. however , several precorneal factors such as lacrimal secretion ( tear turn over and reflux tearing ) , tear protein binding , ph , shorter contact time , and other corneal constraints limit drug penetration .
moreover , presence of various uptake and efflux transporters in cornea also reposted to further complicate the ocular bioavailability . therefore
conventionally , the drugs intended for oral administrations have been developed in consideration of their physicochemical properties .
this enables to enhance the pharmacokinetic properties , efficacy and reduces the toxicity of lead compound . in drug discovery exploitation of in silico techniques to expedite the process of lead optimization in drug discovery is rampant . among such techniques , quantitative structure property relationship ( qspr )
approach correlates the biological activity of a molecule with its physicochemical properties through variety of descriptors . in recent years
, qspr approach has been exploited for the development of models to predict penetration of drugs across physiological barriers such as cns , blood , and intestinal .  
the drugs used for ophthalmic indications are arbitrarily developed from the oral or systemic indications , rather than systematically ocular specific studies . to date , very few drugs have been designed , developed , and studied for ocular specific use . however , the ocular pharmacokinetics of a drug is known to be different and complicated compared to any other indications .
thus , in this context a drug intended for oral use is expected to behave differently when used empirically for the topical application . as physicochemical properties such as lipophilicity , molecular size , charge , degree of ionization , solubility , and ph , affect the rate and extent of corneal permeability .    in ophthalmology
these agents were initially discovered , designed , and developed for systemic infections and further extended for ophthalmic use .
their broad - spectrum activity , bactericidal property , better ocular penetration , and relative safety embark its use in ophthalmology .
most of the fluoroquinolones for topical use lack regress understanding of their corneal penetration , residence time , required spectrum , optimum frequency of usage , and corneal toxicity despite of their widespread use in ophthalmics . therefore
, an emphasis on qspr strategy to optimize ocular pharmacokinetic properties along with antimicrobial efficacy is desirable .
previously reported qspr models to predict corneal permeability for congeneric and noncongeneric drugs have been developed based upon in vitro studies .
a weak correlation is reported to exist between the in vitro and in vivo studies [ 8 , 9 ] .
eventually their applicability of these models to predict in vivo corneal penetration remains unclear .    in present study we developed novel qspr based in silico model to predict corneal permeability for fluoroquinolones based upon in vivo
the applicability of previously reported models based upon in vitro data to predict corneal permeability for fluoroquinolone was also studied .
furthermore , the generated qspr model was evaluated for its aptness using the other training sets ( -blockers ) .
pure samples of norfloxacin , ciprofloxacin hcl , gatifloxacin , and lomefloxacin hcl were generously gifted by dr .
reddy labs ( hyderabad , india ) , lupin labs ( pune , india ) , sun pharmaceuticals ( mumbai , india ) , and organics ltd . , ( hyderabad , india ) , respectively .
gratis samples of ofloxacin , pefloxacin mesylate , and sparfloxacin were obtained from cipla ltd . , ( mumbai , india ) .
moxifloxacin and levofloxacin were obtained as a generous gift from capital pharma ( baddi , india ) .  
other chemicals used in the study were of analytical grade and procured from standard drug companies .
a total of nine fluoroquinolones ( table 1 ) were randomly divided into 2 groups wherein , group a consists of ofloxacin , sparfloxacin , pefloxacin mesylate , and gatifloxacin and group b consists of norfloxacin , ciprofloxacin hcl , lomefloxacin hcl , levofloxacin , and moxifloxacin . in both groups ,
thus , the total fluoroquinolones concentration in group a and group b were 0.4% and 0.5% , respectively .
sterile boric acid ( 1.9% w / v ) in water was used as the aqueous media and the final formulations were filtered using 0.22   filter and autoclaved further before use .  
study protocol and experimental procedures were approved by the institutional animal ethics committee of all india institute of medical sciences ( aiims ) , new delhi , india .
new zealand albino rabbits of either sex ( 1.52.0  kg ) were obtained from central animal facility , aiims .
animals were housed at standard laboratory conditions temperature - controlled room at 24  2c and humidity 55  15% and given food and water ad libitum .
all experiments were performed in accordance to the association for research in vision and ophthalmology ( arvo ) statement for the use of animals in ophthalmic and vision research .
the sterile cocktail formulations of group a and group b were individually instilled ( 50  l ) on the lower fornix of rabbit eyes ( n = 4 ) with the help of a calibrated micropipette .
aqueous paracentesis was performed under the influence of topical anesthesia at 5 , 15 , 30 , 60 , 120 , and 240  min after the instillation of cocktail formulation . for each time point , a volume amounting to 50  l of aqueous humor was aspirated through the corneal surface .
a thermo finnigan ( thermo electron corporation , usa ) hplc equipped with degasser , quaternary pump , autosampler , and pda detector was employed for quantification of fluoroquinolones in samples . in the chromatographic quantification
,   analytical separation was performed using a c18 symmetry shield column ( 4.6  150  mm , 5  m , waters , usa ) under a gradient flow of methanol , acetonitrile , and   potassium phosphate buffer ( 20  mm , ph 2.5 ) at different ratio and time . for each spiked compound
an external calibration curve was plotted and the analyte 's spectra was assessed by matching them with custom made pda spectra of inbuilt library of chromquest version 4 ( thermo electron corporation , usa ) .  
samples were deproteinized with pure acetonitrile ( ratio of 1  :  2  v / v ) , vortexed , and centrifuged at 3500  g for 10  min .
the dried concentrate was reconstituted with 100  l mixture of water and acetonitrile ( 1  :  1 ) , and 20  l of the obtained supernatant was injected for quantification .
available literature reveals existence of two models correlating the corneal permeability of compounds with their physiochemical properties .
therefore , present study evaluated the suitability of these reported models to predict in vivo corneal penetration for fluoroquinolones .
the first model reported by yoshida and topliss   was based upon two molecular descriptors , log  p and   log  d to predict corneal permeability coefficient ( logpc ) .
algorithm ( 1 ) is proposed to predict corneal permeability for noncongeneric compounds 
 ( 1)logpc=0.404(  0.114)log  p+0.141(  0.090)log  d  3.862(  0.451 ) , 
									 wherein logpc denotes permeability coefficient , log  p expresses the difference between the octanol - water partition coefficients ( log  poctanol ) and alkane - water partition coefficients ( log  palkane ) , and   log  d denotes dissociation constant   as reported , log  p was calculated using logpstar software in training sets of 32 diverse noncongeneric compounds including steroids and -blockers . since logpstar was currently unavailable and obsolete .
log  p was derived as the difference in log  p(o / w ) to log  p(cyclohexane / water ) by using shake flask method given in oecd guidelines of chemical testing ( no .
the other molecular descriptor log  d was calculated using  
 ( 2)log  d(ph)=log  plog  ( 1 + 10(pkaph)).log 
molecular descriptors ( log  p and log  d ) were derived for the studied fluoroquinolones ( norfloxacin , ciprofloxacin , lomefloxacin , ofloxacin , levofloxacin , sparfloxacin , pefloxacin , gatifloxacin , and moxifloxacin ) and logpc was determined using algorithm ( 1 ) .
the derived logpc from algorithm ( 1 ) was correlated with that obtained from controlled in vivo experiment in rabbits .
model 2 evaluated reported by fu and liang   was based upon charge and molecular volume as the molecular descriptors to predict logpc .
algorithm ( 3 ) was reported to predict corneal permeability for noncongeneric compounds 
 ( 3)logpc=5.566qh2 + 3.027qh0.155qo ,
n  9.413104  v4.278 
									 wherein logpc denotes permeability coefficient ,  qh   is sum of the absolute values of net atomic charge of hydrogen atom , and qo , n   is sum of the absolute values of the net atomic charges of oxygen and nitrogen atoms .
the charge ( qh , qh , qo , n ) for all fluoroquinolones was calculated by using gamess software and molecular volume by drug design software developed at super computing facility , indian institute of technology , new delhi .  
structures of all fluoroquinolones were drawn hyperchem version 11.0 and optimized the geometry to lowest energy state .
the net charge on each atom was calculated as the sum of all atoms present in the particular structure .
the molecular descriptors used in algorithm ( 3 ) were derived for the studied nine fluoroquinolones to predict logpc .
the derived logpc from algorithm ( 3 ) was also correlated with in vivo experimentally obtained logpc .
a novel qspr model was generated using pooled molecular descriptors determined using in vitro , in vivo , and in silico approaches for fluoroquinolones .    
 in vitro datapartition coefficient ( log  p )
107 and 117 ) using biphasic system of octanol / water at 25c and 37c . 
 
partition coefficient ( log  p ) was determined using oecd shake flask method for chemical testing ( no .
107 and 117 ) using biphasic system of octanol / water at 25c and 37c . 
 in vivo datapermeability coefficients ( logpc ) were obtained from controlled in vivo experiment conducted in rabbits using cassette dosing ( n - in - one ) approach . 
 
permeability coefficients ( logpc ) were obtained from controlled in vivo experiment conducted in rabbits using cassette dosing ( n - in - one ) approach . 
 in silico datadifferent molecular descriptors
were generated using softwares like cache scientific ( fujitsu version 6.1.12.33 , japan ) , acd / chemsketch ( freeware version 10 ) , chemdraw and chem biodraw ultra from cambridge soft ( trial version ) , calculator plugins of chem axon 's marvin version 5.2.5.1 , chem axon ltd .
all fluoroquinolone structures were drawn in respective workspace and standard molecular mechanics were run before geometry optimization .
the   descriptors like molecular weight , log  p , topological polar surface area ( tpsa ) , molar refractivity , number of  h-bond donors / acceptor , dipole moment , lowest unoccupied molecular orbitals ( lumo ) , highest unoccupied molecular orbital ( humo ) , gap , molecular volume , connolly accessible area , connolly molecular area , principal moment , dipole moment , molecular weight , wiener index , melting point , polar surface area , number of rotatable bonds and molar refractivity , molar volume , polarizibility , parachor , index of refraction , surface tension , density , monoisotopic mass , nominal mass , average mass , apka , and charge on the each   atom , that is , qn , qo , n , qh , qf and qc were extracted using different kind of softwares . 
 
different molecular descriptors were generated using softwares like cache scientific ( fujitsu version 6.1.12.33 , japan ) , acd / chemsketch ( freeware version 10 ) , chemdraw and chem biodraw ultra from cambridge soft ( trial version ) , calculator plugins of chem axon 's marvin version 5.2.5.1 , chem axon ltd .
all fluoroquinolone structures were drawn in respective workspace and standard molecular mechanics were run before geometry optimization .
the   descriptors like molecular weight , log  p , topological polar surface area ( tpsa ) , molar refractivity , number of 
h-bond donors / acceptor , dipole moment , lowest unoccupied molecular orbitals ( lumo ) , highest unoccupied molecular orbital ( humo ) , gap , molecular volume , connolly accessible area , connolly molecular area , principal moment , dipole moment , molecular weight , wiener index , melting point , polar surface area , number of rotatable bonds and molar refractivity , molar volume , polarizibility , parachor , index of refraction , surface tension , density , monoisotopic mass , nominal mass , average mass , apka , and charge on the each   atom , that is , qn , qo , n , qh , qf and qc were extracted using different kind of softwares . to ensure the suitability of newly developed qspr model ,
the congeneric compounds used by yoshida and topliss   and fu and liang   were pooled .
all the congeneric compounds ( -blockers , n = 15 ) were pooled and molecular descriptors used in newly developed qspr model were extracted .
the -blockers pooled include acebutolol , alprenolol , atenolol , betaxolol , bevantolol , bufuralol , levobunolol , metoprolol , nadolol , oxprenolol , penbutolol , pindolol , propanolol , sotalol , and timolol .
the logpc derived using newly developed qspr model was correlated with reported logpc for all the -blockers .
two different hplc - pda method were developed and validated to elute all fluoroquinolones in group a and b.   for the analysis of group a ( ofloxacin , sparfloxacin , pefloxacin , and gatifloxacin ) the gradient mobile phase consisted of different ratios of methanol , acetonitrile , and potassium phosphate buffer ( 20  mm , ph 2.5 ) over the period of 12  min ( table 2 ) .
for the analysis of fluoroquinolones in group b ( norfloxacin , ciprofloxacin , lomefloxacin , levofloxacin , and gatifloxacin ) the gradient mobile phase consisted of different ratios of methanol , acetonitrile , and potassium phosphate buffer ( 20  mm , ph 2.5 ) over the period of 10  min ( table 2 ) .  
the representative chromatograms of all fluoroquinolones eluted in group a and group b are shown in figures 1(a ) and 1(b ) .  
the validation parameters regarding the accuracy and precision were found to be within the allowable limits according to ich guidelines for hplc in bioanalysis . the mean concentration versus time plot for all fluoroquinolones ( group a and b )
the derived pharmacokinetics parameters like cmax , tmax , auc , logpc at 30  min and 240  min generated for all fluoroquinolones are tabulated in table 3 . both molecular descriptors ( logp and logd ) derived for fluoroquinolones in algorithm ( 1 ) to derive logpc showed a weak spearman correlation ( 0.133 ) with that obtained from in vivo experiment ( table 4 ) .  
the weak correlation was observed at 30  min ( r = 0.0699 ) and 240  min ( r = 0.0137 ) .
the statistically insignificant correlation suggests that algorithm ( 1 ) is unable to appropriately predict corneal permeability for fluoroquinolones ( figure 3(a ) ) .  
algorithm ( 3 ) reported by fu and liang   was employed to derive logpc for all studied fluoroquinolones ( table 4 ) .
a very weak spearman correlation of 0.134 was observed between the logpc derived experimentally at both 30  min and 240  min with that logpc derived using algorithm ( 3 ) ( figure 3(b ) ) .
the statistically insignificant correlation suggests that algorithm ( 3 ) is unable to appropriately predict corneal permeability for fluoroquinolones .  
a total of 72 molecular descriptors were extracted for all nine topically studied fluoroquinolones ( norfloxacin , ciprofloxacin , lomefloxacin , ofloxacin , levofloxacin , sparfloxacin , pefloxacin , gatifloxacin and moxifloxacin ) using in vitro , in vivo , and in silico approaches .
all sets of data were subjected to multilinear regression ( mlr ) statistical analysis by sigma stat software ( version 3.5 , germany ) . for the generation of algorithm
the in vivo data of logpc calculated for absorption phase ( 30  min ) and elimination phase ( 240  min ) was used .
the algorithms developed with log  p and apka either with gap ( algorithms ( 4 ) and ( 5 ) ) and or with tpsa ( algorithms ( 6 ) and ( 7 ) ) exhibited good correlation 
 ( 4)logpc  30  min  = 13.972+(1.529log  p )  (1.375apka)+(1.308gap),r=0.908  rsqr=0.825  adj  rsqr=0.720 , 
 ( 5)logpc  240  min  = 9.946+(1.368log  p )  (1.429apka)+(0.952gap)r=0.940  rsqr=0.883  adj  rsqr=0.813 , 
							 wherein logpc denotes logarithm of permeability coefficient , log  p is partition coefficient at water 25  1c for 30  min , gap is the difference in humo and lumo energy levels , and apka is acid dissociation constant .
algorithms ( 6 ) and ( 7 ) were developed using logp , tpsa , and apka as molecular descriptor at 30  min and 240  min . 

( 6)log  pc  30  min  = 1.453+(1.726log  p )  (0.708apka)+(0.0104tpsa)r=0.934  rsqr=0.872  adj  rsqr=0.796 , 
 ( 7)log  pc  240  min  = 2.726+(1.439log  p )  (0.672apka)+(0.00421tpsa)r=0.937  rsqr=0.877  adj  rsqr=0.803 , 
							 wherein logpc denotes logarithm of permeability coefficient , log  p as partition coefficient at water 36  1c for 5  min , tpsa as topological polar surface area , apka is acid dissociation constant . 

figure 4 shows the pictorial representation of newly developed qspr model using fluoroquinolone as model group .   in the four newly developed algorithms ( algorithms ( 4 ) , ( 5 ) , ( 6 ) , and ( 7 ) ) log  p and apka are common molecular descriptors , signifying the key descriptors affecting penetration of fluoroquinolones across the cornea .
algorithms ( 4 ) , ( 5 ) , ( 6 ) , and ( 7 ) showed a positive correlation with log  p and inverse correlation with apka .  
tpsa and gap also showed a positive correlation with permeability coefficient in all newly developed algorithms .
newly developed qspr model showed a positive spearman correlation of 0.831 and 0.887 between the newly developed algorithms ( 4 ) and ( 5 ) with already reported logpc ( figure 5(a ) ) .   a positive spearman correlation of 0.881 and 0.803 between the logpc generated for -blockers using newly developed algorithms ( 6 ) and ( 7 ) and reported logpc ( figure 5(b ) ) .
conventionally , antimicrobial drugs developed and approved for systemic infections are extended for ocular infections .
an antimicrobial agent having good corneal penetration and efficacy is desired in preventing sight threatening infections .
it is well known that less than 5% of the topically applied drug penetrates through the cornea .
therefore , there is an urgent need to understand the constraints exerted by the eye for the development of an ocular specific antimicrobial agent . in present study ,
qspr approach has been used to comprehend the physicochemical factors affecting corneal permeability for topically applied drugs .  
an attempt was made in present study to evaluate the suitability of in silico models in predicting the in vivo corneal permeability of fluoroquinolones . to ascertain the obtained results ,
additionally , in vivo corneal permeability was determined in rabbits employing cassette dosing approach , a high throughput pharmacokinetic screening technique which has been exploited for various indication [ 1214 ] .
so far this approach has been limited to in vitro and few in vivo models in ophthalmic drug research [ 1517 ] . however , for the first time , we employed cassette dosing technique to study the in vivo pharmacokinetic profile of topically applied fluoroquinolones and to derive a controlled in vivo permeability coefficient nine topically used fluoroquinolones were dissolved in two cassettes : group a with four and group b with five fluoroquinolones .
being weakly basic in nature fluoroquinolones are expected to exist in ionized form at ph 4.5 .  
therefore , ph of both formulations was maintained at 5.0 and osmolarity as 307  mosm / l using boric acid .
boric acid ( 1.9% ) has been reported to be an appropriate vehicle for the preparation of ophthalmic solutions having basic nature .
in addition , it is reported to avoid any interaction between fluoroquinolones and di / monovalent cations .   in the literature
the first model was reported by yoshida and topliss   based upon log  p and log  d as molecular descriptors .   in this model
, log  p mainly correlates with the solute hydrogen bonding acidity or basicity and to lesser extend dipolarity or polarizability .
the second model was reported by fu and liang   was based upon charge and molecular volume as the molecular descriptors .
unfortunately , both the earlier reported models were unsuitable to predict in vivo corneal permeability of fluoroquinolones . a poor correlation between the permeability coefficient derived using reported models [ 10 , 11 ] with that derived from present in vivo study was observed .
this may be due to the fact that reported models were developed based upon permeability coefficients ( logpc ) pooled from various in vitro studies .
the in vitro conditions denote a static system rather than actual dynamic conditions which exists in eye .
moreover , the involvement of various drug transporters and precorneal factors is not considered in such studies and are also believed to have major role . thus , reported models [ 10 , 11 ] based upon in vitro corneal permeability are unable to correlate with in vivo corneal permeability for fluoroquinolones .
therefore , a new in silico model based upon in vivo permeability coefficient data was felt desirable .
also the in silico model should be able to correlate with parameters like ionizing property , transporter susceptibility , and lipophilicity , precorneal ph of compound .
a novel qspr model was developed based upon in vivo corneal permeability along with molecular descriptors like log  p , apka , gap , and tpsa .
civiale and coworkers   also reported that corneal permeation process can be confined at the ocular epithelium layer .
studies have been reported that in corneal epithelium the drugs are expected to undergo transcellular pathway [ 21 , 22 ] . whereas the penetrating molecules are expected in hydrophilic form as a result of ph or after hydrolysis due to enzymes ( by prodrug attempt ) to cross hydrophilic stroma .
the dissociation constant ( pka ) of the compound determines the hlb ( hydrophilic / lipophilic balance ) in the cornea .
based upon the presence of ionizable / functional groups molecules can posses more than one pka .
an assumption was made in the newly developed qspr model that for fluoroquinolones apka has more implication on the availability of the species .
other studies also report that corneal penetration can be enhanced by selecting the drug molecule with appropriate pka and offering optimal lipid solubility [ 23 , 24 ] . in general , adjusting ph so that a drug is mostly in the unionized form increases its lipophilicity and thus , its transcellular permeability , and ocular absorption .  
another molecular descriptor gap , which is difference in energy between ehumo and elumo , has also reported to be an important stability index and related to transporters susceptibility .
the ehumo measures the electron donating and elumo measures electron accepting property of the molecule .
a humo and lumo energy separation has been used as a conventional measure of kinetic stability for various -electron systems .
a large gap has been reported to relate with high stability for a molecule in the sense of its lower sensitivity in chemical reaction [ 26 , 27 ] .  
tpsa is defined as the sum of surfaces of polar atoms in a molecule and known to correlate with transporter susceptibility .
tpsa makes use of functional group based upon large database of structures that avoids the need to calculate ligand 3d structure or to decide which one is relevant biological conformation .
therefore , in this analysis , tpsa has been taken into account to define the transcorneal penetration of congeneric compounds .
fernandes and coworkers   suggested that compounds with high tpsa are transported , while those with low tpsa are not .
moreover , conjugation to compounds like gsh is reported to increase the tpsa values as a favoring transport mechanism .
the algorithm developed either with tpsa or gap proved to predict the intraocular penetration appropriately as compared with other molecular descriptors tried with highest degree of correlation ( r > 0.9 )   the applicability of the newly developed algorithms ( 4 ) , ( 5 ) , ( 6 ) , and ( 7 ) on other sets of compounds apart from fluoroquinolones was also tested .
the congeneric compound trial sets taken for this analysis belong to the category of -blockers where the ioniziability and ph - dependent changes in the lipophilicity are not much of concern .
their structures predominately lacking primary amino groups or carboxylic acids ( except atenolol having primary amine ) therefore , ph - induced changes are not expected to play a major role .
this study further evaluated the applicability of the developed algorithm on the noncongeneric compounds using similar training sets .
the newly developed in silico model is based upon in vivo data and hence may predict corneal permeability for congeneric compounds other than fluoroquinolone more appropriately .
the previously reported algorithms based on in vitro data failed to predict in vivo corneal permeability for fluoroquinolones .
a novel qspr model consisting of four new algorithms were developed using gap , tpsa , logp , and apka as molecular descriptors to predict in vivo corneal permeability .
the hypothesis generated showed high degree of applicability to predict transcorneal penetration as it was based upon the in vivo corneal permeability coefficients data .
moreover , the developed model was also found to predict corneal permeability of the congeneric -blockers ( r > 0.6 ) reported in the literature .
further studies are in progress to evaluate its utility in large number of other congeneric compounds .
 this study was undertaken to determine in vivo permeability coefficients for fluoroquinolones and to assess its correlation with the permeability derived using reported models in the literature . 
 further , the aim was to develop novel qspr model to predict corneal permeability for fluoroquinolones and test its suitability on other training sets . 
 the in vivo permeability coefficient was determined using cassette dosing ( n - in - one ) approach for nine fluoroquinolones ( norfloxacin , ciprofloxacin , lomefloxacin , ofloxacin , levofloxacin , sparfloxacin , pefloxacin , gatifloxacin , and moxifloxacin ) in rabbits . 
 the correlation between corneal permeability derived using in vivo studies with that derived from reported models was determined . 
 novel qspr - based model was developed using in vivo corneal permeability along with other molecular descriptors . 
 the suitability of developed model was tested on -blockers ( n = 15 ) . 
 the model showed better prediction of corneal permeability for fluoroquinolones ( r2 > 0.9 ) 
  as well as -blockers ( r2 > 0.6 ) . 
 the newly developed qspr model based upon in vivo generated data was found suitable to predict corneal permeability for fluoroquinolones as well as other sets of compounds . 
1. Introduction
2. Materials and Methods
3. Results
4. Discussion
5. Conclusions