### Using Integration to make a Mathematical Model of Deflection for Single Linear Polymers

## by Suzanne Li

Submitted : Spring 2013

The mechanics of scaffolds play a key role in directing proper cell differentiation. Type I collagen molecules are triple helical molecules that form the basis of the naturally occurring scaffolds for tissues such as skin, bone, cornea, etc. Type I collagen has been demonstrated to effectively support *in vitro* cell differentiation and migration. Understanding the mechanics of collagen across all relevant length scales will lead to an informed rational design and construction of biomimetic scaffolds. The stiffness of molecular collagen is strongly influenced by the type and concentration of ions in a solution. To better understand how the collagen molecule folds, this paper will use integration to derive a formula to find the deflection of the molecule as a function of distance, and use experimentally gathered data to make a mathematical model of the curve under the most standard conditions.

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