Research Paper

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

[+] Author and Article Information
Asit K. Saha

Center for Allaying Health Disparities through Research and Education (CADRE), Department of Mathematics and Computer Science, Central State University, Wilberforce, OH 45384asaha@centralstate.edu

Sean S. Kohles1

Reparative Bioengineering Laboratory, Department of Mechanical and Materials Engineering, Portland State University, Portland, OR 97201; Department of Surgery, Oregon Health and Science University, Portland, OR 97201kohles@cecs.pdx.edu


Corresponding author.

J. Nanotechnol. Eng. Med 1(3), 031005 (Aug 10, 2010) (8 pages) doi:10.1115/1.4001934 History: Received May 10, 2010; Revised June 01, 2010; Published August 10, 2010; Online August 10, 2010

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.

Copyright © 2010 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Schematic diagram of the simplified interactions between the critical influences on extracellular matrix turnover associated with anabolic and catabolic pathways

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Figure 2

Simulated time-dependent GAG and collagen accumulation from experimental parameters where collagen content was greater than GAG content, each with unique kinetic characteristics (36). Abundance is shown over dimensionless time with mechanical stimuli having a consistent scaling factor of ρ1(T)=ρ2(T)=1 and load components of (a) ξ1(T)=ξ2(T)=0.0, (b) ξ1(T)=ξ2(T)=0.02, and (c) ξ1(T)=ξ2(T)=1.0.

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Figure 3

GAG and collagen accumulation over time from an experimental scenario with GAG content much greater than collagen content, albeit with differing dynamic characteristics (37). The mechanical loads were included with a consistent scaling factor of ρ1(T)=ρ2(T)=1 and load components of (a) ξ1(T)=ξ2(T)=0.0, (b) ξ1(T)=ξ2(T)=0.02, and (c) ξ1(T)=ξ2(T)=1.0.

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Figure 4

Dynamic GAG and collagen accumulation modeled from experiments with collagen content being both greater in content and similar in form as the GAG accumulation (38). As with all of the models, mechanical stimulation had a consistent scaling factor of ρ1(T)=ρ2(T)=1 and load components of (a) ξ1(T)=ξ2(T)=0.0, (b) ξ1(T)=ξ2(T)=0.02, and (c) ξ1(T)=ξ2(T)=1.0.

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Figure 5

The cyclic phase-limit solutions describing the steady state progression in the relationship between growth factor and cytokine accumulation. In this analysis, time dependence was not included, thus eliminating the biokinetic rate differences between the three experimental input studies (36-38). These scenarios were all run with constant scaling factors of ρ1(T)=ρ2(T)=1. Mechanical load components were constrained to (a) ξ1(T)=ξ2(T)=1.0, (b) ξ1(T)=ξ2(T)=25.0, and (c) ξ1(T)=ξ2(T)=100.0. As development progresses during dimensionless culture time, the relative relationship loops clockwise as well as from the outward toward the central steady state condition until the mechanical stimulus disrupts the spiral progression, leading to an increase in growth factors with low cytokine levels, and presumably active ECM synthesis.




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