A Distinct Catabolic to Anabolic Threshold Due to Single-Cell Static Nanomechanical Stimulation in a Cartilage Biokinetics Model

Abstract

Understanding physicochemical interactions during biokinetic regulation will be critical for the creation of relevant nanotechnology supporting cellular and molecular engineering. The impact of nanoscale influences in medicine and biology can be explored in detail through mathematical models as an in silico testbed. In a recent single-cell biomechanical analysis, the cytoskeletal strain response due to fluid-induced stresses was characterized (Wilson, Z. D., and Kohles, S. S., 2010, "Two-Dimensional Modeling of Nanomechanical Strains in Healthy and Diseased Single-Cells During Microfluidic Stress Applications," J. Nanotech. Eng. Med., 1(2), p. 021005). Results described a microfluidic environment having controlled nanometer and piconewton resolution for explorations of multiscale mechanobiology. In the present study, we constructed a mathematical model exploring the nanoscale biomolecular response to that controlled microenvironment. We introduce mechanical stimuli and scaling factor terms as specific input values for regulating a cartilage molecule synthesis. Iterative model results for this initial multiscale static load application have identified a transition threshold load level from which the mechanical input causes a shift from a catabolic state to an anabolic state. Modeled molecule homeostatic levels appear to be dependent upon the mechanical stimulus as reflected experimentally. This work provides a specific mathematical framework from which to explore biokinetic regulation. Further incorporation of nanomechanical stresses and strains into biokinetic models will ultimately lead to refined mechanotransduction relationships at the cellular and molecular levels.

Periodic Nanomechanical Stimulation in a Biokinetics Model Identifying Anabolic and Catabolic Pathways Associated With Cartilage Matrix Homeostasis

“…6). Both GAG and collagen concentrations at the steady state are now much higher than those observed in the situations without any loading [22] and with the lowest amount of loading ρ =0.02 (Figs. 2 and 3).…”

“…It was also observed that although the collagen molecule accumulation is very high at about the 1,000th dimensionless time step, its abundance is reduced to a much lower value by the steady state condition. In the case of the other modeled structural molecule GAG, no dramatic change is observed between its peak concentration at the 10,000th dimensionless time step and its steady state values [22]. …”

“…Mechanical stresses are defined as static or dynamic, a constant load acting continuously on the tissue or through variable loading, respectively. We previously identified a catabolic to anabolic threshold due to static nanomechanical loading [22]. In the present study, we describe a biokinetic balance achieved through a periodic loading with respect to time.…”

“…(4), can be obtained from the following relationship [22]: $$(C_{ss},G_{ss},{\text{collagen}}_{ss},\text{and}{\text{GAG}}_{ss})=\left(\left\{{\mathrm{\Omega }}_1+\frac{{\beta }_2}{{\alpha }_2}\right\},\left\{{\mathrm{\Omega }}_2-\frac{{\beta }_1}{{\alpha }_1}\right\},\left\{\frac{{\lambda }_1{G}_{ss}}{{\delta }_1(1+C_{ss})}\right\},\text{and}\left\{\frac{{\lambda }_2{G}_{ss}}{{\delta }_2(1+C_{ss})}\right\}\right)$$…”

“…All simulations were run using commercial software (MATHCAD 14.0, Parametric Technology Corp., Needham, MA). Phase one described the dynamics of anabolic and catabolic pathways and the consequent ECM molecule deposition with and without a static mechanical stress [21,22]. In phase two presented here, the results of the biokinetics of the anabolic and catabolic networks and the consequent ECM molecule deposition are shown due to an imposed dynamic stress (periodic loading).…”