Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy

Abstract

Molecular motors in cells typically produce highly directed motion; however, the aggregate, incoherent effect of all active processes also creates randomly fluctuating forces, which drive diffusive-like, nonthermal motion. Here, we introduce force-spectrum-microscopy (FSM) to directly quantify random forces within the cytoplasm of cells and thereby probe stochastic motor activity. This technique combines measurements of the random motion of probe particles with independent micromechanical measurements of the cytoplasm to quantify the spectrum of force fluctuations. Using FSM, we show that force fluctuations substantially enhance intracellular movement of small and large components. The fluctuations are three times larger in malignant cells than in their benign counterparts. We further demonstrate that vimentin acts globally to anchor organelles against randomly fluctuating forces in the cytoplasm, with no effect on their magnitude. Thus, FSM has broad applications for understanding the cytoplasm and its intracellular processes in relation to cell physiology in healthy and diseased states.

Figure 1. Movements of microinjected tracer particles in living cells

(A) Bright-field image of a A7 cell with microinjected 200-nm-diameter fluorescence particles (green) and two-minute trajectories (black) superimposed on top. PEG coated particles are microinjected into cells grown on collagen I coated glass-bottom dish. Particle trajectories in the cytoplasm look very similar with thermal Brownian motion. Scale bar, 5 μm. (B) Two dimensional ensemble-averaged mean-square displacement (MSD) <Δr²(τ)> of PEG-coated tracer particles of various sizes are plotted against lag time on a log-log scale, in living A7 cells. Red, green and blue symbols and lines represent particles that are 100 nm, 200 nm and 500 nm in diameter, respectively. Dashed lines indicate a logarithmic slope of 1. Measurements are done with more than 200 tracer particles in about 25 individual cells for each particle size. (C) Ensemble-averaged MSD scaled with particle diameter, in untreated (solid symbols), blebbistatin treated (open symbols) and ATP-depleted (solid lines) A7 cells. See also Figure S1 and Movie S1.

Figure 2. Optical-tweezer active microrheology measurement shows that the cytoplasm is a weak elastic gel

(A) Schematic shows the experimental setup used to measure the intracellular mechanics. (B) Typical displacements of the trapped bead and the optical trap oscillating at 1Hz. (C) Effective spring constant K₀ of the intracellular environment measured directly with active microrheology using optical tweezers shows that the intracellular elastic stiffness (solid symbols) dominates over the dissipative resistance (open symbols). Blue circles, grey squares, light grey triangles represent untreated, 10 mM blebbistatin treated, and ATP depleted A7 cells, respectively. Both the blebbistatin treatment and ATP depletion reduce the cytoplasmic stiffness by about two folds. Error bars represent standard deviation (n=15). The corresponding shear moduli of the cytoplasm are shown in Figure S2. See also Figures S2 and S3A.

Figure 3. Conceptual basis of FSM

(A) Schematic illustration of cytoplasmic fluctuating forces enhancing intracellular movements. The aggregate effect of all the motors and active processes working at random directions and random times contribute an incoherent background of fluctuating forces. These active forces drive fluctuating deformations of the cytoplasmic network and substantially enhance intracellular movement over a broad range of length scales, from sub-micron organelles to nanometer-sized proteins. (B) Basic procedure of FSM. (i) A sound wave in the time domain can be represented in the frequency domain by taking its Fourier transform, thereby revealing its frequency composition. (ii) By analogy to the sound wave, we Fourier transform the MSD and express it in the frequency domain. (iii) The cytoplasmic material property, specifically the spring constant, is measured directly using optical tweezers, also in the frequency domain. (iv) Analogous to a stretched spring, if the spring deformation and spring constant are known, the stretching force can be calculated; in cells, the randomly fluctuating force at each frequency is calculated as <f²(υ)> = |K(υ)|²<x²(υ)>.

Figure 4. Ensemble aggregate intracellular force spectrum probed by FSM

(A) Cytoplasmic force spectrum calculated from spontaneous fluctuations of tracer particles and the active microrheology measurement, through <f²(υ)>=|K(υ)|²<x²(υ)>, inside control untreated (red), myosin II inhibited (blue) and ATP-depleted (black) A7 cells. Data are shown as mean values (dotted lines) and vertical error bars (n>). For comparison, theoretical predictions are shown for an elastic medium with a shear modulus as shown in Figure S2, with three levels of activities; the red solid line corresponds to about 1/μm³ density of myosin II filaments applying a force ~ pN, the blue solid line corresponds to a 90% reduction of myosin motor activity by 10 μM blebbistatin (Kovacs et al., 2004), and the black solid line corresponds to no active motors. The yellow dash dotted line represents the theoretical prediction of only active contributions and excludes thermal effects. Dashed lines indicate logarithmic slopes of −0.85 and −2. Vertical bars represent standard error (n=15). (B) Comparison of force spectra probed by FSM in untreated A7 cells, using the spontaneous fluctuations of injected tracer particles (red dotted line, same as that in Figure 4A), endogenous vesicles and protein complexes (black circle) and mitochondria (blue triangle). The spring constant is measured by active microrheology with probe particles, as shown in Figure 2. The force spectrum measured with vesicles and protein complexes is in excellent accord with that measured for probe particles. The force spectrum for mitochondria exhibits the same frequency dependence as that for probe particles, but is larger in amplitude; this is consistent with mitochondria are also occasionally directly transported by specific motors within the cell.

Figure 5. Intracellular mechanics, dynamics and forces in benign and malignant tumor cells

(A) Two dimensional MSD <Δr²(τ)> of 500 nm tracer particles are plotted against lag time on a log-log scale, in the benign breast cells MCF-10A (red circle) and malignant breast tumor cells MCF-7 (black triangle), respectively. The fluctuating movement of tracer particles is stronger in the malignant cells, as compared to the benign cells. (B) Cytoplasmic mechanics measured by active microrheology using optical tweezers. The effective spring constant of the cytoplasm is larger in the MCF-10A (red circle), as compared to the MCF-7 (black triangle); this suggests that the cytoplasm of benign cells is stiffer than malignant cells. (C) The spectrum of intracellular forces calculated based on the fluctuating movement of tracer particles and the cytoplasmic mechanics measurement. The intracellular forces are stronger in the malignant tumor cells MCF-7 (black triangle), than the benign cells MCF-10A (red circle). Error bars represent standard deviation (n=6). See also Figures S4 and S5.

Figure 6. Logarithmic slope and processivity time analyzed from MSD of single tracer particles and cytoplasmic organelles

(A) Individual MSD curves of single 100-nm particles. Colored lines highlight representative deviations from the ensemble average. The full data set is shown in Figure S1B. (B) Distribution of the average logarithmic slopes of single particle’s MSD curve in untreated A7 cells, calculated between 1 to 2 second lag time as indicated by the red dashed lines in the inset. The mean and standard deviation of the slopes are 1.1 and 0.26, respectively, and the mode is about 1.2. (C) Distribution of processivity times τ_p associating with the random intracellular fluctuations, calculated from the transition between the diffusive-like regime and the long time saturation of the time-averaged MSD of each single particle, as pointed by a red arrow in (A). Inset, schematic of the time-dependent force due to activity of myosin filament. (D) Two dimensional MSD of the movement of intracellular vesicles and protein complexes, in untreated (solid squares) and blebbistatin treated (open squares) A7 cells, tracked by bright-field microscopy. (E, F) Logarithmic slopes (E) and distribution of processivity times (F) are calculated from MSD curves of single vesicle and protein complex in the untreated cells. See also Movie S2.

Figure 7. Movement of Dendra2 in cells is increased with ATP

(A) Typical confocal fluorescence images of the red-channel of Dendra2 during photoconversion by a 405 nm pulse. Before photoconversion, cells have low background red fluorescence; the flashed region rapidly converts to red, and begins to move throughout the cell over several seconds. Comparing the untreated and ATP depleted conditions, we see that red fluorescence spreads more quickly in cells with ATP. (B) By quantifying the red fluorescence intensity as a function distance (along the red dashed line in (A)) at several different times, we see that ATP approximately doubles Dendra2 transport over longer length scales. (C) Plotting the spatial width of the red fluorescence intensity as a function of time demonstrates that, without ATP, photoconverted Dendra2 spreads more slowly. (Inset) Replotting in log-log format shows that with or without ATP Dendra2 spreads proportional to t^1/2, demonstrating that both cases movement appears random. Error bars, 145 ms (based on measurement uncertainty from limited imaging frequency). See also Figure S6 and Movie S3.