This thesis contains several contributions to the theoretical description and interpretation of biophysical single-molecule measurements: (i) For semiflexible polymers, we derive an efficient formulation of their local transverse dynamics in terms of a Generalized Langevin Equation. The elastic and frictional properties of the polymer are condensed into a memory kernel that is a function of the polymer\'s length and stiffness, the level of backbone tension, the position of the force probe along the polymer backbone and the boundary conditions at the polymer ends. At short times, the memory kernel attains a universal limiting form that depends neither on the polymer length nor on the boundary conditions; we obtain analytical results that accurately describe this regime. We discuss how to quickly and reliably evaluate the memory kernel for arbitrary times using a spectral decomposition method, and use an extensive body of numerical data to obtain analytical approximations to the memory kernel that cover the complementary long-time limit wherein polymer friction can be subsumed under a renormalized drag coefficient. (ii) Based on a systematic nonequilibrium treatment of an overdamped, one-dimensional stochastic escape process driven by external force, we develop a theory of Dynamic Force Spectroscopy (DFS) that generalizes previously available DFS theories to the high loading rates realized in novel experimental assays and in computer simulations. (iii) Extrapolating to future DFS experiments that may operate at far higher time resolution than presently achievable, we discuss the fast nonequilibrium relaxation of a semiflexible linker after bond rupture. Based on a rigorous theory of tension propagation in semiflexible polymers, we predict the relaxation of force within the force actuator, show that this relaxation is dominated by linker contraction, and demonstrate quantitative agreement of our predictions with experimental data obtained by a collaborating experimentalist group.

This thesis contains several contributions to the theoretical description and interpretation of biophysical single-molecule measurements: (i) For semiflexible polymers, we derive an efficient formulation of their local transverse dynamics in terms of a Generalized Langevin Equation. The elastic and frictional properties of the polymer are condensed into a memory kernel that is a function of the polymer\''s length and stiffness, the level of backbone tension, the position of the force probe along the polymer backbone and the boundary conditions at the polymer ends. At short times, the memory kernel attains a universal limiting form that depends neither on the polymer length nor on the boundary conditions; we obtain analytical results that accurately describe this regime. We discuss how to quickly and reliably evaluate the memory kernel for arbitrary times using a spectral decomposition method, and use an extensive body of numerical data to obtain analytical approximations to the memory kernel that cover the complementary long-time limit wherein polymer friction can be subsumed under a renormalized drag coefficient. (ii) Based on a systematic nonequilibrium treatment of an overdamped, one-dimensional stochastic escape process driven by external force, we develop a theory of Dynamic Force Spectroscopy (DFS) that generalizes previously available DFS theories to the high loading rates realized in novel experimental assays and in computer simulations. (iii) Extrapolating to future DFS experiments that may operate at far higher time resolution than presently achievable, we discuss the fast nonequilibrium relaxation of a semiflexible linker after bond rupture. Based on a rigorous theory of tension propagation in semiflexible polymers, we predict the relaxation of force within the force actuator, show that this relaxation is dominated by linker contraction, and demonstrate quantitative agreement of our predictions with experimental data obtained by a collaborating experimentalist group.