(52b) Predicting Enzymatic Degradation of Silk Scaffolds through Reaction-Diffusion Analytical Modeling

Biomaterials formed from silk fibroin have many potential clinical uses for repair and rehabilitation of damaged or diseased tissues (1,2). One major advantage of sponges formed from silk fibroin is the slow enzymatic degradation of the material into simple amino acids or small peptides in vivo (3). The slow, and potentially tunable, in vivo degradation rate affords additional advantages to the implanted silk-based biomaterial over traditional natural materials with similar structures, such as collagen sponges. These advantages include features of the silk sponges that can be independently controlled during the actual sponge formation process. Silk sponges can be tuned during formulation by modulating the silk fibroin polymer chain length, the concentration of silk fibroin protein incorporated into the sponge, the temperature at which the silk solution is frozen (dictating sponge pore size), and the level of induced crystallinity in the silk fibroin protein (4-6). Together, these independently tunable parameters modulate the final mechanical properties of the sponge and are what afford tunability in degradation rates in vivo. Thus, these parameters should be taken into consideration as we evaluate or predict in vivo degradation rates to enable intelligent and guided design of biomaterials for specific clinical applications. Consequently, it is critical to understand what components of the original scaffold formulation drive in vivo degradation. We have chosen to do this through development of a mathematical model that takes into consideration the initial scaffold conditions, silk fibroin crystallinity levels, and the enzymatic status of the implant location to enable predictability of the rate of scaffold degradation upon implantation.

To achieve the first steps in this process, degradation rates of silk materials were measured in vitro using common protein-degrading enzymes such as Proteinase K and Protease XIV. The concentration of the enzyme in solution was varied (1 U/mL, 0.1 U/mL) along with one silk sponge formulation parameter: the level of crystallinity within the samples (6 vs. 12 hours of water annealing). We held the silk concentration, polymer chain length and scaffold pore size constant as an initial set of experimental data for model development and validation. Preliminary experimental results suggest the enzyme itself and enzyme concentration within the system are the major components dictating silk sponge degradation. To build a model represent our data and enable future predictions of intermediate parameter values, a partial differential equation including reaction terms to account for the breakdown of the silk protein and diffusion terms to account for the diffusion of the silk protein peptides into the bulk enzyme solution was developed. Currently, the partial differential model uses a modified Michaelis-Menten term to approximate silk peptide generation due to enzymatic degradation of the silk sponge and diffusion of the generated silk peptides or “silk bits” in a spherical geometry to obtain enzyme effects on the biodegradation of silk in biological media. The model was solved analytically to provide information about the relevant variables and parametric functions that relate material mass loss, time, and enzyme composition. We assumed, in our in vitro experiments, that enzyme diffusion into the bulk of the scaffold was negligible and therefore enzyme concentration was uniform throughout the scaffold system. We recognize that in vivo, this assumption will not hold and future experiments and alterations to the model will be needed. However, the next step in this process is to determine how and if experimental parameters such as enzyme concentration, enzyme activity, and scaffold formulation variables can be incorporated into the constants in the mathematical model. Future work will look at understanding how the constants in these terms relate to the acquired experimental data to determine the influence of silk sponge formation variables on the resulting degradation fits. These results will guide biomaterial design to achieve semi-predicable biomaterial performance for the large array of tissue engineering applications a priori, leading to better clinical outcomes following implantation.

1. Huang, W.; Ling, S.; Li, C.; Omenetto, F. G.; Kaplan, D. L., Silkworm silk-based materials and devices generated using bio-nanotechnology. Chem Soc Rev 2018, 47 (17), 6486-6504.
2. Stoppel, W. L.; Raia, N.; Kimmerling, E.; Wang, S.; Ghezzi, C. E.; Kaplan, D. L., 2.12 Silk Biomaterials. In Comprehensive Biomaterials II, Ducheyne, P., Ed. Elsevier: Oxford, 2017; pp 253-278.
3. Cao, Y.; Wang, B., Biodegradation of silk biomaterials. International journal of molecular sciences 2009, 10 (4), 1514-1524.
4. Rnjak-Kovacina, J.; Wray, L. S.; Burke, K. A.; Torregrosa, T.; Golinski, J. M.; Huang, W.; Kaplan, D. L., Lyophilized Silk Sponges: A Versatile Biomaterial Platform for Soft Tissue Engineering. ACS Biomater Sci Eng 2015, 1 (4), 260-270.
5. Wray, L. S.; Rnjak-Kovacina, J.; Mandal, B. B.; Schmidt, D. F.; Gil, E. S.; Kaplan, D. L., A silk-based scaffold platform with tunable architecture for engineering critically-sized tissue constructs. Biomaterials 2012, 33 (36), 9214-9224.
6. Stoppel, W. L.; Hu, D. J.; Domian, I. J.; Kaplan, D. L.; Black, L. D., Anisotropic silk biomaterials containing cardiac extracellular matrix for cardiac tissue engineering. Biomedical Materials 2015, 10 (3), 034105.