In cell biology,  ion trapping  is the build-up of a higher concentration of a chemical across a  cell membrane  due to the  pKa  value of the chemical and difference of  pH  across the cell membrane. [ 1 ] [ 2 ]  This results in basic chemicals accumulating in acidic bodily fluids such as the  cytosol , and acidic chemicals accumulating in basic fluids.


Many  cells  have other mechanisms to pump a  molecule  inside or outside the cell against the  concentration gradient , but these processes are active ones, meaning that they require  enzymes  and consume cellular  energy . In contrast, ion trapping does not require any enzyme or energy. It is similar to  osmosis  in that they both involve the  semipermeable  nature of the cell membrane.


Cells have a more acidic  pH  inside the cell than outside ( gastric mucosal  cells being an exception). Therefore, basic drugs (like  bupivacaine ,  pyrimethamine ) are more charged inside the cell than outside. The  cell membrane  is permeable to non-ionized (fat-soluble) molecules; ionized (water-soluble) molecules cannot cross it easily. Once a non-charged molecule of a basic chemical crosses the cell membrane to enter the cell, it becomes charged due to gaining a hydrogen ion because of the lower pH inside the cell, and thus becomes unable to cross back. Because transmembrane equilibrium must be maintained, another unionized molecule must diffuse into the cell to repeat the process. Thus its concentration inside the cell increases many times that of the outside. The non-charged molecules of the drug remain in equal concentration on either side of the cell membrane.


The charge of a molecule depends upon the pH of its solution. In an acidic medium, basic drugs are more charged and acidic drugs are less charged. The converse is true in a basic medium. For example,  Naproxen  is a  non-steroidal anti-inflammatory drug  that is a weak acid (its  pKa  value is 5.0). The  gastric juice  has a pH of 2.0. It is a three-fold difference (due to log scale) between its pH and its pKa; therefore there is a 1000× difference between the charged and uncharged concentrations. So, in this case, for every one molecule of charged  Naproxen , there are 1000 molecules of uncharged Naproxen at a pH of 2. [ 3 ]  This is why weak acids are better absorbed from the stomach and weak bases from intestine where the pH is alkaline. When pH of a solution is equal to pKa of dissolved drug, then 50% of the drug is ionized, another 50% is unionized. This is described by the  Henderson-Hasselbalch equation . [ citation needed ]


Ion trapping is the reason why basic (alkaline) drugs are secreted into the stomach (for example  morphine ), where pH is acidic, and acidic drugs are excreted in urine where the conditions are alkaline. Similarly, ingesting  sodium bicarbonate  with  amphetamine , a weak base, causes better absorption of amphetamine (in stomach) and its lesser excretion (in urine), thus prolonging its actions. Ion trapping can cause partial failure of certain anti-cancer chemotherapies. [ 4 ]


Ion trapping is also important outside of  pharmacology . For example, it causes weakly acidic  hormones  to accumulate in the cytosol of cells. This is important in keeping the external concentration of the hormone low in the extracellular environment where many hormones are sensed. Examples of plant hormones that are subjected to ion trapping are  abscisic acid ,  gibberellic acid  and  retinoic acid . Examples of animal hormones subjected to ion trapping include  Prostacyclin  and  Leukotrienes .


Release  ( Liberation ) is the first step in the process by which medication enters the body and liberates the   active ingredient  that has been administered. The  pharmaceutical drug  must separate from the   vehicle  or the  excipient  that it was mixed with during   manufacture . Some authors split the process of liberation into three steps: disintegration, disaggregation and dissolution. A limiting factor in the adsorption of pharmaceutical drugs is the degree to which they are ionized, as cell membranes are relatively impermeable to ionized molecules.


The characteristics of a medication's excipient play a fundamental role in creating a suitable environment for the correct absorption of a drug. This can mean that the same dose of a drug in different forms can have different  bioequivalence , as they yield different plasma concentrations and therefore have different therapeutic effects.  Dosage forms  with  modified release  (such as delayed or extended release) allow this difference to be usefully applied.


In a typical situation, a pill taken orally will pass through the  oesophagus  and into the  stomach . As the stomach has an aqueous environment, it is the first place where the pill can dissolve. The rate of dissolution is a key element in controlling the duration of a drug's effect. For this reason, different forms of the same medication can have the same active ingredients but different dissolution rates. If a drug is administered in a form that is not rapidly dissolved, the drug will be absorbed more gradually over time and its action will have a longer duration. A consequence of this is that patients will comply more closely to a prescribed course of treatment, if the medication does not have to be taken as frequently. In addition, a slow release system will maintain drug concentrations within a therapeutically acceptable range for longer than quicker releasing delivery systems as these result in more pronounced peaks in plasma concentration.


The dissolution rate is described by the  Noyes–Whitney equation :


As the solution is already in a dissolved state, it does not have to go through a dissolution stage before absorption begins.


Cell membranes present a greater barrier to the movement of ionized molecules than non-ionized liposoluble substances. This is particularly important for substances that are weakly   amphoteric . The stomach's acidic  pH  and the subsequent alkalization in the  intestine  modifies the degree of ionization of acids and weak bases depending on a substance's  pKa . [ 1 ]  The pKa is the pH at which a substance is present at an equilibrium between ionized and non-ionized molecules. The  Henderson–Hasselbalch equation  is used to calculate pKa.


Lipophilic efficiency [ 1 ]  ( LiPE ), sometimes referred to as  ligand-lipophilicity efficiency  ( LLE ) is a parameter used in  drug design  and  drug discovery   to evaluate the quality of research compounds, linking potency and  lipophilicity  in an attempt to estimate  druglikeness . [ 2 ] [ 3 ]  For a given compound LiPE is defined as the  pIC 50  (or  pEC 50 ) of interest minus the  LogP  of the compound.


In practice, calculated values such as cLogP or calculated LogD are often used instead of the measured LogP or LogD. LiPE is used to compare compounds of different potencies (pIC 50 s) and lipophilicities (LogP). High potency (high value of pIC 50 ) is a desirable attribute in drug candidates, as it reduces the risk of non-specific, off-target pharmacology at a given concentration. When associated with low clearance, high potency also allows for low total dose, which lowers the risk of  idiosyncratic drug reaction . [ 4 ] [ 5 ]


On the other hand, LogP is an estimate of a compound's overall lipophilicity, a value that influence its behavior 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. [ 6 ]  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.


LiPE allows capturing both values in a single parameter, and empirical evidence suggest that quality drug candidates have a high LiPE (>6); this value corresponds to a compound with a pIC 50  of 8 and a LogP of 2. Plotting LogP against pIC 50  for a range of compounds allows ranking series and individual compounds.


An alternative equation uses the logarithm of the ratio of potency (measured as binding energy) and the partition coefficient to compute a lipophilic  ligand efficiency  index (LE) with a different scale. [ 7 ]


The following review discusses LipE in the context of other compound efficiency metrics. [ 8 ]


In  pharmacokinetics , a  loading dose  is an initial higher dose of a drug that may be given at the beginning of a course of treatment before dropping down to a lower  maintenance dose . [ 1 ]


A loading dose is most useful for drugs that are eliminated from the body relatively slowly, i.e. have a long  systemic   half-life .  Such drugs need only a low maintenance dose in order to keep the amount of the drug in the body at the appropriate  therapeutic level , but this also means that, without an initial higher dose, it would take a long time for the amount of the drug in the body to reach that level.


Drugs which may be started with an initial loading dose include  digoxin ,  teicoplanin ,  voriconazole ,  procainamide  and  fulvestrant .


One or series of doses that may be given at the onset of therapy with the aim of achieving the target concentration rapidly.


For an example, one might consider the
hypothetical drug  foosporin .  Suppose it has a long  lifetime in the body , and only ten percent of it is cleared from the blood each day by the liver and kidneys.  Suppose also that the drug works best when the total amount in the body is exactly one gram.  So, the maintenance dose of  foosporin  is 100 milligrams (100 mg) per day—just enough to offset the amount cleared.


Suppose a patient just started taking 100 mg of  foosporin  every day.


As one can see, it would take many days for the total amount of drug within the body to come close to 1 gram (1000 mg) and achieve its full therapeutic effect.


For a drug such as this, a doctor might prescribe a loading dose of  one gram  to be taken on the first day.  That immediately gets the drug's concentration in the body up to the therapeutically-useful level.


Four variables are used to calculate the loading dose:


The required loading dose may then be calculated as


For an intravenously administered drug, the bioavailability  F  will equal 1, since the drug is directly introduced to the bloodstream. If the patient requires an oral dose, bioavailability will be less than 1 (depending upon absorption, first pass metabolism etc.), requiring a larger loading dose.


In  pharmacokinetics , a  maintenance dose  is the maintenance rate [mg/h] of drug administration equal to the rate of elimination at steady state.  This is not to be confused with  dose regimen , which is a type of drug therapy in which the  dose  [mg] of a  drug  is given at a regular dosing interval on a repetitive basis. Continuing the maintenance dose for about 4 to 5  half-lives  (t 1/2 ) of the drug will approximate the  steady state  level. [ 1 ]  One or more doses higher than the maintenance dose can be given together at the beginning of therapy with a  loading dose . [ 2 ]


A loading dose is most useful for drugs that are  eliminated from the body  relatively slowly.  Such drugs need only a low maintenance dose in order to keep the amount of the drug in the body at the appropriate level, but this also means that, without an initial higher dose, it would take a long time for the amount of the drug in the body to reach that level.


The required maintenance dose may be calculated as:


Microdosing , or  micro-dosing , involves the administration of sub-therapeutic doses of  drugs  to study their effects in humans, aiming to gather preliminary data on safety,  pharmacokinetics , and potential therapeutic benefits without producing significant physiological effects.  This is called a " Phase 0  study" and is usually conducted before clinical  Phase I  to predict whether a drug is viable for the next phase of testing. Human microdosing aims to reduce the resources spent on non-viable drugs and the amount of testing done on animals.  [ 1 ]


Less commonly, the term "microdosing" is also sometimes used to refer to precise dispensing of small amounts of a drug substance (e.g., a powder API) for a drug product (e.g., a capsule) [ 2 ]  and, when the drug substance also happens to be liquid, this can potentially overlap what is termed  microdispensing . For example,  psychedelic microdosing . [ 3 ]


The basic approach is to  label  a candidate drug using the radio  isotope   carbon-14 , [ 4 ]  then administer the compound to human volunteers at levels typically about 100 times lower than the proposed therapeutic dosage (from around 1 to 100  micrograms  but not above). [ citation needed ]


As only microdose levels of the drug are used, analytical methods are limited. Extreme sensitivity is needed.  Accelerator mass spectrometry  (AMS) is the most common method for microdose analysis. AMS was developed in the late 1970s from two distinct research threads with a common goal: [ 5 ]  an improvement in radiocarbon dating that would make efficient use of datable material and that would extend the routine and maximum reach of radiocarbon dating. AMS is routinely used in geochronology and archaeology, [ 6 ]  but biological applications began appearing in 1990 mainly due to the work of scientists at Lawrence Livermore National Laboratory. AMS service is now more accessible for biochemical quantitation from several private companies and non-commercial access to AMS is available at the National Institutes of Health (NIH) Research Resource at Lawrence Livermore National Laboratory, [ 7 ]  or through the development of smaller affordable spectrometers. AMS does not measure the radioactivity of carbon-14 in microdose samples. AMS, like other mass spectrometry methods, measures ionic species according to mass-to-charge ratio.


Psychedelic microdosing is the practice of using sub-threshold doses (microdoses) of  serotonergic   psychedelic drugs  in an attempt to improve creativity, boost physical energy level, emotional balance, increase performance on problems-solving tasks and to treat anxiety, depression and addiction, [ citation needed ]  though there is very little evidence supporting these purported effects as of 2019. [ 8 ]


In 2021 it was reported in a study done that an increased conscientiousness was seen due to microdosing.  [ 9 ]  Microdosing was seen to have improved mental health after microdosing with psychedelics after 30 days. [ 10 ]  More research is needed to ultimately decide whether or not microdosing helps those who suffer from depression and anxiety.  [ 10 ]  Microdosing has not seen to improve participants motor responses, attention, and cognitive problem-solving abilities. [ 10 ]  Microdosing is still under investigation as to whether it works or not. Researchers are investigating into microdosing more and more, the placebo effect causes difficulties in research on this topic. [ 11 ]


In January 2006, the European Union Microdose AMS Partnership Programme (EUMAPP) was launched. [ 12 ]  Ten organizations from five different countries (United Kingdom, Sweden, Netherlands, France, and Poland) will study various approaches to the basic AMS technique. The study is set to be published in 2009. [ 13 ]


One of the most meaningful potential outcomes of Phase-0/Microdosing studies is the early termination of development. In 2017, Okour et al published the first example in literature of a termination of an oral drug based on IV microdose data. [ 14 ]


Oculomucocutaneous syndrome  is characterized by  keratoconjunctivitis sicca  ( dry eyes ) and the resulting  scarring ,  fibrosis ,  metaplasia , and shrinkage of the  conjunctiva . [ 1 ]  It is a drug  side effect  observed in  practolol  and  eperisone . It is speculated that  antibodies  against drug  metabolites  cause the syndrome. [ 2 ]


This cutaneous condition article is a  stub . You can help Wikipedia by  expanding it .


Open flow microperfusion  ( OFM ) is a sampling method for clinical and preclinical drug development studies and  biomarker  research. OFM is designed for continuous sampling of analytes from the  interstitial fluid  (ISF) of various tissues. It provides direct access to the ISF by insertion of a small, minimally invasive, membrane-free probe with macroscopic openings. [ 1 ]  Thus, the entire biochemical information of the ISF becomes accessible regardless of the analyte's molecular size, protein-binding property or  lipophilicity . [ citation needed ]


OFM is capable of sampling lipophilic and hydrophilic compounds, [ 2 ]  protein bound and unbound drugs, [ 3 ] [ 4 ]   neurotransmitters ,  peptides  and  proteins ,  antibodies , [ 5 ] [ 6 ] [ 7 ]   nanoparticles  and  nanocarriers ,  enzymes  and  vesicles .


The OFM probes are perfused with a physiological solution (the perfusate) which equilibrates with the ISF of the surrounding tissue. Operating flow rates range from 0.1 to 10 μL/min. OFM allows unrestricted exchange of compounds via an open structure across the open exchange area of the probe. This exchange of compounds between the probe’s perfusate and the surrounding ISF is driven by convection and diffusion, and occurs non-selectively in either direction (Figure 1).


The direct liquid pathway between the probe’s perfusate and the surrounding fluid results in collection of ISF samples. These samples can be collected frequently and are then subjected to bioanalytical analysis to enable monitoring of substance concentrations with temporal resolution during the whole sampling period. [ 8 ] [ 9 ]


The concentric OFM probe (Figure 2) works according to the same principle. The perfusate is pumped to the tip of the OFM probe through the inner, thin lumen and exits beyond the Open Exchange Area, where it then mixes with exogenous substances present in the ISF before being withdrawn through the outer, thick lumen. [ citation needed ]


The first OFM sampling probe to be used as an alternative to  microdialysis  was described in an Austrian patent application filed by Falko Skrabal in 1987, where OFM was described as a device, which can be implanted into the tissue of living organisms. [ 10 ]  In 1992, a US patent was filed claiming a device for determining at least one medical variable in the tissue of living organisms. [ 11 ]  In a later patent by Helmut Masoner, Falko Skrabal and  Helmut List  a linear type of the sampling probe with macroscopic circular holes was also disclosed. [ 12 ]  Alternative and current OFM versions for  dermal  and  adipose tissue  application were developed by  Joanneum Research , and were patented by Manfred Bodenlenz et al. [ 13 ] [ 14 ]  Alternative materials featuring low absorption were used to enable manufacturing of probes with diameters of 0.55 mm and exchange areas of 15 mm in length. For cerebral application, special OFM probes were patented by Birngruber et al. [ 15 ]  Additionally, a patent was filed to manage the fluid handling of the ISF by using a portable peristaltic pump with a flow range of 0.1 to 10 μL/min that enables operation of up to three probes per pump. [ 16 ]


Two types of OFM probes are currently available: Linear OFM probes for implantation into superficial tissues such as skin (dermal OFM, dOFM) and subcutaneous adipose tissue (adipose OFM, aOFM) as well as concentric probes for implantation into various regions of the  brain  (cerebral OFM, cOFM). [ citation needed ]


OFM is routinely applied in pharmaceutical research in preclinical (e.g. mice, rats, pigs, primates) and in clinical studies in humans (Figure 3). OFM-related procedures such as probe insertions or prolonged sampling with numerous probes are well tolerated by the subjects. [ 1 ]


dOFM (Figure 4) allows the investigation of transport of drugs in the dermis and their penetration into the dermis after local, topical or systemic application, and dOFM is mentioned by the  U.S. Food and Drug Administration  as a new method for assessment of bioequivalence of topical drugs. [ 17 ] [ 18 ] [ 19 ]


dOFM is used for:


Head-to-head settings with OFM have proven particularly useful for the evaluation of topical generic products, which need to demonstrate  bioequivalence [ 9 ]  to the reference listed drug product to obtain market approval.


Applications of dOFM include  ex vivo  studies with tissue explants and preclinical and clinical  in vivo  studies.


aOFM (Figure 4) allows continuous on-line monitoring of metabolic processes in the subcutaneous adipose tissue, e.g.  glucose  and  lactate , [ 21 ] [ 22 ] [ 23 ]  as well as larger analytes such as  insulin  (5.9 kDa). [ 24 ] [ 23 ]  The role of polypeptides for metabolic signaling ( leptin ,  cytokine  IL-6, TNFα) has also been studied with aOFM. [ 25 ]  aOFM allows the quantification of proteins (e.g. albumin size: 68 kDa) in adipose tissue [ 4 ]  and thus opens up the possibility to investigate protein-bound drugs directly in peripheral target tissues, such as highly protein-bound insulin analogues designed for a prolonged, retarded insulin action. [ 26 ]  Most recently, aOFM has been used to sample agonists to study  obesity ,  lipid metabolism  and immune-inflammation. Applications of aOFM include  ex vivo  studies with tissue explants and preclinical and clinical  in vivo  studies. [ citation needed ]


cOFM (Figure 5) is used to conduct PK/PD preclinical studies in the animal brain. Access to the brain includes monitoring of the  blood-brain barrier  function and drug transport across the intact blood-brain barrier. [ 27 ]  cOFM allows taking a look behind the blood-brain barrier and assesses concentrations and effects of  neuroactive  substances directly in the targeted brain tissue. [ 28 ]


The blood-brain barrier is a natural shield that protects the brain and limits the exchange of  nutrients ,  metabolites  and  chemical messengers  between blood and brain. The blood-brain barrier also prevents potential harmful substances from entering and damaging the brain. However, this highly effective barrier also prevents neuroactive substances from reaching appropriate targets. For researchers that develop neuroactive drugs, it is therefore of major interest to know whether and to what extent an active pharmaceutical component can pass the blood-brain barrier. Experiments have shown that the blood-brain barrier has fully reestablished 15 days after implantation of the cOFM probe in the brain of rats. [ 29 ]  The cOFM probe has been specially designed to avoid a reopening of the blood-brain barrier or causing additional  trauma  to the brain after implantation. cOFM enables continuous sampling of cerebral ISF with intact blood-brain barrier cOFM and thus allows continuous PK monitoring in brain tissue. [ citation needed ]


ISF compounds can be quantified either indirectly from merely diluted ISF samples by using OFM and additional calibration techniques, or directly from undiluted ISF samples which can be collected with additional OFM methods. Quantification of compounds from diluted ISF samples requires additional application of calibration methods, such as Zero Flow Rate, [ 30 ]  No Net Flux [ 31 ]  or Ionic Reference. [ 32 ]  Zero Flow Rate has been used in combination with dOFM by Schaupp et al. [ 3 ]  to quantify  potassium ,  sodium  and glucose in adipose ISF samples. No Net Flux has been applied to quantify several analytes in OFM studies in subcutaneous adipose,  muscle  and dermal ISF: the absolute lactate concentrations [ 33 ]  and the absolute glucose concentrations in adipose ISF, [ 3 ]  the absolute  albumin  concentration in muscle ISF [ 4 ]  and the absolute insulin concentration in adipose and muscle ISF have been successfully determined. [ 34 ]  Dragatin et al. [ 5 ]  used No Net Flux in combination with dOFM to assess the absolute ISF concentration of a fully human therapeutic antibody. Ionic Reference has been used in combination with OFM to assess the absolute glucose concentration [ 3 ]  and the absolute lactate concentration in adipose ISF. [ 33 ]  Dermal OFM has also been used to quantify the concentrations of human insulin and an insulin analogue in the ISF with inulin as exogenous marker. [ citation needed ]


Additional OFM methods, such as OFM recirculation and OFM suction can collect undiluted ISF samples from which direct and absolute quantification of compounds is feasible. [ 35 ]  OFM recirculation to collect undiluted ISF samples recirculates the perfusate in a closed loop until equilibrium concentrations between perfusate and ISF are established. Using albumin as analyte, 20 recirculation cycles have been enough to reach equilibrium ISF concentrations. OFM suction is performed by applying a mild vacuum, which pulls ISF from the tissue into the OFM probe. [ citation needed ]


In  medicinal chemistry ,  parallel artificial membrane permeability assay  ( PAMPA ) is a method which determines the permeability of substances from a donor compartment, through a  lipid -infused artificial membrane into an acceptor compartment. [ 1 ]   A multi-well microtitre plate is used for the donor and a membrane/acceptor compartment is placed on top; the whole assembly is commonly referred to as a “sandwich”.  At the beginning of the test, the drug is added to the donor compartment, and the acceptor compartment is drug-free. After an incubation period which may include stirring, the sandwich is separated and the amount of drug is measured in each compartment.   Mass balance allows calculation of drug that remains in the membrane.


To date, PAMPA models have been developed that exhibit a high degree of correlation with permeation across a variety of barriers, including  Caco-2  cultures, [ 2 ] [ 3 ]  the  gastrointestinal tract , [ 4 ]   blood–brain barrier [ 5 ]  and skin.


The donor and/or acceptor compartments may contain solubilizing agents, or additives that bind the drugs as they permeate.  To improve the  in vitro  -  in vivo  correlation and performance of the PAMPA method, the lipid, pH and chemical composition of the system is often designed with biomimetic considerations in mind.


Although  active transport  is not modeled by the artificial PAMPA membrane, up to 95% of known drugs are absorbed by  passive transport . [ 6 ]  Some experts support a lower figure, so the amount is open to some interpretation.  Microtiter plates with 96 wells can be used for the assay which increases the speed and lowers the per sample cost.


Since the first publication by Kansy and coworkers, [ 7 ]  several companies developed their own versions of the assay.  Early models incorporated iso-pH conditions in the compartments separated by a simple lipid membrane; subsequently, commercial products were introduced which incorporated more sophisticated lipid membranes. [ 8 ]   The commercial products helped ensure that medicinal chemists across different corporate labs within a worldwide organization used the same standardized methodology, reagents and obtained equivalent system performance as demonstrated with a set of test compounds.  This has proved very useful as various operational activities have been outsourced to other countries.


A  Patlak plot  (sometimes called  Gjedde–Patlak plot ,  Patlak–Rutland plot , or  Patlak analysis ) [ 1 ] [ 2 ]  is a  graphical  analysis technique based on the  compartment  model that uses  linear regression  to identify and analyze  pharmacokinetics  of tracers involving irreversible uptake, such as in the case of  deoxyglucose . [ 3 ] [ 4 ]  It is used for the evaluation of  nuclear medicine   imaging  data after the injection of a  radioopaque  or  radioactive tracer .


The method is model-independent because it does not depend on any specific compartmental model configuration for the tracer, and the minimal assumption is that the behavior of the tracer can be approximated by two compartments – a "central" (or reversible) compartment that is in rapid equilibrium with  plasma , and a "peripheral" (or irreversible) compartment, where tracer enters without ever leaving during the time of the measurements. [ 1 ] [ 2 ]   The amount of tracer in the  region of interest  is accumulating according to the equation:


where

 t

 {\displaystyle t}

  represents time after tracer injection,

 R
 (
 t
 )

 {\displaystyle R(t)}

  is the amount of tracer in  region of interest ,

 C

 p

 (
 t
 )

 {\displaystyle C_{p}(t)}

  is the concentration of tracer in plasma or blood,

 K

 {\displaystyle K}

  is the  clearance  determining the rate of entry into the peripheral (irreversible) compartment, and

 V

 0

 {\displaystyle V_{0}}

  is the  distribution volume  of the tracer in the central compartment. The first term of the right-hand side represents tracer in the peripheral compartment, and the second term tracer in the central compartment.


By  dividing  both sides by

 C

 p

 (
 t
 )

 {\displaystyle C_{p}(t)}

 , one obtains:


The unknown constants

 K

 {\displaystyle K}

  and

 V

 0

 {\displaystyle V_{0}}

  can be obtained by  linear regression  from a  graph  of

 R
 (
 t
 )

 C

 p

 (
 t
 )

 {\displaystyle {R(t) \over C_{p}(t)}}

  against

 ∫

 0

 t

 C

 p

 (
 τ
 )

 d
 τ

 /

 C

 p

 (
 t
 )

 {\displaystyle \int _{0}^{t}C_{p}(\tau )\,d\tau /C_{p}(t)}

 .


PEGylation  (or  pegylation ) is the process of both covalent and non-covalent attachment or amalgamation of  polyethylene glycol  (PEG, in pharmacy called  macrogol ) polymer chains to molecules and macrostructures, such as a drug, therapeutic protein or vesicle, which is then described as  PEGylated . [ 1 ] [ 2 ] [ 3 ] [ 4 ]  PEGylation affects the resulting derivatives or aggregates interactions, which typically slows down their coalescence and degradation as well as elimination in vivo. [ 5 ] [ 6 ]


PEGylation is routinely achieved by the incubation of a reactive derivative of PEG with the target molecule. The covalent attachment of PEG to a drug or therapeutic protein can "mask" the agent from the host's immune system (reducing  immunogenicity  and  antigenicity ), and increase its hydrodynamic size (size in solution), which prolongs its circulatory time by reducing  renal  clearance. PEGylation can also provide water solubility to  hydrophobic  drugs and proteins. Having proven its  pharmacological  advantages and acceptability, PEGylation technology is the foundation of a growing multibillion-dollar industry. [ 7 ]


PEGylation is the process of attaching the strands of the polymer PEG to molecules, most typically  peptides ,  proteins , and  antibody  fragments, that can improve the safety and efficiency of many  therapeutics . [ 9 ] [ 10 ]  It produces alterations in the physiochemical properties including changes in  conformation ,  electrostatic   binding ,  hydrophobicity  etc. These physical and chemical changes increase systemic retention of the therapeutic agent. Also, it can influence the binding affinity of the therapeutic moiety to the cell receptors and can alter the absorption and distribution patterns.


PEGylation, by increasing the molecular weight of a  molecule , can impart several significant pharmacological advantages over the unmodified form, such as improved  drug  solubility, reduced dosage frequency with potentially reduced  toxicity  and without diminished efficacy, extended circulating life, increased  drug  stability, and enhanced protection from proteolytic degradation; PEGylated forms may also be eligible for patent protection. [ 11 ]


The attachment of an inert and  hydrophilic  polymer was first reported around 1970 to extend blood life and control  immunogenicity  of  proteins . [ 12 ]   Polyethylene glycol was chosen as the polymer. [ 13 ] [ 14 ]  In 1981 Davis and Abuchowski founded Enzon, Inc., which brought three PEGylated drugs to market. Abuchowski later founded and is CEO of Prolong Pharmaceuticals. [ 15 ]


The clinical value of PEGylation is now well established. ADAGEN (pegademase bovine) manufactured by Enzon Pharmaceuticals, Inc., US was the first PEGylated protein approved by the  U.S. Food and Drug Administration  (FDA) in March 1990, to enter the market.  It is used to treat a form of   severe combined immunodeficiency syndrome  (ADA-SCID), as an alternative to  bone marrow transplantation  and enzyme replacement by  gene therapy . Since the introduction of ADAGEN, a large number of PEGylated protein and peptide  pharmaceuticals  have followed and many others are under clinical trial or under development stages. Sales of the two most successful products, Pegasys and Neulasta, exceeded $5 billion in 2011. [ 16 ] [ 17 ]  All commercially available PEGylated pharmaceuticals contain methoxypoly(ethylene glycol) or mPEG. PEGylated pharmaceuticals on the market (in reverse chronology by FDA approval year) have included: [ 18 ]


The PEGylated  lipid   nanoparticle drug delivery  (LNP) system of the  mRNA vaccine  known as  mRNA-1273  has been the subject of ongoing patent litigation with  Arbutus Biopharma , from whom  Moderna  had previously licensed LNP technology. [ 25 ] [ 26 ]   On 4 September 2020,  Nature Biotechnology  reported that Moderna had lost a key challenge in the ongoing case. [ 27 ]


PEGylation has practical uses in biotechnology for protein delivery, [ 28 ]  cell  transfection , and  gene editing  in non-human cells. [ 29 ]


The first step of the PEGylation is the suitable functionalization of the PEG polymer at one or both ends. PEGs that are activated at each end with the same reactive moiety are known as " homobifunctional ", whereas if the functional groups present are different, then the PEG derivative is referred as " heterobifunctional " or " heterofunctional ". The chemically active or activated derivatives of the PEG polymer are prepared to attach the PEG to the desired molecule. [ 30 ]


The overall PEGylation processes used to date for  protein conjugation  can be broadly classified into two types, namely a solution phase batch process and an on-column fed-batch process. [ 31 ]  The simple and commonly adopted batch process involves the mixing of  reagents  together in a suitable  buffer solution , preferably at a temperature between 4 and 6 °C, followed by the separation and purification of the desired product using a suitable technique based on its  physicochemical properties , including  size exclusion chromatography  (SEC),  ion exchange chromatography  (IEX),  hydrophobic interaction chromatography  (HIC) and  membranes  or  aqueous   two-phase systems  ( ATPS ). [ 32 ] [ 33 ]


The choice of the suitable functional group for the PEG derivative is based on the type of available reactive group on the molecule that will be coupled to the PEG. For proteins, typical reactive amino acids include  lysine ,  cysteine ,  histidine ,  arginine ,  aspartic acid ,  glutamic acid ,  serine ,  threonine  and  tyrosine . The N-terminal amino group and the C-terminal  carboxylic acid  can also be used as a site specific site by conjugation with  aldehyde  functional  polymers . [ 34 ]


The techniques used to form first generation PEG derivatives are generally reacting the PEG polymer with a group that is reactive with  hydroxyl  groups, typically  anhydrides ,  acid chlorides ,  chloroformates  and  carbonates . In the second generation PEGylation chemistry more efficient functional groups such as aldehyde,  esters ,  amides  etc. are made available for conjugation.


As applications of PEGylation have become more and more advanced and sophisticated, there has been an increase in need for heterobifunctional PEGs for conjugation. These heterobifunctional PEGs are very useful in linking two entities, where a  hydrophilic , flexible and  biocompatible  spacer is needed. Preferred end groups for heterobifunctional PEGs are  maleimide ,  vinyl sulfones ,  pyridyl disulfide ,  amine ,  carboxylic acids  and  NHS  esters. [ 35 ] [ 36 ] [ 37 ]


Third-generation pegylation agents, where the polymer has been branched, Y-shaped or comb-shaped are available and show reduced viscosity and lack of  organ accumulation . [ 38 ]  Recently also  enzymatic  approaches of PEGylation have been developed, thus further expanding the conjugation tools. [ 39 ] [ 40 ]  PEG-protein conjugates obtained by enzymatic methods are already in clinical use, for example:  Lipegfilgrastim ,  Rebinyn ,  Esperoct .


Unpredictability in clearance times for PEGylated compounds may lead to the accumulation of large-molecular-weight compounds in the liver leading to  inclusion bodies  with no known toxicologic consequences. [ 41 ]  Furthermore, alteration in the chain length may lead to unexpected clearance times  in vivo . [ 42 ]
Moreover, the experimental conditions of PEGylation reaction (i.e. pH, temperature, reaction time, overall cost of the process and molar ratio between PEG derivative and peptide) also have an impact on the stability of the final PEGylated products. [ 43 ]
To overcome the above-mentioned limitations different strategies such as changing the size (Mw), the number, the location and the type of linkage of PEG molecule were offered by several researchers. [ 44 ] [ 45 ]  Conjugation to biodegradable  polysaccharides , which is a promising alternative to PEGylation, is another way to solve the  biodegradability  issue of PEG. [ 46 ]


Physical pharmacy  is the branch of  pharmacy  that concentrates on the applications of  physics  and  chemistry  to the study of pharmacy. In other words, it is the study of the effects that  dosage forms  have on their environment by addressing issues at the molecular level. [ 1 ]  It emphasis on the physical characteristics and actions of the  drug delivery system  before the same is given to the patient. [ 1 ]  It forms the basis for  design , manufacture, and distribution of drug products and serves as the foundation for the stable and proper use of  medical drugs . [ 2 ]  It covers areas such as  solubility ,  pharmacokinetics  and drug delivery.


Physical pharmacy serves as principles that guide the pharmaceutical developments. [ 2 ]  It also serves as a basis for the understanding of drug  absorptions ,  distributions ,  metabolism , and  eliminations  that happen during the course of drug treatment. [ 2 ]


Physical pharmacy deals with the science that works on the following aspects which are related to the development of a  drug product . [ 2 ]


Physiologically based pharmacokinetic (PBPK) modeling  is a  mathematical modeling  technique for predicting the absorption, distribution, metabolism and excretion (ADME) of synthetic or natural chemical substances in humans and other animal species. PBPK modeling is used in pharmaceutical research and drug development, and in health  risk assessment  for cosmetics or general chemicals.


PBPK models strive to be mechanistic by mathematically transcribing anatomical, physiological, physical, and chemical descriptions of the phenomena involved in the complex ADME processes. A large degree of residual simplification and empiricism is still present in those models, but they have an extended domain of applicability compared to that of classical, empirical function based,  pharmacokinetic  models. PBPK models may have purely predictive uses, but other uses, such as statistical inference, have been made possible by the development of  Bayesian  statistical tools able to deal with complex models. [ 1 ]  That is true for both toxicity risk assessment and therapeutic drug development.


PBPK models try to rely  a priori  on the anatomical and physiological structure of the body, and to a certain extent, on biochemistry. They are usually  multi-compartment models , with compartments corresponding to predefined organs or tissues, with interconnections corresponding to blood or lymph flows (more rarely to diffusions). A system of  differential equations  for concentration or quantity of substance on each compartment can be written, and its parameters represent blood flows, pulmonary ventilation rate, organ volumes etc., for which information is available in scientific publications. Indeed, the description they make of the body is simplified and a balance needs to be struck between complexity and simplicity. Besides the advantage of allowing the recruitment of  a priori  information about parameter values, these models also facilitate inter-species transpositions or extrapolation from one mode of administration to another ( e.g. , inhalation to oral). An example of a 7-compartment PBPK model, suitable to describe the fate of many solvents in the mammalian body, is given in the Figure on the right.


The first pharmacokinetic model described in the scientific literature [ 2 ]
was in fact a PBPK model. It led, however, to computations intractable at that time. The focus shifted then to simpler models, [ 3 ]
for which analytical solutions could be obtained (such solutions were sums of exponential terms, which led to further simplifications.) The availability of computers and numerical integration algorithms marked a renewed interest in  physiological models  in the early 1970s. [ 4 ] [ 5 ]
For substances with complex kinetics, or when inter-species extrapolations were required, simple models were insufficient and research continued on physiological models. [ 6 ] [ 7 ] [ 8 ]
By 2010, hundreds of scientific publications had described and used PBPK models, and at least two private companies have based their business on their expertise in this area.


The model equations follow the principles of mass transport, fluid dynamics, and biochemistry in order to simulate the fate of a substance in the body. [ 9 ]
Compartments are usually defined by grouping organs or tissues with similar blood perfusion rate and lipid content ( i.e.  organs for which chemicals' concentration  vs.  time profiles will be similar). Ports of entry (lung, skin, intestinal tract...), ports of exit (kidney, liver...) and target organs for therapeutic effect or toxicity are often left separate. Bone can be excluded from the model if the substance of interest does not distribute to it. Connections between compartment follow physiology ( e.g. , blood flow in exit of the gut goes to liver,  etc. )


Drug distribution into a tissue can be rate-limited by either perfusion or permeability. [ 10 ] [ 11 ]  Perfusion-rate-limited kinetics apply when the tissue membranes present no barrier to diffusion. Blood flow, assuming that the drug is transported mainly by blood, as is often the case, is then the limiting factor to distribution in the various cells of the body. That is usually true for small lipophilic drugs. Under perfusion limitation, the instantaneous rate of entry for the quantity of drug in a compartment is simply equal to (blood) volumetric flow rate through the organ times the incoming blood concentration. In that case; for a generic compartment  i , the differential equation for the quantity  Q i  of substance, which defines the rate of change in this quantity, is:


d

 Q

 i

 d
 t

 =

 F

 i

 (

 C

 a
 r
 t

 −

 Q

 i

 P

 i

 V

 i

 )

 {\displaystyle {dQ_{i} \over dt}=F_{i}(C_{art}-{{Q_{i}} \over {P_{i}V_{i}}})}


where  F i  is blood flow (noted  Q  in the Figure above),  C art  incoming arterial blood concentration,  P i  the tissue over blood partition coefficient and  V i  the volume of compartment  i .


A complete set of differential equations for the 7-compartment model shown above could therefore be given by the following table:


The above equations include only transport terms and do not account for inputs or outputs.
Those can be modeled with specific terms, as in the following.


Modeling inputs is necessary to come up with a meaningful description of a chemical's pharmacokinetics. The following examples show how to write the corresponding equations.


When dealing with an oral  bolus  dose ( e.g.  ingestion of a tablet), first order absorption is a very common assumption. In that case the gut equation is augmented with an input term, with an absorption rate constant  K a :


d

 Q

 g

 d
 t

 =

 F

 g

 (

 C

 a
 r
 t

 −

 Q

 g

 P

 g

 V

 g

 )
 +

 K

 a

 Q

 i
 n
 g

 {\displaystyle {dQ_{g} \over dt}=F_{g}(C_{art}-{{Q_{g}} \over {P_{g}V_{g}}})+K_{a}Q_{ing}}


That requires defining an equation for the quantity ingested and present in the gut lumen:


d

 Q

 i
 n
 g

 d
 t

 =
 −

 K

 a

 Q

 i
 n
 g

 {\displaystyle {dQ_{ing} \over dt}=-K_{a}Q_{ing}}


In the absence of a gut compartment, input can be made directly in the liver. However, in that case local metabolism in the gut may not be correctly described. The case of approximately continuous absorption ( e.g. via  drinking water) can be modeled by a zero-order absorption rate (here  R ing  in units of mass over time):


d

 Q

 g

 d
 t

 =

 F

 g

 (

 C

 a
 r
 t

 −

 Q

 g

 P

 g

 V

 g

 )
 +

 R

 i
 n
 g

 {\displaystyle {dQ_{g} \over dt}=F_{g}(C_{art}-{{Q_{g}} \over {P_{g}V_{g}}})+R_{ing}}


More sophisticated gut absorption model can be used. In those models, additional compartments describe the various sections of the gut lumen and tissue. Intestinal pH, transit times and presence of active transporters can be taken into account
. [ 12 ]


The absorption of a chemical deposited on skin can also be modeled using first order terms. It is best in that case to separate the skin from the other tissues, to further differentiate exposed skin and non-exposed skin, and differentiate viable skin (dermis and epidermis) from the  stratum corneum  (the actual skin upper layer exposed). This is the approach taken in [Bois F., Diaz Ochoa J.G. Gajewska M., Kovarich S., Mauch K., Paini A., Péry A., Sala Benito J.V., Teng S., Worth A., in press, Multiscale modelling approaches for assessing cosmetic ingredients safety, Toxicology. doi: 10.1016/j.tox.2016.05.026]


Unexposed  stratum corneum  simply exchanges with the underlying viable skin by diffusion:


d

 Q

 s
 c

 u

 d
 t

 =

 K

 p

 ×

 S

 s

 ×
 (
 1
 −

 f

 S

 e

 )
 ×
 (

 Q

 s

 u

 P

 s
 c

 V

 s
 c

 u

 −

 C

 s
 c

 u

 )

 {\displaystyle {dQ_{{sc}_{u}} \over dt}=K_{p}\times S_{s}\times (1-f_{S_{e}})\times ({Q_{s_{u}} \over {P_{sc}V_{{sc}_{u}}}}-C_{{sc}_{u}})}


where

 K

 p

 {\displaystyle K_{p}}

  is the partition coefficient,

 S

 s

 {\displaystyle S_{s}}

  is the total skin surface area,

 f

 S

 e

 {\displaystyle f_{S_{e}}}

  the fraction of skin surface area exposed, ...


For the viable skin unexposed:


d

 Q

 s

 u

 d
 t

 =

 F

 s

 (
 1
 −

 f

 S

 e

 )
 (

 C

 a
 r
 t

 −

 Q

 s

 u

 P

 s

 V

 s

 u

 )
 −

 d

 Q

 s
 c

 u

 d
 t

 {\displaystyle {dQ_{s_{u}} \over dt}=F_{s}(1-f_{S_{e}})(C_{art}-{{Q_{s_{u}}} \over {P_{s}V_{s_{u}}}})-{dQ_{{sc}_{u}} \over dt}}


For the skin  stratum corneum  exposed:


d

 Q

 s
 c

 e

 d
 t

 =

 K

 p

 ×

 S

 s

 ×

 f

 S

 e

 ×
 (

 Q

 s

 e

 P

 s
 c

 V

 s
 c

 e

 −

 C

 s
 c

 e

 )

 {\displaystyle {dQ_{{sc}_{e}} \over dt}=K_{p}\times S_{s}\times f_{S_{e}}\times ({Q_{s_{e}} \over {P_{sc}V_{{sc}_{e}}}}-C_{{sc}_{e}})}


for the viable skin exposed:


d

 Q

 s

 e

 d
 t

 =

 F

 s

 f

 S

 e

 (

 C

 a
 r
 t

 −

 Q

 s

 e

 P

 s

 V

 s

 e

 )
 −

 d

 Q

 s
 c

 e

 d
 t

 {\displaystyle {dQ_{s_{e}} \over dt}=F_{s}f_{S_{e}}(C_{art}-{{Q_{s_{e}}} \over {P_{s}V_{s_{e}}}})-{dQ_{{sc}_{e}} \over dt}}


dt(QSkin_u) and dt(QSkin_e) feed from arterial blood and back to venous blood.


More complex diffusion models have been published [reference to add].


Intravenous injection is a common clinical route of administration. (to be completed)


Inhalation occurs through the lung and is hardly dissociable from exhalation (to be completed)


There are several ways metabolism can be modeled. For some models, a linear excretion rate is preferred. This can be accomplished with a simple differential equation. Otherwise a  Michaelis-Menten  equation, as follows, is generally appropriate for a more accurate result.


PBPK models are compartmental models like many others, but they have a few advantages over so-called "classical" pharmacokinetic models, which are less grounded in physiology. PBPK models can first be used to abstract and eventually reconcile disparate data (from physicochemical or biochemical experiments,  in vitro  or  in vivo  pharmacological or toxicological experiments,  etc. ) They give also access to internal body concentrations of chemicals or their metabolites, and in particular at the site of their effects, be it therapeutic or toxic. Finally they also help interpolation and extrapolation of knowledge between:


Some of these extrapolations are "parametric" : only changes in input or parameter values are needed to achieve the extrapolation (this is usually the case for dose and time extrapolations). Others are "nonparametric" in the sense that a change in the model structure itself is needed ( e.g. , when extrapolating to a pregnant female, equations for the foetus should be added).


Owing to the mechanistic basis of PBPK models, another potential use of PBPK modeling is hypothesis testing.  For example, if a drug compound showed lower-than-expected oral bioavailability, various model structures (i.e., hypotheses) and parameter values can be evaluated to determine which models and/or parameters provide the best fit to the observed data.  If the hypothesis that metabolism in the intestines was responsibility for the low bioavailability yielded the best fit, then the PBPK modeling results support this hypothesis over the other hypotheses evaluated.


As such, PBPK modeling can be used,  inter alia , to evaluate the involvement of carrier-mediated transport, clearance saturation, enterohepatic recirculation of the parent compound, extra-hepatic/extra-gut elimination; higher  in vivo  solubility than predicted  in vitro ; drug-induced gastric emptying delays; gut loss and regional variation in gut absorption. [ 15 ]


Each type of modeling technique has its strengths and limitations.  PBPK modeling is no exception.  One limitation is the potential for a large number of parameters, some of which may be correlated.  This can lead to the issues of parameter identifiability and redundancy. However, it is possible (and commonly done) to model explicitly the correlations between parameters (for example, the non-linear relationships between age, body-mass, organ volumes and blood flows).


After numerical values are assigned to each PBPK model parameter, specialized or general computer software is typically used to numerically integrate a set of ordinary differential  equations like those described above, in order to calculate the numerical value of each compartment at specified values of time (see Software).  However, if such equations involve only linear functions of each compartmental value, or under limiting conditions (e.g., when input values remain very small) that guarantee such linearity is closely approximated, such equations may be solved analytically to yield explicit equations (or, under those limiting conditions, very accurate approximations) for the time-weighted average (TWA) value of each compartment as a function of the TWA value of each specified input (see, e.g., [ 16 ] [ 17 ] ).


PBPK models can rely on chemical property prediction models ( QSAR  models or predictive chemistry models) on one hand. For example, QSAR models can be used to estimate partition coefficients.  They also extend into, but are not destined to supplant,  systems biology  models of metabolic pathways. They are also parallel to  physiome  models, but do not aim at modelling physiological functions beyond fluid circulation in detail. In fact the above four types of models can reinforce each other when integrated. [ 18 ]


Further references:


Dedicated software:


General software:


Plasma protein binding  refers to the degree to which  medications  attach to  blood proteins  within the  blood plasma . A  drug 's  efficacy  may be affected by the degree to which it binds. The less bound a drug is, the more efficiently it can traverse or diffuse through  cell membranes . Common  blood proteins  that drugs bind to are  human serum albumin ,  lipoprotein ,  glycoprotein , and α, β‚ and γ  globulins .


A drug in blood exists in two forms: bound and unbound. Depending on a specific drug's affinity for  plasma proteins , a proportion of the drug may become bound to the proteins, with the remainder being unbound. If the protein binding is reversible, then a  chemical equilibrium  will exist between the bound and unbound states, such that:


Notably, it is the unbound fraction which exhibits pharmacologic effects. It is also the fraction that may be  metabolized  and/or excreted. For example, the "fraction bound" of the  anticoagulant   warfarin  is 97%. This means that out of the amount of warfarin in the blood, 97% is bound to plasma proteins. The remaining 3% (the fraction unbound) is the fraction that is actually active and may be excreted.


Protein binding can influence the drug's  biological half-life . The bound portion may act as a reservoir or depot from which the drug is slowly released as the unbound form. Since the unbound form is being metabolized and/or excreted from the body, the bound fraction will be released in order to maintain equilibrium.


Since albumin is alkalotic, acidic and neutral drugs will primarily bind to  albumin .  If albumin becomes saturated, then these drugs will bind to  lipoprotein . Basic drugs will bind to the acidic  alpha-1 acid glycoprotein .  This is significant because various medical conditions may affect the levels of albumin, alpha-1 acid glycoprotein, and lipoproteins.


Only the unbound fraction of the drug undergoes metabolism in the liver and other tissues. As the drug dissociates from the protein, more and more drug undergoes metabolism. Changes in the levels of free drug change the volume of distribution because free drug may distribute into the tissues leading to a decrease in plasma concentration profile. For the drugs which rapidly undergo metabolism,  clearance  is dependent on the hepatic blood flow.  For drugs which slowly undergo metabolism, changes in the unbound fraction of the drug directly change the clearance of the drug.


The most commonly used methods for measuring drug concentration levels in the plasma measure bound as well as unbound fractions of the drug.


The fraction unbound can be altered by a number of variables, such as the concentration of drug in the body, the amount and quality of plasma protein, and other drugs that bind to plasma proteins.  Higher drug concentrations would lead to a higher fraction unbound, because the plasma protein would be saturated with drug and any excess drug would be unbound.  If the amount of plasma protein is decreased (such as in  catabolism ,  malnutrition ,  liver disease ,  renal disease ), there would also be a higher fraction unbound.  Additionally, the quality of the plasma protein may affect how many drug-binding sites there are on the protein.


Using 2 drugs at the same time can sometimes affect each other's fraction unbound.  For example, assume that Drug A and Drug B are both protein-bound drugs.  If Drug A is given, it will bind to the plasma proteins in the blood.  If Drug B is also given, it can displace Drug A from the protein, thereby increasing Drug A's fraction unbound.  This may increase the effects of Drug A, since only the unbound fraction may exhibit activity.


Note that for Drug A, the % increase in unbound fraction is 100% – hence, Drug A's pharmacological effect can potentially double (depending on whether the free molecules get to their target before they are eliminated by metabolism or excretion).  This change in pharmacologic effect could have adverse consequences.


However, this effect is really only noticeable in closed systems where the pool of available proteins could potentially be exceeded by the number of drug molecules. Biological systems, such as humans and animals, are open systems where molecules can be gained, lost or redistributed and where the protein pool capacity is almost never exceeded by the number of drug molecules. A drug that is 99% bound means that 99% of the drug molecules are bound to blood proteins not that 99% of the blood proteins are bound with drug. When two, highly protein-bound drugs (A and B) are added into the same biological system it will lead to an initial small increase in the concentration of free drug A (as drug B ejects some of the drug A from its proteins). However, this free drug A is now more available for redistribution into the body tissues and/or for excretion. This means the total amount of drug in the system will decrease quite rapidly, keeping the free drug fraction (the concentration of free drug divided by the total drug concentration) constant and yielding almost no change in clinical effect. [ 1 ]


The effects of drugs displacing each other and changing the clinical effect (though important in some examples) is vastly overestimated usually and a common example incorrectly used to display the importance of this effect is the anticoagulant  warfarin . Warfarin is highly protein-bound (>95%) and has a low  therapeutic index . Since a low therapeutic index indicates that there is a high risk of toxicity when using the drug, any potential increases in warfarin concentration could be very dangerous and lead to hemorrhage. In horses, it is very true that if warfarin and  phenylbutazone  are administered concurrently, the horse can develop bleeding issues which can be fatal. This is often explained as being due to the effect of phenylbutazone ejecting warfarin from its plasma protein, thus increasing the concentration of free warfarin and increasing its anticoagulant effect. However, the real problem is that phenylbutazone interferes with the liver's ability to metabolize warfarin so free warfarin cannot be metabolized properly or excreted. This leads to an increase in free warfarin and the resulting bleeding problems. [ citation needed ]


The  plateau principle  is a  mathematical model  or  scientific law  originally developed to explain the time course of drug action ( pharmacokinetics ). [ 1 ]  The principle has wide applicability in pharmacology, physiology, nutrition, biochemistry, and system dynamics. It applies whenever a drug or nutrient is infused or ingested at a relatively constant rate and when a constant fraction is eliminated during each time interval. Under these conditions, any change in the rate of infusion leads to an exponential increase or decrease until a new level is achieved. This behavior is also called an  approach to  steady state  because rather than causing an indefinite increase or decrease, a natural balance is achieved when the rate of infusion or production is balanced by the rate of loss.


An especially important use of the plateau principle is to study the renewal of tissue constituents in the human and animal body. In adults, daily synthesis of tissue constituents is nearly constant, and most constituents are removed with a first- order   reaction rate . Applicability of the plateau principle was recognized during  radioactive tracer  studies of protein turnover in the 1940s by  Rudolph Schoenheimer [ 2 ]  and  David Rittenberg . [ 3 ]  Unlike the case with drugs, the initial amount of tissue or tissue protein is not zero because daily synthesis offsets daily elimination. In this case, the model is also said to approach a  steady state  with  exponential  or  logarithmic   kinetics . Constituents that change in this manner are said to have a  biological half-life .


A practical application of the plateau principle is that most people have experienced "plateauing" during regimens for weight management or training for sports. After a few weeks of progress, one seems unable to continue gaining in ability or losing weight. This outcome results from the same underlying quantitative model. This entry will describe the popular concepts as well as development of the plateau principle as a scientific, mathematical model.


In the sciences, the broadest application of the plateau principle is creating realistic time signatures for change in kinetic models (see  Mathematical model ). One example of this principle is the long time required to effectively change human body composition. Theoretical studies have shown that many months of consistent physical training and food restriction are needed to bring about permanent weight stability in people who were previously  overweight . [ 4 ]


Most drugs are eliminated from the  blood plasma  with first- order   kinetics . For this reason, when a drug is introduced into the body at a constant rate by  intravenous therapy , it approaches a new steady concentration in the blood at a rate defined by its  half-life . Similarly, when the intravenous infusion is ended, the drug concentration decreases exponentially and reaches an undetectable level after 5–6 half-lives have passed. [ 5 ] [ 6 ]  If the same drug is administered as a  bolus (medicine)  with a single injection, peak concentration is achieved almost immediately and then the concentration declines exponentially.


Most drugs are taken by mouth. In this case, the assumption of constant infusion is only approximated as doses are repeated over the course of several days. The plateau principle still applies but more complex models are required to account for the  route of administration .


Derivation of equations that describe the time course of change for a system with zero- order  input and first-order elimination are presented in the articles  Exponential decay  and  Biological half-life , and in scientific literature. [ 1 ] [ 7 ]


The relationship between the elimination rate constant and half-life is given by the following equation:


Because ln 2 equals 0.693, the half-life is readily calculated from the elimination rate constant. Half-life has units of time, and the elimination rate constant has units of 1/time, e.g., per hour or per day.


An equation can be used to forecast the concentration of a compound at any future time when the fractional degration rate and steady state concentration are known:


The exponential function in parentheses corresponds to the fraction of total change that has been achieved as time passes and the difference between  C ss  and  C 0  equals the total amount of change. Finally, at steady state, the concentration is expected to equal the rate of synthesis, production or infusion divided by the first-order elimination constant.


Although these equations were derived to assist with predicting the time course of drug action, [ 1 ]  the same equation can be used for any substance or quantity that is being produced at a measurable rate and degraded with first-order kinetics. Because the equation applies in many instances of  mass balance , it has very broad applicability in addition to  pharmacokinetics . The most important inference derived from the steady state equation and the equation for fractional change over time is that the elimination rate constant ( k e ) or the sum of rate constants that apply in a model determine the time course for change in mass when a system is perturbed (either by changing the rate of inflow or production, or by changing the elimination rate(s)).


When experimental data are available, the normal procedure for estimating rate parameters such as  k e  and  C ss  is to minimize the  sum of squares  of differences between observed data and values predicted based on initial estimates of the rate constant and steady state value. This can be done using any software package that contains a  curve fitting  routine. An example of this methodology implemented with spreadsheet software has been reported. [ 8 ]  The same article reports a method that requires only 3 equally spaced data points to obtain estimates for kinetic parameters. Spreadsheets that compare these methods are available. [ 8 ]


Dr.  Wilbur O. Atwater , who developed the first database of food composition in the United States, recognized that the response to excessive or insufficient nutrient intake included an adjustment in efficiency that would result in a plateau. He observed: "It has been found by numerous experiments that when the nutrients are fed in large excess, the body may continue for a time to store away part of the extra material, but after it has accumulated a certain amount, it refuses to take on more, and the daily consumption equals the supply even when this involves great waste." [ 9 ]


In general, no  essential nutrient  is produced in the body. Nutrient kinetics therefore follow the plateau principle with the distinction that most are ingested by mouth and the body must contain an amount adequate for health. The plateau principle is important in determining how much time is needed to produce a deficiency when intake is insufficient. Because of this, pharmacokinetic considerations should be part of the information needed to set a  dietary reference intake  for essential nutrients.


The blood plasma concentration of  vitamin C  or  ascorbic acid  as a function of dose attains a plateau with a half-life of about 2 weeks. [ 10 ]   Bioavailability  of vitamin C is highest at dosages below 200 mg per day. Above 500 mg, nearly all of excess vitamin C is excreted through urine.


Vitamin D metabolism is complex because the  provitamin  can be formed in the skin by ultraviolet irradiation or obtained from the diet. Once hydroxylated, the vitamin has a half-life of about 2 months. [ 11 ]
Various studies have suggested that current intakes are inadequate for optimum bone health and much current research is aimed at determining recommendations for obtaining adequate circulating vitamin D 3  and calcium while also minimizing potential toxicity. [ 12 ]


Many healthful qualities of foods and beverages may be related to the content of phytochemicals (see  List of phytochemicals in food ). Prime examples are  flavonoids  found in green tea, berries,  cocoa , and  spices  as well as in the skins and seeds of apples, onions, and grapes.


Investigations into healthful benefits of phytochemicals follow exactly the same principles of pharmacokinetics that are required to study drug therapy. The initial concentration of any non-nutritive phytochemical in the blood plasma is zero unless a person has recently ingested a food or beverage. For example, as increasing amounts of green tea extract are consumed, a graded increase in plasma  catechin  can be measured, and the major compound is eliminated with a half-life of about 5 hours. [ 13 ]  Other considerations that must be evaluated include whether the ingested compound interacts favorably or unfavorably with other nutrients or drugs, and whether there is evidence for a threshold or  toxicity  at higher levels of intake.


It is especially common for people who are trying to lose weight to experience plateaus after several weeks of successful weight reduction. The plateau principle suggests that this leveling off is a sign of success. Basically, as one loses weight, less  food energy  is required to maintain the resting metabolic rate, which makes the initial regimen less effective. [ 14 ]  The idea of weight plateaus has been discussed for subjects who are participating in a  calorie restriction experiment   [ 15 ]  Food energy is expended largely through work done against gravity (see  Joule ), so weight reduction lessens the effectiveness of a given workout. In addition, a trained person has greater skill and therefore greater efficiency during a workout. Remedies include increasing the workout intensity or length and reducing portion sizes of meals more than may have been done initially.


The fact that weight loss and dieting reduce the metabolic rate is supported by research. In one study, heat production was reduced 30% in obese men after a weight loss program, and this led to resistance to further lose body weight. [ 16 ]  Whether body mass increases or decreases, adjustments in the  thermic effect of food , resting energy expenditure, and non-resting energy expenditure all oppose further change. [ 17 ]


Any athlete who has trained for a sport has probably experienced plateaus, and this has given rise to various strategies to continue improving. [ 18 ]  Voluntary  skeletal muscle  is in balance between the amount of muscle synthesized or renewed each day and the amount that is degraded. Muscle fibers respond to repetition and load, and increased training causes the quantity of exercised muscle fiber to increase exponentially (simply meaning that the greatest gains are seen during the first weeks of training). Successful training produces  hypertrophy  of muscle fibers as an adaptation to the training regimen. In order to make further gains, greater workout intensity is required with heavier loads and more repetitions, although improvement in skill can contribute to gains in ability.


When a bodily constituent adjusts exponentially over time, it usually attains a new stable level as a result of the plateau principle. The new level may be higher than the initial level ( hypertrophy ) in the case of strength training or lower in the case of dieting or disuse  atrophy . This adjustment contributes to  homeostasis  but does not require  feedback  regulation. Gradual, asymptotic approach to a new balance between synthesis and degradation produces a stable level. Because of this, the plateau principle is sometimes called the  stability principle.  Mathematically, the result is  linear  dynamics despite the fact that most biological processes are non-linear (see  Nonlinear system ) if considered over a very broad range of inputs.


Data from the  Minnesota Starvation Experiment  by  Ancel Keys  and others [ 19 ]  demonstrate that during food restriction, total body mass, fat mass and lean body mass follow an exponential approach to a new steady state. [ 20 ]  The observation that body mass changes exponentially during partial or complete starvation seems to be a general feature of adaptation to energy restriction. [ 21 ]


Each cell produces thousands of different kinds of  protein  and  enzymes . One of the key methods of cellular regulation is to change the rate of  transcription  of  messenger RNA , which gives rise to a change in the rate of synthesis for the protein that the messenger RNA encodes. The plateau principle explains why the concentration of different enzymes increases at unique rates in response to a single  hormone . Because each enzyme is degraded with at a unique rate (each has a different  half-life ), the rate of change differs even when the same stimulus is applied. This principle has been demonstrated for the response of liver enzymes that degrade amino acids to  cortisone , which is a  catabolic  hormone. [ 7 ]


The method of approach to steady state has also been used to analyze the change in messenger RNA levels when synthesis or degradation changes, and a model has also been reported in which the plateau principle is used to connect the change in messenger RNA synthesis to the expected change in protein synthesis and concentration as a function of time. [ 22 ]


Excessive gain in body weight contributes to the  metabolic syndrome , which may include elevated fasting  blood sugar  (or  glucose ), resistance to the action of  insulin , elevated  low-density lipoprotein  (LDL cholesterol) or decreased  high-density lipoprotein  (HDL cholesterol), and elevated  blood pressure .  Obesity  was designated as a disease in 2013 by the American Medical Association. It is defined as a chronic, relapsing, multi-factorial, neurobehavioral disease, wherein an increase in body fat promotes adipose tissue dysfunction and abnormal fat mass physical forces, resulting in adverse metabolic, biomechanical, and psychosocial health consequences. [ 23 ]  Because body mass, fat mass and fat free mass all change exponentially during weight reduction, it is a reasonable hypothesis to expect that symptoms of metabolic syndrome will also adjust exponentially towards normal values.


Scientists have evaluated turnover of bodily constituents using  radioactive tracers  and  stable isotope  tracers. [ 24 ]  If given orally, the tracers are absorbed and move into the  blood plasma , and are then distributed throughout the bodily tissues. In such studies, a  multi-compartment model  is required to analyze turnover by  isotopic labeling . The isotopic marker is called a  tracer  and the material being analyzed is the  tracee .


In studies with humans, blood plasma is the only tissue that can be easily sampled. A common procedure is to analyze the dynamics by assuming that changes can be attributed to a sum of exponentials. A single mathematical  compartment  is usually assumed to follow first-order kinetics in accord with the plateau principle. There are many examples of this kind of analysis in nutrition, for example, in the study of metabolism of zinc, [ 25 ]  and carotenoids. [ 26 ]


The commonest assumption in compartmental modeling is that material in a homogeneous compartment behaves exponentially. However, this assumption is sometimes modified to include a saturable response that follows  Michaelis–Menten kinetics  or a related model called a  Hill equation . When the material in question is present at a concentration near the  K M , it often behaves with pseudo first-order kinetics (see  Rate equation ) and the plateau principle applies despite the fact that the model is non-linear.


Compartmental modeling in biomedical sciences primarily originated from the need to study metabolism by using tracers. In contrast,  System dynamics  originated as a simple method of developing mathematical models by  Jay Wright Forrester  and colleagues. System dynamics represents a compartment or pool as a  stock  and movement among compartments as  flows . In general, the rate of flow depends on the amount of material in the stock to which it is connected. It is common to represent this dependence as a constant proportion (or first-order) using a  connector  element in the model.


System dynamics is one application of the field of  control theory . In the biomedical field, one of the strongest advocates for computer-based analysis of physiological problems was Dr.  Arthur Guyton . For example, system dynamics has been used to analyze the problem of body weight regulation. [ 27 ]  Similar methods have been used to study the spread of epidemics (see  Compartmental models in epidemiology ).


Software that solves systems of equations required for compartmental modeling and system dynamics makes use of  finite difference  methods to represent a set of  ordinary differential equations . An expert appraisal of the different types of dynamic behavior that can be developed by application of the plateau principle to the field of system dynamics has been published. [ 28 ]


In  biotechnology ,  polymersomes [ 1 ]  are a class of artificial  vesicles , tiny hollow spheres that enclose a solution. Polymersomes are made using  amphiphilic  synthetic block  copolymers  to form the vesicle membrane, and have radii ranging from 50 nm to 5 μm or more. [ 2 ]  Most reported polymersomes contain an  aqueous solution  in their core and are useful for encapsulating and protecting sensitive molecules, such as drugs, enzymes, other proteins and peptides, and  DNA  and  RNA  fragments. The polymersome membrane provides a physical barrier that isolates the encapsulated material from external materials, such as those found in biological systems.


Synthosomes  are polymersomes engineered to contain channels ( transmembrane proteins ) that allow certain chemicals to pass through the membrane, into or out of the vesicle. This allows for the collection or enzymatic modification of these substances. [ 3 ]


The term "polymersome" for vesicles made from block copolymers was coined in 1999. [ 1 ]  Polymersomes are similar to  liposomes , which are vesicles formed from naturally occurring  lipids . While having many of the properties of natural liposomes, polymersomes exhibit increased stability and reduced permeability. Furthermore, the use of synthetic polymers enables designers to manipulate the characteristics of the membrane and thus control permeability, release rates, stability and other properties of the polymersome.


Several different morphologies of the block copolymer used to create the polymersome have been used. The most frequently used are the linear diblock or triblock copolymers. In these cases, the block copolymer has one block that is  hydrophobic ; the other block or blocks are  hydrophilic . Other morphologies used include comb copolymers, [ 4 ] [ 5 ]  where the backbone block is hydrophilic and the comb branches are hydrophobic, and  dendronized block copolymers , [ 6 ]  where the  dendrimer  portion is hydrophilic.


In the case of diblock, comb and dendronized copolymers the polymersome membrane has the same  bilayer  morphology of a liposome, with the hydrophobic blocks of the two layers facing each other in the interior of the membrane. In the case of triblock copolymers the membrane is a  monolayer  that mimics a bilayer, the central block filling the role of the two facing hydrophobic blocks of a bilayer. [ 7 ]


In general they can be prepared by the methods used in the preparation of liposomes. Film rehydration, direct injection method or dissolution method.


Polymersomes that contain active enzymes and that provide a way to selectively transport substrates for conversion by those enzymes have been described as nanoreactors. [ 8 ]


Polymersomes have been used to create controlled release  drug delivery  systems. [ 9 ]   Similar to coating liposomes with  polyethylene glycol , polymersomes can be made invisible to  the immune system  if the hydrophilic block consists of polyethylene glycol. [ 10 ]  Thus, polymersomes are useful carriers for targeted medication.


For  in vivo  applications, polymersomes are  de facto  limited to the use of  FDA -approved polymers, as most pharmaceutical firms are unlikely to develop novel  polymers  due to cost issues. Fortunately, there are a number of such polymers available, with varying properties, including:


Hydrophilic blocks


Hydrophobic blocks


If enough of the block copolymer molecules that make up a polymersome are  cross-linked , the polymersome can be made into a transportable powder. [ 2 ]


Polymersomes can be used to make an  artificial cell  if  hemoglobin  and other components are added. [ 13 ] [ 14 ]  The first artificial cell was made by  Thomas Chang . [ 15 ]


Polypharmacy  (polypragmasia) is an  umbrella term  to describe the simultaneous use of multiple medicines by a patient for their conditions. [ 1 ] [ 2 ]  The term polypharmacy is often defined as regularly taking five or more medicines but there is no standard definition and the term has also been used in the context of when a person is prescribed 2 or more medications at the same time. [ 1 ] [ 3 ] [ 4 ]  Polypharmacy may be the consequence of having multiple long-term conditions, also known as  multimorbidity  and is more common in people who are older. [ 5 ] [ 6 ]  In some cases, an excessive number of medications at the same time is worrisome, especially for people who are older with many chronic health conditions, because this increases the risk of an adverse event in that population. [ 7 ] [ 8 ]  In many cases, polypharmacy cannot be avoided, but 'appropriate polypharmacy' practices are encouraged to decrease the risk of adverse effects. [ 9 ]  Appropriate polypharmacy is defined as the practice of prescribing for a person who has multiple conditions or complex health needs by ensuring that medications prescribed are optimized and follow 'best evidence' practices. [ 9 ]


The prevalence of polypharmacy is estimated to be between 10% and 90% depending on the definition used, the age group studied, and the geographic location. [ 10 ]  Polypharmacy continues to grow in importance because of  aging populations . Many countries are experiencing a fast growth of the older population, 65 years and older. [ 11 ] [ 12 ] [ 13 ]  This growth is a result of the  baby-boomer  generation getting older and an increased  life expectancy  as a result of ongoing improvement in health care services worldwide. [ 14 ] [ 15 ]  About 21% of adults with  intellectual disability  are also exposed to polypharmacy. [ 16 ]  The level of polypharmacy has been increasing in the past decades. Research in the USA shows that the percentage of patients greater than 65 years-old using more than 5 medications increased from 24% to 39% between 1999 and 2012. [ 17 ]  Similarly, research in the UK found that the number of older people taking 5 plus medication had quadrupled from 12% to nearly 50% between 1994 and 2011. [ 18 ]


Polypharmacy is not necessarily ill-advised, but in many instances can lead to negative outcomes or poor treatment effectiveness, often being  more harmful than helpful  or presenting  too much risk for too little benefit . Therefore,  health professionals  consider it a situation that requires monitoring and review to validate whether all of the medications are still necessary. Concerns about polypharmacy include increased  adverse drug reactions ,  drug interactions ,  prescribing cascade , and higher costs. [ 19 ]  A prescribing cascade occurs when a person is prescribed a drug and experiences an adverse drug effect that is misinterpreted as a new medical condition, so the patient is prescribed another drug. [ 20 ]  Polypharmacy also increases the burden of medication taking particularly in older people and is associated with  medication non-adherence . [ 21 ]


Polypharmacy is often  associated with  a decreased  quality of life , including decreased  mobility  and  cognition . [ 22 ]  Patient factors that influence the number of medications a patient is prescribed include a high number of chronic conditions requiring a complex drug regimen. Other systemic factors that impact the number of medications a patient is prescribed include a patient having multiple prescribers and multiple pharmacies that may not communicate.


Whether or not the advantages of polypharmacy (over taking single medications or  monotherapy ) outweigh the disadvantages or risks depends upon the particular combination and diagnosis involved in any given case. [ 23 ]  The use of multiple drugs, even in fairly straightforward illnesses, is not an indicator of poor treatment and is not necessarily  overmedication . Moreover, it is well accepted in  pharmacology  that it is impossible to accurately predict the side effects or clinical effects of a combination of drugs without studying that particular combination of drugs in test subjects. Knowledge of the pharmacologic profiles of the individual drugs in question does not assure accurate prediction of the side effects of combinations of those drugs; and effects also vary among individuals because of  genome -specific  pharmacokinetics . Therefore, deciding whether and how to reduce a list of medications ( deprescribe ) is often not simple and requires the experience and judgment of a practicing clinician, as the clinician must weigh the pros and cons of keeping the patient on the medication. However, such thoughtful and wise review is an ideal that too often does not happen, owing to problems such as poorly handled  care transitions  (poor continuity of care, usually because of  siloed information ), overworked physicians and other clinical staff, and  interventionism .


While polypharmacy is typically regarded as undesirable, prescription of multiple medications can be appropriate and therapeutically beneficial in some circumstances. [ 24 ]  “Appropriate polypharmacy” is described as prescribing for complex or multiple conditions in such a way that necessary medicines are used based on the best available evidence at the time to preserve safety and well-being. [ 24 ]  Polypharmacy is clinically indicated in some chronic conditions, for example in  diabetes mellitus , but should be discontinued when evidence of benefit from the prescribed drugs no longer outweighs potential for harm (described below in Contraindications). [ 24 ]


Often certain medications can interact with others in a positive way specifically intended when prescribed together, to achieve a greater effect than any of the single agents alone. This is particularly prominent in the field of anesthesia and pain management – where atypical agents such as  antiepileptics ,  antidepressants ,  muscle relaxants ,  NMDA antagonists , and other medications are combined with more typical analgesics such as  opioids ,  prostaglandin  inhibitors,  NSAIDS  and others. This practice of pain management  drug synergy [ 25 ]  is known as an  analgesia sparing  effect.


People who are at greatest risk for negative polypharmacy consequences include  elderly  people, people with  psychiatric  conditions, patients with intellectual or developmental disabilities, [ 28 ]  people taking five or more drugs at the same time, those with multiple  physicians  and  pharmacies , people who have been recently hospitalized, people who have concurrent  comorbidities , [ 29 ]  people who live in rural communities, people with inadequate access to education, [ 30 ]  and those with impaired vision or dexterity. Marginalized populations may have a greater degrees of polypharmacy, which can occur more frequently in younger age groups. [ 31 ]


It is not uncommon for people who are dependent or addicted to substances to enter or remain in a state of polypharmacy misuse. [ 32 ]  About 84% of prescription drug misusers reported using multiple drugs. [ 32 ]  Note, however, that the term  polypharmacy  and its variants generally refer to legal drug use as-prescribed, even when used in a negative or critical context.


Measures can be taken to limit polypharmacy to its truly legitimate and appropriate needs. This is an emerging area of research, frequently called  deprescribing . [ 33 ]  Reducing the number of medications, as part of a clinical review, can be an effective healthcare intervention. [ 34 ]  Clinical pharmacists can perform drug therapy reviews and teach physicians and their patients about drug safety and polypharmacy, as well as collaborating with physicians and patients to correct polypharmacy problems. Similar programs are likely to reduce the potentially deleterious consequences of polypharmacy such as adverse drug events, non-adherence, hospital admissions, drug-drug interactions, geriatric syndromes, and mortality. [ 35 ]  Such programs hinge upon patients and doctors informing pharmacists of other medications being prescribed, as well as herbal, over-the-counter substances and supplements that occasionally interfere with prescription-only medication. Staff at residential aged care facilities have a range of views and attitudes towards polypharmacy that, in some cases, may contribute to an increase in medication use. [ 36 ]


The risk of polypharmacy increases with age, although there is some evidence that it may decrease slightly after age 90 years. [ 2 ]  Poorer health is a strong predictor of polypharmacy at any age, although it is unclear whether the polypharmacy causes the poorer health or if polypharmacy is used because of the poorer health. [ 2 ]  It appears possible that the risk factors for polypharmacy may be different for younger and middle-aged people compared to older people. [ 2 ]


The use of polypharmacy is correlated to the use of potentially inappropriate medications. Potentially inappropriate medications are generally taken to mean those that have been agreed upon by expert consensus, such as by the  Beers Criteria . These medications are generally inappropriate for older adults because the risks outweigh the benefits. [ 37 ]  Examples of these include urinary  anticholinergics  used to treat  incontinence ; the associated risks, with anticholinergics, include constipation, blurred vision, dry mouth, impaired cognition, and falls. [ 38 ]  Many older people living in long term care facilities experience polypharmacy, and under-prescribing of potentially indicated medicines and use of high risk medicines can also occur. [ 37 ]  Medicine use rises from 6.0 ± 3.8 regular medicines on average when people enter long term care to 8.9 ± 4.1 regular medicines after two years. [ 39 ]


Polypharmacy is associated with an increased risk of falls in elderly people. [ 40 ] [ 41 ]  Certain medications are well known to be associated with the risk of falls, including cardiovascular and  psychoactive medications . [ 42 ] [ 43 ]  There is some evidence that the risk of falls increases cumulatively with the number of medications. [ 44 ] [ 45 ]  Although often not practical to achieve, withdrawing all medicines associated with falls risk can halve an individual's risk of future falls.


Every medication has potential adverse side-effects. With every drug added, there is an additive risk of side-effects. Also, some medications have  interactions  with other substances, including foods, other medications, and herbal supplements. [ 46 ]  15% of older adults are potentially at risk for a major drug-drug interaction. [ 47 ]  Older adults are at a higher risk for a drug-drug interaction due to the increased number of medications prescribed and  metabolic  changes that occur with aging. [ 48 ]  When a new drug is prescribed, the risk of interactions increases exponentially. Doctors and  pharmacists  aim to avoid prescribing medications that interact; often, adjustments in the dose of medications need to be made to avoid interactions. For example,  warfarin  interacts with many medications and supplements that can cause it to lose its effect. [ 48 ] [ 49 ]


Pill burden is the number of pills (tablets or capsules, the most common dosage forms) that a person takes on a regular basis, along with all associated efforts that increase with that number - like storing, organizing, consuming, and understanding the various medications in one's regimen. The use of individual medications is growing faster than pill burden. [ 50 ]  A recent study found that older adults in long term care are taking an average of 14 to 15 tablets every day. [ 51 ]


Poor medical adherence is a common challenge among individuals who have increased pill burden and are subject to polypharmacy. [ 52 ]  It also increases the possibility of adverse medication reactions ( side effects ) and  drug-drug interactions . High pill burden has also been associated with an increased risk of hospitalization, medication errors, and increased costs for both the pharmaceuticals themselves and for the treatment of adverse events. Finally, pill burden is a source of dissatisfaction for many patients and family carers. [ 21 ]


High pill burden was commonly associated with  antiretroviral drug  regimens to control  HIV , [ 53 ]  and is also seen in other patient populations. [ 52 ]  For instance, adults with multiple common chronic conditions such as  diabetes ,  hypertension ,  lymphedema ,  hypercholesterolemia ,  osteoporosis ,  constipation ,  inflammatory bowel disease , and  clinical depression  may be prescribed more than a dozen different medications daily. [ 54 ]  The combination of multiple drugs has been associated with an increased risk of adverse drug events. [ 55 ]


Reducing pill burden is recognized as a way to improve medication  compliance , also referred to as adherence. This is done through " deprescribing ", where the risks and benefits are weighed when considering whether to continue a medication. [ 56 ]  This includes drugs such as  bisphosphonates  (for  osteoporosis ), which are often taken indefinitely although there is only evidence to use it for five to ten years. [ 56 ]  Patient educational programs, reminder messages, medication packaging, and the use of memory tricks has also been seen to improve adherence and reduce pill burden in several countries. [ 48 ]  These include associating medications with mealtimes, recording the dosage on the box, storing the medication in a special place, leaving it in plain sight in the living room, or putting the prescription sheet on the refrigerator. [ 48 ]  The development of applications has also shown some benefit in this regard. [ 48 ]  The use of a  polypill  regimen, such as combination pill for HIV treatment, as opposed to a multi-pill regimen, also alleviates pill burden and increases adherence. [ 52 ]


The selection of long-acting active ingredients over short-acting ones may also reduce pill burden. For instance,  ACE inhibitors  are used in the management of  hypertension . [ medical citation needed ]  Both  captopril  and  lisinopril  are examples of ACE inhibitors. However, lisinopril is dosed once a day, whereas captopril may be dosed 2-3 times a day. Assuming that there are no contraindications or potential for drug interactions, using lisinopril instead of captopril may be an appropriate way to limit pill burden. [ medical citation needed ]


The most common intervention to help people who are struggling with polypharmacy is  deprescribing . [ 57 ]  Deprescribing can be confused with medication simplification, which does not attempt to reduce the number of medicines but rather reduce the number of dose forms and administration times. [ 58 ]  Deprescribing refers to reducing the number of medications that a person is prescribed and includes the identification and discontinuance of medications when the benefit no longer outweighs the harm. [ 59 ]  In elderly patients, this can commonly be done as a patient becomes more frail and treatment focus needs to shift from  preventative  to  palliative . [ 59 ]  Deprescribing is feasible and effective in many settings including residential care, communities and hospitals. [ 57 ]  This preventative measure should be considered for anyone who exhibits one of the following: (1) a new symptom or adverse event arises, (2) when the person develops an end-stage disease, (3) if the combination of drugs is risky, or (4) if stopping the drug does not alter the disease trajectory. [ 9 ]


Several tools exist to help physicians decide when to deprescribe and what medications can be added to a  pharmaceutical  regimen. The  Beers Criteria  and the STOPP/START criteria help identify medications that have the highest risk of  adverse drug events  (ADE) and  drug-drug interactions . [ 60 ] [ 61 ] [ 62 ]  The  Medication appropriateness tool for comorbid health conditions during dementia  (MATCH-D) is the only tool available specifically for people with dementia, and also cautions against polypharmacy and complex medication regimens. [ 63 ] [ 64 ]


Barriers faced by both physicians and people taking the medications have made it challenging to apply deprescribing strategies in practice. [ 65 ]  For physicians, these include fear of consequences of deprescribing, the prescriber's own confidence in their skills and knowledge to deprescribe, reluctance to alter medications that are prescribed by specialists, the feasibility of deprescribing, lack of access to all of patients' clinical notes, and the complexity of having multiple providers. [ 65 ] [ 66 ] [ 67 ]  For patients who are prescribed or require the medication, barriers include attitudes or beliefs about the medications, inability to communicate with physicians, fears and uncertainties surrounding deprescribing, and influence of physicians, family, and the media. [ 65 ]  Barriers can include other health professionals or carers, such as in residential care, believing that the medicines are required. [ 68 ]


In people with multiple long-term conditions (multimorbidity) and polypharmacy deprescribing represents a complex challenge as clinical guidelines are usually developed for single conditions. In these cases tools and guidelines like the Beers Criteria and STOPP/START could be used safely by clinicians but not all patients might benefit from stopping their medication. There is a need for clarity about how much clinicians can do beyond the guidelines and the responsibility they need to take could help them prescribing and deprescribing for complex cases. Further factors that can help clinicians tailor their decisions to the individual are: access to detailed data on the people in their care (including their backgrounds and personal medical goals), discussing plans to stop a medicine already when it is first prescribed, and a good relationship that involves mutual trust and regular discussions on progress. Furthermore, longer appointments for prescribing and deprescribing would allow time explain the process of deprescribing, explore related concerns, and support making the right decisions. [ 69 ] [ 70 ]


The effectiveness of specific interventions to improve the appropriate use of polypharmacy such as  pharmaceutical care  and computerised decision support is unclear. [ 9 ]  This is due to low quality of current evidence surrounding these interventions. [ 9 ]  High quality evidence is needed to make any conclusions about the effects of such interventions in any environment, including in care homes. [ 71 ]  Deprescribing is not influenced by whether medicines are prescribed through a paper-based or an electronic system. [ 72 ]  Deprescribing rounds has been proposed as a potentially successful methodology in reducing polypharmacy. [ 73 ]  Sharing of positive outcomes from physicians who have implemented deprescribing, increased communication between all practitioners involved in patient care, higher compensation for time spent deprescribing, and clear deprescribing guidelines can help enable the practice of deprescribing. [ 67 ]  Despite the difficulties, a recent blinded study of deprescribing reported that participants used an average of two fewer medicines each after 12 months showing again that deprescribing is feasible. [ 74 ]


PottersWheel  is a  MATLAB  toolbox for mathematical modeling of time-dependent  dynamical systems  that can be expressed as  chemical reaction networks  or  ordinary differential equations  (ODEs). [ 1 ]  It allows the automatic calibration of model parameters by fitting the model to experimental measurements. CPU-intensive functions are written or – in case of model dependent functions – dynamically generated in C. Modeling can be done interactively using graphical user interfaces or based on MATLAB scripts using the PottersWheel function library. The software is intended to support the work of a mathematical modeler as a real  potter's wheel  eases the modeling of pottery.


The basic use of PottersWheel covers seven phases from model creation to the prediction of new
experiments.


The dynamical system is formalized into a set of reactions or differential equations using a visual model designer or a text editor. The model is stored as a MATLAB *.m ASCII file. Modifications can therefore be tracked using a version control system like  subversion  or  git . Model import and export is supported for  SBML . Custom import-templates may be used to import custom model structures.  Rule-based modeling  is also supported, where a pattern represents a set of automatically generated reactions.


Example for a simple model definition file for a reaction network A → B → C → A with observed species A and C: