Table 1.

List of symbols used and their definitions

SymbolDefinition
ωr First natural frequency
k C Linear spring constant
ωr A First natural frequency after protein layer attachment
ωr B First natural frequency after target analyte capture
m C Effective mass of the cantilever
m A Effective mass of the protein layer
m B Mass of the target analyte biomolecule
Δωr A Change in resonant frequency after protein layer attachment
Δωr B Change in resonant frequency after target analyte biomolecules capture
k C+A Linear spring constant of the cantilever after protein layer attachment
L C Length of cantilever beam
W C Width of cantilever beam
t C Thickness of cantilever beam
t A Thickness of protein layer
A C Surface area of cantilever beam
L C,T Transition length of cantilever that predicts reversal of sign of Δωr A after protein layer attachment
t C,T Transition thickness of cantilever that predicts reversal of sign of Δωr A after protein layer attachment
E comp Young’s modulus of the composite protein/cantilever layer
ρcomp Density of the composite protein/cantilever layer
ρC Density of the cantilever material
ρA Density of the protein layer
k B Boltzmann’s constant
T Temperature of surrounding medium
B Measurement bandwidth
Q Unloaded quality factor of cantilever beam
ÂSquare root of the mean-square amplitude of the vibration of the cantilever