Cross-Linkable Gelatins with Superior Mechanical Properties Through Carboxylic Acid Modification: Increasing the Two-Photon Polymerization Potential

The present work reports on the development of photo-cross-linkable gelatins sufficiently versatile to overcome current biopolymer two-photon polymerization (2PP) processing limitations. To this end, both the primary amines as well as the carboxylic acids of gelatin type B were functionalized with photo-cross-linkable moieties (up to 1 mmol/g) resulting in superior and tunable mechanical properties (G′ from 5000 to 147000 Pa) enabling efficient 2PP processing. The materials were characterized in depth prior to and after photoinduced cross-linking using fully functionalized gelatin-methacrylamide (gel-MOD) as a benchmark to assess the effect of functionalization on the protein properties, cross-linking efficiency, and mechanical properties. In addition, preliminary experiments on hydrogel films indicated excellent in vitro biocompatibility (close to 100% viability) both in the presence of MC3T3 preosteoblasts and L929 fibroblasts. Moreover, 2PP processing of the novel derivative was superior in terms of applied laser power (≥40 vs ≥60 mW for gel-MOD at 100 mm/s) as well as post-production swelling (0–20% vs 75–100% for gel-MOD) compared to those of gel-MOD. The reported novel gelatin derivative (gel-MOD-AEMA) proves to be extremely suitable for direct laser writing as both superior mimicry of the applied computer-aided design (CAD) was obtained while maintaining the desired cellular interactivity of the biopolymer. It can be anticipated that the present work will also be applicable to alternative biopolymers mimicking the extracellular environment such as collagen, elastin, and glycosaminoglycans, thereby expanding current material-related processing limitations in the tissue engineering field.

When the material is irradiated in this state, the functional groups will be in close proximity, thereby enabling an efficient crosslinking reaction. Additionally, these crosslinks make sure that the triple helix structure is "locked", thereby providing additional structural integrity, even when surpassing the UCST. 1830 However, when the gelatin is heated above its UCST, the material is present as random polymer chains. When the crosslinking is induces, random bridges will be formed inside this random network, thereby making it insoluble. Additionally, when afterwards decreasing the temperature below the UCST, the triple helix formation will be hampered, and the increase in mechanical properties due to this phase transition will be very limited. 1830 (see Fig. S3) Figure S3. Influence of triple helix formation during physical gelation on the final mechanical properties.
Effect of gelatin functionalization and -concentration on the hydrogel gel fraction, water uptake capacity & network density

Rubber Elasticity theory
The network density of a hydrogel can be calculated using the average molecular weight, the equilibrium swelling ratio and the mechanical properties using the rubber elasticity theory. 24,31,32 This theory allows to calculate an estimation of several important parameters including the polymer volume fraction in the swollen state (v2,s), the volumetric swelling ratio (Q), the average molecular weight between crosslinks ( Mc ), the network mesh size (ξ) and the crosslink density (ρx).
Q and v2,s are both indications for the amount of liquid that can be imbibed inside a hydrogel which can be calculated starting from the mass swelling ratio q: 24,33 Herein, Vp and Vg represent respectively the polymer volume and the hydrogel volume at equilibrium swelling, while 2 and represent the density of water and gelatin respectively. The density of water is 1 g/cm³ while the density of gelatin was estimated to be around 1.36 g/cm³ based on previous reports from literature. 22,24,34,35 Since all network chains within the characterized hydrogels follow the Gaussian statistics model (Fig. S4), the obtained volumetric swelling ratio could be applied to determine in which G is the shear modulus (atm), c is the concentration of gelatin in the solution, R is the universal gas constant (L*atm*K -1 *mol -1 ), T is the temperature (K) and Mc is the average molecular weight between crosslinks (Da). Literature states that the shear modulus of hydrogels can be derived from the mean peak value of the storage modulus G', since the contribution of the loss modulus G" to the shear modulus can be considered negligible for all analyzed hydrogel samples. 24,37,38 Figure S4. Plot of log G vs log Q for all analyzed hydrogel films used in the rubber elasticity theory calculations (Eq (5)).
To obtain the average weight between crosslinks ( Mc ), equation (5) can be rewritten as: Once the average molecular weight between crosslinks ( with Cn being the Flory characteristic ratio which corresponds to 8.26 for gelatin based on reports from literature 30 , Mr is the average molecular weight of one repeating unit or one amino acid (assumed to be around 94.7 g/mol). 30,39 and l is the length of a bond along the polymer backbone. Furthermore, it should be noted that equation (7) is derived from the Flory-Rehner theory which is only strictly valid for simple systems like vinyl polymers. Therefore, the factor 2 has to be replaced by a factor 3 since the repetitive unit contains 2 bonds in contrast to 1 bond in vinyl polymers. 30 For the same reason, the bond length along the polymer backbone was approximated as the average bond length of one bond along the polymer backbone, taken as the arithmetic mean of one carbonyl C-C bond (1.53 Å) one C-N bond next to the carbonyl (1.32 Å) and a C-N bond (1.47 Å). 30,40 The crosslink density ρx is a measure for the number of crosslinks present per unit of volume and can be calculated from Mc and  , where  corresponds to the specific volume of gelatin, which was determined to be 0.735 cm³/g according to a previous study. 24

Voxel size calculations
The voxel size was calculated by approximating the illumination point spread function based by a three dimensional gaussian volume. To calculate this Gaussian volume the 1/e width in the lateral ( ) and axial ( ) dimension was calculated using the following formulas as The numerical aperture (NA) corresponds to 0.85 as provided by Zeiss. The refractive index was estimated to be 1.33 as the solutions consist primarily out of water..