Surfing along Filopodia: A Particle Transport Revealed by Molecular-Scale Fluctuation Analyses

Abstract

Filopodia perform cellular functions such as environmental sensing or cell motility, but they also grab for particles and withdraw them leading to an increased efficiency of phagocytic uptake. Remarkably, withdrawal of micron-sized particles is also possible without noticeable movements of the filopodia. Here, we demonstrate that polystyrene beads connected by optical tweezers to the ends of adherent filopodia of J774 macrophages, are transported discontinuously toward the cell body. After a typical resting time of 1-2 min, the cargo is moved with alternating velocities, force constants, and friction constants along the surface of the filopodia. This surfing-like behavior along the filopodium is recorded by feedback-controlled interferometric three-dimensional tracking of the bead motions at 10-100 kHz. We measured transport velocities of up to 120 nm/s and transport forces of ∼ 70 pN. Small changes in position, fluctuation width, and temporal correlation, which are invisible in conventional microscopy, indicate molecular reorganization of transport-relevant proteins in different phases of the entire transport process. A detailed analysis implicates a controlled particle transport with fingerprints of a nanoscale unbinding/binding behavior. The manipulation and analysis methods presented in our study may also be helpful in other fields of cellular biophysics.

Figure 1

Transport of beads along adherent filopodia initiated and analyzed by optical tweezers. (A) Sketch of the mechanistic model describing the transport process along an adherent filopodium toward the cell body. The transported bead is tracked interferometrically in 3D. (B) Kelvin-Voigt model for the bead interacting with the surrounding fluid (friction (γ_b)), the optical trap (trap stiffness (κ_opt)), and the cellular protrusion (with elements γ_c and κ_c). (C) DIC image series of J774 macrophage transporting a bead along a filopodium toward its cell body. The bead is captured and tracked inside the focused laser beam during the entire retraction process. To see this figure in color, go online.

Figure 2

Temporal variation of binding strength and friction during transport. The transport process can be divided into intervals of resting (t < 111 s), pure transport (111–340 s), and approach to the cell body (t > 340 s), as indicated by the vertical dashed lines. (A) The mean bead movement, ${\mathbf{r}}_{lp}\left(t\right)=\left(x_{lp}\left(t\right),y_{lp}\left(t\right),z_{lp}\left(t\right)\right)$, is shown in the rotated coordinate system, with x denoting the direction of transport, y the perpendicular horizontal component, and z the approximate vertical component. (B and C) The stiffness, ${\kappa }_i(\mathbf{r},t)$ (B), and friction parameters, ${\gamma }_i(\mathbf{r},t)$, change with space and time and are determined within time intervals of 100 ms of the highpass-filtered trace. Each data point represents the mean values in a time window of 3 s. Error bars correspond to the standard deviation within the 3 s intervals. (D) The 1 Hz lowpass-filtered velocity, $v_{lp}(\mathbf{r},t)$, in the direction of filopodial extension changes significantly during the pure-transport phase. To see this figure in color, go online.

Figure 3

Changes in the bead-center fluctuations during rest. (A) Bead-center trajectory during the rest time, t_rest, showing abrupt jumps in different directions, indicated by arrows 1–6. (B) Sketch of a mechanistic model explaining jumps in the bead-center fluctuations (red double arrow) as a result of molecular unbinding/binding events at the surface. (C) Magnification of jump number 6, indicating a temporal relaxation with exponential fit. The fits provide the decay times τ₁ = 25 ± 1 ms, τ₂ = 16 ± 1 ms, τ₃ = 6.7 ± 0.5 ms, τ₄ = 2.5 ± 0.5 ms, τ₅ = 3,4 ± 0.2 ms, and τ₆ = 4.8 ± 0.4 ms at the respective points in time, as indicated in (A). To see this figure in color, go online.

Figure 4

Trace at the starting point of the actual transport. (A) The position-versus-time plots were fitted by exponential functions resulting in the stated decay times (see Fig. 3 legend). The distances of the abrupt movement can be determined to be 119 nm, 64 nm, and 196 nm for x, y, and z directions, respectively, resulting in a total distance of 238 nm. (B) Stiffness parameters resulting from thermal fluctuations. Mean values before and after t = t_rest are indicated by the dashed lines in the corresponding color. (C and D) Mechanistic model for the release of a locking bond, A (C), and the start of transport through a second bond, B (D), at t > t_rest. (E and F) Sketch of a corresponding Kelvin-Voigt model with stiffness parameters κ_A and κ_B, friction parameters γ_A and γ_B, and equilibrium positions r_A and r_B. To see this figure in color, go online.

Figure 5

Analysis of orientational changes. (A) Mechanistic sketch of bead attached to filopodium illustrating the angle φ. (B) 2D elliptical-position histogram perpendicular to the filopodium axis with minimal and maximal connection stiffness, κ_min and κ_max. The angle φ indicates the tilt of the fluctuation volume. (C) Change in connection stiffness, κ_c(ϕ), for different angles of analysis and at three different times during transport. To see this figure in color, go online.

Figure 6

Change in transport velocity and binding configuration. (A) Temporal change of the longitudinal connection stiffness, κ_c,x, and the maximal and minimal stiffnesses, κ_max and κ_min. (B) Temporal change of the angle ϕ_max, at which the connection stiffness is maximal. (C) Temporal change of the transport velocity, v_tp(t). Dashed line indicates the end of directed transport. To see this figure in color, go online.

Figure 7

Detection of steps during transport. (A) 2D bead center position histogram in the xy plane in a time window of 2 s. The overlaid dark red trace is from a lowpass-filtered trajectory (100 Hz, Hamming window). (B) Unfiltered bead-position x(t) (green), lowpass-filtered bead-position (gray), and stepped traces evaluated by the step-finding algorithm (black). The mean slope of the trace corresponds to a velocity of 〈v〉 = 60 nm/s. (C) Steppedness, S, as a function of corresponding mean step size 〈s〉. (D) Histogram of ∼800 detected steps with step sizes obtained by the fit, which corresponds to the maximum value of the steppedness in (C). To see this figure in color, go online.

Figure 8

Change in 3D binding strength upon binding to other filopodia. (A) Lateral components of stiffness parameter κ(t) during the approach to the cell body. The parameters for minimal, κ_min(t), and maximal, κ_max(t), lateral stiffness are shown by the brown and black curves, respectively. (B and C) DIC microscopy images illustrate the bead position (blue circle) relative to the cell body and other filopodia (green lines) at time points indicated by arrows in (A), revealing strong changes in the maximal stiffness, κ_max. To see this figure in color, go online.