Kinetics of Loop Closure in Disordered Proteins: Theory vs Simulations vs Experiments

Satija, Rohit; Das, A. K.; Mühle, Steffen; Enderlein, Joerg; Makarov, Dmitrii E.

doi:10.1021/acs.jpcb.0c01437

Cited by 12 publications

(13 citation statements)

References 69 publications

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“…Given the heterogeneous cytosol composition with macromolecules of different sizes and shapes together with the time scale separation between tumbling and translational motions, this single-exponential approximation is unlikely to be accurate but can easily be generalized to include multiple exponentially decaying terms with different characteristic time scales. 18 Within the exponential memory kernel approximation, the electric friction is characterized by two parameters: the strength of the electric field fluctuations ⟨E 2 ⟩ and the memory time τ e . When the time scale of interest is much longer than τ e , however, the effect of electric friction can be characterized by a single parameter, the electric friction coefficient (8) This parameter corresponds to the Markovian approximation to the GLE, where the friction memory kernel is approximated by the delta function, Γ(t) ≈ 2δ(t) ∫ 0 ∞ Γ(τ) dτ = 2ξ e δ(t), and thus the electric friction force in eq 4 is approximated simply by −ξ e x(t).…”

Section: Resultsmentioning

confidence: 99%

“…(Note that ⟨ E ⟩ = 0 for a randomly tumbling dipole.) As a result, the friction memory kernel is also an exponential function, Given the heterogeneous cytosol composition with macromolecules of different sizes and shapes together with the time scale separation between tumbling and translational motions, this single-exponential approximation is unlikely to be accurate but can easily be generalized to include multiple exponentially decaying terms with different characteristic time scales …”

Section: Resultsmentioning

confidence: 99%

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Does Electric Friction Matter in Living Cells?

Makarov

Hofmann

2021

J. Phys. Chem. B

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The thermal motion of charged proteins causes randomly fluctuating electric fields inside cells. According to the fluctuation–dissipation theorem, there is an additional friction force associated with such fluctuations. However, the impact of these fluctuations on the diffusion and dynamics of proteins in the cytoplasm is unclear. Here, we provide an order-of-magnitude estimate of this effect by treating electric field fluctuations within a generalized Langevin equation model with a time-dependent friction memory kernel. We find that electric friction is generally negligible compared to solvent friction. However, a significant slowdown of protein diffusion and dynamics is expected for biomolecules with high net charges such as intrinsically disordered proteins and RNA. The results show that direct contacts between biomolecules in a cell are not necessarily required to alter their dynamics.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Does Electric Friction Matter in Living Cells?

Makarov

Hofmann

2021

J. Phys. Chem. B

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“…In particular, even in the extreme of infinitely short memory (i.e., the Markov limit, eq ), eq can still be used to determine the friction coefficient γ. Indeed, utility of eq has been tested in application to experimentally observed dynamics of a micrometer-sized dielectric bead in a dual optical trap and in application to simulated loop closure dynamics in intrinsically disordered proteins …”

Section: If Dynamics Is Non-markovian Then What Kind Of Dynamics Is I...mentioning

confidence: 99%

Barrier Crossing Dynamics from Single-Molecule Measurements

Makarov

2021

J. Phys. Chem. B

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Chemists visualize chemical reactions as motion along one-dimensional "reaction coordinates" over free energy barriers. Various rate theories, such as transition state theory and the Kramers theory of diffusive barrier crossing, differ in their assumptions regarding the mathematical specifics of this motion. Direct experimental observation of the motion along reaction coordinates requires single-molecule experiments performed with unprecedented time resolution. Toward this goal, recent singlemolecule studies achieved time resolution sufficient to catch biomolecules in the act of crossing free energy barriers as they fold, bind to their targets, or undergo other large structural changes, offering a window into the elusive reaction "mechanisms". This Perspective describes what we can learn (and what we have already learned) about barrier crossing dynamics through synergy of single-molecule experiments, theory, and molecular simulations. In particular, I will discuss how emerging experimental data can be used to answer several questions of principle. For example, is motion along the reaction coordinate diffusive, is there conformational memory, and is reduction to just one degree of freedom to represent the reaction mechanism justified? It turns out that these questions can be formulated as experimentally testable mathematical inequalities, and their application to experimental and simulated data has already led to a number of insights. I will also discuss open issues and current challenges in this fast evolving field of research.

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“…This match is in agreement with our finding that SSS-theory (which assumes one-dimensional Markovian end-to-end dynamics, see page 142) correctly predicts the scaling behavior of the contact rate as a function of chain length. For further reading, we refer to the published manuscript [171].…”

Section: Kinetics Of Loop Closure In Disordered Proteinsmentioning

confidence: 99%

“…At the same time, the transition path times for loop closure in longer polypeptide chains show significant non-Markov effects; at intermediate times, these effects are better captured by the generalized Langevin equation model. At long times, however, atomistic simulations predict long tails in the distributions of transition path times, which are at odds with both the one-dimensional diffusion model and the generalized Langevin equation model.This project was published in the Journal of Physical Chemistry B on April 7th 2020[171]. The research for it was done by Rohit Satija and Dmitrii Makarov.…”

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confidence: 99%

Nanoscale Brownian Dynamics of Semiflexible Biopolymers

Steffen¹

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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.

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Kinetics of Loop Closure in Disordered Proteins: Theory vs Simulations vs Experiments

Cited by 12 publications

References 69 publications

Does Electric Friction Matter in Living Cells?

Does Electric Friction Matter in Living Cells?

Barrier Crossing Dynamics from Single-Molecule Measurements

Nanoscale Brownian Dynamics of Semiflexible Biopolymers

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