Ex-militia fighters in post-war Lebanon

Dima de Clerck

After the end of Lebanon's war (1975Lebanon's war ( -1990) ) a political decision to disarm and demobilize all militias was taken on 28 March 1991. An Amnesty Law (26 August 1991) covered all political and wartime crimes prior to 28 March. Most militias had officially handed over heavy weaponry, headquarters and barracks to Lebanese or Syrian army officials ahead of the 30 April deadline. But some 50,000 militia fighters from all denominations had 'vanished'estimates differ regarding the 1990 numbers of militia fighters among Lebanon's estimated population of around 3.25 million, from 1.25 per cent (40,000) to 3 per cent (nearly 100,000). In reality, post-war militias sold armaments abroad, hid heavy weapons in remote mountainous areas, kept light and medium weapons to hand and continued to train potential fighters.

Demobilisation was highly selective, largely because of Syria's interest in keeping its proxies armed. Exemptions included Palestinian militias and Hezbollahas a resistance force against ongoing Israeli occupation. The Israeli proxy, the South Lebanon Army (SLA) rejected a proposal for its integration into the regular forces. Continued collaboration with Israel prevented them from benefiting from Lebanon's Amnesty Law. When Israel withdrew from south Lebanon in 2000, many SLA members fled to Israel or emigrated.

Today, sectarian groups in Lebanon show characteristics of minorities 'under siege', anxious about their future and wary of rivals within and enemies without. This mindset perpetuates the militarization of Lebanese society, while lasting political stalemate hampers the consolidation of peace.

Reintegration into the state

As part of the official demobilisation effort, on 5 May 1991 the government offered to 'rehabilitate' 20,000 militia fightersdivided between Christians and Muslimsin administrative and military state institutions. Law 88 (June 1991) allowed the integration of 6,000 militia fighters (out of which 5,000 Muslims) into the army and interior security forces. An estimated 2,000 were recruited into the civil administration, but no further phases of demobilisation followed.

Syrian stewardship of post-Taif Lebanon was an important factor in dealing with the different militias. The primary 'winners' in the rehabilitation process were Syrian allies and clients, including the Druze Progressive Socialist Party, Shia Amal, the Frangieh's Marada, followers of Elias Hobeika -former commander of the Lebanese Forces (LF) militia turned Syrian ally in 1986, the Sunni Popular Nasserist Organisation, and the secular Baath and Syrian Social Nationalist Parties. Former militia warlords, now cemented as sectarian leaders, were able to place their supporters at all levels of national institutions. Insertion and amnesty gave peacetime legitimacy to militia fighters. Along with the persistence of 'gun culture' and predatory behaviour in society, militia fighters were able to pervade the administration and further corrupt it, instead of becoming 'civilianised'.

The leaders of the defeated LF found themselves in a weaker position to negotiate integration of their fighters. Their incorporation into the army failed and emigration was facilitated for hundreds of undesirable LF elements. Only a few who had the required credentials and were backed by post-war political Muslim elites were able to join the public sector. The government's neglect of sustained reintegration is attributable amongst other things to its fear from new polarization risks in the Army, and from intensifying ex-combatants' self-perceptions as a distinctive social group capable of challenging sectarian leaders' authority. With no comprehensive strategy for insertion, the civilian administration was encumbered with a surplus of recruits and a depleted budget. Rafiq al-Hariri's governments (1992-98) granted his Sunni, Shia and Druze allies ministries, administrative positions and funds, but abandoned further plans to insert militia fighters. Hariri feared he could not control them, since he had no militia of his own while exmilitia leaders ran the core of the administration.

Many ex-militia fighters who successfully enrolled in the army were posted to their hometowns, which effectively legitimised their wartime causes and allowed for bonds to be created between the sectarian population and the military institution. In some cases, ex-militia fighters moved from secular militias to religious armed groups: jihadist networks for Sunnis and Hezbollah for Shia. Many ex-combatants of all factions turned to religion more generally, which often played a major role in their recovery. Some concentrated on theological studies to better understand the religion in whose name they fought; others became monks or sheikhs.

It is common for ex-fighters (including those living abroad) to have maintained strong group identities and kept ties with their former leaders. When militias were 'civilianised' in the 1990s, morphing into political parties, ex-fighters were encouraged to rejoin the newly reconditioned structures. Some even got elected to parliament; others as members of local municipalities.

Reintegration into society

Former militia fighters have had uneven experiences reintegrating back into Lebanese society and economy. Former militia leaders were able to place their men in private firms in Lebanon or abroad. Demand for their services was high during the 1992-96 post-war economic boom, due to the absence of a skilled workforce in Lebanon owing to massive emigration and wartime disruptions, such as schooling. Some were directed towards domestic or foreign private security companies, for instance in Iraq from 2003. Religious institutions and their associated social and educational networks employed some ex-fighters, but fewer than expectedprobably fearing this might leave the impression that they condoned their wartime conduct.

de Clerck Dima, 2012, "Ex-militia fighters in post-war Lebanon", in Accord Positive peace for Lebanon: reconciliation, reform and resilience, Issue 24 (2012), London, p.24-26.

Society has looked upon former militia in different ways. Ex-fighters described by Najib Hourani as 'iconic' -poor and somehow 'pre-modern'as well as those reputed as having been especially sanguinary, have struggled most to find employment. Children of the upper classes found a safe haven in their families regardless of whatever crimes they had committed. Those on society's bottom rungs found it harder to re-socialise: their increased wartime status and power did not upgrade them in their families' eyes, especially as the army would not integrate them. Nevertheless, strong kinship ties have helped people to cope in times of crisis, particularly in rural communities and city suburbs, where families live close together. Families filled the void when there was no institutional support for reintegration and caring for the wounded and disabled after political parties stopped paying indemnities or hospital fees.

Young men became involved in the war believing they were protecting their community and way of life. Once it was over, however, some found themselves neglected by those communities. The Sunni Murâbitûn who fought alongside the National Movement, for example, were disregarded by the new Sunni elite. In contrast, the Druze community honoured its fighters as having acted as shields against their adversaries.

Today, few ex-fighters are inactive; 40 per cent are self-employedas businesspeople, contractors, carpenters, plumbers, mechanics, taxi-drivers, etc. Around 15 per cent are employed by private companies or banks. Others (mostly women) are in social work and entertainment. Those who resumed their studies achieved professional conversion more easily. According to a 2008 UMAM poll, 72.3 per cent of fighters who stayed in Lebanon claimed to have achieved complete integration in their environment, even if 38 per cent do still consider emigration, mainly for economic reasons.

Psychological and ethical challenges

In the absence of a viable public rehabilitation policy, ex-combatants were left to struggle with psychological disorders on their ownpost-traumatic stress or depression. Very few ex-militia fighters have undergone psychological treatment. Many have kept war reflexes, suffer from severe paranoia or feel vulnerable without weapons. Alcohol, drugs, domestic violence and divorce are common. Dealing with authority in a work environment is often problematic. Some ex-fighters have become involved in illegal or criminal activities, have ended up murdered or dead from drug overdoses or suicide. An estimated 12-20 per cent of ex-fighters have served prison sentences for murder, rape, assault with a deadly weapon, crimes related to state security, smuggling, fraud and drugs.

Nevertheless, many ex-fighters claim to have reintegrated reasonably well into Lebanon's post-conflict reality. If some blame the war for their troubles, most avoid talking about it. They tend to evade responsibility for violence through denial, and the state-sponsored 'collective amnesia' certainly helps. Very few concede that their wartime actions were horrific, sedating themselves by adhering to their self-proclaimed innocence. According to the UMAM survey, 57 per cent say they have no regrets at all, and 62 per cent will not apologise for their deeds.

Conclusions

The lack of a comprehensive rehabilitation programme has helped encourage new young militia recruits from post-war generations, who carry their fathers' frustrations and romanticise the civil war. The main pre-war incentives for militia mobilisation in the early 1970sfrustration, fear of the enemy within, lack of education, unemploymentremain today. Political tensions and poverty have deepened since 2005. Fuelled by propaganda, these dynamics put pressure on people and could help to propel them towards violence.

Post-war, militias are able to recruit and train a new generation of young by exploiting their 'heroic' image, a delusion facilitated by the widespread unwillingness to speak about horrors of war. By neglecting 'demobilisation of the mind', sectarian leaders have kept new and former fighters ready to mobilise at any time: 33 per cent in the UMAM poll declared their readiness to fight another war. Some harbour frustration about past defeats and think of revenge and continue to train for combat along with their children.

In the two last decades the deliberate deficiency of state demobilisation, disarmament and reintegration has not been addressed by international engagement, by states or NGOs -except isolated and extremely limited programmes such as was introduced by Moral Re-Armament, dedicated to effecting social change through personal change.

What is urgently needed is proactive international engagement to help complete the disarmament and reintegration of ex-combatants into civilian life as part of broader peace building strategy, assisting them reconcile their personal perspectives with Lebanon's current social reality, and combating the prevailing gun culture. This could start with a thorough census of all ex-combatants and their grown-up children, to identify the most vulnerable (ie the least integrated and most zealous) and offer them psychological and economic assistance.

Working with ex-fighters and involving them in reconciliation activities is the best way to endow Lebanese society with 'bottom-up' immunity to the country's tendency to war. Without this, there can be no guarantees for peace in Lebanon.

  de Clerck Dima, 2012, "Ex-militia fighters in post-war Lebanon", in Accord Positive peace for Lebanon: reconciliation, reform and resilience, Issue 24 (2012), London, p.24-26.


Clifford W Fong Eigenenergy
email: cwfong@internode.on.net

A novel predictive model for the anti-bacterial, anti-malarial and hERG cardiac QT prolongation properties of fluoroquinolones

Keywords: Fluoroquinolones, anti-bacterial, anti-malarial, hERG cardiac QT prolongation, quantum mechanics Abbreviations

FQs Fluoroquinolones, BBB Blood brain barrier, TdP Torsades de Pointes, GI gastrointestinal tract, IC 50 Half maximal Inhibitory concentration , MIC Minimum inhibitory concentrations, ZW zwitterion, steady state uptake (R ss ), F blood plasma concentrations, CBP Chronic bacterial prostatis, BSA bovine serum albumin, MRP2 Multidrug resistance-associated protein 2 or specific organic anion transporter 1 (cMOAT) or ATP-binding cassette sub-family C member 2 (ABCC2), OATP organic anion uptake transporter, OCT organic cation influx transporter, ΔG desolvation free energy of water desolvation, ΔG lipophilicity free energy of lipophilicity or hydrophobicity, ΔG desolv,CDS free energy of water desolvation of the cavitation dispersion solvent structure (CDS), ΔG lipo,CDS free energy of lipophilicity or hydrophobicity for the CDS, DM dipole moment DM, SASA solvent accessible surface area, R 2 multiple correlation coefficient, F the F test of significance, SEE standards errors for the estimates, SE(ΔG desolvation ) standard errors of ΔG desolvation , SE(ΔG lipophilicity ), standard errors of ΔG lipophilicity , SE(Dipole Moment) standard errors for dipole moments, SE (Molecular Volume) standard errors for molecular volumes as calculated from "t" distribution statistics, QM quantum mechanics, Where R 2 = 0.921, SEE = 0.293, SE(ΔG solvation ) = 0.062, SE(ΔG lipophilicity ) = 0.115, SE(Dipole Moment) = 0.036, SE(Molecular Volume) = 0.005, F=11.61, Significance F = 0.018 Equilibrium solubility of 9 floxacins: Sarafloxacin, Norfloxacin, Difloxacin, Enrofloxacin, Lomefloxacin, Ciprofloxacin, Sparfloxacin, Danofloxacin treated as neutral species, Ofloxacin as zwitterion Equation 9 Log solubility = 0.085 ΔG solvation + 0.188 ΔG lipophilicity -0.006 Dipole Moment -0.009 Molecular Volume + 5.684 Where R 2 = 0.838, SEE = 0.419, SE(ΔG solvation ) = 0.121, SE(ΔG lipophilicity ) = 0.170, SE(Dipole Moment) = 0.172, SE(Molecular Volume) = 0.010, F5.56, Significance F = 0.070

Introduction

We have previously shown [START_REF] Fong | The effect of desolvation on the binding of inhibitors to HIV-1 protease and cyclin-dependent kinases: causes of resistance[END_REF][2][START_REF] Fong | Permeability of the Blood-Brain Barrier: Molecular Mechanism of Transport of Drugs and Physiologically Important Compounds[END_REF][START_REF] Fong | Statins in therapy: Understanding their hydrophilicity, lipophilicity, binding to 3-hydroxy-3-methylglutaryl-CoA reductase, ability to cross the blood brain barrier and metabolic stability based on electrostatic molecular orbital studies[END_REF][START_REF] Fong | Drug discovery model using molecular orbital computations: tyrosine kinase inhibitors[END_REF] that four parameter equation (the general equation) can be successfully applied to:

• the transport of drugs and physiologically important molecules across the blood brain barrier (BBB): passive (simple permeation and facilitated) diffusion • the competitive binding of statins to HMG CoA reductase • the passive and active competitive transport of statins by organic anion transporters • the competitive binding of a number of tyrosine kinase inhibitors and multi-kinase inhibitors to a range of kinase enzymes • the active competitive transport of these tyrosine kinase inhibitors by the hOCT3, OATP1A2 and OCT1 transporters • the binding of inhibitors to cyclin-dependent kinases (CDK) including multi-drug resistant CDK • the binding of inhibitors to HIV-1 proteases and poly(ADP-ribose) polymerases (PARP) • kinetic and equilibrium solubility in water of a large number of drugs • intestinal drug absorption of a large number of drugs: permeation and active transport • human intestinal permeation rates and human intestinal absorption for a large number of common drugs • Caco-2, PAMPA, Everted Gut Sac, Sartorius membrane permeability of a large number of drugs

• drug-MRP2 permeability interactions in Caco-2 cells have been evaluated by determining the A-to-B and B-to-A permeability of MRP2 inhibitors

The model comprises four main drug properties calculated by quantum mechanical methods: (a) desolvation energy in water (b) lipophilicity or hydrophobicity based on the solvation energy in a hydrophobic solvent such as n-octane or n-octanol; lipophilicity being a measure of how well a drug can interact with lipophilic cell membrane bilayers, and hydrophobicity being a measure of non-polar interaction between a drug and the hydrophobic sectors of a protein (c) dipole moment in water, as a measure of the polar attraction between the drug and its receptor target or cell membrane (d) the molecular volume of the drug in water as a measure of how well the prospective drug fits into the cavity of the target receptor protein or active protein transporter, or how well a drug can diffuse through a cell membrane.

General Equation:

Transport or Binding = ΔG desolvation + ΔG lipophilicity + Dipole Moment + Molecular Volume Or

Transport or Binding = ΔG desolv,CDS + ΔG lipophilicity + Dipole Moment + Molecular Volume ΔG desolvation = ΔG electrostatic + ΔG CDS where CDS is the cavity dispersion solvent structure. The CDS involves non-bulk solvent electrostatic contributions to the free energy of hydration.

The SMD solvation model is based on ΔG S o = ΔG ENP + G CDS where ENP is the electronic nuclear polarization: the change in the solute free energy due to electrostatic interactions between the solute and the bulk solvent and distortion of the solute's electronic structure in solution. The solvent is modelled as a dielectric continuum. The CDS represents first solvation shell effects. It involves atomic surface tension (geometry dependent proportionality constants). The CDS has been parameterized using extensive experimental data sets for optimization, and has the advantage of including a realistic experimentally based hydrogen bonding model. The CDS covers shorter-range polarization effects and shorterrange non-electrostatic effects such as cavitation, dispersion, and solvent structural effects (which includes both hydrogen bonding) and exchange repulsion effects. [START_REF] Marenich | Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions[END_REF] [Marenich 2009 [START_REF] Marenich | Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions[END_REF] ] ΔG desol,CDS can be substituted for ΔG desolvation where this non-polar term may be more representative of the interaction processes being studied, as for example in a ligand-protein binding study within the protein binding pocket where the dielectric constant for that environment is ca. ε=7-10 compared to ε=78.3 for the bulk water environment where the use of ΔG desolvation is more appropriate. [START_REF] Fong | The effect of desolvation on the binding of inhibitors to HIV-1 protease and cyclin-dependent kinases: causes of resistance[END_REF][START_REF] Fong | Drug discovery model using molecular orbital computations: tyrosine kinase inhibitors[END_REF][START_REF] Rayne | Accuracy of computational solvation free energies for neutral and ionic compounds: Dependence on level of theory and solvent model[END_REF][START_REF] Rizzo | Estimation of Absolute Free Energies of Hydration Using Continuum Methods: Accuracy of Partial Charge Models and Optimization of Nonpolar Contributions[END_REF] [Fong 2016 [START_REF] Fong | The effect of desolvation on the binding of inhibitors to HIV-1 protease and cyclin-dependent kinases: causes of resistance[END_REF][START_REF] Fong | Drug discovery model using molecular orbital computations: tyrosine kinase inhibitors[END_REF] ,Rayne 2010 [START_REF] Rayne | Accuracy of computational solvation free energies for neutral and ionic compounds: Dependence on level of theory and solvent model[END_REF] , Rizzo 2006 8 ] When a solvated ligand enters a protein binding cavity and begins to bind with the protein, the desolvation processes involving the protein and ligand may involve extensive rearrangement of water molecules, and possibly some expulsion of water molecules from the cavity. A significant change in solvation entropy should then occur on the side on the ligand and the protein receptor. It is postulated that the ΔG desolv,CDS values may be a close approximation of how a solvated inhibitor reacts as it approaches and starts to enter the binding pocket (dielectric constant ε=20-30) and leaves the bulk water environment (ε =78.3) and binding starts to occur (ε=7-10). This scenario has been modelled using more intensive molecular mechanics computations. [START_REF] Shan | How Does a Drug Molecule Find its Target Binding Site?[END_REF][START_REF] Setny | How Can Hydrophobic Association Be Enthalpy Driven?[END_REF][START_REF] Mondal | Role of Desolvation in Thermodynamics and Kinetics of Ligand Binding to a Kinase[END_REF] A modified form of the general equation 1 using the free energy of water desolvation (ΔG desolv,CDS ) and the lipophilicity free energy (ΔG lipophilicity ), where CDS represents the first solvation shell solvent properties, may be a good approximation of the drug approaching the entry of the protein receptor pocket or the surface of the protein transporter. Desolvation of water from the drug (ΔG desolv,CDS ) before binding in the receptor pocket is required, and hydrophobic interactions between the drug and protein (ΔG lipo,CDS ) is a positive contribution to binding.

In this study, the general equation will be applied to the critical steps as shown in Figure 1 as they affect the overall anti-bacterial and anti-malarial properties of the fluoroquinolones FQs, and the potential serious cardiac side effects of FQ-hERG induced QT prolongation and Torsades de Pointes (TdP)

Figure 1. Flow chart of fluoroquinolone FQ processes involved in anti-bacterial or antimalarial therapy or serious side effects (a) FQ oral intake, dissolution, gastrointestinal fluid diffusion

Oral administration is the most commonly used drug administration route. The ability to predict the rate and extent of absorption of candidate drugs after oral administration is crucial during the preclinical phase of development. Drug absorption from the gastrointestinal (GI) tract is affected by many factors, including the physiological conditions of the GI tract (including absorptive surface area, local pH, food effects, intestinal transit time, passive intestinal permeability) and the physio-chemical properties of the drug (including solubility, molecular size, polarity, lipophilicity, stability). Intestinal active drug transporters are also involved in controlling oral drug permeability and absorption. The drug intestinal permeability measure P eff is widely used indicator of both the rate and/or extent of drug absorption (F a ) in humans. A good correlation exists between the human jejunal permeability (P eff ) measured using single-pass perfusion techniques and the fraction of dose absorbed from an immediate-release, rapidly dissolving drug. [START_REF] Dahan | The Fraction Dose Absorbed, in Humans, and High Jejunal Human Permeability Relationship[END_REF][START_REF] El-Kattan | Oral Absorption, Intestinal Metabolism and Human Oral Bioavailability, Topics on Drug Metabolism[END_REF][START_REF] Hou | Recent Advances in Computational Prediction of Drug Absorption and Permeability in Drug Discovery[END_REF][START_REF] Waterbeemd | ADMET in silico modelling[END_REF] The solubility of orally administered drugs is a critical rate determining factor in determining bioavailability. FQs are generally fairly insoluble in water, with most modern FQs being zwitterionic, having both a carboxylic acid (pK a ~5.5-6.3) and basic amine group (pK a ~ 7.6-9.3). Minimum solubility is around the physiological pH ~ 7.4, where all concentrations of the cationic, neutral, anionic and zwitterionic species vary according to the pK a of the various FQs. The isoelectric point pI for many FQs is around 6.8-7.6 where the mole fractions of the neutral and zwitterionic species are maximal where their ratio is invariant and pH independent. [START_REF] Sorgel | Pharmacokinetics of gyrase inhibitors I, Basic chemistry and gastrointestinal disposition[END_REF][START_REF] Liu | Determination for isoelectric points of 8 kinds of fluoroquinolones by using affinity capillary electrophoresis[END_REF][START_REF] Takacs-Novak | Protonation equilibria of quinolone antibacterials[END_REF][START_REF] Ross | Physicochemical properties of the fluoroquinolone antimicrobials. II. Acid ionization constants and their relationship to structure[END_REF][START_REF] Zhang | Predicting the minimal inhibitory concentration of fluoroquinolones for Escherichia coli using an accumulation model[END_REF] [Sorgel 1993 [START_REF] Sorgel | Pharmacokinetics of gyrase inhibitors I, Basic chemistry and gastrointestinal disposition[END_REF] , Liu [START_REF] Liu | Determination for isoelectric points of 8 kinds of fluoroquinolones by using affinity capillary electrophoresis[END_REF] , Takacs-Novak 1990 [START_REF] Takacs-Novak | Protonation equilibria of quinolone antibacterials[END_REF] , Ross 1992 19 , Zhang 2014 20 ] We have previously shown that the general equation applies to a wide range of equilibrium and kinetic solubilities of drugs. These observed correlations are sensitive to the various charged, neutral and zwitterionic forms of drug species. [START_REF] Fong | The effect of desolvation on the binding of inhibitors to HIV-1 protease and cyclin-dependent kinases: causes of resistance[END_REF][2][START_REF] Fong | Permeability of the Blood-Brain Barrier: Molecular Mechanism of Transport of Drugs and Physiologically Important Compounds[END_REF][START_REF] Fong | Statins in therapy: Understanding their hydrophilicity, lipophilicity, binding to 3-hydroxy-3-methylglutaryl-CoA reductase, ability to cross the blood brain barrier and metabolic stability based on electrostatic molecular orbital studies[END_REF][START_REF] Fong | Drug discovery model using molecular orbital computations: tyrosine kinase inhibitors[END_REF] [Fong 2015 [START_REF] Fong | The effect of desolvation on the binding of inhibitors to HIV-1 protease and cyclin-dependent kinases: causes of resistance[END_REF][2][START_REF] Fong | Permeability of the Blood-Brain Barrier: Molecular Mechanism of Transport of Drugs and Physiologically Important Compounds[END_REF][START_REF] Fong | Statins in therapy: Understanding their hydrophilicity, lipophilicity, binding to 3-hydroxy-3-methylglutaryl-CoA reductase, ability to cross the blood brain barrier and metabolic stability based on electrostatic molecular orbital studies[END_REF][START_REF] Fong | Drug discovery model using molecular orbital computations: tyrosine kinase inhibitors[END_REF] The lipophilicity of these FQs can vary according to the pH and pI points. As lipophilicity is a critical factor in drug discovery and pharmacology, the determination is critical. A common used method is logP (neutral species) or logD (ionic species) derived from water-octanol partitioning experiments. LogP measurements of FQ have been made [START_REF] Takacs-Novak | Lipophilicity of antibacterial fluoroquinolones[END_REF] [Takacs-Novak 1992] but a major criticism of logP partitioning is that n-octanol contains 2.8M water at equilibrium, a possible major error for sparingly soluble drugs. ΔG lipophilicity calculated from the solvation energy of the drug in n-octane (or n-octanol) is a better measure, and can be applied to neutral, ionized or zwitterionic species quickly and accurately.

It has been concluded that MICs of FQs for E. coli (Gram negative) involved mainly neutral and zwitterionic forms (as well as cationic and anionic species). However since drug transport into Gram negative bacteria is dominated by porin transport, this result is not surprising. [Zhang 2014] In one study an amphoteric eburnane alkaloid, it was concluded that the zwitterionic form was the dominant form in membrane penetration because it was the dominant species present, despite the zwitterionic form having far lower lipophilicity (log D) than the neutral form (log P). [START_REF] Mazak | Zwitterions Can Be Predominant in Membrane Penetration of Drugs: Experimental Proof[END_REF] [Mazak 2012] (b) FQ membrane permeation: uptake in blood and systemic circulation Passive membrane diffusion is comprised of two pathways: the paracellular pathway, where the drug diffuses through the aqueous pores at the tight junctions between the intestinal enterocytes, and the trans-cellular pathway, which requires the drug to permeate the cell membrane of the enterocyte. The paracellular pathway is thought to be important for intestinal transport of smaller (MW less than 250) and more hydrophilic drugs which are not repelled by the net negative charge of the junctional complex. The junctions only comprise 0,01% of the surface area of the intestinal membrane, and become progressively tighter moving from the jejunam to the colon. Trans-cellular diffusion is thought to be the major transport pathway (mainly determined by transport across the apical cell membrane) for the uncharged (neutral) and more lipophilic drugs of MW > 300. The vast majority of drug molecules are transported through the transcellular pathway, and the few which rely on the paracellular pathway of transportation typically have a much lower bioavailability. [START_REF] El-Kattan | Oral Absorption, Intestinal Metabolism and Human Oral Bioavailability, Topics on Drug Metabolism[END_REF] [El-Kattan 2012 [START_REF] El-Kattan | Oral Absorption, Intestinal Metabolism and Human Oral Bioavailability, Topics on Drug Metabolism[END_REF] ] Active transport processes in enterocytes express several transporters, belonging to the adenosine triphosphate (ATP) binding cassette (ABC) superfamily and the solute carrier (SLC) superfamilies, on the apical and basolateral membranes for the influx or efflux of drugs.

Drugs with a jejunal P eff > 1.5 x 10 -4 cm/s are completely absorbed independent of whether passive or active transport mechanisms are involved. Many drugs that are significantly effluxed in vitro have a rapid and complete intestinal absorption (>85%) mediated by passive transcellular diffusion. The jejunal P eff for drugs transported mainly by absorptive carriers (such as peptide and amino acid transporters) can predict the fraction of the dose absorbed as a consequence of the regional expression. The human intestinal epithelium has a large resistance towards large and hydrophilic compounds, and the paracellular route has a low contribution for compounds larger than approximately molecular weight 200. [START_REF] Lannernas | Intestinal permeability and its relevance for absorption and elimination[END_REF] [Lannernas 2007 23 ] Caco-2 cell permeability is often used as a screening tool for assessing drug oral absorption during the early stages of drug development since these cells possess many structural and functional similarities to normal human enterocytes. Caco-2 permeability has generally correlated well with the fraction of the drug absorbed by the intestinal tissue for many drugs in humans. Caco-2 permeability is widely used as a surrogate for human intestinal permeability. Where active influx and efflux transporters are involved, the jujeunal permeability may sometimes still show a dependency with F a but may show complex segmental permeability for low permeability drugs. Drugs with inherently high intestinal permeability are not affected by intestinal transporters. [START_REF] Dahan | The Fraction Dose Absorbed, in Humans, and High Jejunal Human Permeability Relationship[END_REF] [Dahan 2012 12 ] Most modern FQs have a high bioavailability, eg Ciprofloxacin 70%, Levofloxacin 99%, Moxifloxacin 86%, Gatifloxacin 95%, Norfloxacin 30-40%, Ofloxacin 98%. However, binding to blood serum proteins eg Ciprofloxacin 30%, Levofloxacin 31%, Moxifloxacin 48%, Gatifloxacin 20%, Gemifloxacin 20% can reduce bioavailability, and methods to predict how new FQ will bind to serum proteins are useful during drug discovery. The negative effect of protein binding on antibiotic activity is well established, and other effects include lower elimination, lower glomerular filtration, volume of distribution and half life hence the lowering time above MIC. [START_REF] Schmidt | Significance of protein binding in pharmacokinetics and pharmacodynamics[END_REF] [Schmidt 2010 24 ]

(c) FQ transport across bacterial membranes

The cell walls of gram-negative bacteria follow a more general structural format than that of gram-positive bacteria, which can vary considerably in different species. Gram negative bacteria possess a lipid-rich outer membrane (as well as a plasma membrane) and a thin peptidoglycan layer Gram-positive bacteria are enshrouded in thicker, more resilient cell walls and a thicker peptidoglycan layer in their cell wall.

There are three major routes across the outer membrane: (a) the hydrophobic or bilayer pathway, involving the lipopolysaccahride LPS bilayer, (b) the self-promoted uptake pathway and (c) the hydrophilic or porin pathway involving the water filled trans-membrane proteins (porins). [START_REF] Hancock | The bacterial outer membrane as a drug barrier[END_REF] [Hancock 1997 25 ] For most clinically used antibiotics the hydrophilic or porin pathway is more important. Studies on porins have shown that: (i) molecules of 500 Da and less diffuse easily through the outer membrane, and molecules up to 700 Da must be flexible to allow diffusion, (ii) the charge or hydrophilicity has a large effect, with neutral species diffusing fastest, cations generally diffusing faster than anions; multiple charged molecules diffusing even slower than single charged species; zwitterions diffused faster than anions (iii) there was an inverse relationship between lipophilicity (from log P partitioning) and diffusion rate. [START_REF] Nikaido | Molecular basis of bacterial outer membrane permeability[END_REF][START_REF] Gunn | Bacterial modification of LPS and resistance to antimicrobial Peptides[END_REF][START_REF] Hancock | Antibiotic uptake into gram-negative bacteria[END_REF][START_REF] Ma | Efflux pumps and drug resistance in gramnegative bacteria[END_REF][START_REF] Wiese | Towards antibacterial strategies: studies on the mechanisms of interaction between antibacterial peptides and model membranes[END_REF] Resistance to fluoroquinolones can involve mutations of the target enzyme and changes to microbial cell permeability. Many Gram-negative bacteria contain genes for multiple efflux pumps, used by bacteria as secretion mechanisms for cellular products, and as defence mechanisms against harmful substances present in the environment. These efflux pumps also function as an active antibiotic accumulation barrier, by which a drug is pumped out faster than it can diffuse into the cell. The pumps include: the major facilitator superfamily (MFS), the ABC group, the resistance nodulation division family (RND), the multidrug-and toxic compound extrustion family (MATE), and the small (earlier staphylococcus) multidrug resistance (SMR) family. Of these the RND efflux pumps play the most important role in multidrug resistance in all Gram negatives bacteria.

The MRP2 (or cMOAT or ABCC2) transporter is involved in drug disposition and distribution, particularly of organic anions and drug metabolites such as glucuronides. MRP2 is an efflux transporter that is important in drug biliary excretion and renal excretion, and also prevents xenobiotics from penetrating or accumulating in tissues such as lungs and from crossing the placenta. MRP2 is localized to the apical membrane domain of polarized cells such as hepatocytes, renal proximal tubule and intestinal epithelia, and is also present in the gallbladder, bronchi, and placenta. Multiple ABC transporters contribute to the overall active secretion of some fluoroquinolones (Grepafloxacin), and MRP2 has been demonstrated to mediate biliary excretion of some FQs. [START_REF] Alvarez | Fluoroquinolone efflux mediated by ABC transporters[END_REF] [Alvarez 2008 35 ]

(d) FQ anti-bacterial mechanism

FQs kill bacteria by increasing levels of DNA strand breaks generated by type II topoisomerases. DNA topoisomerases are enzymes that control the topology of DNA in cells. Topoisomerases I and II are involved in the breakage of one or both strands of the DNA, and the passage of one segment of DNA through a break in another. Nearly all bacteria encode two type II topoisomerases, gyrase and topoisomerase IV. DNA gyrase (particularly in Gram negative bacteria) and topoisomerase IV (particularly in Gram positive bacteria) are primary targets for antibacterial agents, including the fluoroquinolones and the coumarins families. DNA gyrase is essential in all bacteria but is not found in humans, so it is an ideal target for antibacterials. The known reactions of topoisomerases include: relaxation and supercoiling, catenation and decatenation, knotting and unknotting. DNA supercoiling activity is unique to gyrase.

It is well known that type II topoisomerases require divalent metal ions in order to cleave DNA. Both type II enzymes are essential for cell survival. Fluoroquinolones (FQ) form a FQ-Topoisomerase II-DNA complex where the enzyme is trapped with the bound DNA. FQ can also form a complex with Topoisomerase IV utilizing a bridge between the ketonecarboxylate moiety of the FQ to a Mg ion linked to the serine and glutamate residues of the Topoisomerase IV, as shown in Figure 2. [START_REF] Redgrave | Fluoroquinolone resistance: mechanisms, impact on bacteria, and role in evolutionary success[END_REF] [Redgrave 2014 36 ] A "water-metal ion bridge" acts as the primary conduit by which clinically relevant quinolones interact with topoisomerase IV. Mutations of the topoisomerase IV residues which form the {FQ-M ++ -H 2 O-Topo IV} bridge are thought to be responsible for resistance to FQs. [START_REF] Aldred | Topoisomerase IV-quinolone interactions are mediated through a water-metal ion bridge: mechanistic basis of quinolone resistance[END_REF] [Aldred 2014 37 ]

(e) Serious side effects of FQs

The long QT syndrome (LQTS) is a disorder of ventricular repolarization that predisposes affected individuals to cardiac arrhythmia and sudden death. It has long been clinically recognized that drug-induced aLQTS is a serious side effect, and the cardiac hERG potassium channels have been related to this QT prolongation. Drugs such as terfenadine (Seldane) cisapride (Propulsid), grepafloxacin (Raxar) and terodiline block the hERG channel to deleterious effect and thus have been withdrawn from the market. Syncope, polymorphic ventricular tachycardia (torsade de pointes or TdP) and sudden cardiac death were particularly associated with terfenadine. Consequently, a hERG assay is now an indispensable step and a high-quality assay must accompany any investigational new drug (IND) application. [START_REF] Brown | Drugs, hERG and sudden death[END_REF] [Brown 2004 38 ] The nonclinical evaluation of the potential for delayed ventricular repolarization (QT interval prolongation) by human pharmaceuticals, issued as CHMP/ICH/423/02, was adopted by CHMP in May 2005. hERG encodes the pore-forming subunit of a delayed rectifier voltage gated K + (VGK) channel. These channels are variously referred to as I Kr , hERG, or Kv11.1 hERG forms the major portion of one of the ion channel proteins (the 'rapid' delayed rectifier current I Kr ) that conducts potassium (K + ) ions out of the muscle cells of the heart, and this current is critical in correctly timing the return to the resting state (repolarization) of the cell membrane during the cardiac action potential. In the laboratory the heterologously expressed hERG potassium channel comprises 4 identical alpha subunits, which form the channel's pore through the plasma membrane. Each hERG subunit consists of 6 transmembrane alpha helices, numbered S1-S6, a pore helix situated between S5 and S6, and cytoplasmically located N-and Ctermini. The S4 helix contains a positively charged arginine or lysine amino acid residue at every 3rd position and is thought to act as a voltage-sensitive sensor, which allows the channel to respond to voltage changes by changing conformations between conducting and non-conducting states (called 'gating'). This channel is also sensitive to drug binding, as well as decreased extracellular potassium levels, both of which can result in decreased channel function and drug-induced (acquired) long QT syndrome. [START_REF] Vandenberg | hERG K + Channels: Structure, Function, and Clinical Significance[END_REF] [Vanderberg 2012 39 ] Among the drugs that can cause QT prolongation, the more common ones include antiarrhythmics (especially Class 1A and Class III), anti-psychotic agents, and certain antibiotics (including quinolones and macrolides). [START_REF] Briasoulis | Prolongation and Torsade de Pointes Induced by Fluoroquinolones: Infrequent Side Effects from Commonly Used Medications[END_REF][START_REF] Sanguinetti | hERG potassium channels and cardiac arrhythmia[END_REF] [START_REF] Briasoulis | Prolongation and Torsade de Pointes Induced by Fluoroquinolones: Infrequent Side Effects from Commonly Used Medications[END_REF]40 , Sanguinetti 2006 41 ] Although there exist other potential targets for cardiac adverse effects, the vast majority of drugs associated with acquired QT prolongation are known to interact with the hERG potassium channel. One of the main reasons for this phenomenon is the larger inner vestibule of the hERG channel, thus providing more space for many different drug classes to bind and block this potassium channel. [START_REF] Milnes | Blockade of HERG potassium currents by fluvoxamine: incomplete attenuation by S6 mutations at F656 or Y652[END_REF] [Milnes 2003 42 ] Fluoroquinolones prolong the QT interval by blocking voltage-gated potassium channels, especially the rapid component of the delayed rectifier potassium current I Kr , expressed by hERG (the human ether-a-go-go-related gene). Moxifloxacin carries the greatest risk of QT prolongation from all available quinolones in clinical practice and it should be used with caution in patients with predisposing factors for Torsades de Pointes (TdP). Gemifloxacin, levofloxacin, and ofloxacin are associated with a lower risk of QT prolongation compared with Moxifloxacin, and Ciprofloxacin appears to be associated with the lowest risk for QT prolongation and the lowest TdP rate. The overall risk of TdP is small with the use of fluoroquinolones. Clinicians can minimize that risk by avoiding prescriptions of multiple medications associated with QT-interval prolongation, especially in high-risk patients. [START_REF] Briasoulis | Prolongation and Torsade de Pointes Induced by Fluoroquinolones: Infrequent Side Effects from Commonly Used Medications[END_REF] [Briasoulis 2011 40 ]

Materials and methods: Experimental methods

All calculations were carried out using the Gaussian 09 package at the B3LYP/6-31 G*(6d, 7f) level of theory with optimised geometries in water, as this level has been shown to give accurate electrostatic atomic charges, and was used to optimize the IEFPCM/SMD solvent model. With the 6-31G* basis set, the SMD model achieves mean unsigned errors of 0.6 -1.0 kcal/mol in the solvation free energies of tested neutrals and mean unsigned errors of 4 kcal/mol on average for ions. [START_REF] Marenich | Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions[END_REF] [Marenich 2009 6 ]The 6-31G** basis set has been used to calculate absolute free energies of solvation and compare these data with experimental results for more than 500 neutral and charged compounds. The calculated values were in good agreement with experimental results across a wide range of compounds. [START_REF] Rayne | Accuracy of computational solvation free energies for neutral and ionic compounds: Dependence on level of theory and solvent model[END_REF][START_REF] Rizzo | Estimation of Absolute Free Energies of Hydration Using Continuum Methods: Accuracy of Partial Charge Models and Optimization of Nonpolar Contributions[END_REF] [Rayne 2010 7 ,Rizzo 2006 8 ] Adding diffuse functions to the 6-31G* basis set (ie 6-31 + G**) had no significant effect on the solvation energies with a difference of less than 1% observed in solvents, which is within the literature error range for the IEFPCM/SMD solvent model. [START_REF] Marenich | Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions[END_REF] [Marenich 2009 6 ] It is noted that high computational accuracy for each species in different environments is not the focus of this study, but comparative differences between various species is the aim of the study. The use of various literature values for K m , IC 50 to develop the multiple regression equations have much higher uncertainties than the calculated molecular properties. The statistical analyses include the multiple correlation coefficient R 2 , the F test of significance, standards errors for the estimates (SEE) and each of the variables SE(ΔG desolvation ), SE(ΔG lipophilicity ), SE(Dipole Moment), SE (Molecular Volume), SE(Molecular Volume), as calculated from "t" distribution statistics. Residual analysis was used to identify outliers. The solvation energies, lipophilicities, dipole moments, molecular volumes of the statins are shown in Table 2.

It is noted that the various equations derived in this study are more indicative rather than highly robust in that statistical precision is taken as the goodness of fit (rather than extensive statistical validation) of the experimental data since insufficient experimental data are not available for highly robustly validated outcomes using the four independent variables. The correlations have used data from a single source where the experimental precision is consistent, as compared to using experimental data from multiple sources, where the interlaboratory experimental error can be very large, even for the same cell line, up to a factor of 10 as found by Aronov [START_REF] Aronov | Predictive in silico modelling for hERG channel blockers[END_REF] . However the fact that the different biological processes in this study (Figure 1) are all well correlated by the general equation indicates that the general equation may a universally valid model for biological processes.

Results

Anti-bacterial properties of FQs

Minimum inhibitory concentrations (MIC, μg/ml, DM4100 E. coli) for 17 FQ drugs: Sarafloxacin 0.086, Sparfloxacin 0.125, Fleroxacin 0.141, Orbifloxacin 0.150, Sitafloxacin 0.015, Gemifloxacin 0.086, Grepafloxacin 0.016, Besifloxacin 0.100, Tosufloxacin 0.050, Lomefloxacin 0.172, Ulifloxacin 0.022, 8-Ethoxy-Moxifloxacin 0.200, Anthofloxacin 0.15, N-Methyl-Gatifloxacin 0.065, PD161144 0.096, Clinafloxacin 0.0095, Balofloxacin 0.484 all as zwitterionic species: [ It is noted that treating the FQs as neutral species for the E.coli MICs gave a very poor correlation.

Anti-malarial properties of FQs

Plasmodium is a genus of parasitic protozoa, many of which cause malaria in their hosts. Antimalarial activities (IC50) of 20 quinolones and fluoroquinolones (Moxifloxacin, Lomefloxacin, Enoxacin, Norfloxacin, Grepafloxacin, Ciprofloxacin, Gatifloxacin, Clinifloxacin, Fleroxacin, Flumequine, Nalidixic Acid, Pipemidic Acid, Piromidic Acid, Chloroquine, Rufloxacin, Trovafloxacin (all as neutral species), Pefloxacin zwitterion (ZW), Sparflox (ZW), Levoflocacin (ZW), Ofloxacin (ZW) against chloroquine-sensitive (3D7) strains of Plasmodium falciparum in vitro [Mahmoudi 2003 The correlation equations for the 3D7 and NF54-R Plasmodium falciparum strains were very similar if Pefloxacin, Sparflox, Levoflocacin, and Ofloxacin were omitted as large outliers (R 2 0.525, SE 28.65, F 2.77, F significance 0.087 for the 3D7 correlation, and R 2 0.485, SE 213.07, F 2.35, F significance 0.124 for the NF54-R correlation); however including these four FQs as the zwitterionic species gave the two equation 2 and 3 above which are better statistical correlations. This result shows that these correlations can differentiate between the neutral and zwitterionic forms of the FQs in their ability to inhibit Plasmodium falciparum strains. This observation strongly suggests that it is mainly the neutral form of the FQs that determines the overall efficacy against the Plasmodium falciparum strains, despite the many steps that must be involved in FQ pharmacokinetics for the FQ to achieve their anti-malarial efficacy.

Antimalarial activities of 10 quinolones and fluoroquinolones (Norfloxacin, Ciprofloxacin, Clinifloxacin, Piromidic Acid, Rufloxacin, Trovafloxacin, Sparfloxacin (all as neutral species), Pefloxacin ZW, Ofloxacin ZW, Grepafloxacin ZW) against hepatic stages of P. yoelii yoelii at 48 h. [ Comparison of eq 4 with eq 4a shows that by including Grepafloxacin (which showed the greatest effect against P. yoelii yoelii) as a zwitterion is a better statistical correlation than by simply omitting Grepafloxacin as an outlier from eq 4a. This outcome gives confidence that these correlations can distinguish amongst the zwitterionic and neutral forms of the various FQs in exerting their anti-malarial effect.

Ring stage parasitized erythrocytes were used for the 3D7 and NF54-R Plasmodium falciparum sudies. Mouse or human hepatocyte cultures were incubated for 24 h before sporozoite inoculation for the P. yoelii yoelii studies. [START_REF] Mahmoudi | In Vitro Activities of 25 Quinolones and Fluoroquinolones against Liver and Blood Stage Plasmodium spp[END_REF] [Mahmoudi 2003 44 ] Comparison of eqs 2,3 with eq 4 show that the effect of the anti-malarials on the erythrocytes is very different from the effect on the hepatocytes with a large sensitivity on the lipophilicity and dipole moment (and lesser effect on the desolvation) for the hepatocytes. This observation is consistent with the more lipophilic environment in the liver tissue than for the red blood cells where a far more hydrophilic environment exists.

Chronic bacterial prostatis (CBP)

CBP is mainly caused by Gram-negative (and some Gram-positive) uropathogens, and FQs are the drugs of choice because of the favourable pharmacokinetics and anti-microbial spectrum. The concentrations of FQs in human seminal and prostatic fluids (and prostatic tissue) are important guides to efficacy of the FQs against CBP. [START_REF] Weidner | Table 3, oral doses except Ciprofloxacin and Ofloxacin (IV), 400mg doses, time period usually 3-4 hours, healthy volunteers[END_REF] [Weidner 2008 [START_REF] Weidner | Table 3, oral doses except Ciprofloxacin and Ofloxacin (IV), 400mg doses, time period usually 3-4 hours, healthy volunteers[END_REF] ] The median concentrations in prostatic fluid:plasma ratios (normalized to a 400 mg dose) for Moxifloxacin, Lomefloxacin, Enoxacin, Norfloxacin, Ciprofloxacin, Gatifloxacin, Levofloxacin, Ofloxacin, all treated as neutral species (Fleroxacin omitted as outlier). All FQs were orally administered except Ciprofloxacin and Ofloxacin were IV.

FQ uptake into rat brains and brain:blood plasma concentrations

In vivo study of the steady state uptake (R ss ) of FQ into rat brains and the ratio of brain to blood plasma concentrations (F) were determined for gatifloxacin, ofloxacin, ciprofloxacin, lomefloxacin, rufloxacin, pazufloxacin, norfloxacin, prulifloxacin, balofloxacin, caderofloxacin as neutral species, and sparfloxacin as the zwitterion. Sparfloxin was a clear outlier from the correlations with the neutral FQs, and omitting sparfloxacin or including it as a zwitterion gave similar statistical results. Treating all species as zwitterions gave a very poor correlation. [

FQ oral intake, dissolution, gastrointestinal fluid diffusion

Water solubility data (internally consistent very accurate equilibrium and kinetic solubility data base from the Goodman laboratory 47 ) for 9 closely structurally related FQs was examined, ranging from Difloxacin 251.311 to Danofloxacin 1260 μM for 8 drugs, but with a very high solubility (apparent outlier) for Oxfloxacin 54262.5 μM [ Goodman 46 ]. There was a good correlation when treating the drugs as neutral species, with Ofloxacin being a clear outlier unless treated as a zwitterion. Treating all FQs as zwitterions gave a fairly poor correlation R 2 0.621, F significance 0.32). However, the best correlation was obtained when treating the drugs as anions, and Oxfloxocin as a zwitterion. Equations 11 and 12 show the same floxacin data analysed using kinetic solubility. 47 [Goodman] Kinetic solubility is the concentration of a compound in solution when an induced precipitate first appears, whereas equilibrium solubility is the concentration of compound in a saturated solution when excess solid is present, and solution and solid are at equilibrium. Kinetic solubility is commonly used in early drug discovery protocols. Equations 11 and 12 are very similar to those for eq 8,9 and 10.

FQ human intestinal permeability, renal organic anion transporters, BBB permeability

Avdeef [START_REF] Avdeef | Human jejunal permeability predicted from Caco-2 assay, a biophysical model applied to fluoroquinolone antimicrobials[END_REF] and Wang [START_REF] Wang | Predicting the human jejunal permeability and fraction absorbed of fluoroquinolones based on a biophysical model[END_REF] have sought to calculate human jejunal permeability and absorption from experimental Caco-2 data, assuming passive diffusion (transcellular and paracelloular). Intestinal Jejunal permeability Caco-2 pH 6.5 for 14 fluoroquinolones: Sarafloxacin, Norfloxacin, Ofloxacin, Difloxacin, Enrofloxacin, Lomefloxacin, Ciprofloxacin, Sparfloxacin, Danofloxacin, Gatifloxacin, Grepafloxacin, Pefloxacin, Flumequine, Moxifloxacin treated as neutral species. Log values are negative. Correlation with all FQ as ionic species was much worse F significance 0.604. Avdeef 2010 [START_REF] Avdeef | Human jejunal permeability predicted from Caco-2 assay, a biophysical model applied to fluoroquinolone antimicrobials[END_REF] Calculated human jejunal permeability rates (passive permeabilities 10 -4 cm/s) from experimental Caco-2 values (pH 6.5), from Avdeef 2010 [START_REF] Avdeef | Human jejunal permeability predicted from Caco-2 assay, a biophysical model applied to fluoroquinolone antimicrobials[END_REF] and Wang 2014 [START_REF] Wang | Predicting the human jejunal permeability and fraction absorbed of fluoroquinolones based on a biophysical model[END_REF] for the 14 FQ treated as neutrals species. Log permeabilities are negative values.

Equation 14

The influence of the peak free plasma concentrations of the FQs on the IC 50 values has also been investigated.

Discussion

FQ whole organism activity

It has been shown that the general equation can describe the anti-bacterial (E. coli, eq 1) and anti-malarial activity (parasitic protozoa, Plasmodium falciparum, chloroquine-sensitive 3D7, eq 2) and (Plasmodium falciparum, chloroquine-resistant NF54-R, eq 3). Plasmodium yoelii yoelii is also strongly correlated eq 4 and 4a.

The essential difference between the FQ activity against the Plasmodium falciparum chloroquine-sensitive 3D7 strain and chloroquine-resistant NF54-R strain is a greater sensitivity to lipophilicity (and lesser sensitivity to desolvation and dipole moment) for the resistant strain. This may imply that hydrogen bonding and polar interactions are relatively reduced in resistant strains when bound to FQs (see discussion below on FQ mechanism).

Ring stage parasitized erythrocytes were used for the 3D7 and NF54-R Plasmodium falciparum sudies. Mouse or human hepatocyte cultures were sporozoite inoculations for the P. yoelii yoelii studies. [START_REF] Schwanz | Structural features of fluoroquinolone-class antibiotics that affect lethal activities and DNA binding[END_REF] [Mahmoudi 2003 43 ] Comparison of eqs 2,3 with eq 4 show that the effect of the anti-malarials on the erythrocytes is very different from the effect on the hepatocytes with a large sensitivity on the lipophilicity and dipole moment (and lesser effect on the desolvation) for the hepatocytes. This observation is consistent with the more lipophilic environment in the liver tissue than for the red blood cells where a far more hydrophilic environment exists.

Since the FQs can exist in various neutral, ionic or zwitterionic forms around the physiological pH, the correlations were tested against the various species, focussing on the strength of the correlations and using outlier analysis. It was shown that E. coli eq 1 gave a very poor correlation using neutral FQs, but a strong correlation using zwitterionic FQs. Siimilarly the Plasmodium correlations found that in eq 2 and 3 Pefloxacin, Sparfloxacin, Levoflocacin and Ofloxacin were far better correlated when treated as zwitterions, whereas the other 16 FQs were treated as neutral species. It appears that the general equation can differentiate amongst the various FQ species statistically, possibly indicating mechanistic differences within a species, and between different microbe families.

The general equation also accurately describes the concentrations of FQs in human seminal and prostatic fluids (and prostatic tissue) ie the prostatic fluid:plasma in treating chronic bacterial prostatis, eq 5. All FQs were treated as the neutral species.

The general equation also accurately describes the in vivo study of the steady state uptake (R ss ) of FQs into rat brains and the ratio of brain to blood plasma concentrations (F) when treated as neutral species in eq 6 and 7.

The overall results from eq 1-7 clearly demonstrate the general equation can successfully describe whole organism efficacy of FQs, as it applies to bacterial species, parasitic protozoa, humans and rats.

FQ oral intake, dissolution, gastrointestinal fluid diffusion

The rate determining step for movement of an orally ingested drug into the systematic blood system is the rate of dissolution. Oral Kinetic solubility is the concentration of a compound in solution when an induced precipitate first appears, whereas equilibrium solubility is the concentration of compound in a saturated solution when excess solid is present, and solution and solid are at equilibrium. Kinetic solubility is commonly used in early drug discovery protocols. Equations 11 and 12 for kinetic solubility are very similar to those for eqs 8,9 and 10 which apply to equilibrium solubility. The best correlations for equilibrium solubility used FQs as the neutral or anionic species (with Ofloxacin as an zwitterion) whereas for kinetic solubility it was FQs in the anionic form which gave the better correlations (with Ofloxacin a zwitterion). Since FQs can exist as charged, neutral or zwitterionic forms at equilibrium at physiological pH, whereas kinetic dissolution requires the change from the solid state (with ionic lattice forces) to solution, these results are consistent with the experimental findings. It is also noted that a much more statistically rigorous analysis of over 70 common drugs also is well described by a similar equation to those in eqs 8-12. [START_REF] Fong | Drug discovery model using molecular orbital computations: tyrosine kinase inhibitors[END_REF] [Fong 2016 5 ]

FQ human intestinal permeability, renal organic anion transporters, BBB permeability

It is widely considered that only neutral species can passively permeate cell membranes, cationic species may also permeate cell membranes, either by passive permeation or facilitated diffusion, but anionic species are widely considered not to passively permeate cell membranes. However, there are active transporters which can transport charged species across cell membranes of enterocytes, such as the ABC and SLC families. [START_REF] El-Kattan | Oral Absorption, Intestinal Metabolism and Human Oral Bioavailability, Topics on Drug Metabolism[END_REF] [El-Kattan 2012 13 ] Avdeef [START_REF] Avdeef | Human jejunal permeability predicted from Caco-2 assay, a biophysical model applied to fluoroquinolone antimicrobials[END_REF] and Wang [START_REF] Wang | Predicting the human jejunal permeability and fraction absorbed of fluoroquinolones based on a biophysical model[END_REF] have calculated human jejunal permeability and absorption from experimental Caco-2 data, assuming passive diffusion (transcellular and paracellular) and have also calculated human jejunal permeability rates (passive permeabilities 10 -4 cm/s). Strong correlations eq 13 and 14 have been found with their permeability data when treating the FQs as neutral species.

The PAMPA intrinsic permeability coefficients for the uncharged forms of 4′N-Rnorfloxacin, 4′N-R-ciprofloxacin, and 4′N-R-3′-methylciprofloxacin (where R=H, Me, n-Pr, n-Bu) was strongly correlated in eq 15 and 16. As PAMPA permeation is purely passive permeation (unlike Caco-2 cells which have some active transporter capability), these equation show how large R substituents can affect the permeability. This is particularly shown in eq 16 where the molecular size coefficient is large compared to the other coefficients. This result reflects the use of ΔG CDS rather than ΔG solvation in eq 16, which is the non-electrostatic contribution of ΔG solvation and so reflects the non-polar contribution made the R substituents to the PAMPA cell permeation ie the relative contribution ΔG solvation in eq 15 is larger than the relative contribution from ΔG CDS in eq 16, so emphasising the molecular volume contribution in eq 16. 17 shows the transport of 9 FQs (mainly as zwitterions, but Ciprofloxacin and Sparfloxacin treated as anions) by renally expressed basolateral SLC22 super family transporters: mOAT (mouse organic anion transporter mOAT3, active in adsorption and excretion of anions). These data are known to include both influx and efflux of renal basolateral cells. The correlation for the active transporter is fairly strong, and the correlation with neutral or all anionic species was very poor.

The steady state in vitro competitive uptake of [START_REF] Hou | Recent Advances in Computational Prediction of Drug Absorption and Permeability in Drug Discovery[END_REF] C Grepafloxacin in rat brain capillary endothelial cells in the presence of bicarbonate ions by 7 FQ drugs (as anions) is shown in eq 18. The effect on in vitro brain capillary endothelial cell competitive uptake of HSR-903 (Olamufloxacin) by FQs (as neutral species) is shown in eq 19. Eq 18 is a relatively poor correlation possible reflecting the alkaline conditions and a dynamic equilibria of species. The in vitro data in Eq 19 more closely approximates the in vivo rat data of eq 6 where the pattern of coefficients are similar in relative magnitudes.

FQ binding to plasma proteins

Plasma protein binding PPB affects antibacterial efficacy for all antimicrobial classes, based on its effects on tissue penetration, elimination half-life and the volume of distribution. However PPB also impacts antimicrobial activity by reducing the available fraction of free drug. PPB leads to significant reduction of antimicrobial activity for moxifloxacin and trovafloxacin. [START_REF] Zeitlinger | Plasma protein binding of fluoroquinolones affects antimicrobial activity[END_REF] [Zeitlinger 2008 60 ] Plasma proteins are comprised of ca 55% serum albumin, globulins 38%, fibrogens 7% and the remainder are regulatory proteins. Eqs 20 and 21 show strong correlations with BSA binding using the zwitterionic forms of FQs. The zwitterionic forms of the FQs are dominant at the physiological pH in blood plasma, and it is expected that binding interactions with the BSA would involve significant ionic and hydrogen bonding interactions. We have previously shown that correlations with ΔG desolvation are more representative of the largely electrostatic bulk water environment (ε=78.3), whereas the correlations with ΔG desol,CDS (which represents the non-polar solvation component of the interaction between the FQ solute and water), is more representative of the interior of the binding pocket of the BSA protein (ε=6-10). Eq 21 is dominated by the non-polar desolvation term, which largely determines binding strength between BSA and the FQs.

FQ serious side effects: hERG cardiac QT prolongation

Hagiwara 2001 [START_REF] Tamai | Transporter-mediated permeation of drugs across the blood-brain barrier[END_REF] has assessed the effects of 10 fluoroquinolones on cardiac repolarization by measuring the action potentials recorded from isolated guinea pig right ventricular myocardia tissue under constant conditions, namely, myocardial preparations were electrically stimulated at the fixed pacing frequency of 1 Hz. Sparfloxacin was the most active drug, at 10 μM, prolonged APD 90 8.4%, and APD 50 9.0%. All other drugs were measured at 100 μM as the APD 90 values. Blockade of I Kr leads to a delay in the cardiac repolarization and prolongs the APD of myocardia and consequently prolongs the QT interval on the ECG. The APD prolonging potency was sparfloxacin > moxifloxacin = grepafloxacin > gatifloxacin > tosufloxacin = gemifloxacin = ciprofloxacin = trovafloxacin = sitafloxacin = levofloxacin. This I Kr blockade order was the same found for rabbit and canine Purkinje fibers, as shown in Table 1. [START_REF] Camm | Risk of QT prolongation and torsades de pointes with antimicrobial and antimalarial drugs. Chapter 8[END_REF] [Camm 2004 61 ] This order closely approximates the order found by Kang 2001 [START_REF] Liu | Interaction between Fluoroquinolones and Bovine Serum Albumin Studied by Affinity Capillary Electrophoresis[END_REF] from inhibition of hERG channel currents using chinese hamster ovary cells (CHO cells) transfected with cDNA encoding the hERG K 1 channel cloned from a human neuroblastoma cell line. These experimental results agree with clinical practice data which is that Moxifloxacin carries the highest risk of I Kr blockade (noting that Grepafloxacin was withdrawn from sale for causing adverse cardiac effects and that Sparfloxacin was also withdrawn from sale in most countries).

Table 1. The effect of fluoroquinolones on I Kr blockade, action potential prolongation (ADP 90 ), QT prolongation, and Torsades de Pointes (TdP). (Camm 2004) Eqs 22 and 23 show reasonably strong correlations for the ADP 90 data when treating the FQs as neutral species (Tosufloxacin, Gemifloxacin, Sitafloxacin as zwitterions) with eq 23 being the more significant.

Kang 2001 [START_REF] Liu | Interaction between Fluoroquinolones and Bovine Serum Albumin Studied by Affinity Capillary Electrophoresis[END_REF] has examined the effect of FQs on chinese hamster ovary cells (CHO cells) transfected with cDNA encoding the hERG K 1 channel cloned from a human neuroblastoma cell line. Sparfloxacin was the most potent compound, IC 50 18 μM, whereas ofloxacin was the least potent compound, IC 50 1420 μM. QT prolongation observed clinically with administration of sparfloxacin and certain other fluoroquinolones showed a relationship with the free plasma levels after therapeutic doses was very similar to those concentrations that inhibit HERG channel current. However, levofloxacin, ciprofloxacin, and ofloxacin inhibition of HERG occurred at concentrations much greater than those observed clinically. It was concluded that clinically relevant hERG channel inhibition is not a class effect of the fluoroquinolone antibacterials but is highly dependent upon specific substitutions within this of compounds. Eq 24 shows a good correlation with IC 50 for the CHO cells which can be compared to eq 22 for the APD 90 data from isolated guinea pig right ventricular myocardia tissue. The equations are similar but the signs of the independent variables are opposite, but the magnitudes are similar.

Eqs 24 and 25 or 26 and 27 where the IC 50 values are corrected for the peak plasma concentrations of the FQs are very similar except the coefficients are roughly 12 times less sensitive for eq 25 (compared to eq 24) and 11 times less sensitive for eq 27 (compared to eq 26). These equations clearly show that the concentration inside the cells where activity occurs are lowered proportionally to the peak free plasma concentrations of the FQs.

Ryu 2013 [START_REF] Ryu | The synergic modeling for the binding of fluoroquinolone antibiotics to the hERG potassium channel[END_REF] have examined the binding modes of Levofloxacin and Sparfloxacin with the hERG channel which is a tetrameric protein and binds with a 1:1 stoichiometry. It was concluded that two Tyr652s in the neighbouring subunits and one or two Phe656s in the diagonal subunits contributed to the blockade in the case of both compounds, and Ser624 was also involved. Docking studies suggested that the protonated carboxyl group in the compounds strongly interacts with Phe656 as a π acceptor.

Binding of drugs in the hERG channel has been previously considered to be dominated by: (a) hydrophobicity and or π-stacking interactions with Tyr652 and Phe656 on the S6 helix of the channel. Multiple aromatic or aromatic groups are critical for high affinity block. (b) flexibility to allow conformational change in the channel, (c) increasing the number of aromatic rings, (d) the presence of a charged amine group can (but not always) increase potency, (e) hydrophilic groups can decrease binding. The inhibitor orients itself along the pore axis, with the lipophilic end facing the opening to the cytosol and the polar tail facing the selectivity filter. One or two hydrophobic moieties interact with Phe656 side chains, probably via π-stacking(Figure 3). Multiple ligand binding sites exist on hERG that are capable of modulating channel activity. [Vanderburg 2012 39 , Aronov 2005 61 ] Eqs 22-27 show that FQ binding to the tetrameric protein of the hERG channel is multifaceted, with desolvation of the FQ (and probably of the protein at Ser624) is critical as well as the hydrophobic interactions at Phe656s and Tyr652s, the dipole moment (as an indicator of polar interactions between the FQ and protein) and molecular sizes of the FQs.

A major hurdle when constructing models using literature data has been the large discrepancy observed for hERG IC 50 values determined in different laboratories. Inter-laboratory variability of greater than 10-fold is not uncommon, even in cases when inhibition was measured using the same cell line. [START_REF] Aronov | Predictive in silico modelling for hERG channel blockers[END_REF] [Aronov 2005 63 ] This is generally true when assessing biological activity data for ligand drugs and particularly protein receptors, and using internally consistent data from the same sources has been found to be crucial in defining relationships where mechanistic conclusions are sought. 1-5 [Fong 2015]

FQ anti-bacterial mechanism

The inhibition of gyrase supercoiling activity (IC 50 ) by 12 FQ and Q drugs and the binding of FQ and Q drugs to 6-mer single stranded DNA oligonucleotides (apparent K D ) has been analysed in eqs 28,29 and 30. The correlations with the non-electrostatic CDS values as opposed to the desolvation energy were superior, as shown in equation 29 and 30 as expected since non-electrostatic CDS correlations have been shown to better represent drug-protein binding within the binding pocket. Eqs 29 indicates that the potency of FQ inhibition of gyrase supercoiling activity is primarily dependent on lipophilicity and dipole moment of the FQ, with smaller but significant dependencies on desolvation and molecular volume. Eqs 30 indicates that the potency of FQ binding to ssDNA is primarily dependent on desolvation and lipophilicity, with smaller but significant dependencies on dipole moment and molecular volume.

Figure 2. Schematic representation of fluoroquinolone-Mg-Topoisomerase bridging interaction

It has been proposed that one mode of resistance to fluoroquinolones may be associated with the magnesium ion water bridge to the bacterial type IV topoisomerases where the bridge is anchored to the serine and glutamic acid residues (Figure 2). The mechanism of quinolone resistance is suggested to be a result of serine mutations in the topoisomerase which causes partial loss of the Mg-H 2 O-topoisomerase bridge. [START_REF] Aldred | Topoisomerase IV-quinolone interactions are mediated through a water-metal ion bridge: mechanistic basis of quinolone resistance[END_REF] The thermochemical analysis of the Moxifloxacin--Mg--(Serine, Glutamate) complex gave ΔG values (298K) for the MoxifloxacinMg to Serine,Glutamate interaction in the range of 7.5-9.5 kcal/mol in water. The values are estimates only, as no account was taken of any wider topoisomerase interaction other than direct hydrogen and ionic bonding to the serine and glutamate residues, and the hydrogen bond lengths are not precisely known from the Xray structure. It is possible to compare these values with the thermodynamically derived complex interaction (using fluorescence emission spectroscopy) between DNA and several quinolones (Norfloxacin, Ciprofloxacin, and Ofloxacin) which gave ΔG values between 4.5 and 5.5 kcal/mol. [START_REF] Lee | A Thermodynamic Study on the Interaction of Quinolone Antibiotics and DNA[END_REF] [Lee 2009 66 ] It has been shown that the potency of a series of fluoroquinolones is related to the binding to 6-mer single stranded DNA oligonucleotides. 57 [Noble 2003 57 ] The presence of the MoxifloxacinMg ion, and the glutamate ion, is expected to significantly increase the interaction with Serine/Glutamate residues of the topoisomerase compared to bare fluoroquinolones interacting with DNA. These data suggest that the Mg ion may play a significant role in fluoroquinolone activity through a fairly strong interaction with topoisomerase residues.

The physiological bacterial concentration of free Mg ++ is about 1-2 mM 67 [Snavely 1990 67 ], while the intracellular concentration of fluoroquinolone has been calculated to be ~0.1mM. [START_REF] Lecomte | Effect of magnesium complexation by fluoroquinolones on their antibacterial properties[END_REF] [Lecomte 1994 68 ] The binding constant for Mg(II) to ciprofloxacin is K a = 1.30x10 3 M -1 [Lecomte 1994 68 ] (the binding constant [START_REF] Palu | Quinolone binding to DNA is mediated by Mg ions[END_REF] [Palu 1992 69 ] for Mg ++ to DNA is K a = 22x10 3 M -1 ). It can therefore be readily assumed that fluoroquinolones are complexed with Mg ++ in the bacterial cell, though the equilibrium constants can vary with different fluoroquinolones and bacteria.

These detailed mechanistic results are consistent with the findings from this study, in particular eqs 28,29 and 30 describing the inhibition of gyrase supercoiling activity and the binding to 6-mer single stranded DNA oligonucleotides. Desolvation of the FQs prior to protein binding is clearly a critical step that would be involved in establishing FQ-Mg-water-Ser,Glu bridging.

It is also noted above (eq 2,3) that the essential difference between the FQ activity against the Plasmodium falciparum chloroquine-sensitive 3D7 strain and chloroquine-resistant NF54-R strain is a greater sensitivity to lipophilicity (and lesser sensitivity to desolvation and dipole moment) for the resistant strain. This indicates that hydrogen bonding and polar interactions are relatively reduced in resistant strains when bound to FQs. Similarly desolvation has been shown to be the dominant factor influencing the effect of inhibitors against the cyclindependent kinases, but lipophilicity and dipole moment are also significant factors in the resistance shown by MDR proteases to the anti-viral drugs.

Conclusions

It has been shown that the general equation can accurately describe the activity of FQs against whole organism anti-bacterial and anti-malarial parasites, the steady state uptake into rat brains, and the concentrations of FQs in human seminal and prostatic fluids (and prostatic tissue) when treating chronic bacterial prostatis. The reason that the general equation can describe whole organism effects is that many of the important individual pharmacological steps that contribute to such whole organism effects are also described by the same general equation.

Desolvation / solvation effects have been shown to be an important (but usually overlooked) aspect of the most of the pharmacologically processes involved in FQ dissolution, intestinal permeation, systematic circulation, clearance, plasma protein binding, uptake and efflux into bacteria, binding to topoisomerases -DNA, and hERG QT prolongation. Most of these processes involve multi-faceted interactions amongst desolvation, lipophilicity, polar interaction and molecular size of the FQs and the environment, membrane, active anion membrane transporter, protein or hERG transport channel, or binding inhibitory interactions with gyrase supercoiling and 6-mer single stranded DNA oligonucleotides.

Results from the study of sensitive and resistant strains of the malarial Plasmodium parasite show a greater sensitivity to lipophilicity (and lesser sensitivity to desolvation and dipole moment) for the resistant strain. This indicates that hydrogen bonding and polar interactions are relatively reduced in resistant strains when bound to FQs. This conclusion is supported by detailed binding free energies of the FQ-Mg-water-Ser,Glu bridging in type IV topoisomerases.

It is also shown that serious side effects of FQs such as hERG QT prolongation can be predicted for new FQs. Another important conclusion that arises from this study is that the various neutral, ionic and zwitterionic species which can exist around the physiological pH can be differentially involved in the various processes.

The general equation or its modified form is a useful guide to drug discovery and design, particularly the allowing examination of the various species of a potential drug that may predominate at different pH levels, or by making changes to the molecular structure to predict binding or transport properties.

  [Setny 2010 9 , Shan 2010 10 , Mondial 2014 11 ]

  Schwanz 2012 43 ] Equation 1 Log MIC = -0.049 ΔG desolvation + 0.142 ΔG lipophilicity + 0.121 Dipole Moment + 0.009 Molecular Volume + 0.902 Where R 2 = 0.624, SEE = 0.325, SE(ΔG desolvation ) = 0.030, SE(ΔG lipophilicity ) = 0.073, SE(Dipole Moment) = 0.062, SE(Molecular Volume) = 0.003, F = 5.0, Significance F = 0.013

44 ] Equation 2 IC 50 = 4 . 3 IC 50 = 2 .

 4425043502 96 ΔG desolvation + 7.10 ΔG lipophilicity -3.27 Dipole Moment -0.26 Molecular Volume + 135.55 Where R 2 = 0.656, SEE = 20.18, SE(ΔG desolvation ) = 2.37, SE(ΔG lipophilicity ) = 7.16, SE(Dipole Moment) = 2.69, SE(Molecular Volume) = 0.23, F=7.16, Significance F = 0.002, n=20 Antimalarial activities (IC50) of 20 quinolones and fluoroquinolones (Moxifloxacin, Lomefloxacin, Enoxacin, Norfloxacin, Grepafloxacin, Ciprofloxacin, Gatifloxacin, Clinifloxacin, Fleroxacin, Flumequine, Nalidixic Acid, Pipemidic Acid, Piromidic Acid, Chloroquine, Rufloxacin, Trovafloxacin (all as neutral species), Pefloxacin zwitterion (ZW), Sparflox (ZW), Levoflocacin (ZW), Ofloxacin (ZW) against chloroquine-resistant (NF54-R) strains of Plasmodium falciparum in vitro [Mahmoudi 2003 44 ] Equation 42 ΔG desolvation + 5.84 ΔG lipophilicity -0.29 Dipole Moment -0.06 Molecular Volume + 60.63 Where R 2 = 0.481, SEE = 17.53, SE(ΔG desolvation ) = 1.42, SE(ΔG lipophilicity ) = 4.30, SE(Dipole Moment) = 1.61, SE(Molecular Volume) = 0.14, F=3.47, Significance F = 0.033, n=20

  Mahmoudi 2003 44 ] Equation 4 IC 50 = 0.92 ΔG desolvation -5.32 ΔG lipophilicity -4.56 Dipole Moment + 1.64 Molecular Volume -288.26 Where R 2 = 0.756, SEE = 18.90, SE(ΔG desolvation ) = 2.25, SE(ΔG lipophilicity ) = 6.17, SE(Dipole Moment) = 2.64, SE(Molecular Volume) = 0.433, F=3.87, Significance F = 0.085, n=10 Antimalarial activities of 10 quinolones and fluoroquinolones (Norfloxacin, Ciprofloxacin, Clinifloxacin, Piromidic Acid, Rufloxacin, Trovafloxacin, Sparfloxacin (all as neutral species), Pefloxacin ZW, Ofloxacin ZW, Grepafloxacin omitted) against hepatic stages of P. yoelii yoelii at 48 h. [Mahmoudi 2003 44 ] Equation 4a IC 50 = -0.27 ΔG desolvation -8.28 ΔG lipophilicity -3.96 Dipole Moment + 1.18 Molecular Volume -288.26 Where R 2 = 0.767, SEE = 17.70, SE(ΔG desolvation ) = 2.30, SE(ΔG lipophilicity ) = 6.21, SE(Dipole Moment) = 2.52, SE(Molecular Volume) = 0.53, F=3.30, Significance F = 0.137, n=9

Equation 5 Prostatic

 5 fluid:plasma = -0.31 ΔG desolvation -0.27 ΔG lipophilicity + 0.21 Dipole Moment -0.01 Molecular Volume + 2.95 Where R 2 = 0.933, SEE = 0.21, SE(ΔG desolvation ) = 0.06, SE(ΔG lipophilicity ) = 0.07, SE(Dipole Moment) = 0.11, SE(Molecular Volume) = 0.01, F=10.52, Significance F = 0.041, n=8

Liu 2005 46 ] Equation 6 R ss = - 12 .

 612 1ΔG desolvation -31.2ΔG lipophilicity +12.5 Dipole Moment + 0.7 Molecular Volume -367.0 Where R 2 = 0.858, SEE = 88.9, SE(ΔG desolvation ) = 11.2, SE(ΔG lipophilicity ) = 41.1, SE(Dipole Moment) = 28.5, SE(Molecular Volume) = 1.9, F=9.05, Significance F = 0.010 Equation 7 F = -0.017ΔG desolvation +0.010ΔG lipophilicity +0.040 Dipole Moment + 0.000 Molecular Volume -367.0 Where R 2 = 0.754, SEE = 0.061, SE(ΔG desolvation ) = 0.007, SE(ΔG lipophilicity ) = 0.028, SE(Dipole Moment) = 0.020, SE(Molecular Volume) = 0.001, F=4.59, Significance F = 0.048

Equilibrium solubility of 9

 9 floxacins: Sarafloxacin, Norfloxacin, Difloxacin, Enrofloxacin, Lomefloxacin, Ciprofloxacin, Sparfloxacin, Danofloxacin treated as anionic species, Ofloxacin as zwitterion Equation 8 Log solubility = 0.054 ΔG solvation + 0.270 ΔG lipophilicity + 0.165 Dipole Moment -0.009 Molecular Volume + 13.420 Equilibrium solubility of 9 floxacins: Sarafloxacin, Norfloxacin, , Difloxacin, Enrofloxacin, Lomefloxacin, Ciprofloxacin, Sparfloxacin, Danofloxacin treated as anionic species, Ofloxacin as zwitterion, Equation 10 Log solubility = 0.035 ΔG CDS + 0.344 ΔG lipophilicity + 0.142 Dipole Moment -0.007 Molecular Volume + 11.512 Where R 2 = 0.914, SEE = 0.306, SE(ΔG solvation ) = 0.056, SE(ΔG lipophilicity ) = 0.105, SE(Dipole Moment) = 0.026, SE(Molecular Volume) = 0.005, F=10.61, Significance F = 0.021

  Kinetic solubility of 9 floxacins: Sarafloxacin, Norfloxacin, Difloxacin, Enrofloxacin, Lomefloxacin, Ciprofloxacin, Sparfloxacin, Danofloxacin treated as anionic species, Ofloxacin as zwitterion Equation 11 Log solubility = 0.053 ΔG solvation + 0.226 ΔG lipophilicity + 0.130 Dipole Moment -0.014 Molecular Volume + 14.806 Where R 2 = 0.709, SEE = 0.524, SE(ΔG solvation ) = 0.111, SE(ΔG lipophilicity ) = 0.206, SE(Dipole Moment) = 0.065, SE(Molecular Volume) = 0.009, Significance F = 0.204 Kinetic solubility of 9 floxacins: Sarafloxacin, Norfloxacin, Difloxacin, Enrofloxacin, Lomefloxacin, Ciprofloxacin, Sparfloxacin, Danofloxacin treated as anionic species, Ofloxacin as zwitterion Equation 12 Log solubility = 0.167ΔG CDS + 0.372ΔG lipophilicity + 0.106Dipole Moment -0.014 Molecular Volume + 11.512 Where R 2 = 0.906, SEE = 0.299, SE(ΔG solvation ) = 0.056, SE(ΔG lipophilicity ) = 0.102, SE(Dipole Moment) = 0.025, SE(Molecular Volume) = 0.004, Significance F = 0.025

  , Wang 2014 49 Eq 13 Log Caco-2 permeability = -0.274 ΔG desolvation -0.268 ΔG lipophilicity + 0.22 Dipole Moment -0.012 Molecular Volume -2.450 Where R 2 = 0.600, SEE = 0.616, SE(ΔG solvation ) = 0.108, SE(ΔG lipophilicity ) = 0.185, SE(Dipole Moment) = 0.126, SE(Molecular Volume) = 0.015, F=3.4, Significance F = 0.061

  [Noble 2003 59 ] Equation 28 Log IC 50 = -0.007 ΔG desolvation -0.195 ΔG lipophilicity -0.058 Dipole Moment -0.014 Molecular Volume -0.816 Where R 2 = 0.753, SEE = 0.427, SE(ΔG desolvation ) = 0.056, SE(ΔG lipophilicity ) = 0.093, SE(Dipole Moment) = 0.089, SE(Molecular Volume) = 0.006, Significance F = 0.027 Equation 29 Log IC 50 = 0.083 ΔG CDS -0.217 ΔG lipophilicity -0.100 Dipole Moment -0.012 Molecular Volume -0.821 Where R 2 = 0.801, SEE = 0.383, SE(ΔG CDS ) = 0.064, SE(ΔG lipophilicity ) = 0.067, SE(Dipole Moment) = 0.048, SE(Molecular Volume) = 0.005, Significance F = 0.013 The binding of FQ and Q drugs to 6-mer single stranded DNA oligonucleotides is correlated with potency IC 50 . 59 [Noble 2003 59 ] The binding (apparent K D ) to ss-DNA for Difloxacin, Enofloxacin, Norfloxacin, Pefloxacin. Ciprofloxacin, 8-Fluoro-Ciprofloxacin, 8-Chloro-Ciprofloxacin, 8-Bromo-Ciprofloxacin, 8-Ethoxy-Ciprofloxacin, Oxalinic Acid, as anionic species shows the following relationship Equation 30 Log App K D = 0.050 ΔG CDS + 0.034 ΔG lipophilicity -0.007 Dipole Moment + 0.013 Molecular Volume + 4.067 Where R 2 = 0.704, SEE = 0.178, SE(ΔG CDS ) = 0.030, SE(ΔG lipophilicity ) = 0.040, SE(Dipole Moment) = 0.002, SE(Molecular Volume) = 0.022, Significance F = 0.130

  [Aldred 2014 [START_REF] Aldred | Topoisomerase IV-quinolone interactions are mediated through a water-metal ion bridge: mechanistic basis of quinolone resistance[END_REF] ] The X-ray structures (PDB 2XKK) show the Moxifloxacin bond lengths C 4 =O 1.26A, chelated carboxyl C=O 1.21A, C 4 =O-Mg 1.99A, carboxyl C=O-Mg 1.90A. The 4 water molecules octahedrally co-ordinated to Mg were set at 2.07A as per the X-ray structure (2XKK) and the separately characterised Mg(Ofloxacin) 2 complex.[START_REF] Wohlkonig | Structural basis of quinolone inhibition of type IIA topoisomerases and target-mediated resistance[END_REF][START_REF] Dravensek | X-Ray crystallographic, NMR and antimicrobial activity studies of magnesium complexes of fluoroquinolones -racemic ofloxacin and its S-form, levofloxacin[END_REF] [Wohlkonig 201064 , Dravensek 2006 65 ] The hydrogen bonds between the serine O-H 2 O-Mg and glutamic acid carboxylate C=O ---H 2 O-Mg were arbitrarily varied from 2.60-3.0A and 2.30-2.80A to reflect the weaker hydrogen bond to the serine residue and the ionic bridge to the glutamate carboxylate anion.

1 [Figure 3 .

 13 Figure 3. Fluoroquinolone binding in the pore cavity of hERG channels. Solvated fluoroquinolone enters the channel, and partially desolvates prior to binding to channel proteins. Residues involved in fluoroquinolone binding possibly include Thr623, Ser624, and Val625 close to the intracellular entrance to the selectivity filter as well as two aromatic residues Tyr652 and Phe656. Open state only shown, but binding can possibly occur in inactived state. (adapted from Vanderberg 2012 39 )

  [Dahan 2012 12 , El-Kattan 2012 13 , Hou 2006 14 , Waterbeemd 2003 15 ]

  [Nikaido 1985 [START_REF] Nikaido | Molecular basis of bacterial outer membrane permeability[END_REF] , Gunn 2001[START_REF] Gunn | Bacterial modification of LPS and resistance to antimicrobial Peptides[END_REF] , Hancock 1988 28 , Ma 1994 29 , Wiese 2003 30 ] Mutations to the LPS bilayer can increase drug resistance. More importantly, porin deficiency has been associated with increased bacterial resistance in nearly all Gram-negative species involved in hospital-acquired infections.[START_REF] Charrel | Prevalence of outer membrane porin alteration in beta-lactam-antibiotic-resistant Enterobacter aerogenes[END_REF][START_REF] Yigit | Carbapenem resistance in a clinical isolate of Enterobacter aerogenes is associated with decreased expression of OmpF and OmpC porin analogs[END_REF][START_REF] Cornaglia | Relative importances of outer membrane permeability and group 1 beta-lactamase as determinants of meropenem and imipenem activities against Enterobacter cloacae[END_REF][START_REF] Domenech-Sanchez | Role of Klebsiella pneumoniae OmpK35 porin in antimicrobial resistance[END_REF] [Charrel 1996 31 , Yigit 2002 32 , Cornaglia 1995 33 , Domenech-Sanchez 2003 34 ]

Eq 27 IC 50 /[Plasma] = 13.07 ΔG desol,CDS + 0.77 ΔG lipophilicity + 2.46 Dipole Moment

  The inhibition (IC 50 μM/[Plasma]) of the hERG cardiac K + channel by the FQs Sparfloxacin 18, Moxifloxacin 129, Grepafloxacin 50, Gatifloxacin 130, Ciprofloxacin 966, Levofloxacin 815 (as Zwitterion), Ofloxacin 1420 (as zwitterion)[Kang 2001 57 ] Piromidic Acid, Pipemidic Acid, as anionic species. (Ofloxacin was omitted as an outlier, which is consistent with Ofloxacin being a racemic mixture, with the S isomer having twice the anti-bacterail activity of the R isomer[START_REF] Morrissey | Mechanism of Differential Activities of Ofloxacin Enantiomers[END_REF] [Morrissey 1996

	+ 0.13
	Molecular Volume + 70.48
	Where R 2 = 0.966, SEE = 15.48, SE(ΔG desolvation ) = 3.85 SE(ΔG lipophilicity ) = 8.00, SE(Dipole Moment) = 4.68,
	SE(Molecular Volume) = 0.59, F=14.00, Significance F = 0.068, n=7
	Eqs 26 and 27 using ΔG desol,CDS where the IC 50 values are corrected for the peak plasma
	concentrations of the FQs are very similar except the coefficients are roughly 11 times less
	sensitive for eq 27
	FQ anti-bacterial mechanism
	Inhibitory concentrations (IC 50 , μM, inhibition of gyrase supercoiling activity) for 12 FQ and
	Q drugs: Difloxacin, Enofloxacin, Norfloxacin, Pefloxacin. Ciprofloxacin, 8-Fluoro-
	Ciprofloxacin, 8-Chloro-Ciprofloxacin, 8-Bromo-Ciprofloxacin, 8-Ethoxy-Ciprofloxacin,
	Oxalinic Acid,

[START_REF] Morrissey | Mechanism of Differential Activities of Ofloxacin Enantiomers[END_REF]

]). Ciprofloxacin and its 8-substituted derivatives, (8-F, 8-Cl, 8-Br, 8-Ethoxy) had the lowest IC50s (the most potent), and the nonfluorinated compounds oxolinic acid, pipemidic acid, and piromidic acid had the highest IC50s.

Where R2 = 0.965, SEE = 183.91, SE(ΔG desolvation ) = 45.77, SE(ΔG lipophilicity ) = 95.09, SE(Dipole Moment) = 55.59, SE(Molecular Volume) = 7.04, F=13.86, Significance F = 0.067, n=7

Log calculated human permeability rates = -0.075 ΔG desolvation -0.107 ΔG lipophilicity + 0.059 Dipole Moment -0.004 Molecular Volume - 3.251 Where R 2 = 0.436, SEE = 0.243, SE(ΔG solvation ) = 0.042, SE(ΔG lipophilicity ) = 0.073, SE(Dipole Moment) = 0.050, SE(Molecular Volume) = 0.006, F=1.75, Significance F = 0.225 Since PAMPA membranes have no transporter capability, whereas Caco-2 membranes do have transporter capability, a comparison between PAMPA and Caco-2 transport of FQs may shed light on their intestinal permeability.

PAMPA intrinsic permeability coefficients (P e 10 -6 cm/s) for the uncharged forms of 4′N-Rnorfloxacin: 0.7 (R=H), 49 (Me), 132 (n-Pr), 365 (n-Bu); 4′N-R-ciprofloxacin: 2.7 (H), 37 (Me), 137 (n-Pr), 302 (n-Bu); 4′N-R-3′-methylciprofloxacin: 3.8 (H), 20 (Me), 51 (Et), 160 (n-Pr), 418 (n-Bu). The alkyl chain length at the 4′N-position of the piperazine residue was varied as a function of pH from 4 to 10. Rat in situ permeability measurements were correlated with the PAMPA P e measurements (r 2 =0.87). [START_REF] Barmejo | PAMPA-a drug absorption in vitro model: 7. Comparing rat in situ, Caco-2, and PAMPA permeability of fluoroquinolones[END_REF] [Barmejo 2004 50 ] The substitution of various alkyl groups at the 4′N-position of the piperazine is related to a secondary FQgyrase a binding mode that may overcome gyrase A mediated FQ resistence. [START_REF] Malik | Suppression of gyrase-mediated resistance by C7 aryl fluoroquinolones[END_REF] Transport of FQs by renally expressed basolateral SLC22 super family transporters: mOAT (mouse organic anion transporter mOAT3, active in adsorption and excretion of anions). Enoxacin, fleroxacin, levofloxacin, lomefloxacin, moxifloxacin, prulifloxacin, sparfloxacin*, norfloxacin, and ciprofloxacin* exhibit competitive inhibition for mOat3 with K i = 396, 817, 515, 539, 1356, 299, 205, 558 and 198 μM respectively. [START_REF] Mulgaonkar | Fluoroquinolone disposition: Identification of the contribution of renal secretory and reabsorptive drug transporters[END_REF] [Mulgaonkar 2012 52 ] A very poor correlation (R 2 0.187, F significance 0.908) was obtained using the anionic FQ species, but Ciprofloxacin and Sparfloxacin were clear outliers. A better correlation was found using all species as zwitterions (R 2 0.517, F significance 0.474), but again Ciprofloxacin and Sparfloxacin were clear outliers. Treating all species as zwitterions but with Ciprofloxacin* and Sparfloxacin* treated as anions gave a vastly improved correlation as shown below.

Competitive basolatal renal inhibition of mOAT3 for 9 FQ drugs, [START_REF] Mulgaonkar | Fluoroquinolone disposition: Identification of the contribution of renal secretory and reabsorptive drug transporters[END_REF] The in vivo brain distribution of the FQ HSR-903 (Olamufloxacin), grepafloxacin and possibly other FQ were strongly influenced by efflux transporters, including P-gp at the BBB. The effect of 9 FQ on steady state uptake (%) of HSR-903 on in vitro primary-cultured monolayers of brain capillary endothelial cells was studied.

Effect on in vitro brain capillary endothelial cell uptake of HSR-903 (Olamufloxacin) by the following FQs: Grepafloxacin 360.

FQ binding to plasma proteins

Bovine serum albumin BSA has been used as a proxy for human serum albumin -drug binding interactions. The binding constants for eight fluoroquinolone antibiotics (ciprofloxacin, enoxacin, fleroxacin, levofloxacin, lomefloxacin, norfloxacin, ofloxacin, pefloxacin) and bovine serum albumin (BSA) are known, (K b 10 4 M -1 ). [START_REF] Liu | Interaction between Fluoroquinolones and Bovine Serum Albumin Studied by Affinity Capillary Electrophoresis[END_REF] The correlations using the neutral forms of the FQs were very poor.

FQ serious side effects: hERG cardiac QT prolongation

Hagiwara 2001 [START_REF] Hagiwara | A Comparative Study of the Fluoroquinolone Antibacterial Agents on the Action Potential Duration in Guinea Pig Ventricular Myocardia[END_REF] has assessed the effects of 10 fluoroquinolones on cardiac repolarization by measuring the action potentials recorded from isolated guinea pig right ventricular myocardia under constant conditions, namely, myocardial preparations were electrically stimulated at the fixed pacing frequency of 1 Hz. Sparfloxacin was the most active drug, at 10 μM, prolonged APD 90 8.4%, and APD 50 9.0%. All other drugs were measured at 100 μM as the APD 90 values. Blockade of I Kr leads to a delay in the cardiac repolarization and prolongs the APD of myocardia and consequently prolongs the QT interval on the ECG. The action potential duration (APD 90 100 μM) recorded from isolated guinea pig ventricular myocardia from ten fluoroquinolone antibacterial agents: Sparfloxacin 40.8, Moxifloxacin 25.1, Grepafloxacin 23.8, Gatifloxacin 12.7, Ciprofloxacin 3.3, Trovafloxacin 2.9, Levofloxacin 0.8 (all as neutral species), Tosufloxacin ZW 5.2, Gemifloxacin ZW 4.2, Sitafloxacin ZW 2.4% [Hagiwara 2001 The influence of the peak free plasma concentrations of the FQ on the IC 50 values has also been investigated.