We present a new theory for modeling spectral lineshapes available from single-particle 

forced indentation experiments. The theory considers weakly non-linear Hertzian deformation due 

to a physical contact between the indenter and the biological particle, and bending deformations of 

other portions of the particle structure modeled as ‘vertical beams’. The bending of beams beyond 

the critical point sets in the particle dynamic transition to the collapsed state, an extreme event leading 

to the catastrophic force drop as observed in the force (F)-deformation (X) spectra (FX curves). 

The theory interprets fine features of the spectra, i.e. the slope of the FX curves and the force-peak 

signal, in terms of mechanical characteristics such as the Young’s moduli for Hertzian and bending 

deformations, and the Weibull probability distribution of the maximum strength with the scale parameter 

and shape parameter. The theory is applied to model the FX curves for several spherically shaped 

virus particles – CCMV, TrV, and AdV.