Development of ultrafast camera-based single fluorescent-molecule imaging for cell biology.

The spatial resolution of fluorescence microscopy has recently been greatly enhanced. However, improvements in temporal resolution have been limited, despite their importance for examining living cells. Here, we developed an ultrafast camera system that enables the highest time resolutions in single fluorescent-molecule imaging to date, which were photon-limited by fluorophore photophysics: 33 and 100 µs with single-molecule localization precisions of 34 and 20 nm, respectively, for Cy3, the optimal fluorophore we identified. Using theoretical frameworks developed for the analysis of single-molecule trajectories in the plasma membrane (PM), this camera successfully detected fast hop diffusion of membrane molecules in the PM, previously detectable only in the apical PM using less preferable 40-nm gold probes, thus helping to elucidate the principles governing the PM organization and molecular dynamics. Furthermore, as described in the companion paper, this camera allows simultaneous data acquisitions for PALM/dSTORM at as fast as 1 kHz, with 29/19 nm localization precisions in the 640 × 640 pixel view-field.

Ultrafast single-molecule imaging reveals focal adhesion nano-architecture and molecular dynamics.

Using our newly developed ultrafast camera described in the companion paper, we reduced the data acquisition periods required for photoactivation/photoconversion localization microscopy (PALM, using mEos3.2) and direct stochastic reconstruction microscopy (dSTORM, using HMSiR) by a factor of ≈30 compared with standard methods, for much greater view-fields, with localization precisions of 29 and 19 nm, respectively, thus opening up previously inaccessible spatiotemporal scales to cell biology research. Simultaneous two-color PALM-dSTORM and PALM-ultrafast (10 kHz) single fluorescent-molecule imaging-tracking has been realized. They revealed the dynamic nanoorganization of the focal adhesion (FA), leading to the compartmentalized archipelago FA model, consisting of FA-protein islands with broad diversities in size (13-100 nm; mean island diameter ≈30 nm), protein copy numbers, compositions, and stoichiometries, which dot the partitioned fluid membrane (74-nm compartments in the FA vs. 109-nm compartments outside the FA). Integrins are recruited to these islands by hop diffusion. The FA-protein islands form loose ≈320 nm clusters and function as units for recruiting FA proteins.

Confined diffusion of transmembrane proteins and lipids induced by the same actin meshwork lining the plasma membrane.

The mechanisms by which the diffusion rate in the plasma membrane (PM) is regulated remain unresolved, despite their importance in spatially regulating the reaction rates in the PM. Proposed models include entrapment in nanoscale noncontiguous domains found in PtK2 cells, slow diffusion due to crowding, and actin-induced compartmentalization. Here, by applying single-particle tracking at high time resolutions, mainly to the PtK2-cell PM, we found confined diffusion plus hop movements (termed "hop diffusion") for both a nonraft phospholipid and a transmembrane protein, transferrin receptor, and equal compartment sizes for these two molecules in all five of the cell lines used here (actual sizes were cell dependent), even after treatment with actin-modulating drugs. The cross-section size and the cytoplasmic domain size both affected the hop frequency. Electron tomography identified the actin-based membrane skeleton (MSK) located within 8.8 nm from the PM cytoplasmic surface of PtK2 cells and demonstrated that the MSK mesh size was the same as the compartment size for PM molecular diffusion. The extracellular matrix and extracellular domains of membrane proteins were not involved in hop diffusion. These results support a model of anchored TM-protein pickets lining actin-based MSK as a major mechanism for regulating diffusion.

Kinetics of self-assembly via facilitated diffusion: Formation of the transcription complex.

We present an analytically solvable model for self-assembly of a molecular complex on a filament. The process is driven by a seed molecule that undergoes facilitated diffusion, which is a search strategy that combines diffusion in three dimensions and one dimension. Our study is motivated by single-molecule-level observations revealing the dynamics of transcription factors that bind to the deoxyribonucleic acid at early stages of transcription. We calculate the probability that a complex made up of a given number of molecules is completely formed, as well as the distribution of completion times, upon the binding of a seed molecule at a target site on the filament (without explicitly modeling the three-dimensional diffusion that precedes binding). We compare two different mechanisms of assembly where molecules bind in sequential and random order. Our results indicate that while the probability of completion is greater for random binding, the completion time scales exponentially with the size of the complex; in contrast, it scales as a power law or slower for sequential binding, asymptotically. Furthermore, we provide model predictions for the dissociation and residence times of the seed molecule, which are observables accessible in single-molecule tracking experiments.

Lateral diffusion in a discrete fluid membrane with immobile particles.

Due to the coupling between the plasma membrane and the actin cytoskeleton, membrane molecules such as receptor proteins can become immobilized by binding to cytoskeletal structures. We investigate the effect of immobile membrane molecules on the diffusion of mobile ones by modeling the membrane as a two-dimensional (2D) fluid composed of hard particles and performing event-driven molecular dynamics simulations at a particle density where the system is in an isotropic liquid state. We show that the diffusion coefficient sharply decreases with increasing immobile fraction, dropping by a factor of ∼ 3 as the fraction of immobile particles increases from 0 to 0.1, in a system-size dependent manner. By combining our results with earlier calculations, we estimate that a factor-of-∼ 20 reduction in diffusion coefficients in live cell membranes, a puzzling finding in cell biology, can be accounted for when less than ∼ 22% of the particles in our model system is immobilized. Furthermore, we investigate the effects of confinement induced by a correlated distribution of immobile particles by calculating the distribution of the time it takes for particles to escape from a corral. In the regime where the particles can always escape from the corral, it is found that the escape times follow an exponential distribution, and the mean escape time grows exponentially with the density of obstacles at the corral boundary, increasing by a factor of 3-5 when immobile particles cover 50% of the boundary, and is approximately proportional to the area of the corral. We believe that our findings will be useful in interpreting (1) single molecule observations of membrane molecules and (2) results of particle based simulations that explore the effect of fluid dynamics on molecular transport in a 2D fluid.

Distribution of population-averaged observables in stochastic gene expression.

Observation of phenotypic diversity in a population of genetically identical cells is often linked to the stochastic nature of chemical reactions involved in gene regulatory networks. We investigate the distribution of population-averaged gene expression levels as a function of population, or sample, size for several stochastic gene expression models to find out to what extent population-averaged quantities reflect the underlying mechanism of gene expression. We consider three basic gene regulation networks corresponding to transcription with and without gene state switching and translation. Using analytical expressions for the probability generating function of observables and large deviation theory, we calculate the distribution and first two moments of the population-averaged mRNA and protein levels as a function of model parameters, population size, and number of measurements contained in a data set. We validate our results using stochastic simulations also report exact results on the asymptotic properties of population averages which show qualitative differences among different models.

Ultrafast diffusion of a fluorescent cholesterol analog in compartmentalized plasma membranes.

Cholesterol distribution and dynamics in the plasma membrane (PM) are poorly understood. The recent development of Bodipy488-conjugated cholesterol molecule (Bdp-Chol) allowed us to study cholesterol behavior in the PM, using single fluorescent-molecule imaging. Surprisingly, in the intact PM, Bdp-Chol diffused at the fastest rate ever found for any molecules in the PM, with a median diffusion coefficient (D) of 3.4 µm²/second, which was ∼10 times greater than that of non-raft phospholipid molecules (0.33 µm²/second), despite Bdp-Chol's probable association with raft domains. Furthermore, Bdp-Chol exhibited no sign of entrapment in time scales longer than 0.5 milliseconds. In the blebbed PM, where actin filaments were largely depleted, Bdp-Chol and Cy3-conjugated dioleoylphosphatidylethanolamine (Cy3-DOPE) diffused at comparable Ds (medians = 5.8 and 6.2 µm²/second, respectively), indicating that the actin-based membrane skeleton reduces the D of Bdp-Chol only by a factor of ∼2 from that in the blebbed PM, whereas it reduces the D of Cy3-DOPE by a factor of ∼20. These results are consistent with the previously proposed model, in which the PM is compartmentalized by the actin-based membrane-skeleton fence and its associated transmembrane picket proteins for the macroscopic diffusion of all of the membrane molecules, and suggest that the probability of Bdp-Chol passing through the compartment boundaries, once it enters the boundary, is ∼10× greater than that of Cy3-DOPE. Since the compartment sizes are greater than those of the putative raft domains, we conclude that raft domains coexist with membrane-skeleton-induced compartments and are contained within them.

Impact of molecular clustering inside nanopores on desorption processes.

Understanding the sorption kinetics of nanoporous systems is crucial for the development and design of novel porous materials for practical applications. Here, using a porous coordination polymer/quartz crystal microbalance (PCP/QCM) hybrid device, we investigate the desorption of various vapor molecules featuring different degrees of intermolecular (hydrogen bonding) or molecule-framework interactions. Our findings reveal that strong intermolecular interactions lead to the desorption process proceeding via an unprecedented metastable state, wherein the guest molecules are clustered within the pores, causing the desorption rate to be temporarily slowed. The results demonstrate the considerable impact of the chemical nature of an adsorbate on the kinetics of desorption, which is also expected to influence the efficiency of certain processes, such as desorption by gas purge.

Dynamic organizing principles of the plasma membrane that regulate signal transduction: commemorating the fortieth anniversary of Singer and Nicolson's fluid-mosaic model.

The recent rapid accumulation of knowledge on the dynamics and structure of the plasma membrane has prompted major modifications of the textbook fluid-mosaic model. However, because the new data have been obtained in a variety of research contexts using various biological paradigms, the impact of the critical conceptual modifications on biomedical research and development has been limited. In this review, we try to synthesize our current biological, chemical, and physical knowledge about the plasma membrane to provide new fundamental organizing principles of this structure that underlie every molecular mechanism that realizes its functions. Special attention is paid to signal transduction function and the dynamic aspect of the organizing principles. We propose that the cooperative action of the hierarchical three-tiered mesoscale (2-300 nm) domains--actin-membrane-skeleton induced compartments (40-300 nm), raft domains (2-20 nm), and dynamic protein complex domains (3-10 nm)--is critical for membrane function and distinguishes the plasma membrane from a classical Singer-Nicolson-type model.

Confining domains lead to reaction bursts: reaction kinetics in the plasma membrane.

Confinement of molecules in specific small volumes and areas within a cell is likely to be a general strategy that is developed during evolution for regulating the interactions and functions of biomolecules. The cellular plasma membrane, which is the outermost membrane that surrounds the entire cell, was considered to be a continuous two-dimensional liquid, but it is becoming clear that it consists of numerous nano-meso-scale domains with various lifetimes, such as raft domains and cytoskeleton-induced compartments, and membrane molecules are dynamically trapped in these domains. In this article, we give a theoretical account on the effects of molecular confinement on reversible bimolecular reactions in a partitioned surface such as the plasma membrane. By performing simulations based on a lattice-based model of diffusion and reaction, we found that in the presence of membrane partitioning, bimolecular reactions that occur in each compartment proceed in bursts during which the reaction rate is sharply and briefly increased even though the asymptotic reaction rate remains the same. We characterized the time between reaction bursts and the burst amplitude as a function of the model parameters, and discussed the biological significance of the reaction bursts in the presence of strong inhibitor activity.

Archipelago architecture of the focal adhesion: membrane molecules freely enter and exit from the focal adhesion zone.

The focal adhesion (FA) is an integrin-based structure built in/on the plasma membrane, mechanically linking the extracellular matrix with the termini of actin stress fibers, providing key scaffolds for the cells to migrate in tissues. The FA was considered as a micron-scale, massive assembly of various proteins, although its formation and decomposition occur quickly in several to several 10 s of minutes. The mechanism of rapid FA regulation has been a major mystery in cell biology. Here, using fast single fluorescent-molecule imaging, we found that transferrin receptor and Thy1, non-FA membrane proteins, readily enter the FA zone, diffuse rapidly there, and exit into the bulk plasma membrane. Integrin ß3 also readily enters the FA zone, and repeatedly undergoes temporary immobilization and diffusion in the FA zone, whereas approximately one-third of integrin ß3 is immobilized there. These results are consistent with the archipelago architecture of the FA, which consists of many integrin islands: the membrane molecules enter the inter-island channels rather freely, and the integrins in the integrin islands can be rapidly exchanged with those in the bulk membrane. Such an archipelago architecture would allow rapid FA formation and disintegration, and might be applicable to other large protein domains in the plasma membrane.

Reaction kinetics in the plasma membrane.

A great puzzle in science is establishing a bottom up understanding of life by revealing how a collection of molecules gives rise to a living cell that can survive, communicate, and reproduce. In the confines of physics, chemistry, or material science laboratories where it possible to study complex interactions between molecules in a well-defined environment, our understanding of collective behavior is substantially developed. However, the environment in which molecules of a biological cell perform their functions is far from ideal or controllable. The environment inside cellular regions such as the plasma membrane is heterogeneous and dynamic, and functional molecules such as proteins are both dynamic and promiscuous, as they interact with countless other molecules. This makes it extremely challenging to grasp the inner mechanism of the cells, both experimentally and theoretically. On the bright side, this presents scientists with a colorful playground that waits to be explored: the mesoscopic world inside the cell. This review covers some of the recent experimental and theoretical developments in the study of molecular interactions in the plasma membrane, viewed as a heterogeneous medium where the number of reactants can be small, sometimes countable, and its implications for biological function.

Porous coordination polymer hybrid device with quartz oscillator: effect of crystal size on sorption kinetics.

A new strategy to synthesize monodispersed porous coordination polymer (PCP) nanocrystals at room temperature was developed and utilized for the formation of PCP thin films on gold substrates with fine control over the crystal sizes using the coordination modulation method. Hybridization of these PCP thin films with an environment-controlled quartz crystal microbalance system allowed determining the adsorption properties for organic vapors (methanol and hexane). In the case of high sensitivity (at the low-concentration dosing of analytes), the sensor response depended on the crystal size but not on the type of analyte. In contrast, at the high-concentration dosing, a clear dependence of the sorption kinetics on the analyte was observed due to significant sorbate-sorbate interaction.

Fundamental and functional aspects of mesoscopic architectures with examples in physics, cell biology, and chemistry.

How small can a macroscopic object be made without losing its intended function? Obviously, the smallest possible size is determined by the size of an atom, but it is not so obvious how many atoms are required to assemble an object so small, and yet that performs the same function as its macroscopic counterpart. In this review, we are concerned with objects of intermediate nature, lying between the microscopic and the macroscopic world. In physics and chemistry literature, this regime in-between is often called mesoscopic, and is known to bear interesting and counterintuitive features. After a brief introduction to the concept of mesoscopic systems from the perspective of physics, we discuss the functional aspects of mesoscopic architectures in cell biology, and supramolecular chemistry through many examples from the literature. We argue that the biochemistry of the cell is largely regulated by mesoscopic functional architectures; however, the significance of mesoscopic phenomena seems to be quite underappreciated in biological sciences. With this motivation, one of our main purposes here is to emphasize the critical role that mesoscopic structures play in cell biology and biochemistry.