Alternative to the steady-state method: derivation of reaction rates from first-passage times and pathway probabilities.

Abstract

An alternative method for deriving rate equations in enzyme kinetics is presented. An enzyme is followed as it moves along the various pathways allowed by the reaction scheme. The times spent in various sections of the scheme and the pathway probabilities are computed, using simple rules. (5,6): If one starts with a population of A molecules and watches their evolution, one finds (i) that for any t(Ao --Ai) = 1/(k1+ k2 + . . . + kn). [2] It is independent of the state of arrival. Note also that p = kit. The general idea in the method I shall develop is to take one enzyme and follow its fate as it progresses along the reaction scheme. The time spent on a pathway is obtained by adding (with an adequate weighting) the relaxation times. The rate is obtained by computing, for various sections of the reaction scheme, (i) the probability that a molecule of product is formed, and (ii) the time spent by the enzyme in the considered section. Times and probabilities are then concatenated over larger and larger sections.

Kinetic modelling indicates that fast-translating codons can coordinate cotranslational protein folding by avoiding misfolded intermediates

“…To solve these reaction schemes analytically, we utilize Ninio's probabilistic approach 23 . Instead of calculating the concentration of a particular species as a function of time, as is traditionally performed in chemical kinetics modelling, in this approach one calculates the probability of taking a particular path along the reaction scheme.…”

“…Here we use a probabilistic approach to provide such analytical equations 13,23 . Within this approach, the probability of taking a particular path through a reaction scheme representing the cotranslational folding of a domain can be exactly computed.…”

Ribosome kinetics and aa-tRNA competition determine rate and fidelity of peptide synthesis

“…Ninio (1987) described an alternative approach to derive kinetic expressions for enzymatic reactions. The principal idea of the Ninio approach is to track a single enzyme/template complex over time and determine its average behavior.…”

A quantitative model of error accumulation during PCR amplification

“…The kinetic mechanisms and structure/function relationships of T7 DNA polymerase, KlenTaq DNA polymerase, and a Bacillus DNA polymerase which have been worked out in some detail (Johnson, 1993;Kiefer et al, 1998;Li and Waksman, 2001;Patel et al, 1991), suggested that all DNA polymerases have the same broadly conserved molecular properties and mechanisms, but that each polymerase also has unique features (Jager and Pata, 1999). Viljoen et al, (2005) and Griep et al, (2005) developed a macroscopic model of PCR kinetics which is based on the probabilistic kinetic approach described by Ninio (1987 …”