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Modelação matemática das espécies oxidantes e nitrosantes em sistemas biológicos
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Abstract(s)
As espécies reativas de oxigénio e azoto desempenham um papel importante em certas funções fisiológicas, como na inflamação, mas em situações de sobreprodução ou desregulação podem ter vários efeitos lesivos para as biomoléculas.
O objetivo foi construir um modelo matemático de equações diferenciais ordinárias (ODEs) que descrevesse a rede de reações químicas entre as diferentes espécies reativas e as biomoléculas. Para tal:
a) foram recolhidas da literatura e utilizadas as constantes cinéticas das várias reações para escrever as equações cinéticas de todas as reações que constituíram o sistema estudado;
b) com base nas várias equações cinéticas foram construídas as equações diferenciais que descreviam a evolução temporal de cada espécie química no sistema, recorrendo à abordagem do tipo Continuously Stirred Batch Reactor (CSBR);
c) otimizou-se os parâmetros do modelo de modo a obter um sistema em estado estacionário que mimetizou as condições observadas na circulação sistémica;
d) foi feita a análise do modelo com recurso à análise de fluxos e de coeficientes de controlo, que identificaram quais os principais pontos de controlo do sistema.
Com estes passos obteve-se um modelo matemático robusto que permitiu a simulação de situações fisiológicas como a desregulação dos sistemas de produção de espécies reativas ou o efeito de antioxidantes sobre o nível global de espécies reativas e sobre o nível de lesões induzidas às biomoléculas:
▪ As concentrações de estado estacionário das espécies tamponantes do sangue bem como da água, do hidrónio e do anião hidróxido mantiveram-se constantes em todas as variações;
▪ As variações do óxido nítrico e do superóxido ocorreram exatamente de acordo com o que se esperava;
▪ A variação da concentração do anião nitrato correspondeu à variação da concentração do peroxinitrito, indicando a composição do mesmo;
▪ Todas as espécies reativas tiveram a variação das suas concentrações como esperado em relação da variação das concentrações de estado estacionário dos antioxidantes.
Contudo, não foi possível obter um modelo que descreva adequadamente o sistema de tamponamento do sangue, tendo-se identificado a origem desse erro no excessivo detalhe utilizado para descrever essas reações.
Reactive oxygen and nitrogen species play an important role in certain physiological functions, such as in inflammation, but in situations of overproduction or deregulation, they may have several detrimental effects on biomolecules. The goal was to construct a mathematical model of ordinary differential equations (ODEs) that describes the network of chemical reactions between different reactive species and biomolecules. For such: a) they were collected from literature and kinetic constants of the various reactions were used to write the kinetic equations of all the reactions that constituted the studied system; b) based on the various kinetic equations the differential equations that described the temporal evolution of each chemical specie in the system were constructed, using the Continuously Stirred Batch Reactor (CSBR); c) the model parameters were optimized to obtain a steady-state system that mimicked the conditions observed in the systemic circulation; d) the analysis of the model using flow and control coefficients analysis was performed, which identified the main control points of the system. These steps yielded a robust mathematical model that allowed the simulation of physiological situations such as the deregulation of reactive species production systems or the effect of antioxidants on the global level of reactive species and on the level of biomolecule induced lesions: ▪ Steady-state concentrations of the buffering species in the blood as well as water, hydronium and hydroxide anion remained constant in all variations; ▪ Changes of nitric oxide and superoxide went exactly according to what was expected; ▪ The variation of the concentration of the nitrate anion corresponded to the variation of the peroxynitrite concentration, indicating its composition; ▪ All reactive species had the variation of their concentrations as expected in relation to the variation of the steady-state concentrations of the antioxidants. However, it was not possible to obtain a model that adequately describes the blood-buffering system, and the origin of this error was identified in the excessive detail used to describe these reactions.
Reactive oxygen and nitrogen species play an important role in certain physiological functions, such as in inflammation, but in situations of overproduction or deregulation, they may have several detrimental effects on biomolecules. The goal was to construct a mathematical model of ordinary differential equations (ODEs) that describes the network of chemical reactions between different reactive species and biomolecules. For such: a) they were collected from literature and kinetic constants of the various reactions were used to write the kinetic equations of all the reactions that constituted the studied system; b) based on the various kinetic equations the differential equations that described the temporal evolution of each chemical specie in the system were constructed, using the Continuously Stirred Batch Reactor (CSBR); c) the model parameters were optimized to obtain a steady-state system that mimicked the conditions observed in the systemic circulation; d) the analysis of the model using flow and control coefficients analysis was performed, which identified the main control points of the system. These steps yielded a robust mathematical model that allowed the simulation of physiological situations such as the deregulation of reactive species production systems or the effect of antioxidants on the global level of reactive species and on the level of biomolecule induced lesions: ▪ Steady-state concentrations of the buffering species in the blood as well as water, hydronium and hydroxide anion remained constant in all variations; ▪ Changes of nitric oxide and superoxide went exactly according to what was expected; ▪ The variation of the concentration of the nitrate anion corresponded to the variation of the peroxynitrite concentration, indicating its composition; ▪ All reactive species had the variation of their concentrations as expected in relation to the variation of the steady-state concentrations of the antioxidants. However, it was not possible to obtain a model that adequately describes the blood-buffering system, and the origin of this error was identified in the excessive detail used to describe these reactions.
Description
Keywords
Espécies reativas de oxigénio Espécies reativas de azoto Modelação matemática Análise de controlo Modelo de ação de massas Reactive oxygen species Reactive nitrogen species Mathematical modelling Control analysis Mass action law model