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).

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<...

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 ce...

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)