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

Drug discovery model using molecular orbital computations: tyrosine kinase inhibitors

Keywords: discovery model using molecular orbital computations: tyrosine kinase inhibitors. 2016 QSAR model, tyrosine kinase inhibitors, multi-kinase inhibitors, kinase binding, active protein transporters, quantum mechanics

Drug discovery model using molecular orbital computations: tyrosine kinase inhibitors

Introduction

Drug efficacy in the broadest sense can be described as the efficiency of the processes of drug delivery or transport to its intended target, followed by the drug binding or interacting with its target receptor. For an orally administered drug, these processes include intestinal solubility and the full range of ADMET (absorption, distribution, metabolism, excretion, and toxicity) processes which include transport across cellular membranes. In many cases, the target is a protein or enzyme, and drug binding within a receptor pocket is a crucial phase of the efficacy process. In many cases, there are multiple receptor pockets in the same enzyme, so unintended side effects may occur.

A common model for both processes based on 4 molecular physico-chemical properties of the prospective drugs has been previously applied to passive and facilitated diffusion, and active organic anion transporter drug membrane transport and some competitive statin-CYP enzyme binding processes. [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: Cellular transport, side effects, drug-drug interactions and cytotoxicity -the unrecognized role of lactones[END_REF][ Fong 2015[START_REF] Fong | Statins in therapy: Cellular transport, side effects, drug-drug interactions and cytotoxicity -the unrecognized role of lactones[END_REF] The model comprises four main properties: (a) desolvation energy in water (b) lipophilicity or hydrophobicity based on solvation energy in 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. The basic model is shown in equation 1.

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

The method uses quantum mechanical methods to compute each of the 4 independent variables for the drug and relies on multiple correlation with experimental values for transport or binding processes, preferably from the same source to minimize errors in experimentally determined values. Since sufficient experimental data are generally not available for a robust multi-variate statistical analysis, it is important that there are other physico-chemical studies that can verify the validity and appropriateness of using each of the four independent variables.

The application of equation 1 to membrane transport has shown that desolvation is a dominant feature for passive and facilitated diffusion, and organic anion transporter processes before the drug can enter the membrane or transporter. Lipophilicity or hydrophobicity, the dipole moment and molecular volume become important within the membrane or transporter. It can be seen that the passage of a drug through a lipophilic membrane, or within the interior of a transporter, is similar to the binding of a drug within a largely lipophilic pocket of an enzyme. We have also shown that eq 1 fits the solubility of a wide range of drugs in water. [START_REF] Fong | A general model of drug solubility in water[END_REF] [Fong, 2015] A full quantum mechanical (QM) study of the binding of imatinib and nilotinib with the Bcr-ABL tyrosine kinase has shown that desolvation of the binding pocket and the inhibitor is required during the binding process in the enzyme pocket. Also the total hydrophobic or van der Waals interaction between the inhibitor and kinase is much larger than the electrostatic or coulombic interaction (from hydrogen bonding, polar bonding) between the inhibitor and kinase. [START_REF] Fong | Binding energies of tyrosine kinase inhibitors: Error assessment of computational methods for imatinib and nilotinib binding[END_REF] [Fong 2015]

Water: Desolvation in binding pocket

In molecular dynamics studies of the binding of dasatinib to src-tyrosine kinase, it has been shown that almost complete desolvation of the binding pocket occurs before complex formation does occur. [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][START_REF] Shan | How Does a Drug Molecule Find its Target Binding Site?[END_REF][Setny 2010, Mondial 2014, Shan 2011] As the ligand approaches the protein pocket, complete dewetting of pocket occurs (mainly enthalpy driven) even though the pocket could accommodate the first shell of hydration around ligand. Disorganized water in the cavity can have more entropy than in the bulk solvent & its release eliminates water fluctuation within the pocket, while the release of water from the hydrophobic environment within pocket to bulk water results in a gain of enthalpy. These studies are consistent with the QM study of imatinib and nilotinib binding in the Bcr-ABL tyrosine kinase pocket, where the calculation of drug-protein binding energy included complete desolvation of the drug and the inner area of the protein pocket immediately surrounding the bound drug before binding with the protein. [START_REF] Fong | Binding energies of tyrosine kinase inhibitors: Error assessment of computational methods for imatinib and nilotinib binding[END_REF] [Fong 2015] These computational studies are supported by the analysis on a large set of proteins which showed that the average dielectric constant inside the protein is relatively low, about 6-7, and reaches a value of about 20-30 at the protein's surface. [START_REF] Li | Constant" of Proteins: Smooth Dielectric Function for Macromolecular Modeling and Its Implementation in DelPhi[END_REF] [START_REF] Li | Constant" of Proteins: Smooth Dielectric Function for Macromolecular Modeling and Its Implementation in DelPhi[END_REF]] Since bulk water has a dielectric constant of 78.3D, the environment surrounding an incoming drug changes from 78.3D in the bulk water solvent to ca. 20-30 at the opening of the protein pocket, to ca. 6-7 inside the pocket after binding. Thermodynamically, this transition must lead to energy intensive desolvation of the drug. In a study of the desolvation energies required for K + and Na + ions to bind with the carrier ionophores valinomycin or crown ethers, it was found that desolvation energies were the dominant factors governing binding of K + and Na + to the valinomycin. [START_REF] Fong | Physiology of ionophore transport of potassium and sodium ions across cell membranes: Valinomycin and 18-Crown-6 Ether[END_REF][ [START_REF] Fong | Physiology of ionophore transport of potassium and sodium ions across cell membranes: Valinomycin and 18-Crown-6 Ether[END_REF] Protein crystal structures (105 at atomic resolution ≤1.0 Å) with a high level of hydration water were examined by calculating the experimental water-protein radial distribution function or surface distribution function (SDF) and the water radial distribution function (RDF). The first maximum at 2.75Å represents the centre of the inner layer of hydration water formed by hydrogen bonds between water and polar atoms of the protein. The second maximum at 3.65Å represents the outer layer of hydration water formed by water-water hydrogen bonds and van der Waals interactions between water and non-polar atoms of the protein forming clathrate-hydrate-like structures. The SDF describes the density of water as a function of the distance from the protein surface (the closest non-hydrogen atom). The RDF describes the density of water as a function of the distance from a particular water molecule. There was a significant difference in the water structure and water potentials between hydration water and bulk water in protein crystals. The first and second maxima of the RDF are at 2.75 and 4.5Å, respectively, the same distances as those of bulk water. However, the maxima/minima of the RDF of hydration water are higher/lower than those of bulk water, indicating that hydration water is denser and narrowly defined, likely due to stronger interactions induced by the protein. [START_REF] Chen | Hydration water and bulk water in proteins have distinct properties in radial distributions calculated from 105 atomic resolution crystal structures[END_REF] [START_REF] Chen | Hydration water and bulk water in proteins have distinct properties in radial distributions calculated from 105 atomic resolution crystal structures[END_REF]] As the X-ray structures of various TKIkinase complexes show polar bonding with tyrosine kinase proteins fall within the 2.75-4.5Å range, it appears then that it is the first or inner solvent shells of the TKI and kinases that are the important indicators for gauging the extent of desolvation that must occur for TKI-kinase complex binding to occur. The X-ray protein hydration results are consistent with desolvation of the protein pocket before binding by the inhibitor, as found in molecular mechanics studies for dasatinib-src-tyrosine kinase [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][START_REF] Shan | How Does a Drug Molecule Find its Target Binding Site?[END_REF][Setny 2010, Mondial 2014, [START_REF] Shan | How Does a Drug Molecule Find its Target Binding Site?[END_REF] or quantum mechanical studies of nilotinib-and imatinib-ABL tyrosine kinase. [START_REF] Fong | Binding energies of tyrosine kinase inhibitors: Error assessment of computational methods for imatinib and nilotinib binding[END_REF] [Fong 2015]

Dipole moment: polar and non-polar interactions

The DM of a drug in water is a vector measure of the product of the magnitude of the positive and negative electrostatic charges on the molecule and the distance separating the charges. The DM is a measure of the overall polarity of the molecule. Drug molecules usually have a mixture of hydrophilic and hydrophobic groups, the proportion and distribution of which determines the overall DM. Reversible competitive inhibition of a proteins usually involves an intermolecular non-covalent interaction between an inhibitor and a protein receptor. These interactions can be electrostatic, π-effects, van der waals forces and hydrophobic effects. Hydrogen bonding is usually the strongest of the electrostatic interactions, followed by salt bridges, often of the order of 4-10 kcal/mol. π-effects, van der waals forces and hydrophobic effects are usually much smaller in magnitude, usually much less than ca. 1-2 kcal/mol. Hydrophobic interactions are not specific, but occur between non-polar hydrocarbon groups on the drug and receptor sites which tend to exclude water molecules in the binding region. Hydrophobic interactions are usually very small, but numerous, and can arise from the burying of hydrophobic surfaces during drug-receptor binding. The solvent accessible surface area (SASA) of the drug is commonly taken as a proxy of the extent of the hydrophobic effect, and the extent of this effect is thought to be between 5 and 45 cal/(Å 2 mol). 11-13][ [START_REF] Sharp | Reconciling the magnitude of the microscopic and macroscopic hydrophobic effects[END_REF][START_REF] Nt Southall | A View of the Hydrophobic Effect[END_REF][START_REF] Pw Snydera | Mechanism of the hydrophobic effect in the biomolecular recognition of arylsulfonamides by carbonic anhydrase[END_REF]] Olsson [14][2008] have examined the SCORPIO data base of published isothermal titration calorimetric results for a range of protein and small ligand interactions with changes in solvation (using the polar and non-polar solvent accessible surface area of the ligand and changes resulting from the protein-ligand complexation). Most interactions were enthalpy driven. The strongest correlation was between non-polar surface area burial upon complexation and the binding free energy, consistent with an entropy driven process (with TΔS o being about double ΔH o ). However the free energy contribution per unit area buried was only about 30-50% of previous similar studies of transfer free energies of small ligands. The transfer of an overall polar drug like nilotinib, (13.1D) or a charged drug like imatinib ion (46.0D) from water with a dielectric constant of 78.3 to a nonpolar media with dielectric constant of ~3 (lipid bilayer) or 4 to 10 (interior of proteins) costs significant energy [START_REF] Baldwin | Chapter 6. Weak Interactions in Protein Folding: Hydrophobic Free Energy, van der Waals Interactions, Peptide Hydrogen Bonds, and Peptide Solvation[END_REF] [START_REF] Baldwin | Chapter 6. Weak Interactions in Protein Folding: Hydrophobic Free Energy, van der Waals Interactions, Peptide Hydrogen Bonds, and Peptide Solvation[END_REF]]. Analysis on a large set of proteins shows that (a) the average dielectric constant inside the protein is relatively low, about 6-7, and reaches a value of about 20-30 at the protein's surface, and (b) high average local dielectric constant values are associated with charged residues while low dielectric constant values are assigned to the regions occupied by hydrophobic residues. [START_REF] Li | Constant" of Proteins: Smooth Dielectric Function for Macromolecular Modeling and Its Implementation in DelPhi[END_REF] [START_REF] Li | Constant" of Proteins: Smooth Dielectric Function for Macromolecular Modeling and Its Implementation in DelPhi[END_REF]] N-Octane has a dielectric constant of 1.94 and should be a good proxy for the interior of a protein.

One estimate gives a free energy gain of ~ 0.03 kcal/mol/Å 2 (buried polar surfaces giving up 0.1 kcal/mol/Å 2 ), such that every 46 Å 2 of buried hydrophobic surface area (for example a Me group) gives a 10 increase in potency. [START_REF] Baldwin | Chapter 6. Weak Interactions in Protein Folding: Hydrophobic Free Energy, van der Waals Interactions, Peptide Hydrogen Bonds, and Peptide Solvation[END_REF] [START_REF] Baldwin | Chapter 6. Weak Interactions in Protein Folding: Hydrophobic Free Energy, van der Waals Interactions, Peptide Hydrogen Bonds, and Peptide Solvation[END_REF]] Another estimate is that every methylene unit added to a hydrocarbon chain increases the free energy of transfer into water by a fixed amount, by between 0.025 and 0.033 kcal/mol/Å 2 [START_REF] Nt Southall | A View of the Hydrophobic Effect[END_REF][Southall 2002] Hydrophobic interactions appear to be the dominant driving force for induced fit of receptors around drugs, and can also be described as hydrophobic induced fit collapse of a receptor around a drug. Charge-reinforced hydrogen bonds can contribute up to 3000-fold in binding, but the more common neutral-neutral hydrogen bonds may contribute anything between zero and 15-fold. So the more numerous hydrophobic interactions can easily dominate hydrogen bonding in drug receptor binding [START_REF] Davis | Hydrophobic Interactions, and Failure of the Rigid Receptor Hypothesis[END_REF][START_REF] Baldwin | Chapter 6. Weak Interactions in Protein Folding: Hydrophobic Free Energy, van der Waals Interactions, Peptide Hydrogen Bonds, and Peptide Solvation[END_REF]] It has also been shown that studies of the binding of drugs to biological receptors using molecular force fields cannot adequately incorporate hydrophobic interactions or conformational changes during binding, and can use ad hoc values of 0.02 to 0.04 kcal/mol/Å 2 for all types of atoms. [START_REF] Davis | Hydrophobic Interactions, and Failure of the Rigid Receptor Hypothesis[END_REF] [START_REF] Davis | Hydrophobic Interactions, and Failure of the Rigid Receptor Hypothesis[END_REF]] A study of the binding of the imatinib ion and nilotinib with Bcr-ABL tyrosine kinase has shown that the major error in inhibitor -kinase binding energy calculations lies in the non-polar solvation terms of the solvation calculations. The quantum mechanically reverse calculated hydrophobic proxy factors for transfer from water to n-octane were 28.0 and 34.6 cal/(mol/Å 2 ) for the imatinib ion and nilotinib respectively, which were very different from the arbitrary PBSA solvation values previously used in molecular mechanics literature studies. [START_REF] Fong | Binding energies of tyrosine kinase inhibitors: Error assessment of computational methods for imatinib and nilotinib binding[END_REF] [Fong 2015]

Hydrophobicity or lipophilicity

As discussed above, the hydrophobic effect is a measure of the non-polar interaction between a drug and a protein within the binding pocket. Hydrophobicity is also related to lipophilicity, a concept widely used in the drug industry. The role of lipophilicity in drug discovery and design is a critical one. Lipophilicity is a key physicochemical property that plays a crucial role in determining the solubility and ADMET (absorption, distribution, metabolism, excretion, and toxicity) properties and the overall suitability of drug candidates. LogP, (the partition coefficient of a drug between water and n-octanol), is a widely used estimate of a compound's overall lipophilicity, a value that influence its behaviour in a range of biological processes relevant to a drug discovery, such as solubility, permeability through biological membranes, hepatic clearance, lack of selectivity and non-specific toxicity. For oral drugs, a logP value comprised between 2 and 3 is often considered optimal to achieve a compromise between permeability and first-pass clearance. [START_REF] Hughes | Physiochemical drug properties associated with in vivo toxicological outcomes[END_REF][START_REF] Arnott | The influence of lipophilicity in drug discovery and design[END_REF][START_REF] Arnott | Lipophilicity Indices for Drug Development[END_REF] [START_REF] Hughes | Physiochemical drug properties associated with in vivo toxicological outcomes[END_REF][START_REF] Arnott | The influence of lipophilicity in drug discovery and design[END_REF],2013] However, wet octanol solution is a poor proxy for proteins or biological membranes because it contains ~2M of water, and cyclohexane would be a much better proxy. A set of solvation parameters derived for the protein interior from protein engineering data was also different from octanol scale: it was close to cyclohexane scale for nonpolar atoms but intermediate between cyclohexane and octanol scales for polar atoms. [START_REF] Radzicka | Comparing the polarities of the amino acids: sidechain distribution coefficients between the vapor phase, cyclohexane, 1-octanol, and neutral aqueous solution[END_REF][START_REF] Lomize | Interatomic potentials and solvation parameters from protein engineering data for buried residues[END_REF][Radicza 1988, Lomize 2012]

Drug molecular volume Vs binding pocket volume

The molecular volume of a ligand can be easily measured, either as a bare molecule, or solvated. However the volume of a protein receptor pocket is more difficult to estimate, and the relationship between this volume and the volume of a ligand is unknown. An analysis of over 100 protein-ligand structures has shown that ligand volume and binding site volume are somewhat correlated when binding site volume is < or =700 Å 3 , but the ligand seldom occupies the entire site. [START_REF] Liang | Anatomy of protein pockets and cavities: measurement of binding site geometry and implications for ligand design[END_REF] [START_REF] Liang | Anatomy of protein pockets and cavities: measurement of binding site geometry and implications for ligand design[END_REF]] A wide scale analysis of protein-ligand binding pockets reveals that the number of distinct pockets is small. Similar pockets occur in unrelated protein structures. The small number of pockets suggests that off-target interactions among diverse proteins are inherent in kinases, proteases and phosphatises, and minor side effects cannot be avoided. For an example, sorafenib is one of FDA approved anti-cancer drugs that have multiple targets in the family of protein kinases. Two of these kinases, B-Raf and VGFR2, have been crystallized in complex with the drug molecule and the structures show two structurally similar binding complex regions, despite a low global protein similarity. Protein kinases generally share high level structural similarity in its catalytic domain. [START_REF] Skolnick | Implications of the small number of distinct ligand binding pockets in proteins for drug discovery, evolution and biochemical function[END_REF] [START_REF] Skolnick | Implications of the small number of distinct ligand binding pockets in proteins for drug discovery, evolution and biochemical function[END_REF]] These observations illustrate that within a certain protein pocket volume, and where the catalytic domain is similar, it may be possible to utilize the drug volume as one contributing key physical indicator to gauge drug-protein binding interaction. Similarly, where drug-active transporter interactions are involved, the drug molecular volume is also a critical factor. [START_REF] Fong | Statins in therapy: Cellular transport, side effects, drug-drug interactions and cytotoxicity -the unrecognized role of lactones[END_REF] [Fong 2015] For diffusion controlled drug permeation and facilitated diffusion through cell membranes, it has been shown that molecular volume is a critical factor. [

1][Fong 2014]

Quantitative structure activity models (QSAR) which seek to relate physico-chemical properties of drugs to biological binding or interaction with proteins or enzymes (eg K m , K i , IC 50 etc) rarely have sufficient experimental data to be statistically robust, and the measurement accuracy of these properties varies very significantly from laboratory to laboratory. The measurement of physico-chemical properties of drugs are more accurate especially for small drugs less than about 500 Da, but errors can still be significant. To minimize errors in QSAR relationships, the use of comparative data from single sources is best, with rigorous statistical analysis, and the use of a minimal number of independent variables which have demonstrated independent physico-chemical rationales for their use.

In this study quantum mechanical studies of the TKI are applied, which have been conformationally optimised in water. Neutral and ionic species have been characterised based on the known pKa values of the drugs, and the four independent variables are calculated using the same high level computational method: comparative differences between these absolute calculations also minimize errors. This study will apply equation 1 to some competitive binding interactions of tyrosine kinase inhibition and to some competitive interactions of TKI with hOTP3, OATP, OCT influx transporters. [24,25.26 Chronic myeloid leukaemia (CML) is a cancer of blood-forming cells in the bone marrow. Abnormal cells gradually fill the bone marrow and spill into the bloodstream. The disease typically develops very slowly and symptoms such as anaemia, bleeding problems or infections may not occur for years after the disease starts. Bcr-Abl tyrosine-kinase inhibitors (TKI) are the first-line therapy for most patients with CML. Most cases of CML are caused by a chromosomal abnormality that results in the formation of a so-called Philadelphia chromosome which is a fusion between the Abelson (Abl) tyrosine kinase gene and the break point cluster (Bcr) gene, resulting in a chimeric oncogene (Bcr-Abl). This causes the production of tyrosine kinase. TKI inhibit the phosphorylation, a key step in the kinase activation of many proteins by signal transduction cascades. TKIs operate by four different mechanisms: they can compete with adenosine triphosphate (ATP), the phosphorylating agent, the substrate or both, or can act in an allosteric fashion, by binding to a site outside the active site, affecting its activity by a conformational change. [START_REF] Posner | Kinetics of inhibition by tyrphostins of the tyrosine kinase activity of the epidermal growth factor receptor and analysis by a new computer program[END_REF] [START_REF] Posner | Kinetics of inhibition by tyrphostins of the tyrosine kinase activity of the epidermal growth factor receptor and analysis by a new computer program[END_REF]] Secondgeneration TKIs such as dasatinib and nilotinib have been approved for the treatment of CML patients who are refractory or intolerant to imatinib. In vitro tests of these new TKIs show considerably higher activity in comparison with imatinib, with a 40-fold increased potency for nilotinib and a 325-fold for dasatinib. Nilotinib and dasatinib are able to overcome imatinib resistance caused by several BCR-ABL tyrosine kinase domain mutations. [START_REF] O'hare | In vitro activity of Bcr-Abl inhibitors AMN107 and BMS-354825 against clinically relevant imatinib-resistant Abl kinase domain mutants[END_REF] [O'Hare 2005] A schematic representation of the interaction of a TKI with a tyrosine kinase is shown in Figure 1.

Results and discussion

Before absorption can occur a drug first has to be in a soluble state. The solubility of orallyadministered drugs is dependent on their chemical properties and often by the intragastric pH the drug is exposed to in the process of absorption. Weakly basic drugs may show decreased absorption, while the absorption of weakly acidic drugs may increase at higher intragastric pH. Because kinase inhibitors (KI) are typically weakly basic, they can be present in either ionised or non-ionised forms. In vivo, the bioavailability of KI are pH dependent which depends upon the pKa of the KI as well as the pH of the gastrointestinal (GI) tract. For example, the solubility of imatinib and nilotinib rapidly declines above pH 5.5 and 4.5 respectively. Nilotinib or Tasigna/Nilotinib.HCl is practically insoluble in buffer solutions of pH 4.5 and higher pH values. (Novartis/ Tasigna fact sheet). Erlotinib becomes more soluble in a mildly acidic environment (pH 5.42) (Genentech fact sheet, 2013). Each segment of the GI tract has its own characteristic pH level: acidity declines over the GI tract from the stomach (pH 1-3) to the small intestine (pH 5-7) and the colon (pH 7-8). For imatinib and nilotinib solubility and absorption therefore rapidly decreases after the stomach. This is further supported by the relative short time to reach maximum plasma concentration (T max ) for these drugs; 2-4 hours for imatinib and 3 hours for nilotinib. Hence, due to the physicochemical properties of imatinib and nilotinib, the stomach is essential for dissolution and absorption of these TKIs. For sunitinib however, solubility does not decline until pH 6.8. Sunitinib is absorbed from the GI tract, reflected by a long time to reach maximum plasma concentration of sunitinib, e.g. 6-12 hours [START_REF] De Wit | Effect of gastrointestinal resection on sunitinib exposure in patients with[END_REF][de Wit 2014].

As many tyrosine-kinase inhibitors show pH-dependent solubility in the physiologically relevant pH range, they can be susceptible to gastric pH-dependent drug-drug interactions when co-administered with acid-suppressive agents. Such drug-drug interactions could reduce the systemic exposure of tyrosine kinase inhibitors, and lead to loss of therapeutic benefit. Concomitant use of acid-suppressing agents (eg proton pump inhibitors, H 2 antagonists, antacids) will shift the stomach environment to a higher pH, making it less acidic and, therefore, affecting the chemical bioavailability. [START_REF] Yu | Drug interactions between tyrosine-kinase inhibitors and acid suppressive agents: more than meets the eye[END_REF][Guo 2014] Imatinib, dasatinib, nilotinib, gefitinib, erlotinib, sorafinib, sunitinib, pazopanib, lapatinib are orally administered multi-targeted TKI with high activity towards several families of receptor and non-receptor tyrosine kinases involved in angiogenesis, tumour growth and metastatic progression of cancer. The absolute bioavailability in humans for imatinib is almost 100% with pazopanib between 14-39% and estimates have been made for nilotinib (31%), sorafenib (50%) and sunitinib (50%). The pH dependence of the solubility and concentrations of the ionized forms of drugs such as the TKI are critical factors in determining bioavailability. The ionized forms have a large bearing on the ability of drugs such as the TKI to be transported across cellular membranes, particularly where large free energies of desolvation are required before the TKI can bind with the enzyme in the binding pocket. [START_REF] Di Gion | Clinical pharmacokinetics of tyrosine kinase inhibitors: focus on pyrimidines, pyridines and pyrroles[END_REF][de Gion 2011, [START_REF] Fong | Binding energies of tyrosine kinase inhibitors: Error assessment of computational methods for imatinib and nilotinib binding[END_REF][START_REF] Setny | How Can Hydrophobic Association Be Enthalpy Driven?[END_REF] [ [START_REF] Fong | Statins in therapy: Cellular transport, side effects, drug-drug interactions and cytotoxicity -the unrecognized role of lactones[END_REF]Fong , 2015] ] A significant issue relating to TKI (and other drugs) is what is the actual species involved in vivo compared to those used in vitro studies conducted during drug discovery and definition. Solubility and pKa are critical properties usually defined in vitro. There are laboratory measurements and calculated values of pKa for most TKI, but few studies of what are the actual species involved in ionization processes. Using spectroscopic techniques, it has been shown that gefitinib protonates at the tertiary N of the morpholino group and at the N1 site of the quinazolino group, and lapatinib diprotonates at the secondary NH 2 and N1 of the quinazolino groups. [START_REF] Song | Acid-Base Interactions of Polystyrene Sulfonic Acid in Amorphous Solid Dispersions Using a Combined UV/FTIR/XPS/ssNMR Study[END_REF][Song 2016] As several of the approved TKI have multiple basic sites, the actual species in vivo may have important clinical effects. A detailed study of the protonation sites of bosutinib shows 4 possible protonation sites, with experimetal pKa values of 11.2 (aromatic amine), 8.1 (4-piperidine), 4.3 (quinoline) and 3.5 (1-piperidine). Noteworthy observations were the overlapping of the 8.1 and 4.3 values forming a diprotic system, and the potential dipotonation of the piperidine group. The latter observation may explain the X-ray crystal structures where imatinib (which contains the same piperidine group) binds to the kinase as the diprotonated piperidine species (3K5V, 3GVU). It is also notable that despite the pKa values indicating that only very small concentrations of the diprotonated species being present in solution, the diprotonated-kinase complex can still crystallise from solution. The use of computational techniques to examine multiple possible species that could exist in vitro and in vivo for both transport and binding, coupled with equation 1 can be useful diagnostic indicators in drug development.

The specificities of nine approved TKI (imatinib, dasatinib, nilotinib, gefitinib, erlotinib, lapatinib, sorafenib, sunitinib, and pazopanib) have been determined by activity-based kinase profiling using a large panel of human recombinant active kinases. Profiling was at the physiological level K m and 1 mM for ATP to determine which kinases were susceptible to inhibition by the TKI. [START_REF] Kitagawa | Activity-based kinase profiling of approved tyrosine kinase inhibitors[END_REF][ [START_REF] Kitagawa | Activity-based kinase profiling of approved tyrosine kinase inhibitors[END_REF] The competitive inhibition (apparent K m and IC 50 ) of ATP by various TKI have been analysed using equation 1 for the following kinases: ABL, DDR1, DDR2, PDGFR α , PDGFR β which have (minimally) sufficient data for analysis using equation 1.

The actual species in solution at pH 7 (the Kitagawa in vitro experimental conditions) have been determined from the known pKa values of the TKI (see Experimental). X-ray crystal structures have been examined where available to see if protonated inhibitors are bound to the kinase. Protonated forms of imatinib (2HYY, 3HEC PDB structures) and dasatinib (3D5G, 2GQG) have been found to bind to kinase enzymes, but there is no structural evidence that nilotinib (3CS9), erlotinib (1M17), sorafinib (3HEG), sunitinib (3GOE), pazopanib (3CJG), gefitinib (4WKQ), or lapatinib (1XKK) bind in the protonated forms. There are even examples where imatinib binds to the kinase as the diprotonated (on the piperidine moiety) species (3K5V, 3GVU). Sunitinib can bind in the protonated form (3MIY) and nonprotonated form (3GOE) to different kinases. The complexities of thermodynamic control that govern complex crystallization versus kinetic control that govern determinations of K m or IC 50 under competitive binding conditions in pH dependent solubility conditions are difficult to disentangle. In many studies, protonated salts of the TKI are used to study in vitro binding to improve solubility of the inhibitor at pH 7. Using Kitagawa's pH 7 data, protonated forms of imatinib, dasatinib, gefitinib, sunitinib, the diprotonated form of lapatinib, and neutral forms of nilotinib, erlotinib, sorafinib and pazopanib were used, based on the form of the starting inhibitor as a salt or neutral base, pKa, and X-ray structures for the imatinib, dasatinib and sunitinib complexes. The same forms of species were used to examine Giacomini's in vitro hOCT3 transporter studies.

Kinase inhibition at a physiological ATP level of 1 mM ATP was used to profile of these tyrosine kinase inhibitors. K m is the apparent value of ATP. The IC 50 values for inhibitors against the various kinases studied are affected by the apparent K m values. [START_REF] Kitagawa | Activity-based kinase profiling of approved tyrosine kinase inhibitors[END_REF][Kitagawa 2012] Equation 2 and 3 show reasonable correlations for the TKI properties against K m for the ABL tyrosine kinase. The ΔG desolvation and ΔG lipophilicity are calculated using the SMD solvation model and represent bulk solvation properties of the drug in water at pH 7. Eq 3 differs from eq 2 in using ΔG desolv,CDS and ΔG lipo,CDS where CDS is the cavitation dispersion solvent structure, involving 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[END_REF]] In this study it is postulated that the ΔG desolvCDS and ΔG lipoCDS values may be a close approximation of how a solvated inhibitor reacts as it approaches and starts to enter the kinase binding pocket (dielectric constant 20-30) and leaves the bulk water environment (dielectric constant 78.3) and desolvation binding starts to occur. This scenario has been modelled using more intensive molecular mechanics computations. [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][START_REF] Shan | How Does a Drug Molecule Find its Target Binding Site?[END_REF][Setny 2010, Mondial 2014, Shan 2011 Eq 2 and 3 show similar sensitivities to the independent variables, but the signs are reversed for ΔG desolvation and ΔG desolv,CDS . A positive term is expected for inhibitor desolvation as energy has to be expended to desolvate the incoming inhibitor, which is counter balanced by the hydrophobic (ΔG lipophilicity ) and polar (dipole moment) interactions between the protein and inhibitor. Eq 3 shows a strong correlation between K m for the TKI and the independent variables, showing the negative effect of desolvation and positive effect of the hydrophobic interaction (negative ΔG lipo,CDS ) quite clearly. Most receptor tyrosine kinases are single subunit receptors, and ligand binding to the extracellular domain induces formation of receptor dimers. Each monomer has a single hydrophobic transmembrane-spanning domain, an extracellular N terminal region, and an intracellular C terminal region. [START_REF] Hubbard | Structural analysis of receptor tyrosine kinases[END_REF] [START_REF] Hubbard | Structural analysis of receptor tyrosine kinases[END_REF]]. Inhibition of receptor tyrosine kinases may be expected to a complex interplay involving these regions. Inhibition of several receptor tyrosine kinases have been analysed using equation 1: DDR1, DDR2, PDGFR α and PDGFR β.

DDR1 is a receptor tyrosine kinase involved in cancer cell invasion. Eq 4 and 5 show similar patterns to the equivalent eq 2 and 3 for the ABL kinase. Eq 5 shows a moderate correlation between K m for the TKI and the independent variables, showing the negative effect of desolvation and positive effect of the hydrophobic effect (negative ΔG lipo,CDS ) quite clearly. Eq 5 and 6 are similar showing that the comparison of Km and IC 50 seem to be valid, though the reliability of the individual coefficients is not high in view of the only moderate statistical correlations. Eq 7and 8 for DDR2 appear to be quite different from the same equations for DDR1 even though they belong to the same family. This may be related to DDR1 and DDR2 being transmembrane receptors and the differences in receptor regions. Also erlotinib fits the equations best as the protonated form, based on the large outlier behaviour if treated as a neutral species. Eqn 7 and 8 are very similar, although only moderately correlated with K m and IC 50 . Eq 9-12 9-11show moderate only correlations with PDGFR α and PDGFR β kinases. Plateletderived growth factor receptors (PDGFR) are cell surface tyrosine kinase receptors for members of the platelet-derived growth factor (PDGF) family. PDGF subunits α and β are important factors regulating cell proliferation, cellular differentiation, cell growth, development and many diseases including cancer. Also erlotinib fits the equations best as the protonated form, based on the large outlier behaviour if treated as a neutral species. Eq 9-12 show strong similarities with those for DDR2 but not DDR1. Eq 12-15 show correlations of K m and IC 50 for TKI in inhibiting metformin uptake by the active transporter hOCT3. [START_REF] Ra Johnston | Selective Inhibition of Human Solute Carrier Transporters by Multikinase Inhibitors[END_REF] [START_REF] Minematsu | Interactions of Tyrosine Kinase Inhibitors with Organic Cation Transporters and Multidrug and Toxic Compound Extrusion Proteins[END_REF]] The organic cation uptake transporter 3 (OCT3) also known as the solute carrier family 22 member 3 (SLC22A3) is a protein that in humans is encoded by the SLC22A3 gene. As the substrate concentration in the inhibition study was low compared with the Michaelis-Menten constant Km, the IC50 values are virtually equal to the inhibition constant Ki values, assuming competitive or noncompetitive inhibition. Eq 13 correlation with ΔG desolv,CDS and ΔG lipo,CDS is similar to eq 12, but shows the negative effect of desolvation and the positive effect of the hydrophobic effect (ie negative ΔG lipo,CDS lowers IC 50 ) quite clearly. Eq 14 show the correlation with IC 50 assuming all the TKI are in the ionized form. Equation 15shows the correlation assuming inhibitors are neutral species, which seems unlikely given the low solubilities at pH 7. However in view of the large desolvation penalties for the ionized forms, one possibility is the small concentrations of the neutral forms in equilibrium at pH 7 might be the preferred species transported by hOCT3. In vivo the situation is even more complex since it is known that TKI complex with blood serum and plasma proteins under clinical steady state conditions. TKI taken daily orally develop steady state plasma concentration within 2-3 weeks. [START_REF] Honeywell | Tyrosine kinase inhibitor pharmacokinetics: Discrepancies between plasma, serum, whole blood and cellular concentrations of various tyrosine kinase inhibitors[END_REF] [Honeywell] Tyrosine kinase inhibitors (imatinib ion, dasatinib ion, nilotinib, gefitinib ion, erlotinib, sorafinib, sunitinib ion, lapatinib diion) inhibiting active metformin uptake by hOCT3 Equations 16-18 Show the application of the general equation 1 to the organic anion transporting polypeptide OATP1A2, and the organic cation transporter OCT1 data of Johnson 2014 [START_REF] Ra Johnston | Selective Inhibition of Human Solute Carrier Transporters by Multikinase Inhibitors[END_REF]. The inhibition of a wide range of multi-kinase inhibitors (MKI) to the uptake of the substrates anion E3S (estrone-3-sulphate) by OATP1A2 and the cation MPP + (1-methyl-4-pyridium acetate) by OCT1 have been analysed. A critical question that arises in this study is the form of the inhibitor that interacts with anion and cation transporters, since the MKI are predominantly in the protonated form at pH 7, but small concentrations may exist in the neutral form as well, as discussed above in eq 12-15 above for the hOCT3 data.

Analysis of the raw IC 50 data for OATP1A2 indicates that lapatinib, bosutinib and soratinib lie well outside the range of all other MKI, possibly indicating that these inhibitors are interacting in the protonated forms. There is also evidence (vide supra) that lapatinib and bosutinib can exist as diions. Statistical residual analysis suggests that lapatinib and bosutinib are better fits as diions, and soratinib is clearly an outlier (and can exist only as monoprotonated species). Eq 16 compares all MKI as ionic species with eq 17 with all MKI as neutral species (with lapatinib and bosutinib as diions in both eq 16 and 17 The above equations can only be indicative and not clearly definitive since competitive inhibition under the experimental conditions is clearly a complex series of reactions, and insufficient experimental data is not available to derive highly robust statistical correlations. However, a consistent pattern of correlations which emerges from the 23 equations all under different conditions, widely different TKI and MKI, various kinases and transporters gives confidence that the general equation 1 may have a widespread or even fairly universal application for small ligand-protein interactions.

Conclusions

It has been shown that equation 1 can be successfully applied to the competitive binding of a number of tyrosine kinase inhibitors and multi-kinase inhibitors to a range of kinase enzymes. Equation 1 also applies to the active competitive transport of these tyrosine kinase inhibitors by the hOCT3, OATP1A2 and OCT1 transporters. There is strong independent evidence from the literature that ΔG desolvation , ΔG lipophilicity , the dipole moment and molecular volume are good inherent indicators of the transport or binding ability of drugs. A modified form of equation 1 using the free energy of water desolvation (ΔG desolv,CDS ) and the lipophilicity free energy (ΔG lipo,CDS ), 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. Equation 1 or its modified form may be useful guides 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.

Experimental

Computational 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[END_REF] [START_REF] Marenich | Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric[END_REF]] 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][ [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]] 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.

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.

4

 4 Competitive inhibition of ATP by ABL tyrosine kinase by imatinib ion, dasatinib ion, nilotinib, gefitinib ion, erlotinib, sorafinib, sunitinib ion, pazopanib Equation 2 K m = -38.3ΔG desolvation -44.2ΔG lipophilicity +50.4 Dipole Moment -20.7Molecular Volume+ 6621.0 Where R 2 = 0.939, SEE = 326.7, SE(ΔG desolvation ) = 17.7, SE(ΔG lipophilicity ) = 63.9, SE(Dipole Moment) = 44.0, SE(Molecular Volume) =11.6, F=8.1, Significance=0.036 Competitive inhibition of ATP by ABL tyrosine kinase by imatinib ion, dasatinib ion, nilotinib, gefitinib ion, erlotinib, sorafinib, sunitinib ion, pazopanib where ΔG desolv,CDS and ΔG lipoCDS are desolvation and lipophilicity free energies using the CDS solvation energy. Equation 3 K m = -76.9ΔG desolv,CDS -274.2ΔG lipo,CDS +20.5 Dipole Moment -37.0Molecular Volume +8398.Where R 2 = 0.933, SEE = 343.0, SE(ΔG desolvCDS ) = 117.4, SE(ΔG lipoCDS ) = 121.1, SE(Dipole Moment) = 10.5, SE(Molecular Volume) = 6.7, F=10.4, Significance=0.041

4

 4 Competitive inhibition of ATP by DDR1 kinase by imatinib ion, dasatinib ion, nilotinib, ion, erlotinib, sorafinib, sunitinib ion, pazopanib, lapatinib diion Equation 4 K m = -11.5ΔG desolvation -97.7ΔG lipophilicity -78.5 Dipole Moment +3.8Molecular Volume -2102.2 Where R 2 = 0.976, SEE = 315.8, SE(ΔG desolv ) = 16.0, SE(ΔG lipo ) = 34.0, SE(Dipole Moment) =12.2, SE(Molecular Volume) = 3.8, F=40.8, Significance=0.002 Competitive inhibition of ATP by DDR1 by imatinib ion, dasatinib ion, nilotinib, gefitinib ion, erlotinib, sorafinib, sunitinib ion, pazopanib, lapatinib diion where ΔG desolv,CDS and ΔG lipoCDS are desolvation and lipophilicity free energies using the CDS solvation energy. Equation 5 K m = -418.7ΔG desolv,CDS -110.5ΔG lipo,CDS +6.8 Dipole Moment +11.0Molecular Volume +8411.Where R 2 = 0.727, SEE = 1068.1, SE(ΔG desolvCDS ) = 117.4, SE(ΔG lipoCDS ) = 374.2, SE(Dipole Moment) = 21.5, SE(Molecular Volume) = 20.2, F=2.7, Significance=0.180 Competitive inhibition of ATP by DDR1 by imatinib ion, dasatinib ion, nilotinib, gefitinib ion, erlotinib, sorafinib, sunitinib ion, pazopanib, lapatinib diion where ΔG desolv,CDS and ΔG lipoCDS are desolvation and lipophilicity free energies using the CDS solvation energy. Equation 6 IC 50 = -4.0ΔG desolv,CDS +22.5ΔG lipo,CDS +6.8 Dipole Moment -1.5Molecular Volume +848.5 Where R 2 = 0.775, SEE = 71.5, SE(ΔG desolvCDS ) = 3.5, SE(ΔG lipoCDS ) = 9.4, SE(Dipole Moment) = 21.5, SE(Molecular Volume) = 0.9, F=2.6, Significance=0.230

  Competitive inhibition of ATP by DDR2 tyrosine kinase by imatinib ion, dasatinib ion, nilotinib, gefitinib ion, erlotinib ion, sorafinib, sunitinib ion, pazopanib Equation 7 K m = -20.0ΔG desolvation -91.0ΔG lipophilicity -44.9 Dipole Moment -1.7Molecular Volume -429.4 Where R 2 = 0.877, SEE = 213.1, SE(ΔG desolvation ) = 11.2, SE(ΔG lipophilicity ) = 28.0, SE(Dipole Moment) = 11.7, SE(Molecular Volume) =2.7, F=5.4, Significance=0.100 Competitive inhibition of ATP by DDR2 kinase by imatinib ion, dasatinib ion, nilotinib, gefitinib ion, erlotinib ion, sorafinib, sunitinib ion, pazopanib Equation 8 IC 50 = -152.9ΔG desolvation -715.0ΔG lipophilicity -359.5 Dipole Moment -13.9Molecular Volume -3372.5 Where R 2 = 0.893, SEE = 1574.3, SE(ΔG desolvation ) = 82.6, SE(ΔG lipophilicity ) = 205.0, SE(Dipole Moment) = 86.3, SE(Molecular Volume) =20.1, F=3.8, Significance=0.150

2

 2 Competitive inhibition of ATP by PDGFR α kinase by imatinib ion, dasatinib ion, nilotinib, ion, erlotinib ion, sorafinib, sunitinib ion, pazopanib Equation 9 K m = -19.4ΔG desolvation -76.2ΔG lipophilicity -31.0 Dipole Moment -2.5Molecular Volume -45.6 Where R 2 = 0.902, SEE = 148.5, SE(ΔG desolvation ) = 7.8, SE(ΔG lipophilicity ) = 19.4, SE(Dipole Moment) = 8.2, SE(Molecular Volume) =1.9, F=6.9 Significance=0.071 Competitive inhibition of ATP by PDGFR α kinase by imatinib ion, dasatinib ion, nilotinib, gefitinib ion, erlotinib ion, sorafinib, sunitinib ion, pazopanib Equation 10 IC 50 = -230.8ΔG desolvation -921.5ΔG lipophilicity -294.5 Dipole Moment -34.2Molecular Volume -1520.6 Where R 2 = 0.918, SEE = 1474.4, SE(ΔG desolvation ) = 77.6, SE(ΔG lipophilicity ) = 194.0, SE(Dipole Moment) = 80.8, SE(Molecular Volume) =18.8, F=8.4, Significance=0.055 Competitive inhibition of ATP by PDGFR β kinase by imatinib ion, dasatinib ion, nilotinib, gefitinib ion, erlotinib ion, sorafinib, sunitinib ion, pazopanib Equation 11 K m = -23.7ΔG desolvation -89.6ΔG lipophilicity -36.7 Dipole Moment -2.1Molecular Volume -259.Where R 2 = 0.898, SEE = 171.0, SE(ΔG desolvation ) = 9.0, SE(ΔG lipophilicity ) = 22.5, SE(Dipole Moment) = 9.4, SE(Molecular Volume) =2.2, F=6.6 Significance=0.076

  Where R2 = 0.884, SEE = 6.91, SE(ΔG desolvation ) = 0.35, SE(ΔG lipophilicity ) = 0.75, SE(Dipole Moment) = 0.26, SE(Molecular Volume) =0.08, F=5.7 Significance=0.090 Tyrosine kinase inhibitors (imatinib ion, dasatinib ion, nilotinib, gefitinib ion, erlotinib, sorafinib, sunitinib ion, lapatinib diion) inhibiting active metformin uptake by hOCT3 Equation 13 IC 50 = -8.7ΔG desolv,CDS -3.4ΔG lipo,CDS +0.3 Dipole Moment -0.1Molecular Volume -77.2 Where R 2 = 0.727, SEE = 1068.1, SE(ΔG desolvCDS ) = 2.7, SE(ΔG lipoCDS ) = 3.7, SE(Dipole Moment) = 3.0, SE(Molecular Volume) = 0.2, F=2.5, Significance=0.240 Tyrosine kinase inhibitors (all ionic species) inhibiting active metformin uptake by hOCT3 Equation 14 IC 50 = 0.83ΔG desolvation +0.46ΔG lipophilicity +0.11 Dipole Moment -0.26Molecular Volume +205.0 Where R 2 = 0.903, SEE = 7.83, SE(ΔG desolvation ) = 0.55, SE(ΔG lipophilicity ) = 0.98, SE(Dipole Moment) = 0.38, SE(Molecular Volume) =0.16, F=7.1 Significance=0.070 Tyrosine kinase inhibitors (all neutral species) inhibiting active metformin uptake by hOCT3 Equation15 IC 50 = 5.1ΔG desolvation -3.8ΔG lipophilicity +4.2 Dipole Moment -1.4Molecular Volume +205.0 Where R 2 = 0.953, SEE = 4.42, SE(ΔG desolvation ) = 0.78, SE(ΔG lipophilicity ) = 1.20, SE(Dipole Moment) = 0.91, SE(Molecular Volume) =0.22, F=15.1 Significance=0.025

Equation 1 :

 1 Transport or Binding = ΔG desolvation + ΔG lipophilicity + Dipole Moment + Molecular Volume OrTransport or Binding = ΔG desolv,CDS + ΔG lipo,CDS + Dipole Moment + Molecular Volume

-0.54ΔG desolvation -2.21ΔG lipophilicity -0.61 Dipole Moment -0.10Molecular Volume - 73.5

  ).Eq 23 below compares with eq 21, but uses the ΔG desolv,CDS and ΔG lipo,CDS parameters. Multi kinase inhibitors (gefitinib, lapatinib diion, nilotinib, sunitinib, bosutinib diion, vandetanib, afatinib, cediranib, erlotinib, pelitinib, neratinib, foretinib, soratinib ion) inhibiting active MPP + uptake by OCT1 Equation

	Multi kinase inhibitors (gefitinib ion, lapatinib diion, nilotinib ion, sunitinib ion, bosutinib
	diion, vandetinib ion, afatinib ion, cediratinib ion, erlotinib ion, pelitinib ion, neratinib ion,
	foretinib ion) inhibiting active E3S uptake by OATP1A2	Equation 16
	IC 50 =

23 IC 50 = -10.04ΔG desolv,CDS -6.68ΔG lipo,CDS -1.02 Dipole Moment -0.29Molecular Volume - 31.0

	Where R 2 = 0.803, SEE = 13.54, SE(ΔG desolvCDS ) = 2.44, SE(ΔG lipoCDS ) = 1.95, SE(Dipole Moment) = 0.28, SE(Molecular
	Volume) = 0.10, F=8.16, Significance=0.006

Multi kinase inhibitors (gefitinib, lapatinib diion, nilotinib, sunitinib, bosutinib diion, vandetanib, afatinib, cediranib, erlotinib, pelitinib, neratinib, foretinib) inhibiting active E3S uptake by OATP1A2 Equation 17 IC 50 = 0.16ΔG desolvation -0.80ΔG lipophilicity -0.71 Dipole Moment -0.02Molecular Volume -5.3

Where R 2 = 0.983, SEE = 4.00, SE(ΔG desolvation ) = 0.28, SE(ΔG lipophilicity ) = 0.58, SE(Dipole Moment) = 0.18, SE(Molecular Volume) =0.02, F=101.3 Significance=0.000 Eq 18 below compares with eq 16, but uses the ΔG desolv,CDS and ΔG lipo,CDS parameters. Multi kinase inhibitors (gefitinib ion, lapatinib diion, nilotinib ion, sunitinib ion, bosutinib diion, vandetanib ion, afatinib ion, cediranib ion, erlotinib ion, pelitinib ion, neratinib ion, foretinib ion) inhibiting active E3S uptake by OATP1A2


Janos J Sarbo
email: janos@cs.ru.nl

A Semiotic Approach to Integrative Negotiation

Keywords: Negotiation, Abduction, Peircean theory, Sign aspects, Cognitive model

An analysis of two-party integrative negotiation reveals the potential of this type of bargaining for being interpreted as a conceptualization process. Past research on a semiotic model of human processing shows the possibility of a definition of a uniform representation of knowledge. In this paper we suggest that by combining the above results integrative negotiation can be positioned as an abductive process. We justify our hypothesis by means of experimental data.

Introduction

Arguably the most efficient strategy for negotiation is win-win or two-party integrative negotiation [START_REF] Fisher | Getting to Yes: Negotiating Agreement without Giving in[END_REF], [START_REF] Walton | A Behavioral Theory of Labor Negotiations[END_REF]. In this paper we are concerned with the question how negotiation efficiency can be increased through goal-driven communication between the parties. We show that win-win negotiation involves a process which is isomorphic to a Peircean model of cognitive activity [START_REF] Sarbo | Knowledge in Formation: A Computational Theory of Interpretation[END_REF]. An analysis of the latter process reveals types of information involved by its events. A combination of the above results enables the conclusion to be drawn that, in negotiation, if the parties get stuck at some stage, this could be because of a lack of information necessary for a realization of some event in the bargaining process. Communication of the required information may enable the parties to further develop their negotiation and bring it to a successful end, eventually. We assume that, in order to get hold of the above problem of communication, the parties need to represent, besides their own information, a possible conceptualization of the negotiation process by the other party as well. This is where the Peircean model comes handy. By virtue of its categorical foundation, this model enables a uniform representation of knowledge in any domain (or, from any perspective of interpretation) hence a merging of representations from different perspectives by the parties, into a single representation. Through analyzing the events of the arising process during negotiation, on-line, the parties may derive information that can be helpful for the bargaining other party. This way of communication is akin to abduction, as it may enable to establish a relation between knowledge elements, which relation could not be derived by a party on the basis of his/her actual knowledge, neither in a deductive nor an inductive fashion.

In order to enhance the efficiency of win-win negotiation, various off-line methods have been developed in the past. Examples are template design and evaluation, and algorithms for developing Pareto optimal solutions [START_REF] Raiffa | Negotiation Analysis[END_REF]. A problem shared by those methods is by virtue of their distant relation with the bargaining process.

Experience with a course on negotiation at Radboud University Nijmegen, The Netherlands, shows that the use of integrative negotiation is by far not obvious. Following an analysis of exercises in bargaining, students tend to stuck at some stage in their negotiation, keep repeating their earlier arguments hence make no progress. Unless a trained mediator is involved, integrative negotiation may not arise. In order to make the parties comply with that strategy, this course applies a technique that forces the parties to co-operate. 1 This is achieved by means of setting a shared goal that both parties must agree on, and from which goal the aim of their negotiation necessarily follows. In a concrete example, a couple of students were asked to act as managers of a company. Following their instruction they had competing interests concerning the solution of a problem of the company. The shared goal was set by aiming at an increase of profit by the company. The parties were asked by a mediator (this role was played by a third student) if this goal does comply with their interest. As the answer must be positive (otherwise the managers were not able to correctly function anymore), the parties were 'primed' for acting in a co-operative fashion. Later when they were asked to develop new initiatives for a solution, they could not refuse inventing ideas that at least partly respected the interest of the negotiating other party as well.

Besides win-win bargaining, another example of integrative negotiation is problem elicitation. A distinguishing property of the latter is the existence of a spontaneous interest by the bargaining parties, for achieving a common goal. This may explain why the parties themselves may be able to generate helpful communication thereby enhancing their negotiation process [START_REF] Galinsky | Why it pays to get inside the head of your opponent[END_REF]. In this paper we capitalize on the analogy between the two kinds of negotiation phenomena above and illustrate our approach with an analysis of a case study in problem elicitation. The development of a methodology enabling helpful communication is on our current agenda.

The structure of the paper is the following. We begin with an analysis of integrative negotiation from a process perspective (Sect. 2). This is followed by an introduction of a Peircean model of human information processing (Sect. 3), and how this model may enable a generation of efficient communication in win-win bargaining (Sect. 4). The proposed approach is justified by an analysis of experimental data (Sect. 5). We close the paper with a summary of results (Sect. 6).

Integrative Negotiation as a Conceptualization Process

Integrative negotiation, first introduced in [START_REF] Walton | A Behavioral Theory of Labor Negotiations[END_REF], is a strategy that has the potential to achieve an agreement that gives everyone what they want and this way enables the parties to produce a more satisfactory output. This strategy is different from the one used by positional bargaining, which is based on fixed, opposing viewpoints (cf. positions) and tends to result in a compromise or in no agreement at all. Compromises may not satisfy the true interest of the negotiating parties. An oft-cited example of integrative negotiation and a creation of joint value is that of the dispute between two sisters over an orange [START_REF] Follet | Constructive conflict[END_REF]. Based on their positions, their mother cuts the orange in half and gives each girl one half. This outcome represents a compromise. However, if the mother was able to find out why the girls wanted the orangewhat her interests werethere could have been a different, win-win outcome. This is because one girl wanted to eat the meat of the orange, but the other just wanted the peel to use in baking some cookies. If their mother had known their interests or were able to make the girls elicit their problem, they could have both gotten all of what they wanted, rather than just half.

According to [START_REF] Fisher | Getting to Yes: Negotiating Agreement without Giving in[END_REF], [START_REF] Kirk | Mental contrasting promotes interactive bargaining[END_REF], [START_REF] Spanglar | Integrative or Interest-based Bargaining. Beyond Intractability[END_REF], integrative negotiation can be characterized by a process, in which, first, each side's interest is sorted out. Their needs and why they want that is abstracted into possible demands. Next, they are asked to picture how their demands may be perceived by the other side, what may be standing in the way, which complementary information would enable an agreement, and in that context, how the interests of the two sides could be turned into actual demands. Integrative negotiation reaches its goal when those actual demands by the parties are combined into an agreement or a proposition of a solution of the input problem.

From the above analysis we draw the conclusion that integrative negotiation, as a process, makes use of four types of operation on the input problem appearing as a phenomenon. These are sorting, abstraction, complementation, and predication (proposition formation). In the next section we suggest that this process can be isomorphic to a cognitively based model of human processing. By making use of the potential analogy between the two models we show that integrative negotiation can be positioned as a conceptualization process. An advantage of the application of a cognitively based model is that it may give insight in the types of events of bargaining, and how the efficiency of those events can be increased by means of communication.

Knowledge in Formation (KIF)

The cognitively based model of human processing, introduced by our Knowledge in Formation (KIF) research project, has been presented at various ICISO conferences in the past [START_REF] Sarbo | On Well-formedness in Requirement Elicitation Processes[END_REF], [START_REF] Van Breemen | Beyond Flatland? What does semiotics add to information sciences[END_REF]. The used representation is based on the assumption, suggested by [START_REF] Harnad | Categorical Perception: The groundwork of cognition[END_REF], that the aim of cognitive activity is the generation of a response on the input stimulus. A process model of response generation can be given as follows.

In a single interaction, the stimulus, appearing as an effect, is affecting the observer occurring in some state. The qualities of this state (q 2 ) and effect (q 1 ), which are in focus, and complementary memory knowledge or context (C) triggered by q 2 and q 1 , define the input for information processing ([q 2 q 1 C]). See Fig. 1. The goal of this process is the generation of a relation, explaining why this effect is occurring to this state. In order to achieve this goal, the observer or interpreting system has to sort out the two types of qualities and context ([q 2 ], [q 1 ],[C]); abstract the input qualities in focus into independent collections ((q 2 ), (q 1 )); complete them with complementary knowledge by the interpreting system ((q 2 ,C), (q 1 ,C)); and merge the obtained representations into a single relation ((q 2 ,C)-(q 1 ,C)) through predication. We assume that the above process can be executed in cyclic fashion, recursively. Note that each one of the expressions generated by this process is a representation of an interaction between already existing input expressions interpreted as a state and an effect. For instance, (q 2 ) is a representation of the interaction between [q 2 ] (state) and [q 1 ] (effect) in the sense of relative difference hence an expression of the abstract input state irrespective of the input effect. Another example is (q 2 ,C), which is a representation of the interaction between (q 2 ) (state) and [C] (effect) hence an expression of the abstract input state in context.

The four types of interactions are marked by their characteristic information. In sorting, this is the nature of quality, focus or complementary; in abstraction, the difference between [q 2 ] and [q 1 ]; in complementation, the possible relation(s) between q 2 and [C], and between q 1 and [C]; in predication, the actual relation between (q 2 ,C) and (q 1 ,C). In our model of negotiation, in Sect. 4, we assume that efficient communication may capitalize on the above informational classification of the interpretation events. Fig. 1. The KIF process model of cognitive activity. State (q 2 ) and effect (q 1 ) stand for information in focus. Information, which is not in focus hence complementary, is represented by the context (C). Horizontal lines are used to designate interactions between input representations (cf. positions in the processing schema). Square brackets indicate that an entity is not yet interpreted, usual bracket symbols indicate that some interpretation is already available. The types of interpretation events are displayed on the right-hand side, in italics.

Fig. 2. The Peircean sign aspects (left) and corresponding mundane terms (right).

By virtue of the dependency between the categories, the set of sign aspects defines and induced hierarchy. Sign aspects that are higher in the hierarchy involve all lower category sign aspects.

In [START_REF] Sarbo | Knowledge in Formation: A Computational Theory of Interpretation[END_REF] we have shown that the KIF process model can be assigned a Peircean semiotic interpretation. This is illustrated by the isomorphism between the diagrams in Fig. 1 and Fig. 2. An analogy between positions in the different diagrams can be explained as follows.

The input, [q 2 q 1 C], expressing a potential for information processing, corresponds to the qualisign sign aspect, or an interpretation of a phenomenon only as a quality. The representations obtained by sorting, [q 2 ] (state) and [q 1 ] (effect), expressing a potential for a relation, correspond to the icon and sinsign sign aspects, respectively.

The icon sign aspect is an expression of a relation of constituency or likeness involved in the input state, the sinsign sign aspect an expression of a relation of simultaneity or an actual event involved in the input effect. 2 An explanation of a relation between other positions of the diagrams can be found in [START_REF] Sarbo | Knowledge in Formation: A Computational Theory of Interpretation[END_REF]. Below we can make use of the above relation between the diagrams, in Fig. 1 and Fig. 2, by referring to a stage in information processing by its Peircean sign aspect.

By virtue of its categorical foundation, KIF theory enables a definition of uniform models of information processing in any domain. As a result, different representations can be combined into a single one by means of structural coordination. This potential of the KIF process model can be used for merging individual conceptualization processes, e.g., by the bargaining parties, into a single process. The obtained structure enables pending events to be analyzed from an informational perspective in order to reveal the type of information (and communication) necessary for their realization.

According to our process model, communication can be assigned a twofold interpretation. On the one hand, it is a final relation generated by one of the parties (cf. sender), on the other hand, it is an input quality offered for processing by the other party (cf. receiver). As, in the second case, interpretation can be in need of memory information, in order to get hold of the problem of efficient communication we introduce a conceptual memory model in the next section.

Efficient Communication

Following [START_REF] Sarbo | Knowledge in Formation: A Computational Theory of Interpretation[END_REF], we assume that memory information can be represented by a graph, in which nodes stand for a collection of qualities perceived in earlier observations, edges for a relation between a pair of nodes. The above model enables our definition of qualities to be refined for interactions between memory information: q 2 can be defined by the qualities 3 shared by the nodes responding the input stimulus, q 1 by the difference between the qualities of those nodes. Formally, for a pair of nodes, n 1 and n 2, triggered by the input stimulus, q 2 :=n 1 ∩n 2, q 1 := n 2 \n 1 ("\" designates the operation relative difference). 4 Hence q 2 is an expression of information shared by observations of stimuli similar to the current one (cf. a state), q 1 is an expression of a change (cf. an effect). The relation between stimulus and memory response, which can be in the sense of agreement and possibility, enables memory information to be represented as focus-and complementary-type qualities, respectively. Fig. 3. Sample interpretation of memory information: n 1 ∩n 2 =A (state), n 2 \n 1 =B (effect)

An algorithm for efficient communication can be defined as follows. We assume that the parties develop a representation of the negotiation process by themselves and by the bargaining other party, through merging (cf. Sect. 3). Communication (c) by one of the parties (sender) is offered for processing by the other party (receiver), who generates a hypothetical interpretation of c from the perspective of its import in the solution of the negotiation problem. As a result, a position (p) and a sign aspect is assigned to c, by receiver. By interpreting c, as an input quality, receiver may find out if, according to his representation of the negotiation process, there is an expression5 c', in position p', which is in interaction with c. By analyzing the relation between memory response triggered by c and c', receiver may generate information from the perspective of the type of interaction between p and p', as follows. Qualities involved by a pair of connected nodes triggered by c and c', e.g., n 1 and n 2 , respectively, can be used for the definition of a state (n 1 ∩n 2 ) and an effect (n 1 \n 2 ). Information involved in the relation between this state and effect can be communicated to the other party, in the sense of difference (cf. abstraction), possibility (cf. complementation), and agreement (cf. predication).

6

Qualities representing the enforced perspective by receiver may enable sender to adjust his representations in p and p', and this way, enhance his interpretation process.

Through communication the parties may force one another to broaden their focus, 'see' the input from a new perspective, apply their knowledge in an abductive fashion, in order to develop a solution for their common negotiation problem.

A Case Study in Problem Elicitation

In a case study at the Dutch software firm Sogeti Nederland B.V., we analysed an actual elicitation process by a team of clients [START_REF] Van Breemen | Knowledge representation as a tool for Intelligence Augmentation[END_REF]. In this process, three clients and a professional mediator were involved in the specification of a problem with the clients' database system. The entire elicitation process, that took 4 hours, was recorded and transcribed.

A problem with the clients' application software, 'myAssignment', is instigated in an elicitation process. The goal of myAssignment is to provide adequate information to employees, managers and client(s), about assignments and, most importantly, about communication between the participants of a project. The elicitation process was conducted in a separate room, in a usual setting, without intervention by the observer whose only task was to operate the fixed camera.

A sample elicitation session is displayed in Fig. 4. The goal of this session is the disclosure of missing functionalities in myAssignment. Utterances of the sample text are interpreted from the perspective of this goal. The results of the analysis are given below. The representations generated are recapitulated in Fig. 5. Peter admits that in the current application he is missing (cf. event) steps that he finds logical (cf. state). ( 2) what already happened:= 'icon', no events and result:= 'sinsign'.

(Pe

Peter refines his judgment, by paraphrasing his earlier concepts. (3) no history:= 'legisign'.

Finally, Caroline recognizes the habitual concept of 'no history', in the instance ('no overview') and corresponding form ('logical steps') suggested by Peter. (4) description of assignment:= 'rheme'; communication to employee:= 'index'.

Similarly so, Peter recognizes an abstract concept involved in the input problem: 'description of the assignment'. He also refers to 'communication' towards the 'employee'. That concept is not further explained in this session (nor in the encompassing text) hence it must refer to background information. From the fact that Peter is expressing his 'doubt' in a proposition about the input problem (description of assignment to employee is lacking communication history:= 'argument') we conclude that all less developed sign aspects7 must be generated as well, such as the 'lack of a communication history': lack of communication history:= 'symbol' and, the 'description of the assignment' communicated to the employee: description of assignment to employee:= 'dicent'. ( 5) check mark:= 'icon'; presence:= 'sinsign'.

Peter is justifying his conclusion, by referring to a possible 'presence' (cf. effect) of 'check marks' (cf. state), in myAssignment. (6) confirmation:= 'index'.

Peter's doubt is related to his question about the existence of a conventional logging of 'confirmations' and, corresponding 'confirmed assignments': confirmation of assignment:= 'dicent'; lack of confirmation history:= 'symbol'. [START_REF] Sarbo | Towards meaningful information processing: A unifying representation for Peirce's signs sytems[END_REF] working out:= 'index'.

Peter doubts, if logging is actually 'worked out' by the employee. The appearance of this background information enables a re-evaluation of all more developed expressions: assignment worked out by employee:= 'dicent'; lack of logging history:= 'symbol', assignment by employee is not logged:= 'argument'. [START_REF] Sarbo | Knowledge in Formation: A Computational Theory of Interpretation[END_REF] reaching agreement:= 'index'.

Caroline admits having the same doubts as Peter has. She points out that the employee, not the application software is providing her with information about reaching agreement with the client. According to her, a lack of logging is what is meant by 'missing communication history'. Hereby she is referring to 'reaching agreement' as a nested conceptualization process: assignment is in agreement:= 'argument', degenerately represented by a pointer: reaching agreement:= 'index', in the encompassing process of interpretation. 8 By introducing a new 'index' expression, Caroline shows her interpretation of a common term involved in the generation of Peter's conclusion (note that a generation of the 'dicent' and 'symbol' positions is coordinated by the context ('index'), in the interpretation process). ( 9)-( 10) Caroline is further elaborating on her conceptualization of the nested process.

In (9) she pinpoints: date of last update:= 'icon'; agreement:= 'sinsign'. In [START_REF] Walton | A Behavioral Theory of Labor Negotiations[END_REF] she introduces: no automatic mail, no mutation information:= 'index'; lack of agreement information:= 'symbol' By making use of dependencies between the sign aspects and, the assumption that 'agreement' (cf. effect) must be related to an 'assignment', enables the nested conceptualization process to be completed: assignment:= 'rheme'; agreement:= 'legisign'; that what is changed in the assignment:= 'dicent'. [START_REF] Van Breemen | Beyond Flatland? What does semiotics add to information sciences[END_REF] myAssignment is missing history:= 'argument'.

Through a proposition of the nested process, the element of a 'no mutation information' is inherited in the index position of the encompassing conceptualization process. The appearance of this information as an index expression, this time not as a sign of doubt, but as one of a hypothesis, triggers a re-evaluation of all more developed input expressions. Assuming ( 11) is providing a conclusion of the conceptualization process so far, it follows that the subject of the process Caroline is referring to (although not explicitly mentioning) must be the application program itself: myAssignment:= 'rheme'; no mutation information in myAssignment:= 'dicent'; lack of mutation history:= 'symbol'. She concludes: myAssignment is missing history:= 'argument'. The above elicitation session includes two examples of efficient communication. In (1), Peter explains his first impression of a problem with myAssignment, which he paraphrases in [START_REF] Follet | Constructive conflict[END_REF]. Although he develops different icon and sinsign expressions of the input problem, e.g., 'logical steps' and 'no overview', he is unable to abstract the input and represent it from the perspective of the rheme and legisign sign aspects. Caroline, noticing Peter's problem, interprets the difference between the icon (c'='logical steps') and sinsign positions (c='(no) overview'), and communicates this to Peter (c\c'='(no) history'). This information, which must be familiar to Peter ('Yes, history'), although in his conceptualization process he was not able to 'see' it, enables him to realize his pending icon-sinsign event and represent the arising relation (cf. abduction) in the legisign position ('no history').

The other example, in [START_REF] Sarbo | Knowledge in Formation: A Computational Theory of Interpretation[END_REF], is Caroline's communication, 'reaching agreement'. In (4), Peter was able to recognize an abstract element (state) involved in the input problem (c'='description of assignment'), in the rheme position, and introduce an interpretation of this concept (c='description of assignment to employee'), in the dicent position. However, he was unable to express the context information involved. This refers to a potential asymmetry in Peter's interpretation process. Although he was able to conceptualize the input state from the perspectives of increasingly more meaningful sign aspects, he was unsuccessful in a similar development of representations of the input effect. Caroline's communication (c\c') has a twofold contribution. It explains Peter's input representation, in the dicent position, and on top of this, it enables an interpretation of the legisign expression, 'no history', in context ('lack of logging history'). The important element in Caroline's information about a possible relation, 'reaching agreement' (over an 'assignment'), is coordination, between the rheme-index and index-legisign interactions, which is the essential function of representations in the index position.

Summary

Integrative negotiation can be abstracted in a process, which is isomorphic to a Peircean model of cognitive activity. The cognitive process can be analysed from an informational perspective, in order to reveal the types of information that can be necessary for a realization of the events of this process. Those types can be used for a generation of goal-driven communication increasing the efficiency of negotiation.

Fig. 4 .

 4 Fig. 4. A sample conceptualization of an elicitation session by Pe (Peter) and Ca (Caroline)

Fig. 5 .

 5 Fig. 5. A sample conceptualization session (Peircean sign aspects are recapitulated in bold face)

  ) What, what I miss, ehh, in the current application ... is that ehh ... that I have an overview, ehh ... of the steps that I find most logical. So, I also miss the history, like ehh ... what was the initial assignment.

	(Ca) Hmm, hmm (with approval)
	2. (Pe) What already happened.
	(Ca) Yes.
	(Pe) And ehh ... what turned out to be the result.
	3. (Ca) History.
	4. (Pe) Yes, history …
	(Ca) Yes.
	(Pe) ... went that, that, ehh, that description of the assignment to the ehh...
	employee?
	5. (Pe) For, I think I see a check mark of that application ...
	(Ca) Yes.
	6. (Pe) But I do not get a confirmation of anything, of ehh ...
	(Ca) No.
	(Pe) whether it, ... it has been sent.
	7. (Pe) And I also do not know if it has been worked out by the employee.
	(Ro) Hmm, hmm.
	(Pe) Do you, ehh...?
	8. (Ca) No, no I only know it because they tell me, like "Hi, I consulted and
	reached agreement and ehh ... that ehh ..."
	9. (Ca) Yes of course, in the end you can read it off from the date of the last
	update, but you do not get ...
	(Pe) O.K.
	10. (Ca) ... an automatic mail or, or a mutation. For it is impossible to see
	what has been changed in the brief.
	(Pe) OK.
	11. (Ca)

Jan van den Broek (pers. comm.,

2009)

Note that a state may occur in itself, an effect always assumes the existence of a state.

A definition of the qualities themselves is beyond the horizon of this paper.

We assume that q2 is always defined by a non-empty collection of qualities.

Information by c' may have been generated by any one of the two parties (p and p' must be neighboring positions of the process model, depicted in Fig.1). If it is generated by receiver, it can be tacit.

If c does not trigger memory, or n1 and n2 are not connected, this may trigger a generation of a request for a re-formulation of c or a re-analysis of the input, by sender (cf. sorting).

The set of sign aspects defines an induced hierarchy. See Fig.2(a).

Due to a lack of space, expressions of this process are omitted in Fig.5.