2 Quantitative DMPKQuantitative DMPK involves the measurement of a number of pharmacokinetic parameters which describe the fate of compounds in the body.These can be used to compare compounds, to highlight deficiencies in compounds (e.g. high metabolism) and to predict how the potential drug will behave in man – generate dose predictions.Quantitative DMPK involves the measurement of a number of PK paramters which describe the fate of compounds in the body.A fundamental assumption of drug action is that the pharmacological response of the drug can be correlated with concentration at the site of action i.e. there is a relationship between drug dose, drug concentration & pharmacological effectThis depends on the processes described last week, absorption, distribution of compound, rate of metabolism and excretion. We want to be able to predict the time course of a drug in human body at a pharmacologically effective dose avoiding side effects. Carrying out DMPK studies can help identify weaknesses in compounds/chemical series (metabolism, absorption etc.) and guide the lead optimisation process.
3 The One Compartment Model The simplest model to describe the fate of a compound in the body is the ‘one compartment model’, which is analogous to the metabolism of the compound in a beaker containing an enzyme solution.Although simplistic, many of the basic parameters of pharmacokinetics (half-life, clearance and volume of distribution) are well illustrated using this model.InjectionBLOODVarious mathematical models are used to investigate the processes of absorption, distribution and elimination.Simplest model is the one compartment (single compartment) model. – assumes that the drug is administered intravenously and that it distributes/equilibrates rapidly with all tissues. Assumes that changes in blood/plasma concentrations reflect changes in overall tissue concentration and is illustrated on the slide.This model, although simplistic, is very useful in allowing us to explain the basic parameters of half-life, clearance and volume of distribution.
4 Half-Life (T1/2) and the Elimination Rate Constant (kel) Following an iv injection, we might expect the plasma concentration of a compound to vary over time as shown below:PlasmaconcTimexln c = ln co - keltln cC = Coe-keltx- kel = slopexxxxxTimeUnder first order kinetics, rate of metabolism is proportional to the compound concentration, so the rate (and gradient) decreases over time.By plotting ln c vs. time, we can determine the elimination rate constant (kel) from the slope of the line and, by extrapolation back to t = 0, the initial plasma concentration c0.The main use of kel is to determine the half-life (t1/2) of the compound, defined as:The time taken for the concentration of drug in the blood or plasma to decline to half of its original value.Following an iv (intravenous) injection, we might expect the plasma concentration of a compound to vary over time as shown in the LHS graph. The plot shows the decrease in plasma concentration as time increases from the initial concentration C0. With the one compartment model, the rate of metabolism is proportional to the concentration of compound, so the rate (and concentration) decrease over time.This information can be used to determine the elimination rate constant kel (see RHS graph), which itself is used to determine the half life. The half-life is the time taken for the concentration of the compound to drop to half the initial value and can be related to the elimination rate constant by the formula t1/2 = 0.693/kel.Half-life is a very important pharmacological parameter as it reflects the length of time that a drug will exist in the body and therefore impacts on drug dose, dosage interval, peak and steady state concentrations, and drug accumulation. However, half life is a hybrid pharmacokinetic parameter, a function of two parameters, the clearance of the compound and its volume of distribution.cco0.69312t1/2At ,t1/2==ln (0.5) =- kelt1/2,kel
5 Volume of Distribution (VD) Timeln cConsider now the case where a compound is dissolved in double the volume, what would happen to t1/2?When the volume doubles (red line), the initial concentration halves and the half life doublesIn biological systems, compounds can distribute out of the plasma into tissues.The volume of distribution (VD) is therefore:The theoretical volume (L) that all the drug in the body would have to occupy if it were present at the same concentration as that found in plasma.It is a measure of how readily drug diffuses out of the plasma into the tissues and can affect t1/2.Low VD: drug confined to plasma (vulnerable to the liver and metabolism)High VD: drug equilibrates with tissuesWhen a compound is dissolved in double the volume of liquid (plasma), the initial concentration halves, and the halflife doubles. Compound can partition out of plasma into various tissues, meaning that the plasma concentration is therefore lower.Volume of distribution is a theoretical parameter - the theoretical volume that a drug would occupy if it were present at the same concentration as in the plasma. VD is effectively a dilution factor, for example, in an average 70Kg man, total volume of blood is ~5L, extracellular fluid is 12L and total body water is 42L, expressed as a percentage of total body weight, blood represents ~7% of total body weight, The minimum VD must be at least 0.07 L kg-1.Few drugs have a value that is physiologically relevant, highlighting that this is a hypothetical parameter. e.g. chloroquine (antimalarial) has a VD of L kg-1 in manCompounds which partition into tissues have low plasma concentration and hence high volumes of distribution, low volume compounds are found in much higher concentration in the plasma. Generally, acids have low volumes of distribution as they are typically highly bound to plasma proteins. Bases often have high volume, having affinity for negatively charged phospholipids in membranes and hence partitioning into tissues.Generally: Acids - high PPB, low VDNeutrals - ready equilibration, but not necessarily retained in the tissue - higher VDBases - high affinity for phospholipids in membranes (negatively charged) - highest VD
6 Rate of elimination (ng/min) = Clearance x concentration (ng/ml) Clearance (Cl)Clearance (Cl) is a measure of how readily compounds are eliminated (i.e. metabolised or excreted)It is defined as:The volume of plasma (or blood) from which all drug is removed per unit time. (n.b. units of Cl are units of flow ml/min)Cl is a constant, characteristic of a drug in a particular species. It is a scaling factor that relates the plasma concentration of a compound to the rate of eliminationRate of elimination (ng/min) = Clearance x concentration (ng/ml)( )dDdtClearance is defined as ‘the volume of blood from which all drug is removed per unit time, it is a constant characteristic of a compound in a particular species.Drug elimination may take place at a number of different sites in the body (liver, kidneys) via a number of mechanisms (metabolism, biliary excretion, renal excretion) but whatever the combination, the net effect is a reduction in drug concentration.The rate of elimination dD/dt is Cl x concentration, so Cl = rate/Conc.Rate of elimination (ng/min)concentration (ng/ml)Clearance (ml/min) =
7 Clearance (Cl) Over a small interval of time, dt: Amount eliminated during interval dt = Cl x Conc x dtIntegrating this over the whole concentration-time profile gives:Total amount eliminated = Dose = Cl x AUCCl = Dose/AUCkel = Conc. x ClClearance is related to t1/2 and VD. If Cl halves, then the half life doubles (because the rate of metabolism halves) and, as we have seen, doubling the volume doubles the half-life (because the concentration at the metabolising enzyme has halved).The precise equation is: t1/2 = x VD/ClPlasmaConcTimedtOver a small period of time dt, the amount eliminated is:Cl x concentration x time,Integrated over the whole time period gives:Total amount eliminated = Dose = Cl x AUC.Or Cl = Dose/AUC.
8 Clearance, Volume and Half-Life Half-life is not predictable from clearance alone- clearance characterises elimination of drug from plasma/blood- half-life also depends on distribution of drug outside the plasma (systemic circulation not a closed system)For a rapid (bolus) iv dose; where D is the amount of drug in the body at time t;dtdDRate ofh elimination,= kelD = Clearance x concentrationClBut D = VD x concentration, so kel x VD = Clor kel =VD0.6930.693 x VDHalf-life cannot be predicted from Cl alone, as clearance characterises the elimination of compound from plasma, but half-life depends on distribution also (i.e. partitioning into other compartments tissues).Rate of elimination = dD/dt = kelD = Cl x Conc.D (amount of drug, is Volume x Conc.) so kel x VD = Cl, or Kel = Cl/VDThe equation:t 1/2 = x VD / Clshows the relationship between Cl, V and t ½ which is fundamental. As Cl increases, i.e. more metabolism, compound being removed from the body faster, the half life shortens. As volume increases (greater distribution into tissues - basic compounds), half life increases.When trying to optimise the DMPK properties of compounds – look either to drive Cl down or increase volume of distribution to improve the half-life.Rem:t1/2=,t1/2=kelClNB: t½ is NOT a measure of how rapidly the drug is metabolised
9 Clearance, Extraction and Absorption For the three main elimination processes, metabolism, renal, and biliary,clearances are additive, i.e.ClT = ClM + ClR + ClBCan relate clearance to liver blood flow (Q):Cl = E x Q (E = extraction ratio)If Cl ~ Q (i.e. E~1), then 1st pass metabolism is a likely problem.e.g. If ClT = 20ml/min/Kg and %dose as parent in urine = 20% Then ClR = 4ml/min/KgQ: Rat ~ 70 ml/min/kgDog ~ 40 ml/min/kgMan ~ 20 ml/min/kgQ = flow(ml/min)E = (Cin –Cout) / CinIn terms of routes of elimination, we discussed last week metabolism and excretion routes (biliary and renal). These processes are all additive in terms of thinking about Cl.i.e. when you measure Cl it is the cumulative effects of all the elimination processes that are going on – total Cl = metabolic Cl + renal Cl + biliary clearance.Cl – being a volume of blood from which all drug is removed per unit time, can be related to liver blood flow. Each time blood from the body is pumped through the liver, some of the compound is metabolised and lost. Q = liver blood flow, E =the extraction ratio which relates the liver blood flow to ClFrom the diagram, blood is pumped through the liver at a particular rate. E, the extraction ratio, is the proportion of the compound which is extracted or removed from the bloodstream by the liver each time it passes throughIf E = 1, it means that all the compound is being removed by the liver, therefore 1st pass metabolism is likely to be a problem.Fraction absorbed (fa)can now be worked outif know %FCin = conc. entering liverCout = conc. leaving liver
10 The Two Compartment Model k12InjectionBLOODTISSUESk21The two compartment model more accurately describes observed DMPK data. In this model, the compound is viewed as being able to equilibrate with a second compartment as, in addition to metabolism, drug is distributing into the tissues.Drug accumulates in the tissues because the plasma concentration is initially greater than the tissue concentration and so k12>k21. However, eventually the plasma concentration falls to such an extent that the net drug movement is from tissues back into blood. At this point in time, plasma concentration begins to fall far more slowly as diffusion from tissues back into blood becomes more and more significant.Timeln cxPlasmaconcWith the two compartment model – the drug is viewed as being able to equilibrate with a second compartment (‘tissues’).Initally, all the drug is in the blood stream (compartment 1), and then starts to accumulate in the tissues (as well as being eliminated). K12 greater than K21. However, the plasma concentration eventually drops to such an extent that the concentration is lower than that in the tissues and there is then net movement back into the blood from tissues. At this point, concentration falls more slowly as the diffusion from tissues is rate limiting.This model describes the actual data we see from a DMPK experiment more accurately.xDistribution phasexcp = c1e-k1t + c2e-k2txxElimination phasexxTime
11 Oral Dosing - Bioavailability TimeivoralPlasmaconcUpon oral dosing of a drug, there is an initial increase in the systemic concentration of the drug, as it is absorbed from the gut.As absorption is completed and the compound is eliminated from the body, the concentration of drug decreases over time.Absorption phaseElimination phaseOral Bioavailability (F%) is defined as:The fraction of the dose which makes it to the systemic circulation (i.e. survives 1st pass metabolism).F = AUC after an oral doseSo far we have looked at compounds dosed iv, where you get an instantaneous introduction of compound to the bloodstream which then reduces over time.With oral dosing of a compound, the data curves look more like that shown by the graph (as discussed last week, we see the initial increase in concentration and then a subsequent decrease over time).Oral bioavailability (F) is defined as the fraction of the dose which makes it to the systemic circulation. It has to be stable , permeable and survive 1st pass metabolism from the liver.F = AUC after oral dose/AUC after IV dose.Factors which limit bioavailability include acid instability of the conmpound (stomach), incomplete absorption, solubility, permeability, no. of H bond donors/acceptors, log P/D, metabolism, (gut wall, efflux, 1st pass etc.)AUC after an equivalent iv doseLimiting factors include: Chemical instability, eg acid sensitive compound in the stomachIncomplete absorption - solubility, formulationGut wall metabolism, 1st pass metabolism - labile functional groups
12 Predicting in vivo DMPK using in vitro Measurements A number of DMPK parameters may be predicted from in vitro assays to build up understanding of compound properties – predict behaviour in manAbsorption – Pampa, Caco-2Clearance - Microsomes, HepatocytesDistribution - Plasma protein binding,Cytochrome P450 inhibition (5 major isozymes)Physical parameters – log D, pKa, solubilityA whole array of in vitro tests have been developed to look at aspects of drug discovery including DMPK. We can predict the in vivo behaviour of compounds using these tools and filter out those compounds that are not good enough.Examples of assays are the use of Caco-2 / PAMPA for absorption, and the use of microsomes and hepatocytes for metabolism studies, PPB measurement, CYP inhibition, & other physical property measurements (Log D, pKa, solubility) to build up a picture of compound properties.These assays are used extensively to profile compounds and filter out those that do not possess the required properties to be drugs.
13 Permeability in vitro Pampa (Parallel Artificial Membrane Permeability Assay)Artificial membrane separates 2 compartmentsModels transcellular (passive) absorption onlyNo tissue cultureAssay 96 cpd(2 days experimental and analysis)Caco-2 Human colon adenocarcinomaHuman colon carcinoma cell line which grow asmonolayers, similar to small intestine enterocytesAll mechanisms modelled - express key transporterproteins (e.g. PGP)Culturing over several daysAssay 96 cpds AB or 48 cpd BACan investigate different directions (A-B) and (B-A)drugApical chamber(gut lumen)Absorptive Flux (A-B)drugCellmonolayerBasolateralChamber (blood)PAMPA and CaCo-2 are permeability assays, used to give an understanding of the likelihood of absorption of compounds.PAMPA - an artifical membrane (egg lecithin) separates 2 compartments. Compound is added to one side, and the ability to transfer to the other compartment is measured. It models transcellular (passive absorption) only.Caco-2 is a human cell line (colon carcinoma) - grow as monolayers. All mechanisms are modelled – transporters such as PGP are expressed. The assay is lower throughput but you get both an A-B (apical to basolateral) and a B-A measurement together with an efflux ratio – i.e. if the compound is effluxed out of the cell by transporters.Both assays show a good correlation with human fraction absorbed.Secretory flux (B-A)drugApparent permeability (Papp) measurements calculated (units are cm/sec x 1E-6)Typically use PAMPA assay as primary assay for absorption followed by oral data in two speciesBoth can be related to human fraction absorbed
14 In vitro Measurement of Metabolism In vivo Cl can also be predicted using in vitro assays:Microsomes (species – rat, dog, human)A subcellular fraction obtained by centrifugation of liver cells. Mainly composed of vesicles containing CYP450 enzymes formed from fragmented endoplasmic reticulum. Perform Phase I reactions.Hepatocytes (species – rat, dog, human)Isolated whole liver cells. Capable of performing both Phase I and II reactions.Rates of metabolism are reported as intrinsic clearance - Clint (ul/min/106 cells)Typically: Rat Hepatocytes Clint Low (< 10), Moderate (10-20), High (> 20)Human Microsomes Clint Low (< 15), Moderate (15-30), High (> 30)Cl predicted using two assays, microsomes & hepatocytes.Microsomes – subcellular fraction, vesicles containing CYP450 enzymes from fragmented endoplasmic reticulum. Carry out Phase I (oxidations).Hepatocytes - whole liver cells, capable of both Phase I and II metabolism (conjugation), not stored. Typically hard to get hold of human hepatocytes, Usually measure RH, HM, then progress to HH.Metabolism rates are reported as intrinsic clearance – ul/min/106 cells, and give an indication of likely Cl when a compound is dosed in vivo.High metabolism compounds are excluded – they will never have a long enough half life to be a drug.Typical figures - <10 in rat heps, <15 in human mics.
15 In vitro – In vivo scaling Cannot measure in vivo human PK until phase I trials. If we can predict consistently how a compound will behave in other species, then we can have greater confidence that it will behave predictably in man. In vitro - in vivo scaling is the prediction of in vivo Cl from Clint measured in hepatocytes.The in vitro assay gives the maximum possible metabolic rate – but need to factor in drug delivery i.e. liver size, PPB, liver blood flow etc, extrahepatic clearance.Clint: ml/min/106 cellsClint*: ml/min/kgLiver120 x 106 hu hepsper gram liverg liver per kg body weightml to mlml/min/g liverSpecies 1Species 2HumanHeps lowCompound scalesHu heps lowIn vitroIn vivoFTIMWe are looking for a compound that gives a long enough half-life and a low enough dose to make it as a drug (potency).We need a clear understanding of how the compound behaves in terms of its DMPK – we cannot measure human PK until phase I trials. However, if we can consistently predict how a compound behaves in other species, then we can have confidence that it will behave predictably in man.Scaling is the prediction of in vivo Cl from in vitro Cl. The in vitro assay gives the intrinsic rate of clearance by the liver cells, but we also need to factor in the liver size, PPB, liver blood flow, bilary and/or renal clearance.This gives us a predicted value of Cl that we can compare against when we dose the compound.DMPK well understood, predictable from hepatocytes, PPB etc.
16 Dose Prediction to Man Toxic Therapeutic Ineffective DMPK measurements enable prediction of human PK parameters. Incorporation of potency and safety data enables Dose to Man (DtM) and safety margin predictions.Predicted human PK appropriate for once a day oral dosing:Therapeutic Dose < 5mg/kg uidPred. Human DMPK t1/2 6-12h, F > 30%TimePlasmaconcTherapeuticToxicIneffectiveCssmin(typically 3 x potency)CssmaxSafetyMarginPlasmaconcTimeFrom all the data collected on properties such as potency, Cl, CaCo-2, iv Cl, F etc. we predict the likely PK parameters of the compound and work out the dose required to get coverage at the receptor, and establish whether the compound is likely to make it.Our target profile for a once a day compound is a dose of less than 5 mg kg day and a half life of 6-12h, F>30%.Essentially it’s about understanding the data, predicting how often we need to dose and how much to have a therapeutic effect without running into toxicity problems. We need appropriate cover, good safety margins etc.
17 Summary Absorption Elimination Distribution fa Cl VD %F t1/2 Definitions and qualitative aspects of absorption, distribution and elimination.Quantitative PK studies allowing the determination of:AbsorptionEliminationDistributionPermeabilityEffluxAqueoussolubilityRenalexcretionMetabolicstabilityBiliaryexcretionProteinbindingTissuebindingfaClVD%Ft1/2(poor/med/high)(UID/BID/>3-4x)Knowledge of these parameters allows identification of where improvements need to be made to end up with a pharmacokinetically optimized drug.