Single-particle tracking: effects of corrals.

Structural proteins of the membrane skeleton are thought to form "corrals" at the membrane surface, and these corrals may restrict lateral diffusion of membrane proteins. Recent experimental developments in single-particle tracking and laser trapping make it possible to examine the corral model in detail. Techniques to interpret these experiments are presented. First, escape times for a diffusing particle in a corral are obtained from Monte Carlo calculations and analytical solutions for various corral sizes, shapes, and escape probabilities, and reduced to a common curve. Second, the identification of corrals in tracking experiments is considered. The simplest way to identify corrals is by sight. If the walls are impermeable enough, a trajectory fills the corral before the diffusing particle escapes. The fraction of distinct sites visited before escape is calculated for corrals of various sizes, shapes, and escape probabilities, and reduced to a common curve. This fraction is also a measure of the probability that the diffusing species will react with another species in the corral before escaping. Finally, the effect of the sampling interval on the measurement of the short-range diffusion coefficient is examined.     

Single-particle tracking: the distribution of diffusion coefficients.

In single-particle tracking experiments, the diffusion coefficient D may be measured from the trajectory of an individual particle in the cell membrane. The statistical distribution of single-trajectory diffusion coefficients is examined by Monte Carlo calculations. The width of this distribution may be useful as a measure of the heterogeneity of the membrane and as a test of models of hindered diffusion in the membrane. For some models, the distribution of the short-range diffusion coefficient is much narrower than the observed distribution for proteins diffusing in cell membranes. To aid in the analysis of single-particle tracking measurements, the distribution of D is examined for various definitions of D and for various trajectory lengths.     

Single-particle tracking: Brownian dynamics of viscoelastic materials

A unifying theoretical framework for analyzing stochastic data from single-particle tracking (SPT) in viscoelastic materials is presented. A generalization of the bead-spring model for linear polymers is developed from a molecular point of view and from the standpoint of phenomenological linear viscoelasticity. The hydrodynamic interaction in the former is identified as the dashpots in the latter. In elementary terms, the intimate correspondence between time-correlation of the fluctuation measurements and transient relaxation kinetics after perturbation is discussed, and the central role of the fluctuation-dissipation relation is emphasized. The work presented here provides a bridge between the microscopic and the macroscopic views of linear viscoelastic biological materials, and is applicable to membrane protein diffusion, linear DNA chain dynamics, and mechanics of intracellular cytoskeletal networks.     

Single-particle tracking for DNA tether length monitoring

We describe a simple single-particle tracking approach for monitoring the length of DNA molecules in tethered particle motion experiments. In this method, the trajectory of a submicroscopic bead tethered by a DNA molecule to a glass surface is determined by videomicroscopy coupled to image analysis. The amplitude of motion of the bead is measured by the standard deviation of the distribution of successive positions of the bead in a given time interval. We were able to describe theoretically the variation of the equilibrium value of the amplitude of the bead motion with the DNA tether length for the entire applicable DNA length range (up to ~3500 bp). The sensitivity of the approach was illustrated by the evidence obtained for conformational changes introduced into a Holliday junction by the binding of the Escherichia coli RuvA protein. An advantage of this method is that the trajectory of the tethered bead, rather than its averaged motion, is measured, allowing analysis of the conformational dynamics of DNA chains at the single-molecule level.     

Single-particle tracking of quantum dot-conjugated prion proteins inside yeast cells

Yeast is a model eukaryote with a variety of biological resources. Here we developed a method to track a quantum dot (QD)-conjugated protein in the budding yeast Saccharomyces cerevisiae. We chemically conjugated QDs with the yeast prion Sup35, incorporated them into yeast spheroplasts, and tracked the motions by conventional two-dimensional or three-dimensional tracking microscopy. The method paves the way toward the individual tracking of proteins of interest inside living yeast cells.     

Single-particle tracking of oriC-GFP fluorescent spots during chromosome segregation in Escherichia coli

DNA regions close to the origin of replication were visualized by the green fluorescent protein (GFP)-Lac repressor/lac operator system. The number of oriC-GFP fluorescent spots per cell and per nucleoid in batch-cultured cells corresponded to the theoretical DNA replication pattern. A similar pattern was observed in cells growing on microscope slides used for time-lapse experiments. The trajectories of 124 oriC-GFP spots were monitored by time-lapse microscopy of 31 cells at time intervals of 1, 2, and 3 min. Spot positions were determined along the short and long axis of cells. The lengthwise movement of spots was corrected for cell elongation. The step sizes of the spots showed a Gaussian distribution with a standard deviation of approximately 110 nm. Plots of the mean square displacement versus time indicated a free diffusion regime for spot movement along the long axis of the cell, with a diffusion coefficient of 4.3+/-2.6x10(-5) microm2/s. Spot movement along the short axis showed confinement in a region of the diameter of the nucleoid ( approximately 800 nm) with an effective diffusion coefficient of 2.9+/-1.7x10(-5) microm2/s. Confidence levels for the mean square displacement analysis were obtained from numerical simulations. We conclude from the analysis that within the experimental accuracy--the limits of which are indicated and discussed--there is no evidence that spot segregation requires any other mechanism than that of cell (length) growth.     

Electrolyte absorption by gallbladders: models of transport.

A model of electrolyte absorption by gallbladder epithelium has been presented previously on the basis of studies on gallbladders of 12 species, including fishes, frogs, toad, turtle, guinea pig, rabbit, cat and dog. This model incorporates several physiologic and morphologic characteristics common to other transporting epithelia (e.g., intestine) such as energy-dependent solute pumps, osmotically-induced water flow into the lateral intercellular space and bulk flow of fluid driven by hydrostatic pressure along the lateral space toward the basement membrane. Because the transepithelial PD across the gallbladders of each of these species was near zero under most experimental conditions, the active transport mechanism (or, “pump”) at the basolateral membrane was considered to move Na and Cl in a coupled, one-for-one manner. The carrier mechanism was postulated to have a binding site for Na and one for Cl; it would function only if both sites were filled.Gallbladders from six other species investigated more recently (including man, monkeys, goose and Necturus) have serosa-positive transepithelial PDs of 2–8 mV. The possibility was suggested that rheogenic Na transport from mucosa to serosa might account for the PD in this group of tissues and the original model of transport would be inappropriate. This review will explore the possibility that a single model of electrolyte transport accounts for the data collected on gallbladders with PDs near zero and those having significant transepithelial PDs.An important finding which helps to reconcile the experimental observations on the two groups of gallbladders was the demonstration of coupled flux of Na and Cl from the mucosal solution into the epithelial cells. It appears that this rigid coupling of Na and Cl influx accounts for the lack of a significant PD in gallbladders of those species investigated in the earlier studies, and that rheogenic Na transport may be a property common to gallbladders of all species.     

Energy-barrier models for membrane transport.

Energy-barrier models are analyzed to find hidden assumptions and establish ranges of validity. The analysis proceeds by comparison with integrated results for model continuum membranes. The main conclusions are that a simple energy-barrier model has a wide range of validity, is remarkably accurate even when its conditions of validity are not strictly met, and is almost always superior to the analogous equations of irreversible thermodynamics. Its major limitations are a possible nonphysical divergence at high electric fields or volume flows caused by breakdown of the transition-state approximation, and the inability to treat multicomponent mixtures except in a pseudobinary (Nernst-Planck) approximation.     

Lateral diffusion in an archipelago. Single-particle diffusion.

Several laboratories have measured lateral diffusion of single particles on the cell surface, and these measurements may reveal an otherwise inaccessible level of submicroscopic organization of cell membranes. Pitfalls in the interpretation of these experiments are analyzed. Random walks in unobstructed systems show structure that could be interpreted as free diffusion, obstructed diffusion, directed motion, or trapping in finite domains. To interpret observed trajectories correctly, one must consider not only the trajectories themselves but also the probabilities of occurrence of various trajectories. Measures of the asymmetry of obstructed and unobstructed random walks are calculated, and probabilities are evaluated for random trajectories that resemble either directed motion or diffusion in a bounded region.     

Two-carrier models for mediated transport. I. Theoretical analysis of several two-carrier models.

Several possible models of two sequential and two simultaneous carriers of different affinities are theoretically analysed. Following the analysis we suggest for each model an experimental procedure capable of testing and rejecting the model.     

Double-labeled rabies virus: live tracking of enveloped virus transport

Here we describe a strategy to fluorescently label the envelope of rabies virus (RV), of the Rhabdoviridae family, in order to track the transport of single enveloped viruses in living cells. Red fluorescent proteins (tm-RFP) were engineered to comprise the N-terminal signal sequence and C-terminal transmembrane spanning and cytoplasmic domain sequences of the RV glycoprotein (G). Two variants of tm-RFP were transported to and anchored in the cell surface membrane, independent of glycosylation. As shown by confocal microscopy, tm-RFP colocalized at the cell surface with the RV matrix and G protein and was incorporated into G gene-deficient virus particles. Recombinant RV expressing the membrane-anchored tm-RFP in addition to G yielded infectious viruses with mosaic envelopes containing both tm-RFP and G. Viable double-labeled virus particles comprising a red fluorescent envelope and a green fluorescent ribonucleoprotein were generated by expressing in addition an enhanced green fluorescent protein-phosphoprotein fusion construct (S. Finke, K. Brzozka, and K. K. Conzelmann, J. Virol. 78:12333-12343, 2004). Individual enveloped virus particles were observed under live cell conditions as extracellular particles and inside endosomal vesicles. Importantly, double-labeled RVs were transported in the retrograde direction over long distances in neurites of in vitro-differentiated NS20Y neuroblastoma cells. This indicates that the typical retrograde axonal transport of RV to the central nervous system involves neuronal transport vesicles in which complete enveloped RV particles are carried as a cargo.     

Linear network representation of multistate models of transport.

By introducing external driving forces in rate-theory models of transport we show how the Eyring rate equations can be transformed into Ohm's law with potentials that obey Kirchhoff's second law. From such a formalism the state diagram of a multioccupancy multicomponent system can be directly converted into linear network with resistors connecting nodal (branch) points and with capacitances connecting each nodal point with a reference point. The external forces appear as emf or current generators in the network. This theory allows the algebraic methods of linear network theory to be used in solving the flux equations for multistate models and is particularly useful for making proper simplifying approximation in models of complex membrane structure. Some general properties of linear network representation are also deduced. It is shown, for instance, that Maxwell's reciprocity relationships of linear networks lead directly to Onsager's relationships in the near equilibrium region. Finally, as an example of the procedure, the equivalent circuit method is used to solve the equations for a few transport models.     

Discrimination criteria for apparent two-site transport models.

The medical beliefs of a people have in the past been studied principally by cultural anthropologists. The focus of these studies is usually on intrasocietal dynamics and cultural relativism—a striking orientation. However, beliefs about disease are integral to the way groups have and continue to adapt, and are thus important to both social and biological scientists. In order to study the role of medical beliefs in the adaptation of the group, a comparative approach is needed. This requires viewing these beliefs more generically, comparing their symbolic properties, and analyzing how they are used in explaining and dealing with actual occurrences of disease. The concept of a taxonomy of disease is introduced, as well as the notion of different semantic regions in the taxonomy. In the attempt to clarify the biological significance of a group's taxonomy of disease, and of its mode of operation, the ideas of uncertainty and information are employed. The significance and fruitfulness of this approach is discussed.     

Testing transport models and transport data by means of kinetic rejection criteria.

The proenzyme form of C1r catalytic domains was generated by limited proteolysis of native C1r with thermolysin in the presence of 4-nitrophenyl-4'-guanidinobenzoate. The final preparation, isolated by high-pressure gel permeation in the presence of 2 M-NaCl, was 70-75% proenzyme and consisted of a dimeric association of two gamma B domains, each resulting from cleavage of peptide bonds at positions 285 and 286 of C1r. Like native C1r, the isolated domains autoactivated upon incubation at 37 degrees C. Activation was inhibited by 4-nitrophenyl-4'-guanidinobenzoate but was nearly insensitive to di-isopropyl phosphorofluoridate; likewise, compared to pH 7.4, the rate of activation was decreased at pH 5.0, but was not modified at pH 10.0. In contrast, activation of the (gamma B)2 domains was totally insensitive to Ca2+. Activation of the catalytic domains, which was correlated with an irreversible increase of intrinsic fluorescence, comparable with that previously observed with native C1r [Villiers, Arlaud & Colomb (1983) Biochem. J. 215, 369-375], was reversibly inhibited at high ionic strength (2 M-NaCl), presumably through stabilization of a non-activatable conformational state. Detailed comparison of the properties of native C1r and its catalytic domains indicates that the latter contain all the structural elements that are necessary for intramolecular activation, but probably lack a regulatory mechanism associated with the N-terminal alpha beta region of C1r.     

Two-carrier models for mediated transport I. Theoretical analysis of several two-carrier models

Several possible models of two sequential and two simultaneous carriers of different affinities are theoretically analysed. Following the analysis we suggest for each model an experimental procedure capable of testing and rejecting the model.     

Biokinetics of magnetic carriers for directed transport of drugs

Localization of intravenously injected magnetic drug carriers in the affected areas of the host is complicated by the carrier capture in the liver and other nonaffected organs and tissues. In vivo kinetics of radiolabeled magnetically targeted drug carriers was studied and one-exponent kinetics was shown. A mathematical model of the carrier capture in animal tissues based on the capture mechanism and mass transfer processes in circulating blood was proposed. Biodistribution and capture intensity of carbohydrate-and albumin-coated magnetic microparticles of different sizes were compared. A one-animal biokinetic test based on the model proposed proved to be effective in detecting insignificant differences in the magnetic carrier biokinetics usually hidden by individual differences of the animals.