Folding of Protein L with Implications for Collapse in the Denatured

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Folding of Protein L with implications for collapse in the denatured state ensemble Hiranmay Maity, and Govardhan Reddy J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.5b11300 • Publication Date (Web): 02 Feb 2016 Downloaded from http://pubs.acs.org on February 3, 2016

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Journal of the American Chemical Society

Folding of Protein L with implications for collapse in the denatured state ensemble Hiranmay Maity and Govardhan Reddy⇤ Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore, Karnataka, India 560012 E-mail: [email protected] Phone: +91-80-22933533. Fax: +91-80-23601310 Abstract A fundamental question in protein folding is whether the coil to globule collapse transition occurs during the initial stages of folding (burst-phase) or simultaneously with the protein folding transition. Single molecule fluorescence resonance energy transfer (FRET) and small angle X-ray scattering (SAXS) experiments disagree on whether Protein L collapse transition occurs during the burst-phase of folding. We study Protein L folding using a coarse-grained model and molecular dynamics simulations. The collapse transition in Protein L is found to be concomitant with the folding transition. In the burst-phase of folding, we find that FRET experiments overestimate radius of gyration, Rg , of the protein due to the application of Gaussian polymer chain end-to-end distribution to extract Rg from the FRET efficiency. FRET experiments estimate ⇡ 6˚ A decrease in Rg when the actual decrease is ⇡ 3˚ A on Guanidinium Chloride denaturant dilution from 7.5M to 1M, and thereby suggesting pronounced compaction in the protein dimensions in the burst-phase. The ⇡ 3˚ A decrease is close to the statistical uncertainties of the Rg data measured from SAXS experiments, which suggest no compaction, leading to a disagreement with the FRET experiments. The transition

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state ensemble (TSE) structures in Protein L folding are globular and extensive in agreement with the

-analysis experiments. The results support the hypothesis that

the TSE of single domain proteins depend on protein topology, and are not stabilised by local interactions alone.

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Introduction There is an ongoing debate 1–5 on whether the denatured ensemble of single domain proteins undergoes a coil to globule transition during the burst-phase of folding as the denaturant concentration is diluted to lower values. Proteins are heteropolymers and behave like random coils at high temperatures or denaturant concentrations. 6–8 An interesting question is whether proteins akin to polymers undergo a collapse transition in the burst-phase of folding as the conditions are made conducive for folding. 9–11 Single domain proteins unlike polymers are finite sized, and are composed of a specific sequence of amino acids which are hydrophobic and hydrophilic in character. The finite size e↵ects and heteropolymer character are the reasons attributed to the marginal stability of proteins, and the near overlap of the collapse and folding transition temperatures, which makes them fold efficiently. 12,13 The collapse transition in proteins is generally studied using single molecule fluorescence resonance energy transfer (FRET), and small angle X-ray scattering (SAXS) experiments. Although FRET and SAXS experiments agree that proteins like Cytochrome c 14–17 and Monellin 18–20 collapse during the burst-phase of folding, their results disagree for Protein L. FRET experiments for Protein L 21–23 infer collapse, whereas SAXS experiments 24,25 conclude no collapse in the burst-phase of folding on dilution of Guanidine Hydrochloride [GuHCl]. Both FRET and SAXS estimate the radius of gyration, Rg , of the protein to infer the size of the protein in the unfolded ensemble. The di↵erence in the Rg predictions of FRET 21,22 and SAXS 24,25 experiments for Protein L during the burst-phase of folding is statistically significant. The reasons for the disagreement between these experiments for Protein L are not completely clear. Understanding the impact of various approximations used in these methods to estimate the size of the protein can not only aid in resolving the disagreement between FRET and SAXS but also to understand the problem of protein collapse better. Single domain proteins close to the melting temperature or the mid-point denaturant concentration generally fold in a 2-state manner through an ensemble of transition state structures (TSE).

-analysis experiments for Protein L 26–29 predict that the TSE is po3



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larised with only the N-terminal -hairpin present. Whereas the

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-analysis experiments 30

predict that the TSE is globular and extensive with both the N and C-termini -hairpins present along with some non-native interactions in the C-terminal -hairpin. The -analysis experiments support that the TSE and the folding pathways for the single domain proteins depend on the protein topology, 31 whereas the -analysis experiments conclude that the TSE is mostly stabilised by local interactions. 32 Various aspects of Protein L folding such as folding pathways, transition state structures, and properties of the unfolded ensemble are studied 33–40 using both coarse-grained and atomistic simulations. In this manuscript, we study the burst-phase folding of Protein L to understand the origin of discrepancy between the FRET 21,22 and SAXS 24,25 experiments using the native-centric self-organised polymer model with side chains (SOP-SC) 41,42 and molecular dynamics simulations. The e↵ect of [GuHCl] on Protein L conformations is taken into account using the molecular transfer model (MTM). 11,43 The computed FRET efficiency, hEi, for Protein L in the burst-phase of folding is in quantitative agreement with the FRET experiments of Eaton et al., 22 and only in partial agreement with the experiments of Haran et al. 21 The FRET experiments are found to overestimate Rg compared to the actual values computed directly from the simulations owing to the use of the Gaussian polymer chain end-to-end distribution function to extract Rg from hEi. The deviation between FRET-extracted and actual Rg increased with [GuHCl]. As a result, FRET experiments 22 estimate ⇡ 6˚ A decrease in Rg and infer protein collapse in the burst-phase, when the actual decrease is ⇡ 3˚ A as [GuHCl] is diluted from 7.5M to 1M. The equilibrium Rg computed as a function of [GuHCl] is in near quantitative agreement with the SAXS experiments. 25 The SAXS experiments 25 infer no protein collapse as the burst-phase Rg at [GuHCl] = 4.0M and 0.67M are not statistically di↵erent. In the simulations, the burst-phase Rg at [GuHCl] = 4M and 1M are 25.1 ± 4.0˚ A and 23.8 ± 3.9˚ A, respectively, a di↵erence of ⇡ 1.3˚ A, which is well within the standard deviation

Rg

⇡ 4˚ A.

From this analysis, which is similar to the SAXS analysis, we can infer no collapse as the

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change in protein dimensions are not statistically significant, leading to a disagreement with the FRET experiments. The TSE of Protein L at the melting temperature is inferred using Pf old calculations. 44 The TSE is found to be globular and extensive with both the N and C termini -hairpins present resembling a topology similar to that of the folded structure. The results are in agreement with the

-analysis experiments 30 and only in partial agreement with the

-

analysis experiments. 26–29 The inferred TSE support the hypothesis that the transition state structures of single domain homologous proteins are extensive and depend on the protein topology. 45

Methods Self Organised polymer-Side Chain (SOP-SC) Model: We used the SOP-SC (selforganized polymer-side chain) model 41,42 in which each amino acid residue is represented by two beads. One bead is at the C↵ position representing the backbone atoms, and the other bead is at the center of mass of the side chain representing the side chain atoms. The e↵ective energy of a protein conformation in the SOP-SC model is a sum of bonded and non-bonded interactions. The bonded interactions (EB ) are present between a pair of connected beads. N NN The non-bonded interactions are a sum of native (EN B ) and non-native (EN B ) interactions

(see Supporting Information (SI) for more details). The native interactions for protein L are identified using the crystal structure 46 (Protein Data Bank ID: 1HZ6) (Fig 1A). The number of residues in the crystal structure, Nres = 64. The native interactions between the beads representing the amino acid side chains interact via a residue dependent BetancourtThirumalai statistical potential. 47 The coarse-grained force-field in the SOP-SC model for a protein conformation given by the co-ordinates {r} in the absence of denaturants, [C] = 0, is N NN ECG ({r}, 0) = EB + EN B + EN B .

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(1)


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Description of the various energy terms in Equation 1 and the parameters used in the energy function are given in the SI. These parameters are identical to the values previously used to successfully study the folding properties of the proteins Ubiquitin 48 and GFP. 49 We used the same force-field to study the properties of di↵erent proteins, and as a result this force-field satisfies the criterion of a transferable force-field.

Molecular Transfer Model: To simulate Protein L folding thermodynamics and kinetics in the presence of [GuHCl] we used the Molecular Transfer Model (MTM). 11,43 In the presence of a denaturant of concentration [C], the e↵ective coarse-grained force field for the protein using MTM is given by

ECG ({r}, [C]) = ECG ({r}, 0) +

where ECG ({r}, 0) is given by Eq. 1,

Gtr ({r}, [C]),

(2)

Gtr ({r}, [C]) is the protein-denaturant interaction

energy in a solution with denaturant concentration [C], and is given by

Gtr ({r}, [C]) =

N X

gtr,k ([C])↵k ({r})/↵Gly

k Gly ,

(3)

k=1

where N (=Nres ⇥ 2 = 128) is the number of beads in coarse-grained Protein L, gtr,k ([C]) is the transfer free energy of bead k, ↵k ({r}) is the solvent accessible surface area (SASA) of the bead k in a protein conformation described by positions {r}, ↵Gly of the bead k in the tripeptide Gly

k

k Gly

is the SASA

Gly. The radii for amino acid side chains to com-

pute ↵k ({r}) are given in Table S2 in Ref. 48 The experimental 11,50,51 transfer free energies gtr,i ([C]), which depend on the chemical nature of the denaturant, for backbone and side chains are listed in Table S3 in Ref. 42 The values for ↵Gly

k Gly

are listed in Table S4 in Ref. 42

Simulations and Data Analysis: Low friction Langevin dynamics simulations 52 are used to generate protein conformations as a function of T in [C] = 0M conditions. To com6


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pute thermodynamic properties of the protein in a denaturant solution of concentration [C], Gtr ({r}, [C]) is treated as perturbation to ECG ({r}, 0) in Eq. 2, and Weighted Histogram Method 11,43,53 is used to compute average value of various physical quantities at any [C]. Brownian dynamics simulations 54 are used with the full Hamiltonian (Eq. 2) to simulate the burst-phase folding kinetics of the protein in a denaturant solution of concentration [C] (see SI for details). We computed structural overlap function, 55

, and radius of gyration, Rg , to moni-

tor protein L folding kinetics. The structural overlap function is defined as = 1 N tot P 1 ⇥( |ri ri0 |). Here, Ntot (= 777) is the number of pairs of beads in the SOPNtot i=1

SC model of Protein L assuming that the bead centers are separated by at least 2 bonds, ri

is the distance between the ith pair of beads, and ri0 being the corresponding distance in the folded state, ⇥ is the Heaviside step function, and

= 2˚ A. Using

as an order parameter,

we calculated the fraction of molecules in the NBA, fN BA as a function of [GuHCl](see SI P for details and Fig. S2). Rg , is calculated using Rg = (1/2N 2 )( ~rij2 )1/2 , where ~rij is the i,j

vector connecting the beads i and j. The extent of long-range contacts in the TSE structures compared to the coarse-grained PDB structure is analysed using the relative contact NP nat order, 56,57 RCO, which is defined as RCO = Nres1Nnat Li , where Nnat is the number of i=1

pairs of beads with native interactions in the protein conformation (see SI), and Li is the number of residues separating the contact pair i.

Results and Discussion Thermodynamics of Protein L folding: The protein in the folded state has one ↵-helix (↵1 ) and four -strands (

1

-

4)

(Fig. 1A and S1A). Low friction Langevin dynamics simula-

tions performed at di↵erent temperatures, T , ranging from 300K to 430K show that folding occurs in a two-state manner (see SI, Fig. S1). The melting temperature, TM , of protein

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L obtained from the heat capacity, Cv , plot is 374.5K (Fig. S1), and the value observed in experiments 58 is 348.5K. The di↵erence in TM between experiments and simulations can be attributed to the simplified coarse-grained SOP-SC model. At TM , the protein transitions between the native basin of attraction (NBA) and the unfolded basin of attraction (UBA) (Fig. S2). Protein L folding thermodynamics and kinetics in the presence of the denaturant GuHCl is studied using the molecular transfer model (MTM). 11,43 In order to compare the denaturant-dependent folding properties of the protein computed from simulations with the experiments, a simulation temperature TS (= 357.7K) at which theoretically obtained free energy di↵erence between the NBA and UBA, the experimentally 29 measured value,

GSim N U (= GN (TS )

GU (TS )) matches with

GExp N U (= -4.6 kcal/mole), at [GuHCl] = 0M is used.

This is the only adjustable parameter in the model, which is equivalent to matching the energy scales between the simulations and experiments. The structural overlap parameter,

(see methods), is used to distinguish between the

NBA and UBA protein conformations (Fig. S2). The protein conformations with belong to the NBA, and conformations with

 0.47

> 0.47 belong to the UBA (Fig. S2B). The

fraction of molecules in NBA, fN BA , as a function of [GuHCl] computed from simulations is in quantitative agreement with the experiments 23,29,59 (Fig. 1B). The mid-point [GuHCl] at which the protein unfolds is ⇡ 2.5M . The average radius of gyration, hRg i, of Protein L as a function of [GuHCl] is in quantitative agreement with the SAXS experiments 25 (Fig. 1C). The standard deviation of Rg in the protein unfolded state,

Rg

⇡ 4˚ A, indicates that Rg fluc-

tuates between 22˚ A/ Rg /30˚ A. As [GuHCl] is diluted from 8M to 4M, the hRg i decreases from ⇡ 26.5˚ A to ⇡ 24.7˚ A almost linearly with a slope of 0.42 ˚ AM 1 . The experimental data 25 fits equally well with a horizontal line or a line with slope 0.33±0.35 ˚ AM 1 . The average Rg of the protein conformations in the UBA basin, hRgU BA i, as a function of [GuHCl] show that the size of the protein decreases from ⇡ 26.5˚ A to ⇡ 22.5˚ A as [GuHCl] is diluted from 7.5M to 0.25M.

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Denaturant-dependent FRET efficiency: Average FRET efficiency, hEi, as a function of [GuHCl] is computed from the Langevin dynamics simulations (Fig. 2A). In FRET experiments, 21,22 the donor (AlexaFluor 488) and acceptor (AlexaFluor 594) dyes are attached near the N and C termini of Protein L. All-atom simulations 60 have shown that the dyes have negligible e↵ect on the size of disordered protein structures. The hEi is calculated using hEi =

ZL 0

P (Ree ) dRee , 1 + ( RRee0 )6

(4)

where P (Ree ) is the end-to-end distance, Ree , probability distribution function of the protein, L(= 248˚ A) is the contour length of the protein, and R0 (= 54˚ A) is the Forster radius for the donor-acceptor dyes used in the experiments. 21,22 The equilibrium hEi transitions from lower values (< 0.5) to higher values (⇡ 0.85) as the protein folds from an unfolded state upon [GuHCl] dilution (Fig. 2A). The large standarddeviation,

E

⇡ 0.3, for [GuHCl] > 2.5M (Fig. S3) indicates that the protein in the UBA

basin samples conformations with large size fluctuations in agreement with the Rg data (Fig. 1C). The average FRET e↵eciency computed for the UBA ensemble, hE U BA i, to study whether the protein collapses in the early stages of folding is in quantitative agreement with the experiments of Eaton et al., 22 where as they are in disagreement with the experiments of Haran et al. 21 for the denaturant concentrations 1M / [GuHCl] / 3M (Fig. 2A). hE U BA i gradually increases from 0.37 to 0.6 as [GuHCl] is diluted from 8M to 0.25M pointing to an average decrease in the size of the protein (Fig. 2A). The average FRET efficiency hE Burst i is also computed from the initial 0.25 milliseconds (ms) of the Brownian dynamics simulations performed to study the folding kinetics of Protein L. The initial 0.25 ms of the folding trajectories are used to check whether the protein decreases in size in the burst-phase of folding when [GuHCl] is diluted from 7.5M to lower concentrations. The initial unfolded protein conformation to initiate the folding simulations in various [GuHCl] are obtained from simulations performed at [GuHCl] = 7.5M . 20 inde-

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pendent simulations starting from di↵erent initial protein conformations are performed for each [GuHCl]. hE Burst i computed for the early stages of folding is in quantitative agreement with the experiments of Eaton et al. 22 for all [GuHCl], and deviates from the values obtained from the experiments of Haran et al. 21 for the [GuHCl] range 1M / [GuHCl] / 3M (Fig. 2B). hE Burst i increases from 0.38 to 0.53 as [GuHCl] is diluted from 7.5M to 1.0M signifying that the protein on an average decreases in size. The standard deviation of burstphase FRET efficiency,

E

⇡ 0.3, show that hE Burst i varies between 0.2 and 0.8 indicating

that the protein in the initial stages of folding samples conformations with a significant variation in size (Fig. 2B). The Rg plot as a function of time shows that it varies in the range 15˚ A/ Rg / 30˚ A during the initial hundreds of microseconds after folding is initiated for [GuHCl] = 1M and 2M conditions (Fig. S4).

FRET overestimates radius of gyration in high [GuHCl]: We mimicked the FRET experiments 21,22 to estimate hRgF RET i from hE Burst i. The Gaussian polymer chain end-toend probability distribution is given by

P (Ree ) =

2 4⇡Ree

✓

3 2 i 2⇡hRee

◆3/2

exp

✓

2 3Ree 2 i 2hRee

◆

.

(5)

The P (Ree ) given by Eq. 5 is used in Eq. 4 to estimate the average end-to-end distance p 2 2 i/6. hRF RET i square, hRee i, from hEi. hRg i is calculated using the relation, 61 hRg i = hRee g

values estimated from hE Burst i (Fig. 2B) using equations 4 and 5 at di↵erent [GuHCl] are in near quantitative agreement with the experimentally 22 estimated values (Fig. 3A). On diluting [GuHCl] from 7.5M to 1M, hRgF RET i decreases from ⇡ 30˚ A to ⇡ 24˚ A, nearly a 6˚ A change in the size of the protein, which is in agreement with the experiments 22 of Eaton et al. However, hRgF RET i deviates from the hRgBurst i values computed directly from the protein conformations obtained from the simulation trajectories (Fig. 3A). hRgBurst i decreases from ⇡ 26.7˚ A to ⇡ 23.8˚ A, a decrease of only ⇡ 3˚ A upon [GuHCl] dilution from 7.5M to 1M

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(Fig. 3A). This shows that FRET overestimates the size of the protein especially in higher [GuHCl], and this gives rise to the appearance of pronounced compaction in the dimensions of the protein in the burst-phase as [GuHCl] is diluted. The standard deviation,

Rg

⇡ 4˚ A,

of hRgBurst i shows that at all [GuHCl], the protein samples conformations with Rg varying from ⇡ 22˚ A to ⇡ 28˚ A (Fig. 3A), and the 3˚ A decrease in hRgBurst i upon [GuHCl] dilution is within the

Rg .

The deviation between hRgF RET i and hRgBurst i at high [GuHCl] was also

emphasised in the work of O’Brien et al. 62 and the reasons for the deviation are attributed to the use of Gaussian chain P (Ree ) to extract hRgBurst i. The problems associated with the use of Gaussian chain P (Ree ) to extract information about protein dimensions is also highlighted in previous other studies. 63–66 The deviation between hRgF RET i and hRgBurst i increases with [GuHCl], and the reasons for the discrepancy can be understood using the 2 relation hRee i = hRee i2 + F RET hRee i and

F RET Ree

2 Ree ,

where

Ree

is the standard deviation in Ree .

estimated from the Gaussian polymer chain P (Ree ) to compute

hRgF RET i deviate from the values hRgBurst i computed directly from the initial 0.25ms of the F RET Protein L folding trajectories (Fig. 3B and C). At high [GuHCl](= 7.5M ), hRee i and F RET Ree

estimated from the Gaussian chain P (Ree ) are 67.3˚ A and 28.3˚ A, respectively, which

Burst deviate from the hRee i and

Burst Ree

values 62.7˚ A and 20.5˚ A respectively (Fig. 3B), computed

directly from the simulations. As a result FRET overestimates q ⇣ p ⌘ F RET )2 i/6 = F RET i2 + ( F RET )2 ]/6 compared to hRBurst i in high hRgF RET i = h(Ree [hRee g Ree

[GuHCl] (Fig. 3A). As [GuHCl] decreases, the deviation between hRgF RET i and hRgBurst i F RET decreases (Fig. S5). In low [GuHCl](= 1.0M ), the hRee i values computed from the Burst Gaussian chain P (Ree ), and hRee i computed from simulations are in good agreement,

where as the

F RET Ree

values deviate from

Burst Ree

(Fig. 3C). Due to this the deviation between

hRgBurst i and hRgF RET i is small in low [GuHCl], and increases with [GuHCl] (Fig. 3 and S5). To conclude, during the burst-phase of folding, hRgBurst i for Protien L decreases from ⇡ 26.7(±4)˚ A to ⇡ 23.8(±4)˚ A, a decrease of ⇡ 3˚ A upon [GuHCl] dilution from 7.5M to 1M (Fig. 3A). However, FRET overestimates the size of the protein in high [GuHCl](⇡ 7.5M )

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due to the application of the Gaussian polymer chain P (Ree ) to estimate hRgF RET i. During the burst-phase hRgF RET i estimated from FRET decreases from ⇡ 30˚ A to ⇡ 24˚ A upon [GuHCl] dilution from 7.5M to 1M (Fig. 3A). Due to the ⇡6˚ A decrease in hRgF RET i, FRET experiments 21,22 suggest pronounced compaction in the protein size during the burst-phase of folding.

Disagreement between FRET and SAXS experiments on Protein L compaction in burst-phase folding: In simulations, the average radius of gyration in the burst-phase folding, hRgBurst i, decreased by ⇡ 3˚ A when [GuHCl] is diluted from 7.5M to 1M. The ⇡ 3˚ A decrease in hRgBurst i is close to statistical uncertainties of the Rg data obtained from SAXS experiments 25 for Protein L. The Rg data from SAXS experiments for 3M / [GuHCl] / 7M can fit a horizontal line or a line with slope 0.33±0.35 ˚ AM

1

equally

well. 25 Using this slope to compute the Rg change upon [GuHCl] dilution from ⇡7.5M to 1M gives a Rg decrease of 2.1 ± 2.3˚ A. The SAXS experiments 25 report that Rg of Protein L in the burst phase upon [GuHCl] dilution to 1.3M and 0.67M are ⇡ 23.5 ± 2.1˚ A and 24.9±1.12˚ A, respectively which are statistically not di↵erent from the value 23.7 ± 0.4 at [GuHCl] = 4.0M. In the simulations, hRgBurst i at [GuHCl] = 4M and 1M are 25.1±4.0˚ A and 23.8 ± 3.9˚ A, respectively, a di↵erence of ⇡ 1.3˚ A, which is well within

Rg

⇡ 4˚ A. This analysis

similar to the SAXS analysis leads to the conclusion of minimal Protein L compaction within statistical uncertainties on [GuHCl] dilution in agreement with the SAXS experiments, 25 and disagreement with the FRET experiments. 21,22 Recent FRET experiments 67 on polyethylene glycol (PEG) showed that FRET efficiency decreased as [GuHCl] is increased when hydrophilic PEG is unlikely to expand on increasing [GuHCl]. This led to questions about the interpretation of the FRET data to study protein collapse in low [GuHCl]. We find that the computed variation in hEi and hRg i as a function of [GuHCl] for Protein L to be in quantitative agreement with at least one of the FRET experiments 22 (Fig. 2) and also in agreement with SAXS experiments 25 within the

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statistical uncertainties (Fig. 1C and 3A). The results points to the use of Gaussian polymer chain statistics to extract Rg from FRET efficiency data to be the cause for the discrepancy between the SAXS and FRET experiments in estimating Rg .

The coil-globule transition in Protein L is concomitant with the folding transition: In polymers the ratio of the radius of gyration to the hydrodynamic radius, Rg /Rh , can point to the coil-globule collapse transition. The Rg /Rh ratio for a polymer in a good solvent 68 is ⇡ 1.56, where as the ratio in a poor solvent 61 is ⇡ 0.77. We used the KirkwoodRiseman approximation 69 to compute the hydrodynamic radius of the protein, which is given P by Rh = (1/2N 2 ) 1/ |~ ri r~j |, where N is the number of beads in the coarse-grained proi6=j

tein, r~i and r~j are the position vectors of beads i and j. The Rg /Rh ratio for the burst-phase

folding decreases from ⇡ 1.31 to ⇡ 1.28 as [GuHCl] is diluted from 7.5M to 1M indicating that this is not a coil-globule transition observed in polymers (Fig. 4). The single domain proteins which are finite in size compared to polymers are predicted to have a near overlap of the collapse and folding transition temperatures. 12,13 In agreement, the equilibrium ratio of Rg /Rh decreases from ⇡ 1.3 to ⇡ 0.98 as the folding transition occurs (Fig. 4). The Rg /Rh ratio does not approach 0.77 as the protein folds because the Kirkwood-Riseman approximation 69 used to compute Rh does not hold for the protein in the folded state as it assumes all the beads are equally bathed by the solvent. The absence of coil-globule transition in the burst-phase of protein L folding does not imply that the collapse transition or significant protein compaction is universally absent in the burst-phase folding of all single domain proteins. Both FRET and SAXS experiments agree that the protein Monellin 18–20 shows compaction during the burst-phase of folding. Although both the experimental techniques observe compaction in the case of Cytochrome c, 14–17 the FRET experiments show that this compaction, a sub-100µs event, is barrier limited and it is due to the formation of marginally stable partially folded structures. 14 Experiments 8 show that for the protein CyclophilinA, the Rg /Rh ratio decreases from a value between 1.1-1.2 to a value between 0.9-1.0

13



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Page 14 of 41

as [GuHCl] is diluted from 8M to 0M indicating a coil-globule transition in the burst-phase of folding.

Transition State Ensemble (TSE): The transition state ensemble of Protein L at the melting temperature, TM , is identified using the Pf old analysis 44 (see SI for details). 12 out of 108 putative transition state structures (TSE) which satisfy the condition, 0.4 < Pf old < 0.6 are labeled as TSE (Fig. S6). The transition state structures (TSE) are globular, extensive and homogenous, with most of the secondary and tertiary contacts formed (Fig. 5). The -analysis experiments 30 predict that TSE contains all the four -sheet strands ( The TSE from simulations show that both the N and C-termini hairpins the contacts between the strands

1 4

1 2

and

1 3 4,

4 ).

and

are present in the structures in agreement with the

-analysis experiments 30 (Fig. 5B). The

-analysis experiments on two residue pairs, K28-E32 and A35-T39, present in the

helical region of the protein gave -values 0.26 and ⌧ 0, respectively, indicating that contacts between these pairs of residues is largely absent, and concluded that helix ↵1 is mostly not present in the TSE. 30 The contact map of the TSE obtained from the simulations show that the side chains of the residue pairs K28-E32 and A35-T39 form contacts with a probability of 0.41 and 0.08, respectively. The simulations further indicate that a cluster of residues between S31 and A37 present approximately at the center of the helix containing 3 Ala residues (A33, A35 and A37) can form stable contacts in the TSE (Fig. 5B). The

-analysis experiments 31,70 predict a relationship between the relative contact order,

RCO (see methods), of the native protein topology and TSE, RCOT SE ⇡ 0.7RCON ative , which shows the extent of long-range contacts present in the TSE compared to the nativestate. The TSE structures extracted from the simulations show RCOT SE /RCON ative = 0.77, which is in reasonable agreement with the value of 0.75 estimated from

-analysis

experiments. 30 The simulations using the coarse-grained protein model support the basic topology of the TSE structures predicted by the

14

-analysis experiments.


Page 15 of 41

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The folding simulations of only the C-terminal hairpin (

3 4)

using atomistic models pre-

dicted the presence of non-native contacts, a 2 amino acid register shift, in the TSE. 30 We do not observe this 2 amino acid register shift in the C-terminal hairpin because the SOP-SC model includes only native-interactions. The predicted TSE is only in partial agreement with the

-analysis experiments 27–29,71 which predicted a polarised structure with only

1 2

hairpin. The results support the hypothesis that folding pathways and TSE of single domain proteins are influenced by the topology of the folded structure in agreement with the experiments. 45

Concluding Remarks: In summary, we have studied Protein L folding in the presence of the denaturant Guanidine Hydrochloride using the SOP-SC coarse-grained model and molecular dynamics simulations. The e↵ect of [GuHCl] on the protein is taken into account using the molecular transfer model. 11,43 The study mainly focussed on whether there is a coil-globule collapse transition in the burst-phase of folding after the denaturant concentration is diluted to lower values. The main findings of this study is the coil-globule transition in Protein L is concomitant with the folding transition. It is not observed during the burst phase. The FRET experiments overestimate the Rg of the protein at high [GuHCl] concentrations owing to the use of the Gaussian polymer chain end-to-end distribution function to extract Rg from FRET efficiency. As a result, in the burst-phase of folding, FRET observes pronounced compaction in the size of the protein as [GuHCl] is diluted. The actual decrease in the size of the protein (⇡ 3˚ A) observed during the burst-phase is close to statistical uncertainties of the Rg data measured from SAXS experiments, 25 and these experiments conclude that there is no collapse leading to a discrepancy with the FRET experiments. It is highly desirable to formulate a method to accurately extract the distances between the donor and acceptor dyes used in the FRET experiments. However, it is a non-trivial inverse problem as we seek to accurately extract a probability distribution of the distances between the dyes from the average FRET efficiency measured in experiments, especially in

15



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Page 16 of 41

cases like Protein L where the compaction in protein dimensions is small on denaturant dilution. Previous studies 62 have shown that even other polymer models such as the selfavoiding chain or the worm-like-chain model are also not very accurate quantitatively to predict the small subtle changes in the protein dimensions. The results presented in this manuscript clearly point out the aspects of the Gaussian chain model, which leads to over estimating the size of the protein when used to analyse the FRET data. The results show that the Gaussian chain model fails in accurately capturing the width of the protein end-to-end probability distribution, which is essential to compute the radius of gyration. For any method to be quantitatively accurate it should capture the peak position as well as the width of the probability distribution accurately, and this is a challenging task because we need to estimate probability distribution from an average value, and also the method should be reliable enough to work on proteins with di↵erent amino acid composition and native folds. To check the accuracy of the distance between the dyes extracted from the FRET efficiency data using the Gaussian polymer model assumption, a self-consistency check can be performed to see if the assumption is valid or not for the protein under study. 62 If the dyes are 2 attached at locations i and j in the protein, and hRij i is the average distance square extracted 2 from FRET efficiency, and similarly if hRkl i is the average distance square extracted from 2 2 FRET efficiency with dyes at positions k and l, then the relation hRij i/hRkl i = |j

i|/l

k|

should hold if the protein behaves as a Gaussian chain. If the relation is not satisfied, then one should be cautious in quantitatively inferring results about the protein dimensions assuming that the protein in the unfolded state behaves as a Gaussian chain. The magnitude of protein compaction in the burst-phase folding of single domain proteins upon denaturant dilution is not uniform, and it should depend on protein length, sequence and composition of amino acids. For example SAXS experiments on Protein L 25 and Ubiquitin 72 infer no compaction in the protein dimensions in the burst-phase, while experiments on Cytochrome c 14 and Monellin 20 observe compaction. The key features in the single domain

16


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proteins responsible for compaction in protein dimensions on denaturant dilution needs to be identified. In addition to temperature and denaturants, force can also be used to unfold proteins and study protein folding. Experiments 73 and simulations 74,75 show that a protein unfolded by force when allowed to refold in the presence of lower quenching forces undergoes a rapid compaction in the initial stages of folding. This compaction of the protein is driven by entropy because the protein in the stretched state is in a low entropic state and upon force quench undergoes rapid compaction in the first stage of folding until entropy is maximised. 75 The extent of protein compaction in the initial stages of folding also depends on the experimental probes used to study protein folding. The transition state structures inferred from the Pf old analysis are globular and extensive with both the C and N-termini hairpins 1 4.

1 2

and

These results are in agreement with the

3 4,

and interactions between the strands

-analysis experiments 30 and support the

hypothesis that for single domain globular proteins the transition state structures depend on the protein native-state topology and are not stabilised by local interactions alone.

Acknowledgement GR acknowledges startup grant from Indian Institute of Science-Bangalore, and funding from Nano mission, Department of Science and Technology, India. Hiranmay Maity acknowledges research fellowship from Indian Institute of Science-Bangalore. Supporting Information: Description of the simulation methods; Table S1; Figures S1-S6. This material is available free of charge via the Internet at http://pubs.acs.org

17



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Page 22 of 41

(A)

β1 β2

α1

β3 β4 (B)

1.0

Sim Expt (Baker Expt (Haran Expt (Lapidus

0.8 0.6 NBA

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.4 0.2 0.0 0

1

2

3

4

5

6

[GuHCl] (M)

(C)

30 25

(Å)

Page 23 of 41

20

EXP

10 0

2

4

[GuHCl] (M)

6

8

Figure 1: (A) Crystal structure of Protein L (PDB ID: 1HZ6). The ↵-helix is in green (↵1 ), and the four -strands are in blue ( 1 ), red ( 2 ), magenta ( 3 ), and cyan ( 4 ). (B) The fraction of the protein in the native basin of attraction, fN BA , as a function of [GuHCl]. Data in red triangles is from simulations. Data in blue circles, black squares and green diamonds are from the experiments of Haran et al., 59 Lapidus et al 23 and Baker et al. 29 respectively. (C) The radius of gyration, Rg as a function of [GuHCl]. Data in red circles and green squares is from simulations and experiments, 25 respectively. hRg i of UBA and NBA basins computed from simulations are shown in blue triangles and black inverted triangles, respectively.

23



(A) 0.9 EXP

0.8

(Haran)

EXP

(Eaton)

Equil

NBA

UBA

0.4 0.3 0

2

4

6

8

[GuHCl] (M)

(B)

Burst

(Haran)

EXP

(Eaton)

0.6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 41

0.4 0.2

0

2

4

6

8

[GuHCl] (M) Figure 2: (A) Equilibrium FRET efficiency, hE Equil i, as a function of [GuHCl] is in red circles. Experimental data are shown in green squares 22 and cyan diamonds. 21 hEi for the protein conformations in the NBA and UBA basins are shown in blue triangles and black inverted triangles, respectively. (B) hE Burst i shown in red circles is computed from the initial 0.25 ms of Protein L Brownian dynamics folding trajectories at T = 357.7K in various [GuHCl] . Data in green squares and cyan diamonds is the same as in (A).

24


Page 25 of 41

(A)

Burst

FRET

EXP

SAXS

(Å)

28 26 24 22 20 0

2

4

6

8

[GuHCl] (M)

(B) 0.020

[GuHCl]=7.5M Gaussian P(Ree) Simulation P(Ree)

0.015

Burst

P(Ree)

= 62.7 Å FRET

20.5

0.010

= 67.3 Å

σRBurst = 20.5 Å ee FRET σRee = 28.3 Å

0.005 67.3

0.000 0

50

100

150

Ree (Å)

(C)

[GuHCl] = 1.0M Gaussian P(Ree) Simulation P(Ree)

0.025 0.020

Burst

= 54.2 Å

P(Ree)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


FRET

0.015

= 54.8 Å

0.005 54.2

54.8

0.000 0

20

40

60

80

100 120 140

Ree (Å)

Figure 3: (A) hRgF RET i estimated from hE Burst i is in blue diamonds. hRgBurst i computed from the initial 0.25ms of the Protein L folding trajectories is in red circles. Data in green squares and black triangles is from FRET 22 and SAXS 25 experiments, respectively. (B) The end-to-end distance, Ree , probability distribution function P (Ree ) during the burst phase (initial 0.25ms) of protein L folding at T = 357.7K and [GuHCl] = 7.5M is in red circles. P (Ree ) estimated from hE Burst i and Guassian polymer chain statistics in green squares. (C) same as in (B) except that [GuHCl] = 1.0M .

25



1.4 1.3

Rg/Rh

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 41

1.2 1.1 Equil Burst-phase

1.0 2

4

6

8

[GuHCl] (M) Figure 4: The ratio of the radius of gyration to the hydrodynamic radius, Rg /Rh , for the burst phase (solid circles) and equilibrium (empty circles) conditions.

26


Page 27 of 41

(A)

β1β4 β3β4 β1β2

(B)

1 120

β3β4

β1β4

0.8

100

Bead Number

80

0.6

α1

60

0.4

β1β2

40

0.2 20

0 120

100

80

60

40

20

0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Bead Number

Figure 5: (A) Representative transition state structure from the transition state ensemble obtained using the Pf old analysis. (B). The contact map of the the transition state ensemble is shown in the upper half of the diagonal. The experimental 30 -values for the transition state structure are show in the lower half of the diagonal. The -values for the ↵-helix residue pairs K28-E32 and A35-T39 from experiments 30 are 0.26 and ⌧ 0, respectively. The -value used for the residue pair A35-T39 is 0 in the plot. The small -values for ↵-helix are not visible in the plot.

27



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Unfolded state (Coil) Coil-globule transi8on

Coil-globule and folding transi8on

Folding transi8on Collapsed state Folded state (Globule) Figure 6: Table of Contents (TOC) figure

28


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Supporting Information for “Folding of Protein L with implications for collapse in the denatured state ensemble” Hiranmay Maity and Govardhan Reddy⇤ Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore, Karnataka, India 560012 E-mail: [email protected]

S1



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Page 30 of 41

SI Text

Self Organized Polymer-Side Chain (SOP-SC) model for Protein L: We used the SOP-SC (self-organized polymer-side chain) model 1,2 in which each amino acid residue is represented by two beads. One bead is at the C↵ position representing the backbone atoms, and the other bead is at the center of mass of the side chain representing the side chain atoms. The number of residues in Protein L, Nres = 64. The e↵ective energy of a protein conformation in the SOP-SC model is a sum of bonded and non-bonded interactions. The bonded interactions, EB , are present between a pair of connected beads. N NN The non-bonded interactions are a sum of native, EN B , and non-native, EN B , interactions.

The native interactions for protein L are identified using the crystal structure 3 (Protein Data Bank ID: 1HZ6) (Fig 1A), and they are present between a pair of beads separated by at least 3 bonds, and if the distance between them in the crystal structure is less than Rc (Table S1). The coarse-grained force-field in the SOP-SC model for a protein conformation represented by the co-ordinates, {r}, in the absence of denaturants, [C] = 0, is N NN ECG ({r}, 0) = EB + EN B + EN B .

(S1)

The bonded interaction energy, EB , for all pairs of bonded beads is modelled by finite extensible nonlinear elastic (FENE) potential,

EB =

NB X k i=1

2

⇣ R02 log 1

(ri

rcry,i )2 ⌘ , R02

(S2)

where NB (= 127) is the total number of pairs of bonds in the SOP-SC model of the protein. N The values of k and R0 are listed in table S1. Non-bonded native interaction energy, EN B,

S2


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is modelled by Lennard-Jones type of potential energy and is given by bb

N EN B

=

NN X

i=1 ss NN

+

X

✏bb h

⇥ rcry,i ri

N bs

12

N ⇥ rcry,i rcry,i 6 ⇤ X 2 + ✏bs h ri ri i=1

✏ss i )300kB

0.5(0.7

i=1

⇥ rcry,i ri

12

2

12

2

rcry,i 6 ⇤ , ri

rcry,i 6 ⇤ ri

(S3)

where NNbb , NNbs and NNss denote the number of native contact pairs between backbonebackbone, backbone - side chain and side chain - side chain, respectively. The values of NNbb , NNbs and NNss are 172, 432 and 173, respectively. kB is the Boltzmann constant, ri denotes the distance between ith pair of beads, and rcry,i denotes the corresponding distance in the bs ss crystal structure. ✏bb h , ✏h and ✏i denote the strength of backbone - backbone, backbone -

side chain and side chain - side chain interactions, respectively (Table S1). The values of ✏ss i are taken from the Betancourt-Thirumalai statistical potential. 4 NN The non-native interactions, EN B , are purely repulsive interactions and are given by

NN EN B

=

N NN X i=1

✏l

i 6

ri

+

3N X4 i=1

✏l

i,i+2 6

ri,i+2

,

where NN N (=6973) is the total number of pairs of non-native interactions.

(S4)

i

is the sum of

the radii of ith pair of beads. The second sum on the right hand side of equation S4 mimics the bond angle potential between beads i and i + 2.

i,i+2

is the sum of the radii of beads i

and i + 2. Values of the side chain radii are given in Table S2 in Ref. 5 The values of the parameters used in the energy function (Table S1) are identical to the values previously used to successfully study the folding properties of the proteins GFP 5 and Ubiquitin. 6 We have used the same force-field to study the properties of di↵erent proteins, and as a result this force-field satisfies the criterion of a transferable force-field. Molecular Transfer Model: To simulate Protein L folding thermodynamics and kinetics in the presence of Guanidine Hydrochloride we used the Molecular Transfer Model

S3



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Page 32 of 41

(MTM). 7,8 In the presence of a denaturant of concentration [C], the e↵ective coarse-grained force field for the protein using MTM is given by

ECG ({r}, [C]) = ECG ({r}, 0) +

where ECG ({r}, 0) is given by Eq. S1,

Gtr ({r}, [C]),

(S5)

Gtr ({r}, [C]) is the protein-denaturant interaction

energy in a solution with denaturant concentration [C], and is given by

Gtr ({r}, [C]) =

N X

gtr,k ([C])↵k ({r})/↵Gly

k Gly ,

(S6)

k=1

where N (=Nres ⇥ 2 = 128) is the number of beads in coarse-grained Protein L, gtr,k ([C]) is the transfer free energy of bead k, ↵k ({r}) is the solvent accessible surface area (SASA) of the bead k in a protein conformation described by positions {r}, ↵Gly the bead k in the tripeptide Gly

k

k Gly

is the SASA of

Gly. The radii for amino acid side chains to compute

↵k ({r}) are given in Table S2 in Ref. 6 The experimental 7,9,10 transfer free energies gtr,i ([C]), which depend on the chemical nature of the denaturant, for backbone and side chains are listed in Table S3 in Ref. 2 The values for ↵Gly

k Gly

are listed in Table S4 in Ref. 2

Simulations: The SOP-SC model of the polypeptide chain is simulated using Langevin dynamics at di↵erent temperatures ranging from 300K to 430K in low friction using the energy function given by eq. S1 to compute the average thermodynamic properties of the protein. The equations of motion are integrated using the equation mr~¨i =

⇣ r~˙i + F~c + ~ ,

(S7)

where m is the mass of a protein beads, ⇣ is the friction coefficient, r~i is the position of the bead i, F~c =

@ET OT @ r~i

, ~ is the random force with a white noise spectrum. The autocorrelation

function of the random force in the discretised form is given by h (t) (t + nh)i = where n = 0, 1, ... and

0,n

2⇣kB T 0,n , h

is the Kronecker delta function. The Langevin equation is S4


Page 33 of 41

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integrated using the velocity Verlet algorithm. 11,12 We used ⇣ = 0.05m/⌧L and h = 0.005⌧L , where ⌧L is the unit of time used to advance the simulation. To compute thermodynamic properties of the protein in a denaturant solution of concentration [C],

Gtr ({r}, [C]) is treated as perturbation to ECG ({r}, 0) in Eq. S5, and Weighted

Histogram Method 7,8,13 is used to compute average value of various physical quantities at any [C]. The average value of a physical property A, at temperature T , and denaturant concentration [C] is computed using the equation

hA([C], T )i = Z([C], T )

1

nk R X X Ak,t e

(Ek,t ({rk,t },[0])+ Gtr ({rk,t },[C]))/kB T

R P

k=1 t=1

n m e fm

,

(S8)

Ek,t ({rk,t },[0])/kB Tm

m=1

where R is the number of simulation trajectories, nk is the number of protein conformations from the k th simulation, Ak,t is the value of the property of the tth conformation from the k th simulation, Tm and fm are the temperature and free energy respectively from the mth simulation, Ek,t ({rk,t }, [0]) and

Gtr ({rk,t }, [C])) are the internal energy at [C] = 0 and

MTM energy respectively of the tth conformation from the k th simulation, and Z([C], T ) is the partition function given by

Z([C], T ) =

nk R X X e k=1 t=1

(Ek,t ({rk,t },[0])+ Gtr ({rk,t },[C]))/kB T R P

nm

.

(S9)

efm Ek,t ({rk,t },[0])/kB Tm

m=1

We performed Brownian dynamics simulations with the full Hamiltonian given by Eq. S5, and a friction coefficient, which approximately corresponds to that of water to study the burst-phase folding kinetics of Protein L. The equations of motion are integrated using the Ermak-McCammon algorithm, 14 r~i (t+h) = r~i (t)+ h⇣ F~c + ~ . Here ~ is a random displacement with a Gaussian distribution with mean zero and variance h (h)2 i =

2kB T h . ⇣

The friction

coefficient ⇣ = 31.2m/⌧H approximately corresponds to the value in water and, the value of h varies from 0.001⌧H to 0.01⌧H depending on the denaturant concentration. In the simulations, the characteristic unit of length a = 1˚ A, energy ✏ = 1kcal/mole, and mass

S5



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

m = 1.8 ⇥ 10

22

g (typical mass of the bead). The unit of time in Langevin dynamics p simulations is ⌧L (= ma2 /✏) = 1.3ps. In Brownian dynamics, simulation time is mapped into real time, ⌧H using ⌧H ⇡

⇣H a2 kB T

=

(⇣H ⌧L /m)✏ ⌧L kB T

⇡ 47ps.

Transition State Analysis: 108 putative transition state structures (TSS) from the Langevin dynamics trajectory at TM = 374.5K are identified using the conditions 14˚ A Rg 16.2˚ A and 0.5

0.6 (Fig. S2) for the Pf old analysis. To compute Pf old for each

putative TSS, 500 short simulation trajectories each of 0.15µs in length are initiated using the putative TSS as the initial conformation to compute the fraction of the trajectories, which land up in the NBA or the UBA (Fig. S6).

References (1) Hyeon, C. B.; Dima, R. I.; Thirumalai, D. Structure 2006, 14, 1633–1645. (2) Liu, Z.; Reddy, G.; O’Brien, E. P.; Thirumalai, D. Proc. Natl. Acad. Sci. USA 2011, 108, 7787–7792. (3) O’Neill, J. W.; Kim, D. E.; Baker, D.; Zhang, K. Y. J. Acta Crystallogr. Sect. D-Biol. Crystallogr. 2001, 57, 480–487. (4) Betancourt, M. R.; Thirumalai, D. Prot. Sci. 1999, 8, 361–369. (5) Reddy, G.; Liu, Z.; Thirumalai, D. Proc. Natl. Acad. Sci. USA 2012, 109, 17832–17838. (6) Reddy, G.; Thirumalai, D. J. Phys. Chem. B 2015, 119, 11358–11370. (7) O’Brien, E. P.; Ziv, G.; Haran, G.; Brooks, B. R.; Thirumalai, D. Proc. Natl. Acad. Sci. USA 2008, 105, 13403–13408. (8) Liu, Z.; Reddy, G.; Thirumalai, D. J. Phys. Chem. B 2012, 116, 6707–6716. (9) Auton, M.; Bolen, D. W. Biochemistry 2004, 43, 1329–1342. S6


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Page 35 of 41

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(10) O’Brien, E. P.; Brooks, B. R.; Thirumalai, D. Biochemistry 2009, 48, 3743–3754. (11) Veitshans, T.; Klimov, D.; Thirumalai, D. Fold Des 1997, 2, 1–22. (12) Swope, W. C.; Andersen, H. C.; Berens, P. H.; Wilson, K. R. J. Chem. Phys. 1982, 76, 637–649. (13) Kumar, S.; Rosenberg, J. M.; Bouzida, D.; Swendsen, R. H.; Kollman, P. A. J. Comput. Chem. 1992, 13, 1011–1021. (14) Ermak, D. L.; Mccammon, J. A. J Chem Phys 1978, 69, 1352–1360.

S7



(A)

β1β4

120

α1β4

12

(kcal/mol)

α1β2

60

α1β3 α1

0.6

β1β2

0

6

2

20

40

60

80

100

0.010

0.7

0.008

0.5

0.006

0.4

0.004

0.3

0.002

0.2

24

20 15

20

10

16

5

0.000 380

400

12 340

400

(Å)

0.6

360

380

T (K)

(D)

0.8

340

360

120

Bead Number

(C)

0 340

0

0

4

-100

0.2

20

8

0

-50

0.4

40

10

(Å)

Bead Number

α1β1

80

50

Cv (kcal/mol/K)

0.8

100

(B)

1

β3β4

d/dT

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 41

360

380

400

T (K)

T (K)

Figure S1: (A) The contact map of Protein L shows contacts between various secondary structural elements in the folded state. (B) Average internal energy, hU i (empty circles in black), and heat capacity, Cv (empty squares in red), as a function of temperature, T . (C) Structural overlap factor, h i (empty circles in black), and dh i/dT (empty squares in red), as a function of T . (D) Root mean square deviation, hRM SDi (empty circles in red), and Radius of gyration, hRg i (empty squares in black), as a function of T .

S8


Page 37 of 41

(A)

TM = 374.5 K

0.8 0.6

χ

A

0.4 0.2 0

2

4

6

8

10

time (µs) (B)0.14 0.12

P(χ)

0.10 0.08 0.06 0.04

χc = 0.47

0.02 0.00 0.2

(c)

0.4

χ

0.6

0.8 0

0.8 −1

0.7

−2

0.6 0.5

−3

0.4

−4

χ

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.3

−5

0.2

−6

0.1 10

15

20

25

Rg (Å)

30

35

40

−7

Figure S2: (A) Structural overlap factor, , plotted as a function of time at the melting temperature, TM = 374.5K. (B) Probability distribution of , P ( ), at TM . The value c = 0.47 separates the unfolded basin of attraction (UBA) and native basin of attraction (NBA). (C) The free energy projected onto and Rg using the relation, G = kB TM ln(P (Rg , )), where P (Rg , ) is joint probability distribution of Rg and at TM , and kB is the Boltzmann constant. The two basins corresponding to the UBA and NBA show two-state behaviour at TM . S9



1.0 Sim (Equil)

0.8

0.6 0.4 0.2 0.0 0

2

4

6

8

[GuHCl] (M) Figure S3: Average FRET efficiency, hEi, as a function of [GuHCl] at T = 357.7K.

[GuHCl] = 1 M [GuHCl] = 2 M

35 30

Rg (Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 41

25 20 15 0

100

200

300

400

500

t( Figure S4: Radius of gyration, Rg , plotted as a function of time, t, for Protein L folding trajectories in [GuHCl] = 1M (blue) and 2M (green) at T = 357.7K. S10


Page 39 of 41

(A) 0.025

[GuHCl] = 2.0 M Gaussian P(Ree) Simulation P(Ree)

P(Ree)

0.020 0.015 17.3

0.010

24.3

0.005

57.08

55.23

0.000 0

40

80

120

Ree

(B)


0.020

P(Ree)

0.015 18.6

0.010

25.0

0.005

59.4

56.7

0.000 0

(C)

40

80

Ree

0.020

120

160


0.015

P(Ree)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


19.1

0.010

27.6

0.005 60.89

65.6

40

80

0.000 0

Ree

120

160

Figure S5: The end-to-end distance, Ree , probability distribution function P (Ree ) during the burst phase (initial 0.25ms) of protein L folding is in red circles. P (Ree ) estimated from hE Burst i and Guassian polymer chain statistics in green squares. (A) [GuHCl] = 2.0M , T = 357.7K (B) [GuHCl] = 4.0M , T = 357.7K and (C) [GuHCl] = 6.0M , T = 357.7K

S11



(A) 10

P(χ)

8 6 4 2 0 0.2

0.4

0.6

0.8

χ

(B) 0.8 0.7 0.6

χ

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 41

0.5 0.4 0.3 0.2 0

5000

10000

15000

20000

time (τBD) Figure S6: (A) The distribution of the final structural overlap factor, , for each transition state structure at the end of 0.15µs computed from 500 simulation trajectories. Data for 5 di↵erent structures is shown. (B) Simulation trajectories spawned using a transition state structure as the starting conformation land up in UBA and NBA.

S12


Page 41 of 41

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Table S1: Parameters for the SOP-Side Chain model Parameters Protein Ro 2.0 ˚ A k 20 kcal/mol/˚ A2 Rc 8˚ A bb 1 ✏h 0.45 kcal/mol a ✏bs 0.45 kcal/mol h a ✏l 0.9 kcal/mol bb 3.8 ˚ A

S13


Folding of Protein L with Implications for Collapse in the Denatured

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