The authors note that on page 4454, left column, 2nd full paragraph, lines 7-9, "For example, oxidation catalysts are able to reduce N 2 O emissions ∼70% compared with models without the technology (22)" should instead appear as "For example, advanced three-way catalysts are able to reduce N 2 O emissions ∼65% compared with models without the technology (22)."

Internal friction, which reflects the "roughness" of the energy landscape, plays an important role for proteins by modulating the dynamics of their folding and other conformational changes. However, the experimental quantification of internal friction and its contribution to folding dynamics has remained challenging. Here we use the combination of single-molecule Förster resonance energy transfer, nanosecond fluorescence correlation spectroscopy, and microfluidic mixing to determine the reconfiguration times of unfolded proteins and investigate the mechanisms of internal friction contributing to their dynamics. Using concepts from polymer dynamics, we determine internal friction with three complementary, largely independent, and consistent approaches as an additive contribution to the reconfiguration time of the unfolded state. We find that the magnitude of internal friction correlates with the compactness of the unfolded protein: its contribution dominates the reconfiguration time of approximately 100 ns of the compact unfolded state of a small cold shock protein under native conditions, but decreases for more expanded chains, and approaches zero both at high denaturant concentrations and in intrinsically disordered proteins that are expanded due to intramolecular charge repulsion. Our results suggest that internal friction in the unfolded state will be particularly relevant for the kinetics of proteins that fold in the microsecond range or faster. The low internal friction in expanded intrinsically disordered proteins may have implications for the dynamics of their interactions with cellular binding partners.energetic roughness | Kramers theory | protein folding | Rouse model | single-molecule FRET C onformational changes in proteins, including those involved in protein folding, are driven by thermal fluctuations. In the dense environment of an aqueous solution, these processes thus typically exhibit diffusive dynamics (1-4). A theoretical framework for describing such diffusive processes in the condensed phase is provided by Kramers-type theories, which have been successful in quantifying key properties of protein folding reactions (5-12). These theories predict the rate of folding to depend exponentially on the height of the folding free energy barrier, with a prefactor representing the "attempt frequency" of crossing the barrier. The latter is related to the inherent timescale at which the protein can diffusively explore its conformational space. As a result, the reaction rate is expected to depend on the friction (13). For simple reactions, only solvent friction may need to be taken into account, but in proteins, where the amino acid residues are only partially exposed to solvent, other dissipative, "internal friction" mechanisms are possible and result in a slowdown of the conformational dynamics. In particular, intrachain collisions, dihedral angle rotation, and other interactions within the polypeptide chain (1, 14, 15) lead to an increased "roughness" of the underlying energy landscape, thereby slowing...

We used single-molecule FRET in combination with other biophysical methods and molecular simulations to investigate the effect of temperature on the dimensions of unfolded proteins. With singlemolecule FRET, this question can be addressed even under nearnative conditions, where most molecules are folded, allowing us to probe a wide range of denaturant concentrations and temperatures. We find a compaction of the unfolded state of a small cold shock protein with increasing temperature in both the presence and the absence of denaturant, with good agreement between the results from single-molecule FRET and dynamic light scattering. Although dissociation of denaturant from the polypeptide chain with increasing temperature accounts for part of the compaction, the results indicate an important role for additional temperaturedependent interactions within the unfolded chain. The observation of a collapse of a similar extent in the extremely hydrophilic, intrinsically disordered protein prothymosin ␣ suggests that the hydrophobic effect is not the sole source of the underlying interactions. Circular dichroism spectroscopy and replica exchange molecular dynamics simulations in explicit water show changes in secondary structure content with increasing temperature and suggest a contribution of intramolecular hydrogen bonding to unfolded state collapse.FRET ͉ polymer ͉ protein folding ͉ secondary structure ͉ chain dimensions T here is an increasing interest in the properties of unfolded proteins and their roles in the folding and cellular functions of proteins. A key motivation is that many proteins are marginally stable and only fold in the presence of their ligands or binding partners, opening new regulatory possibilities (1, 2). An important reason for recent progress is the growing availability of methods that provide structural information on these conformationally heterogeneous systems, such as NMR (3), scattering methods (4, 5), and single-molecule . Although NMR provides mostly local details, small-angle X-ray scattering (SAXS), dynamic light scattering (DLS), and single-molecule FRET provide overall hydrodynamic or long-range distance information. An important advantage of single-molecule FRET is the separation of folded and unfolded subpopulations (9). As a result, unfolded state properties can be investigated even in the presence of folded molecules (i.e., under near-native conditions, which are physiologically most relevant). This advance has led to the observation of a continuous collapse of the unfolded state with decreasing denaturant concentrations (10), a behavior that now has been demonstrated for a large number of proteins (11-18) and peptides (19). Recent advances in the application of theoretical models have led to a quantitative description of this unfolded state collapse in terms of polymerphysical concepts (15,(20)(21)(22)(23). Such chain compaction also has been demonstrated to result in increased internal friction and a slowdown of intramolecular dynamics of the polypeptide (19, 26), which can affect...

Intrinsically disordered proteins (IDPs) are characterized by a large degree of conformational heterogeneity. In such cases, classical experimental methods often yield only mean values, averaged over the entire ensemble of molecules. The microscopic distributions of conformations, trajectories, or sequences of events often remain unknown, and with them the underlying molecular mechanisms. Signal averaging can be avoided by observing individual molecules. A particularly versatile method is highly sensitive fluorescence detection. In combination with Förster resonance energy transfer (FRET), distances and conformational dynamics can be investigated in single molecules. This chapter introduces the practical aspects of applying confocal single-molecule FRET experiments to the study of IDPs.

The structural response of isometrically contracting insect flight muscle (IFM) to rapid length-step transients was analyzed by applying multivariate data analysis to 38.7 nm repeating subvolumes (repeats) in electron tomograms of quick frozen fibers that were mechanically monitored, rapidly frozen by slamming against a liquid helium cooled copper block, freeze-substituted, sectioned and stained. IFM fibers were frozen 5.5 ms after a step stretch of 6 nm/half-sarcomere in 2 ms. In the step release experiment fibers were frozen 6.5 ms following a release of 9 nm/half-sarcomere in 2.5 ms. Tomograms sampled thin sections cut %6 mm below impact surface, recovering 1157 repeats from stretched fibers and 782 repeats from released fibers. Resolution of the actin helix and the stagger of troponin densities in the thin filament facilitated fitting a quasiatomic thin filament model independent of myosin positions, allowing objective recognition whether modeled cross-bridges were weak-or strong-binding. Strong myosin attachments are largely restricted to four actin subunits midway between successive troponin complexes, with a single exception in quick-stretched fibers. Significant changes in the types, distribution and structure of actin-myosin attachments were observed. Prepowerstroke, weak myosin attachments in the target zone are greatly reduced after the transient. However, myosin contacts with tropomyosin in and immediately M-ward of the target zone remain and are more frequent after a release. Weak attachments outside of the target zone remain relatively constant indicating a constant rate for formation of non-productive collision complexes. Following a stretch, there is an increase in the proportion of 2-headed cross-bridges. Myosin contacts with troponin are greatest after a release, and are reduced in frequency following a stretch. The results are interpreted in terms of the shortening cycle of stretch activated IFM. Supported by NIGMS and NIAMSD.