Stress Fluctuation in Living Cells
We study material properties and dynamics in living cells with microinjected particles, and clarify that the passive microrheology cannot be used to measure material properties in living cells that are not in thermal equilibrium due to the presence of biological motors. By tracking inert particles inside living cells, we demonstrate that their motion, specifically MSD, can be understood as an active diffusion, or say their diffusive-like motion is induced by active stress fluctuation in an elastic network. By combining these observations with direct active microrheology with optical tweezers on the same particle, we quantify the spectrum of forces acting on these particles, which we show to be consistent with predictions based on motor activity within cells. We also demonstrate that the active diffusion reflects the processivity time of the underlining motor activity.
Figure 1. Spontaneous fluctuations of microinjected tracer particles in living cells. (A) Two dimensional mean square displacement (MSD) <∆r2(τ)> of PEG-coated tracer particles of various sizes measured with particle tracking method are plotted against lag time on a log-log scale, in wild type (solid symbols), blebbistatin treated (open symbols) and ATP depleted (solid lines) A7 cells. Red, green and blue symbols and lines represent particles with 100 nm, 200 nm and 500 nm in diameter, respectively. Dashed lines indicate a logarithmic slope of 1. Inset shows that MSD is scaled with particle diameter. If we interpret the above data using passive microrheology, the data suggest an elastic material at high frequency, and a viscous material at low frequency.
Figure 2. Intracellular material properties measured with one-particle active microrheology using optical tweezers shows an elastic property inside living cells. Microinjected 500 nm PEG-coated tracer particle in living A7 cells is trapped and manipulated by a spatially oscillating optical trap to test the material properties of the surrounding microenvironment inside living cells. The shear moduli are represented as a function of frequency in wild type A7 cells. Typical displacements of the trapped tracer particle and the optical trap oscillating at 1Hz are shown in the plot as an inset.
Figure 3. The scaling of MSD with intracellular shear modulus square (G2) under minor osmotic compression indicates that the spontaneous fluctuation of inert tracer particles is due to the active energy rather than thermal energy in living cells. If motion is due to thermal fluctuations, one should have: MSD ~ kT/viscosity*t ~ kT/G, which leads to a scaling of MSD*G. However, if motion is due to internal active stresses, say f ~ G*x, then one should have MSD ~ f2/G2, which leads to the scaling of MSD*G2, as shown in Figure 3.
Figure 4. Force spectrum calculated from spontaneous fluctuations of tracer particles and the active microrheology measurement, inside control wild type (red solid line), blebbistatin treated (blue solid line) and ATP depleted (black solid line) cells.
Figure 5. (Left) Distribution of the average logarithmic slopes between 1 to 2 second of single particle's MSD curve in wild type A7 cells. The mean and standard deviation of the slopes are 1.09 and 0.26, respectively. Inset: individual mean square displacement functions of single particles. (Right) Distribution of the collective motor processivity time calculated from the saturating of single particle's MSD curve.
Cell Stiffness Correlates with Cell Volume
Using confocal microscopy and OMTC, we measure the volume and stiffness of adherent cells while controlling substrate stiffness, available spreading area and osmotic pressure in the medium. We find that the cell stiffness correlates with the cell volume, which decreases with substrate stiffness, available spreading area and osmotic pressure.
Figure 1. Morphology and volume of adherent cells change with increasing substrate stiffness. (A) 3 dimensional images of fixed A7 cells on stiff and soft polyacrylamide gel substrates, coated with collagen I. Cells are fixed with formaldehyde, then labeled with Alexa Fluor 488 (green, Actin) and DRAQ-5 (red, nucleus). (B) The projected cell area increases with increasing substrate stiffness. (C) Cell center height and (D) cell volume decrease with increasing substrate stiffness.
Figure 2. Cell volume increases when we decrease the available cell spreading area with micro-patterned collagen 'islands' on glass. (A) 3D images of cells on micropatterned island with different sizes on glass. Cells are labeled with CMFDA. Scale bars are 10 micron, except for the left image. (B) bar plot of cell volume versus cell spreading area on glass. (C) The relation of cell volume as a function of their projected area, for cells on substrates with different stiffnesses, cells on stiff substrate but have different available spreading area, and a dynamic spreading cell follow the same trend.
Figure 3. Cell volume dependence on substrate stiffness under different conditions of A7 cells. (A-C) 3D images of labeled A7 cells on stiff substrates, including control, ATP depleted and extreme osmotic compression conditions. (D-F) images of cells on soft substrates under the same conditions. Cytoplasm is labeled with CMFDA, and nucleus is labeled with DRAQ-5. (G) Cells without active contraction (blebbistatin treated and ATP depleted) and under extreme osmotic compression don't show the volume dependence with substrate stiffness.The control data is same as in Fig.1D.
Figure 4. Stiffness of cell cortex correlates with cell volume. The cell cortex stiffness increases while the cell volume decreases with greater substrate stiffness, larger available spreading area and higher osmotic pressure.
Figure 5. Cortex stiffness of adherent A7 cells is not necessarily correlated to the substrate stiffness. Cortex stiffness of A7 cells grown on polyacrylamide gels coated with 0.1 mg/mL collagen increases with increasing substrate stiffness (control, open bar). This is completely suppressed if we prevent spreading with small micropattens (black bar).
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