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Register a new userComparing Single Molecule Tracking and correlative approaches: an application to the datasets recently presented in Nature Methods by Chenuard et al
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Recent efforts to survey the numerous softwares available to perform single molecule tracking (SMT) highlighted a significant dependence of the outcomes on the specific method used, and the limitation encountered by most techniques to capture fast movements in a crowded environment. Other approaches to identify the mode and rapidity of motion of fluorescently labeled biomolecules, that do not relay on the localization and linking of the images of isolated single molecules are, however, available.This direct comparison shows that correlative imaging analysis approaches complement effectively current SMT methods in circumstances when, due to either the density of the sample, the low signal to noise ratio or molecular blinking, trajectory linking does not allow to capture long-range or fast motion.
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Here, we discuss a collection of cutting-edge techniques and applications in use today by some of the leading experts in the field of correlative approaches in single-molecule biophysics. A key difference in emphasis, compared with traditional single-molecule biophysics approaches detailed previously, is on the emphasis of the development and use of complex methods which explicitly combine multiple approaches to increase biological insights at the single-molecule level. These so-called correlative single-molecule biophysics methods rely on multiple, orthogonal tools and analysis, as opposed to any one single driving technique. Importantly, they span both in vivo and in vitro biological systems as well as the interfaces between theory and experiment in often highly integrated ways, very different to earlier traditional non-integrative approaches. The first applications of correlative single-molecule methods involved adaption of a range of different experimental technologies to the same biological sample whose measurements were synchronised. However, now we find a greater flora of integrated methods emerging that include approaches applied to different samples at different times and yet still permit useful molecular-scale correlations to be performed. The resultant findings often enable far greater precision of length and time scales of measurements, and a more understanding of the interplay between different processes in the same cell. Many new correlative single-molecule biophysics techniques also include more complex, physiologically relevant approaches as well as increasing number that combine advanced computational methods and mathematical analysis with experimental tools. Here we review the motivation behind the development of correlative single-molecule microscopy methods, its history and recent progress in the field.
Assessing the quality of parameter estimates for models describing the motion of single molecules in cellular environments is an important problem in fluorescence microscopy. We consider the fundamental data model, where molecules emit photons at random times and the photons arrive at random locations on the detector according to complex point spread functions (PSFs). The random, non-Gaussian PSF of the detection process and random trajectory of the molecule make inference challenging. Moreover, the presence of other nearby molecules causes further uncertainty in the origin of the measurements, which impacts the statistical precision of estimates. We quantify the limits of accuracy of model parameter estimates and separation distance between closely spaced molecules (known as the resolution problem) by computing the Cramer-Rao lower bound (CRLB), or equivalently the inverse of the Fisher information matrix (FIM), for the variance of estimates. This fundamental CRLB is crucial, as it provides a lower bound for more practical scenarios. While analytic expressions for the FIM can be derived for static molecules, the analytical tools to evaluate it for molecules whose trajectories follow SDEs are still mostly missing. We address this by presenting a general SMC based methodology for both parameter inference and computing the desired accuracy limits for non-static molecules and a non-Gaussian fundamental detection model. For the first time, we are able to estimate the FIM for stochastically moving molecules observed through the Airy and Born & Wolf PSF. This is achieved by estimating the score and observed information matrix via SMC. We sum up the outcome of our numerical work by summarising the qualitative behaviours for the accuracy limits as functions of e.g. collected photon count, molecule diffusion, etc. We also verify that we can recover known results from the static molecule case.
Numerous biological approaches are available to characterise the mechanisms which govern the formation of human embryonic stem cell (hESC) colonies. To understand how the kinematics of single and pairs of hESCs impact colony formation, we study their mobility characteristics using time-lapse imaging. We perform a detailed statistical analysis of their speed, survival, directionality, distance travelled and diffusivity. We confirm that single and pairs of cells migrate as a diffusive random walk. Moreover, we show that the presence of Cell Tracer significantly reduces hESC mobility. Our results open the path to employ the theoretical framework of the diffusive random walk for the prognostic modelling and optimisation of the growth of hESC colonies. Indeed, we employ this random walk model to estimate the seeding density required to minimise the occurrence of hESC colonies arising from more than one founder cell and the minimal cell number needed for successful colony formation. We believe that our prognostic model can be extended to investigate the kinematic behaviour of somatic cells emerging from hESC differentiation and to enable its wide application in phenotyping of pluripotent stem cells for large scale stem cell culture expansion and differentiation platforms.
ANDy , Activity Networks with Delays, is a discrete time framework aimed at the qualitative modelling of time-dependent activities. The modular and concise syntax makes ANDy suitable for an easy and natural modelling of time-dependent biological systems (i.e., regulatory pathways). Activities involve entities playing the role of activators, inhibitors or products of biochemical network operation. Activities may have given duration, i.e., the time required to obtain results. An entity may represent an object (e.g., an agent, a biochemical species or a family of thereof) with a local attribute, a state denoting its level (e.g., concentration, strength). Entities levels may change as a result of an activity or may decay gradually as time passes by. The semantics of ANDy is formally given via high-level Petri nets ensuring this way some modularity. As main results we show that ANDy systems have finite state representations even for potentially infinite processes and it well adapts to the modelling of toxic behaviours. As an illustration, we present a classification of toxicity properties and give some hints on how they can be verified with existing tools on ANDy systems. A small case study on blood glucose regulation is provided to exemplify the ANDy framework and the toxicity properties.
The conformational kinetics of enzymes can be reliably revealed when they are governed by Markovian dynamics. Hidden Markov Models (HMMs) are appropriate especially in the case of conformational states that are hardly distinguishable. However, the evolution of the conformational states of proteins mostly shows non-Markovian behavior, recognizable by non-monoexponential state dwell time histograms. The application of a Hidden Markov Model technique to a cyclic system demonstrating semi-Markovian dynamics is presented in this paper and the required extension of the model design is discussed. As standard ranking criteria of models cannot deal with these systems properly, a new approach is proposed considering the shape of the dwell time histograms. We observed the rotational kinetics of a single F1-ATPase alpha3beta3gamma sub-complex over six orders of magnitude of different ATP to ADP and Pi concentration ratios, and established a general model describing the kinetics for the entire range of concentrations. The HMM extension described here is applicable in general to the accurate analysis of protein dynamics.
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