Steady state distribution of actin filaments
It is known that cell adhesion and spreading involves complex and dynamic rearrangements of the actin cytoskeleton (Dobereiner et al. 2004
) that are coordinated and controlled by the Arp2/3 complex (Lai et al. 2008
). The nucleation function of the Arp2/3 complex is activated by a member of the Wiskott-Aldrich syndrome family protein, N-WASP (Anton et al. 2007
; Chesarone and Goode 2009
) located on the membrane
Initially simulations were run for a sufficiently long time to achieve a steady state and to generate a distribution of actin filaments that is similar to those observed in spread cells. In this case, high concentrations of short filaments reside near the edge of lamellipodium while longer filaments are present toward the center of the cell. To produce this filament distribution, the concentration of N-WASP is taken to be small (5 to 20 molecules/μm2
) on the majority of the plasma membrane but greatly increases (25 to 200 molecules/μm2
) in regions within 2.5 μm of the cell edge. A similar pattern of N-WASP distribution was reported in (Sukumvanich et al. 2004
). For each parameter set, the model initially was simulated for 200 s, which was sufficient to allow all concentrations to come to steady state. The steady state concentration profiles were used later as the initial conditions for the FRAP or CALI simulations.
demonstrates the cell geometry () and initial conditions for simulation. shows the concentration of N-WASP at the beginning of the simulation while presents the distribution of active Arp2/3, which has been recruited to the membrane by N-WASP, after a 200 s simulation. An example of the filament length distributions at equilibrium is given in . The differences in the average filament lengths between the lamellipodium (~540 nm, or 200 actin monomers) and the cell center (~710 nm, or 300 actin monomers) is clearly visible.
FIGURE 2 Initial conditions for simulations. (a) X-Z depiction of the cell geometry, used for simulations (cell dimension R= 25μm). (b) Concentration of N-WASP at the beginning of simulation. (c) Equilibrated distribution of active Arp2/3 after a 200 s (more ...)
To investigate how the amounts of N-WASP and CP influence the actin filament distribution and the concentrations of free/capped barbed ends, we performed additional simulations with different total amounts of N-WASP and CP (). The results show that, indeed, increasing the CP concentration produces shorter filaments with higher concentration. Simulations with a tenfold increase in the abundance of N-WASP (50 molecules/μm2 over the entire plasma membrane and an additional 200 molecules/μm2 near the edges) also decreased the filament length, but the effect was weaker than that of the CP.
Simulation of CP FRAP kinetics
Before attempting to model the CALI data, we used the model to fit FRAP data and estimate the values of key model parameters. The recovery kinetics of EGFP-CP following photobleaching depend on several factors: (1) the total concentrations of EGFP-CP and barbed ends that bind CPs; (2) rate constants for EGFP-CP binding to and dissociating from barbed ends; and (3) diffusion coefficients for EGFP-CP and actin filaments in the cytosol. We investigated how each of these parameters affects the recovery curve. We assumed that all endogenous CPs are replaced by EGFP-CP which exhibit identical chemical properties as endogenous CP. Furthermore, we assumed that transport and binding properties of bleached EGFP-CP were identical to those of unbleached EGFP-CP.
The experimental FRAP measurements were performed on an Olympus FV1000 confocal microscope in the tornado scanning mode, which allows generation of a circular bleaching spot within a short time interval (t=200 ms). To mimic the experimental setup in the simulation, we uniformly ’bleached’, in 200 ms, a 5 μm diameter cylinder through the cytoplasm positioned so that its center was located 5 μm from the cell edge. The parameter characterizing the laser intensity (I) has the dimension of s−1 similar to the rate constant for a zero-order reaction. This parameter was adjusted to reduce fluorescence in the bleached region to 2% of the initial fluorescence, similar to that measured in the experiments.
In our simulation the fluorescence intensity is proportional to total concentration (bound and free) of unbleached EGFP-CP, and, during the recovery phase, the change in fluorescence was monitored within the entire bleached region. show the distribution of fluorescence within the cell and the result of laser photobleaching of EGFP-CP in side and top views, respectively.
The fluorescence in the simulation recovers nearly completely, with the failure to reach 100% recovery due to the ~ 1% of the total EGFP-CP that was bleached. In experimental FRAP measurements, there is generally an immobile fraction that leads to less than 100% recovery (Fig. S1 in the Supplementary Material
). We estimated from analyzing each separate data curve that recovery was nearly complete (95%) between 42 s and 48 s after photobleaching. Using this estimation, the immobile part of experimental fluorescence recovery was extracted and experimental FRAP data was normalized by dividing each time point in the recovery curve by the 100% fluorescence recovery value for that curve (). This procedure did not change the value of the half-time for fluorescence recovery after bleaching. After normalization, the immobile fraction for each curve can be estimated by the comparing the fluorescence value before the photobleaching to that after recovery is deemed complete.
FIGURE 3 Simulation of FRAP experiments. (a,b) Fluorescence distribution immediately after photobleaching applied to an equilibrated system. Laser beam diameter = 5μm; time of photobleaching = 200 ms. White dashed line on (a) shows where the cross-sectional (more ...)
Initially, all simulations were performed using kon
, respectively as values for the association and dissociation rate constants for EGFP-CP to and from the barbed ends respectively (Schafer et al. 1996
). However, simulations with these rate constants derived from in vitro
measurements, failed to reproduce the experimental results even when other parameters important for the recovery kinetics were varied widely. In particular, the CP diffusion coefficient was varied between 0.1 to 20 μm2
/s, the CP concentration was varied from 0.5 to 4 μM, and the concentration of barbed ends was varied from 0.5 to 2 μM (). By contrast, good fit between the simulations and experimental data was obtained when the uncapping rate was increased by one order of magnitude (koff
= 0.1 s−1
) (). This requirement for a large value of the rate constant for uncapping is supported by the results of single speckle microscopy experiments performed recently by two independent research groups. Iwasa & Mullins showed that the average lifetime for CP on barbed ends is ~15 s (koff
) (Iwasa and Mullins 2007
), and Watanabe’s group (Miyoshi et al. 2006
) measured an unexpectedly fast dissociation rate for CPs at the leading edge (koff
Simulations with various diffusion coefficients for CP and a dissociation rate constant equal to 0.1 s−1 () show that a diffusion coefficient between 5 and 15 μm2/s produce results that fit the experimental data within two standard deviations. Fixing the diffusion coefficient for CP at 5μm2/s and varying the dissociation rate constant between 0.05 s−1 and 0.2 s−1 revealed that the best fit was obtained for koff=0.1 s−1 ().
Simulation of CALI experiments performed on capping proteins
Our first approach to model the effect of CALI was to use the same scheme as for the FRAP simulations, but with one significant difference: Laser inactivated EGFP-CP can not bind to barbed ends, so kon for inactive EGFP-CP (species Cap_dark in Vcell scheme) is equal to zero (). The dissociation rate, koff, for inactive (photodamaged) EGFP-CP was varied for different simulations.
To compare the simulations to experimental results, we assumed that an increase in filament length corresponds to the dorsal ridges observed experimentally in fibroblasts (Vitriol et al. 2007
). This assumption is justified by the additional f-actin associated with these structures (Vitriol et al. 2007
). For quantification, the number of ridges in concentric rings centered on the optical axis was counted using an image processing algorithm that detects edges (Vitriol et al. 2007
) and plotted versus time. This experimental time dependence was compared qualitatively with simulated filament length in corresponding areas.
The time of simulated laser inactivation was chosen to equal the experimental irradiation time of 100 ms. The model parameter that corresponds to laser intensity was chosen to produce ≥ 95% inactivation of CP on the optical axis. The laser beam has a Gaussian intensity profile () characterized by a 1/e2 diameter where the intensity drops to 1/e2 of the maximum value on the optical axis of the microscope; this diameter was 23.4 μm. The laser optical axis was located 10 μm from the cell edge.
We ran several CALI simulations using different parameter sets. shows the time course of average F-actin length inside a circle of radius 6 um centered on the optical axis. As seen, these simulations produced the expected elongation of F-actin inside the irradiated zone, but the time course of this increase differed significantly from experimental observations (). The elongation phase was too rapid and reached maximum within 15– 20 s. By contrast, the experiments exhibited slower kinetics, reaching a maximum between 100–120 s. Also, the experiments showed that new actin-filled ridges after CALI diminished slowly and many of them persisted for the entire observation period whereas the simulations produced a rapid diminution of the long filaments. An attempt to slow down the elongation phase by decreasing the dissociation rate for CALI damaged EGFP-CP (, (black)) from 1 s−1 to 0.1 s−1 did not substantially slow the growth phase but simply produced a smaller increase in F-actin.
FIGURE 4 Comparison between experimental growth of protrusive ridges and V-cell modeling of the F-actin increase after CALI. (a) Pseudocolored image shows the distribution of laser intensity and 6,10,15 μm distance from optical axis; (b) Experimental results (more ...)
These results can be explained by the fast diffusion of free CPs. The concentration of free undamaged EGFP-CP inside the irradiated area is restored to nearly 80% of normal level within the first 20–40 s () and the rapid binding of CPs to filaments quickly inhibits further F-actin elongation. We analyzed the fluorescence recovery after photobleaching inside an area with a 12μm radius. The computational results predict that the half-time for fluorescence recovery (corresponding to the sum of free and bound EGFP-CP) according to our model should be around 50s (Fig. S2
) which contradicts the experimental results where substantial recovery of fluorescence inside the CALI’ed region was observed only after 150 s following irradiation (Vitriol et al. 2007
FIGURE 5 Time development for the replacement of active CP after CALI in the irradiated region. (a) Kinetics for the repopulation of free undamaged CP inside the irradiated region. Rapid diffusion of free CP results in a nearly uniform distribution with a slightly (more ...)
The comparison between computational and experimental data suggests that the cells have an additional mechanism to regulate capping dynamics that is absent in our model. To properly capture persistent filament elongation following CALI that lasts for hundreds of seconds, an anti-capping mechanism is required. We propose that ENA/VASP family of proteins are prime candidates for this role; these proteins have been shown to antagonize CP activity (Bear et al. 2002
; Breitsprecher et al. 2008
; Trichet et al. 2008
). We introduced VASP protein into the Vcell modeling scheme and assumed that VASP molecules bind barbed ends independently of their ATP/ADP status. The VASP-Barbed end complex can participate in all reactions that free barbed ends can, but it cannot be capped by CP ().
- In vitro, all barbed ends are capped despite a 20–25 -fold molar excess of VASP (Breitsprecher et al. 2008; Pasic et al. 2008) which indicates that the affinity of CPs for barbed ends is a 2–3 orders of magnitude greater than the VASP affinity for barbed ends.
- Titration of cell lysates revealed that the molar ratios of VASP to CPs are approximately 5:1 with the concentration of VASP being 4±1μM (Breitsprecher et al. 2008; Laurent et al. 1999). The concentration of free CP in theintact cell was estimated to be approximately 1–2 μM. Thus, there appearedto be enough high affinity cappers to cap all the barbed ends in vivo (DiNubile et al. 1995). Indeed, a simple simulation shows that 5μM of VASP with a Kd=5μM together with 1μM of CP (Kd= 0.01 μM) results in 95% of the barbed ends being capped. Nevertheless, immediately after lysis with detergent, cells contained large number of barbed ends that are not capped and are able to bind pyrenyl-G-actin resulting in filament elongation (DiNubile et al. 1995).
- Several investigations (Breitsprecher et al. 2008; Samarin et al. 2003) show that dense packing of VASP bound to beads significantly enhanced actin assembly even in the presence of CP, suggesting that if VASP molecules are located on the barbed ends in close proximity to each other, they are able to support processive filament elongation, possibly by protecting filaments from capping.
- Applewhite & coworkers (Applewhite et al. 2007) performed a series of FRAP experiments which showed that EGFP-VASP exhibits rapid recovery in lamellipodia but almost no recovery in filopodia. This observation suggests that, in resting cells, VASP molecules in the lamella and lamellipodia have a high dissociation rate, in which case actin filaments grow only to short lengths before being capped. However, when barbed ends are concentrated, such as in filopodia, dissociation of VASP is much slower, allowing VASP to remain complexed with filaments for longer times, thereby protecting them from being capped and permitting filaments to elongate.
We modeled this effect using the following equation for the VASP-Barbed end dissociation rate constant, kdis
is dissociation rate in the absence of VASP-Barbed end complexes, VASP_B is the concentration of VASP/Barbed end complexes, α is a scaling coefficient that determines the concentration of complex at which the dissociation rate is half its maximum, and n is a coefficient of cooperativity. This equation captures our suggestion that the dissociation of VASP from barbed ends decreases with increasing concentrations of VASP/Barbed end complexes in a cooperative fashion.
This equation was incorporated into the Vcell simulations of the EGFP-CP CALI experiment. shows simulation results for the average filament length as a function of time derived in several regions (concentric circles R=6,10,15 μm) centered on the optical axis. The good qualitative agreement between the model and experimental results () supports the hypothesis that VASP binds cooperatively to barbed ends. In fact, a coefficient of cooperativity smaller than 4 did not produce a stable effect in time and a coefficient higher than 4 replaces all capping protein with anti-capper too quickly to match the experimental kinetics. These figures clearly indicate that where the intensity is highest at the center of the laser beam, filament growth is most pronounced corresponding to the strongest CALI effect.
Dynamics and position of morphological changes are similar in the model and experiments
By monitoring the dynamics of filament growth, we found that the position of stable morphological changes depends not only on the irradiation intensity but also on the distance from the cell edge. Shortly after inactivation, the majority of filament growth shifted toward the cell edge (, t=40s). This effect occurs for two reasons. First, due to geometric considerations, the diffusional recovery of active CP is anisotropic, resulting in delayed replacement close to edge as compared to more central locations. Second, the higher concentration of free barbed ends near the edge requires more CP to halt growth, so depletion of this protein has a more pronounced effect near the cell edge. As a result, uncapped barbed ends at the cell edge collect more VASP molecules which increases the probability of VASP clustering and resultant stabilization at barbed ends, in turn protecting those barbed ends from being recapped when the concentration of active EGFP-CP is restored by diffusion.
The panels of show a time course for the concentration of free active EGFP-CP as it recovers following CALI. The panels in show a time course for the kinetics of fluorescence recovery, which takes into account the formation of new EGFP-CP-barbed end complexes. Note that free EGFP-CP quickly reaches a uniform distribution inside the cell due to the rapid diffusion of this protein. However, EGFP-CP bound to barbed ends exhibits a distinctive pattern with lower concentration close to the cell edge inside the irradiated region
The simulations produce a number of satisfying similarities with the experimental results. presents three different cells with developed dorsal ridges after CALI and pseudocolored fluorescent images of actin filament barbed-ends labeled with Alexa Fluor 568-conjugated G-actin at 3 min post-CALI (Vitriol et al. 2007
). The computational panel () shows the increased filament length after CALI. The dashed circle on both panels marks the region where the laser beam is applied. Inspection of these figures reveals that the increase in filament length (corresponding to the protrusive ridges in the experiment) persists proximate to the cell edge longer than in the other parts of the cell.
FIGURE 6 Similarities in the location of morphological changes development between the experimental (a–d) and computational (e) results. Dashed circle shows the 1/e2 width of applied laser beam. (a–c) Microscope images of three different cells (more ...)
Simulation of FRAP and CALI experiments with various irradiation conditions
To determine how the development of the EGFP-CP CALI phenotype depends on irradiation conditions, we ran additional simulations with different laser intensities and beam radii. The typical FRAP bleaching power is between 0.5–30 mW, which is less than 5% of the CALI laser intensity used in our experiment (I=650 mW, measured on the specimen plane). A FRAP experiment with laser beam 1/e2 width = 23.4 μm and intensity equal to 5% of that used for CALI revealed that no appreciable changes in filament length occur after irradiation ().
FIGURE 7 Simulation of CALI experiments with various irradiation conditions. (a) Montage showing FRAP of EGFP-CP (center) with no appreciable CALI phenotype developing (DIC image before and after FRAP). Laser beam d=23.4μm. (b–d) Simulation with (more ...)
To simulate possible collateral damage in a FRAP experiment, we performed additional CALI simulations using Vcell with the same parameters as above, but with laser intensity only 5%–10% of that previously used in the simulations. Thus, during the CALI step, the laser beam inactivated only 10% of EGFP-CP on the optical axis, instead of the >95% as in previous simulations (). The results show that no elongation of actin filaments developed after irradiation (). Thus, our simulations also indicate that in the case of EGFP-CP, the FRAP experiments can be performed using different sizes of laser beam (5–25μm) without developing a CALI phenotype.
A small radius of irradiation does not produce the CALI phenotype
The experimental results reported earlier in (Vitriol et al. 2007
) demonstrated that when cells were irradiated with a smaller beam size with high laser intensity (5 μm; 6.1 mW/μm2
), no increase in dorsal surface protrusive ridges occurred. In that study it was suggested that the CALI effects require inactivating a large enough fraction of the EGFP-CP pool to avoid rapid recovery of active CP through diffusion. Using Vcell, we tested this prediction. In the simulations, a beam diameter of 5 μm was used and the laser intensity was varied from I=20 s−1
to I=100 s−1
, which is consistent with the experimental conditions. The dissociation rate constant was taken as koff
for active CP and koff
for inactivated CP. The pseudocolor image of active CP concentration immediately following CALI is shown in . The recovery of active EGFP-CP in the center of the irradiated area and kinetics of filament length are presented in . The results of this simulation demonstrate that filament length does not increase after a high intensity irradiation in a small area.
The dissociation rate of photodamaged EGFP-CP is another parameter that can affect the development of morphological change after CALI. More rapid EGFP-CP dissociation from filament tips after CALI will enhance the probability of VASP binding to vacant barbed ends before the diffusional replacement of active EGFP-CP occurs. Table S1 in Supporting Material
presents results for different combinations of intensity and koff
for inactive EGFP-CP, where ‘N’ means that the simulation produced no filament growth while ’Y’ means that substantial filament growth occurred. The table shows that employing a 5μm diameter of inactivation, with a laser intensity even 5–10 times higher than that normally used for wide beam CALI, does not produce increased filament growth unless the off rate for inactivated EGFP-CP is appreciably increased.
CALI without knockdown of endogenous capping protein
CALI experiments also were performed on a cell line in which both endogenous CP and EGFP-CP are present (Vitriol et al. 2007
). To reproduce this condition in the model, we assumed that total concentration of CP in the cell is higher than was used in the previous simulations and equal to 1.5μM, with only half of this being EGFP-CP We ran simulations for 200s to allow the new system to reach steady state. Next we performed CALI with a laser intensity that was able to inactivate only 50% of available CP (). The results of this simulation () demonstrate that under this condition CALI does not induce changes in filament length.
After VASP protein was introduced into the actin polymerization model, we repeated all our simulations for fluorescence recovery after photobleaching of EGFP-CP. The recovery kinetics were identical to those already reported for the FRAP experiments (data not shown), which showed that the VASP molecules did not interfere substantially with CPs binding to the barbed ends. This means that under resting conditions, the local concentration of free barbed ends is not high enough to create conditions for VASP_Barbed-end cooperative behavior. This result also supports several experimental observations (Pasic et al. 2008
; Sechi and Wehland 2004
) which demonstrated that in resting cells VASP molecules do not play significant role in actin dynamics; by contrast, VASP activity is required to regulate the rate of actin filament elongation and provide a mechanism to recruit barbed ends during assembly of specialized actin filament structures (Pasic et al. 2008
; Sechi and Wehland 2004