Stranded protein folding and complex formation.\ (**a**) A schematic showing the three-helix bundle (HBD) domain of P4-R with its central helices shown in green and blue. (**b**) The *in vitro* folding of P4-R HBD (residues 1--99) from a denatured state to a folded state was probed by the cysteine-trapping method. The denatured protein was diluted 100-fold into 100 mM MES, pH 6.5, to promote protein folding. Unfolded P4-R HBD (3--12 mM) readily reacts with the thiol reagent N-ethylmaleimide (NEM), but forms non-reactive trapped intermediate species (red circles) and folded-state HBD (green triangles) during folding. (**c**) The reaction of the denatured P4-R HBD in (**b**) with Cys(A7C/G26C) yields two major species: non-trapped intermediate species (circled) and unfolded-state HBD (triangles), consistent with unfolding of the central helices. (**d**) Hierarchical folding of the HBD domain of P4-R using the single-mixing cysteine-trapping method: the denatured HBD at 5 μM was mixed with Cys(A7C/G26C) at 5 μM to form the non-trapped intermediate state, which was subsequently diluted with fresh Cys(A7C/G26C) to trap unfolded intermediates and folded HBD, as indicated by asterisks. The folding of HBD is complete after a first-order reaction with a rate constant of 1.6 s^−1^ (top) or 2.3 s^−1^ (bottom), corresponding to a refolding time of \~1 ms or \~2 ms. The folded protein was separated from unfolded and non-trapped intermediates by IEF as shown at the bottom.](srep44150-f3){#f3} ![Cooperativity in the folding of a small protein.\ (**a**) The two-color photocycle kinetics of P4-R is characterized by two phases of fluorescence quenching, the fast rate of phototransformation, and the slow rate of fluorescence recovery (bottom and top, respectively). The rate constants are 0.44 s^−1^ and 0.14 s^−1^ and relative amplitudes are 0.62 and 0.38, respectively. The amplitude for the slow phase does not change over time as expected for a reaction that has reached equilibrium. (**b**) The refolding of P4-R with Cys(A7C/G26C) at 5 μM. The denatured protein was mixed with Cys(A7C/G26C) at 5 μM to form non-trapped intermediate state (I) and was diluted with fresh Cys(A7C/G26C) to trap unfolded intermediates and folded P4-R. The kinetics of refolding is characterized by a two-step process: a first order reaction with a rate constant of 0.5 s^−1^ and a second exponential refolding process with a rate constant of 0.03 s^−1^, consistent with the slower first phase and the initial relaxation time of the folded P4-R. (**c**) Concentration dependence of the refolding rate constants for P4-R from the bottom panel of (**b**). The observed rates of fluorescence recovery were determined by fitting the recovery curves with single-exponential functions. The results are fitted to a Michaelis-Menten model to determine the maximal rate and concentration of P4-R required to achieve 50% of the maximal refolding rate. The inset shows the dependence of the maximal rate on the protein concentration. The solid line shows the fit to a hyperbola, which yields a K~M~ = 0.25 μM. In addition, the kinetic fits yield a maximal rate for refolding of 0.47 s^−1^ (or 0.43 s^−1^), corresponding to a relaxation time of \~250 ms (or 600 ms), in good agreement with the relaxation time of the fast phase in the time traces in [Fig. 3d](#f3){ref-type="fig"}.](srep44150-f4){#f4} ![A small molecule binding to the central helix and a slow transition in P4-R folding.\ (**a**) The two-color fluorescent emission of P4-R excited at 295 nm was followed for 100 seconds. In the absence of 1 mM Lut (the small molecule, center panel), the P4-R excited state fluorescence is consistent with folding and no photobleaching of the protein during the experiment. The addition of Lut (the small molecule, right panel) inhibits the fluorescence recovery of P4-R during the experiment. (**b**) The recovery rate of P4-R fluorescence increases as a function of Lut concentration. A hyperbolic function was fit to the data to determine the maximum refolding rate in the absence of Lut (1.23 s^−1^) and in the presence of Lut (2.15 s^−1^). For these fits, the initial point was excluded (black circles), which demonstrates that the initial refolding rates increase with increasing Lut concentration. (**c**) The dependence of the relaxation times, or folding rates, on Lut concentration. The dependence of the relaxation time on the Lut concentration is sigmoidal, which is consistent with a two-state reaction. The data are fit to a Michaelis-Menten model to yield a K~D~ of 8 μM and a maximal folding rate of 1.4 s^−1^ (at the apparent Lut saturation point).](srep44150-f5){#f5} ![The kinetics of protein folding in a crowded environment.\ The folding of P4-R was monitored by a single cysteine at G26C after mixing the protein (10 μM) with various concentrations of PEG (1 kDa). (**a**) The single-exponential refolding kinetics of P4-R with PEG 200 g/l are faster than the folding and photocycle kinetics of P4-R without PEG, consistent with an effect of PEG on the rate of refolding. (**b**) The rate constants of refolding of P4-R in the presence and absence of PEG are similar, but that of the photocycle is enhanced in the presence of PEG, suggesting that the protein-PEG interactions affect the rate of refolding. (**c**) The effect of protein crowding on the fluorescence properties of P4-R was further probed by measuring the two-color fluorescence of P4-R. In the presence of PEG (150 g/l) the decay phase is prolonged, as shown in the inset (top). Addition of PEG (150 g/l) to the denatured protein slows refolding as compared to the refolding without PEG (bottom). (**d**) The refolding rate constants in the presence of PEG are shown as a function of PEG concentrations. The refolding rate constants are similar with and without PEG, indicating that PEG increases the rate of folding but not the refolding rate constant.](srep44150-f6){#f6} ![P4-R undergoes rapid folding without formation of an intermediate species on a time scale of milliseconds.\ The recovery of the steady state fluorescence of P4-R from a photoproduct was measured after photobleaching at 350 nm (red bar) at various times. (**a**) The refolding kinetics for P4-R at an overall concentration of 5 μM as monitored by the change in the fluorescence at 355 nm was fit to single exponentials. (**b**) The dependence of the relaxation time constants for refolding kinetics on the protein concentration in the presence of 1 mM Lut. The relaxation times, or folding rates, are similar for all protein concentrations examined (0--2.5 μM), which suggests that there is no detectable formation of an intermediate structure during the refolding kinetics.](srep44150-f7){#f7} ![A 3D model of the folding pathway of P4-R with a C-cap.\ (**a**) A three-helix bundle (HBD) of P4-R (PDB entry 1P4G). The central helices, which form the N-cap, is indicated in blue. (**b**) A model of the HBD domain of P4-R in which the central helix of the HBD forms a C-cap, as shown in (**c**). (**c**) The N-cap acts as a lid to stabilize the central helices in the folded HBD. (**d**) The mechanism for forming the C-cap and folding a small protein.](srep44150-f8){#f8} [^1]: Present address: Department of Physics, The University of Texas at Austin, Austin, TX 78712, USA.