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Kinetic analysis of sequential multistep reactions.

ABSTRACT: Many processes in biology and chemistry involve multistep reactions or transitions. The kinetic data associated with these reactions are manifested by superpositions of exponential decays that are often difficult to dissect. Two major challenges have hampered the kinetic analysis of multistep chemical reactions: (1) reliable and unbiased determination of the number of reaction steps, and (2) stable reconstruction of the distribution of kinetic rate constants. Here, we introduce two numerically stable integral transformations to solve these two challenges. The first transformation enables us to deduce the number of rate-limiting steps from kinetic measurements, even when each step has arbitrarily distributed rate constants. The second transformation allows us to reconstruct the distribution of rate constants in the multistep reaction using the phase function approach, without fitting the data. We demonstrate the stability of the two integral transformations by both analytic proofs and numerical tests. These new methods will help provide robust and unbiased kinetic analysis for many complex chemical and biochemical reactions.

SUBMITTER: Zhou Y

PROVIDER: S-EPMC2646179 | biostudies-literature | 2007 Dec

REPOSITORIES: biostudies-literature

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Kinetic analysis of sequential multistep reactions.

Zhou Yajun Y Zhuang Xiaowei X

The journal of physical chemistry. B 20071110 48

Many processes in biology and chemistry involve multistep reactions or transitions. The kinetic data associated with these reactions are manifested by superpositions of exponential decays that are often difficult to dissect. Two major challenges have hampered the kinetic analysis of multistep chemical reactions: (1) reliable and unbiased determination of the number of reaction steps, and (2) stable reconstruction of the distribution of kinetic rate constants. Here, we introduce two numerically s ...[more]

PMID: 17994718

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Project description:We induce and study reactions of polyoxometalate (POM) molecules, [PW12O40]3- (Keggin) and [P2W18O62]6- (Wells-Dawson), at the single-molecule level. Several identical carbon nanotubes aligned side by side within a bundle provided a platform for spatiotemporally resolved imaging of ca. 100 molecules encapsulated within the nanotubes by transmission electron microscopy (TEM). Due to the entrapment of POM molecules their proximity to one another is effectively controlled, limiting molecular motion in two dimensions but leaving the third dimension available for intermolecular reactions between pairs of neighbouring molecules. By coupling the information gained from high resolution structural and kinetics experiments via the variation of key imaging parameters in the TEM, we shed light on the reaction mechanism. The dissociation of W-O bonds, a key initial step of POM reactions, is revealed to be reversible by the kinetic analysis, followed by an irreversible bonding of POM molecules to their nearest neighbours, leading to a continuous tungsten oxide nanowire, which subsequently transforms into amorphous tungsten-rich clusters due to progressive loss of oxygen atoms. The overall intermolecular reaction can therefore be described as a step-wise reductive polycondensation of POM molecules, via an intermediate state of an oxide nanowire. Kinetic analysis enabled by controlled variation of the electron flux in TEM revealed the reaction to be highly flux-dependent, which leads to reaction rates too fast to follow under the standard TEM imaging conditions. Although this presents a challenge for traditional structural characterisation of POM molecules, we harness this effect by controlling the conditions around the molecules and tuning the imaging parameters in TEM, which combined with theoretical modelling and image simulation, can shed light on the atomistic mechanisms of the reactions of POMs. This approach, based on the direct space and real time chemical reaction analysis by TEM, adds a new method to the arsenal of single-molecule kinetics techniques.

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Kinetic analysis of sequential multistep reactions.

Publications

Kinetic analysis of sequential multistep reactions.

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