2008
DOI: 10.1007/s11538-008-9307-4
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Mean Lifetime and First-Passage Time of the Enzyme Species Involved in an Enzyme Reaction. Application to Unstable Enzyme Systems

Abstract: Taking as starting point the complete analysis of mean residence times in linear compartmental systems performed by Garcia-Meseguer et al. (Bull. Math. Biol. 65:279-308, 2003) as well as the fact that enzyme systems, in which the interconversions between the different enzyme species involved are of first or pseudofirst order, act as linear compartmental systems, we hereby carry out a complete analysis of the mean lifetime that the enzyme molecules spend as part of the enzyme species, forms, or groups involved … Show more

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Cited by 5 publications
(4 citation statements)
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“…Finding the very first such time, τ ¼ infft j W ðtÞ ¼ 1g; known as the "first passage" of the process through the boundary B = 1, is easier said than done, one of those classical problems whose concise statements conceal their difficulty (1-4). For general fluctuating random processes, the first-passage time problem is both extremely difficult (5-9) and highly relevant, due to its manifold practical applications: it models phenomena as diverse as the onset of chemical reactions (10)(11)(12)(13)(14), transitions of macromolecular assemblies (15)(16)(17)(18)(19), time-to-failure of a device (20)(21)(22), accumulation of evidence in neural decision-making circuits (23), the "gambler's ruin" problem in game theory (24), species extinction probabilities in ecology (25), survival probabilities of patients and disease progression (26)(27)(28), triggering of orders in the stock market (29)(30)(31), and firing of neural action potentials (32)(33)(34)(35)(36)(37).…”
mentioning
confidence: 99%
“…Finding the very first such time, τ ¼ infft j W ðtÞ ¼ 1g; known as the "first passage" of the process through the boundary B = 1, is easier said than done, one of those classical problems whose concise statements conceal their difficulty (1-4). For general fluctuating random processes, the first-passage time problem is both extremely difficult (5-9) and highly relevant, due to its manifold practical applications: it models phenomena as diverse as the onset of chemical reactions (10)(11)(12)(13)(14), transitions of macromolecular assemblies (15)(16)(17)(18)(19), time-to-failure of a device (20)(21)(22), accumulation of evidence in neural decision-making circuits (23), the "gambler's ruin" problem in game theory (24), species extinction probabilities in ecology (25), survival probabilities of patients and disease progression (26)(27)(28), triggering of orders in the stock market (29)(30)(31), and firing of neural action potentials (32)(33)(34)(35)(36)(37).…”
mentioning
confidence: 99%
“…When more than one zero input are made simultaneously in different compartments, for example, $x_{m_1 }^0, \, x_{m_2 }^0, \cdots x_{m_w }^0 $ in the corresponding compartments $X_{m_1 }, \, X_{m_2 }, \cdots, X_{m_w } $ , then the MRT, $r_{i,m_1, m_2, \cdots,m_w } $ in any compartment, X i , as well as in the entire system under study, $r_{m_1, m_2, \cdots, m_w } $ , are given by eqs. (1) and (2), respectively, according to Arribas et al,50 after adaptation of the notation: …”
Section: Resultsmentioning
confidence: 99%
“…Several contributions on MRT in general or specific compartmental systems refer to different fields. Thus, in enzyme kinetics of unstable enzymes, the MRT of an enzyme form means the mean time that this form remains active 38, 50–52. Pharmacokinetic residence time theory is the basis of our knowledge of how drugs are distributed in the plasma and in the different organs 35, 53–55.…”
Section: Introductionmentioning
confidence: 99%
“…The earliest approaches to FPT processes by Schrödinger [4] and von Smoluchowski [5] considered a free particle with Brownian dynamics diffusing in a medium of high viscosity. Since then, the interest on this topic has increased considerably and, in particular, has experienced a surge of renewed attention in the last two decades, including studies on both Markovian and non-Markovian processes in areas as diverse as physics and astrophysics , mathematics and statistics [40][41][42][43][44][45][46][47][48][49][50], biology and neuroscience [51][52][53][54][55][56][57][58][59][60][61][62], chemistry [63][64][65][66][67][68][69], and finance [70][71][72]. In fact, applications of the FPT problem are widely found in problems ranging from the exciton trapping in photosynthesis processes [51] to neural coding [61], mean lifetimes in chemical reactions [68] and the optimal time to sell an asset in finance [72], to name a few.…”
Section: Introductionmentioning
confidence: 99%