The Mechanics of (Poro-)Elastic Contractile Actomyosin Networks As a Model System of the Cell Cytoskeleton

Summary

In this work, an in vitro reconstitution approach is employed to study the poroelasticity of actomyosin gels under controlled conditions. The dynamics of the actomyosin gel and the embedded solvent are quantified, through which the network poroelasticity is demonstrated. We also discuss the experimental challenges, common pitfalls, and relevance to cell cytoskeleton mechanics.

Abstract

Cells can actively change their shapes and become motile, a property that depends on their ability to actively reorganize their internal structure. This feature is attributed to the mechanical and dynamic properties of the cell cytoskeleton, notably, the actomyosin cytoskeleton, which is an active gel of polar actin filaments, myosin motors, and accessory proteins that exhibit intrinsic contraction properties. The usually accepted view is that the cytoskeleton behaves as a viscoelastic material. However, this model cannot always explain the experimental results, which are more consistent with a picture describing the cytoskeleton as a poroelastic active material-an elastic network embedded with cytosol. Contractility gradients generated by the myosin motors drive the flow of the cytosol across the gel pores, which infers that the mechanics of the cytoskeleton and the cytosol are tightly coupled. One main feature of poroelasticity is the diffusive relaxation of stresses in the network, characterized by an effective diffusion constant that depends on the gel elastic modulus, porosity, and cytosol (solvent) viscosity. As cells have many ways to regulate their structure and material properties, our current understanding of how cytoskeleton mechanics and cytosol flow dynamics are coupled remains poorly understood. Here, an in vitro reconstitution approach is employed to characterize the material properties of poroelastic actomyosin gels as a model system for the cell cytoskeleton. Gel contraction is driven by myosin motor contractility, which leads to the emergence of a flow of the penetrating solvent. The paper describes how to prepare these gels and run experiments. We also discuss how to measure and analyze the solvent flow and gel contraction both at the local and global scales. The various scaling relations used for data quantification are given. Finally, the experimental challenges and common pitfalls are discussed, including their relevance to cell cytoskeleton mechanics.

Introduction

Living cells have unique mechanical properties. Besides the ability to passively react to applied forces, they are also capable of actively generating forces in response to external stimuli¹. These characteristics, which are essential for a variety of cellular processes, notably during cell motility, are primarily attributed to the mechanical and dynamic properties of the cell cytoskeleton, especially the actomyosin cytoskeleton, which is an active gel of polar actin filaments, myosin molecular motors, and accessory proteins. These actomyosin networks exhibit intrinsic self-organization and contraction properties driven by the myosin motor proteins, which crosslink the actin filaments and actively generate mechanical stresses in the network fueled by ATP hydrolysis².

Numerous experimental and theoretical studies have been conducted to study the material properties of the cytoskeleton³. The commonly accepted view is that the cytoskeleton behaves as a viscoelastic material⁴. This means that on short timescales, the cytoskeleton behaves as an elastic material, and on long timescales, it behaves as a viscous fluid due to the crosslinking proteins and myosin motor detachment (and reattachment), which allows the network to dynamically turnover. In many situations, however, the viscoelastic model cannot describe the experimental results, which are more consistent with a picture describing the cytoskeleton and, more generally, the cell cytoplasm being described as a poroelastic active material^5,6. Two main features characterize these types of materials. (i) The first main feature is the generation of a flow of the penetrating cytosol (the "solvent") across the gel pores by contractility gradients driven by the myosin motors, which underlies processes such as cell blebbing⁷, motility⁸, and cell shape oscillations⁹. The emergence of such cytosolic flows can be local, for blebbing, or global, like in cell motility. In the latter case, the contractile-applied stresses at the cell rear drive the flow of the cytosolic fluid toward the cell front, which replenishes the protein pool needed for lamellipodia assembly⁸. (ii) The second main feature is that the relaxation of stresses is diffusive and is characterized by an effective diffusion constant, , which depends on the gel elastic modulus, gel porosity, and solvent viscosity⁵. The poroelastic diffusion constant determines how fast the system responds to an applied stress. Higher diffusion constants correspond to faster stress redistribution. This, in turn, determines how long it takes for the intracellular cytosolic fluid to be redistributed within the cell following applied mechanical stress, be it external or internal, such as the active contractile stresses generated by myosin motors. These examples, thus, demonstrate that the mechanics of the cytoskeleton and the cytosol are tightly coupled and cannot be treated separately³.

As cells can regulate their mechanical properties in a variety of ways, the interplay between network mechanics and fluid flow dynamics remains poorly understood. A powerful alternative approach is to use in vitro reconstituted systems that allow for full control of the various microscopic constituents and the system parameters, which renders these model systems optimal for physical analysis^10,11. This approach has been successfully employed to study the impact of protein composition and system geometry on actin-based motility^{12,13,14,15,16,17,18}, the 2D patterning of actomyosin networks^19,20,21,22, and the interplay between network contractility and fluid flow dynamics of poroelastic actomyosin gels, which is the focus of this paper²³.

In this manuscript, the preparation of contractile elastic actomyosin networks of controllable dimensions and material properties is discussed based on the work of Ideses et al.²³. The dynamics of the contracting gel and the drained solvent are analyzed and quantified, through which it is demonstrated that these actomyosin gels can be described as a poroelastic active material. Studying the effect of solvent viscosity on stress diffusivity further confirms the poroelastic nature of these networks. The various scaling relations used for data quantification are provided. Finally, the experimental challenges, the common pitfalls, and the relevance of the experimental results to the cell cytoskeleton are also discussed.

Protocol

1. Glass surface treatment and passivation:

NOTE: This section includes three major steps (see Figure 1): (i) cleaning and hydrophilization, (ii) silanization, and (iii) surface passivation.

1. Cleaning and hydrophilization
   1. Use Piranha solution for glass surface cleaning.
      NOTE: Piranha solution is a mixture of 30% H₂O₂ and 70% H₂SO₄ (Table of Materials). Its prime goal is to remove organic contaminations from coverslip surfaces and expose the OH groups on the glass surface. In this manner, the glass surface becomes hydrophilic.
   2. Place 10-12 #1.5 (22 mm x 22 mm) glass coverslips (Table of Materials) in a homemade polytetrafluoroethylene holder (base area: 5.5 cm x 5.5 cm). Transfer the polytetrafluoroethylene holder into a 400 mL beaker (Table of Materials), and incubate it with 300 mL of Piranha solution for 2 h. Do this step on ice and in a chemical hood.
      NOTE: The polytetrafluoroethylene pole screwed to the holder base is 12 cm long, longer than the beaker (11 cm), which allows for the safe transfer/pull-out of the holder into/from the Piranha solution. Since the Piranha solution can still be highly reactive and very hot, it is imperative to stop the reaction. The easiest way to stop the reaction is to pour the Piranha solution into (tap) water to achieve a 50x dilution (at least). The solution can then be safely discarded. Never keep the used Piranha solution in a closed glass bottle – this could end in a bottle explosion.
   3. Transfer the polytetrafluoroethylene holder into a clean beaker filled with fresh double-distilled water (DDW) to wash excess Piranha from the coverslips.
   4. Transfer the beaker into a sonication bath (Table of Materials), and sonicate at 80 Hz at full power for 10 min at 25 °C. Repeat this step two more times with fresh DDW. Use fresh DDW at each time.
2. Silanization
   1. Transfer the holder into a clean beaker (400 mL) filled with 300 mL of pure methanol (Table of Materials) and then into a sonication bath (Table of Materials). Sonicate at 80 Hz at full power for 30 min at 25 °C.
   2. After sonication, transfer the holder into a silane solution prepared using 15 mL of DDW, 3.1 mL of acetic acid (Table of Materials), 340 mL of methanol, and 7.6 mL of silane ((3-Mercaptopropyl) trimethoxysilane) (Table of Materials). Seal the beaker with parafilm, and keep it in the fridge at 4 °C overnight.
      NOTE: The preparation and handling of the silane solution must be performed in a chemical hood. After the silanization step, put the used silane solution (waste) in a dedicated glass bottle within the chemical hood.
   3. On the next day, transfer the holder into a clean beaker filled with 300 mL of pure methanol for 15 s. Then, transfer the holder into a clean beaker, not before drying the bottom of the polytetrafluoroethylene holder to remove excess methanol. Transfer the beaker to the oven (Table of Materials) to dry the glass coverslips for 5 min at 120 °C.
3. Surface passivation with an inert polymer
   1. Achieve surface passivation by incubating the glass coverslips with an inert polymer (Table of Materials). For each experiment, take two coverslips and place them in a Petri dish coated with a parafilm layer initially cleaned with ethanol (EtOH) (DDW/EtOH: 30/70 vol/vol) (Table of Materials).
   2. Incubate each coverslip with 1 mL of a 4 mg·mL⁻¹ 5 kDa molecular weight methoxy polyethylene glycol maleimide (mPEG-mal, M_w = 5 kDa) (Table of Materials) in 1x phosphate buffered saline (PBS) (Table of Materials) for 1 h at 22 °C.
      NOTE: Placing the coverslips on a hydrophobic parafilm layer confines the hydrophilic PEG polymer solution to the glass coverslip surface. The incubation time is critical for achieving optimal passivation. Use incubation times ranging between 45 min and 2 h. Above this incubation time, the glass coverslips surface can deteriorate, leading to protein adhesion and a loss of transparency.
   3. At the end of the incubation process, rinse each coverslip with 5 mL of DDW, and dry with a flow of N₂ (gas). Do not dry the coverslips under a vacuum. Since the coverslips must be kept wet after passivation, immediately put 1 mL of 10 mM Tris on the pegylated surfaces. Use the coverslips within 2 h.
      ​NOTE: The various steps must be performed in a laminar flow chamber to prevent glass surface contamination.

2. Protein purification

1. Purify G-actin from rabbit skeletal muscle acetone powder using the gel filtration method²⁴.
   1. Actin purification takes 1 week. Keep the purified G-actin in G-buffer (5 mM Tris pH 7.8, 0.01% NaN₃, 0.1 mM CaCl₂, 0.2 mM ATP, and 1 mM DTT), and store it on ice. Use the solution within 2 weeks.
      NOTE: Replace the ice every couple of days.
   2. Label the actin with a maleimide-modified fluorescent dye¹⁶ (Table of Materials). Purify the GST-fascin based on the method of Ono et al.²⁵. Flash-freeze both proteins in liquid N₂, and store at −80 °C.
2. Use a standard protocol to purify myosin II from rabbit skeletal muscle²⁶. The purified myosin II (dimers) stock buffer includes 10 mM Tris pH 7.4, 0.5 M KCl, and 35% w/v sucrose. Flash-freeze the myosin in liquid N₂, and store at −80 °C.
   NOTE: The high concentration of KCl keeps the myosin motors in a dimeric form, while the high percentage of sucrose assures that the activity of the motors is not hampered upon freezing. Use a dedicated pipette for viscous fluid handling when working with myosin II stock solutions (Table of Materials).
   1. Label the myosin II dimers with a fluorescent dye (Table of Materials) at pairs of engineered cysteine residues^19,27. Use a chicken gizzard RLC mutant A for that purpose²⁶. Flash-freeze the labeled myosin II in liquid N₂, and store at −80 °C.
      NOTE: This labeling procedure assures that the labeled myosin is active as the native myosin II protein.
3. Use a UV-Vis spectrophotometer (Table of Materials) to measure the absorbance of the stock protein solutions, and deduce the protein concentrations with the Beer-Lambert law using the following extinction coefficients: G-actin (ε₂₉₀ = 26,460 M⁻¹·cm⁻¹), GST-fascin (ε₂₈₀ = 99,330 M⁻¹·cm⁻¹), myosin II dimer (ε₂₈₀ = 268,800 M⁻¹·cm⁻¹), and RLC mutant A (ε₂₈₀ = 3,960 M⁻¹·cm⁻¹)¹⁹.

3. Sample preparation

NOTE: Polymerize the actin monomers in the presence of large aggregates of myosin II motors and the strong passive crosslinker fascin to produce macroscopically contractile elastic actomyosin networks^19,23. Adding fluorescent beads to the solution allows for tracking the solvent flow during gel contraction.

1. Protein ("actomyosin") solution
   1. Except for G-actin, keep the proteins at −80°C in small aliquots, and thaw them at 37 °C before use. The actomyosin solution's total volume is 40 µL.
   2. Prepare the solution by mixing 10 mM Tris pH 7.4, 2 mM MgCl₂, 25 mM KCl, 1 mM ATP, an ATP regenerating system (0.5 mg·mL−1 creatine kinase and 5 mM creatine phosphate), 200 µM EGTA (chelates Ca²⁺ ions), an anti-bleaching solution (0.1 mg·mL⁻¹ glucose oxidase, 0.018 mg·mL⁻¹ catalase, and 5 mg·mL⁻¹ glucose), 5 µM G-actin, 280 nM GST-fascin, and 1.67 nM myosin II. The percentage of labeled G-actin is 5% (molar percentage).
      NOTE: Use a low percentage of labeled G-actin to avoid the saturation of the fluorescent signal at the advanced stages of gel contraction.
2. Preparing myosin II motor aggregates
   1. Add the myosin motors to the protein solution in the form of aggregates. To form large myosin aggregates (150 myosin dimers/aggregate), dilute the myosin stock solution with 10 mM Tris pH 7.4 to reach a final concentration of 25 mM KCl.
   2. Keep the diluted myosin solution for 10 min at room temperature (RT), and then transfer it to ice until use. The motors are fully active for up to 2 h.
3. Measuring the solvent flow
   1. To track the solvent flow across the gel pores, add the fluorescent beads to the actomyosin solution. Reduce the interaction between the beads and the actomyosin network by passivating the beads. Practically, incubate 1 µL of beads (Table of Materials) with 5 µM G-actin for 20 min at RT, and then remove excess G-actin by centrifugation (Table of Materials) (conditions: 6,000 x g for 5 min at 4 °C).
   2. Repeat this step with 10 mg·mL⁻¹ bovine serum albumin (BSA) (Table of Materials) to block (possibly) the remaining uncoated surface. Use the beads at a final dilution of 1:10,000 vol/vol in the experiments.
      NOTE: It is important to adapt the beads' diameter to the gel pore size such that the bead/pore size ratio is <1 at all stages.
4. Effect of solution viscosity
   1. Control the viscosity of the solution by adding glycerol (Table of Materials) to the actomyosin solution. Adding glycerol at a weight percent ranging from 0% to 34% induces a corresponding increase in the solution viscosity from η_ω to 2.76 η_ω, where η_ω is the viscosity of water at 20 °C²⁸.
      ​NOTE: It is essential to use a dedicated pipette for viscous fluid handling when working with glycerol (Table of Materials).

4. Running an experiment

1. Homemade sample holder handling
   1. Take one of the PEG-passivated coverslips, place a greased parafilm spacer on top of it, and place it in the sample holder.
      NOTE: One can replace the parafilm spacer with any spacer.
2. Preparing the actomyosin solution
   1. Prepare the actomyosin solution on ice in a microcentrifuge tube by incorporating the various microscopic constituents, adding the myosin II motor aggregates, and adding EGTA last. Mix the solution well. The addition of EGTA initiates actomyosin network polymerization, which sets the starting time of the experiment.
3. Put 1.1 µL of that solution on the holder-mounted coverslip, and place the second coverslip on top. Screw the holder to seal the sample. This process slightly squeezes the drop, which adopts a disc-like shape. The drop diameters range between 2,800-3,000 µm.
4. Place the sample holder on the microscope, and start the acquisition. Prepare the microscope in advance to reduce the initial acquisition time. It typically takes 1-2 min after mixing to start the sample imaging.

5. Microscopy techniques

1. Image the samples using an inverted fluorescent microscope (Table of Materials) controlled by dedicated software (Table of Materials).
   1. Use low magnifications of 2.5x/0.075 Plan-NEOFLUAR objective (Table of Materials) to visualize the whole gel area and follow its macroscopic contraction with time.
   2. Use a 10x/0.3 Ph1 UPlanFL objective (Table of Materials) to characterize the network porosity and structure and to follow the network self-organization and contraction with time.
      NOTE: This objective is also useful for localizing the myosin II motor aggregates within the network and following the movement of fluorescent beads across the gel pores. Higher magnifications can be used at the expense of a reduced field of view, which is even more significant in dual-color imaging mode (Table of Materials).
2. Excite the samples at 488 nm (actin/fluorescent beads) and 561 nm (myosin motor aggregates/fluorescent beads). Acquire the images at 100 ms per frame with dedicated software (Table of Materials) in streaming mode with an electron multiplying charge-coupled device (EMCCD) camera (Table of Materials).
   NOTE: The fluorescent lamp (Table of Materials) intensity should be kept at the lowest possible value to avoid signal saturation during network contraction.
3. Simultaneous two-color imaging
   1. Use this mode for two purposes: (i) detecting the localization of the myosin motor aggregates within the actin network, and (i) characterizing the outward solvent flow inside and outside during network contraction.
   2. Excite the actin and myosin II motors at 488 nm and 561 nm, respectively, and record the images simultaneously on an EMCCD camera (Table of Materials) using a dual-emission apparatus (Table of Materials). Use the same imaging system to simultaneously image the actin gel (488 nm) and the fluorescent beads (561 nm).

Representative Results

Two glass coverslips are used per experiment. The glass coverslips are cleaned and passivated with PEG polymers. Passivation is essential for preventing the solubilized proteins from adhering to the glass surfaces at the early experimental stages and for minimizing the interaction of the contracting network with the glass walls. Failure to achieve good passivation can lead to inefficient contraction and, in extreme cases, can even inhibit actin network formation.

Figure 1 describes the three main steps of the surface treatment procedure. These steps include the following: (i) surface cleaning and hydrophilization using a Piranha solution, which removes organic contamination from the coverslip surfaces and exposes the OH groups on the glass surface; (ii) surface silanization with (3-Mercaptopropyl)trimethoxysilane, which aims to covalently bind the silane to the glass surface, where each silane molecule ends up with an SH group; (iii) passivation with PEG polymers (mPEG-mal, 5 kDa)-in this step, the maleimide group of the PEG polymer interacts covalently with the SH group on the (3-Mercaptopropyl)trimethoxysilane, resulting in the formation of a PEG monolayer on the glass surface.

For Piranha treatment and silanization, 10-12 glass coverslips #1.5 (22 mm x 22 mm) are placed in a polytetrafluoroethylene holder (Figure 2A), and that holder is transferred to a 400 mL beaker. For the passivation step, two glass coverslips are transferred onto a parafilm-coated Petri dish (Figure 2B). Placing the coverslips on a hydrophobic parafilm layer ensures that the hydrophilic PEG polymer solution remains confined to the glass surface throughout the incubation time. Each coverslip is incubated with 1 mL of 4 mg·mL⁻¹ 5 kDa mPEG-mal in 1x PBS for 1 h at 22 °C (Figure 2B). For this PEG polymer molecular weight and concentration, glass passivation leads to the formation of a PEG monolayer, where each PEG-polymer is in a mushroom-like conformation²⁹. At the end of the incubation process, each coverslip is rinsed with 5 mL of DDW and dried with a flow of N₂ (gas). If the coverslips are not used immediately, 1 mL of 10 mM Tris should be put on the pegylated surfaces to keep the coverslip surfaces wet. The coverslips are dried with a flow of N₂ (gas) just before starting an experiment. It is better to use the coverslips within 2 h.

Macroscopically contractile elastic actomyosin networks are formed by mixing 5 µM G-actin with 16.7 nM myosin, which is added in the form of large aggregates (~150 myosin dimers/aggregates), and 280 nM of the strong crosslinker fascin. The solution includes 1 mM ATP, which is kept constant using an ATP-regenerating system and an anti-bleaching solution (see details in the protocol section). To analyze the flow of the penetrating solvent, fluorescent beads are added to the actomyosin solution.

The experiments are run in a homemade sample holder, which fits the dimensions of a standard microscope stage (Figure 3). A greased parafilm spacer of thickness h (~150 µm) is placed on one of two PEG-passivated coverslips, and that coverslip is placed in the sample holder (Figure 3A). Then, the actomyosin solution is prepared on ice in a microcentrifuge tube by incorporating the various microscopic constituents, adding last the G-actin, myosin aggregates, and then EGTA, which triggers actin polymerization. The solution must be mixed well-this sets the starting time of the experiments (t = 0). Immediately, 1.1 µL of that solution is placed on the coverslip (Figure 3B), the second PEG-passivated coverslip is placed on top of it (Figure 3C), and the holder is screwed to confine the drop in between them (Figure 3D). For this drop volume and spacer type, the drop diameter is about 3,000 µm, but researchers should not rely on these estimated values. The actual drop thickness and diameter should always be measured directly from the microscopy images. For the thickness, a confocal microscope should be used.

The sample holder is placed on the microscope, and the acquisition is started. The microscope should be prepared in advance to reduce the time to starting the acquisition to a minimum. It typically takes 1-2 min to start the sample imaging. The samples are excited at 488 nm and/or 561 nm and imaged using an inverted fluorescent microscope controlled by a dedicated software. The images should be acquired at a rate of 100 ms per frame (or less) in streaming mode with an EMCCD camera. To simultaneously image the actin network and the myosin motor aggregates, or the fluorescent beads in the solution, a dual-emission system should be used. The intensity of the fluorescent lamp should be kept as low as possible to avoid signal saturation at the advanced stages of network contraction.

A 2.5x/0.075 Plan-NEOFLUAR objective is used to characterize the lateral contraction dynamics of the gel and the fluid flow directionality and velocity on the length scale of the gel. These are low-resolution images that are useful for following the changes in gel radius with time, from which the gel radial (lateral) contraction velocity can be deduced. To resolve the structure and porosity of the network, the location of the myosin motor aggregates within the network and the movement of individual fluorescent beads across the gel pores, higher magnification objectives should be used (e.g., a 10x/0.3 Ph1 UPlanFL objective). Higher magnifications can also be used but at the expense of a reduced field of view, which is more significant if the dual-color imaging mode is employed. The (2D) fluorescence microscopy data should be complemented with confocal imaging of the contracting gel in 3D to characterize the contraction dynamics in both the lateral and vertical directions. Confocal microscopy is used to measure the spacing between the two coverslips-this distance defines the initial gel thickness. Additionally, the thickness of the gel should be measured at the end of the experiment when a mechanically stable state is achieved.

Several criteria need to be fulfilled to show that the actomyosin networks behave as a poroelastic material: (i) the network does not remodel, which would infer that it behaves as an elastic material (Figure 4), (ii) the water (solvent) flow across the gel pores is driven by myosin contractility (Figure 5), and (iii) the elastic stress relaxation is characterized by an effective diffusion constant, D ~ κ/γ, which depends on the gel effective elastic modulus, κ, and the effective friction constant, γ, which accounts for the friction between the moving solvent and the gel pores (Figure 6). Below, we discuss each criterion separately and demonstrate how they are fulfilled in the current system.

Aim (i)

Firstly, the gel structure and porosity should be analyzed, and it should be determined whether the network is dynamically remodeling. A schematic representation of the actomyosin network is depicted in Figure 4A. Network formation starts with the spontaneous nucleation and polymerization of the actin filaments, which subsequently bundle (Figure 4B). The network then actively self-organizes into a macroscopically isotropic interconnected network of actin bundles, which dynamically coarsens with time and eventually contracts. Network self-organization and contraction are driven by the myosin aggregates, which predominantly localize at the intersection points of the filament bundles (Figure 4C). The myosin aggregates remain attached to the network through gel contraction, from which it can be concluded that these actomyosin gels behave as elastic active materials (Figure 4C). Furthermore, in these actomyosin gels, contraction is governed by filament sliding, as deduced by comparing the filament bundles' end-to-end distances, l_end-to-end, and contour lengths, l_cont (Figure 4D,E). This contrasts with the contraction of loose actin bundles crosslinked by α-actinin, which are dominated by actin filament buckling²⁹.

The porosity of the gel is characterized by the size of the gel pores through which the solvent flow moves. For purified actin networks, the mesh size, which defines the distance between crosslinks in the gel (here, the myosin aggregates), provides a good estimate also of the gel pore size. The mesh size can be extracted directly from the (2D) fluorescence images and is evaluated from the geometric mean of the distances between pairs of opposing actin bundles in a gel pore (Figure 4B). Since the network is isotropic up to contraction onset, the mean mesh sizes in the vertical (i.e., across the thickness) and lateral (along the radius) directions are the same, ξ_0, = ξ_0,ll = ξ₀ (= 67 µm). Since the actin bundles remain straight during contraction, the mesh and pore sizes shrink in proportion to the changes in gel thickness and diameter. For the current experimental system, the in-plane (radial) contraction initiates after the vertical contraction practically ends (not shown), such that radial contraction proceeds at a constant gel thickness smaller than the initial thickness by a factor of ~0.3. Consequently, while the mesh size within the contraction plane, ξ_ll (t) = r(t)/R, decreases during radial contraction, where r(t) is the radius of the gel at time t, the mean mesh size in the perpendicular direction is constant, ξ = 20μm²³. These values of the mesh/pore sizes are used to evaluate the gel elastic modulus, κ, and friction coefficient, γ, as detailed below (Aim [iii], Figure 6).

Aim (ii)

This aim involves demonstrating that an outward solvent flow is generated by myosin contractility. To track the solvent flow, fluorescent beads are added to the actomyosin solution. The beads are passivated to reduce the interaction between the moving beads and the actomyosin network. Overall, 1 μL of beads (Table of Materials) is incubated with 5 µm G-actin for 20 min at room temperature, and excess G-actin is removed by centrifugation (Table of Materials, see the protocol section for details). This step is repeated with 10 mg·mL^-1 BSA (Table of Materials). The beads are added to the protein solution at a final dilution of 1:10,000 v/v. Since the aim is to allow the beads to move freely across the gel pore, it is important to adapt the beads' diameters to the gel pore size, such that their size ratio is always <<1. As such, 2,300 nm diameter beads are used to analyze the initial and intermediate stages of contraction (Figure 5A,B) when the average pore size is larger than 15 µm, and 200 nm diameter beads are used when the pore size is smaller (Figure 5D-G). The beads' center-of-mass position is extracted for each time, t, (x(t),y(t))_bead, using a standard particle tracking algorithm (Table of Materials), from which the trajectory (Figure 5B) and local bead velocity, , can be deduced. The beads, and, thus, the penetrating solvent, move on average in the outward radial direction (Figure 5A,B), while the gel contracts inward, as shown from particle image velocimetry (PIV) analysis (see the green arrows in Figure 6A). This radial motion can be further elaborated by extracting the local beads' radial velocity, ν_r, which is evaluated by projecting the local bead velocity onto the radial direction defined by the unity vector, , connecting the gel center (x₀, y₀) and the bead center-of-mass position at time t:  where

The data show that as the beads move outward from the gel center, their velocities initially increase, and they then slow down as they approach the gel boundary (Figure 5C). Notably, the bead velocity can be 20 times greater than the gel radial contraction velocity (blue curve in Figure 5C). The filled circles mark the time the beads leave the gel. The beads continue to move after exiting the gel boundary for some time. This movement cannot result from inertial effects, since the Reynold number is <10^-4. The radial bead velocity decreases with time concomitant with the decrease in gel contraction; notably, when the gel radial contraction velocity has significantly decreased, the velocity of the beads fluctuates significantly.

To test if these fluctuations result from the porous structure of the actomyosin, the network tracks the motion of the beads at a higher spatial resolution, which is possible when the contraction of the gel has significantly slowed down (Figure 5D-F). The trajectory of the beads is indeed tortuous (Figure 5D,E), with significant fluctuations in the beads' local velocity, which reflects the porous structure of the gel-that is, the local velocity is fastest close to the pore center and slowest in the vicinity of an actin bundle (Figure 5F).

Finally, calculating the gel velocity-solvent velocity correlation function demonstrates that locally the fluid flow is directed opposite to the contracting gel. Using local bright spots in the gel as fiducial markers, their center-of-mass position for each time point, t, (x(t),y(t))_gel, can be calculated, and the local gel velocity can be derived: . Then, for each bead and a nearby point in the gel, the local bead velocity-gel velocity pair correlation is calculated to extract the angle, θ, between the two vectors: , where  and  are the local speeds (magnitude) of the bead and the gel, respectively. The data show that independent of the position of the bead within the gel pore, locally, the fluid flow is directed in the opposite direction with respect to the gel (Figure 5G). Overall, the results show that an outward fluid flow is generated by myosin contractility, as expected for a poroelastic active material^3,7,23,30.

Aim (iii)

This aim involves demonstrating that stress relaxation is characterized by an effective poroelastic diffusion constant, D, which depends on the network elastic modulus, porosity, and solvent viscosity. First, the lateral (in-plane) velocity of the contracting gel is quantified (Figure 6A). Firstly, the fluorescence images are binarized, and the gel projected area at each time point t, A(t), is extracted. Then, the gel radius is calculated,  (Figure 6B). From this, the radial contraction velocity at time point t, , is derived which describes the gel edge velocity (Figure 6C). The edge velocity shows a typical temporal evolution profile characterized by an initial linear phase, in which the edge velocity increases at a constant rate, , until a maximal velocity, ν_max, is reached at time t_max. The velocity then decays exponentially with a characteristic relaxation time, τ, until a mechanically stable state is reached (Figure 6C). The r_max is the gel radius at the beginning of that relaxation phase.

For a poroelastic material, the relaxation time , where  is an effective poroelastic diffusion constant, κ is an effective elastic gel modulus, and γ is an effective friction constant that accounts for the movement of the aqueous solution through the actin gel pores. The elastic modulus has units of energy per unit volume and is inversely proportional to the volume of a unit cell in the gel, determined by the distance between crosslinks or the mesh size, such that . The friction coefficient, γ, depends on the pore facet perpendicular to the solvent flow. For in-plane gel contraction, the relevant pore facet is , and, consequently, the friction coefficient , where η is the solvent viscosity^31,32. Overall, we obtain the following relation: , where the relevant in-plane pore size  is evaluated at t_max. Altogether, we obtain , which infers that the relaxation time should scale linearly with solvent viscosity²³.

To test if this relation is obeyed, the experiments are repeated with different amounts of glycerol. The use of glycerol is advantageous as it is not expected to affect the activity of proteins, particularly the myosin motors. Moreover, correlations between the viscosity of water-glycerol solutions and the amount of added glycerol are available in the literature²⁸. These correlations show that an increase in glycerol weight percent from 0% to 34% leads to a proportional increase in water-glycerol solution viscosity from η_ω to 2.76η_ω, where η_ω is the water viscosity at 20 °C. In this glycerol range and for the same initial drop diameter, 2R = 2,800 µm, an increase in viscosity increases the duration of the network polymerization and self-organization phases, though the linear acceleration and maximal radial contraction velocity (ν_max) are grossly unchanged. This evidence suggests that both network reorganization (porosity) and myosin activity are unaffected by the solution viscosity²³, and the effect of solvent viscosity should be essentially reflected in the time it takes for the elastic stresses to relax. Indeed, the relaxation time shows a linear dependence on the solution viscosity (Figure 6D), which infers that the scaling relation derived above is obeyed, further confirming the poroelastic nature of the system.

Figure 1: Schematic description of the three main steps of the glass coverslip surface treatment procedure. (i) Glass surface cleaning (Piranha treatment) and hydrophilization, (ii) surface silanization, and (iii) passivation with mPEG-mal. Please click here to view a larger version of this figure.

Figure 2: Glass coverslip passivation. (A) Piranha cleaning and silanization are performed in a 400 mL beaker using a homemade polytetrafluoroethylene holder consisting of 12 linear grooves. (B) Surface passivation is performed in a parafilm-coated Petri dish. Each coverslip is incubated with 1 mL of 5 kDa mPEG-mal at 4mg·mL⁻¹ in 1x PBS (Table of Materials) for 1 h at 22 °C. The hydrophobic parafilm layer assures that the hydrophilic PEG polymer solution remains confined to the glass surface throughout the incubation time. Please click here to view a larger version of this figure.

Figure 3: Running an experiment-the homemade sample holder. Experiments are run in a homemade sample holder that fits the dimensions of a standard microscope stage. (A) A greased parafilm spacer of thickness h (~150 µm) is placed on a PEG-passivated coverslip, and that coverslip is placed in the sample holder. (B) The actomyosin solution is prepared on ice in an Eppendorf tube, and 1.1 µL of that solution is placed on the coverslip; then (C) a second PEG-passivated coverslip is placed on top of it, and (D) the sample holder is screwed to confine the drop, which adopts a disc-like shape. Please click here to view a larger version of this figure.

Figure 4: Poroelasticity aim (i). The actomyosin network behaves as an elastic material. (A) Schematic representation of an actomyosin network. (B) Actomyosin network formation. Fluorescence microscopy images demonstrate that the actin filaments spontaneously nucleate and polymerize into an isotropic interconnected network that coarsens with time and eventually contracts macroscopically. The porosity of the network is characterized by the network mesh size, ξ (double arrow). (C-E) Actomyosin network contraction is driven by actin filament bundle sliding. (C) Network contraction initiates at the gel periphery ("P") and propagates inward into the gel bulk. The white arrows show the direction of contraction. The gel center is marked with a "C". The fluorescent images show that the myosin motor aggregates (561 nm, red dots) are embedded in the actin network (488 nm, green) and remain attached to it throughout network contraction. (D) The actin filament bundles remain straight during network contraction. The ratio of the contour length, l_cont, and end-to-end distance, l_end-to-end, as a function of time. (E) Distribution of the ratio between the contour length and the end-to-end distance at t = 316 s (solid red) and t = 327 s (striped, gray). Inset: contour length (blue) and end-to-end distance (white) of a typical bundle. Conditions: (B,C,E[inset]): Images are acquired on an inverted fluorescent microscope with an EMCCD camera and a 10x/0.3 Ph1 UPlanFL air objective in regular mode (B) and in dual imaging mode after image overlay (C,E[inset]). Scale bars are (B,C) 100 µm and (E[inset]) 50 µm. This figure has been reproduced with permission from Ideses et al.²³. Please click here to view a larger version of this figure.

Figure 5: Poroelasticity aim (ii). An outward solvent flow is generated by myosin motor contractility. (A) Imaging the gel at a low magnification at intermediate stages of contraction: simultaneous fluorescence imaging of a contracting actin network (488 nm, left) and 2,300 nm fluorescent beads added to the solution (561 nm, right) as a function of time. The circles mark the positions of four beads. The arrows mark the global direction of the bead motion. (B) The trajectories of nine selected beads are depicted. The arrows mark the global radial direction of the beads' movement. The encircled cross denotes the gel center (x0,y0) (C) Local radial bead velocity ν_r (open circles) and (radial) gel edge velocity (blue dots) versus time. The filled circles indicate the time a given bead exits the gel boundary. (D-F) Resolving the network porosity and the movement of the solvent across the gel pores at advanced stages of contraction. (D) Epifluorescence images of the contracting gel and 200 nm diameter fluorescent beads added to the solution. Both the actin and beads are excited at 488 nm. The red circles follow the position of a bead with time. The gray line indicates the gel boundary. (E) Trajectory of the bead shown in (D). In the field shown, the gel contracts on average toward to bottom. The coordinates are measured relative to the origin of the camera. (F) The bead's local velocity reflects the porous structure of the gel. Top: Local bead speed (open circles), local gel speed (grey circles), and gel edge speed (blue circles) versus time. Bottom: Snapshots show the position of the bead for selected times. The bead is marked by a red circle. The dashed line marks the time the bead exits the gel. (G) Distribution of angles between the local gel and local bead velocities. Conditions: Images are acquired on an inverted fluorescent microscope with an EMCCD camera and (A) a 2.5x/0.075 Plan-NEOFLUAR objective and (D,F) a 10x/0.3 Ph1 UPlanFL objective. The scale bars are (A) 400 µm, (D) 100 µm, (F) and 50 µm. This figure has been reproduced with permission from Ideses et al.²³. Please click here to view a larger version of this figure.

Figure 6: Poroelasticity aim (iii). stress relaxation is characterized by an effective poroelastic diffusion constant. (A) Top view fluorescence images of a contracting actomyosin gel at low magnification from the mixing time up to the steady state. The velocity field (green arrows) is extracted from the PIV analysis. The images are acquired on an inverted fluorescent microscope with an EMCCD camera and a 2.5x/0.075 Plan-NEOFLUAR objective. The excitation wavelength is 488 nm (actin). The scale bar is 500 µm. (B) Gel radius and (C) radial contraction velocity,  (i.e., the gel edge velocity versus time). a denotes the acceleration, v_max denotes the maximal velocity, and τ is a characteristic relaxation time. (D) The actomyosin networks behave as a poroelastic active material.  and solvent viscosity, η, versus glycerol weight percent (wt%). The quantities are normalized to their values at 0 wt% glycerol. The gel's initial radius is R = 1,400 µm. The error bars are the standard deviations of the experimental values. This figure has been reproduced with permission from Ideses et al.²³. Please click here to view a larger version of this figure.

Discussion

Here, an in vitro approach is employed to characterize the mechanics of poroelastic actomyosin gels as a model system of the cell cytoskeleton and, more generally, of the cell cytoplasm, which has been shown to behave as a poroelastic material^3,5. The rheology of the cell cytoskeleton (cytoplasm) has been characterized by a poroelastic diffusion constant, which dictates how long it takes for the intracellular cytosolic fluid to redistribute within the cell following applied mechanical stress. Cells have been proposed to use this mechanism to regulate their shape⁵.

Motivated by these findings, we have developed a framework to study poroelasticity in vitro. Using the proposed model system, we provide insights into how myosin contractility contributes to the emergence of a fluid flow and how network velocity and solvent velocity directionality and speed correlate in time and space. Through this, we demonstrate that the network and embedded solvent are interconnected and cannot be considered separate objects. We describe the experimental setup and provide a detailed protocol for preparing the gels and running an experiment. A detailed framework for data quantification is also presented. The proposed framework can be easily adapted to study poroelasticity in a variety of experimental setups and systems, regardless of the specificity of the experimental system investigated.

We validate the poroelasticity of the actomyosin networks by analyzing the changes in the time scale of stress relaxation. We choose to demonstrate this by varying the viscosity of the medium by adding various amounts of glycerol to the actomyosin solution. The advantage of using glycerol is that it does not affect the porosity and structure of the networks, and, thus, the sole effect on stress relaxation is the increase in friction between the moving solution and the gel pores²³. Changes in network porosity would have engendered an additional complication, as both the elastic modulus and network pore size influence the relaxation time in a non-linear manner^23,31,32.

Running successful experiments requires the passivation of the glass coverslips with an inert polymer. This step is crucial. The procedure employed here for glass passivation can be replaced with other procedures if the quality of the passivation is preserved^33,34. Defective surface passivation can give rise to massive protein adhesion, which can inhibit network assembly. Glass passivation is also important to prevent the interaction of the contracting gel with the glass surfaces. This would lead to an additional friction term, in addition to the fluid-gel friction considered here, which would be much more difficult to estimate or quantify. Aside from surface passivation, successful experiments require the use of fresh actin. Moreover, the activity of the motors is also crucial, and the preparation of fresh batches of myosin should be repeated every 3-4 months.

Overall, this experimental approach has been shown to be successful for studying poroelasticity in vitro. A limitation of the currently employed experimental procedure is how to control the initial gel dimensions more robustly. One option would be to use preformed chambers of controllable dimensions. The use of preformed chambers would also allow not only the researcher to better control the system size but also to easily change the geometry of the system.

Materials

Name	Company	Catalog Number	Comments
(3-Mercaptopropyl)trimethoxysilane	Sigma-Aldrich Company	175617	Stored under Argon atmosphere at 4 °C
Acetic acid	Bio-Lab ltd	1070521
Alexa-Fluor 488	Invitrogene	A10254	Diluted with DMSO, stored under Argon atmosphere at -20 °C
Alexa-Fluor 647	Invitrogene	A20347	Diluted with DMSO, stored under Argon atmosphere at -20 °C
BSA	Sigma -Aldrich Company	A3059	Stored at 4 °C
Catalase	Sigma -Aldrich Company	C9322	The stock bottle is kept under dry atmosphere (silica gel) at -20 °C
Coverslips	Mezel-glaser	CG2222-1.5	Kept in milliQ-water after the Piranha treatment and used within 3 weeks
Creatine kinase	Roche Life Science Products	10736988001	Prepared fresh in glycine buffer, kep on ice, and used within 3 days.  The stock bottle is kept under dry atmosphere (silica gel) at 4 °C
Creatine phosphate	Roche Life Science Products	10621714001	When dissolved should be kept at -20 °C and used within 3 months. The stock bottle is kept under Argon atmosphere and stored at 4 °C
DTT	Roche Life Science Products	10708984001	When dissolved should be kept at -20 °C and used within 3 months
Dual view Simultaneous Imaging System	Photometrics	DV2-CUBE
EGTA	MP Biomedicals	195174
EM-CCD Camera	Andor Technology Ltd	DV 887
EM-CCD Camera	Photometrics	Evolve Delta
Ethanol	Bio-Lab ltd	525050300
Flourescence Lamp	Rapp Optoelectronic
Fluoresbrite YG Microspheres	Polysciences	17151-10	200 nm diameter
Glucose	ICN Biomedicals Inc	194024	When dissolved should be kept at -20 °C and used within 3 months.
Glucose oxidase	Sigma-Aldrich Company	G7141	Kept in -20 °C and used within 3 months. The stock powder is kept under Argon atmosphere and kept at -20 °C
Glycerol	ICN Biomedicals Inc	800687
Glycine	MP Biomedicals	808822
Hydrogen Peroxide	Sigma-Aldrich Company	216763	Stored at 4 °C
KCl	EMD Millipore Corp.	529552
Methanol	Bio-Lab ltd	1368052100
MgCl2	EMD Millipore Corp.	442615
Microscope	Leica Microsystems	DMI3000
mPEG-mal	Nanocs	PG1-ML-5k	Mw = 5000 Da. Divided to small batches by weight. Stored under Argon atmosphere at -20 °C
Nile red microspheres	Spherotech	FP-2056-2	2300 nm diameter
Objective (10x)	Leica Germany	HC PL AP0	UPlanFL Numerical Aperture = 0.3
Objective (2.5x)	Leica Germany	506304	Plan-NEOFLUAR Numerical Aperture = 0.075
Oven	WTC Binder
Parafilm	Amcor	PM-996
PBS Buffer	Sigma-Aldrich Company	P4417
Shutter Driver	Vincet Associates	VMM D1
Silica gel	Merck	1.01907.5000
Sonicator	Elma	Elmasonic P
Sulfuric acid	Carlo Erba reagents	410301
DV2 Dual-Channel Simultaneous-Imaging System	Photometrics
TRIS	MP Biomedicals	819620
UV-VIS Spectrophotometer	Pharmacia	Ultraspec 2100 pro
MICROMAN E	Gilson	FD10001	1–10 uL
MATLAB R2017b	MathWorks		Data quantification
MetaMorph	Molecular devices		Control software of the optical imaging system; data quantification (particle tracking analysis, network mesh size)