Actin burst Shielding effect
CapZ (capping protein z) Figure 2.8: Cooperative effects of Coronin 1A and Aip1. Incubation with Coronin 1A causes the actin filament to burst (left). Shielding depolymerization when actin filaments are incubated with capping proteins and shielding of capping proteins when incubated with depolymerization factors (right).
2.4 Dynamical properties and time scales of the signaling cascade and actin cytoskeleton
As a living organism, the biological processes inside a cell operate at different time scales in order to confront the survival demands imposed by external cues.
In the case of Dictyostelium discoideum the dynamics of the biological processes have been investigated for several years . Although these processes are complex in nature, their study on the basis of nonlinear dynamics and pattern formation has been shown useful to understand them better [43, 102, 4, 121, 48]. The times scales involved in these phenomena ranges from fast time scales in the order of mil-liseconds to slower ones in the range of hours. A given time scale is not associated to an specific component of the actin cytoskeleton or signaling system, instead several time scales can be observed in the same component. Here we review the observed dynamical properties sorted by the time scales in which they appear.
2.4. DYNAMICAL PROPERTIES AND TIME SCALES OF THE SIGNALING CASCADE AND ACTIN CYTOSKELETON
2.4.1 Fast time scales, order ∼ 1 s
As discussed before the first step in the detection of cAMP is carried out by binding to the CAR. The dissociation rates of the cAMP receptors are in the order of 1 s−1 according to their phosphorylation state [106] and the association rate is 5.6µM−1s−1[3]. As we will review this is the fastest process for the signaling cascade and therefore there are three orders of magnitude in the difference between the time scales with the slowest time scale which is related to cAMP production.
2.4.2 Intermediate time scales, order ∼ 10 s
The dynamics of the signaling network present variations in time scales of two order of magnitude between autonomous and induced responses. By changing the external background concentration of cAMP, Ras becomes transiently acti-vated [100]. From response initiation to adaptation to a new cAMP background takes around 20 s [93]. The ability of the cell to adapt to external background changes has been investigated, on [61] it was proposed that the adaptation kinet-ics can be explained by an incoherent feedforward loop model which the authors named LEGI (Local excitation and global inhibition). The model relies in the existence of a hypothetical fast activation process that acts on the cell membrane while a slower diffusive inhibition process changes the sensitivity to the environ-ment. This hypothesis was tested by comparing the responses of Ras to external doses of cAMP, it was concluded an incoherent feedforward model fits best the data than an integral feedback model (which also shows adaptation). From this study it was proposed that RasGEF acted as the fast activator and RasGAP as the slow inhibitor [101].
Under external cAMP stimulation the responses of PIP3 and PTEN have the same time scales as Ras (∼ 20 s) [32]. As mentioned in a previous section it is known that the presence of PTEN is essential for a cell to guide towards the chemoattractant. In Etzrodt et al. [32] the cAMP responses of several components of the cytoskeleton were measured, such as Aip1 and Coronin 1A. It was shown that these proteins exhibit similar response time scales of around 20s. In this work we will concentrate in the time scales of the components of the actin cytoskeleton.
Periodic forcing with pulses of cAMP revealed a resonance of around 20 s (a
2.4. DYNAMICAL PROPERTIES AND TIME SCALES OF THE SIGNALING CASCADE AND ACTIN CYTOSKELETON
detailed account of these experiments will be given later) [114]. But also it has been observed by the author of this work and colleagues that the cytoskeleton also shows time scales of around 10 s with periodic polymerization/depolymerization cycles.
2.4.3 Slow time scales, order ∼ 100 s
Developmental and genetical processes inside cells occur over the time scales of hours. For example, the expression of cAMP receptors can be induced in labo-ratory by withholding nutrients from the cell and pulsing external cAMP every six minutes for six hours [100]. After expressing CAR the cells will emit pulses of cAMP, the periodicity of the pulses changes over time and can range from 30 min to 6 min after 5 and 7 hours of nutrient deprivation respectively. In experiments using perfusion chamber it was found that the ratio between cell density and flow speed was a critical parameter for the initiation of cAMP pulsing [43].
The phosphatidylinositol (PIP2 and PIP3) system is the one that has its dy-namics characterized better. In cells treated with Latrunculin A, which depolymer-izes the cytoskeleton, it was observed that in a confocal slice of the cell membrane displays rotating PIP3 waves. The time series obtained from a single point dis-play fast time scales associated with concentration changes and slow ones in which concentrations are nearly stable. This process has a periodicity of T ∼200 s and is reminiscent to relaxation oscillations [4]. Observations on the lower part of the cell membrane from another study have shown the existence of spiral waves, and it was claimed by the authors that the nucleation and collision of resulting phase singularities with the cell edges are correlated to morphological changes [102].
Motile cells exhibit patches of PIP3 that are related to pseudopod extension, with a typical lifetime of one minute [86]. The mechanism proposed for this obser-vation has been an excitable system, in which the inhibiting variable diffuses faster resulting in small patches [46]. In [121] the authors performed numerical studies and concluded that coupling the LEGI model with an excitable system reproduces many of the observed features in cells. In steady state the cell membrane has a low PIP3 and a high PTEN concentration, occasionally the PTEN levels are de-pleted in small regions that travel around [40]. These domains termed holes where