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Cell Adhesion Measurement Device
Cell sits between two plates
One plate fixed, one plate attached to linear spring
Actuator pulls spring into tension
Adhesion of Cell
Cell will have a smooth outer membrane or flagellum
Both exhibit non-linear cell/plate separation
Flagellum
Smooth Membrane
http://library.thinkquest.org/16985/cellmain.htm
http://fig.cox.miami.edu/Faculty/Dana/105F00_4.html
Diagram and Variables
6 variables: D2, P2, ks, D1, P1, kc
2 equations can be derived: P1 = D1*(kc + ks) – D2*ks
P2 = ks*(D2 – D1)
D2
P2
ks kc
D1
P1
D2 is controlled by nano-tractor
P2 is the force needed for nano-tractor
P1 is the force needed to pull the cell
D1 is the displacement of the cell
kc is the spring constant of the cell
ks is the spring constant of the spring
Assumptions
P2 is not needed
Assumptions need to be made for other variables in order to find values for k’s
D2
P2
ks kc
D1
P1
Finding kc
Assumptions Cell is a cylinder Diameter equals length Diameter roughly 10-50 um
Calculation kc = E*pi*d/4 kc = .0076-.0393 N/m
Finding ks
D2
P2
ks kc
D1
P1
Assumptions P1 = 1-100 nN D2 = 11 um – ls + D1
Due to limit of optical measuring tool Assume ls = 8 um
Made spreadsheet ks = 0.0246 N/m
Verification Find increment for D2 that works for range
Must be greater than 40 nm Selected 250 nm
Check if increment will be detectable
Overview of Range
Case Ks (N/m)
Kc (N/m)
P1 (nN)
D1 (um)
D2 (um)
# of Increments
Most Elastic Cell
.0246 .0076 100 22.0 25.0 100
Least Elastic Cell
.0246 .0393 1 1.74 4.74 20