We postulate that one will be able to quantitatively infer changes in the mechanical properties of proteins, cells, and other biological objects (BO) by measuring the shifts of several thermally excited resonance frequencies of atomic force microscopy cantilevers in contact with BOs. Here, we provide a method to extract spring constants and molecular damping factors of BOs in biologically relevant phosphate buffered saline medium and using compliant AFM cantilevers with a small aspect ratio (a ratio of length to width).
REFERENCES
We calculate the Young's modulus using a formula for a two-layer composite beam—Ref. 27 in the paper of Gavan et al.36—comprised of 50 nm gold and silicon nitride. Thickness of the silicon nitride itself is estimated within 114 nm to 186 nm.35 Error in the Young modulus is obtained using the results of of Gavan et al.,36 who measured Young's moduli of thin silicon nitride films.
Frequency of the 1st torsional resonance is calculated from , where the Poisson ratio for a SiNx cantilever is obtained from Ref. 33.
The PBS density of 998 kg/m3 was measured in Ref. 47 at temperature of about 22 °C.
A t-Student test is used to test H0: a2 = 0. To do so, a calculated t-Student coefficient for a2 is compared with its tabulated value for a given number of degrees of freedom and at a 99% confidence level. From the data in Fig. 4, we get a value of a2 = 0.059 and its standard deviation . Thus, the calculated t-Student coefficient is . This value is larger than a tabulated value t(17;0.01) = 2.9 read from the statistical tables for 17° of freedom and at 99% confidence level (P. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill Book Company, New York, 1969). Thus, H0 is not accepted.
