What protein folding teaches us about biological function and molecular machines

Whitford, Paul C.; Onuchic, José N.

doi:10.1016/j.sbi.2014.12.003

Cited by 31 publications

(33 citation statements)

References 44 publications

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“…The present analysis suggests that the "effective" landscape that a protein may experience on its journey towards the native state is smoothened by higher dimensionality. Thus, multidimensionality is a way to understand the "Principle of minimum frustration" advocated by Wolynes, Onuchic and co-workers [25, [56][57][58][59]. As a walker can get trapped in 1d, having an extra dimension really can help in making the effective landscape (that is the landscape explored) smooth and minimally frustrated.…”

Section: Discussionmentioning

confidence: 99%

Anomalous dimensionality dependence of diffusion in a rugged energy landscape: How pathological is one dimension?

Seki

Bagchi²,

Bagchi

2016

The Journal of Chemical Physics

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Diffusion in one dimensional rugged energy landscape (REL), is predicted to be pathologically different (from any higher dimension) with much larger chance of encountering broken ergodicity (D. L. Stein and C. M. Newman, AIP Conf. Proc. 1479Proc. , 620 (2012). However, no quantitative study of this difference has been reported, despite prevalence of multidimensional physical models in literature (like a high dimensional funnel guiding protein folding/unfolding). Paradoxically, some theoretical studies of these phenomena still employ a one dimensional diffusion description for analytical tractability. We explore the dimensionality dependent diffusion on REL by carrying out an effective medium approximation based analytical calculations and compare them with the available computer simulation results. We find that at intermediate level of ruggedness (assumed to have 2 a Gaussian distribution), where diffusion is well-defined, the value of the effective diffusion coefficient depends on dimensionality and changes (increases) by several factors (~5-10) in going from 1d to 2d. In contrast, the changes in subsequent transitions (like 2d to 3d and 3d to 4d and so on) are far more modest, of the order of 10-20% only. When ruggedness is given by random traps with an exponential distribution of barrier heights, the mean square displacement is sub-diffusive (a well-known result), but the growth of MSD is described by different exponents in one and higher dimensions.The reason for such strong ruggedness induced retardation in the case of one dimensional REL is discussed. We also discuss the special limiting case of infinite dimension (d= ∞ ) where the effective medium approximation becomes exact and where theoretical results become simple. We discuss, for the first time, the role of spatial correlation in the landscape on diffusion of a random walker.

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Section: Discussionmentioning

confidence: 99%

Anomalous dimensionality dependence of diffusion in a rugged energy landscape: How pathological is one dimension?

Seki

Bagchi²,

Bagchi

2016

The Journal of Chemical Physics

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“…1C; described in 48 ). According to Equation 3, an individual contact Q s j has a value of 1 if the corresponding residue pair is within 1Å of the distance found in configuration s. If the pair is extended by more than 1Å, then its contribution decays according to a Gaussian function. Equation 2 has the property that (for W j = 1), if all pairs are within 1Å of their distances found in conformation s, then Q s will reach a maximum value of 1.…”

Section: Contact-based Collective Coordinatesmentioning

confidence: 99%

“…By describing conformational motions in terms of diffusive movements across an energy landscape, it is possible to directly connect free-energy barriers and biomolecular kinetics. [1][2][3] Within this framework, the transition state ensemble (TSE) corresponds to the set of configurations that are positioned at a saddle point on the free-energy surface (i.e. the free-energy barrier), and transition paths refer to individual barrier-crossing events.…”

Section: Introductionmentioning

confidence: 99%

Dissecting the energetics of subunit rotation in the ribosome

Levi

Whitford

2019

Preprint

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The accurate expression of proteins requires the ribosome to efficiently undergo elaborate conformational rearrangements. The most dramatic of these motions is subunit rotation, which is necessary for tRNA molecules to transition between ribosomal binding sites. While rigid-body descriptions provide a qualitative picture of the process, obtaining quantitative mechanistic insights requires one to account for the relationship between molecular flexibility and collective dynamics. Using simulated rotation events, we assess the quality of experimentally-accessible measures for describing the collective displacement of the ∼ 4000-residue small subunit. For this, we ask whether each coordinate is able to identify the underlying free-energy barrier and transition state ensemble (TSE). We find that intuitive structurally-motivated coordinates (e.g. rotation angle, interprotein distances) can distinguish between the endpoints, though they are poor indicators of barriercrossing events, and they underestimate the free-energy barrier. In contrast, coordinates based on inter-subunit bridges can identify the TSE. We additionally verify that the committor probability for the putative TSE configurations is 0.5, a hallmark feature of any transition state. In terms of structural properties, these calculations implicate a transition state in which flexibility allows for asynchronous rearrangements of the bridges as the ribosome adopts a partially-rotated orientation.These calculations provide a theoretical foundation, upon which experimental techniques may precisely quantify the energy landscape of the ribosome.

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“…Extensive experimental and computational studies have provided significant mechanistic insight into folding pathways (1)(2)(3)(4)(5). These proteins, which fold rapidly, have been shown to possess relatively smooth energy landscapes (6,7). However, the emergence of classes of topologically complex knotted protein structures in recent years (8)(9)(10)(11) challenges some longstanding views in the field as such proteins have to avoid kinetic traps and also overcome significant topological barriers during folding.…”

mentioning

confidence: 99%

Knotting and unknotting of a protein in single molecule experiments

Ziegler

Lim

Mandal

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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Spontaneous folding of a polypeptide chain into a knotted structure remains one of the most puzzling and fascinating features of protein folding. The folding of knotted proteins is on the timescale of minutes and thus hard to reproduce with atomistic simulations that have been able to reproduce features of ultrafast folding in great detail. Furthermore, it is generally not possible to control the topology of the unfolded state. Single-molecule force spectroscopy is an ideal tool for overcoming this problem: by variation of pulling directions, we controlled the knotting topology of the unfolded state of the 5 2 -knotted protein ubiquitin C-terminal hydrolase isoenzyme L1 (UCH-L1) and have therefore been able to quantify the influence of knotting on its folding rate. Here, we provide direct evidence that a threading event associated with formation of either a 3 1 or 5 2 knot, or a step closely associated with it, significantly slows down the folding of UCH-L1. The results of the optical tweezers experiments highlight the complex nature of the folding pathway, many additional intermediate structures being detected that cannot be resolved by intrinsic fluorescence. Mechanical stretching of knotted proteins is also of importance for understanding the possible implications of knots in proteins for cellular degradation. Compared with a simple 3 1 knot, we measure a significantly larger size for the 5 2 knot in the unfolded state that can be further tightened with higher forces. Our results highlight the potential difficulties in degrading a 5 2 knot compared with a 3 1 knot.knotted proteins | protein folding | single molecule | optical tweezers | ubiquitin C-terminal hydrolase

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What protein folding teaches us about biological function and molecular machines

Cited by 31 publications

References 44 publications

Anomalous dimensionality dependence of diffusion in a rugged energy landscape: How pathological is one dimension?

Anomalous dimensionality dependence of diffusion in a rugged energy landscape: How pathological is one dimension?

Dissecting the energetics of subunit rotation in the ribosome

Knotting and unknotting of a protein in single molecule experiments

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