Information Bounds and Optimal Analysis of Dynamic Single Molecule Measurements

Watkins, Lucas P.; Yang, Haw

doi:10.1529/biophysj.103.037739

Cited by 112 publications

(178 citation statements)

References 61 publications

Supporting

Mentioning

175

Contrasting

Order By: Relevance

“…This report represents the application of several recent developments in fluorescence single-molecule techniques based on information theory that use the information carried by each detected photon in an unbiased way (31,32,45). Our data-driven approach allows us to quantitatively account for photon-detection statistics, follow the time-dependent FRET distance changes photon-by-photon with the best possible time and distance resolution, and to unambiguously recover the entire FRET distance distribution.…”

Section: Discussionmentioning

confidence: 99%

“…To minimize error and bias in calculating time-dependent donor-acceptor distances from single-molecule trajectories (see SI Materials and Methods), a change-point analysis (45) was applied to the data to determine the precise moment at which the dyes bleach. Distance vs. time data were extracted from trajectories using the maximumlikelihood analysis method (31). Data were then combined to form a probability distribution function using the Gaussian kernel method.…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Illuminating the mechanistic roles of enzyme conformational dynamics

Hanson

Duderstadt

Watkins

et al. 2007

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

Self Cite

276

430

View full text Add to dashboard Cite

Many enzymes mold their structures to enclose substrates in their active sites such that conformational remodeling may be required during each catalytic cycle. In adenylate kinase (AK), this involves a large-amplitude rearrangement of the enzyme's lid domain. Using our method of high-resolution single-molecule FRET, we directly followed AK's domain movements on its catalytic time scale. To quantitatively measure the enzyme's entire conformational distribution, we have applied maximum entropy-based methods to remove photon-counting noise from single-molecule data. This analysis shows unambiguously that AK is capable of dynamically sampling two distinct states, which correlate well with those observed by x-ray crystallography. Unexpectedly, the equilibrium favors the closed, active-site-forming configurations even in the absence of substrates. Our experiments further showed that interaction with substrates, rather than locking the enzyme into a compact state, restricts the spatial extent of conformational fluctuations and shifts the enzyme's conformational equilibrium toward the closed form by increasing the closing rate of the lid. Integrating these microscopic dynamics into macroscopic kinetics allows us to model lid opening-coupled product release as the enzyme's rate-limiting step.conformational equilibrium ͉ rate-limiting step ͉ single-molecule FRET ͉ adenylate kinase P roteins such as enzymes are flexible with a range of motions spanning from picoseconds for localized vibrations to seconds for concerted global conformational rearrangements (1). Despite their randomly fluctuating environment, in which stochastic collisions with solvent molecules drive changes in tertiary structure, enzymes have evolved to catalyze reactions efficiently and specifically. Indeed, conformational transitions have been postulated to play a central role in enzyme functions in a wide variety of ways, including direct contribution to catalysis (2), allosteric regulation (3), and large-scale conformational changes in response to ligand binding (4). Most of our current understanding of structural motions in solution comes from NMR experiments (5) as well as from molecular dynamics simulations (6), approaches that are best suited to study dynamics in the picoto millisecond time scales. Because catalysis in enzymes frequently occurs in the submillisecond to minute time regime, our current understanding of the relationship between enzyme function and conformational dynamics comes from NMR experiments involving relatively localized motions of active site forming loops on the submillisecond time scale (7-10). However, many enzymes contain active sites located in between domains in which large-amplitude, low-frequency domain motions are required to complete their Michaelis-Menten enzyme-substrate complexes. Even simple questions regarding these transitions remain generally unanswered: What is the number and range of conformational states accessible to enzymes during their catalytic cycle? How does the enzyme's conformation respond to interac...

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Illuminating the mechanistic roles of enzyme conformational dynamics

Hanson

Duderstadt

Watkins

et al. 2007

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

Self Cite

276

430

View full text Add to dashboard Cite

show abstract

“…This is therefore also the probability of observing a PR value equal to x = A/S for bursts of S photons (11) Limiting ourselves to rational values x, this can be rewritten (12) where we define χ N (t) as the characteristic function of natural numbers (13) The total probability to observe the PR value x requires summing eq 12 over all burst sizes S, weighted by their probability, given by the burst size distribution (14) where B is the total number of bursts in the BSD, and S min (respectively, S max ) the smallest (respectively, largest) burst size taken into consideration. Introducing the characteristic function of rational numbers in [0, 1] (15) one obtains (16) Using eq 10, we end up with our final prediction of the probability distribution of PR values (in the absence of background) (17) To obtain the predicted PRH, a natural way could be to compute the number of predicted occurrences of each PR value x by multiplying eq 17 by the total number of bursts B and histogram these values with the same bin numbers as the PRH. In practice, however, this means calculating eq 17 for each possible rational value x accessible from bursts in the BSD, which number is close to (we neglect that, as shown in Figure 2, identical values can be obtained for several different burst sizes) (18) Since the calculations in eq 17 involve S max − S min + 1 terms, each one requiring a test of rationality of xS and evaluation of a CPU intensive expression, this approach may take quite some time for BSD with very large bursts.…”

Section: Shot-noise Contribution To the Prhmentioning

confidence: 99%

Shot-Noise Limited Single-Molecule FRET Histograms: Comparison between Theory and Experiments

et al. 2006

View full text Add to dashboard Cite

We describe a simple approach and present a straightforward numerical algorithm to compute the best fit shot-noise limited proximity ratio histogram (PRH) in single-molecule fluorescence resonant energy transfer diffusion experiments. The key ingredient is the use of the experimental burst size distribution, as obtained after burst search through the photon data streams. We show how the use of an alternated laser excitation scheme and a correspondingly optimized burst search algorithm eliminates several potential artifacts affecting the calculation of the best fit shot-noise limited PRH. This algorithm is tested extensively on simulations and simple experimental systems. We find that dsDNA data exhibit a wider PRH than expected from shot noise only and hypothetically account for it by assuming a small Gaussian distribution of distances with an average standard deviation of 1.6 Å. Finally, we briefly mention the results of a future publication and illustrate them with a simple two-state model system (DNA hairpin), for which the kinetic transition rates between the open and closed conformations are extracted.

show abstract

“…38 Because some subsequences involving one step transitions in the ON/OFF time series were removed from the analyses, 16 it is desired to confirm how such removals would affect in the analyses based on change point detection method. 36,38 It should also be noted that the SSN scheme groups a set of past subsequences (into a single state) whose transition probability distributions are regarded as identical within an error tolerance determined by the significance level. The grouping and resultant states depend on this significance level and even if two past subsequences are grouped into a certain state for a specific significance level, it might not be the case for another significance level.…”

Section: Discussionmentioning

confidence: 99%

“…The symbolization and the number of symbols depend on the nature of time series, experimental setup, signal-to-noise ratio, and so forth. 23,36,38 The second step is to evaluate the transition probabilities from different subsequences (called past subsequences) to the future symbols, e.g., the transition probability P(s i |s 2 s 1 ) for any symbol s i (i=1,..., the total number of symbols) to appear at a time, say t, following a particular subsequence s 2 s 1 in which one observes s 1 at time t − 1 and s 2 at time t − 2. Similarly, the transition probabilities for all other past subsequences s j s k with past length two will be evaluated.…”

Section: A a Brief Description Of How To Construct Ssnmentioning

confidence: 99%

Non-Markovian properties and multiscale hidden Markovian network buried in single molecule time series

Sultana

Takagi

Morimatsu

et al. 2013

The Journal of Chemical Physics

View full text Add to dashboard Cite

We present a novel scheme to extract a multiscale state space network (SSN) from single-molecule time series. The multiscale SSN is a type of hidden Markov model that takes into account both multiple states buried in the measurement and memory effects in the process of the observable whenever they exist. Most biological systems function in a nonstationary manner across multiple timescales. Combined with a recently established nonlinear time series analysis based on information theory, a simple scheme is proposed to deal with the properties of multiscale and nonstationarity for a discrete time series. We derived an explicit analytical expression of the autocorrelation function in terms of the SSN. To demonstrate the potential of our scheme, we investigated single-molecule time series of dissociation and association kinetics between epidermal growth factor receptor (EGFR) on the plasma membrane and its adaptor protein Ash/Grb2 (Grb2) in an in vitro reconstituted system. We found that our formula successfully reproduces their autocorrelation function for a wide range of timescales (up to 3 s), and the underlying SSNs change their topographical structure as a function of the timescale; while the corresponding SSN is simple at the short timescale (0.033-0.1 s), the SSN at the longer timescales (0.1 s to ∼3 s) becomes rather complex in order to capture multiscale nonstationary kinetics emerging at longer timescales. It is also found that visiting the unbound form of the EGFR-Grb2 system approximately resets all information of history or memory of the process.

show abstract

Information Bounds and Optimal Analysis of Dynamic Single Molecule Measurements

Cited by 112 publications

References 61 publications

Illuminating the mechanistic roles of enzyme conformational dynamics

Illuminating the mechanistic roles of enzyme conformational dynamics

Shot-Noise Limited Single-Molecule FRET Histograms: Comparison between Theory and Experiments

Non-Markovian properties and multiscale hidden Markovian network buried in single molecule time series

Contact Info

Product

Resources

About