Mathematical modelling of the impact of non-steroidal anti-inflammatory drugs on aspirin intolerance in asthma

Pri približno 10−20 % astmatičnih bolnikov se po zaužitju aspirina, ibuprofena ali katerega drugega nesteroidnega antirevmatika (NSAR) razvije bronhokonstrikcija, vnetje sluznic nosu, žrela in vnetje oči ter izpuščaji na koži. Ta pojav imenujemo aspirinska intoleranca. Raziskave kažejo, da so pri aspirinsko-intolerantnih astmatikih v primerjavi z aspirinsko-tolerantnimi astmatiki in neastmatiki bistveno spremenjene genske ekspresije encimov prostaglandin H sintaz 1 in 2 (PGHS1 in PGHS2) ter levkotrien C4 sintaze (LTC4S) pri presnovi arahidonske kisline (AA) v belih krvnih celicah. Ključnega pomena pri razvoju bronhokonstrikcije in drugih simptomov aspirinske intolerance sta produkta presnove AA: vnetni mediator levkotrien C4 (LTC4) in protivnetni prostaglandin E2 (PGE2). NSAR inhibirajo PGHS1 in PGHS2, kar zniža koncentracijo PGE2 in poviša koncentracijo LTC4 v celicah. V doktorskem delu izdelamo matematični model, ki omogoča študij vpliva NSAR na pojav aspirinske intolerance. Osredotočimo se na modeliranje ciklooksigenazne in lipoksigenazne poti presnove AA, pri čemer upoštevamo tudi inhibitorni učinek NSAR na encima PGHS1 in PGHS2. Časovni potek koncentracije NSAR v krvni plazmi po zaužitju zdravila pa opišemo s standardnim farmakokinetičnim modelom, v katerem upoštevamo fazo absorpcije zdravila v krvno plazmo in eliminacije iz krvne plazme. Razmerje med koncentracijama PGE2 in LTC4 uporabimo kot osrednji kriterij za napoved bronhokonstrikcije, pri čemer je tveganje za pojav bronhokonstrikcije večje, kadar je razmerje med koncentracijama PGE2 in LTC4 manjše od ena. Z modelom preučujemo pojav aspirinske intolerance na treh različnih ravnehnajprej na ravni ekspresij encimov PGHS1, PGHS2 in LTC4S, nato na ravni produkcije ključnih metabolitov PGE2 in LTC4 v celici in nato še na ravni organov, kjer preučujemo, kako je pojav bronhokonstrikcije odvisen od doze različnih NSAR. Izvedemo simulacije, v katerih napovemo časovne poteke koncentracij PGE2 in LTC4 v odvisnosti od različnih ekspresij encimov PGHS1, PGHS2 in LTC4S pri neastmatikih, aspirinsko-tolerantnih astmatikih in treh različnih populacijah aspirinsko-intolerantnih astmatikov. Simulacije izvedemo brez ali ob prisotnosti NSAR. Pokažemo, da je pojav bronhokonstrikcije odvisen od doze uporabljenega NSAR. Za aspirin, ibuprofen in celecoxib ocenimo mejne doze, pri katerih je povišano tveganje za pojav bronhokonstrikcije. Napovemo, koliko časa po zaužitju NSAR se pojavi bronhokonstrikcija in koliko časa traja. Študiramo tudi strategijo, ki bi aspirinsko-intolerantnim astmatikom omogočila varno doziranje NSAR, brez tveganja bronhokonstrikcije. Predlagamo strategijo, pri kateri bi v kombinaciji z NSAR dozirali učinkovini, ki delujeta kot inhibitorja encima 5-lipoksigenaze (5-LOX): sintetični analog PGE2 − nocloprost in učinkovina ABT-761. Rezultati kažejo, da bi spremenjeni ekspresiji PGHS1 in LTC4S utegnili biti osrednja vzroka, ki po zaužitju NSAR vodita do bronhokonstrikcije, znižana ekspresija PGHS2 pa najverjetneje vodi do drugih simptomov aspirinske intolerance. Napovedane mejne doze za aspirin in celecoxib so primerljive z eksperimentalno določenimi, o katerih poročajo v literaturi, za ibuprofen pa so nekoliko nižje. Z modelom napovedana časa od zaužitja NSAR do pojava bronhokonstrikcije in časovni interval trajanja bronhokonstrikcije sta enakega velikostnega reda, kot poročajo v literaturi. Podrobna analiza strategije doziranja NSAR z inhibitorjema 5-LOX kaže, da je nocloprost v kombinaciji z aspirinom potrebno dozirati le enkrat, v kombinaciji z ibuprofenom pa večkrat zaporedoma v različnih dozah, pri čemer so čas doziranja, doza in število doz nocloprosta odvisni od doze ibuprofena. Strategija se bistveno poenostavi, kadar namesto nocloprosta uporabimo ABT-761, ki je močan inhibitor 5-LOX s počasno fazo eliminacije iz krvne plazme.In around 10-20 % of asthmatic patients ingestion of aspirin, ibuprofen and other non-steroidal anti-inflammatory drugs (NSAIDs) induces bronchoconstriction, inflammation of upper airways and skin rash. This phenomenon is called aspirin intolerance. Clinical data show that altered expressions of enzymes prostaglandin H synthases 1 and 2 (PGHS1 and PGHS2) and leukotriene C4 synthase (LTC4S) in arachidonic acid (AA) metabolism could be of central importance for occurrence of aspirin intolerance. The main role is attributed to AA metabolites: inflammatory mediator leukotriene C4 (LTC4) and anti-inflammatory prostaglandin E2 (PGE2). NSAIDs inhibit the enzymes PGHS1 and PGHS2 thus increase LTC4 production and decrease PGE2 production. In this work, a mathematical model is elaborated that enables the study of the impact of different NSAIDs on the occurrence of aspirin intolerance. Mathematical model of lipoxygenase and cyclooxygenase pathway in AA metabolism is developed in which inhibitory effect of NSAID on the enzymes PGHS1 and PGHS2 is taken into account. The time course of NSAID plasma concentration is described by the standard pharmacokinetic model with absorption and elimination phases. The ratio between PGE2 and LTC4 concentrations is used as the central criterion in predictions of bronchoconstriction. The risk of bronchoconstriction is increased when the ratio between PGE2 and LTC4 concentrations is lower than 1. The occurrence of aspirin intolerance is studied on three different levels: on the level of enzymes PGHS1, PGHS2 and LTC4S expressions, on the level of PGE2 and LTC4 production in the cell and on the tissue or organ level, where the occurrence of bronchoconstriction is studied in dependence on different NSAIDs and their doses. We show that the risk of bronchoconstriction depends on the type of NSAID as well as on its dose. The limiting doses of aspirin, ibuprofen and celecoxib that may induce bronchoconstriction are calculated for different populations of aspirin-intolerant asthmatics. Further, we theoretically estimate the time between NSAID dosing and bronchoconstriction as well as duration of bronchoconstriction. We propose the strategy, which could enable safe managing of NSAIDs to aspirin-intolerant patients. The strategy is proposed in which different 5-LOX inhibitors, such as synthetic PGE2 analogue – nocloprost or ABT-761, are used in combination with NSAIDs in order to avoid bronchoconstriction. Our results identify altered expression of PGHS1 and LTC4S as the key elements of aspirin intolerance that lead to bronchoconstriction. Decreased expression of PGHS2 may lead to other symptoms of aspirin intolerance. Predicted limiting doses for aspirin and celecoxib are in the same range as measured threshold doses reported in literature. For ibuprofen, limiting doses are lower than measured threshold doses. Theoretically estimated time between NSAID dosing and bronchoconstriction, as well as the estimated duration of bronchoconstriction for different populations of aspirin-intolerant patients, are in the same order of magnitude as those observed in clinical studies. When nocloprost is used in combination with aspirin only one dose of nocloprost is needed to avoid bronconstriction. In case of ibuprofen, several consecutive doses of nocloprost should be applied. This strategy is remarkably simplified when instead of nocloprost, ABT-761 is used in combination with NSAID

Self-organization of enzyme-catalyzed reactions studied by the maximum entropy production principle

The self-organization of open reaction systems is closely related to specific mechanisms that allow the export of internally generated entropy from systems to their environment. According to the second law of thermodynamics, systems with effective entropy export to the environment are better internally organized. Therefore, they are in thermodynamic states with low entropy. In this context, we study how self-organization in enzymatic reactions depends on their kinetic reaction mechanisms. Enzymatic reactions in an open system are considered to operate in a non-equilibrium steady state, which is achieved by satisfying the principle of maximum entropy production (MEPP). The latter is a general theoretical framework for our theoretical analysis. Detailed theoretical studies and comparisons of the linear irreversible kinetic schemes of an enzyme reaction in two and three states are performed. In both cases, in the optimal and statistically most probable thermodynamic steady state, a diffusion-limited flux is predicted by MEPP. Several thermodynamic quantities and enzymatic kinetic parameters, such as the entropy production rate, the Shannon information entropy, reaction stability, sensitivity, and specificity constants, are predicted. Our results show that the optimal enzyme performance may strongly depend on the number of reaction steps when linear reaction mechanisms are considered. Simple reaction mechanisms with a smaller number of intermediate reaction steps could be better organized internally and could allow fast and stable catalysis. These could be features of the evolutionary mechanisms of highly specialized enzymes

On the Problem of Formulating Principles in Nonequilibrium Thermodynamics

In this work, we consider the choice of a system suitable for the formulation of principles in nonequilibrium thermodynamics. It is argued that an isolated system is a much better candidate than a system in contact with a bath. In other words, relaxation processes rather than stationary processes are more appropriate for the formulation of principles in nonequilibrium thermodynamics. Arguing that slow varying relaxation can be described with quasi-stationary process, it is shown for two special cases, linear nonequilibrium thermodynamics and linearized Boltzmann equation, that solutions of these problems are in accordance with the maximum entropy production principle

On the Problem of Formulating Principles in Nonequilibrium Thermodynamics

In this work, we consider the choice of a system suitable for the formulation of principles in nonequilibrium thermodynamics. It is argued that an isolated system is a much better candidate than a system in contact with a bath. In other words, relaxation processes rather than stationary processes are more appropriate for the formulation of principles in nonequilibrium thermodynamics. Arguing that slow varying relaxation can be described with quasi-stationary process, it is shown for two special cases, linear nonequilibrium thermodynamics and linearized Boltzmann equation, that solutions of these problems are in accordance with the maximum entropy production principle