How fast are the motions of tertiary-structure elements in proteins?

Protein motions occur on multiple time and distance scales. Large-scale motions of protein tertiary-structure elements, i.e. domains, are particularly intriguing as they are essential for the catalytic activity of many enzymes and for the functional cycles of protein machines and motors. Theoretical estimates suggest that domain motions should be very fast, occurring on the nanosecond or microsecond time scales. Indeed, free-energy barriers for domain motions are likely to involve salt bridges, which can break in microseconds. Experimental methods that can directly probe domain motions on fast time scales have appeared only in recent years. This Perspective discusses briefly some of these techniques, including NMR and single-molecule fluorescence spectroscopies. We introduce a few recent studies that demonstrate ultrafast domain motions, and discuss their potential roles. Particularly surprising is the observation of tertiary-structure element dynamics that are much faster than the functional cycles in some protein machines. These swift motions can be rationalized on a case-by-case basis. For example, fast domain closure in multi-substrate enzymes may be utilized to optimize relative substrate orientation. Whether a large mismatch in time scales of conformational dynamics vs. functional cycles is a general design principle in proteins remains to be determined.


Introduction
Proteins are the key functional molecules in the living system, governing nearly all cellular functions and biochemical tasks. For example, proteins facilitate protein folding and prevent protein aggregation, they regulate membranal transport of ions and other chemicals, they participate in metabolic pathways and in many other cellular processes (1)(2)(3)(4). Many proteins operate as machines, which can be quite broadly and somewhat loosely defined as devices that utilize an external energy source to perform a function. In order to coordinate their activities spatially and temporally, multiple protein machines have developed mechanisms for sophisticated regulation. Multiple internal motions in proteins are involved in such regulatory activities, and mapping them has become a major endeavor of modern biophysics, with far-reaching implications not only in basic science but also for the design of new protein functionalities and novel drugs.
The structure of proteins, even large ones, can nowadays be determined using one of an array of methods, from x-ray crystallography (5) through nuclear magnetic resonance spectroscopy (6) to cryo-electron microscopy (7). However, structural models provide only a static picture of a protein, and may miss the rich dynamics that can typically occur on multiple time and length scales (8,9). Importantly, the conformational dynamics of a protein and the relative population distribution among its various structural states might be influenced by external conditions, most interestingly through the binding of ligands, small and large. The effect of ligand binding on the conformation and activity of a protein may occur far away from the binding site. This phenomenon was termed allostery by Monod and coworkers (10,11), and remains a topic of active research (12,13). While early conformationbased allostery models emphasized the thermodynamic states of the transforming proteins, it has been more recently proposed that allostery can also involve changes in conformational dynamics (14,15). There has been much interest in defining the potential role of dynamics in allosteric transitions (16)(17)(18)(19).
How fast are protein motions? The answer to this question is surprisingly complex, as conformational dynamics involve multiple time scales and amplitudes. Local structural changes, such as bond vibrations and transitions between side chain rotamers, occur on the femtosecond to nanosecond time scale. Motions of secondary structure elements, such as loops and helices, are slower, and even slower are the movements of tertiary and quaternary structure elements (domains and subunits, respectively) (9,20,21). In this Perspective we would like to focus on these large-scale conformational changes. As will be seen below, some theoretical estimates suggest that they can in fact be quite fast, taking only microseconds or even shorter times to complete. Experimental methods that can measure and trace largescale (as opposed to local) motions on very short times have only appeared in recent years.
We will introduce these methods, with some emphasis on single-molecule FRET spectroscopy, and provide several examples from our work and others' to demonstrate how fast motions can be probed, how they might be coupled to slower protein functional cycles, and, more generally, what we can learn from them on protein machine function.

How fast can large-scale functional motions be?
Consider a simple model of two protein domains connected with a flexible linker ( Figure 1A).
The relative motion of the two domains to close the gap between them is actually an abundant conformational change that is found in multiple proteins and is termed domain closure, or hinge-bending motion. We can model this relative motion using a simple Langevin equation that takes into account the spring potential (with the spring constant ) and the viscous drag (f) by the aqueous solution ( Figure 1B) (22): where x is the coordinate of motion and F is a random force acting on the moving element.
Analysis shows that the relaxation time characterizing the motion, , is given by Inserting a value for the viscous drag on a 100 kDa protein, ~60 pN . s/m, and a value of 5 pN/nm for  (22), one obtains a value of 12 ns, surprisingly short! In fact, a nanosecond What about experimental estimates? Eaton and coworkers studied the propagation of signals between subunits in hemoglobin, based on optical spectroscopy of ligand rebinding to the heme moieties following photodissociation (29). They concluded that communication between subunits appears on the time range of 1-10 µs. Chakrapani and Auerbach used single-channel recordings of neuromuscular acetylcholine receptors to measure opening and closing rates (30). Analysis of multiple mutants allowed them to offer an upper limit to the channel-opening rate constant of 0.9 s -1 .
To summarize, there is a good reason to believe, based both on theoretical work and somewhat indirect experimental observations, that large-scale conformational changes in proteins should take place on the nanosecond-microsecond time scale. This immediately raises two questions: 1. Can we directly probe these motions experimentally and determine their rates?
2. How are such fast motions commensurate with the typically much slower function of many proteins?
We will start by answering the first question and showing how recent years have led to significant progress in our ability to probe fast motions in proteins. We will then discuss some examples from the literature and from our work, and comment, where possible, on potential answers to the second question.

Methods for studying fast large-scale motions in biomacromolecules
Among the rather small number of methods that can study protein tertiary structure dynamics, a special place is occupied by formidable nuclear magnetic resonance (  protein conformers as they occur and define the exact time constants typifying these dynamics. Single-molecule spectroscopy has therefore become critical to our understanding of molecular function, motion and dynamics. One group of powerful single-molecule spectroscopic tools that have been applied extensively to protein machines involves force spectroscopy (39), and includes optical and magnetic tweezers, as well as atomic force microscopy (40)(41)(42).
Here we focus on a second group of single-molecule methods, based on fluorescence, which are particularly useful for probing internal conformational changes of proteins with minimal intervention. Of the many single-molecule fluorescence spectroscopies introduced over the year, single-molecule fluorescence resonance energy transfer (smFRET) spectroscopy is particularly useful, as it can directly measure intramolecular distances within proteins, and in addition can also characterize the times and amplitudes of their modulation during function (43). smFRET experiments typically rely on excitation energy transfer between two fluorescent dyes attached to a protein, whose interaction depends strongly on their relative distance (44).  Figure 2D).

Ultrafast large-scale motions in proteins and their functional role
The methods discussed in the previous section have been used extensively for operando observation of proteins, especially protein machines. We will introduce here a few notable Phosphoglycerate kinase (PGK), is a glycolytic enzyme that catalyzes the reaction 1,3bisphosphoglycerate + ADP ⇌ glycerate 3-phosphate + ATP, and has been shown to close the cleft between its two domains in order to bring the two substrates together for the chemical reaction. This dramatic conformational change has been termed a hinge-bending motion, as it involves a rigid-body rotation around a helix that connects the two domains (48). Neutron spin-echo spectroscopy was applied to probe the dynamics of PGK (49). Large-scale motions on a time scale of ~50 ns were identified ( Figure 3A), and based on normal mode analysis, and later molecular dynamics simulations (50), it was concluded that these dynamics indeed involve a hinge-bending motion. A more recent molecular dynamics simulation suggested that the hinge-bending motion of PGK is in fact self-similar on timescales from 10 -12 to 10 -5 s (51). The fast domain closure dynamics in PGK are surprising, as the catalytic turnover rate of the enzyme is only 350 s -1 .
A similar situation was discovered in an experiment on a different protein whose reaction involves a domain closure step, adenylate kinase (AK) (19). AK is key to the maintenance of cycles should eventually bring the protein and its substrates to the conformation most conducive for the chemical reaction (19). Thus, the ultrafast domain closure dynamics in PGK and AK may serve to facilitate proper orientation of their substrates for the catalytic step.
Interestingly, this conclusion is supported by findings of Klinman and coworkers on a different enzyme, thermophilic alcohol dehydrogenase (53). These authors performed temperature-jump ensemble measurements to probe time-dependent FRET between tryptophans close to the active site of the enzyme and the cofactor NADH ( Figure 3C-D). They demonstrated a microsecond relaxation process that was activated above 30 C. The authors attributed this process to motions that, while being much faster than catalytic turnover, are able to facilitate the search for the appropriate configuration at the active site.
Ultrafast large-scale conformational changes were also detected in membrane proteins. homodimer of mGluR shuttles between two conformations, resting and active ( Figure 4A-B).
Surprisingly, the exchange between the two states was shown to be ultrafast, taking no more than 100 µs. Interestingly, the binding of ligands did not stabilize the protein in a single, active conformation as might have been expected. Rather, the population ratio between the resting and active states was continuously tuned. Barth Figure 4D). M-domain motion is in fact much faster than the activity of the machine, suggesting that the ratio of the inactive and active conformations, rather than the population of one of them, serves to tune disaggregation.
Indeed, factors that change this ratio, such as the concentration of the co-chaperone DnaK or nucleotides, were found to also modify the rate of disaggregation ( Figure 4E). The mechanism of tunable allosteric switching reported by Olofsson et al. (55) and by Mazal et al. (58) likely involves a low-energy barrier between the active and inactive states. This may be a general way to modulate machine activity through analog (continuous) rather than digital (two-state) switching.

Conclusions and prospects
The recent introduction of experimental methods that can measure large-scale dynamics of proteins on fast time scales has changed dramatically our ability to identify and characterize the motion of tertiary structural elements. In particular, the relative motion of domains and even subunits in proteins can now be directly studied. Both the extent (amplitude) of the   (59)), but is sensitive to larger distances and can be performed at low concentrations.
Based on the studies presented above, it is clear that tertiary structure motions in proteins can indeed be very fast. It is quite likely that such large-scale microsecond motions are much more ubiquitous than is currently assumed. Now, the overall functional cycles of proteins are often limited by chemical steps, such as ATP hydrolysis and related reactions, e.g. release of bound product molecules (60)(61)(62), and are therefore relatively slow. This is also true in the in which the mechanical motion of a machine is fully coupled to nucleotide hydrolysis, and the Brownian ratchet, in which diffusive motions take place in between events of switching of the potential energy surface for motion between two states (63). Fast conformational dynamics might be relevant for the Brownian ratchet mechanism. For example, we have recently found (unpublished results) that the motion of ClpB's pore loops, i.e. the structural elements within the central pore of the machine that are responsible for substrate pulling, is very fast in comparison to substrate translocation time, supporting a Brownian ratchet mechanism for this machine.
A second question of interest in this relation is what physically makes functional cycles so much slower than conformational dynamics. One answer has to do with ligand binding and particularly ligand release. For example, the release of ADP following ATP hydrolysis is often rate limiting. Indeed, we have seen some time ago that the release of ADP from a large protein machine, GroEL, can be slow enough to prevent the protein from reaching equilibrium between its two main conformational states, T and R (64).
Experimental methodology is developing all the time. It is therefore reasonable to expect that the measurements of microsecond motions by equilibrium and non-equilibrium methods alike will become simpler and more robust in the not-to-far future. Improvements in experimental technique and data analysis should make studies of very fast protein dynamics simpler and therefore more abundant. We believe that a particularly thrilling future direction will be the application of these methods to study not only domain motions but also relative subunit motions in large, multi-subunit proteins. The connection of fast motions to the mechanisms of action of proteins is an endeavor that will likely require a combination of experimental results with theoretical/simulation work. This is thus an exciting frontier of protein dynamics that is expected to rapidly move forward in the coming years.