Predicting rates of cell state change caused by stochastic fluctuations using a data-driven landscape model.

We develop a potential landscape approach to quantitatively describe experimental data from a fibroblast cell line that exhibits a wide range of GFP expression levels under the control of the promoter for tenascin-C. Time-lapse live-cell microscopy provides data about short-term fluctuations in promoter activity, and flow cytometry measurements provide data about the long-term kinetics, because isolated subpopulations of cells relax from a relatively narrow distribution of GFP expression back to the original broad distribution of responses. The landscape is obtained from the steady state distribution of GFP expression and connected to a potential-like function using a stochastic differential equation description (Langevin/Fokker-Planck). The range of cell states is constrained by a force that is proportional to the gradient of the potential, and biochemical noise causes movement of cells within the landscape. Analyzing the mean square displacement of GFP intensity changes in live cells indicates that these fluctuations are described by a single diffusion constant in log GFP space. This finding allows application of the Kramers' model to calculate rates of switching between two attractor states and enables an accurate simulation of the dynamics of relaxation back to the steady state with no adjustable parameters. With this approach, it is possible to use the steady state distribution of phenotypes and a quantitative description of the short-term fluctuations in individual cells to accurately predict the rates at which different phenotypes will arise from an isolated subpopulation of cells.

Cell cycle dependent TN-C promoter activity determined by live cell imaging.

The extracellular matrix protein tenascin-C plays a critical role in development, wound healing, and cancer progression, but how it is controlled and how it exerts its physiological responses remain unclear. By quantifying the behavior of live cells with phase contrast and fluorescence microscopy, the dynamic regulation of TN-C promoter activity is examined. We employ an NIH 3T3 cell line stably transfected with the TN-C promoter ligated to the gene sequence for destabilized green fluorescent protein (GFP). Fully automated image analysis routines, validated by comparison with data derived from manual segmentation and tracking of single cells, are used to quantify changes in the cellular GFP in hundreds of individual cells throughout their cell cycle during live cell imaging experiments lasting 62 h. We find that individual cells vary substantially in their expression patterns over the cell cycle, but that on average TN-C promoter activity increases during the last 40% of the cell cycle. We also find that the increase in promoter activity is proportional to the activity earlier in the cell cycle. This work illustrates the application of live cell microscopy and automated image analysis of a promoter-driven GFP reporter cell line to identify subtle gene regulatory mechanisms that are difficult to uncover using population averaged measurements.

Event ordering in live-cell imaging determined from temporal cross-correlation asymmetry.

We use the temporal asymmetry of the cross-correlation function to determine the temporal ordering of spatially localized cellular events in live-cell multichannel fluorescence imaging. The analysis is well suited to noisy, stochastic systems where the temporal order may not be apparent in the raw data. The approach is applicable to any biochemical reaction not in chemical equilibrium, including protein complex assembly, sequential enzymatic processes, gene regulation, and other cellular signaling events. As an automated quantitative measure, this approach allows the data to be readily interpreted statistically with minimal subjective biases. We first test the technique using simulations of simple biophysical models with a definite temporal ordering. We then demonstrate the approach by extracting the temporal ordering of three proteins-actin, sorting nexin 9, and clathrin-in the endocytic pathway.

Design and optimization of a high-speed, high-sensitivity, spinning disk confocal microscopy system.

We describe the principles, design, and systems integration of a flexible, high-speed, high-sensitivity, high-resolution confocal spinning disk microscopy (SDCM) system. We present several artifacts unique to high-speed SDCM along with techniques to minimize them. We show example experimental results from a specific implementation capable of generating 3-D image stacks containing 30 2-D slices at 30 stacks per second. This implementation also includes optics for differential interference contrast (DIC), phase, and bright-field imaging, as well as an optical trap with sensitive force and position measurement.

Spatially resolved fluorescence correlation spectroscopy using a spinning disk confocal microscope.

We develop an extension of fluorescence correlation spectroscopy (FCS) using a spinning disk confocal microscope. This approach can spatially map diffusion coefficients or flow velocities at up to approximately 10(5) independent locations simultaneously. Commercially available cameras with frame rates of 1000 Hz allow FCS measurements of systems with diffusion coefficients D~10(-7) cm(2)/s or smaller. This speed is adequate to measure small microspheres (200-nm diameter) diffusing in water, or hindered diffusion of macromolecules in complex media (e.g., tumors, cell nuclei, or the extracellular matrix). There have been a number of recent extensions to FCS based on laser scanning microscopy. Spinning disk confocal microscopy, however, has the potential for significantly higher speed at high spatial resolution. We show how to account for a pixel size effect encountered with spinning disk confocal FCS that is not present in standard or scanning FCS, and we introduce a new method to correct for photobleaching. Finally, we apply spinning disk confocal FCS to microspheres diffusing in Type I collagen, which show complex spatially varying diffusion caused by hydrodynamic and steric interactions with the collagen matrix.

Experimental observation and characterization of the magnetorotational instability.

Differential rotation occurs in conducting flows in accretion disks and planetary cores. In such systems, the magnetorotational instability can arise from coupling Lorentz and centrifugal forces to cause large radial angular momentum fluxes. We present the first experimental observation of the magnetorotational instability. Our system consists of liquid sodium between differentially rotating spheres, with an imposed coaxial magnetic field. We characterize the observed patterns, dynamics, and torque increases, and establish that this instability can occur from a hydrodynamic turbulent background.

Granular polymer solution.

We have measured the spectrum of fluctuations in the size of a granular polymer in a granular solvent. The system consists of a linear chain of plastic spheres immersed in a planar fluid of self-propelled balls. The time average of the end-to-end length r of the chain scales with the number of links N according to approximately N2nu, with nu=0.75+/-0.01. This provides an experimental test of the theoretical value nu=3 / 4 of the critical exponent for a self-avoiding random walk in two dimensions. The measured probability distribution P(r) is compared with the universal function of the scaling theory.