On the measurement of weak repulsive and frictional colloidal forces by reflection interference contrast microscopy

terference contrast (RIC) microscopy in combination with real-time image processing. The temporal fluctuations of the absolute sphere-to-substrate distance are determined from changes of interference fringe pattern (Newtonian rings). Both the shape about its minimum and the absolute minimum equilibrium distance of the interaction potential can be obtained by analyzing the distribution of distances in terms of a Boltzmann distribution. The timeautocorrelation function of distances yields the hydrodynamic friction. The method has been applied to the interaction of latex spheres with glass substrates in salt solutions of different ionic strength. The results correspond to classical electrostatic double layer theory that leads to a characteristic dependence of the mean separation distance and the mean square displacement on the radius of the spheres. The hydrodynamic friction close to a wall exhibits the predicted inverse proportionality to the sphere-wall distance. It is demonstrated that the method can be applied to study the interaction between biologically relevant objects such as giant vesicles with bilayer covered substrates

Imaging optical thicknesses and separation distances of phospholipid vesicles at solid surfaces

We present the application of reflection interference contrast microscopy (RICM) (1) to map the optical density of supported bilayers and vesicles and (2) to image the contact profile of phospholipid vesicles at surfaces. The resolution in the surface profile is 0.2 $\mu$m laterally and 1 nm out of plane. The optical thickness of the membrane can be determined with 0.2 nm accuracy. We outline the theoretical basis of RICM and derive the interference intensities of adhering vesicles from first principles. An analytical expression for the decaying contrast of the intrference fringes is given. The contact contour of vesicles is determined for various substrates. We further demonstrate that deposition of a magnesium fluoride layer on the glass substrate enhances the contrast and allows the optical density of adsorbed membranes to be imaged. By contrast variation of the buffer solution, the layer thicknesses and the indices of refraction can be measured. The novel method was applied to image lipid domains of different chain lengths in a substrate supported monolayer

Velocity-Dependent Forces in Atomic Force Microscopy Imaging of Lipid Films

We have imaged adsorbed fluid lipid bilayers by atomic force microscopy. The patches were formed by rupture of phospholipid vesicles onto magnesium fluoride. We show that the membrane patches are fluid but can be stably imaged at scan rates higher than 6 p d s . At lower scan rates the tip penetrates through the layer. The penetrating tip does not destroy the fluid patches, and the previous image can be restored after increasing the scanning velocity. The dynamic forces that possibly explain the effect are discussed

SANS studies of liquid crystalline microemulsion gels

We have investigated by small-angle neutron scattering (SANS) the ternary system containing water, alkane and the surfactant mixture benzyltetradecyldimethylammonium chloride and tetradecyltrimethylammonium bromide, which we have found to form a cubic liquid crystalline phase. A contrast variation experiment with equal volume fractions of water and oil showed three Bragg reflections varying in agreement with theoretically calculated scattering amplitudes for an infinite periodic minimal surface (IPMS) with cubic symmetry. We have, in addition, studied the “ringing” gel phases of the system water/octane/didodecyldimethylammonium bromide by SANS and electron microscopy

Non-Markovian data-driven modeling of single-cell motility

Trajectories of human breast cancer cells moving on one-dimensional circular tracks are modeled by thenon-Markovian version of the Langevin equation that includes an arbitrary memory function. When averagedover cells, the velocity distribution exhibits spurious non-Gaussian behavior, while single cells are characterizedby Gaussian velocity distributions. Accordingly, the data are described by a linear memory model whichincludes different random walk models that were previously used to account for various aspects of cell motilitysuch as migratory persistence, non-Markovian effects, colored noise, and anomalous diffusion. The memoryfunction is extracted from the trajectory data without restrictions or assumptions, thus making our approachtruly data driven, and is used for unbiased single-cell comparison. The cell memory displays time-delayedsingle-exponential negative friction, which clearly distinguishes cell motion from the simple persistent randomwalk model and suggests a regulatory feedback mechanism that controls cell migration. Based on the extractedmemory function we formulate a generalized exactly solvable cell migration model which indicates thatnegative friction generates cell persistence over long timescales. The nonequilibrium character of cell motionis investigated by mapping the non-Markovian Langevin equation with memory onto a Markovian model thatinvolves a hidden degree of freedom and is equivalent to the underdamped active Ornstein-Uhlenbeck process

Mesenchymal cell migration on one-dimensional micropatterns

Quantitative studies of mesenchymal cell motion are important to elucidate cytoskeleton function and mechanisms of cell migration. To this end, confinement of cell motion to one dimension (1D) significantly simplifies the problem of cell shape in experimental and theoretical investigations. Here we review 1D migration assays employing micro-fabricated lanes and reflect on the advantages of such platforms. Data are analyzed using biophysical models of cell migration that reproduce the rich scenario of morphodynamic behavior found in 1D. We describe basic model assumptions and model behavior. It appears that mechanical models explain the occurrence of universal relations conserved across different cell lines such as the adhesion-velocity relation and the universal correlation between speed and persistence (UCSP). We highlight the unique opportunity of reproducible and standardized 1D assays to validate theory based on statistical measures from large data of trajectories and discuss the potential of experimental settings embedding controlled perturbations to probe response in migratory behavior.Peer Reviewe

Multi-Level Kinetic Model of mRNA Delivery via Transfection of Lipoplexes

Recent work on the use of mRNA lipoplexes for gene delivery demonstrates the need for a mathematical model that simulates and predicts kinetics and transfection efficiency. The small copy numbers involved make it necessary to use stochastic models and include statistical analysis of the variation observed in the experimental data. The modeling requirements are further complicated by the multi-level nature of the problem, where mRNA molecules are contained in lipoplexes, which are in turn contained in endosomes, where each of these entities displays a behavior of its own. We have created a mathematical model that reproduces both the time courses and the statistical variance observed in recent experiments using single-cell tracking of GFP expression after transfection. By applying a few key simplifications and assumptions, we have limited the number of free parameters to five, which we optimize to match five experimental determinants by means of a simulated annealing algorithm. The models demonstrate the need for modeling of nested species in order to reproduce the shape of the dose-response and expression-level curves