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Folding dynamics of Trp-cage in the presence of chemical interference and macromolecular crowding. I
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10.1063/1.3656691
/content/aip/journal/jcp/135/17/10.1063/1.3656691
http://aip.metastore.ingenta.com/content/aip/journal/jcp/135/17/10.1063/1.3656691

Figures

Image of FIG. 1.
FIG. 1.

(a) Ribbon representation of Trp-cage miniprotein solved by NMR (PDBID: 1L2Y). Residues Tyr3, Trp6, and Leu7 are shown in yellow. Residues Pro12, Pro17, Pro18, and Pro19 are shown in silver. The trace of the protein backbone is colored from red (N-terminus) to blue (C-terminus). (b) Coarse-grained protein model of Trp-cage. (c) Coarse-grained Trp-cage in the presence of spherical confinement. (d) Coarse-grained Trp-cage in the presence of crowding agents.

Image of FIG. 2.
FIG. 2.

Radius of gyration (R g ) as a function of temperature in the absence and presence of different conditions of chemical denaturation: aqueous (black), 2M (red), 4M (green), 6M (blue), and 8M (magenta) urea solution. Each panel represents a different coarse-grained energy functions including urea as described in the Methods. (a) “Urea-SC” energy function, (b) “Urea-SC-DIH” energy function, (c) “Urea-SC-HB” energy function, and (d) “Urea-SC-DIH-HB” energy function. Temperature is given in units of k B T/ε where k B is the Boltzmann constant and ε = 0.6 kcal/mol. Error bars are included.

Image of FIG. 3.
FIG. 3.

(a) Natural logarithm of the mean first passage time, ln(MFPT), of Trp-cage as a function of temperature in aqueous solvent. (b) Probability of unfolded trajectories P u (t) from 2000 folding trajectories at each temperature for several temperatures in aqueous solvent. The maximum folding time is set at 60 μs. Temperature is given in units of k B T/ε where k B is the Boltzmann constant and ε = 0.6 kcal/mol. Error bars are included.

Image of FIG. 4.
FIG. 4.

Probability of unfolded trajectories P u (t) from 2000 folding trajectories built on the “Urea-SC-DIH” energy function at several urea concentrations using the initial conditions quenched from high-temperature simulation at k B T/ε = 1.9. A single exponential function in Eq. (24) was used to fit P u (t) (curve not shown). The results of the fit are presented in Table S5 of the supplementary material.93

Image of FIG. 5.
FIG. 5.

Probability of unfolded trajectories P u (t) from 2000 folding trajectories built on the “Urea-SC-DIH” energy function at several urea concentrations using the initial structures from the simulations at 8M urea. A bi-exponential function in Eq. (26) was used to fit P u (t) (curve not shown). The results of the fit are presented in Table I.

Image of FIG. 6.
FIG. 6.

Clustered transition state ensemble (TSE) from kinetic folding simulations based on the Urea-SC-DIH energy function obtained with the progress variable clustering (PVC) method. (a) The TSE of Trp-cage under aqueous (blue) superpositioned on the TSE in that at 8M urea. Both ensembles belong to Track A of the folding trajectories. (b) The TSE of Trp-cage in aqueous environment (blue) superpositioned on that at 8M urea. Both ensembles belong to Track B of the folding trajectories. (c) Difference in the probability of native contact formation between the TSE of Track A at aqueous and that at 8M urea. (d) Difference in the probability of native contact formation between the TSE of Track B at aqueous and that at 8M urea. Upper triangles represent contacts between backbone hydrogen bonds (HB), while lower triangles contacts are between side chains (SC).

Image of FIG. 7.
FIG. 7.

Dynamic probability of side chain native contact formation as a function of time averaged over multiple folding trajectories based on the Urea-SC-DIH energy function at φ c = 0. (a) Folding trajectories of Track A in aqueous environment; (b) Track A folding trajectories at 8M urea; (c) folding trajectories of Track B in aqueous environment; and (d) folding trajectories of Track B at 8M urea (see Sec. III C for the definition of Tracks A and B). The structural characteristics of TSE for these folding trajectories are analyzed in Table II.

Image of FIG. 8.
FIG. 8.

Folding rate of Trp-cage in aqueous solvent as a function of spherical confinement radius (Rs, black—top scale) and as a function of the volume fraction of crowding agents, φ c (red—bottom scale). Error bars are included.

Image of FIG. 9.
FIG. 9.

(a) Probability of unfolded trajectories P u (t) from 2000 folding trajectories built on the “Urea-SC-DIH” energy function at φ c = 15% under different concentrations of urea. Initial conditions were quenched from the high-temperature ensemble at k B T/ε = 1.9. The inset shows the average folding rate as function of urea concentration for the aqueous condition (solid line) and at φ c = 15% (dashed line). P u (t) is fitted to a bi-exponential function (Eq. (26); curves not shown) and the results of the fit are presented in Table S9 of the supplementary material,93 (b) Probability of unfolded trajectories P u (t) from 2000 folding trajectories built on the “Urea-SC-DIH” energy function for the “Urea-SC-DIH” energy function φc = 15% under different concentrations of urea. Initial conditions were sampled from an ensemble denatured by 8M urea. P u (t) is fitted to a bi-exponential function (Eq. (26); curves not shown) and the results of the fit are presented in Table III.

Image of FIG. 10.
FIG. 10.

(a) Kinetic folding/unfolding rate of Trp-cage, plotted on a logarithmic scale as a function of urea concentration ([urea]) for the Urea-SC-DIH energy function under bulk condition (circles), and at φ c = 15% (inverted triangles). Folding rates are shown plotted in black while unfolding rates are shown in red. The straight lines are fits to Eqs. (27) and (28). (b) Chevron plot for Trp-cage plotting ln(k obs) as a function of urea for the Urea-SC-DIH energy function at bulk (solid line) and at φ c = 15% (dashed line). The curves shown are fitted to Eq. (29).

Image of FIG. 11.
FIG. 11.

Dynamic probability of side chain native contact formation (averaged over multiple trajectories) for the Urea-SC-DIH energy function at φ c = 15%. (a) Track A folding trajectories in aqueous environment and (b) Track A folding trajectories at 8M urea. (c) Track B folding trajectories in aqueous environment and (d) Track B folding trajectories at 8M urea (see Sec. III C for the definition of Tracks A and B).

Tables

Generic image for table
Table I.

Coefficients to fit P u (t) from 2000 kinetic folding trajectories based on the Urea-SC-DIH energy function in aqueous solutions starting from randomly selected initial conditions from an ensemble denatured by 8M urea. A bi-exponential function A 0exp (−A 1 t) + B 0exp (−B 1 t) is used for fitting the different parameters.

Generic image for table
Table II.

Radius of gyration (R g ) and the fraction of native contact formation (QTS) for the dominant clusters of the transition state ensembles (TSEs) in kinetic folding simulations of Trp-cage using the Urea-SC-DIH energy function at bulk conditions. The TSE for the Urea-SC-DIH energy function were separated into Track A and Track B (see Sec. III C for the definition of Tracks A and B and Table I for the exponential fits of the two tracks).

Generic image for table
Table III.

Coefficients to fit P u (t) from 2000 kinetic folding trajectories based on the Urea-SC-DIH energy function at φ c = 15%, using a bi-exponential function A o exp ( −A 1 t) +B o exp (−B 1 t) for the case where the initial conditions were chosen from denatured state ensemble at 8M urea in Figure 9(b). is the average folding rate defined in Eq. (25).

Generic image for table
Table IV.

Radius of gyration (R g ) and the fraction of native contact formation (Q TS) for the dominant clusters of the transition state ensembles (TSEs) in kinetic folding simulations of Trp-cage using the Urea-SC-DIH energy function at φ c = 15%. The structural characteristics of TSE on Tracks A and B were analyzed (see Sec. III C for the definition of Tracks A and B and Table III for the exponential fits of the two tracks).

Generic image for table
Table V.

Parameters used for fitting the folding and unfolding arms of the Chevron plots obtained with the Urea-SC-DIH energy function for bulk conditions and at φ c = 15%. The natural logarithms of folding and unfolding rates at 0M urea concentration ln(k f [urea = 0]) and ln(k u [urea = 0]) were obtained from simulations and were used to fit Eqs. (27) and (28) and to obtain the m f and m u values.

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/content/aip/journal/jcp/135/17/10.1063/1.3656691
2011-11-02
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Folding dynamics of Trp-cage in the presence of chemical interference and macromolecular crowding. I
http://aip.metastore.ingenta.com/content/aip/journal/jcp/135/17/10.1063/1.3656691
10.1063/1.3656691
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