Anisotropic diffusion of macromolecules in the contiguous nucleocytoplasmic fluid during eukaryotic cell division

Extracting, quantifying, and comparing dynamical and biomechanical properties of living matter through single particle tracking

A panoply of new tools for tracking single particles and molecules has led to an explosion of experimental data, leading to novel insights into physical properties of living matter governing cellular development and function, health and disease. In this Perspective, we present tools to investigate the dynamics and mechanics of living systems from the molecular to cellular scale via single-particle techniques. In particular, we focus on methods to measure, interpret, and analyse complex data sets that are associated with forces, materials properties, transport, and emergent organisation phenomena within biological and soft-matter systems. Current approaches, challenges, and existing solutions in the associated fields are outlined in order to support the growing community of researchers at the interface of physics and the life sciences. Each section focuses not only on the general physical principles and the potential for understanding living matter, but also on details of practical data extraction and analysis, discussing limitations, interpretation, and comparison across different experimental realisations and theoretical frameworks. Particularly relevant results are introduced as examples. While this Perspective describes living matter from a physical perspective, highlighting experimental and theoretical physics techniques relevant for such systems, it is also meant to serve as a solid starting point for researchers in the life sciences interested in the implementation of biophysical methods.

Cytoplasmic organization promotes protein diffusion in Xenopus extracts

The cytoplasm is highly organized. However, the extent to which this organization influences the dynamics of cytoplasmic proteins is not well understood. Here, we use Xenopus laevis egg extracts as a model system to study diffusion dynamics in organized versus disorganized cytoplasm. Such extracts are initially homogenized and disorganized, and self-organize into cell-like units over the course of tens of minutes. Using fluorescence correlation spectroscopy, we observe that as the cytoplasm organizes, protein diffusion speeds up by about a factor of two over a length scale of a few hundred nanometers, eventually approaching the diffusion time measured in organelle-depleted cytosol. Even though the ordered cytoplasm contained organelles and cytoskeletal elements that might interfere with diffusion, the convergence of protein diffusion in the cytoplasm toward that in organelle-depleted cytosol suggests that subcellular organization maximizes protein diffusivity. The effect of organization on diffusion varies with molecular size, with the effects being largest for protein-sized molecules, and with the time scale of the measurement. These results show that cytoplasmic organization promotes the efficient diffusion of protein molecules in a densely packed environment.

Cytoplasmic organization is a hallmark of living cells. Here, the authors make use of self-organizing cell extracts to examine how the emergence of large-scale organizations influences the microscopic diffusion of protein molecules in the cytoplasm.

Fractional Brownian motion with random Hurst exponent: Accelerating diffusion and persistence transitions

Fractional Brownian motion, a Gaussian non-Markovian self-similar process with stationary long-correlated increments, has been identified to give rise to the anomalous diffusion behavior in a great variety of physical systems. The correlation and diffusion properties of this random motion are fully characterized by its index of self-similarity or the Hurst exponent. However, recent single-particle tracking experiments in biological cells revealed highly complicated anomalous diffusion phenomena that cannot be attributed to a class of self-similar random processes. Inspired by these observations, we here study the process that preserves the properties of the fractional Brownian motion at a single trajectory level; however, the Hurst index randomly changes from trajectory to trajectory. We provide a general mathematical framework for analytical, numerical, and statistical analysis of the fractional Brownian motion with the random Hurst exponent. The explicit formulas for probability density function, mean-squared displacement, and autocovariance function of the increments are presented for three generic distributions of the Hurst exponent, namely, two-point, uniform, and beta distributions. The important features of the process studied here are accelerating diffusion and persistence transition, which we demonstrate analytically and numerically.

Single-Particle Tracking Reveals Anti-Persistent Subdiffusion in Cell Extracts

Single-particle tracking (SPT) has become a powerful tool to quantify transport phenomena in complex media with unprecedented detail. Based on the reconstruction of individual trajectories, a wealth of informative measures become available for each particle, allowing for a detailed comparison with theoretical predictions. While SPT has been used frequently to explore diffusive transport in artificial fluids and inside living cells, intermediate systems, i.e., biochemically active cell extracts, have been studied only sparsely. Extracts derived from the eggs of the clawfrog Xenopus laevis, for example, are known for their ability to support and mimic vital processes of cells, emphasizing the need to explore also the transport phenomena of nano-sized particles in such extracts. Here, we have performed extensive SPT on beads with 20 nm radius in native and chemically treated Xenopus extracts. By analyzing a variety of distinct measures, we show that these beads feature an anti-persistent subdiffusion that is consistent with fractional Brownian motion. Chemical treatments did not grossly alter this finding, suggesting that the high degree of macromolecular crowding in Xenopus extracts equips the fluid with a viscoelastic modulus, hence enforcing particles to perform random walks with a significant anti-persistent memory kernel.

Microtubules Enhance Mesoscale Effective Diffusivity in the Crowded Metaphase Cytoplasm

Mesoscale macromolecular complexes and organelles, tens to hundreds of nanometers in size, crowd the eukaryotic cytoplasm. It is therefore unclear how mesoscale particles remain sufficiently mobile to regulate dynamic processes such as cell division. Here, we study mobility across dividing cells that contain densely packed, dynamic microtubules, comprising the metaphase spindle. In dividing human cells, we tracked 40 nm genetically encoded multimeric nanoparticles (GEMs), whose sizes are commensurate with the inter-filament spacing in metaphase spindles. Unexpectedly, the effective diffusivity of GEMs was similar inside the dense metaphase spindle and the surrounding cytoplasm. Eliminating microtubules or perturbing their polymerization dynamics decreased diffusivity by ~30%, suggesting that microtubule polymerization enhances random displacements to amplify diffusive-like motion. Our results suggest that microtubules effectively fluidize the mitotic cytoplasm to equalize mesoscale mobility across a densely packed, dynamic, non-uniform environment, thus spatially maintaining a key biophysical parameter that impacts biochemistry, ranging from metabolism to the nucleation of cytoskeletal filaments.

Quantitative assessment of the spatial crowding heterogeneity in cellular fluids

Mammalian cells are crowded with macromolecules, supramolecular complexes, and organelles, all of which equip intracellular fluids, e.g., the cytoplasm, with a dynamic and spatially heterogeneous occupied volume fraction. Diffusion in such fluids has been reported to be heterogeneous, i.e., even individual single-particle trajectories feature spatiotemporally varying transport characteristics. Complementing diffusion-based experiments, we have used here an imaging approach to assess the spatial heterogeneity of the nucleoplasm and the cytoplasm in living interphase cells. As a result, we find that the cytoplasm is more crowded and more heterogeneous than the nucleoplasm on several length scales. This phenomenon even persists in dividing cells, where the mitotic spindle region and its periphery form a contiguous fluid but remain nucleoplasmlike and cytoplasmlike, respectively.

Anomalous dynamics of the endoplasmic reticulum network

Large portions of the endoplasmic reticulum (ER) in eukaryotic cells are organized as dynamic networks whose segments are connected by three-way junctions. Here we show that ER junctions move subdiffusively with signatures of fractional Brownian motion and a strong dependence on the cytoskeleton's integrity: The time-averaged mean square displacement scales as 〈r^{2}(τ)〉_{t}∼τ^{α} with α≈0.5 in untreated cells and α≈0.3 when disrupting microtubules, with successive steps being anticorrelated in both cases. We explain our observations by considering ER junctions to move like monomers in (semi)flexible polymer segments immersed in a viscoelastic environment. We also report that ER networks have a nontrivial fractal dimension d_{f}≈1.6 on mesoscopic scales and we provide evidence that the organelle's dynamics is governed by fractons.

Use of Xenopus cell-free extracts to study size regulation of subcellular structures

Striking size variations are prominent throughout biology, at the organismal, cellular, and subcellular levels. Important fundamental questions concern organelle size regulation and how organelle size is regulated relative to cell size, also known as scaling. Uncovering mechanisms of organelle size regulation will inform the functional significance of size as well as the implications of misregulated size, for instance in the case of nuclear enlargement in cancer. Xenopus egg and embryo extracts are powerful cell-free systems that have been utilized extensively for mechanistic and functional studies of various organelles and subcellular structures. The open biochemical nature of the extract permits facile manipulation of its composition, and in recent years extract approaches have illuminated mechanisms of organelle size regulation. This review largely focuses on in vitro Xenopus studies that have identified regulators of nuclear and spindle size. We also discuss potential relationships between size scaling of the nucleus and spindle, size regulation of other subcellular structures, and extract experiments that have clarified developmental timing mechanisms. We conclude by offering some future prospects, notably the integration of Xenopus extract with microfluidic technology.

Measurement of Rapid Protein Diffusion in the Cytoplasm by Photo-Converted Intensity Profile Expansion

The fluorescence microscopy methods presently used to characterize protein motion in cells infer protein motion from indirect observables, rather than measuring protein motion directly. Operationalizing these methods requires expertise that can constitute a barrier to their broad utilization. Here, we have developed PIPE (photo-converted intensity profile expansion) to directly measure the motion of tagged proteins and quantify it using an effective diffusion coefficient. PIPE works by pulsing photo-convertible fluorescent proteins, generating a peaked fluorescence signal at the pulsed region, and analyzing the spatial expansion of the signal. We demonstrate PIPE's success in measuring accurate diffusion coefficients in silico and in vitro and compare effective diffusion coefficients of native cellular proteins and free fluorophores in vivo. We apply PIPE to measure diffusion anomality in the cell and use it to distinguish free fluorophores from native cellular proteins. PIPE's direct measurement and ease of use make it appealing for cell biologists.

Heterogeneity of crowded cellular fluids on the meso- and nanoscale

Cellular fluids are complex media that are crowded with macromolecules and membrane-enclosed organelles on several length scales. Many studies have shown that crowding can significantly alter transport and reaction kinetics in biological but also in bio-mimetic fluids. Yet, experimental insights on how well bio-mimetic fluids can capture the complexity of cellular fluids are virtually missing. Therefore, we have combined fluorescence correlation spectroscopy (FCS) and fluorescence lifetime imaging microscopy (FLIM) to compare the spatial heterogeneities of biological and simple bio-mimetic crowded fluids. As a result, we find that these artificial fluids are capable of mimicking the average diffusion behavior but not the considerable heterogeneity of cellular fluids on the mesoscale (∼100 nm). On the nanoscale, not even the average properties are captured. Thus, cellular fluids feature a distinct, heterogeneous crowding state that differs from simple bio-mimetic fluids.

Motion blur filtering: A statistical approach for extracting confinement forces and diffusivity from a single blurred trajectory

Single particle tracking (SPT) can aid in understanding a variety of complex spatiotemporal processes. However, quantifying diffusivity and confinement forces from individual live cell trajectories is complicated by inter- and intratrajectory kinetic heterogeneity, thermal fluctuations, and (experimentally resolvable) statistical temporal dependence inherent to the underlying molecule's time correlated confined dynamics experienced in the cell. The problem is further complicated by experimental artifacts such as localization uncertainty and motion blur. The latter is caused by the tagged molecule emitting photons at different spatial positions during the exposure time of a single frame. The aforementioned experimental artifacts induce spurious time correlations in measured SPT time series that obscure the information of interest (e.g., confinement forces and diffusivity). We develop a maximum likelihood estimation (MLE) technique that decouples the above noise sources and systematically treats temporal correlation via time series methods. This ultimately permits a reliable algorithm for extracting diffusivity and effective forces in confined or unconfined environments. We illustrate how our approach avoids complications inherent to mean square displacement or autocorrelation techniques. Our algorithm modifies the established Kalman filter (which does not handle motion blur artifacts) to provide a likelihood based time series estimation procedure. The result extends A. J. Berglund's motion blur model [Phys. Rev. E 82, 011917 (2010)PLEEE81539-375510.1103/PhysRevE.82.011917] to handle confined dynamics. The approach can also systematically utilize (possibly time dependent) localization uncertainty estimates afforded by image analysis if available. This technique, which explicitly treats confinement and motion blur within a time domain MLE framework, uses an exact likelihood (time domain methods facilitate analyzing nonstationary signals). Our estimator is demonstrated to be consistent over a wide range of exposure times (5 to 100 ms), diffusion coefficients (1×10^{-3} to 1μm^{2}/s), and confinement widths (100 nm to 2μm). We demonstrate that neglecting motion blur or confinement can substantially bias estimation of kinetic parameters of interest to researchers. The technique also permits one to check statistical model assumptions against measured individual trajectories without "ground truth." The ability to reliably and consistently extract motion parameters in trajectories exhibiting confined and/or non-stationary dynamics, without exposure time artifacts corrupting estimates, is expected to aid in directly comparing trajectories obtained from different experiments or imaging modalities. A Python implementation is provided (open-source code will be maintained on GitHub; see also the Supplemental Material with this paper).

New Insights into Mechanisms and Functions of Nuclear Size Regulation

Nuclear size is generally maintained within a defined range in a given cell type. Changes in cell size that occur during cell growth, development, and differentiation are accompanied by dynamic nuclear size adjustments in order to establish appropriate nuclear-to-cytoplasmic volume relationships. It has long been recognized that aberrations in nuclear size are associated with certain disease states, most notably cancer. Nuclear size and morphology must impact nuclear and cellular functions. Understanding these functional implications requires an understanding of the mechanisms that control nuclear size. In this review, we first provide a general overview of the diverse cellular structures and activities that contribute to nuclear size control, including structural components of the nucleus, effects of DNA amount and chromatin compaction, signaling, and transport pathways that impinge on the nucleus, extranuclear structures, and cell cycle state. We then detail some of the key mechanistic findings about nuclear size regulation that have been gleaned from a variety of model organisms. Lastly, we review studies that have implicated nuclear size in the regulation of cell and nuclear function and speculate on the potential functional significance of nuclear size in chromatin organization, gene expression, nuclear mechanics, and disease. With many fundamental cell biological questions remaining to be answered, the field of nuclear size regulation is still wide open.

Superdiffusion dominates intracellular particle motion in the supercrowded cytoplasm of pathogenic Acanthamoeba castellanii

Acanthamoebae are free-living protists and human pathogens, whose cellular functions and pathogenicity strongly depend on the transport of intracellular vesicles and granules through the cytosol. Using high-speed live cell imaging in combination with single-particle tracking analysis, we show here that the motion of endogenous intracellular particles in the size range from a few hundred nanometers to several micrometers in Acanthamoeba castellanii is strongly superdiffusive and influenced by cell locomotion, cytoskeletal elements, and myosin II. We demonstrate that cell locomotion significantly contributes to intracellular particle motion, but is clearly not the only origin of superdiffusivity. By analyzing the contribution of microtubules, actin, and myosin II motors we show that myosin II is a major driving force of intracellular motion in A. castellanii. The cytoplasm of A. castellanii is supercrowded with intracellular vesicles and granules, such that significant intracellular motion can only be achieved by actively driven motion, while purely thermally driven diffusion is negligible.