NDLI: An Inverse Power-Law Distribution of Molecular Bond Lifetimes Predicts Fractional Derivative Viscoelasticity in Biological Tissue

Content Provider	PubMed Central
Author	Palmer, Bradley M. Tanner, Bertrand C. W. Toth, Michael J. Miller, Mark S.
Copyright Year	2013
Abstract	Viscoelastic characteristics of many materials falling under the category of soft glassy substances, including biological tissue, often exhibit a mechanical complex modulus Y(ω) well described by a fractional derivative model: Y(ω) = E(iω/ϕ) k , where E = a generalized viscoelastic stiffness; i = (−1)1/2; ω = angular frequency; ϕ = scaling factor; and k = an exponent valued between 0 and 1. The term “fractional derivative” refers to the value of k: when k = 0 the viscoelastic response is purely elastic, and when k = 1 the response is purely viscous. We provide an analytical derivation of the fractional derivative complex modulus based on the hypothesis that the viscoelastic response arises from many intermittent molecular crosslinks, whose lifetimes longer than a critical threshold lifetime, t crit, are distributed with an inverse power law proportional to t -(k+2). We demonstrate that E is proportional to the number and stiffness of crosslinks formed at any moment; the scaling factor ϕ is equivalent to reciprocal of t crit; and the relative mean lifetime of the attached crosslinks is inversely proportional to the parameter k. To test whether electrostatic molecular bonds could be responsible for the fractional derivative viscoelasticity, we used chemically skinned human skeletal muscle as a one-dimensional model of a soft glassy substance. A reduction in ionic strength from 175 to 110 mEq resulted in a larger E with no change in k, consistent with a higher probability of interfilament molecular interactions. Thick to thin filament spacing was reduced by applying 4% w/v of the osmolyte Dextran T500, which also resulted in a larger E, indicating a greater probability of crosslink formation in proportion to proximity. A 10°C increase in temperature resulted in an increase in k, which corresponded to a decrease in cross-bridge attachment lifetime expected with higher temperatures. These theoretical and experimental results suggest that the fractional derivative viscoelasticity observed in some biological tissue arises as a mechanical consequence of electrostatic interactions, whose longest lifetimes are distributed with an inverse power law.
Related Links	http://dx.doi.org/10.1016/j.bpj.2013.04.045
Ending Page	2552
Page Count	13
Starting Page	2540
File Format	PDF
ISSN	00063495
e-ISSN	15420086
Journal	Biophysical Journal
Issue Number	11
Volume Number	104
Language	English
Publisher	The Biophysical Society
Publisher Date	2013-06-01
Access Restriction	Open
Rights Holder	The Biophysical Society
Subject Keyword	Biophysics Research in Higher Education
Content Type	Text
Resource Type	Article
Subject	Biophysics

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