End-to-surface reaction dynamics of a single surface-attached DNA or polypeptide

Experimental Measurement of Surface Charge Effects on the Stability of a Surface-Bound Biopolymer

Quantitative experimental studies of the thermodynamics with which biopolymers interact with specific surfaces remain quite limited. In response, here we describe experimental and theoretical studies of the change in folding free energy that occurs when a simple biopolymer, a DNA stem-loop, is site-specifically attached to a range of chemically distinct surfaces generated via self-assembled monolayer formation on a gold electrode. Not surprisingly, the extent to which surface attachment alters the biopolymer's folding free energy depends strongly on the charge of the surface, with increasingly negatively charged surfaces leading to increased destabilization. A simple model that considers only the excluded volume and electrostatic repulsion generated by the surface and models the ionic environment above the surface as a continuum quantitatively recovers the observed free energy change associated with attachment to weakly charged negative surfaces. For more strongly charged negative surfaces a model taking into account the discrete size of the involved ions is required. Our studies thus highlight the important role that electrostatics can play in the physics of surface-biomolecule interactions.

Theoretical and computational validation of the Kuhn barrier friction mechanism in unfolded proteins

A long time ago, Kuhn predicted that long polymers should approach a limit where their global motion is controlled by solvent friction alone, with ruggedness of their energy landscapes having no consequences for their dynamics. In contrast, internal friction effects are important for polymers of modest length. Internal friction in proteins, in particular, affects how fast they fold or find their binding targets and, as such, has attracted much recent attention. Here we explore the molecular origins of internal friction in unfolded proteins using atomistic simulations, coarse-grained models and analytic theory. We show that the characteristic internal friction timescale is directly proportional to the timescale of hindered dihedral rotations within the polypeptide chain, with a proportionality coefficient b that is independent of the chain length. Such chain length independence of b provides experimentally testable evidence that internal friction arises from concerted, crankshaft-like dihedral rearrangements. In accord with phenomenological models of internal friction, we find the global reconfiguration timescale of a polypeptide to be the sum of solvent friction and internal friction timescales. At the same time, the time evolution of inter-monomer distances within polypeptides deviates both from the predictions of those models and from a simple, one-dimensional diffusion model.

Dynamics of the reaction between the free end of a tethered self-avoiding polymer and a flat penetrable surface: a renormalization group study

The average time τr for one end of a long, self-avoiding polymer to interact for the first time with a flat penetrable surface to which it is attached at the other end is shown here to scale essentially as the square of the chain's contour length N. This result is obtained within the framework of the Wilemski-Fixman approximation to diffusion-limited reactions, in which the reaction time is expressed as a time correlation function of a "sink" term. In the present work, this sink-sink correlation function is calculated using perturbation expansions in the excluded volume and the polymer-surface interactions, with renormalization group methods being used to resum the expansion into a power law form. The quadratic dependence of τr on N mirrors the behavior of the average time τc of a free random walk to cyclize, but contrasts with the cyclization time of a free self-avoiding walk (SAW), for which τr ∼ N(2.2). A simulation study by Cheng and Makarov [J. Phys. Chem. B 114, 3321 (2010)] of the chain-end reaction time of an SAW on a flat impenetrable surface leads to the same N(2.2) behavior, which is surprising given the reduced conformational space a tethered polymer has to explore in order to react.

Universality in the timescales of internal loop formation in unfolded proteins and single-stranded oligonucleotides

Understanding the rate at which various parts of a molecular chain come together to facilitate the folding of a biopolymer (e.g., a protein or RNA) into its functional form remains an elusive goal. Here we use experiments, simulations, and theory to study the kinetics of internal loop closure in disordered biopolymers such as single-stranded oligonucleotides and unfolded proteins. We present theoretical arguments and computer simulation data to show that the relationship between the timescale of internal loop formation and the positions of the monomers enclosing the loop can be recast in a form of a universal master dependence. We also perform experimental measurements of the loop closure times of single-stranded oligonucleotides and show that both these and previously reported internal loop closure kinetics of unfolded proteins are well described by this theoretically predicted dependence. Finally, we propose that experimental deviations from the master dependence can then be used as a sensitive probe of dynamical and structural order in unfolded proteins and other biopolymers.

A mechanistic study of electron transfer from the distal termini of electrode-bound, single-stranded DNAs

Electrode-bound, redox-reporter-modified oligonucleotides play roles in the functioning of a number of electrochemical biosensors, and thus the question of electron transfer through or from such molecules has proven of significant interest. In response, we have experimentally characterized the rate with which electrons are transferred between a methylene blue moiety on the distal end of a short, single-stranded polythymine DNA to a monolayer-coated gold electrode to which the other end of the DNA is site-specifically attached. We find that this rate scales with oligonucleotide length to the -1.16 ± 0.09 power. This weak, approximately inverse length dependence differs dramatically from the much stronger dependencies observed for the rates of end-to-end collisions in single-stranded DNA and through-oligonucleotide electron hopping. It instead coincides with the expected length dependence of a reaction-limited process in which the overall rate is proportional to the equilibrium probability that the end of the oligonucleotide chain approaches the surface. Studies of the ionic strength and viscosity dependencies of electron transfer further support this "chain-flexibility" mechanism, and studies of the electron transfer rate of methylene blue attached to the hexanethiol monolayer suggest that heterogeneous electron transfer through the monolayer is rate limiting. Thus, under the circumstances we have employed, the flexibility (i.e., the equilibrium statistical properties) of the oligonucleotide chain defines the rate with which an attached redox reporter transfers electrons to an underlying electrode, an observation that may be of utility in the design of new biosensor architectures.