Tuesday, February 26, 2008

Beyond the cell: Tracking its invisible patterns

Cell Motion

Figure 2.2: Cell paths resulting from applying the tracking algorithm to two microscope slides. (i) A control experiment, prepared as in Fang et al. (1999), with no electric field. (ii) A treatment experiment, with an electric field off 100 mV/mm. The cathode is at the top of the page.

How cells move? random or coherent or both? spiralling, rotating, fractalling, etc. Is there an invisible path? a common pattern?

Statistical Analysis of Cell Motion by Edward Luke Ionides

Some Background to Cell Motion

Active migration of blood and tissue cells is essential to a number of physiological processes such as inflammation, wound healing, embryogenesis and tumor cell metastasis (Bray, 1992). It also plays an important role in the functioning of many bioartificial tissues and organs (Langer and Vacanti, 1999), such as skin equivalents (Parenteau, 1999) and cartilage repair (Mooney and Mikos, 1999). Modern techniques in microscopy, genetics and pharmacology helped to make some progress in unraveling the complex biophysical processes involved in cell motion (Maheshwari and Lauffenburger, 1998). Although different cell types show diverse methods of locomotion, there are general principles that are widely applicable for cells moving along a substrate. First a cell extends a protrusion by actin filament polymerization (Mogilner and Oster, 1996), which then attaches to the substrate using integrin adhesion receptors (Huttenlocher et al., 1995). A contractile force is next generated which moves the cell body. Finally the cell must attach from the substrate at its trailing end.

Various mathematical models incorporating the above principles of cell motion have been proposed. The most ambitious of them attempt to represent all the physical and chemical processes involved in the motion of an entire cell (Tranquillo and Alt, 1996; Dickinson and Tranquillo, 1993; Dembo, 1989). Others concentrate on a specific process such as extension of a protrusion (Mogilner and Oster, 1996) or receptor dynamics (Lauffenburger and Linderman, 1993). The primary purpose of these biophysical models is to demonstrate that the proposed mechanisms can in fact produce the forces and behaviors observed experimentally.

Another approach to modeling cell motion is phenomenological in nature. The so-called correlated random walks of Alt (1980), Dunn and Brown (1987) and Shenderov and Sheetz (1997) have been proposed to describe observations of isolated cells locomoting on a substrate. For applications, the behavior of cell populations may be of more direct interest, and here diffusion approximations to population behavior are widely used, for example in Ford et al. (1991). The theoretical relationships between single cell models and population models are studied in Alt (1980), Dickinson and Tranquillo (1995), Ford and Lauffenburger (1991). An empirical comparison between single cell and cell population models is given in Farrell et al. (1990). Phenomenological models are used for quantifying experimentally observed cell behavior, and do not require justification in terms of a proposed mechanism. Nevertheless the line dividing biophysical from phenomenological models is in fact only a difference in complexity, and can become blurred as even the simpler phenomenological models can have implications concerning underlying biophysical mechanisms (Dunn and Brown, 1987).

The questions of scientific and engineering interest about cell motion can be broadly summarized into the following: What biophysical processes are involved in cell motion? How can the speed and direction of the motion be modeled? One approach toward answering these questions is to collect temporal sequences of images of moving cells. This is the data type that will be considered in later chapters. Various experimental protocols for studying cell motion are discussed in Alt, Deutsch and Dunn (1997) and Alt and Hoffmann (1990).
Source: Statistical Analysis of Cell Motion by Edward Luke Ionides - B.A. (Cambridge University) 1994M.A. (University of California, Berkeley) 1998 - A dissertation submitted in partial satisfaction of there quirements for the degree of Doctor of Philosophy in Statistics in the GRADUATE DIVISION of the UNIVERSITY OF CALIFORNIA, BERKELEY.

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