Modeling and simulation of biological systems from image data

Abstract

This essay provides an introduction to the terminology, concepts, methods, and challenges of image-based modeling in biology. Image-based modeling and simulation aims at using systematic, quantitative image data to build predictive models of biological systems that can be simulated with a computer. This allows one to disentangle molecular mechanisms from effects of shape and geometry. Questions like "what is the functional role of shape" or "how are biological shapes generated and regulated" can be addressed in the framework of image-based systems biology. The combination of image quantification, model building, and computer simulation is illustrated here using the example of diffusion in the endoplasmic reticulum.

Figure 1

Example of a FRAP experiment with ssGFP-KDEL (pure GFP with an ER targeting and retention sequence) expressed in a VERO cell (data: Helenius lab, ETH Zurich). A: A time-lapse sequence of confocal micrographs before bleaching (top), immediately after bleaching the region of interest (ROI) given by the orange square (middle), and 2 minutes after bleaching (bottom). For each time point we measure the total fluorescence intensity in the ROI, relative to the pre-bleach intensity. B: FRAP curve showing the fluorescence recovery due to influx of unbleached protein into the bleached region. This influx only happens along ER tubules and hence depends on the geometry of the organelle in the vicinity of the ROI.

Figure 2

Workflow of the example used throughout this text. We consider the problem of using fluorescence recovery after photobleaching (FRAP) experiments , to measure the molecular diffusion constant in a complex-shaped organelle, the endoplasmic reticulum (ER) , . The workflow of the image-based solution starts from recording a pre-bleach confocal z-stack, which is used to reconstruct the ER geometry in 3D in the computer. This reconstruction is then used for in-silico simulation of the FRAP recovery dynamics in the same geometry and with the bleached region of interest (ROI) at the same location as in the experiment. Comparing the simulation output with the experimentally measured FRAP curve then allows the identification of the unknown molecular diffusion constant D of the fluorescently tagged protein. Finally, a post-FRAP z-stack is recorded to check that the organelle has not significantly moved or deformed during the course of the experiment.

Figure 3

Image processing in the ER FRAP example . A: Three example slices from a confocal pre-bleach z-stack of the fluorescently labeled (ssGFP-KDEL) ER in a VERO cell (images: Helenius lab, ETH Zurich). B: Using per-pixel thresholding, the 3D shape of the ER is reconstructed in the computer as an intensity iso-surface. C: Magnification of a part of the geometry to illustrate the level of detail of the reconstruction.

Figure 4

Simulation of a continuous/deterministic diffusion model in image-derived ER geometries . A: The ER is “filled with particles” that discretize the fluorescence concentration field. Each particle contains a certain amount of fluorescence. Particles in the bleached region are initially empty (not shown). B: In order to simulate the process of diffusion, particles exchange fluorescence with their neighbors according to Fick's law, which states that the flux j between any pair of particles is given by the concentration gradient ▿c between these two particles, multiplied with the diffusion constant D. In each time step of the simulation, all particles interact with their neighbors according to this deterministic rule . In the figure, bright particles contain more fluorescent protein; the magnitudes of the fluxes are reflected by the thicknesses of the arrows. C: As the simulation steps forward through time, the FRAP curve can be computed by summing up the total fluorescence of the particles in the bleached region (orange box) at each time point. This leads to a simulated FRAP curve and allows visualizing the 3D intensity distribution over time (insets).

Figure 5

Parameter identification in the ER FRAP example . A: The unknown molecular diffusion constant is the only parameter in the model. It can be identified by fitting simulation output to experimental FRAP measurements, as shown. The dynamics in different cells is markedly different due to different ER geometries. Nevertheless, the diffusion constants that lead to the best fit are in the same range of 34 ± 0.95 µm²/seconds for ssGFP-KDEL in the ER lumen of VERO cells. This shows that a large portion of the observed variability in FRAP curves could be due to geometric effects. B: Quantification of the non-controllable geometric effects using the in silico model. Using the same molecular diffusion constant in simulations in different reconstructed ER geometries causes the recovery half-time (orange dashed lines) to vary by about 250%. This variation is purely geometry-induced. The fact that we can control the diffusion constant in the simulations allows disentangling the effects of geometry from the effects of molecular diffusion.