Cytoskeleton-inspired artificial protein design to enhance polymer network elasticity

Abstract

Reducing topological network defects to enhance elasticity in polymeric materials remains a grand challenge. Efforts to control network topology, primarily focused on crosslinking junctions, continue to underperform compared to theoretical estimations from idealized networks using affine and phantom network theories. Here, artificial protein technology was adapted for the design of polymer-network hydrogels with precisely defined coil-like and rod-like strands to observe the impact of strand rigidity on the mechanical properties of polymeric materials. Cytoskeleton-inspired polymer-network hydrogels incorporated with rod-like protein strands nearly tripled the gel shear elastic modulus and relaxation time compared to coil-like protein strands, indicating an enhanced effective crosslinking density. Furthermore, asymmetric rod-coil protein designs in network strands with an optimal rod:coil ratio improved the hydrogel relaxation time, enhancing the stability of physical macromolecular associations by modulating crosslinker mobility. The careful design of strand rigidity presents a new direction to reduce topological defects for optimizing polymeric materials.

Introduction

Polymer-network materials, consisting of strands connected by crosslinker functionalities at junction points, exhibit a comprehensive range of applications due to their customizable physical properties, such as self-healing, resilience, fatigue resistance, toughness, and large extensibility.^1–10 However, the properties of conventional polymer-network materials are limited by elastically ineffective strands due to topological defects, including unreacted functionalities in free and dangling chains, loop defects forming inefficient crosslinking junctions, and network density inhomogeneity due to poor diffusion of crosslinkers during gelation.^11–14 Efforts to control polymer network topology focus on improving effective crosslinking, reducing unreacted functionalities and loop defects by altering the binding characteristics of crosslinkers,^14–16 which have yet to reach the shear elastic modulus (G’) from theoretical estimations for idealized polymer-network materials.^17–21

Altering the chain length of polymer strands has been identified as another key parameter for enhancing mechanical properties by reducing defects.^13,22–26 However, the effect of other strand properties, such as rigidity, as mechanisms for reducing topological defects in polymer-network materials are not well characterized. Reticular chemistry techniques using rigid organic building blocks have synthesized frameworks for controlling topology to engineer specific geometries, but the resulting polymers typically lack adequate elasticity, stability, and processability for conventional applications.¹⁴ Investigations into semiflexible proteins show they are responsible for controlling cell elasticity, maintaining stability in the cytoskeletal network.^20,27–31 These investigations into how natural biopolymers form organized networks led us to hypothesize that the rigidity of structured proteins, compared to flexible coils in conventional polymeric materials, limits their stretching, bending, and torsional mobility to ensure precise spacing and alignment in biological networks, potentially reducing topological network defects. This inspired us to investigate how the rigidity of network strands impact the elasticity of polymer-network materials.

To evaluate strand rigidity, a well-characterized model crosslinking system is required to maintain adequate network homogeneity and precise control over strand properties. Chemical crosslinking systems, joined by covalent bonds, are strong but often require complex methods to distribute junctions homogeneously in the network, essential to developing a model for evaluating topological defects.^14,32 Physical crosslinkers can exchange associating molecules depending on their physical affinities and diffusion, capable of transient network reorganization that improves network junction homogeneity.^33–36 The submolecular dissociation dynamics of these physical associations, characterized by the critical frequency during rheology frequency sweeps,³⁴ is correlated with the characteristic relaxation time of polymer-network materials that measure the stability of polymer network junctions.^{16,20,37–39} Furthermore, when characterizing these materials above a threshold angular frequency, exchanges between physical associations do not occur, permitting the evaluation of network topology by correlating the plateau G’ with the effective crosslinking density.^16,20,33 Therefore, physical crosslinkers were used in the development of a customizable polymer-network model with various protein components to analyze the effect of strand rigidity in a controlled and reliable manner.

Artificially engineered proteins, with junction-forming end-blocks connected by a flexible midblock strand (Figures 1a and S1), have been used extensively as a model polymer system to evaluate topological defects, characterizing how crosslinking functionality and binding orientation influence the prevalence of topological defects in polymer networks.^14,15,25 Compared to conventional polymers, artificial proteins are ideal for developing design rules because of established methods for specific customization at the genetic level and biosynthesis of identical proteins with a uniform dispersity (Figure S2). With this advantage, flexible unstructured C_n proteins, containing n repeats of a 9 amino acid sequence (AGAGAGPEG)_n, have been used as a midblock to model strands used in conventional synthetic polymer networks. Parallel coiled-coil crosslinkers (P), consisting of a single alpha-helix protein that self-associates into a pentameric structure, were adapted onto either end of the C_n midblock to prepare polymer-network hydrogels (Figure 1b). This design reduced topological defects, such as primary loops, compared to antiparallel coiled-coil crosslinkers by increasing the bending and torsional energy required to contort the midblock in order to associate in a parallel conformation.¹⁵ This well-characterized polymer system was implemented as a flexible control to compare coil-like and rod-like protein strands.

Figure 1.

Schematic of coil- and rod-like protein models. (a) The telechelic biopolymer design consists of coiled-coil crosslinkers surrounding a coil-like midblock, C₂₄. (b) Coiled-coil crosslinkers as end blocks in the biopolymer design self-associated into pentamers that form the hydrogel network.¹⁵ Conventional flexible polymers exhibit significant topological molecular defects and strand entanglements^11,14 (c-d) C₂₄ and the rod-like protein model, NI₆C, have a similar number of amino acids, equating to a similar contour length of approximately 92 nm (~250 amino acids × 0.365 nm). However, the condensed α-helical structures and their hydrophobic interactions within NI₆C compact its structure into a rigid solenoid macromolecule measuring approximately 8 nm end-to-end using molecular visualization programs. The NI₆C ribbon diagram was built by duplicating NI₃C (PDB code: 2QYJ) using a root mean square displacement fitting procedure.^37,40,41

Ankyrin repeat (AR) protein, responsible for maintaining the integrity of the red blood cell membrane by anchoring beta-spectrin subunits with integral proteins,^42,43 inspired our design of a rod-like model (Figures 1c and 1d). Individual ARs, consisting of a β-turn and two antiparallel α-helices, tightly stack to form a stable macromolecular structure.^40,44 Consensus sequences of natural AR proteins produce synthetic ARs that construct a solenoid structure with up to 10 ARs,⁴¹ enhancing chemical and thermal stability by increasing the number of ARs.^40,45 NI₆C, composed of six internal synthetic ARs (I₆) with outer N- and C-capping sequences to improve structural stability and solubility,⁴⁴ was analyzed using circular dichroism spectroscopy at each stage of protein synthesis, confirming the stability of its tertiary protein structures prior to hydrogel preparation (Figure S3). Based on these results, NI₆C was determined to be a stable rod-like protein model and incorporated into an artificial protein design surrounded by P crosslinkers, assembling P-NI₆C-P.

We performed rheological characterization of artificial protein-based polymer-network hydrogels (Figures 2 and S4) to determine how rigid strands influence key mechanical properties that measure crosslinking efficiency, including the plateau G’, relaxation time, and loss tangent (tan δ). As a control, we prepared unstructured flexible C₂₄ with a similar contour length (250 × 0.365 nm) as NI₆C (253 × 0.365 nm), based on the number of residues multiplied by the approximate length of a single amino acid (Figure 1; Table S1).^46–48 Demonstrating the precise control of artificial protein technology, this study investigates the modular design of flexible and rigid co-block strands. Organizing strands with coil and rod protein structures at specific length ratios and spatial positioning, we gain an understanding of how strand properties dictate crosslinker mobility, submolecular dissociation dynamics, and elasticity within polymer-network materials.

Figure 2.

Shear mechanical properties of hydrogels with rigid rod (P-NI₆C-P) and flexible coil (P-C₂₄-P and P-C₂-P) midblocks. a) Boxplots comparing the G’ of each hydrogel (F(2,15.31) = 117.97, p = 4.98 × 10⁻¹⁰), determined by averaging the G’ within the linear viscoelastic region for each strain sweep experiment, performed at a constant angular frequency of 10 rad s⁻¹, within the plateau G’ region of each frequency sweep (Figures 2b and S4). Affine and Phantom network model calculations predicted G’ for P-C₂₄-P and P-C₂-P (Table S3). b) Representative rheological frequency sweep curves measured from 0.01 to 100 rad s⁻¹ angular frequency at a constant 1% shear strain, within the linear viscoelastic region (Figure S4). c) Boxplots comparing the critical frequency of each hydrogel (F(2, 10.26) = 2277.5, p = 2.58 × 10⁻¹⁴). The critical frequency is indicated by the crossover point, where G’ = G”. The hydrogel relaxation time, τ_c, is equivalent to the inverse of the critical frequency. d) Relaxation spectrum of each hydrogel with maxima at τ_c, denoted by dashed lines, estimated using a fitting procedure^9,16 to experimental data from (a). P-NI₆C-P (N = 10), P-C₂₄-P (N = 7), and P-C₂-P (N = 10) datasets were evaluated with Welch’s one-way ANOVA and Games-Howell post-hoc tests to compare protein hydrogel datasets (*p < 0.001, **p < 0.0001, ***p < 1 × 10⁻⁷, ****p < 1 × 10⁻⁹). Boxplots in all figures have the median represented as a line, average represented by a “×”, a box indicating upper and lower quartiles, and error bars indicating upper and lower deciles.

Experimental Methods

Protein Expression.

All gene sequences, summarized in Figure S1, were purchased and subcloned (GenScript, USA) into pET26b expression plasmids using BamHI and HindIII restriction enzyme sites. Plasmids for each engineered gene were transformed into BL21(DE3) E. coli cells (NEB, USA), amplified in 900 μL SOC media for 2 hours shaking at 220 RPM and 37°C, and cultured on kanamycin-resistant agar plates overnight. Individual colonies were used to inoculate cultures of 5 mL TB media with 50 μg L⁻¹ kanamycin shaking at 220 RPM and 37°C overnight. In each 2.8 L protein expression flask, 10 ml of overnight culture and 1 mL of 50 mg mL⁻¹ kanamycin stock were added, then cell amplification occurred in a shaking incubator at 37°C and 220 RPM until the optical density at a wavelength of 600 nm (OD₆₀₀) ~ 1, approximately 4 hours. The OD₆₀₀ absorbance was measured using a Cary 60 UV-Vis spectrophotometer (Agilent Technologies, USA). Protein overexpression was induced by adding 0.5 mM isopropyl-1-beta-D-thiogalactoside (IPTG) to each 1 L culture and incubating in a shaking incubator overnight at 24°C and 220 RPM. Cells were harvested by centrifugation at 10,000 rcf for 5 min, then cell pellets were frozen at −80°C for at least 1 hour.

Protein Purification.

Each cell pellet from 1L of protein expression was thawed and suspended in 100 mL of buffer containing 8 M urea, 100 mM sodium phosphate monobasic, and 10 mM tris at pH 8.0 using the shaking incubator at 24°C and 220 RPM. Samples were transferred to 500 mL wide-mouth bottles and sonicated (Branson Sonifier 250, Branson Ultrasonics, Danbury, CT, USA) until the sample viscosity was similar to water, typically three to four times for 12 minutes at 50% duty cycle and 4 output control, to lyse the cells. To remove insoluble cell debris and protein, samples were centrifuged twice at 29,000 rcf for 30 min at 4°C, discarding the pellet and transferring the protein supernatant to new 50 mL centrifuge tubes between centrifugations. Target proteins, containing 6 Histidine amino acid residues at the C-terminus to ensure purification of only fully expressed proteins, were extracted using affinity column chromatography with Ni-NTA beads (QIAGEN, USA). Protein electrophoresis on SDS/PAGE gels was performed to verify the protein’s yield and purity at each stage of purification. Elutions, selected based on yield and purity, were dialyzed against tris buffer at pH 8.0. To further purify the protein, Fast Protein Liquid Chromatography (FPLC) was performed in 6 M urea buffer at pH 8.0 using an anion exchange column. FPLC elutions with high yield and purity were dialyzed against 20 mM tris buffer at pH 8.0 then deionized water until salt impurities were removed. Purified protein samples were flash frozen using liquid nitrogen, lyophilized, and stored at −20°C.

Artificial Protein Hydrogel Preparation.

Lyophilized proteins from multiple expressions and purification experiments were used for experimentation, emphasizing the reproducibility of protein synthesis and purification techniques. Lyophilized proteins were dissolved in 20mM tris buffer at 10% w/v and incubated at 4°C overnight. Hydrogels were centrifuged to remove potential air bubbles, then incubated at 4°C for 1 hour prior to rheological characterization.

Rheology.

The viscoelastic mechanical properties of artificial protein hydrogels were characterized using small amplitude oscillatory shear (SAOS) rheology on a Discovery Hybrid Rheometer 2 (TA Instruments, New Castle, DE, USA) with a sandblasted 20 mm cone-and-plate geometry at a 1° angle and a sandblasted stage. Inertia, friction, and rotational mapping calibrations were performed prior to each experiment. A Peltier temperature-controlled stage maintained 25°C for all rheology testing. Artificial protein hydrogels were transferred to the stage and the geometry was lowered to the trim gap height of 55 μm. Excess gel was removed from the edges of the geometry before lowering it to the testing gap height at 50 μm. To control evaporation, a mineral oil barrier was placed around the edges of the geometry and the geometry was encased in a solvent trap with a water seal.³¹ Hydrogels relaxed for 1 hour prior to experimentation. Strain sweeps were performed from 0.01 to 1000% shear strain at a constant 10 rad s⁻¹ angular frequency. G’, G”, and tan(δ) were determined by averaging the data points within the linear viscoelastic region of the strain sweep (Figure S4). Frequency sweeps were performed from 0.01 to 100 rad s⁻¹ at a constant 1% shear strain, within the linear region of the strain sweep. The critical frequency was recorded as the frequency at which G’ and G” are equivalent.

Circular Dichroism (CD) Spectroscopy.

CD spectra were obtained using an Olis DSM-20 Circular Dichroism spectrometer and a quartz cuvette with a 0.1 cm path length. Measurements between 260 and 190 nm were collected with a 5 second integration time. Spectra for all proteins were measured in 20 mM Tris buffer at pH 7.5 with a protein concentration of 0.2 mg mL⁻¹. The intensities from three experiments were averaged, calibrated using the control buffer signal intensity, and converted to mean residue ellipticity (MRE) using the following equation:

$${\theta }_{MRE}=\frac{100\times signal}{Cnd}$$ (1)

where signal is the average CD output of three experiments, C is the protein concentration, n is the number of residues, and d is the path length of the cuvette.

Statistical Data Analysis.

Rheology datasets pertaining to each hypothesis were analyzed using a one-way ANOVA followed by Tukey Honest Significant Differences (HSD) post-hoc tests to compare protein groups (RStudio, US). For cases where groups had unequal variances, a Welch’s one-way ANOVA and Games-Howell post-hoc tests were utilized. All ANOVA and post-hoc test results are reported in each figure legend. All results written throughout the manuscript represent the mean ± the standard deviation, unless otherwise noted.

Theoretical Calculations

Network Model Calculations.

The affine (Equation 2) and phantom (Equation 3) network models were used to calculate the theoretical shear elastic modulus (G′) of P-C₂₄-P and P-C₂-P biopolymers (Figure 2a and Table S3).^11,15

$$G^{\prime }=v{K}_{b}T$$ (2)

$$G^{\prime }=v{K}_{b}T\left(\frac{f-2}{f}\right)$$ (3)

where v is the effective chain density, K_b is the Boltzmann constant, T is temperature in Kelvin, and f is the functionality of the crosslinker. Experiments were conducted at 298.15 K. P coiled coil crosslinkers have a functionality equal to 5. The effective chain density was calculated using equation 4:

$$v=\frac{1000C{N}_A}{M_w}$$ (4)

where C is the protein concentration, M_w is the protein molecular weight (Table S2), and N_A is Avogadro’s number. All protein hydrogels were prepared and measured at 100 g L⁻¹.

Relaxation Spectrum Calculations.

The relaxation spectrum, H(τ), was calculated by fitting experimental G’ and G” frequency sweep data (Figure 1a and S4) to the parallel series Maxwell model using equations 5 and 6: ¹¹

$$G^{\prime }\left(\omega \right)={\int }_{-\infty }^{\infty }H\left(\tau \right)\frac{{\omega }^2{\tau }^2}{1+{\omega }^2{\tau }^2}dln\left(\tau \right)$$ (5)

$$G^{″}\left(\omega \right)={\int }_{-\infty }^{\infty }H\left(\tau \right)\frac{\omega \tau }{1+{\omega }^2{\tau }^2}dln\left(\tau \right)$$ (6)

Solving for H(τ), we estimate the relaxation spectrum:

$$H\left(\tau \right)=A\exp \left(-\frac{{\left(\ln \left(\tau \right)-\ln \left({\tau }_c\right)\right)}^2}{2{\sigma }^2}\right)$$ (7)

where A, τ_c, and σ are constants that were optimized through a nonlinear fitting method, using the MATLAB function lsqcurvefit.

Results and Discussion

Representing the flexible strands of conventional polymers, hydrogels prepared with P-C₂₄-P proteins were tested to gain a better understanding of how topological defects diminish the mechanical properties. With an average plateau G’ of 2.64 ± 0.40 kPa (N=7; Figure 2a and 2b), P-C₂₄-P gels exhibited similar elasticity to prior studies.^15,35,37 Compared to the theoretical G’ using affine and phantom network models, measured G’ of P-C₂₄-P gels decreased by 66% and 43%, respectively (Figure 2b; Table S2). As observed in conventional polymer networks, G’ was limited compared to the predictions, affected by topological defects that reduce crosslinking efficiency in the polymer network.

To investigate the impact of rod-like protein strands on hydrogel elasticity, P-NI₆C-P hydrogels were characterized in comparison to coil-like P-C₂₄-P. Despite having the same crosslinkers and similar number of amino acid residues, P-NI₆C-P hydrogels nearly tripled the G’ (7.1 ± 0.8 kPa; N = 10) and relaxation time (7.5 ± 0.4 s; N = 10) relative to P-C₂₄-P (2.6 ± 0.4 kPa; 2.1 ± 0.5 s; N = 7; Figure 2). Due to its ability to form rod-like protein structures using intramolecular interactions, NI₆C cannot be evaluated with the same purely entropic affine or phantom network theories that model coil-like C₂₄ strands. Instead, P-NI₆C-P hydrogels require a novel rigid network theory to model entropy and enthalpy within the polymer network system. Though, the G’ of P-NI₆C-P gels intriguingly approached the affine network prediction for P-C₂₄-P, demonstrating its potential for reducing topological defects. Furthermore, P-NI₆C-P gels exhibited less energy dissipation under dynamic shear forces compared to P-C₂₄-P, indicated by a decrease in tan δ, calculated by taking the ratio of G” to G’ (Figure S5). This suggests that replacing flexible coil-like strands with rigid rod-like strands results in improved hydrogel elasticity, such as G’ and tan δ, by reducing the defects in the polymer network. However, due to the condensed solenoid structure of NI₆C (Figure 1), this improvement could be due to its shorter strand length.

To determine whether the length of NI₆C is responsible for improving hydrogel elasticity compared to P-C₂₄-P, we designed P-C₂-P, containing a similar midblock contour length (18 × 0.365 nm) to NI₆C length (Figure 1d). Due to its low molecular weight, at 10 w/v% P-C₂-P hydrogel contained nearly triple the number of molecules and crosslinkers compared to P-NI₆C-P hydrogel (Figures S2, S3 and Table S3). According to affine and phantom network theory (Equation 2-4 in the Supporting Information), decreasing molecular weight increases the density of effective crosslinking, thus improving G’. This theoretical prediction remained true as the G’ of P-C₂-P, 3.7 ± 0.5 kPa (N = 10; Figure 2b), improved compared to P-C₂₄-P. However, the impact of topological defects remained prevalent in P-C₂-P with a 75% and 58% decrease in G’ compared to the affine and phantom models, respectively (Table S2). Furthermore, P-NI₆C-P hydrogels were twice the G’ of P-C₂-P, indicating that the decrease in strand length was not the primary factor responsible for improving the elasticity of polymer-network materials with rod-like strands.

While NI₆C is known for its thermal and chemical stability, maintaining its compact solenoid structure, it is capable of unfolding and refolding under applied forces.^40,42–46 During this process, NI₆C exhibits spring-like nanomechanics, extending 11 times its folded length before returning to its original solenoid conformation with minimal energy dissipation.^46,47,49 To ensure NI₆C maintained its original strand length during small amplitude oscillatory shear (SAOS) rheology, the critical strain, marking the maximum deformation within the linear viscoelastic region, was evaluated for P-C₂₄-P, P-C₂-P, and P-NI₆C-P hydrogels. P-NI₆C-P had the lowest critical strain, at 17 ± 10% (N = 10), compared to P-C₂-P and P-C₂₄-P, at 48 ± 4% (N = 10) and 120 ± 14% (N = 7), respectively (Figure S6). Despite its similar strand contour length to the folded end-to-end length of NI₆C, P-C₂-P hydrogels exhibited a critical strain over twice as large as P-NI₆C-P hydrogels, indicating a longer linear viscoelastic region likely due to topological defects (Figure 2). If NI₆C were to unfold, its compact ~8 nm strand length would increase to approximately the contour length of C₂₄, in which case we would expect P-NI₆C-P and P-C₂₄-P hydrogels to have similar critical strains. This summarizes that the low critical strain of P-NI₆C-P gels relative to flexible controls suggests that NI₆C remains in its compact structure as intended during SAOS rheology due to its stabilizing hydrophobic core between ARs.⁴⁵ Altogether, in conjunction with the improved hydrogel elasticity with structured protein strands, we concluded that rigid strands enhanced effective crosslinking in polymer networks.

After identifying that rod-like strands improve mechanical properties of polymer-network hydrogels compared to coil-like strands of varying lengths, we hypothesized that rigid midblocks may increase the number of dangling chains in the network due to the decreased range in motion of the crosslinker end-blocks in P-NI₆C-P. Combined rod- and coil-like protein midblocks in network strands were investigated with varying rod:coil length ratios to identify the optimal characteristics of strands for our polymer-network system. Compared to P-NI₆C-P gel, P-C₂-NI₆C-P gel maintained a similar G’ (Figure 3a) but significantly decreased the critical frequency from 0.13 ± 0.01 (N = 10) to 0.06 ± 0.03 (N = 10) rad s⁻¹, inversely correlating to a 126 % increase in relaxation time (Figure 3b). These results display how crosslinker mobility enhances energy-storing properties with the addition of a flexible coil block to resist large-scale changes under dynamic mechanical loading. Conversely, when the flexible component of the rod-coil midblock doubled in length from C₂ to C₄, the G’ decreased by 71%, indicating a threshold exists where the coil-like block dictates strand flexibility and diminishes the beneficial effects of NI₆C (Figure 3a). Interestingly, the G’ (2.6 ± 0.4 kPa; N = 9) and critical frequency (0.33 ± 0.03 rad s⁻¹; N = 9) of P-C₄-NI₆C-P are not significantly different than P-C₂₄-P (p = 0.06 and p = 0.04, respectively), indicating that a sufficiently long and flexible coil block can overcome the rigid enthalpic effects of NI₆C on mechanical properties. Therefore, it was concluded that an optimal rod:coil midblock length ratio exists to improve energy-storing properties and elasticity in polymer networks by controlling strand stiffness.

Figure 3.

Effect of rod-coil block copolymer designs with controlled coil length on the polymer-network hydrogel properties. a, Boxplots comparing the G’ of P- NI₆C-P, P-C₂-NI₆C-P, and P-C₄-NI₆C-P hydrogels. Inset image shows a schematic representation of a P-C₂-NI₆C-P protein, emphasizing the mobility of the flexible rotating joint because of coil-like C₂ in the C₂-NI₆C midblock. P-NI₆C-P (N = 10), P-C₂-NI₆C-P (N = 10), and P-C₄-NI₆C-P (N = 9) datasets were evaluated with a one-way ANOVA (F(2, 26) = 98.57, p = 7.3 × 10⁻¹³) and Tukey HSD post-hoc tests to compare protein datasets (*p < 0.001, **p < 1 × 10⁻⁸, ***p < 1 × 10⁻¹⁰, ****p < 1 × 10⁻¹¹). b, Boxplots comparing the critical frequency of each protein hydrogel. Inset figure displays the fitted relaxation spectrum of each hydrogel, conveying the shift in dynamic molecular stability of P crosslinkers in response to modulations of strand rigidity. P-NI₆C-P, P-C₂-NI₆C-P, and P-C₄-NI₆C-P datasets were evaluated with Welch’s one-way ANOVA (F(2, 12.43) = 273.83, p = 5.24 × 10⁻¹¹) and Games-Howell post-hoc tests to compare protein hydrogel datasets.

Prior research characterizing the organization of biological networks with rigid and/or flexible components determined that a rigid crosslinker, such as P, connected to a flexible strand forms a rotating joint while a rigid midblock forms a weld joint, restricting motion between the strand and crosslinker and modulating diffusion kinetics.⁵⁰ This spatiotemporal control of hydrogel networks, shown to be vital for mimicking the heterogeneity of native tissue,⁵¹ inspired our efforts to identify how specific designs affect the mechanical properties, producing dynamic microenvironments with potential in tissue engineering applications.⁵² To investigate the ideal organization of rod-coil midblock strands, symmetrical P-C₁-NI₆C-C₁-P was designed to compare with asymmetrical P-C₂-NI₆C-P, maintaining an equivalent rod:coil length ratio. P-C₁-NI₆C-C₁-P reduced G’ by 48% compared to P-C₂-NI₆C-P, determining that asymmetrical rod-coil designs promote more effective crosslinking density in protein polymer-network hydrogels (Figure 4). The increased mobility of rotating joints had a greater tendency to form topological defects, evidenced by the negative impact of having two rotating joints in P-C₁-NI₆C-C₁-P. P-C₂-NI₆C-P, containing one rotating joint and one weld joint, demonstrated optimal performance compared to each other design. Analysis of each artificial protein hydrogel design contributed to our understanding of how to control topological network dynamics using rod-like proteins, mimicking the principles of controlled spacing and alignment in biological networks with a simplified polymer network model to promote efficient junction formation.

Figure 4.

Rheological characterization of hydrogels from asymmetrical (P-C₂-NI₆C-P) and symmetrical (P-C₁-NI₆C-C₁-P) telechelic protein designs. a, Boxplots comparing the G’ of P-C₂-NI₆C-P and P-C1-NI₆C-C₁-P hydrogels (t = 7.13, *p = 3.44 × 10⁻⁶). Inset images show schematic representations of P-C₂-NI₆C-P and P-C₁-NI₆C-C₁-P, with the former coil-rod block copolymer containing one freely rotating joint and the latter coil-rod-coil block copolymer containing two. b, Boxplots comparing the critical frequency of each protein hydrogel (t = 11.20, **p = 1.10 × 10⁻⁸). The dynamic properties of symmetrical and asymmetrical designed hydrogels were evaluated by comparing the fitted relaxation spectrum, shown in the inset figure. P-C₂-NI₆C-P (N = 10) and P-C₁-NI₆C-C₁-P (N = 7) datasets were evaluated with Student’s t-tests to compare protein hydrogels.

Conclusions

In polymer science and materials, validating network theory with experimental results remains a significant challenge due to the lack of customizable models. Through systematic experimental testing, the real elastic network theory (RENT) was established as a modification of the phantom network model that accounts for the effects of multi-order loop defects on bulk elasticity.¹¹ However, since most network theory, including RENT, describe gels dominated by entropy, networks composed of rigid strands, dependent on internal energy, require separate theories that account for strand stiffness and topological constraints on the crosslinker.^20,53–57 Experimental data to validate rigid and semiflexible crosslinked network theories are limited to natural biopolymers, with insufficient control over physical properties, and stiff synthetic polymers, such as polyamides⁵⁸ that form gels through aggregation of rigid segments, resulting in heterogeneous functionalities that are difficult to predict or model. These limitations are overcome using artificial protein design for precise control over components at the nanoscale level to influence material properties at the macroscale. The systematic characterization of rod, coil, and rod-coil strands in crosslinked networks presented in this study offer an experimental approach to increase our understanding of rigid or semiflexible polymer networks, establishing that strand stiffness improves crosslinking efficiency to organize a more effective network with reduced topological defects. This approach demonstrates the ability to modulate hydrogel properties using spatiotemporal control and, in future studies, can be developed into validation tools to evaluate and improve polymer network theories, providing design rules for developing polymer-network materials with predictable mechanical properties.