Nanoscale Brownian Dynamics of Semiflexible Biopolymers

Abstract

Proteins are one of, if not the most, versatile of biology's tools, performing a great variety of functions in living organisms and giving rise to behavior as complex as life itself. They are linear chains of amino acids and therefore heteropolymers from a chemical point of view. Performing diverse tasks while obeying the laws of thermodynamics and microscopic physics, proteins thus invoke the interest of biologists, chemists and physicists alike.While the theoretical foundations for describing molecular motion can be traced back more than a century, experimental techniques allowing us to measure the dynamics of single molecules have only become available in the last twenty years. Here, we aim to link the two together and use data from single-molecule experiments to infer characteristic properties of individual proteins in a systematic and quantitative manner. In particular, we have at our disposal three complementing methods which measure dynamical properties of single molecules. The first is photo-induced electron transfer paired with fluorescence correlation spectroscopy (PET-FCS) which measures their end-to-end or internal-to-end loop formation rate, the second is dual-focus fluorescence correlation spectroscopy (2fFCS) which measures their hydrodynamic radius, and the third is dynamic metal-induced energy transfer (dynaMIET) which measures their reconfiguration time when bound to a surface.In this thesis, we develop a polymer model which enables the efficient interpretation of results from PET-FCS, 2fFCS and dynaMIET experiments. This model is a bead-rod chain which takes into account hydrodynamic interactions, excluded volume effects, bending rigidity and the fluorophore with which the protein is labeled, while including only two free parameters. It quantitatively reproduces systematically measured data from PET-FCS and 2fFCS applied to glycine-serine (GS) repeats -the prototype of an intrinsically disordered protein (IDP). Loop formation dynamics in GS-repeats typically take tens of nanoseconds, and their hydrodynamic radius is around one nanometer. From this data, the model yields a persistence length of l P = 5.2 ± 1.9 Å and one amino acid's hydrodynamic radius of a = 3.5 ± 0.7 Å, while at the same time validating the important role of excluded volume effects in the dynamics of GS-repeats. Thus, we now have at hand a combined method of performing single-molecule experiments and Brownian dynamics simulations for IDPs which yields quantitative insights into their molecular properties. This enables further study of the elastic and hydrodynamic properties associated with different amino acid sequences. Extending the model to take into account secondary structures, inhomogeneities or internal friction effects should be subject to future work. This may improve our understanding of the mechanisms governing protein function and folding, and hence contribute to novel medical treatments and drug design.

Conformational dynamics of electrostatically charged Intrinsically Disordered Proteins

“…Here, we only consider a discretization of the bending energy within the DER model [2,3], neglecting the (more elaborate) model for twist. This is justified by numerical experiments in [8], which show that the twist has only very little influence on contact rates.…”

“…Simulations were conducted using projection-based (second order) retractions, see Section 2.2 of [17] for detail. The starting configuration of the polymer chain was generated from the appropriate Boltzmann distribution via an MCMC sampler, see [8]. Subsequently, the simulations were run for a physical time of 33 µs, each integration step corresponding to about 220 fs.…”

“…where q j is the charge of bead x j and ε the electric permittivity of the surrounding solution. For details on the conformation-dependent entropic force F j P we refer to [8].…”

“…In order to model the dynamics of the Prot-α we follow the approach of [8,9] and define a coarse grained model 1.97 (µs) −1 ) while the experimentally measured rates are displayed in black (left: 4.35 ± 0.33 (µs) −1 ; right: 1.14 ± 0.29 (µs) −1 ). Notice that the slightly changed charge distribution resulting from replacing one positively charged amino acid at position 22 by the quencher has a tremendous impact on the loop closing rates.…”

“…The respective model includes only three free parameters: bending stiffness, bond length, and hydrodynamic radius. These parameters were obtained by fitting the measured conformational dynamics of uncharged polypeptides as reported in a previous publication [8]. We compare our computational results with photo-electron transfer fluorescence correlation spectroscopy (PET-FCS) measurements of the conformational dynamics of the highly charged (-44 e − ) intrinsically disordered protein Prothymosin α.…”