Mechanics of single flexible polymer chains using AFM Nanorheology

Abstract

In this thesis, I investigate the role of Atomic Force Microscope (AFM) nanorheology in quantitative estimate of stiffness for neutral flexible polymers and biopolymers. A major part of my thesis explores the possibility of bias in traditional pulling experiments with single molecule techniques of Atomic Force Microscope (AFM). In past, AFM based pulling experiments produces force-extension relation for polymers which have extensively reported unphysically low value of persistence length, a key and fundamental elasticity parameter. The thesis advances the current state-of-the-art in measuring single polymer elasticity in two aspects. First, it proposes active oscillatory rheology as a method to accurately measure entropic elasticity of polymer. Second, it further validates the methodology of active rheology with a home-built fiber-interferometer AFM. By actively oscillation the AFM cantilever at o -resonance frequency and slow pulling on polymer, we directly estimate stiffness of polymer. The active oscillations of AFM cantilever-probe with sub-nm amplitudes and o -resonance (< 1 KHz) frequencies, ensured that overall response is linear and dominated by elastic response. By simultaneous oscillations and slow pulling on polymer, I found that stiffness measured from oscillatory response showed signi ficant deviation from pulling force-extension curves. This was true only in good solvent whereas polymer in poor solvent showed no deviation. Analysis of stiffness with entropic WLC model yielded a large and physical persistence length in good solvents. The value also matched with constant force measurements done with magnetic tweezers. An additional free energy contribution explains no deviation in poor solvent. The results were rationalized with statistical mechanics of combined cantilever-polymer system and hints at importance of coupling between AFM cantilever-probe and intrinsic polymer response. We also performed oscillatory measurements with home-built fi ber-interferometer AFM. The fi ber-interferometer assembly measures cantilever deflection directly at a local point in contrast to commercial beam deflection methods. This becomes important while oscillating the cantilever base in liquids. A local detection at a pointprovides a straightforward interpretation of stiffness, independent of complications from cantilever hydrodynamics and further validated our methodology. In addition, fluctuations about measured stiffness showed expected dependence on the size ofpolymer chain. This was also not observed in traditional pulling experiments. The last part of my thesis deals with role of mechanical forces in proteins. In this regard, I pursued to understand how mechanical forces dictates the function and self-assembly of proteins. Specifically, I compared protein Titin with mechanical role inside cardiac muscle and a non-mechanical membrane protein using thermal fluctuations.Using fluctuation-dissipation relation, the power spectral density (PSD) of AFM thermal deflection reproduces the elastic response of protein. Compared to active method, we showed that fluctuations are not sensitive to the response of polymer due to dominance of viscous and elastic stiffness of a large AFM cantilever.