"Several biological molecules are known to form helices and coiled structures, such as DNA, collagen, bacterial flagella, and proteins. The backbones of such molecules may be modeled as a curve in three dimensions. A variational problem for the functional of the total free energy required to perturb moving curves in space is considered. The total energy of a curve in three dimensions is minimized y with a general intensive energy, which is a function of position, and the invariants, curvature and torsion. Three types of moduli are identified: stretching, bending and torsional moduli. As a result, three independent force balances are obtained which serve as the equilibrium conditions. Three cases are considered, the case of constant curvature and torsion (forming a helix), the case of no work done in banding the curve, and the case of no work done in twisting the curve. Stability analysis is performed leading to an unstable helix for the case of constant torsion and curvature. The other two cases are not analyzed due to the complexity of the results. It has been assumed that the moduli do not vary with position. However, a model has been provided for the case where the moduli vary slightly and can be used in the results obtained in order to obtain shapes of curves, where the curve will tend to bend to a natural curvature and torsion"--Abstract, page iii.
Neogi, P. (Partho), 1951-
Grow, David E.
Wang, Jee C.
Chemical and Biochemical Engineering
M.S. in Chemical Engineering
Missouri University of Science and Technology
vii, 36 pages
© 2011 Pavan Krishna Kanchi, All rights reserved.
Thesis - Open Access
Library of Congress Subject Headings
Linear free energy relationship
Molecules -- Models
Molecules -- Thermomechanical properties
Three-dimensional imaging in biology
Print OCLC #
Electronic OCLC #
Link to Catalog Recordhttp://laurel.lso.missouri.edu/record=b8713522~S5
Kanchi, Pavan Krishna, "Thermomechanics of curves in space" (2011). Masters Theses. 5291.