## Abstract

In contrast to most synthetic hydrogels, biological gels are made of fibrous networks. This architecture gives rise to unique properties, like low concentration, high porosity gels with a high mechanical responsiveness as a result of strain-stiffening. Here, we used a synthetic polymer model system, based on polyisocyanides, that we crosslinked selectively inside the bundles. This approach allows us to lock in the fibrous network present at the crosslinking conditions. At minimum crosslink densities, we are able to freeze in the architecture, as well as the associated mechanical properties. Rheology and X-ray scattering experiments show that we able to accurately tailor network mechanics, not by changing the gel composition or architecture, but rather by tuning its (thermal) history. Selective crosslinking is a crucial step in making biomimetic networks with a controlled architecture.

## Introduction

Life is supported by hydrogels. They give mechanical properties to cells and their surrounding matrix1,2. Nature is able to precisely regulate the stiffness of these gels in space and time. For instance, the most abundant cytoskeletal protein, F-actin is (reversibly) bundled and crosslinked by various actin-binding proteins, resulting in a soft, porous and fibrous network structure3,4. It is this bundled network architecture that determines the unique mechanical properties of the network: its stiffness, and also its strong increase in stiffness upon deformation of the gel, the so-called strain-stiffening behavior2,5. The linear and nonlinear mechanics are crucial parameters in cellular functions, intracellular communication and tissue protection6,7. Other biogels, such as fibrin, collagen, and intermediate filaments show analogous architectures and properties8,9.

In contrast, synthetic hydrogels that are studied for many biomedical applications commonly have very different architectures (high concentration and dense, single-chain networks) and are not strain-responsive6. To manipulate mechanics in these networks, one routinely changes the polymer or crosslinker concentration, which simultaneously changes the architecture and, for instance, the pore size, and the density and distribution of (bio)functional groups that are conjugated to the polymer10,11. Developing methods to reliably decouple the mechanical properties is still an outstanding challenge.

In this manuscript, we demonstrate a new approach to synthesize networks with different mechanical properties, but all with very similar architectures. The only way to achieve this is to use Nature’s approach. In analogy to actin networks, our synthetic hydrogels are soft, porous fibrillar structures12,13. We then crosslink the polymers selectively inside the bundles, which keeps the network architecture unchanged (Fig. 1a). By changing the crosslinking conditions, the concentration and the nature of the crosslinkers, we can accurately tailor the mechanical properties, both in the linear and in the strain-stiffening regime. This approach is generic for any bundled hydrogel material, either synthetic or biological.

## Results

### Materials

As a model system, we employed the semi-flexible (ethylene glycol)-decorated polyisocyanide (PIC) polymers.13 An aqueous PIC solution reversibly gels when heated above its lower critical solution temperature (LCST) and a branched, bundled gel is formed with an architecture that is broadly distributed in length scales, both in bundle diameters and in pore dimensions. The gel is unique, since it combines the advantages of a synthetic polymer with a strongly biomimetic character in both architecture and mechanical properties12,14. Similar to any other gels, its stiffness strongly depends on concentration, polymer characteristics and conditions, like temperature14 and the ionic strength15 of the solution. In addition, PIC share the strain-stiffening characteristics with bundled structural biological protein-based gels, which means that the gel can become 10–100 times stiffer on deformation2,4. Such bundled hydrogels have great potential in 3D tissue engineering, and also for PIC polymers and gels regenerative medicine16, immunology17,18, and (DNA) sensing applications have been reported19,20.

For crosslinking, we used the efficient strain-promoted azide alkyne cycloaddition (SPAAC) reaction21,22. We decorated the PIC polymer with azide-functional groups by co-polymerizing an azide-functionalized monomer (3.3 mol%) with an inert monomer, resulting in PIC polymer 1 (Fig. 1b). Projected along the backbone, the average azide spacing amounts ~3 nm, but because of the helical backbone conformation, adjacent azide groups, however will be spread out much further. We designed two di-functional crosslinkers based on cyclooctynes with spacer lengths of ~3 nm (2a) and ~10 nm (2b). The spacer length of the crosslinker is crucial in the selectivity of the crosslinking process. Details of the synthesis and characterization are provided in Supplementary Methods.

To form the crosslinked gel, a pre-cooled aqueous solution of crosslinker 2 is added at once to a similar volume of cold solution of polymer 1. This solution then is quickly heated into the gel phase where the SPAAC reaction is allowed to proceed for one hour. CryoSEM images of the crosslinked hydrogel 1+2a (Fig. 1c) show a porous network with features similar to the corresponding hydrogel without the crosslinker present (Fig. 1d). At low temperatures, however, the network structure of crosslinked gel is conserved (Fig. 1e), while the corresponding SEM image of the non-crosslinked material shows an unstructured polymer film (Fig. 1f).

### Controlling mechanics with temperature

In addition, PIC hydrogels uniquely continue to stiffen beyond Tgel because of the increasing stiffness or persistence length of the individual polymer chains following: G′ ~ Te2βT with thermal coefficient β = 0.055 K–1 for 1 and 1 + 2a (Fig. 2a), which roughly corresponds to a tenfold increase in the stiffness every 20 °C. The gel structure during this heating process does not change significantly12, which means that the thermal stiffening behavior is solely attributed to an increase in the persistence length of the bundles. When the crosslinking reaction captures the architecture and the mechanical properties at the crosslinking conditions, varying the crosslinking temperature should give us hydrogels with different mechanical properties, but now with a very similar network architecture; a highly uncommon characteristic of hydrogels and much pursued to study the pure effects of mechanical properties on cell behavior. Since they show different persistence lengths, the structure inside the bundles likely varies with temperature, although the disordered nature of the bundles (compared to biological gels) hampers experimental verification.

We prepared five gels (1 + 2a) that were crosslinked at 25, 30, 40, 50, and 65 °C. After mixing 1 and 2a at 5 °C and applying the solution to the rheometer, the temperature was raised immediately to the desired crosslinking temperature Tcl where bundles form and crosslinking commences (Supplementary Figs. 2 and 3). After 1 h, the crosslinked gels were cooled to 5 °C while measuring the storage modulus (Fig. 2d). Indeed, samples crosslinked at a higher temperature are much stiffer over the entire temperature range than samples crosslinked at lower Tcl. Looking at 20 °C, for instance, the modulus of the sample crosslinked at 65 °C is about 10-fold higher than that of the sample crosslinked at 25 °C. This approach offers a unique opportunity to truly study mechanics without the influence of other parameters, such as network composition or architecture.

The samples that were polymerized at different temperatures were then heated from 5 °C all to 50 °C (Fig. 2e). Up to the crosslinking temperature, G′ follows the same trace as the cooling ramp, showing full reversibility without hysteresis. Beyond Tgel, however, the slope of G′ vs T increases to the value of the pristine heating ramp (G′ ~ Te2βT, with nearly identical β = 0.051 K–1), resulting of convergence of the mechanical properties of all gels at elevated temperatures, irrespective of their crosslinking temperature. Despite the presence of the crosslinks, the polymer chains and with them, the bundles continue to stiffen. In subsequent cooling ramps (Fig. 2f), we find that this stiffening process is irreversible and all samples show similar mechanical properties, independent of the original crosslinking temperature. We anticipate that heating beyond Tcl irreversibly tightens and stiffens the bundle which exposes residual reactive groups that crosslink and irreversibly stiffen the hydrogel19. When we plot the moduli of the gels at T = 20 °C for samples crosslinked at different Tcl (Fig. 2g), we observe a clear difference in stiffness when they are directly cooled after crosslinking where G′ scales not to the actual temperature, but to the original crosslinking temperature: G′ ~ Tcl exp(2βTcl). Once the samples are heated to 50 °C, their difference in mechanical properties at 20 °C has disappeared.

By modifying the length of the crosslinker, we were able to further tailor the network structure and the mechanical properties of the hydrogels. As an illustration, we designed and prepared (see Supplementary Methods) crosslinker 2b, which is much longer (~10 nm) than 2a, but still an order of magnitude smaller than the pore size. Hence, 2b still is expected to give predominantly crosslinks inside the bundle, but will less efficient in keeping the polymer chains in a tight bundle below Tgel. Indeed, although prepared at the same concentrations and conditions (Tcl = 37 °C, 52 µM), the stiffness of gels crosslinked with the longer spacer 2b decreases much stronger with on cooling than gels with 2a (Fig. 2h). Cooling below Tgel reduces the non-covalent interactions between the polymers and while the short crosslinks sustain the tight bundle structure, the longer crosslinks allow for disorganization of the chains in the bundle and consequently, a reduction in the bundle persistence length and the stiffness of the gel. Since the bundled architecture is still in place, the gel remains elastic (G′ G″) and, also, the nonlinear properties are conserved at 5 °C (Fig. 2i). In fact, we find that K′ of 1 + 2b and 1 + 2a fully overlap in the nonlinear regime, which is in line with theory3,25,26 that predicts that compliant crosslinkers have a limited effect on the strain-stiffening behavior of semi-flexible networks.

### Network architecture

The network architecture plays a crucial role in the mechanical properties of the gel, but is challenging to study in-situ, due to the low polymer concentrations and the large distributions in bundle and pore dimensions. We used small angle X-ray scattering (SAXS) to characterize the network structure12. A low-temperature PIC polymer 1 solution containing free polymers (T = 5 °C) is comfortably described by a worm-like chain model by Kholodenko27, which yields the persistence length (lp,0 = 30 nm) and polymer diameter (R = 1.0 nm) from the fitting procedure. In the gel phase, the scattering traces were fitted to the same Kholodenko model (now yielding the average bundle diameter, RB) together with the Ornstein–Zernike model28 which describes the porous network structure. As expected, at high temperatures, crosslinked gel 1 + 2a shows a scattering pattern analogous to the non-crosslinked hydrogel (Supplementary Fig. 4). When the crosslinked sample is cooled to T = 5 °C, the scattering pattern becomes a combination of the pattern of the bundled gel with that of a single polymer (Fig. 3a), i.e., a fraction of the network is re-solvated. The scattering curve is well described by a linear combination of both contributions: the Kholodenko/Ornstein–Zernike model for the bundled network plus a single polymer Kholodenko model (Fig. 3b, c), using most of the earlier found fitting parameters (see Supplementary Methods for the full fitting procedure and Supplementary Table 2 for the fitting results).

## Discussion

Covalent crosslinking is the default method to stabilize hydrogels permanently, but often results in gels with small pores with limited application potential in 3D cell studies. Biology solved this challenge by generating open porous networks of semi-flexible bundles that are crosslinked by dedicated proteins. We followed this example and presented an approach to crosslink polymers predominantly inside the bundles. Provided that the crosslinking reaction is carried out in the presence of the bundles, crosslinker concentrations of 50 µm are sufficient to stabilize the architecture. For the PIC gels, presented here, bundle formation is thermally induced (and reversible), which means that crosslinking should take place above the gelation temperature, which is readily tuned between 10 and 60 °C by simply changing the ethylene glycol tails31. We find that the mechanical properties at the crosslinking conditions are irreversibly captured and cooling shows minor impact on the architecture or the mechanical properties of the material. Further heating, on the other hand will continue to stiffen the network irreversibly. The nature (i.e., length), concentration and, most likely, the functionality of the crosslink are versatile parameters to tailor the mechanothermal response.

This approach is not restricted to polyisocyanide gels, but will be applicable to any bundled gel architecture and will be most effective when the dimensions of the crosslinker are smaller than the distance between the complementary functional groups on the polymer backbone. The genericity renders this strategy highly relevant for biomechanical studies that concentrate on the effect of the tissue mechanics on cell fate.

In addition, our scattering results show that upon cooling a crosslinked gel only the thickest bundles remain, while rheology experiments demonstrate that the stiffness and the mechanical response to stress of the crosslinked gels are barely impacted on cooling. We conclude that in such networks with a large distribution in bundle diameters, the mechanical load is predominantly carried by the thickest bundles and that thinner bundles hardly contribute to the linear or the nonlinear mechanical properties. This conclusion has a significant effect on how we should visualize stress-development in a polydisperse fibrillar network: what are the length scales of (local) deformation, when for instance a cell adheres to a network and strains it?

## Methods

### Materials

The synthesis and chemical characterization of 1 and 2b is described in Supplementary Methods. Crosslinker 2a is commercially available.

### Sample preparation

For rheology and UV–vis experiments, a solution of 1 (2 mg mL−1) was prepared by overnight dissolving dry polymer in the appropriate amount of milliQ water at 4 °C with occasionally shaking. All polymer solutions were stored at −20 °C prior to use. A solution 2a (2 mg mL−1 in DMSO) or 2b (2 mg mL−1 in milliQ water) was diluted with milliQ water such that an equivolumnar mixture of polymer and crosslinker contains the desired ratio azide and DBCO groups (most often 1:1). The solutions were mixed in a pre-cooled glass vial, briefly homogenized and used immediately. For SAXS analysis, more concentrated samples were used: 1 was dissolved in MilliQ water (4.36 mg mL−1), as described above and 2a (4.48 mg mL−1) was dissolved in DMSO/milliQ (1:1). For each sample, 16 µL of the 2a solution and 200 µL of the PIC stock solution were quickly mixed and immediately transferred into a quartz capillary. The capillary was then placed in a water bath at the appropriate Tcl for 1 h, after which the scattering experiments were conducted.

### Mechanical characterization

Rheological measurements were carried out on a TA Instruments Dynamic Hybrid Rheometer 1 or 2 fitted with a 40 mm sandblasted parallel plate geometry. A geometry gap of 500 µm was used. To measure the linear regime (G′), the sample was heated or cooled to the desired temperature, and after a short waiting period for equilibration the complex modulus G* was measured by applying an oscillating deformation of amplitude γ= 0.04 at frequency f= 1 Hz. Temperature-dependent measurements were carried out at a 1 °C min−1 ramp rate. For nonlinear measurements the pre-stress protocol described by Broedersz et al.5 was used.

### Small angle X-ray scattering

SAXS data were recorded at the BM26B station at the European Synchrotron Radiation Facilities in Grenoble. Details of the setup are in Supplementary Methods. The recorded curves were fitted using SASfit software32. In brief, single-polymer solutions were fitted to Kholodenko’s wormlike chain model27:

$$I\left( q \right) = I_{{\mathrm{polymers}}}\left( q \right) = \left( {\Delta {\mathrm{\rho }}} \right)^2\varphi P_0\left( {q,L,2l_{\mathrm{p}}} \right)P_{{\mathrm{CS}}}\left( {q,R} \right)$$
(1)

where scattering intensity I(q) for every wave vector q is a function of the difference in electron density between the polymer chain and the solution Δρ, the polymer volume fraction φ, and semi-flexible polymer chain characteristics, like the contour length L, the persistence length lp the radius R. Scattering profiles of the gel network architectures were described using a combination of the wormlike chain model (now for the bundles) and the Ornstein and Zernike (OZ) model28 for network heterogeneities:

$$I\left( q \right) = I_{{\mathrm{bundles}}}\left( q \right) + I_{{\mathrm{network}}}\left( q \right)$$
(2)
$$I\left( q \right) = \left( {\Delta {\mathrm{\rho }}} \right)^2\varphi P_0\left( {q,L_{\mathrm{B}},2l_{{\mathrm{p}},{\mathrm{B}}}} \right)P_{{\mathrm{CS}}}\left( {q,R_{\mathrm{B}}} \right) + \frac{{I(0)}}{{1 + q^2\xi _{{\mathrm{OZ}}}^2}}$$
(3)

Now, LB and lp,B are the contour length and the persistence length (both beyond the experimental window). The polymer bundle radius RB contains a normal distribution that represents inhomogeneity of bundle diameters. I(0) is the forward scattering of the OZ-term, and ξOZ is the correlation length of the network heterogeneities. For crosslinked gels at low temperatures, a fraction of the gel scatters as single polymers, which was captured by using a linear combination of the two aforementioned models:

$$I\left( q \right) = I_{{\mathrm{polymers}}}\left( q \right) + I_{{\mathrm{bundles}}}\left( q \right) + I_{{\mathrm{network}}}\left( q \right)$$
(4)

For the analysis, many of the fitting parameters were obtained from control experiments and subsequently fixed. A discussion on the analysis procedure is included in Supplementary Methods.

### Data availability

All data supporting the results of this study are available in the article and Supplementary Information Files or from the corresponding author on reasonable request.

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## Acknowledgements

We thank Geert-Jan Janssen (RU General Instrumentation lab) and Dr. Rob Mesman (RU Microbiology) for assistance with the cryo-SEM microscopy and Prof. Giuseppe Portale (University of Groningen) for fruitful discussions on the SAXS analysis. We acknowledge the European Synchrotron Radiation Facilities (ESRF) in Grenoble, France and their staff, in particular Dr. Daniel Hermida Merino, as well as NWO for providing and supporting beam time at the Dutch-Belgium beamline (DUBBLE) for SAXS experiments (Grant BM26-02773). This work was financially supported by NWO Gravitation (Grant 024.001.035).

## Author information

Authors

### Contributions

D.C.S. and P.H.J.K. designed and interpreted the mechanical and architectural studies. A.E.R. and P.H.J.K. supervised the project. All authors contributed to the manuscript.

### Corresponding authors

Correspondence to Alan E. Rowan or Paul H. J. Kouwer.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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Schoenmakers, D.C., Rowan, A.E. & Kouwer, P.H.J. Crosslinking of fibrous hydrogels. Nat Commun 9, 2172 (2018). https://doi.org/10.1038/s41467-018-04508-x

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