction for ligand disposition or empirical 
 models with various descriptors have been deployed . here
, we propose 
 a straightforward solution to the problem of qsar modeling of cell - level 
 data : extend the proven 3d - qsar methods by accounting for the varying 
 ligand disposition in the receptor surroundings using the disposition function ( df ) . the conceptual cell - qsar approach is based on a new correlation equation combining the 3d - qsar 
 expression and the df , whereby the coefficients in both parts can 
 be optimized either simultaneously or separately if the uptake data 
 are available .
the exact form of the correlation equation depends 
 on the kinetics of the processes underlying the drug effects and on 
 the complexity of studied compounds ( common skeleton , similarity of 
 substituents , ability to ionize and form tautomers ) , as discussed 
 in the methods .
the df describes the 
 kinetics of drug disposition and relates the 
 dose or the initial concentration to the concentration in the receptor 
 surroundings ( see eq 2 in the methods ) .
the first df forms were peak - shaped dependencies , 
 on logarithmic scales , of the drug concentration inside the receptor 
 compartment , which was separated from the dosing compartment by a 
 few bilayers , on lipophilicity ( the reference partition coefficient ) .
these dependencies represented the basis of the first qsar techniques , 
 such as the hansch approach and related 
 methods .
subsequently , other parameters , including the ionization 
 constant , the exposure time , the metabolic 
 rate parameters , the ratio of the partition 
 coefficients in alkane / water and 1-octanol / water systems , and the polar surface area as descriptors of h - bonding 
 ability , the partition coefficient between phosphatidylcholine headgroups 
 and hexadecane as a predictor of bilayer localization and partitioning , the membrane - interaction qsar parameters , the polarizability , the cross - sectional 
 area of the molecule , and numerous others , 
 were added .
the df functional forms developed from the parabolic , bilinear , nonequilibrium , equilibrium , and 
 mixed models to the pseudoequilibrium df . some of these dfs predicted reliably outside the used property ranges , 
 in contrast to empirical models .
the df can also be calibrated independently using the data on cellular 
 uptake and disposition , which are obtained by various experimental 
 approaches .
high - content screening techniques provide more detailed 
 information than classical uptake experiments , as demonstrated for the disposition of a small library 
 of lipophilic , fluorescent compounds in living hela cells .
structure - dependent phenomena , such as active 
 influx or efflux and metabolism , could be captured in this process .
the additional effort to obtain and fit the disposition data can 
 be spared in situations when the disposition is not complicated by 
 structure - dependent phenomena .
then the df depends on drug properties 
 characterizing the bilayer transport and accumulation , nonspecific 
 protein binding , hydrolysis , and other nonenzymatic reactions .
an 
 appropriate df can be selected from the armoire of available models 
 and can be calibrated simultaneously with the 3d - qsar model using 
 the cell - level data .
this approach is demonstrated here using the 
 selwood data on filaricidal activities 
 of analogues of antimycin a , which inhibits mitochondrial electron 
 transport and oxidative phosphorylation and induces apoptosis .
these data are 
 regarded as difficult to model and are frequently used to validate 
 qsar methods on the basis of variable selection .
the descriptive ability 
 of the generated models did not exceed 6080% of the explained 
 variance , so there is space for improvement . to the best of our knowledge
, 
 this cell - qsar study represents the 
 first attempt at the qsar modeling of drug effects in complex systems , 
 where both drug  receptor interactions and drug disposition 
 significantly vary among studied compounds and both are conceptually 
 treated using a common correlation equation .
the studied compounds , 
 listed in table 1 , have varying substituents , 
 r1 , on the phenol ring and large lipophilic substructures , 
 r2 , which replace a complex dilactone moiety of the parent 
 compound .
the compounds can be formally divided into three groups : 
 two - ring analogues ( 23 and 31 ) , three - ring 
 analogues ( 216 and 2630 ) , and alkyl - chain analogues ( 1 , 1722 , 24 , and 25 ) . the salicylamide moiety , present in all compounds except 31 , exhibits a peculiar intramolecular h - bonding .
two types of intramolecular h - bonds are formed , depending upon ionization 
 of the hydroxyl ( figure 1 ) .
clogp - predicted 1-octanol / water 
 partition coefficient p. sparc - predicted acidity of the phenolic 
 hydroxyl .
affinities and 
 disposition function 
 values predicted from the df - msmm comfa model .
conformational switching of an intramolecular h - bond in the salicylamide 
 ring of antimycin derivatives upon ionization .
the hydroxyl pka values 
 ( table 1 ) of the studied antimycins were estimated 
 by the 
 sparc method , which seems to take the 
 intramolecular h - bond into account .
the magnitude of the pka values ( range 4.68.0 ) is determined 
 mainly by the electron - withdrawing ability of the r1 substituents 
 on the phenol ring , with the r2 substituents exhibiting 
 a slighter influence . under neutral conditions , the compounds are 
 present in the aqueous solution as a mixture of ionized and nonionized 
 species , with the balance shifted toward the ionized species for most 
 compounds , except compounds 1 , 2 , 4 , 9 , and 1719 having pka > 7 .
formation of tautomers 
 and carbonyl hydrates was negligible , according to the sparc estimates ; 
 otherwise , they would be included in the model in the same way as 
 ionization .
table 1 also contains the activities 
 spanning almost 3 orders of magnitude and the 1-octanol / water partition 
 coefficients p ( clogp estimates for neutral molecules ) .
antimycin a is a known inhibitor 
 of oxidative phosphorylation . therefore , 
 we examined whether the selwood data 
 could be explained by our two - decade - old , conceptual qsar model for 
 uncouplers .
the model describes isoeffective 
 concentrations eliciting a given degree of uncoupling as a nonlinear 
 function containing lipophilicity ( p ) and acidity 
 ( pka ) .
although the surface generated 
 by the fit to the data was reminiscent of the expected shape , the deviations of individual compounds were 
 too large to consider the fit satisfactory .
we hypothesized that the 
 deviations were caused by structure - specific interactions with an 
 unknown receptor ; therefore , we decided to deploy a ligand - based 3d - qsar 
 method .
the cell - qsar correlation 
 equation for the simplest drug effect scenario consists of the product 
 of the drug  receptor association constant k and the df ( eq 3 in the methods ) .
the receptor is unknown in this case , so k was 
 expressed using one of the popular ligand - based methods , comfa .
the antimycin analogues ionize to different 
 degrees and are flexible ; therefore , we applied our multispecies ( ms ) , 
 multimode ( mm ) modification of comfa .
the pseudoequilibrium form of the df ( eq 10 in the methods ) , treating absorption as an instantaneous process , was chosen , because 
 no lag phase was observed in the time course of toxicity .
an additional reason for selecting this df form was the ability 
 of the underlying model to handle speciation 
 of the ligands .
pharmacophores obtained for all 
 species using the galahad procedure , which performs 
 flexible superposition based on the active analogue approach , indicated that the salicylamide moieties are 
 closely superimposed in all cases .
this outcome is consistent with 
 the apparent importance of this moiety for inhibition : an analogue 
 capable of h - bond formation ( figure 1 ) inhibited 
 the cytochrome bc1 complex activity in 
 submitochondrial particles much stronger than a similar analogue lacking 
 this ability . a rigid compound 
 that preferably exhibits
a high activity would be very useful for 
 guiding the superposition of the ligands .
the three - ring 
 compounds contain more rigid aromatic rings than other compounds , 
 so we selected the most active compound in this group and in the entire 
 series ( 7 ) as the template .
because the pharmacophore - generating 
 procedure did not provide clues about the conformation of the lipophilic 
 fragments connected to the salicylamide ring , we used the low - energy 
 conformations of compound 7 as the assumed bound conformations . 

this step is associated with the risk that the overall spatial organization 
 of the binding site model may not completely correspond to that of 
 the actual receptor .
while the binding points will be positioned appropriately 
 around individual rigid rings of the template , the relative positions 
 of the individual groups of points surrounding the rigid fragments 
 may differ from those of the actual receptor because of possible fragment 
 rotations .
this drawback would not affect the predictive ability of 
 the model for compounds which can adopt the template conformation 
 without significant conformational strain .
the conformational 
 space of compound 7 is characterized 
 by four torsions ( figure 2 ) .
conformational 
 analysis identified the minimum - energy conformations for the h - bonded 
 forms of both neutral and ionized molecules ( figure 1 ) .
the common minimum conformations of ionized and neutral 
 species without the intramolecular h - bonds were also looked up , for 
 the possibility that the hydroxyl and the amide groups would interact 
 with the receptor instead of forming the intramolecular bond . two 
 skeleton conformations appear for each of the two species : one closed via the intramolecular h - bond and one open without the h - bond .
four torsions of compound 7 ( table 1 ) characterizing the conformations of three - ring 
 analogues 
 displayed in red color
( c3c4c11o12 ) , 
 2 ( c11n13c15c20 ) , 3 ( c17c18o22c23 ) , and 4 ( c18o22c23c28 ) .  closed  
 and  open  

it has long been recognized that flipping of symmetrical 
 rings 
 with asymmetrically placed substituents results in similar but distinct 
 bound geometries . if the receptor structure is unknown , preferred 
 geometries can not be selected a priori and all geometries should be 
 considered in model building .
a total of 16 of 31 studied compounds ( table 1 ) have substituents in meta - positions on either 
 the middle ring ( 27 , 9 , 10 , 12 , 1416 , 26 , and 28 ) or the third ring 
 ( 13 and 27 ) . for these compounds ,
rotation 
 of the asymmetrically substituted ring by 180 led to doubling 
 of the existing two modes .
the four basic templates of compound 7 were superimposed by the atom fit method in sybyl ( figure 3b ) to ensure the best overlap of the salicylamide 
 moieties , as suggested by the generated pharmacophore .
all other molecules 
 were superimposed on the templates using the flexs procedure ( figure 3c , d ) .
superposition 
 procedure : ( a ) four basic templates of compound 7 , generated 
 by conformational analysis and numbered as in 
 table 2 ; ( b ) superposition of the four basic 
 templates ; ( c ) superpositions of all compounds ( table 1 ) to the four basic templates in respective species and conformations , 
 numbered as in row a ; ( d ) final superpositions , enriched by flipping 
 the benzene rings by 180 for the msmm situation ( i ; 200 molecules 
 = 31 compounds  2 species  2 skeleton conformations  
 1 , 2 , or 4 ring - flipping conformations ) , the mm situation ( ii ; 100 
 molecules created as in situation i but with 1 species ) , and the standard 
 one - mode situation ( iii ; 31 molecules ) . the analysis is based on the 
 correlation equation obtained by taking the logarithm of eq 3 ( x = 0.5 because the ec50 values are modeled ) , with the association constant k expressed by eq 9 , and the df given by eq 10 ( the exposure time t = constant ) 
 combined with eqs 11 and 12 .
for both the receptor - binding and disposition parts , ionization 
 is included and the coefficients are optimized simultaneously .
optimization examines two forms of the df , for the aqueous phases 
 ( shown in eq 10 ) and membranes . if the receptors 
 are localized in a membrane and the compounds bind to them from the 
 hydrocarbon core of the bilayer , eq 10 needs 
 to be multiplied by p ( p is the reference partition coefficient and  is 
 the collander coefficient , which is one of the optimized regression 
 coefficients )
the water and membrane variants of eq 10 are initially used in fully expanded form : each of the coefficients a  d is replaced by eqs 11 and 12 .
the optimization proceeds with 
 gradual forward selection of energies in relevant grid points in the 
 comfa part , which is done separately for the two forms of the df . 

the better df is selected on the basis of the statistical criteria 
 and further optimized by omitting the parameters with higher standard 
 deviations , if the elimination does not cause a significant decrease 
 in statistical criteria .
one , or sometimes both , of the coefficients c and d , describing lipophilicity - dependent 
 and lipophilicity - independent elimination , can frequently be omitted . 
 in each pair of coefficients a  d ( eq 11 ) , the term for one species may or may 
 not be significant .
the combinatorial search for the best df - msmm 
 comfa model was extensive 
 for three reasons : many possible combinations of relevant grid points 
 need to be examined , the df can have multiple functional forms , and 
 many sets of the initial estimates of coefficients need to be tested 
 to avoid trapping in local minima .
the best model was selected on 
 the basis of the r and q ( for the leave - one - out cross - validation in the training 
 set , used to eliminate unstable models ) values and the number of optimized 
 coefficients and and their standard deviations . for illustration
, 
 there were 65  021 models with r  0.6 , 11  142 models with r  0.8 and q  0.6 , and 
 3752 models with r  0.9 and q  0.7 , of which 25 models had less 
 than 11 coefficients , each with smaller than 60% standard deviation .
the best df - msmm comfa model contained the df for the compounds 
 interacting with the receptors in a membrane , with metabolism that 
 was either insignificant or invariant for the studied compounds ( c = 0 and d = 0 ) , and five required comfa 
 grid points .
the final , pruned correlation equation , resulting from 
 eq 3 ( x = 0.5 ) , with the association 
 constant k expressed by eq 9 ( the subscript i was omitted for fractions f ) , and the df given by eqs 1012 , was1the first term is an msmm comfa expression 
 for the receptor binding ( log k ) , and the remaining 
 terms describe disposition ( log df ) .
the fractions of ionized and 
 nonionized molecules , f1 and f2 , respectively , include the pka values and the optimized ph value as shown in eq 12 and are identical in both receptor - binding and disposition 
 terms .
the microscopic association constant kij for each of the m considered 
 modes is represented by a k - summand .
each of the k - summands contains five identical adjustable coefficients , c1c5 , which , 
 for the selected grid points ( coordinates in table 3 ) , multiply the energies xijkl for the given modes .
the addition of multiple modes does not 
 increase the number of optimized coefficients ; it only changes the 
 form of the correlation equation by increasing the number of k - summands .
nonlinear regression analysis resulting in eq 1 provided the following outcome for the best df - msmm 
 model .
for the 
 receptor - binding expression , the results are summarized in table 3 .
the optimal values of the disposition - describing 
 coefficients for the df were a1 = ( 7.142 
  2.213 )  10 , a2 = ( 2.636  1.254 )  10 , b1 = ( 9.989  4.233 )  10 , and ph 7.56  0.32 .
the optimization of the collander coefficient 
  and the coefficient c0 did not 
 lead to a sufficient improvement , so their values were fixed as  
 = 1 and c0 = 0 .
the description statistics , 
 calculated for the training set , consists of the sum of squares of 
 errors ( sse ) , where the error is the difference between calculated 
 and experimental values , and the squared correlation coefficient ( the 
 coefficient of determination , equal to the percentage of explained 
 variance ) r = 1  sse / syy , where 
 syy is the sum of squares of deviations of the experimental log k values from their average .
the prediction statistics contains 
 similar indices calculated for the test set that was not used in the 
 development of the model : predictive sum of squares of deviations 
 between predicted and experimental values ( press ) and the squared 
 correlation coefficient q = 1  
 press / syy .
table 4 summarizes the descriptive 
 ( sse and r for the training set ) and 
 predictive ( q and press for the test 
 set ) statistical criteria for the df - msmm comfa model ( 1 ) and for 
 the reduced models ( 213 ) . for comparison ,
the random scrambling 
 of bioactivities ( 50 runs ) produced no significant correlations , with 
 the average values of sse = 11.12 and r = 0.250 .
optimized eq 1 also provides the 
 affinity ( log k ) and disposition ( log df ) components 
 of bioactivity ( table 1 ) .
a test set ( table 1 , compounds 2 , 11 , 17 , 20 , 24 , and 30 ) 
 covering the entire range of biological activities was selected before 
 optimization .
the use of multiple test sets , which would be a preferred 
 way to examine the predictive abilities of the model , was precluded 
 by the extent of the optimization procedure . for compounds 17 and 30 with semiquantitative activities , the q and press values ( table 4 )
were calculated using the upper limits , i.e. , log(1/ec50 ) = 5 . because only the df - msms comfa model correctly predicted log(1/ec50 ) < 5 ( figure 4b ) , the predictive 
 abilities are probably underestimated for the df - msms comfa model 
 and overestimated for all other models .
the models differ in the use of 
 disposition function ( df ) , multiple or single species ( ms or ss ) , 
 and multiple or single modes ( mm or sm ) .
number of latent variables shown , 
 with the number of all energies given in parentheses .
the energies of all considered modes 
 are averaged and analyzed by standard , one - mode comfa .
prevalent bound species and mode 
 as determined by the df - msmm comfa model used for each compound . calculated and predicted activities plotted against experimental 
 data for the training set ( a ) and test set ( b ) , generated with the 
 df - msmm ( black ) , msmm ( blue ) , ssmm ( red ) , and standard ( green ) comfa 
 models ( models 13 and 11 in table 4 , respectively ) . in plot b , the two experimental values of log(1/ec50 ) = 5 are actually < 5 ( table 1 , 
 compounds 17 and 30 ) , as indicated by the 
 arrows . table 4 demonstrates that 
 all features used 
 in the df - msmm comfa model are necessary for a good prediction .
omission 
 of the disposition leads to a decline in predictive abilities ( press 
 and q ) , even if multiple species and/or 
 modes are considered ( models 2 and 3 ) .
the decline is more severe 
 for standard , one - mode comfa models ( 413 ) , including those 
 with the averaged multiple modes ( models 6 , 9 , and 12 ) and even for 
 the prevalent bound species and modes ( model 13 ) , which were selected 
 by df - msmm comfa model 1 .
although only this indirect , model - based indication 
 is available for the studied case , multiple modes were experimentally 
 proven to occur in many ligand 
interestingly , the descriptive abilities ( sse and r ) were great in all cases .
this may , in part , explain 
 the use of 3d - qsar methods without any description of disposition 
 for cell - level activities .
it is worth mentioning that an exhaustive 
 examination of modes 
 and species for each compound in a standard comfa analysis , seeking 
 a one - mode solution , is technically not feasible .
the 23 compounds 
 of the training set , each present in two species and two conformations 
 ( for simplicity , the ring - flipping conformations are omitted ) , would 
 require 4 analyses or about 2.2 million 
 cpu years , if a single one - mode analysis only lasts 1 s. therefore , 
 the msmm approach , performing an extensive , albeit not exhaustive 
 search lasting several weeks on a few processors , compares favorably .
the calculated bioactivities for the training set and the predictions 
 for the test set compounds are compared with experimental values in 
 parts a and b , respectively , of figure 4 . the 
 use of multiple species and modes and , especially , of the df clearly 
 improves predictivity ( press and q ) . 

descriptive statistical indices for calibration display a similar 
 trend , except for the excellent sse and r values for the standard , one - mode comfa model , utilizing the full 
 set of energies .
the standard model , however , did not confirm its 
 calibration quality in the prediction exercise ( figure 4b ) .
the steric and electrostatic contours 
 for the df - msmm comfa model with various compounds embedded in the 
 background of overall msmm superposition ( figure 3d , situation i ) are displayed in figure 5 , along with representative ligand conformations .
the contour map 
 shows that the binding site model is defined by a sterically favorable 
 region near the salicylamide ring , two sterically unfavorable regions 
 in the midsection of the binding site , an electronegative - favoring 
 region near the second ring of two- or three - ring compounds , and an 
 electropositive - favoring region at the lipophilic end of the molecules . 

the absence of electrostatic regions around the salicylamide ring 
 may result from small differences among the studied compounds in this 
 substructure .
contour maps of the df - msmm comfa model with embedded 
 superposition 
 of all 200 molecules to indicate the applicability space .
green and 
 yellow contours indicate regions that are sterically favorable and 
 unfavorable , respectively .
the following ligands 
 are presented in ball and stick models : ( a ) compound 2 ( table 1 ) binding in ionized and open conformation , 
 ( b ) compound 2 binding in neutral and closed conformation , 
 showing the clash of the 3-cl in the second ring with one of the sterically 
 unfavorable regions , ( c ) compound 18 with a shorter alkyl 
 chain , one of the strongest binders , ( d ) compound 19 with 
 the 3-acetamide group in the salicylamide ring occupying a sterically 
 favorable region , showing clashes of the long chain with one of the 
 sterically unfavorable regions .
the binding conformation in which the bulky chlorine 
 atom in the 
 second ring is closer to the salicylamide oh group and far from a 
 sterically unfavorable region ( figure 5a ) is 
 preferred in 11 out of 15 compounds .
consequenty , the ring - flipped 
 conformation ( figure 5b ) is not populated . 

compounds with lipophilic alkyl groups tend to have a wide range of 
 activities depending on the length of the alkyl chains .
compounds 17 and 18 ( figure 5c ) 
 with six and eight methylene groups , respectively , bind in an extended 
 conformation and show the highest predicted binding affinities ( table 1 , log k > 4 ) , indicating the 
 optimal 
 chain length for binding . on the other hand , compounds with 1214 
 methylene groups ( table 1 , 1 , 1922 ) bind in a packed conformation ( figure 5d ) that results in low affinities ( table 1 ,
log k < 1.7 ) , probably because 
 the folded chain protrudes into the sterically unfavorable regions . 
 for the same reason
, the affinity of compound 25 with 
 16 methylene groups exhibits a further drop ( log k  0.5 ) . this reasoning could also apply to compound 23 showing only average affinity ( log k  1.7 ) , although its 4-tert - butylphenyl ring is similar 
 in length to the optimal n - hexyl chain in the extended 
 conformation ( compound 17 ) but is much bulkier .
the red 
 electronegative - favoring region in the midsection of the binding site 
 improves the affinity ( log k ) of 15 of 31 compounds 
 with an electronegative chlorine atom in the second ring , even though 
 their overall activities differ significantly because of varying disposition . 

this interaction also causes the compounds with the electronegative 
 oxygen ( 211 , 1315 , 27 , 29 ) or carbonyl ( 12 ) linkers between the second and third rings to have a higher binding 
 affinity than compounds with other linkers ( 16 , 26 , 30 ) .
two compounds , 19 and 31 , were excluded 
 from optimization before its start because of singularities caused 
 by molecular parts protruding into subspaces which were not reached 
 by other compounds in the series .
singularity of compound 19 is caused by the 3-acetamide group in the salicylamide ring , which 
 reaches a spot in the vicinity of the sterically attractive region 
 ( figure 5d ) .
the singular region may be an 
 open , water - filled space with no effect on affinity because the prediction 
 for compound 19 by the df - msmm model ( log k + log df = 5.324 , table 1 ) is close to the 
 experimental log(1/ec50 ) = 5.097 .
compound 31 lacks an amine linker between its rings , and therefore , its molecule 
 extends into uncharted space .
compound 31 has a much 
 lower predicted activity ( log k + log df = 2.998 ) 
 than the actual measured log(1/ec50 ) = 6.461 .
this difference 
 indicates that there may be an attractive spot in the midsection of 
 the binding site which the model does not capture because of the lack 
 of molecules occupying this region .
the prevalences , 
 given by the boltzmann distribution shown in eq 8 in the methods , can not be guessed a priori 
 because they are one of the outcomes of optimization .
the prevalences 
 for the df - msmm comfa model ( eq 8) , with individual kijk values calculated as the 
 decadic terms in eq 1 with optimized values 
 of the coefficients cl , are shown in detail in the supporting information and summarized here .
a total of 16 of 31 compounds ( 1 , 2 , 8 , 10 , 11 , 13 , 1518 , 23 , 25 , 27 , 28 , 30 , 31 ) bind predominantly in the closed conformation , 
 maintaining the intramolecular h - bond ( figure 1 ) .
the remaining compounds bind in the open conformation , exposing 
 the salicylamide s polar groups , with at least 50% prevalences . 

compounds 15 , 17 , 18 , and 25 bind 100% in the closed conformation , while compound 20 binds 100% in the open conformation .
the exceptions are compounds 2 , 4 , 9 , 17 , and 18 , for which the neutral species bind with 74% , 53% , 58% , 
 100% , and 100% prevalences , respectively .
figure 6 indicates that the species distributions of bound and free 
 molecules are quite similar for most compounds . for neutral species , 

most compounds have both the fraction in water and binding prevalence 
 less than 10% . for ionized species ,
most compounds have the fraction 
 in water and binding prevalence as high as 90% . about a quarter of 
 the compounds ( 1 , 2 , 4 , 5 , 18 , 19 , 31 ) , however , 
 exhibit significant differences between the fractions in water and 
 binding prevalences .
speciation of free and bound molecules according to the 
 df - msmm 
 comfa model .
neutral and ionized species are shown in blue and red , 
 respectively , as the compound number ( table 1 ) .
the predominant binding species and binding conformations 
 are to 
 a large extent affected by the substituents in the salicylamide ring . 

strong electron - withdrawing groups promote ionization and also contribute 
 to higher activity : only 3 ( 4 , 9 , 31 ) out of 24 compounds with log(1/ec50 ) > 6 
 have 
 pka > 6.5 ( table 1 ) .
however , lipophilic moieties including alkyl chains and two or 
 three ring systems also affect the binding as well as disposition , 
 so the structure  activity relationships are complex .
the strongest binders , 
 compounds 17 and 18 ( table 1 , log k > 4 ) with a 3-formylamino group 
 in 
 the salicylamide ring predominantly bind as neutral species in the 
 closed conformation .
the shorter alkyl chains may allow sufficient 
 conformational freedom for these two compounds to make the best possible 
 interactions in the binding site , leading to high binding affinities . 

long - chain analogues ( compounds 1922 and 24 , table 1 ) predominantly 
 bind in ionized open conformations or sometimes in ionized closed 
 conformations , as seen for compounds 1 and 25 .
all long - chain analogues exhibit low to average binding affinity , 
 possibly because of steric clashes of long chains in packed conformations 
 ( figure 5d ) with the sterically unfavorable 
 regions in the midsection of the binding site .
compounds 
 with a 2-no2 or 5-no2 group in the salicylamide 
 ring bind predominantly as ionized species , either in open or closed 
 conformations , depending upon the presence of a 3-cl substituent in 
 the second ring ( the absence of which seems to be compensated by the 
 presence of a 2-cl or 4-cf3 substituent in the third ring ) . 

compounds 3 , 6 , 12 , 14 , 26 , 28 , and 29 with a 3-cl substituent 
 in the second ring mainly bind in the open conformation , although 
 compounds 12 and 29 bind about equally in 
 the closed conformation as well , and compound 28 shows 
 slightly higher preference for the closed conformation .
this variation 
 is possibly affected by the presence of a carbonyl linker group between 
 the second and third rings in compound 12 and 4-scf3 and 3-cf3 groups in the third ring of compounds 28 and 29 , respectively .
compounds without a 
 3-cl substituent in the second ring ( 8 , 11 , 13 , 23 , 27 , and 30 ) bind predominantly as ionized species and show higher preference 
 for the closed conformation .
the absence of steric hindrance by a 
 chlorine substituent in the second ring allows these compounds to 
 assume the preferred closed conformation with an intramolecular h - bond 
 between the amide nh and phenoxide ion .
compound 16 ( with 
 a 5-no2 group in the first ring and a 3-cl substituent 
 in the second ring ) prefers to bind in the closed conformation , possibly 
 because of the presence of a thioether linkage between the second 
 and third rings , resulting in a longer linker .
the most active in 
 this series , compound 7 with a 5-cn substituent in the 
 salicylamide ring , binds predominantly as an ionized species in the 
 open conformation .
the disposition of antimycins 
 in female worms of dipetalonema viteae after 120 h of exposure can be visualized 
 for individual compounds as the difference between the experimental 
 log(1/ec50 ) values and the log k values 
 ( table 1 ) calculated from the affinity part 
 of the df - msmm comfa model ( eq 1 ) .
these values 
 are plotted as a function of the drugs lipophilicity ( log p ) and acidity ( pka ) in figure 7 , along with the surface given by the disposition 
 part of the df - msmm comfa model ( eq 1 ) with 
 optimized coefficients .
the shape of log df(p , ka ) is remarkably nonlinear : it is essentially 
 composed of interconnected planes positioned at varying angles .
no 
 further curvatures are expected , according to the model , as the planes 
 extend in all four directions to the limit property values , so this 
 conceptual function safely predicts outside of the property ranges .
using the 
 correct form of the df for the correlations is essential , because 
 its peculiar shape ( figure 7 ) is difficult 
 to emulate by polynomials , which are too flexible to approximate the 
 planar areas .
dependence of the pseudoequilibrium , 
 membrane - based df on lipophilicity 
 and acidity , as given by the disposition part of eq 1 with the optimized coefficient values listed in the text . 

the data for best binders with poor disposition ( compounds 17 and 18 , table 1 ) are shown as 
 open points .
the resulting fit ( eq 1 , 
 table 3 and accompanying text ) can be interpreted 
 as follows .
the hypothetical receptors are localized in 
 a membrane , with the drugs accessing the binding site ( the comfa model 
 in figure 5 ) from within the bilayer .
the optimized 
 coefficients are associated with the processes that determine drug 
 disposition : a , with bilayer accumulation and nonspecific 
 protein binding ; b , with accumulation in aqueous 
 phases , with subscripts 1 and 2 indicating the relatedness to the 
 nonionized and ionized species , respectively .
the coefficient b2 was not necessary for a good fit , indicating 
 that accumulation of ionized molecules in the aqueous compartments 
 did not cause significant variation in overall disposition .
the exponent , 
 coming from eq 10 and containing coefficients c and d describing metabolism , need not 
 be used in eq 1 , meaning that c1 = c2 = d1 = d2 = 0 .
the model indicates 
 that the pseudoequilibrium disposition of the studied compounds was 
 not affected by metabolism , which could be either negligible or similar 
 for all compounds .
the internal ph value in terms f1 and f2 ( eq 12 ) was optimized 
 as ph 7.56  0.32 .
this high value can normally be encountered 
 only in one part of the cell : in the matrix of mitochondria .
therefore , 
 the fit indicates that the hypothetical receptors are localized in 
 the bilayer that is in contact with the mitochondrial matrix .
this 
 indication agrees with the current knowledge about antimycin a s 
 mechanism of action , which focuses on inhibition of electron transport .
antimycin a binds at the ubiquinone binding site qi of 
 the complex that is located on the matrix side of the cristae membrane .
notably , the disposition function provides 
 clear guidelines for 
 the optimization of the drug structure for the best disposition .
the 
 top plateau in figure 7 indicates the range 
 of log p and pka values 
 that lead to the maximum drug disposition in the receptor surroundings . 

the region of the maximum disposition can be defined as pka  log p for log p  6 and pka  6 for log p > 6 .
the knowledge of suitable combinations of log p and pka values provides unique 
 clues for optimization of drug structure , also because the lower log p and pka values will lead to 
 increased aqueous solubility .
equation 1 defines two contributions to the 
 affinity : log k ( the first term ) and disposition 
 ( log df ; the remaining terms ) .
the two contributions were enumerated 
 from the calibrated df - msmm comfa model ( eq 1 and the accompanying text , table 3 ) , summarized 
 in table 1 , and plotted against the experimental 
 antifilarial activities ( table 1 ) in figure 8 .
dissection of affinity ( log k ; red symbols ) 
 and 
 disposition ( log df ; blue symbols ) contributions to overall bioactivity 
 by the calibrated df - msmm comfa model .
figure 8 and table 1 show that two weakly active compounds ( 17 and 18 ) are actually the best binders , which are held 
 back by 
 poor disposition .
their disposition can be , in principle , increased 
 by 45 logarithmic units , leading to overall bioactivities 
 approaching log(1/ec50 )  9.5 , which is almost 2 
 orders of magnitude better than that of the most active compound 7 .
disposition is easier to optimize than binding because 
 the former depends on lipophilicity and acidity , which are well understood 
 in terms of drug structure .
the df - msmm comfa model , and cell - qsar 
 models in general , provides unique clues for optimization of the compounds .
the cell - qsar concept adapts ligand - based 
 and receptor - based 3d - qsar 
 approaches for use with the bioactivities measured in cells or more 
 complex systems .
the adaptation consists of the extension of the correlation 
 equation specific for the given 3d - qsar method by the df .
the df describes 
 changes in the concentration of compounds in the receptor surroundings 
 originating from membrane accumulation , binding to nonreceptor proteins , 
 hydrolysis , and possibly other processes .
the cell - qsar concept was 
 used here with the popular ligand - based comfa method .
a conceptual 
 combination of the df with our msmm extension of the comfa model was 
 applied to antifilarial activities of antimycin a analogues , representing 
 a part of the difficult - to - model selwood data set that is often used 
 as a test case for assessment of new variable - selection algorithms . 

the fitting results are very satisfactory and show that each component 
 of the model ( df , ms , mm ) improves the predictive ability .
the optimized 
 form of the disposition function indicates that the compounds bind 
 to the hypothetical , membrane - bound receptor in the cristae bilayer 
 of mitochondria and the differences in their metabolic rates are negligible . 

the perceived complexity of the selwood data set may be explained 
 by the nonlinearity of the model in lipophilicity and acidity in combination 
 with the lack of proper descriptors for acidity in the original set , 
 the peculiar intramolecular h - bonds in the salicylamide moiety that 
 differ for neutral and ionized species , and the structure - specific 
 receptor binding .
the results also illustrate the utility of the cell - qsar 
 approach in medicinal chemistry .
specifically , the cell - qsar approach 
 delineates the affinity and disposition contributions to bioactivity , 
 which provide for a straightforward , separate structure optimization 
 for affinity and disposition .
although further testing is necessary , 
 the cell - qsar concept seems to be a promising direction in the structure - based 
 or ligand - based predictions of bioactivities in cellular or more complex 
 systems and drug structure optimization . for larger and more diverse 
 data sets , better superposition techniques and methods for prediction 
 of species fractions
the model - based nature opens 
 the cell - qsar concept for incorporation of any future improvements 
 in 3d - qsar techniques and the disposition function , as well as new 
 pharmacology and pharmacodynamic scenarios .
the simplest pl / pd scenario consists of a situation when 
 the pl phase is represented by the 1:1 , fast , and reversible ligand 
receptor 
 interaction and the pd phase describes the biological effect , which 
 is a direct and immediate consequence of the drug  receptor 
 interaction and is proportional to the fraction of occupied receptors . 

receptor association constant k is defined using the concentrations ( denoted by square brackets ) 
 of the ligand ( l ) , receptor ( r ) , and complex ( lr ) as k = [ lr]/([l][r ] ) . in a cellular system ,
the free ligand concentration 
 [ l ] varies because of the disposition , and consequently , all three 
 concentrations are time - dependent
. usually , the concentrations are 
 sufficiently low to approximate activities . if the concentration of 
 the free receptors [ r ] is expressed as the difference between the 
 total receptor concentration [ r]0 and [ lr ] , the fraction 
 of occupied receptors is given as [ lr]/[r]0 = k[l]/([l ] + 1 ) = e / emax .
the latter equality comes from the simplest pd phase , describing 
 the primary effect e as being proportional to the 
 fraction of occupied receptors , [ lr]/[r]0 .
secondary effects 
 lacking this simple tie to the receptor modification require more 
 complex pd models .
nevertheless , the 
 above scenario applies to many drug effects caused by competitive 
 enzyme inhibition or receptor binding .
since the receptor - bound drug 
 represents only a small drug fraction in the body , the disposition 
 is not significantly affected by the receptor binding , and the ligand 
 concentration in the receptor surroundings , [ l ] , can be expressed 
 using the df with properties p and time t as variables and the initial ligand concentration c0:2 to obtain a pk / pl / pd expression , [ l ] 
 in the above expression for e / emax is replaced by the product df(p , t ) cx(t ) , where cx(t ) are the 
 isoeffective drug concentrations eliciting the effect , which is equal 
 to the fraction x of the maximum effect . with e / emax = x , 
 the bioactivity , characterized by cx(t ) ,
is described as3equivalent pk / pl / pd dependencies were derived 
 for the irreversible drug  receptor interactions , either single 
 or preceded by a fast , reversible step .
equation 3 and equivalent pk / pl / pd relationships 
 provide the blueprint for a conceptual combination of the disposition 
 function with any ligand - based or receptor - based 3d - qsar method for 
 prediction of binding affinities . the k term in eq 3 needs to be replaced by a suitable conceptual 3d - qsar 
 correlation equation , and the disposition function
this cell - qsar concept 
 represents the recipe for the formulation of conceptual qsars for 
 cell - based assays and other complex systems .
studied antimycin 
 analogues ionize under the conditions of the experiments , and each 
 species forms different intramolecular h - bonds .
the molecules are 
 flexible , and each species can bind to the receptor r in different 
 orientations or conformations ( modes ) .
the generalized multispecies 
 multimode binding equilibria are outlined in the following equation:4each binding equilibrium is characterized 
 by the microscopic association constant kijk ( eq 5 ) and represents the 
 receptor binding of the ith ligand in the jth species and the kth binding mode . in 
 principle , the number of species s and the number 
 of binding modes m can differ for individual ligands . 

in the studied case , there are only two species ( s = 2 , nonionized and ionized , with charges 0 and 1 , respectively ) 
 for each ligand ( table 1 ) .
the number of modes 
 is unknown , since there is no experimental information available on 
 either the receptor or the complex , and can differ for individual 
 ligands . in the general expressions ,
s and m represent the maximum numbers of species and binding modes 
 for the tested ligands . the missing species or modes of some ligands 
 will have zero fractions fij or zero association constants kijk ( see below ) .
the microscopic association 
 constant for the ith molecule s jth species in the kth binding mode is5usually , only the total association constant 
 of the ith ligand ( ki ) is determined , although the microscopic association 
 constants kijk are the 
 relevant quantities to be correlated with the structure . to obtain 
 a conceptual correlation equation for ki
the experimentally measured ki reflects the total concentration 
 of the ligand / receptor complexes 
 in any species and any binding mode .
a series of rearrangements to 
 the definition of ki provides 
 the desired function of kijk , shown in eq 6:6 ( 1 ) the total concentration of the complex 
 [ lri ] is expressed as the sum of bound 
 concentrations of individual species , ( 2 ) each summand is formally 
 multiplied by [ lij]/[lij ] to introduce the fraction of each species , fij = [ lij]/[li ] , and ( 3 ) the bound concentration 
 of each species [ lrij ] is broken down 
 to individual binding modes .
the relationship between the microscopic 
 and total association constants is obtained by expressing the m - summands in eq 6 using eq 5:7here fij is the fraction of the jth molecular species 
 in the ith compound in solution . for compounds present 
 in the solution as one species , the right - hand side of eq 7 is equal to the k - summation . in this case
, 
 eq 7 is in accordance with published analyses 
 of formally analogous situations : the statistical thermodynamic and equilibrium treatment 
 of multimode binding in ligand / protein interactions and kinetic analyses 
 of a reversible unimolecular reaction leading to different products or isomers .
the 
 expressions for the fractions fij of the jth species can be derived from the 
 definition of the ionization constants .
only one molecule of 
 a compound , in any species and any mode , can 
 be bound in each complex .
the distribution of species and modes in 
 the bound state is characterized by their prevalences . for
the kth mode of the jth bound species for the ith compound , the prevalence is8the numerator and denominator 
 come from eqs 5 and 6 , 
 respectively .
the third quasi - equality ensures that the sum of all s  m prevalences equals unity .
the 
 prevalence of the jth bound species in all modes 
 and the prevalence of the kth bound mode in all species 
 can easily be calculated using eq 8 . for 
 the application in comfa ,
eq 7 needs 
 to be logarithmized and the log kijk values 
 must be replaced by the correlation equation for comfa:9here cl are the 
 regression coefficients characterizing the weights of the ligand 
probe 
 interaction energies x in individual cross - sections 
 of a grid surrounding the superimposed ligands .
the subscripts indicate 
 the relatedness to the ith compound , jth species , kth mode , and lth grid 
 point , and g is the total number of grid points . 

other contributions to the binding free energy ( internal ligand energy , 
 binding entropy , desolvation ) can be added to the summation in the 
 exponents . in this case
, we only used the comfa energies because the 
 size of the used data set did not allow a rigorous optimization of 
 more than a dozen coefficients .
the pseudoequilibrium df 
 expresses the time course of the concentration of nonionized ligand 
 molecules in the aqueous phases of the studied biosystem during the 
 elimination period:10here p is the reference partition 
 coefficient ,  is the empirical collander coefficient , and t is the exposure time .
the terms a , b , c , and d characterize 
 the key fate - determining processes the ligand molecules undergo in 
 the biological system : a , accumulation in membranes / protein 
 binding ; b , distribution in aqueous phases ; c , lipophilicity - dependent elimination ; d , lipophilicity - independent elimination . for the receptors localized 
 in the bilayer ,
eq 10 needs to be multiplied 
 by p. if compounds are present 
 in the aqueous phase in the receptor surroundings in s species created by ionization , tautomerism , or carbonyl hydration , 
 the model suggests that each of the parameters a , b , c , and d ( represented 
 by y ) from eq 10 be expanded 
 as11the fractions f of individual 
 species are the same quantities as in eq 9 , 
 except the subscripts i , indicating the compound , 
 are omitted . the subscripts j
the fractions of nonionized , neutral molecules ( subscript j = 1 ) and ionized molecules with an overall charge of 1 
 ( subscript j = 2 ) are given by the definition of 
 the dissociation constant ka for the given 
 ph of the medium and can be written , respectively , as12 generally , on the basis of the probable 
 intracellular localization 
 of the receptors , a reasonable intracellular ph range is 58 , 
 the lower limit being observed in lysozomes and the upper limit in 
 the mitochondrial matrix . the ph value of the cultivation medium could 
 affect these values , but the exact ph of the assay was not published . for this reason and because the receptor localization 
 is unknown , the ph value in eq 12 was treated 
 as one of the adjustable coefficients .
the selwood data set includes in vitro filaricidal 
 activities against d. viteae of 31 
 antimycin analogues ( table 1 ) , which were determined 
 by monitoring the leakage of incorporated radiolabeled adenine from 
 intact female d. viteae after 120 h 
 of exposure .
the ec50 values for 
 adenine leakage were calculated after 120 h of exposure to a range 
 of drug concentrations at 37 c under neutral conditions .
the 1-octanol / water partition coefficients p were calculated by the clogp program in bio - loom software for neutral molecules and are summarized 
 in table 1 .
the values differ from the original 
 data because of the developments in the 
 clogp software .
the differences are within 0.25 log unit , except 
 for compounds 6 ( table 1 , log pold  log pnew = 1.526 ) , 10 ( 0.770 ) , 12 ( 0.638 ) , 14 ( 1.654 ) , and 26 ( 0.325 ) .
the log p values were used with the belief that they properly reflect 
 the relative lipophilicity of the studied compounds , although the 
 values of log p > 7 were marked in the clogp output 
 as unrealistically high .
ionization decreases the log p values by several units , and most compounds were present mainly 
 as ionized species under physiologic conditions .
our multispecies 
 approach can take into account tautomers and hydrates 
 of aldehydes and ketones ; hence , formation of these species was examined 
 using the sparc web server and was found 
 negligible for all compounds on the basis of the following reasoning . as shown in eq 7 , the binding contribution 
 of each species is given by the product of the association constant kij ( represented by the sum 
 of the association constants kijk for individual modes ) and the 
 species fraction fij . 

the fraction limit for a species to be included in the correlation 
 was set to 10 on the basis of the following considerations . 

the interaction of a rare species with the receptor can release about 
 23 kcal / mol more free energy than that of the prevalent species 
 because both species bind by weak interactions and differ in a single , 
 well - defined structural feature .
for this situation , the product fijkij for the rare species would be less than 1% of the 
 same quantity for the prevalent species .
the ligands are first 
 aligned flexibly to each other in torsional space , and then the conformations 
 produced are rigidly aligned in cartesian space .
pharmacophore and 
 steric bitmaps ( tuplet ) representing 
 h - bonding and steric terms , respectively , along with the total ligand 
 energy , serve as input to a multiobjective fitness function . produced 
 pharmacophores indicated that the salicylamide moieties of all compounds 
 in all species are superimposed in all cases . in the absence of structural 
 and other information on the receptor ,
the most active and , at the 
 same time , one of most rigid analogues , compound 7 ( figure 2 , table 1 ) , was selected 
 as the template for superposition .
conformational analysis was 
 performed using the tripos force field in sybyl with an increment of 10 for all considered torsions . 

when the molecule forms an intramolecular h - bond ( figure 1 ) , either as a neutral species ( oho = c ) 
 or as an ionized species ( nho ) , the first torsion 1 is fixed and only 2 , 3 , and 4 are allowed 
 to rotate in conformational analysis . in the opposite case ,
when analogues 
 have no intramolecular h - bond , all four torsions in figure 2 are considered rotatable .
the approximate minimum 
 conformations were further optimized and mulliken charges were calculated 
 in jaguar using the dft / b3lyp method 
 with a 6 - 31 g * * basis set .
charge and spin multiplicity were entered 
 manually for different protonation states . in this way
open conformation , 
 the mode without the intramolecular h - bond has the same optimal geometries 
 for both neutral and ionized species . in the mm approach
, the 
 user is allowed to enter several possible 
 bound conformations of the template in one optimization run .
the msmm 
 approach extends this option to all species which are present in the 
 solution surrounding the receptor .
the four basic template molecules 
 of compound 7 were superimposed by the atom fit method 
 in sybyl ( figure 3a ) .
all studied compounds 
 do not share a common skeleton ; therefore , for each compound , both 
 species in all modes were superimposed on the templates using the 
 flexs procedure as incorporated in sybyl 
 ( figure 3c ) .
first , a base fragment of the 
 ligand is selected and placed on the template .
second , as the rest 
 of the ligand parts are incrementally built , torsion angles are perturbed 
 to generate new conformations , and each conformation is scored for 
 superposition quality .
the obtained conformations of all compounds 
 were minimized by jaguar using the dft / b3lyp method with a 6 - 31 g * * basis set with all torsions 
 fixed .
the superposition was repeated , and 
 the resulting conformations were used in the comfa analyses .
steric and electrostatic interaction 
 energies xijkl with an 
 sp carbon probe with a + 1 charge were calculated for each 
 compound ( subscript i ) in each species ( subscript j ) and each binding mode ( skeleton conformations  
 ring - flipping conformations , subscript k ) . the probe 
 was placed at each lattice intersection ( subscript l ) of a 3d grid ( 2  in each coordinate direction ) .
the grid 
 has the following coordinates : 7 to + 18  along the x - axis , 121  along the y - axis , 
 and 15 to + 11  along the z - axis .
an 
 energy cutoff of 30 kcal / mol was used to cap the maximum used energies .
the correlation equation is obtained 
 by taking the logarithm of eq 3 , in which the 
 association constant log k is replaced by eq 9 and the disposition function df(p , t ) is given by eq 10 , as 
 combined with eq 11 , in which the fractions 
 are expressed by eq 12 .
the receptor - binding 
 and disposition components have , from the optimization viewpoint , 
 quite different properties : eq 9 has only one 
 form , and the descriptive variables need to be selected from a large 
 pool , while eqs 1012 contain only two variables , which are organized in one of two possible 
 functional forms , depending upon the location of the receptors either 
 in the aqueous phase or in membranes . for the receptor - binding part 
 ( eq 9 ) , the coefficients cl are associated with the grid points and 
 are independent of the species and modes . therefore , the final set 
 of optimized coefficients is independent of the numbering of individual 
 species and modes .
notably , the inclusion of multiple species and 
 multiple modes does not increase the number of optimized regression 
 coefficients cl .
the correlation equation is nonlinear in the coefficients cl in eq 9 and the coefficients a  d , ph and  in eqs 1012 .
all statistical procedures were 
 written in c programming language and integrated in sybyl through 
 the sybyl programming language ( spl ) scripts .
the choice of one of 
 the two implemented optimization methods depends on the total number 
 ( n ) of coefficients c in the calibrated 
 model and on the number of compounds ( n ) .
nonlinear 
 regression analysis is applied when n  n/2 . otherwise , the developed software automatically switches 
 to the pls analysis with a linearized form of eq 9 .
therefore , a forward - selection procedure , 
 conceptually similar to that used before for multimode analysis , was a rational choice . before analysis
, 
 the xijkl variables ( energy 
 columns ) were sorted using the following 
 criteria : ( 1 ) high and sustained variability , ( 2 ) the minimal number 
 of colinear columns with similar information , and ( 3 ) even distribution 
 of selected grid points around the ligands . sustained variability 

means that the energy values cover the whole interval more or less 
 evenly and are not clustered .
an extreme case is the situation when 
 all energies in a given column are equal ( usually zero ) and only one 
 mode has a different energy .
these singularities originate when only 
 one molecule protrudes into a subspace and other molecules do not 
 affect the probe interaction energies in that subspace .
singular molecules 
 need to be eliminated from the analysis because they do not provide 
 statistically significant information about the poorly covered subspace .
the model calibration can be steered by user - defined inputs , for 
 which the default values are shown in parentheses .
the process starts 
 with a quick scan through the models consisting of a few ( four ) variables 
 which are randomly selected from the top variables ( 10% ) .
the initial 
 values of the coefficients ( 0.1 ) are systematically evaluated 
 by a grid search . in this step ,
no optimization is applied and the 
 correlation equation is evaluated for the initial coefficients . for 
 the best models ( top 10% r ) ,
the coefficients 
 are optimized . at each of the following steps , a reduction of the 
 number of coefficients
is attempted : the coefficients , which do not 
 lead to a decrease in the r value , are 
 eliminated .
the best models ( top 5% r ) are developed by a gradual addition of groups of a few ( three ) 
 variables until all variables from the selected set ( top 10% ) are 
 used .
the procedure is finalized by fine - tuning of the best models 
 ( top 5% r ) by addition of single variables . 

the best model is selected on the basis of the following criteria : n , r , q for the leave - one - out cross - validation ( applied to the training 
 set only to eliminate unstable models ) , and the standard errors of 
 the parameters .
 we present the cellular quantitative structure  
 activity 
 relationship ( cell - qsar ) concept that adapts ligand - based and receptor - based 
 3d - qsar methods for use with cell - level activities . 
 the unknown intracellular 
 drug disposition is accounted for by the disposition function ( df ) , 
 a model - based , nonlinear function of a drug s lipophilicity , 
 acidity , and other properties . 
 we conceptually combined the df with 
 our multispecies , multimode version of the frequently used ligand - based 
 comparative molecular field analysis ( comfa ) method , forming a single 
 correlation function for fitting the cell - level activities . 
 the resulting 
 cell - qsar model was applied to the selwood data on filaricidal activities 
 of antimycin analogues . 
 their molecules are flexible , ionize under 
 physiologic conditions , form different intramolecular h - bonds for 
 neutral and ionized species , and cross several membranes to reach 
 unknown receptors . 
 the calibrated cell - qsar model is significantly 
 more predictive than other models lacking the disposition part and 
 provides valuable structure optimization clues by factorizing the 
 cell - level activity of each compound into the contributions of the 
 receptor binding and disposition . 
Introduction
Results and Discussion
Conclusions
Methods