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Darren E. Segall

Publications and source records attributed to Darren E. Segall.

2 recordsLinked to original sources
arXiv2005

Excluded-Volume Effects in Tethered-Particle Experiments: Bead Size Matters

The tethered-particle method is a single-molecule technique that has been used to explore the dynamics of a variety of macromolecules of biological interest. We give a theoretical analysis of the particle motions in such experiments. Our analysis reveals that the proximity of the tethered bead to a nearby surface (the microscope slide) gives rise to a volume-exclusion effect, resulting in an entropic force on the molecule. This force stretches the molecule, changing its statistical properties. In particular, the proximity of bead and surface brings about intriguing scaling relations between key observables (statistical moments of the bead) and parameters such as the bead size and contour length of the molecule. We present both approximate analytic solutions and numerical results for these effects in both flexible and semiflexible tethers. Finally, our results give a precise, experimentally-testable prediction for the probability distribution of the distance between the polymer attachment point and the center of the mobile bead.

q-bio.BM↗
arXiv2005

Expanding the Temporal Analysis in Single-Molecule Switching Experiments Through the Auto-Correlation Function: Mathematical Framework

A method is presented that, when used in conjunction with single molecule experimental techniques, allows for the extraction of rates and mechanical properties of a biomolecule undergoing transitions between mechanically distinct states. This analysis enables the exploration of systems where the lifetimes of survival are of order of the intrinsic time constant of the experimental apparatus; permitting the study of kinetic events whose transition rates are an order of magnitude (or two) larger than those that can be studied with traditional averaging methods. Using current experimental techniques, this allows for the study of biomolecules whose lifetime of survival in a given state are as low as milliseconds down to microseconds. The relevant observable is the auto-correlation function of the experimental probe that is attached to the biomolecule of interest. General solutions are expressed in terms of a series. Closed form solutions are found for two physically opposing limits: where transitions between the mechanically distinct states of the biomolecule occur on either much faster or much slower time scales than those governing the motion of the experimental probe. Motivated by the derivation of these opposing bounds, two series solutions for the general case are then presented. We present an error analysis for truncating each series at arbitrary order and obtain a range of parameters for which this method could be applicable to the study of the two state biomolecular problem. Finally, both series (up to third order) are expressed for the two state problem when the system obeys Markov statistics. These solutions should be amiable to the analysis of experimental data, expanding temporal analysis of data from single molecule experiments.

q-bio.BM↗