Motility statistics and directional sensing

When placed in a gradient of cAMP, receptor-mediated signaling pathways translate the external signal into an asymmetric pattern of actin activity inside the cell. A clear leading edge is formed in gradient direction, where enhanced actin polymerization pushes the membrane forward to induces pseudopod formation (Figure 1 inlet). At the same time, the lateral formation of membrane protrusions is suppressed and the rear of the cell contracts, so that, overall, a chemotactic motion arises, where the cell's center of mass is displaced in the direction the a chemical gradient (1).
The aim of our work is to discriminate between the numerous models of directional sensing that exist in the literature. These models are usually based on a Local Excitation Global Inhibition (LEGI) scheme, and predict qualitatively the same results but differ quantitatively (see e.g. 2, 3, 4, 5). In general, chemotaxis of eukaryotic cells may depend both on the gradient steepness and on the average ambient concentration of the chemoattractant. In a recent theoretical work, it was predicted that the efficacy of chemotaxis is determined by a single control parameter only, namely, the signal-to-noise ratio (SNR) (6). The SNR depends on fluctuations related to the binding event of the chemoattractant molecule to the transmembrane receptor and on fluctuations at the level of receptor-induced intracellular second messenger production. We have quantitatively tested this prediction based on a systematic analysis of Dictyostelium chemotaxis in stationary linear gradients of cAMP using microfluidic tools (7, 8) in combination with automated cell tracking (9). Examples of chemotactic trajectories from this study can be seen in Figure 1 and Figure 2.

Figure 1:

A) Definition of the coordinate system. Inlet: On single cell level, to measure the response of the cell, we use the translocation of a PH-domain protein, CRAC, to the membrane of the cell shortly after the gradient of cAMP has been sensed. CRAC binds to the newly formed PIP3 at the "front" of the cell, where the cAMP concentration is the highest. (B) Microfluidic gradient mixer (10). The x-direction of the coordinate system corresponds to the direction of fluid flow in the main channel of the device, the y-direction to the direction of the chemoattractant gradient. (C) Trajectories of chemotactic Dictyostelium cells in a gradient of 0.16 nM/mm cAMP. The starting point of all trajectories was shifted to (0,0). (D) Average chemotactic index as a function of the cAMP gradient. Note that the data point displayed at very low gradient values (10-5nM/┬Ám) corresponds to an experiment where no gradient of cAMP was applied.

Our anaylsis showed that the theory correctly describes the experimental findings for a SNR equal to or smaller than one. For a larger SNR, deviations from the theoretical predictions were observed due to additional events downstream in the signaling cascade. This is illustrated in Figure 2, where the chemotactic index (CI) is displayed as a function of the SNR at the level of the G protein for different average cAMP concentrations.

Figure 2:

(Top). Tracks of chemotactic Dictyostelium cells in a linear gradient with cmin = 0 at the lower and cmax = 50 nM at the upper side of the channel. (bottom) Chemotactic index (CI) as a function of the signal-to-noise ratio at the level of the G protein (SNRG), defined according to (6). Red (black) points represent cells in a high (low) average cAMP concentration. Adapted from (9)

For SNRG ≤ 1 both curves collapse, whereas for SNRG > 1 the CI saturates at a concentration dependent value. Apart from global measures like the chemotactic index, we have focused on detailed descriptions of the chemotactic motion in terms of stochastic differential equations. In particular, we have extended our previous work on non-directed random motion of Dictyostelium cells and derived a statistical model that quantitatively captures the chemotactic motion in a chemical gradient (11, 12). Our Langevin-type model equation describes directional motion as the interplay of deterministic and stochastic contributions. We performed angle-resolved conditional averaging to extract the form of this equation directly from our data. It is characterized by a quadratic damping term and by multiplicative noise.

We have thus provided a probabilistic description that now serves as a starting point to quantify differences in the motion patterns of mutant cells, in order to characterize the role of different signaling molecules and cytoskeletal regulators in the directed locomotion of eukaryotic cells.

Contact: Maren Stella Müller, Carsten Beta, Eberhard Bodenschatz

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