Article Cite This: Macromolecules XXXX, XXX, XXX−XXX
Study of Biomechanical Properties of Protein-Based Hydrogels Using Force-Clamp Rheometry Luai R. Khoury, Joel Nowitzke, Kirill Shmilovich, and Ionel Popa* Department of Physics, University of WisconsinMilwaukee, 3135 North Maryland Ave., Milwaukee, Wisconsin 53211, United States S Supporting Information *
ABSTRACT: Protein-based hydrogels are unique materials that combine the durability and wetting properties of polymeric hydrogels with the biocompatibility and elasticity of proteins. Additionally, protein hydrogels present a promising system to probe the mechanical unfolding and refolding of proteins in an ensemble approach. Current rheometry methods apply tensile deformation under constant elongation while tethered materials experience changes in length and tension due to viscoelastic effects. These approaches limit the pulling speed in stressrelaxation experiments and the ability to extract information on the molecular behavior of proteins within hydrogels. Here we introduce a force-clamp (FC) hydrogel rheometer that can measure the extension of protein hydrogels at controlled setpoint forces. We demonstrate this system using protein hydrogels made of bovine serum albumin (BSA), polymerized via a photoactivated reaction. We measure the mechanical response of these hydrogels by maintaining a setforce using an analog proportional−integral−differential (PID) system. We investigate how protein concentration and solution conditions affect the mechanical properties of protein-based hydrogels in two modes: constant force mode where the hydrogel is exposed to constant pulling and relaxation forces and force ramp mode where the applied stress is linearly increased and decreased. Our measurements suggest that BSA molecules under force inside hydrogels behave similar to a Hoberman sphere. This exciting new method enables new experiments to study the effect of mechanical unfolding through a bulk approach and will pioneer the discovery and characterization of new superelastic biomaterials.
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INTRODUCTION
Several milestones toward this endeavor have been already achieved. Structural proteins such as collagen, elastin, fibrin, and silk have been formulated into hydrogels that can mimic the mechanics of the extracellular environment and become cell scaffolds.7−10 Protein hydrogels made from identical or different engineered polyprotein domains may mimic some mechanical properties of muscles.11,12 However, engineered microtissues do not currently fully recapitulate native tissue elasticity.13 Protein-based materials have a qualitatively similar biomechanical response to force as single molecules measured with force spectroscopy techniques. For example, when exposed to chemical denaturants,11,12 protein-based hydrogels show a reversible softening effect, in agreement with the measured decrease in the mechanical stability of single proteins.14,15 When exposed to changing reducing/oxidizing conditions, the elasticity of protein hydrogels can also be regulated in a reversible manner,16,17 as formation and breaking of covalent bonds inside a protein structure leads to a proportional change in the measured contour length.18
Proteins represent a promising raw resource for biomimetic materials that can display better biocompatibility and a larger elasticity range than polymers. As the essential building blocks for tissues and organs, protein domains are folded into threedimensional structures and transition between folded and unfolded conformations in response to local chemical and mechanical perturbations. The folding transition has several major implications on the nanomechanics of proteins. First, unfolding leads to a release of the amino acids trapped inside the protein fold, and an increase in contour length triggers an immediate decrease in the experienced force at the molecular level.1 Second, connected folded domains are ∼10 times stiffer than an unfolded polypeptide chain.2 Third, (un)folding represents an efficient mechanism of storing and releasing energy that a simple polymeric molecule would lack, as the decrease in the entropic energy due to folding and reduced number of possible conformations is significantly offset by the local interactions within the protein structure, such as hydrogen bonds.3,4 Hence, developing and characterizing macroscopic materials based on proteins is a highly desirable endeavor that may lead to new applications for cartilage replacement, tissue, or skin engineering.5,6 © XXXX American Chemical Society
Received: October 6, 2017 Revised: January 13, 2018
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DOI: 10.1021/acs.macromol.7b02160 Macromolecules XXXX, XXX, XXX−XXX
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hydrogels over a large range of cross-linking concentrations and in various solution conditions.
A milestone that has yet to be achieved is a method to scale down the measured elasticity of hydrogels to the response to force of single proteins. This scaling down would greatly increase the statistics of experiments that investigate the mechanics of proteins and would enable significantly faster measurements when compared to current single molecule techniques, such as atomic force microscopy (AFM), optical, and magnetic tweezers. These single molecule techniques can operate in force-clamp (FC) mode when coupled with an active feedback system to apply pico- to nanonewtons of force to molecules.19,20 Instrumentation was developed for muscle physiology studies to expose single muscle fibers to constant forces in the micronewton range and on the millisecond timescale21,22 or to constant length conditions.23−25 Nevertheless, these custom-made instruments are not adapted to the force range and large extensions that are characteristic for slowoccurring viscoelastic properties typical to polymer and protein hydrogels and can operate in force clamp for short times (few hundreds of microliters) and works for materials above a certain stiffness (usually with Young’s modulus >10 kPa26). These are important limitations for protein hydrogels. Concentrations of hundreds mg/mL are required for gelation, and some hard-toexpress or less stable proteins might not reach this concentration range.11,29 In addition, the majority of protein hydrogels are too soft to be measured with DMA in extension mode due to noncontrollable creeping deformation upon contact with the sample holder.27,30,31 Current experimental methods working with protein hydrogels rely on the more standard shear rheometer, where protein domains inside hydrogels would unfold due to compression forces.32,33 While still mechanical in nature, this approach cannot simulate the pulling effects that drives protein unfolding in vivo. Other approaches based on extension rheometry can apply mechanical force to protein hydrogel in a length-controlled manner (length clamp).11,28,29,34−36 In this case, a hydrogel is extended at one end, and the experienced force is measured at the opposite end. As protein domains unfold and extend inside the hydrogel material, the experienced force decreases as the gel lengthens. This continuous change in force and length with time makes data interpretation extremely cumbersome37 and is a major roadblock in decoupling effects from protein folding with the elasticity of the gel network. Here, we introduce a new force-clamp rheometric technique where hydrogels can be exposed to a pulling force protocol, which readily separates force, length, and time. We demonstrate this system using protein hydrogels made from bovine serum albumin (BSA) in two experimental modes: force ramp and constant force. This new approach is a critical step toward establishing easier and reliable bulk approaches to investigate the nanomechanics of proteins and to reproduce the crowded protein environment that gives tissues their macromechanical properties. This approach utilizes small sample volumes of proteins (∼5 μL per measurement), small chamber volumes (∼200 μL), an analog PID approach that can maintain forceclamp conditions on a minutes-to-hours timescale and allows attachment of soft samples without slipping. As detailed below, this technological advancement allows the study of protein
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EXPERIMENTAL SECTION
Force Sensor Calibration. The forces generated by hydrogel samples were recorded and converted to millinewtons using a SIKG4A force transducer (World Precision Instruments (WPI)) with a custom-made hook. The voltage signal was then amplified by a BAM21-LC amplifier (WPI). To convert the signals from voltages to newtons, the sensor was aligned parallel to the direction of gravitational acceleration, and five different weights were used for calibration. Protein-Based Hydrogel Synthesis and Attachment. Fresh bovine serum albumin (BSA) solutions were prepared at each concentration (5, 4, 3, 2, 1.5, 1, and 0.7 mM) by dissolving BSA powder (66.5 kDa, purchased from Rocky Mountain Biologicals, Inc.) into Tris solution (20 and 150 mM NaCl, pH 7.4). Ammonium persulfate (APS) and tris(bipyridine)ruthenium(II) chloride ([Ru(bpy)3]2+) powder were both purchased from Sigma-Aldrich and prepared by dissolving APS and [Ru(bpy)3]2+ powder into Tris to a final concentration of 1 M and 6.67 mM, respectively. The BSA-based hydrogel was prepared as follows. A 23-gauge needle fixed on 1 mL syringe was inserted into one end of 10 cm PTFE tube (0.022 in inner diameter−0.044 in outer diameter, Cole-Parmer) with a pressed plunger. Tubes were passivated with Sigmacote (Sigma-Aldrich) for 5 min. BSA solution at the desired concentration was mixed with APS and [Ru(bpy)3]2+ at a volume ratio of 15:1:1. The photoactive reaction mixture was then centrifuged at maximum speed for 2 min to remove any bubbles from the solution before injection in the PTFE tube (Supporting Information Figure S3A). The loaded tube was then placed ∼10 cm away from a 100 W mercury lamp to prevent protein denaturation and irradiated for 30 min at room temperature. Afterward, the tube was removed from the needle, and a blunted 24-gauge needle was used to extrude the hydrogel into Tris solution (Figure S3B). The hydrogel was cut into ∼1 cm long pieces using a medical scissors and used directly in our measurements. All gels were synthesized in Tris buffer. During measurements in other buffers, such as GuHCl (6 M) and glycerol (50% v/v), the gel was allowed to equilibrate for 45 min. Protein-Based Hydrogel Attachment. The BSA-based hydrogel attachment process to the FC hydrogel rheometer was done as follows. We first cut sterile sutures (Pro Advantage by NDC) into two equal strands (3−4 cm) and tied a loose double overhand knot into each of them (Figure S5A). The two loops were then placed on the force sensor hook (Figure S5B). The experimental chamber was then filled with the Tris solution, and the protein hydrogel sample was transferred into the filled chamber using a medical tweezers. The voice coil and force sensor hook were placed close to the solution’s surface and aligned in all directions using X−Y−Z positioning manipulators. Both sides of the protein hydrogel were hung on the voice coil and force sensor hooks using a medical tweezers (Figure S6A). Afterward, one suture loop was tightened around the hydrogel sample by holding both suture loop ends with the medical tweezers and pulling them simultaneously (Figure S6B). The same procedure was done for the loop existing on the force sensor hook (Figure S6C). Both suture loops were position on the bend of each hook to prevent the sample from slipping during measurements, and the excess lengths of the sutures were cut (Figure S6D). The attached hydrogel was then moved slowly using X−Y−Z manipulators along the Z-axis toward the experimental chamber to immerse the hydrogel in the experimental solution. FC Tensile Protocols. Controlled Stress−Strain Curves for Different Concentrations of BSA-Based Hydrogels in Different Experimental Solutions. The hydrogel samples at different concentrations (1, 1.5, 2, 3, 4, and 5 mM) were cast and attached to the rheometer as described above. The samples were stretched/ relaxed at a controlled stress/relaxation rate of 0.01 mN/s at room temperature. The same hydrogel sample for each concentration was immersed and stretched/relaxed in five solutions in the following B
DOI: 10.1021/acs.macromol.7b02160 Macromolecules XXXX, XXX, XXX−XXX
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Figure 1. Design and assembly of FC hydrogel rheometer. (A) Rendering of the custom-made force-clamp hydrogel rheometer. Inset: tethered gel inside the fluid chamber. (B) Schematic drawing of the instrument; hydrogels are extended using a voice coil motor (left), and the experienced force is measured through the force sensor (right). A PID system continuously adjusts the voice coil position (and hydrogel extension) such that the measured force by the sensor matches the setpoint, sent from the computer through a D/A card. Inset: (i−iii) schematic drawing shows the voice coil tweezers movement and gel extension/contraction during a constant force pulse protocol. (C) Response of the PID loop as a function of integral gain. The dashed line displays the setpoint. Integral gain (I) is the main component that determines the response time of the loop. (D) Representative slack curve used to determine force sensor drift and zero-force gel length. Horizontal arrow indicates the direction of the movement of voice coil tweezers. First, the voice coil tweezers moves halfway backward and then moves all the way toward the force sensor (light blue arrow). (1−3) indicate the three situation of hydrogel sample during slack measurement. The plateau part when the gel is not under force is used to determine the real zero force, while the intersection between the fit lines measures the true gel length. order: Tris, 6 M guanidine hydrochloride (GuHCl/Tris), Tris, 50% glycerol/Tris (v/v%), and Tris. In each solution, the hydrogel sample was immersed for 45 min at room temperature, then controlled stress/ relaxation cycles were applied on the hydrogel three times in the same solution. After the measurements in 6 M GuHCl or 50% glycerol, the hydrogel was cleaned by immersing it in a Tris solution for 45 min and then moved to a fresh Tris solution for measurements, to prevent any lasting effect from previous solutions. Each curve represents the average of three traces. Relationship between Young’s Modulus, Energy Dissipation, and BSA-Based Hydrogel Concentrations. For measurements describing the relationship between Young’s modulus and different BSA-based hydrogel concentrations, three BSA-based hydrogels were cast from three separate preparations of BSA solutions for each concentration (0.7, 1, 1.5, 2, 3, 4, and 5 mM). The hydrogels were attached, and controlled stress/relaxation cycles at a rate of 0.01 mN/s were applied to the sample in Tris solution at room temperature. The Young’s modulus was calculated as the slope at 20% strain on the stress/relaxation curves for each concentration. In energy dissipation measurements, three BSA-based hydrogels were cast from three separate BSA solutions for each concentration (1, 1.5, 2, 3, 4, and 5 mM) and stretched to a maximum force of 1 mN. The hydrogels were attached and subjected to controlled stress/relaxation cycles with the same rate of 0.01 mN/s in a Tris solution at room temperature. The energy dissipation was calculated as the area enclosed by each stress/relaxation cycle. The average and standard deviation of each of the three different measurements were presented. Characterization of BSA-Based Hydrogel Behavior under Different Constant Forces. A 2 mM BSA-based hydrogel was cast
and attached as described before. A constant force protocol was applied on the hydrogel sample in Tris at room temperature. Each constant force protocol is divided into three sections as follows. First, a 0.1 mN force is applied on the hydrogel sample for 30 s for all traces, second the force increased to 0.6 - 2.4 mN for 120 s, and third a force of 0.1 mN was applied for 300 s for all traces. Each protocol was repeated three times. Each curve represents the average of three different traces. Characterization of BSA-Based Hydrogel Behavior under a Constant Force in Different Experimental Solutions. A 2 mM BSA-based hydrogel is cast and attached as described before, and a constant force protocol was applied on the hydrogel as describe above with a 0.8 mN force being applied in second section. The constant force protocol was applied on the same hydrogel in three different solutions in the following order: Tris, GuHCl 6M, Tris, and 50% glycerol in Tris. The hydrogel sample was immersed in GuHCl solution for 45 min and then measured with the same constant force protocol. After the GuHCl solution, the same hydrogel sample was immersed in Tris for 45 min to wash out the GuHCl and allow the BSA to refold. The hydrogel was then moved to fresh a Tris solution and continued measurements. Each curve represents the average of three different traces. Fluorescence Measurements of BSA Folding and Unfolding inside Hydrogels. To prove domain folding and unfolding inside BSA-based hydrogels, 1 mM BSA solutions and hydrogels made with 1 mM BSA were immersed in solutions with various GuHCl concentrations (0−6 M), in the presence of 6.25 μM 8-anilino-1naphthalenesulfonate (ANS, from Cyman Chemical). Following 30 min incubation, the samples were analyzed visually under UV light, or C
DOI: 10.1021/acs.macromol.7b02160 Macromolecules XXXX, XXX, XXX−XXX
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Figure 2. Force-ramp traces of BSA hydrogels. The stress−strain curves were obtained using of BSA-based hydrogel of various concentrations (between 1 and 5 mM) and ramping the force up and down between 0 and 1 mN, at 0.01 mN/s. The feedback loop maintains the force at the changing setpoint and compensates for any changes in strain due to time-dependent viscoelastic effects. Each gel was measured in Tris, GuHCl 6 M (green), Tris, glycerol 50% v/v (blue), and Tris again. using a Syngene G-Box imaging system, with appropriate UV filters. Gel fluorescence was quantified in Igor Pro (Wavemetrics) using line profile analysis with a pixel width of 5.0, along the largest continuous strand of hydrogel, at each concentration. The extracted averages and standard deviations of BSA hydrogel intensity profiles were then normalized at 0 M GuHCl. Swelling Ratio Measurements. For swelling ratio experiment, triplicates of BSA-based hydrogels at different concentration (1−5 mM) were synthesized as described previously. Then, hydrogels were soaked in Tris solution (20 and 150 mM NaCl, pH 7.4) at 4 °C for 24 h. Thereafter, the hydrogels were removed from the solution; excess buffer was blotted using filter paper and then weighed to obtain the wet weight (Wwet). Then, the same hydrogels were dried using desiccator for 24 h, the hydrogels were weighed, and the dry weight Wdry was obtained. The swelling ratio was calculated using the following equation (Wwet − Wdry)/Wdry × 100. Differential Scanning Calorimetry (DSC) Measurements. The DSC experiments were performed by using TA Instruments Q10, and the technique was used to characterize the thermal properties of BSA protein in free and cross-linked hydrogel conditions. For the first condition, a specific amount of 2 mM BSA-based hydrogels solution mixture was loaded into sample cell (∼10 μL). Then, the samples were capped and sealed using a press. For BSA protein in cross-linked hydrogel condition, the same amount of 2 mM BSA-based hydrogels solution mixture was loaded into the sample cell and placed 10 cm away from the 100 W mercury lamp and irradiated for 30 min at room temperature; then the samples were capped and sealed. An empty capped and sealed cell was used as a reference cell. The cells were equilibrated and stabilized at 25 °C and then heated up to 120 °C with a heating rate of 5 °C/min. Tests were performed in duplicates for each condition.
range of ∼9 mm with a velocity of ∼0.7 m/s and has its own internal feedback mechanism that reads the actual coil position with 150 nm resolution.29,38 To measure the force experienced by the attached biomaterial, we use a force sensor developed for muscle physiology (SI-KG4A from WPI or 403A from Aurora Scientific). The force sensor has its own specific spring constant and response time. WPI has an average response time of 35 ms, while the force sensor from Aurora showed a better response of 5 ms (Figure 1C and Figure S1) but was generally more difficult to work with. The force sensor and voice coil are connected through an analog proportional−integral−differential (PID) system (from Stanford Research Systems), which can continuously adjust the position of the coil to minimize the error between the setpoint from the computer and the measured force, from the force sensor. Protein hydrogels made from bovine serum albumin (BSA) were synthesized following a photoactivated reaction11 and cast into a cylindrical shape using Teflon tubes29 (see Experimental Section for details). Following visual inspection for defects with an optical microscope, the hydrogels were attached to the tethering hooks using surgical sutures (nylon monofilament size 6, Fisher Scientific) and immersed in one of the six chambers from the six-chamber wheel (Figure 1A). The gel was then straightened using the micropositioners for the coil and sensor. To minimize errors due to electronic drift of the force sensor and to measure accurately the gel length, a slack curve was performed before each measurement (Figure 1D). During the slack measurement, the coil is set to a position which exposes the gel to a low force and is moved linearly toward the force sensor. Two distinct linear regimes are measured: one where the gel contracts under force and one where the gel becomes slack and the effective force is zero. The second part of the slack curve is a direct measurement of any electronic drift of the force sensor and is used as an offset in the setpoint command during repeated measurements (F0). The intersection between the
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RESULTS Approach. Any force spectroscopy technique relies on an element that can apply force and one that can measure the effect that the applied force has on the investigated system. As shown in Figure 1, to apply force we use a voice coil system (LFA-2010 from Equipment Solutions), which can move over a D
DOI: 10.1021/acs.macromol.7b02160 Macromolecules XXXX, XXX, XXX−XXX
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Figure 3. Relationship between Young’s modulus, energy dissipation, and protein concentration in BSA hydrogel from force-ramp measurements. (A) Stress−strain curves of BSA hydrogel at different concentration in Tris solution. (B) Young’s moduli of BSA hydrogels versus its concentration in Tris, GuHCl 6 M, and glycerol 50%. The lines represent fits obtained using the points up to 3 mM (before the saturation of BSA) and assuming a dependency on the concentration to the power of 2/3. (C) Relationship between BSA concentration and energy dissipated of BSA hydrogels. The energy dissipation was calculated from the hysteresis area enclosed in the stress−strain curves (marked with gray in part A for one trace). (D) Change in the dissipation energy as a function of cycle number. Low concentration hydrogels show larger hysteresis in the first cycle. The error bars are SD calculated from three trials.
linear fits of the two regimes is used to determine the coil position where the gel is fully oriented to the pulling coordinate. This intersection effectively gives the initial gel length l0 with micrometer resolution. As the protein domains might not fully refold during individual cycles, or might mechanically age,39 the slack curve can also track slow elongation effects in the initial gel length. Force-Ramp Measurements of Protein Hydrogels. In force-ramp measurements, the force is linearly increased and decreased with time. Unlike the regularly used length clamp approach, the PID adjusts the coil position to compensate for both the elastic and viscoelastic effects that protein hydrogels have. The feedback loop allows the application low loading rates, as the viscoelastic effects would lead to a nonlinear change in force. These low loading rates resemble the types of perturbations that hydrogels experience when used in a biomedical application.40 Indeed, unless otherwise specified, we used loading rates of 0.01 mN/s (Figures 2 and 3). We synthesized BSA-based hydrogels at different concentrations (1−5 mM), and we measured their mechanical properties in three solution conditions (Figure 2). When BSA-based hydrogels are tested in Tris (20 mM Tris, 150 mM NaCl, pH 7.4), they showed an impressive elasticity and toughness at low forces compared with globular and multidomain proteins, reported in previous studies.11,12,34 In addition, it is obvious that the mechanical behavior of BSA-based hydrogels differs from other protein-based hydrogels, emphasizing the impor-
tance of protein structure and number of domains in determining the mechanical properties of hydrogels.12,41 Furthermore, from the force-ramp cycles, we can see a significant hysteresis at different hydrogel concentrations. This hysteresis indicates unfolding of the BSA domains, but may also be attributed to other viscoelastic effects, that are reversible (such as intermolecular friction) or irreversible (breaking of weak noncovalent bonds).11,12,41 The force-ramp approach can be also used to investigate how hydrogel elasticity changes with protein concentration and solution conditions. As the protein concentration increases, we measure a stiffening of the hydrogel (Figures 2 and 3A) as well as an increase in the breaking force (data not shown). This increase may be seen through a decrease in force per molecule with increasing concertation and is further rationalized though the Young’s modulus (Figure 3). The Young’s modulus was measured from the linear part of the stress vs strain curves during force increase and represents an effective elastic constant for the hydrogels. It is well-known that proteins unfold in the presence of chemical denaturants such as guanidinium chloride (GuHCl)14,42 and become more stable in the presence of osmolytes, such as glycerol.37,43,44 To understand the reason for hysteresis in BSA-based hydrogel, we exposed the same hydrogel to both these solution environments and measured their mechanical response. In GuHCl 6 M, BSA hydrogels become softer, while glycerol makes gels stiffer. More importantly, in the presence of chemical denaturants, BSA E
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Interestingly, this plateau correlates with the measured Young’s modulus plateau and indicates that a constant cross-linking density is reached. Finally, force-ramp measurements are used to determine the potential energy storage and dissipation during the extension and recoil of the protein hydrogels. This energy is directly determined from the area enclosed by each stress-relaxing curve. When BSA hydrogels are exposed to force ramp cycles up to 1 mN with a loading rate of 0.01 mN/s, the energy difference between extension and recoil varies with concentration from 0.4 to 0.1 kJ/m3 (Figure 3C). Force is expected to have a direct effect on both the extension of folded domains and unfolded polypeptide chains as well as on the unfolding probability. Hence, a decrease in the stored energy with increasing concentration can also be rationalized by considering the decrease in force per molecule with BSA concentration. Similar hysteresis curves are measured in the presence of 50% glycerol, but not in the presence of GuHCl 6 M (Figure 2). As GuHCl is known to chemically denature protein domains, this observation suggests that the hysteresis is an effect of the mechanical unfolding and refolding of protein domains. Glycerol is known to increase the mechanical stability of proteins, and for the same ramp pulse it is expected that less protein domains will unfold, leading to smaller energy dissipations.37,43 Constant Force Measurements of Protein Hydrogels. The force-clamp rheometer excels over other approaches when operated in constant force mode. In this mode, the change in extension over time arising from viscoelastic effects can be decoupled from the change in force over time. In a typical measurement, an initial 30 s low force pulse (0.1 mN) establishes the measurement baseline (Figure 4). A constant extension in the initial force pulse is indicative of the fact that the force is indeed low enough not to unfold proteins but also that there is no instrumental drift. We then apply a high constant force for 120 s. In the high-force part of the pulse, BSA hydrogels in Tris show a fast elastic strain due to the change in force, followed by a slow extension (Figure 4A). At constant force, the strain increases as a function of time to compensate for viscoelastic extension. We then allow the hydrogel to recover its initial length by exposing it to a second low-force pulse for 300 s. The time for the final low force pulse was
hydrogels do not show any significant hysteresis in the stress vs strain curves. Their mechanical behavior is similar to elastic rodlike polymer hydrogels and to (FL)X protein hydrogels when soaked in GuHCl solution.12,28,45 Introducing the hydrogel back in the Tris solution results in a recovery of the initial behavior, suggesting BSA refolding. The results from force-ramp measurements on protein hydrogels are summarized in Figure 3, which examines the effect of protein concentration on mechanical properties of hydrogel over a wide range of concentrations (1−5 mM). As shown in Figure 3A, the stress and strain have a linear dependency as the gels are extended up to 20%, independent of the concentration. This linear part of the stress vs strain curves during the force increase is used to determine the Young’s modulus in this region, which is a direct measurement of the elasticity of the hydrogels (Figure 3B). Increasing the concentration of BSA increases its Young’s modulus from 2.6 to 16 kPa and decreases the overall gel extensibility. Similar values for the Young’s modulus were reported for BSA hydrogels.41,46 However, the disappearance of hysteresis in GuHCl seen in our measurements (Figure 2, green traces) contradicts previous measurements from ref 41, where the opposite effect was seen. The fact that the hysteresis is recovered when the gels are immersed back in Tris is a strong indication that our formulation renders completely cross-linked hydrogels. This behavior reflects the fact that increasing BSA concentration leads to an increased distribution of the applied stress to more molecules, effectively decreasing the force per molecule. The fits represent the variation of the Young’s modulus with the cross-section concentration, Y(C) = aC2/3 (Table 1). As BSA has reached its saturation at a concentration Table 1. Change in Young’s modulus with Concentration for BSA Hydrogels in Various Solvents Condition
a, kN·m/mol (Y(C) = aC2/3)
Tris GuHCl 6 M glycerol 50%
6.4 ± 0.5 10.2 ± 0.8 4.45 ± 0.2
of ∼4 mM, we only included in our fitting procedure the points below 3 mM (see also Figure S2). Furthermore, the swelling ratio is decreasing with concentration from ∼1250% at 1 mM to ∼750% at 2 mM and plateaus after 2 mM (Figure S7).
Figure 4. Characterizing protein hydrogels using constant force protocols. (A) Typical traces showing the change in strain (top) and force (bottom) due to the unfolding and refolding response of a 2 mM BSA-based hydrogel to different constant high forces protocol, measured using FC hydrogel rheometer in Tris solution. Inset: hydrogel contraction as the force is decreased to 0.1 mN. (B) Change in strain as a function of stress during high force (120 s) and low force (300 s), calculated from the difference in position of the first and last points at a given constant force. F
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Figure 5. Constant force separates the elastic and viscoelastic components. (A, B) Normalized extension (A) and recoil (B) at different constant forces show no notable change in the measured raise/decay with changing force (color-coded as in Figure 4A). The dotted lines represent doubleexponential fits. (C, D) Variation of stress vs strain for the elastic part (red), viscoelastic part (green), and both regimes (blue) during force increase (C) and decrease (D).
change in strain that takes place at a given stress, the decay seems to be force independent in the sampled range. This effect goes against the expected increase in the unfolding rate with increasing the applied force and may be specific for BSA hydrogels. Both the extension and recoil parts can be described by double-exponential fits,47 with the extension rates ∼twice as high as the recoil rates (0.3 and 0.02 s−1 for extension and 0.17 and 0.01 s−1 for recoil). The change in strain at a given applied stress can be directly determined from the constant force traces. Importantly, the elastic and viscoelastic effects can be decoupled by comparing the gel strain before the change in force and immediately after. A constant force Young’s modulus (YFC) can be obtained by considering the change of the gel extension with force, between the low force plateau and the last high force point (at time 30 + 120 s). For the BSA 2 mM hydrogel shown in Figure 4A, we obtain ∼12 kPa for 2 mM BSA. This elasticity parameter can be decoupled into elastic Young’s modulus (YFCe = 75−77 kPa, measured between the plateau and the first high force pulse at time ∼30 s) and viscoelastic Young’s modulus (YFCve = 14 kPa, measured between the first and the last high force points at time ∼30 s and 30 + 120 s). Constant force measurements can directly decouple elastic from viscoelastic Young’s moduli, if we assume the total change in elasticity:
chosen such that all domains inside the hydrogel refold and the hydrogel recovers its initial length. Constant force measurements in the presence of glycerol 50% and GuHCl 6 M mirror the force-ramp data. The measured extension in glycerol is smaller than the one in regular Tris buffer, while the extension in GuHCl is larger. Furthermore, no viscoelastic part is measured in the presence of GuHCl, and the measured strain simply follows the applied stress in a purely elastic mode. Constant force measurements allow for a quantitative separation between the elastic and the viscoelastic regimes. The elastic part is defined as the change in the gel length due to an increase in force. In the viscoelastic part the hydrogel continues to extend, even though the force is now maintained constant. When force is quenched to a low value, elastic and viscoelastic behaviors are measured as well. The traces were separated into these two different regimes (Figure 5). Critical to these constant force measurements is the response time of the PID, as the applied force tries to follow a step change in the setpoint and the gel is exposed to a changing load. This allows to accurately separate the elastic and viscoelastic effects, as domain unfolding is most pronounced immediately after the force change. The chosen combination of force sensor and motor coil ensures that these dead times are
