arXiv subjects

Diego Krapf

Publications and source records attributed to Diego Krapf.

29 records · Page 2Linked to original sources

arXiv2020

Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories

Extensive time-series encoding the position of particles such as viruses, vesicles, or individual proteins are routinely garnered in single-particle tracking experiments or supercomputing studies. They contain vital clues on how viruses spread or drugs may be delivered in biological cells. Similar time-series are being recorded of stock values in financial markets and of climate data. Such time-series are most typically evaluated in terms of time-average mean-squared displacements, which remain random variables for finite measurement times. Their statistical properties are different for different physical stochastic processes, thus allowing us to extract valuable information on the stochastic process itself. To exploit the full potential of the statistical information encoded in measured time-series we here propose an easy-to-implement and computationally inexpensive new methodology, based on deviations of the time-averaged mean-squared displacement from its ensemble average counterpart. Specifically, we use the upper bound of these deviations for Brownian motion to check the applicability of this approach to simulated and real data sets. By comparing the probability of deviations for different data sets, we demonstrate how the theoretical bound for Brownian motion reveals additional information about observed stochastic processes. We apply the large-deviation method to data sets of tracer beads tracked in aqueous solution, tracer beads measured in mucin hydrogels, and of geographic surface temperature anomalies. Our analysis shows how the large-deviation properties can be efficiently used as a simple yet effective routine test to reject the Brownian motion hypothesis and unveil crucial information on statistical properties such as ergodicity breaking and short-time correlations.

cond-mat.stat-mech↗

arXiv2020

Anomalous protein kinetics on low-fouling surfaces

In this work, protein-surface interactions were probed in terms of adsorption and desorption of a model protein, bovine serum albumin, on a low-fouling surface with single-molecule localization microscopy. Single-molecule experiments enable precise determination of both adsorption and desorption rates. Strikingly the experimental data show anomalous desorption kinetics, evident as a surface dwell time that exhibits a power-law distribution, i.e. a heavy-tailed rather than the expected exponential distribution. As a direct consequence of this heavy-tailed distribution, the average desorption rate depends upon the time scale of the experiment and the protein surface concentration does not reach equilibrium. Further analysis reveals that the observed anomalous desorption emerges due to the reversible formation of a small fraction of soluble protein multimers (small oligomers), such that each one desorbs from the surface with a different rate. The overall kinetics can be described by a series of elementary reactions, yielding simple scaling relations that predict experimental observations. This work reveals a mechanistic origin for anomalous desorption kinetics that can be employed to interpret observations where low-protein fouling surfaces eventually foul when in long-term contact with protein solutions. The work also provides new insights that can be used to define design principles for non-fouling surfaces and to predict their performance.

physics.chem-ph↗

arXiv2019

Steady-state reaction rate of diffusion-controlled reactions in sheets

In many biological situations, a species arriving from a remote source diffuses in a domain confined between two parallel surfaces until it finds a binding partner. Since such a geometric shape falls in between two- and three-dimensional settings, the behavior of the macroscopic reaction rate and its dependence on geometric parameters are not yet understood. Modeling the geometric setup by a capped cylinder with a concentric disk-like reactive region on one of the lateral surfaces, we provide an exact semi-analytical solution of the steady-state diffusion equation and compute the diffusive flux onto the reactive region. We explore the dependence of the macroscopic reaction rate on the geometric parameters and derive asymptotic results in several limits. Using the self-consistent approximation, we also obtain a simple fully explicit formula for the reaction rate that exhibits a transition from two-dimensional to three-dimensional behavior as the separation distance between lateral surfaces increases. Biological implications of these results are discussed.

physics.chem-ph↗

arXiv2018

Power spectral density of a single Brownian trajectory: What one can and cannot learn from it

The power spectral density (PSD) of any time-dependent stochastic processes $X_t$ is a meaningful feature of its spectral content. In its text-book definition, the PSD is the Fourier transform of the covariance function of $X_t$ over an infinitely large observation time $T$, that is, it is defined as an ensemble-averaged property taken in the limit $T \to \infty$. A legitimate question is what information on the PSD can be reliably obtained from single-trajectory experiments, if one goes beyond the standard definition and analyzes the PSD of a \textit{single} trajectory recorded for a \textit{finite} observation time $T$. In quest for this answer, for a $d$-dimensional Brownian motion we calculate the probability density function of a single-trajectory PSD for arbitrary frequency $f$, finite observation time $T$ and arbitrary number $k$ of projections of the trajectory on different axes. We show analytically that the scaling exponent for the frequency-dependence of the PSD specific to an ensemble of Brownian motion trajectories can be already obtained from a single trajectory, while the numerical amplitude in the relation between the ensemble-averaged and single-trajectory PSDs is a fluctuating property which varies from realization to realization. The distribution of this amplitude is calculated exactly and is discussed in detail. Our results are confirmed by numerical simulations and single particle tracking experiments, with remarkably good agreement. In addition we consider a truncated Wiener representation of Brownian motion, and the case of a discrete-time lattice random walk. We highlight some differences in the behavior of a single-trajectory PSD for Brownian motion and for the two latter situations. The framework developed herein will allow for meaningful physical analysis of experimental stochastic trajectories.

cond-mat.stat-mech↗

arXiv2017

Elucidating distinct ion channel populations on the surface of hippocampal neurons via single-particle tracking recurrence analysis

Protein and lipid nanodomains are prevalent on the surface of mammalian cells. In particular, it has been recently recognized that ion channels assemble into surface nanoclusters in the soma of cultured neurons. However, the interactions of these molecules with surface nanodomains display a considerable degree of heterogeneity. Here, we investigate this heterogeneity and develop statistical tools based on the recurrence of individual trajectories to identify subpopulations within ion channels in the neuronal surface. We specifically study the dynamics of the K$^+$ channel Kv1.4 and the Na$^+$ channel Nav1.6 on the surface of cultured hippocampal neurons at the single-molecule level. We find that both these molecules are expressed in two different forms with distinct kinetics with regards to surface interactions, emphasizing the complex proteomic landscape of the neuronal surface. Further, the tools presented in this work provide new methods for the analysis of membrane nanodomains, transient confinement, and identification of populations within single-particle trajectories.

physics.bio-ph↗

arXiv2017

The Plasma Membrane is Compartmentalized by a Self-Similar Cortical Actin Meshwork

A broad range of membrane proteins display anomalous diffusion on the cell surface. Different methods provide evidence for obstructed subdiffusion and diffusion on a fractal space, but the underlying structure inducing anomalous diffusion has never been visualized due to experimental challenges. We addressed this problem by imaging the cortical actin at high resolution while simultaneously tracking individual membrane proteins in live mammalian cells. Our data confirm that actin introduces barriers leading to compartmentalization of the plasma membrane and that membrane proteins are transiently confined within actin fences. Furthermore, superresolution imaging shows that the cortical actin is organized into a self-similar meshwork. These results present a hierarchical nanoscale picture of the plasma membrane.

physics.bio-ph↗

arXiv2016

Single-Molecule Imaging of Nav1.6 on the Surface of Hippocampal Neurons Reveals Somatic Nanoclusters

Voltage-gated sodium (Na$_\mathrm{v}$) channels are responsible for the depolarizing phase of the action potential in most nerve cells, and Na$_\mathrm{v}$ channel localization to the axon initial segment is vital to action potential initiation. Na$_\mathrm{v}$ channels in the soma play a role in the transfer of axonal output information to the rest of the neuron and in synaptic plasticity, although little is known about Na$_\mathrm{v}$ channel localization and dynamics within this neuronal compartment. This study uses single-particle tracking and photoactivation localization microscopy to analyze cell-surface Na$_\mathrm{v}$1.6 within the soma of cultured hippocampal neurons. Mean-square displacement analysis of individual trajectories indicated that half of the somatic Na$_\mathrm{v}$1.6 channels localized to stable nanoclusters $\sim$230 nm in diameter. Strikingly, these domains were stabilized at specific sites on the cell membrane for >30 min, notably via an ankyrin-independent mechanism, indicating that the means by which Na$_\mathrm{v}$1.6 nanoclusters are maintained in the soma is biologically different from axonal localization. Nonclustered Na$_\mathrm{v}$1.6 channels showed anomalous diffusion, as determined by mean-square-displacement analysis. High-density single-particle tracking of Na$_\mathrm{v}$ channels labeled with photoactivatable fluorophores in combination with Bayesian inference analysis was employed to characterize the surface nanoclusters. A subpopulation of mobile Na$_\mathrm{v}$1.6 was observed to be transiently trapped in the nanoclusters. Somatic Na$_\mathrm{v}$1.6 nanoclusters represent a new, to our knowledge, type of Na$_\mathrm{v}$ channel localization, and are hypothesized to be sites of localized channel regulation.

physics.bio-ph↗

arXiv2016

Strange kinetics of bulk-mediated diffusion on lipid bilayers

Diffusion at solid-liquid interfaces is crucial in many technological and biophysical processes. Although its behavior seems deceivingly simple, recent studies showing passive superdiffusive transport suggest diffusion on surfaces may hide rich complexities. In particular, bulk-mediated diffusion occurs when molecules are transiently released from the surface to perform three-dimensional excursions into the liquid bulk. This phenomenon bears the dichotomy where a molecule always return to the surface but the mean jump length is infinite. Such behavior is associated with a breakdown of the central limit theorem and weak ergodicity breaking. Here, we use single-particle tracking to study the statistics of bulk-mediated diffusion on a supported lipid bilayer. We find that the time-averaged mean square displacement (MSD) of individual trajectories, the archetypal measure in diffusion processes, does not converge to the ensemble MSD but it remains a random variable, even in the long observation-time limit. The distribution of time averages is shown to agree with a Lévy flight model. Our results also unravel intriguing anomalies in the statistics of displacements. The time averaged MSD is shown to depend on experimental time and investigations of fractional moments show a scaling $\langle |r(t)|^q\rangle \sim t^{qν(q)}$ with non-linear exponents, i.e. $ν(q)\neq\textrm{const}$. This type of behavior is termed strong anomalous diffusion and is rare among experimental observations.

cond-mat.stat-mech↗

arXiv2015

Superdiffusive motion of membrane-targeting C2 domains

Membrane targeting domains play crucial roles in the association of signalling molecules to the plasma membrane. For most peripheral proteins, the protein-to-membrane interaction is transient. After proteins dissociate from the membrane they have been observed to rebind following brief excursions in the bulk solution. Such membrane hops can have broad implications for the efficiency of reactions on membranes. We study the diffusion of membrane-targeting C2 domains using single-molecule tracking in supported lipid bilayers. The ensemble-averaged mean square displacement (MSD) exhibits superdiffusive behaviour. However, traditional time-averaged MSD analysis of individual trajectories remains linear and it does not reveal superdiffusion. Our observations are explained in terms of bulk excursions that introduce jumps with a heavy-tail distribution. These hopping events allow proteins to explore large areas in a short time. The experimental results are shown to be consistent with analytical models of bulk-mediated diffusion and numerical simulations.

physics.bio-ph↗

arXiv2014

1/f noise for intermittent quantum dots exhibits non-stationarity and critical exponents

The power spectrum of quantum dot fluorescence exhibits $1/f^β$ noise, related to the intermittency of these nanosystems. As in other systems exhibiting $1/f$ noise, this power spectrum is not integrable at low frequencies, which appears to imply infinite total power. We report measurements of individual quantum dots that address this long-standing paradox. We find that the level of $1/f^β$ noise decays with the observation time. The change of the spectrum with time places a bound on the total power. These observations are in stark contrast with most measurements of noise in macroscopic systems which do not exhibit any evidence for non-stationarity. We show that the traditional description of the power spectrum with a single exponent $β$ is incomplete and three additional critical exponents characterize the dependence on experimental time.

cond-mat.stat-mech↗

arXiv2013

Uncertainty Quantification of Discrete Association Problems in Image Sequence-based Tracking

Applications, ranging from tracking molecular motion within cells to analyzing complex animal foraging behavior, require algorithms for associating a collection of spot-like particles in one image with particles contained in another image. These associations are often made via network flow algorithms. However, it is often the case that many candidate association solutions (the output of network flow algorithms) have nearly optimal scores; in this case, the optimal assignment solution is of dubious quality. Algorithms for reliably computing the uncertainty of candidate association solutions are under-developed in situations where many particles are tracked over multiple frames of data. This is due in part to the fact that exact uncertainty quantification (UQ) in large association problems is computationally intractable because the exact computation exhibits exponential dependence on the number of particles tracked. We introduce a technique that can accurately and efficiently quantify association ambiguity (i.e., UQ for discrete association problems) without requiring the evaluation of the cost of each feasible association solution. Our method can readily be wrapped around existing tracking algorithms and can efficiently handle a variety of 2D association problems. The applications presented are focused on tracking molecules in live cells. Our method is validated via both simulations and experiments. The experimental applications aim to accurately form tracks and quantify diffusion of quantum dot labeled proteins from \emph{in vivo} measurements; here association problems involving cost matrices possessing hundreds to thousands of rows/columns are encountered. For such large-scale problems, we discuss how our approach can efficiently and accurately quantify inherent uncertainty in candidate data associations.

q-bio.QM↗