Memory effects and oscillations in single-molecule kinetics

Vlad, Marcel Ovidiu; Morán, Federico; Schneider, F. W.; Ross, John

doi:10.1073/pnas.192439099

Cited by 26 publications

(35 citation statements)

References 12 publications

(8 reference statements)

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“…Analytical results were obtained by further assuming a separation condition; that is, each transition rate was factorized into a universal component that depended on the control variables and was the same for all transitions and a process-dependent factor that depends on the initial and final state of the transition but not the time. Vlad and Ross 41 explicitly showed that quasi-periodic behavior can be obtained in the fluorescence intensity correlation function for an example similar to our model; the intramolecular fluctuations obey damped oscillatory dynamics (modes with complex eigenvalues) with characteristic time scales comparable to or longer than those of the transitions between observed states. However, that model 41 predicts damped quasi-periodic behavior in the correlation function even at equilibrium, which was not observed in our experiments.…”

Section: Discussionsupporting

confidence: 75%

“…This feature cannot be described without resolving the intrabasin dynamics, and we thus expect other approaches based on only relaxation between discrete states 42 to fail similarly. Vlad and Ross suggest that the apparent violations in detailed balance needed to support oscillations in (cyclic) discrete kinetic schemes can be obtained if they arise from integration over intrastate fluctuations of a more complicated model, 41 but it is not clear what are the specific requirements on the original dynamics for this to be the case or whether typical data would be sufficient to constrain such a model.…”

Section: Discussionmentioning

confidence: 99%

“…Recent work on generating function approaches for systems with time-dependent Hamiltonians could be useful in this regard. 44 The models considered here and in ref 43 can be viewed as explicit realizations of the general scheme outlined in ref 41, which relates the observed statistics (specifically, the fluorescence intensity correlation function) to intramolecular fluctuations by assuming temporally inhomogeneous dynamics. The transition rates between chemical states are random functions of time, and their stochastic properties depend on a set of control variables that represent the fluctuations in the system configuration and, in turn, energy.…”

Section: Discussionmentioning

confidence: 99%

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Models of Single-Molecule Experiments with Periodic Perturbations Reveal Hidden Dynamics in RNA Folding

Liu

et al. 2009

J. Phys. Chem. B

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Traditionally, microscopic fluctuations of molecules have been probed by measuring responses of an ensemble to perturbations. Now, single-molecule experiments are capable of following fluctuations without introducing perturbations. However, dynamics not readily sampled at equilibrium should be accessible to nonequilibrium single-molecule measurements. In a recent study [Qu, X. et al. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 6602-6607], the efficiency of fluorescence resonance energy transfer (FRET) between probes on the L18 loop and 3′ terminus of the 260 nucleotide RNase P RNA from Bacillus stearothermophilus was found to exhibit complex kinetics that depended on the (periodically alternating) concentration of magnesium ions ([Mg 2+ ]) in solution. Specifically, this time series was found to exhibit a quasi-periodic response to a squarewave pattern of [Mg 2+ ] changes. Because these experiments directly probe only one of the many degrees of freedom in the macromolecule, models are needed to interpret these data. We find that Hidden Markov Models are inadequate for describing the nonequilibrium dynamics, but they serve as starting points for the construction of models in which a discrete observable degree of freedom is coupled to a continuously evolving (hidden) variable. Consideration of several models of this general form indicates that the quasi-periodic response in the nonequilibrium experiments results from the switching (back and forth) in positions of the minima of the effective potential for the hidden variable. This switching drives oscillation of that variable and synchronizes the population to the changing [Mg 2+ ]. We set the models in the context of earlier theoretical and experimental studies and conclude that single-molecule experiments with periodic peturbations can indeed yield qualitatively new information beyond that obtained at equilibrium.

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Section: Discussionsupporting

confidence: 75%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Models of Single-Molecule Experiments with Periodic Perturbations Reveal Hidden Dynamics in RNA Folding

Liu

et al. 2009

J. Phys. Chem. B

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“…A theory with a sequence of functional nonequilibrium states could well describe experimental data on optical synchronization of turnover cycles in the photosensitive cytochrome P-450-dependent monooxygenase system (29) and similar models were evoked to describe statistics of nonequilibrium conformational changes in T4 lysozyme molecules (13). An analytical study of a model with nonequilibrium cyclic transitions between many intermediate states has been performed (8).…”

Section: Models Of Single-enzyme Dynamicsmentioning

confidence: 99%

Functional conformational motions in the turnover cycle of cholesterol oxidase

Lerch

Rigler

Mikhailov

2005

Proc. Natl. Acad. Sci. U.S.A.

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Reexamining experimental data of single-molecule fluorescence correlation spectroscopy for cholesterol oxidase, we find that the existing Michaelis-Menten models with dynamical disorder cannot explain strong correlations between subsequent turnover cycles revealed in the diagonal feature in the joint statistical distribution of adjacent ''on'' times of this enzyme. We suggest that functional conformational motions representing ordered sequences of transitions between a set of conformational substates are involved, along with equilibrium conformational fluctuations in the turnover cycle of cholesterol oxidase. A two-channel model of singleenzyme dynamics, including a slow functional conformational motion in one of the channels, is proposed that allows us to reproduce such strong correlations. Functionally important conformational motions are nonequilibrium processes that lead from one state of a protein to another and follow binding or dissociation of a ligand (1, 2). In enzymes, such ordered slow conformational motions can constitute an inherent part of a turnover cycle. Their functions may consist of transporting a substrate to the active center inside a macromolecule or bringing it into an appropriate arrangement with respect to this center. Generally, these are physical intramolecular motions that are needed for the occurrence of catalytic conversion and must precede it. Using time-resolved x-ray methods, functional conformational motions in Ha-ras p21 protein on GTP hydrolysis (3) and in a cytochrome P-450 enzyme (4) were recorded. In these experiments, enzyme molecules formed a crystal but could nonetheless perform their characteristic catalytic cycles. Today, many examples of ordered conformational motions in proteins, resolved by x-ray crystallography methods, are known (5-7) (see also the database at http:͞͞molmovdb.mbb.yale.edu͞molmovdb). Thermal conformational fluctuations for single macromolecules in solution were observed by using fluorescence correlation spectroscopy (FCS) (9, 10) and FRET methods (11). Conformational movements of enzymes in aqueous solvents could also be detected by NMR (12). Using FRET measurements, nonequilibrium conformational changes in single molecules of T4 lysozyme under reaction conditions were observed (13). Single-molecule FCS provides a powerful tool for monitoring chemical transitions during catalytic turnover cycles of individual molecules, and such experiments have been already performed for a number of enzymes, including cholesterol oxidase (14) and horseradish peroxidase (15,16). Simultaneous monitoring of chemical turnover cycles and physical processes of conformational changes was not, however, possible in the single-molecule experiments. Therefore, functional conformational motions during a turnover cycle for enzymic reactions in solution could not be identified. Nonetheless, the presence of such functional motions can be deduced by special statistical analysis of experimental data. In a previous publication, such statistical analysis, based on the memory functio...

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“…Such analysis indicated that widely distributed variation in enzymatic activity on a single-molecule scale appears because of alterations in molecular conformation arising due to thermodynamic fluctuations. This interpretation was later supported by theoretical analysis showing that intramolecular fluctuations appearing on a time scale shorter than the chemical reaction time scale may indeed result in rate coefficients that are different from average values observed for large number of molecules [94]. This means that HRP molecules exist in several thermodynamically slightly different conformations, and each conformation may show different enzymatic activity.…”

Section: Conformational Fluctuations Of Single Moleculesmentioning

confidence: 94%

Study of molecular events in cells by fluorescence correlation spectroscopy

Vukojević

Pramanik

Yakovleva

et al. 2005

CMLS, Cell. Mol. Life Sci.

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To understand processes in a living cell, sophisticated and creative approaches are required that can be used for gathering quantitative information about large number of components interacting across temporal and spatial scales without major disruption of the integral network of processes. A physical method of analysis that can meet these requirements is fluorescence correlation spectroscopy (FCS), which is an ultrasensitive and non-invasive detection method capable of single-molecule and real-time resolution. Since its introduction about 3 decades ago, this until recently emerging technology has reached maturity. As commercially built equipment is now available, FCS is extensively applied for extracting biological information from living cells unattainable by other methods, and new biological concepts are formulated based on findings by FCS. In this review, we focus on examples in the field of molecular cellular biology. The versatility of the technique in this field is illustrated in studies of single-molecule dynamics and conformational flexibility of proteins, and the relevance of conformational flexibility for biological functions regarding the multispecificity of antibodies, modulation of activity of C5a receptors in clathrin-mediated endocytosis and multiplicity of functional responses mediated by the p53 tumor suppressor protein; quantitative characterization of physicochemical properties of the cellular interior; protein trafficking; and ligand-receptor interactions. FCS can also be used to study cell-to-cell communication, here exemplified by clustering of apoptotic cells via bystander killing by hydrogen peroxide.

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Memory effects and oscillations in single-molecule kinetics

Cited by 26 publications

References 12 publications

Models of Single-Molecule Experiments with Periodic Perturbations Reveal Hidden Dynamics in RNA Folding

Models of Single-Molecule Experiments with Periodic Perturbations Reveal Hidden Dynamics in RNA Folding

Functional conformational motions in the turnover cycle of cholesterol oxidase

Study of molecular events in cells by fluorescence correlation spectroscopy

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