Single-Molecule Spectroscopy Study of Crowding-Induced Protein

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Single-Molecule Spectroscopy Study of Crowding-Induced Protein Spontaneous Denature and Crowding-Perturbed Unfolding-Folding Conformational Fluctuation Dynamics ZIjiang Wang, and H. Peter Lu J. Phys. Chem. B, Just Accepted Manuscript • Publication Date (Web): 31 May 2018 Downloaded from http://pubs.acs.org on May 31, 2018

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The Journal of Physical Chemistry

Single-Molecule Spectroscopy Study of Crowding-Induced Protein Spontaneous Denature and Crowding-Perturbed Unfolding-Folding Conformational Fluctuation Dynamics Zijiang Wang, H. Peter Lu* Department of Chemistry and Center for Photochemical Sciences, Bowling Green State University, Bowling Green, Ohio 43403, United States E-mail: [email protected] Tel: 419-372-1840 Supporting Information ABSTRACT: The effects of molecular crowding on protein folding-unfolding processes are of importance for understanding protein function and structure dynamics in living cells. The enhancement of protein stability as a result of reduced entropic effect in the presence of molecular crowding is well understood both experimentally and theoretically. However, due to the complexity and interplay between various interactions existing in an equally favored environment of protein folding and unfolding conformational dynamics, such simple reduced entropic enhancement model does not suffice to describe protein folding conformational dynamics under a protein crowding condition. In this paper, we report our observation on that single protein molecules spontaneously denature into unfolded proteins and folding-unfolding fluctuations in solution of crowding reagent Ficoll 70. We have identified such the protein dynamics involves in a combined mechanism of polymer-polymer interaction, entropic effects, and protein solvation dynamics. We characterize the protein folding-unfolding dynamics by using single-molecule spectroscopy to obtain detailed molecular dynamic scale information on the protein folding-unfolding conformational fluctuation dynamics. Our findings suggest that the complex unfolding dynamic processes are spontaneous denature of single protein molecules induced by molecular crowding effect which has been elusive for analysis in ensembleaveraged measurements. Furthermore, the energy needed for the spontaneous unfolding is at the biological accessible force fluctuation level, which suggests a strong implication of significant human health relevance and importance. The new knowledge of the inhomogeneous protein unfolding processes can serve as a step forward to a mechanistic understanding of human diseases associated with molecular crowding, protein aggregates, fibril formation as well as gene translational regulation processes typically under molecular crowded local environment.

Introduction The interior of a living cell contains a large number of biological macromolecules and cellular components, such as proteins, DNA, RNA, chaperones, endoplasmic reticulum, mito1-4 chondrion, and cell membranes. The volume fraction of 5, 6 occupied macromolecular agents is as large as 40%. The existence of such macromolecular networks has significant 6 effects on the behavior of protein conformational dynamics. For example, enzymatic reactions, gene transcriptional regulation, and amyloid formation are profoundly effected in

6

crowded biological environments. Protein folding process in the presence of molecular crowding is crucial to understand protein folding process inside living cells with a large number of bio-macromolecules. Various molecular scale microenvironments are readily emulated by molecular crowding effect such as extensive protein-macromolecule 7-9 interactions and molecular confinement effect. The effect of macromolecular crowding on protein folding and protein conformational dynamics has been extensively studied by both ensemble-averaged experiments and single-molecule experiments. In vitro studies show almost exclusively an exclusion volume effect to favor the formation of a self-assembled and more compact native protein structures. Intuitively, a reduction of total excluded volume favors a more compact folded state of a protein. However, entropic effect alone is not the only factor that comes into play, especially, when a system involves macromolecular complexes. Remarkably, studies have shown that high concentration of crowding agents could have no effect at all on the refolding of lysozyme and could further cause aggrega5, 10-12 tion. In a living cell, this aggregation process is mostly 6 prevented by chaperones. Nevertheless, diseases induced by unfolded protein responses, such as ALS, Alzheimer’s, Parkinson’s, prion and Huntington’s disease, often have similar protein disorder patterns of protein entanglements and 13-15 aggregations. Significantly, it has been recently reported that the protein folded nature structures can be spontaneously and abruptly ruptured under biological accessible 16, 17 picoNewton compressive forces, and the protein rupture events are highly local environment dependent. It is highly desirable and significant to further investigate the biologically relevant and available forces and energy, quantitatively understanding the physical natures and obtaining characterization of such force and energy, for spontaneously change to protein conformational structures between folded and unfolded protein states. This is the primary focus of this work. Single-molecule spectroscopy and imaging are powerful to probe protein molecular dynamic processes without ensemble averaging, yielding information unobtainable from 1, 3, 4, 18-23 conventional methods. The molecular details of single protein folding are readily observed one molecule at a time in single molecule experiments. Single-molecule fluorescence resonant energy transfer (FRET) allows an identification of folded and unfolded subpopulations, and thus enables a further quantitative analysis of the properties of single 1, 18, 24protein molecule conformational fluctuation dynamics. 29 Since single-molecule FRET can provide distance and protein conformational fluctuation dynamical information with-

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out ensemble-averaging, it is promising to show the intramolecular conformational dynamics to be observed at equilibrium in which the folded and unfolded conformational states 30 are equally favorable statistically. Calmodulin (CaM) is a 148-residue protein responsible 31-34 for intracellular calcium-sensing. It is crucial in many cell signaling biological processes including muscle contraction 31-34 and energy metabolism. CaM has two globular domains, which serves as binding domains for different binding target 31-34 proteins inside living cell. Traditional methods involving nuclear magnetic resonance and X-ray crystallography have provided detailed insights into the mechanisms and dynam31-34 ics of CaM singnaling. As a result of the flexibility and the dumbbell shape of the protein, it is feasible to monitor the conformational dynamics of CaM with single-molecule FRET spectroscopy, reported by our lab and others in recent 18, 30, 31, 35, 36 years. Ficoll 70, a non-reactive and non-interactive polymer, typically serves as biological mimic of intracellular crowded 6 environments. Using Ficoll 70 as a crowding agent has a number of advantages: It is a biologically-compatible polysaccharide, i.e., sucrose epichlorohydrin copolymer with an average molecular mass of 74 kDa; The Ficoll 70, inert and polar, does not interact with proteins; It behaves like a semirigid sphere (radius of ≈5.5nm), which makes it an attractive mimic of globular macromolecules that may be present in the biological setting where proteins normally fold. In addition, it can readily be represented in computer simulations as repulsive hard spheres of the appropriate size. Apparently, the Ficol 70 can be a relevant chemical agent to help on un37, derstanding the chaotropes of macromolecules in solution. 38

Materials and Methods The single CaM molecule is mutated on N-terminal domain at residue 34 and C-terminal domain at residue 110 for replacements of cysteine residues, and fluorescent dye pair Cy3/Cy5 are covalently tethered onto the protein via thiola30 tion. These two dyes serve as a probe for the measurement of conformational fluctuation of the protein molecules in different concentrations of crowding reagent Ficoll 70. It is proved from previous study that the decreased refolding events are not due to the additional friction caused by the crowding agent Ficoll 70, but due to a complex interplay 5, 6, 10-12 between reduced entropic and enthalpic effects. In our experiments, we prepare the samples for single-molecule conformational folding-unfolding dynamics measurements in the presence of crowding reagent Ficoll 70 inside the aga1, 3, 30, 39 rose gel (1% by weight, Type VII, Sigma). We make samples of CaM into different concentrations of denaturant 40-42 solvent GdmCl in the mixture of 200 nM CaM, 1.25μL and oxygen scavenger with Trolox solution to obtain a 10μL mixture of enzyme and denaturant solvent. The Trolox solution is made previously by dissolving about 1 mM 6-hydroxy2,5,7,8-tetramethylchroman-2-carboxylic acid (Trolox) in 1 mg/mL glucose oxidase, 0.8% D-glucose and 0.04 mg/mL catalase in order to protect fluorescent dye from photobleaching or blinking as a result of triplet state formation and other photophysical processes. We then heat the 10μL 1% agarose gel just above its gel-transition temperature (26°C) and quickly mix the above enzyme solution with denaturant solvent solution and the gel between two clean cover glasses to form a sandwich. All solutions are prepared with HEPES buffer at pH 7.4. To probe conformational dy-

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namics of single enzyme molecule at different concentration of Ficoll 70, we carry out concentration dependent experiments with different ratio of mixture in the sample. Single-molecule photon stamping approach is used to record FRET trajectories at different concentration of crowding reagent. This approach records emission of photons from donor and acceptor channel one by one with arrival time of detection, so that we can construct the intensity trajectories as a function of time with desired time bin resolution. The experimental setup is a home-modified inverted confocal microscope (Axiovert 200, Zeiss) which used a continuous wave laser at 532nm for excitation. The Laser beam focuses through a 100× oil immersion objective lens (1.3 NA, 100×, Zeiss) onto the upper surface of cover slip after reflected up by a dichroic beam splitter (z532rdc, Chroma Technology). To obtain confocal microscopy image, we use an x-y closedloop piezo position scanning stage for raster-scanning of the sample. Fluorescence from single molecules is collected through the same objective, and the signal is split by a dichroic beam splitter (640dcxr) into two different wavelengths 570nm for the donor channel and 670nm for the acceptor channel. To detect the signal from two channels, two Si avalanche photodiode single photon counting modules (SPCM-AQR-16, Perkin Elmer Optoelectronics) are used to record photons from donor and acceptor. A more detailed 3, description of the experimental setup is reported elsewhere. 30, 36, 39

We first apply a 2D regional correlation mapping analysis to our single-molecule photon stamping data. This 2D regional correlation mapping analysis calculates a twodimensional cross-correlation amplitude distribution 30, 39, 43 (TCAD). In this analysis, each of the trajectories, {IA(t)} and {ID(t)}, are scanned with different starting and ending time, and the cross-correlation amplitude Ccorss(τ, tstart:tstop) of each time segment with distinct starting and ending time ( tstart and tstop) are calculated (equation 1). We use color bar to indicate the amplitude of cross-correlation. t sto p t sto p C cro ss (τ , t sta rt : t sto p ) = ∫ I A ( t ) I D ( t − τ )d t = ∑ I A ( t ) I D ( t − τ ) t sta rt t sta rt (1) Where IA and ID are the two-band photon count intensities signal of donor and acceptor, and tstart and tstop give the scanning window width. The cross-correlation functions are calculated with different tstart and tstop along a pair of smFRET trajectories IA(t) and ID(t). The cross-correlation functions are calculated with different starting and ending time. Via this method, we identify time segments along a specific trajectory with strong anti-correlation indicated. In our protein conformational dynamics analyses, this method enabled us to reveal real anti-correlated FRET signal fluctuation segments of single molecule trajectories from the shot noises or average intensity drifts due to thermal fluctuation of local environment. We apply auto-correlation (equation 2) to our singlemolecule photo-stamping data after the identification of each anti-correlated single-molecule FRET trajectory segments. The auto-correlation functions are defined to be C a uto ( t ) =

∆ IA ( 0 ) ∆ IA (t ) ∆ IA (0 )

2

=

( I ( 0 ) − I ) ( I (t ) − ( I (0 ) − I ) A

A

A

IA

)

2

A

A

(2) where IA(t) and ID(t) representing acceptor and donor


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intensities, and and are the means of the intensity trajectories, respectively. Cauto(t) is the autocorrelation function. Correlation function analysis is able to capture protein conformational dynamics from a measured fluorescence trajectory. Results and Discussion Figure 1A shows a typical image from our singlemolecule FRET imaging of the CaM molecules. By raster-scan the sample, a 20μm × 20μm sample image yields bright spots of single CaM molecules confined in agarose gel. The spots indicating single protein molecules are diffraction limited with approximately 300nm in diameter. We pin point the laser focus to each specific sample spot to record continuous donor-acceptor (D-A) fluorescence intensity trajectories (Figure 1B). Typically, we gather more than seventy singlemolecule trajectories which are 40 seconds long at different concentrations of denaturant GdmCl, and we calculate the EFRET time trajectories (Figure 1C) from the single-molecule 30, 36, 39 FRET intensity trajectories using the equation 3. IA (t ) (3)

E FRET (t ) =

IA (t ) + ID (t ) × Where

φA

and

φD

φ A×η φ D ×η

A D

are the emission quantum yields of ac-

ceptor and donor dyes, respectively, and

ηA

and η D are the

g/L, the conformational states changes towards unfolded states under the strain of the local environment. Although, Figure 2 primarily shows the ensemble averaged results driven by thermodynamics, the single molecule conformational fluctuation dynamics is much more complex. For example, at single molecule level the conformational fluctuations under compressive force local environment can triggle protein 16, 17 which is not observconformational rupture fluctuations, able from this ensemble-averaged measurement.

Figure 2. Ensemble titration curve using simultaneous recording fluorescence from both the donor and the acceptor channel which characterizes the unfolding of CaM molecule at higher concentration of crowding reagent. All measurements carried out at 2M GdmCl concentration of denaturant.

acceptor and donor detection efficiencies, respectively. Here the correction factor

φ A ×η A φ D ×η D

is ~1 in our experiment condi-

tions. We then deduce the distribution (Figure 1D) from the single-molecule FRET efficiency EFRET trajectory (Figure 1C). In this way, we are able to calculate the mean and the standard deviation of each EFRET distribution under various conditions of the molecular crowding agent (Figure 1D).

Figure 1. Image obtained from Confocal Microscope of single CaM molecule. The bright spots are single molecules with diffraction limited (~300nm in diameter) image. Typical Donor/Acceptor signals and EFRET trajectories. Green and red lines indicate the donor and acceptor channel respectively. The histogram distribution from EFRET trajectory gives the EFRET of a certain single-molecule. We have carried out an ensemble-averaged bulk control experiment to measure the EFRET changes with the crowding agent concentrations (Figure 2). It is typical that the protein conformational state space is compressed under the crowndness agent of Ficol 70 increases from zero to 230 g/L due to stress on the CaM; as the crowdeness increases beyond 230

In Figure 3, the measured ensemble-averaged results reflecting the relative population of the folded CaM states with high EFRET and the unfolded CaM states with low EFRET. Based on the measurement, the folded verses unfolded state population ratio increases as the crowding agent concentration increases; and the ratio starts to decrease as the crowding agent concentration increases beyond about 230 mg/ml and deceases further as the crowding agent concentration further increases to 300 mg/ml. The result of the control experiment clearly shows that the population on unfolded states of CaM decreases when its local environment gets crowded and then increases when its local environment gets over crowded. Single-molecule EFRET changes under different molecular crowding conditions due to the statistical probability of unfolding and refolding states of the single protein molecules (Figure 3). The changes in EFRET are clear evidence of the conformational change of single CaM molecules under different concentrations of Ficoll 70. The single-molecule EFRET distribution is consisting of both the folded subpopulation with EFRET 0.6 and unfolded subpopulation with EFRET 0.35. In this study, we focus on the folding-unfolding fluctuating CaM molecules with EFRET 0.45. An ensemble average measurements and single-molecule measurements yield similar results that the 2M denature condition is the critical point of such titration. The EFRET distribution at 50g/L Ficoll 70 is 0.36 and at 100g/L Ficoll 70 is 0.41, at which CaM molecules start to refold. This conformational change measured by FRET is a strong evidence of single CaM molecules enhanced stability by crowding reagent Ficoll 70. As we increase Ficoll 70 concentration close to living cell macromolecule concentration ~300g/L, a remarkable decrease and broadening of EFRET distribution is observed. Such heterogeneous unfolding process as a result of crowding effect cannot be resolved by conventional ensemble average measurements. We resolve subpopulations of unfold and fold protein conformations and study detailed dynamic fluctuations at the equilibrium.



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Mechanistic understanding of the single molecule protein folding energy landscape can be extracted from this analysis.

Figure 3. EFRET Distributions. Distribution of FRET efficiency of different samples at different concentration of Ficoll 70 from zero to 300 g/L. The shift in peak values characterizes the unfolding of CaM molecule at higher concentration of crowding reagent. We analyze the dynamical behaviors of our data sets by calculating the autocorrelation functions. By fitting the autocorrelation functions with exponential decays, we are able to characterize the time scale of protein conformational fluctuations (Figure 4). Qualitatively, each exponential decay gives correlation lifetime of donor channel, and the broad distribution of the lifetimes is a result of local environment heterogeneity. At high concentration of Ficoll 70, CaM has a typical autocorrelation function with a sharp decay as a result of native protein motion with typical time scale of millisecond. In higher concentration of Ficoll 70, the CaM molecules, in its denatured states, show weak auto-correlation decay. This is due to the unfolding of CaM molecule in crowdedness which turns the proteins into random coils; so that the correlation of protein’s regular motion becomes weaker. The two-dimensional regional cross-correlation analyses help us to identify the time segments with strong anti-correlation of each single-molecule intensity trajectory. We zoom in to study each of the anti-correlated time segments by calculating the auto-correlation. Subtle conformational dynamic signatures can be straightforwardly analyzed by the distribution of on- and off44-47 times. The on-time and off-time are the “waiting time” for the CaM folding and unfolding. In order to characterize such detailed dynamic behavior, we further bin our trajectories to be one millisecond as shown (Figure 4). In order to obtain a folding waiting time distribution, we set up a threshold, at which the folding and unfolding states are separated. For the trajectory shown in Figure 4, we choose the value 7 as the threshold value, and subsequent folding waiting time distribution is shown.

Figure 4. Autocorrelation function calculated from FRET efficiency trajectory. In different concentrations of crowding reagent, the CaM molecule in its native state show a correlation decay. Auto-correlations from intensity trajectory. Donor intensity trajectory obtained from our single-molecule confocal microscopy (1 ms). The black line indicates the threshold criterion separating the on- and off-time. Brown lines are the identified successive on- and off-time. The ontime distribution is a gamma shaped distribution representing a multiple step dynamic scheme. The simulated data is also shown. Noticeably, the folding waiting time distribution is nonexponential resulting from a multiple-state folding-unfolding dynamic scheme, comparing to that exponential temporal distribution should be observed for two-state protein folding-unfolding dynamics according to Poisson statistics. Such 1, 30, distribution is also distinct from a Gaussian distribution. 39, 48 This distinction clearly rules out the possibility of two35, state folding-unfolding dynamics for single CaM molecules. 49, 50 The gamma shaped folding waiting time distribution indicates a more complex dynamic scheme involving multi30, 48 ple intermediates and multiple steps. We attribute the non-exponential folding waiting time distribution to the existence of multiple folding intermediates. To further characterize this multiple intermediate state dynamics, we exploit a one dimensional random walk model, which has been applied successfully in the modeling of multiple step single25,32,51 molecule enzymatic reactions. The basic strategy is as the following: without prior knowledge of the shape of the energy landscape, we assume a uniform rate constant k to each step as a single Poisson process in the multiple step rate processes as a convolution of multiple Poisson processes. The convolution of several Poisson process with uniform k 30, 48 gives gamma function shaped distribution (Formula 4-6). This distribution will reproduce the mean and standard deviation of the original folding waiting time distribution. The number of Poisson steps involved in this convolution calculation gives an estimation of how many Poisson rate processes are involved in the overall protein spontaneous foldingunfolding fluctuation process at equilibrium condition. This number will be the lower bound estimation of the number of intermediate involved in the dynamics process of protein folding.


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P ( t ) = A  e x p ( − t / τ

) 

(4)

where P(t) is the probability distribution of the Poisson rate process step times, τ is the averaged Poisson rate process step time, and A is the distribution weight constant. To calculate the convolution of function f(t) and g(t), the integration equation is t

( f ∗ g )( t ) = ∫0 f ( v ) g ( t − v ) dv P (Tn ) = A n

t n −1  exp ( −t / τ ) 

( n − 1)!

(5)

(6)

Where n (1, 2, 3,…, N) is the index of the intermediate steps; τ is the mean formation time of a folding intermediate through a single-step process and A is the normalizing factor of this probability distribution. Quantitatively, in our case we calculate the number of steps using such model and obtain an upper bound of number of states. The simulated distribution involves two Poisson rate processes which indicated a 2-step three state dynamics. We further analyze our data by employing condensed phase polymer solution theory. Presumably, macromolecular crowding effect plays an enhancing role in protein folding 5, 10-12 process. However from our single-molecule experiment, we deduce polymer crowding might have enhancing and diminishing the protein folding stability in that overcrowdedness could potentially reduce the stability of protein molecules in the matrix. Such behavior is a consequence of a balance amongst hydrophobicity, hydrophiliccity, and solvation thermodynamics and dynamics. Using polymer solution 10-12, 21, 22, 30, 52-54 theory, we understand such counterintuitive phenomenon by calculating Helmholtz free energy and force exerted by the polymer matrix. In concentrated polymer solution of Ficoll 70, the very existence of another polymer will automatically exert a force on the target polymer. Size of 0.5 -0.35 the polymer R=N φ b, where b is the monomer size, φ the volume fraction and N degrees of polymerization. The 2 2 2 5, 10-12 Blob number g=(Nb )/(φ R ). In our current analyses, our target polymer is a single-molecule CaM protein molecule. Since we increase rather than decrease the artificial crowd molecules of Ficoll 70, the Ficoll 70 molecules apply a force on the target CaM protein molecule. The exerted force is at molecular scale force typically at pico-newton scale used to unfolds or manipulates protein molecules. Since polymer force is in principle entropic force originates from thermal fluctuation, it only makes sense to consider such subtle force and time scale in condensed phase protein folding dynamics. To further quantitatively understand the force applied to the target CaM molecule from the crowding local environment in our current experiments, we calculate thermodynamic quantities from equilibrium polymer solution theory. The entropic nature of the forces applied in single-molecule protein folding experiment can be calculated from statistical mechanics. From equipartition theorem, to every degree of freedom, there is a thermal energy kT/2 associated to that degree of freedom solely as a result of entropy and thermal 10-12, 21, 22, 30, 52-54 fluctuation energy. 2 2 2 The Helmholtz free energy F = (kTN)/2g = (kTφ R )/b is essentially the amount of kT thermal energy stored in an extended polymer. The physical picture of polymer solution

chemistry directly implies an extended fibril like equilibrium solution dynamics of single protein molecules. Basically, it means when the concentration of polymer solution is increased, due to monomer-monomer interactions, the polymers automatically reorganize themselves to form the concentrated polymer solution. To estimate the forces in this macroscopic dynamic polymer solution, we differentiate the Helmholtz free energy with respect to R to get the force ex0.5 1.65 erted on target polymer f = -(0.93kTN φ )/b. For Ficoll 70, 5, 10-12 the specific volumeφ is 0.67ml/g. In our experiments, the crowded region has a polymer concentration of 300g/L, the volume fraction of Ficoll 70 is 20%. In this crowded region, we observe protein unfolding resolved from the singlemolecule data. The monomer size of polymer Ficoll 70 is 3.9 Å. Therefore, the calculated force is about -8.7 pN, the negative sign implies a retraction force of extended unfolded single CaM protein molecules. From AFM and optical tweezer experiments, such force is strong enough to denature protein 50, 55-58 into unfolded states.

Figure 5. Molecular scale force as a function of concentration of crowding agent Ficoll 70. Inter-molecular distance as a function of concentration of crowding agent Ficoll 70. We also analyze the protein conformational foldingunfolding fluctuation motion diffusion coefficient from the folding waiting time distribution. From our previous exper30 iments, we already have the mean conformational drift distance

X N (t )

to be 1.22nm. Using equation 7, we calcu-

late the diffusion coefficient D of this 2-step dynamic process -13 2 to be 13.2×10 cm /s. The diffusion coefficient is directly related to the shape of the underlying energy landscape, since it reflects the local mean square fluctuation of the activation barrier of the folding-unfolding dynamic process.

( D=

∆tunfold 2

X N (t )

2 tunfold

)

2

(7)

3

where D is the conformational diffusion coefficient. The mean unfolding time,

tunfold

, and the standard deviation

∆ tunfold 2

， are directly of the unfolding time distribtuion, measured in our experiment. The total drifting distance of X

(t )

the folding-unfolding conformational motion, N , is associated to the folding-unfolding conformational distance change. Theoretically, we estimate the size of single-molecule CaM 2, 22, 30, 49, 54 in the presence of denaturant GdmCl. Although there are different models involving complex intra-chain



molecular interactions, we choose Gaussian chain model because it is the most simplified model and catches the essential properties of an unfolded protein. The unfolded radius of gyration Rg of the single-molecule CaM protein in 0.55 GdmCl, Rg = 0.345N nm is 5.4 nm, which is consistent with 22, 54, 59-62 experimental value of 6.1 ± 0.8 nm. N is the number of monomers in the polypeptide chain. Such scaling relation of Rg is strongly supported by small-angle X-ray scattering. The folding speed limits of single domain proteins are provided experimentally, and the single-molecule single domain protein folding time is well characterized under Gaussian chain assumption. The vast majority of measurements yield the formation time of loop is less than 0.1 μs, and α–helix formation is approximately 0.5 μs. The formation time of β hairpin is greater than 0.5 μs. Since linear scaling theory holds for small degree of polymerization, using the linear length scaling suggested by the homopolymer collapse theory, theoretical upper bound of single-molecule CaM folding time τlimit of 148 amino acid CaM is 3.0μs. Since CaM polypeptide chain is more like of a heteropolymer than a homopolymer there are additional factors to be taken into account while describing protein collapse. The estimation of theoretical upper bound of single-molecule CaM folding time τlimit based on homopolymer collapse theory is essentially accu2 rate. We note that the folding time τ = /(3D) with D as 2 2 1.1 2 the diffusion coefficient and = 6Rg = 0.7N nm is the mean square end-to-end distance of a polymer. We estimat-7 2 ed Dlimit to be 1.9 × 10 cm /s as the theoretical upper bound of single-molecule CaM conformational diffusion. The roughness of the free energy barrier involved in the foldingunfolding dynamic process is determined by D = Dlimit exp(2 2 β ε ), ε is a measurement of the roughness of the singlemolecule CaM protein folding free energy barrier. For CaM folding-unfolding conformational diffusion, the diffusion 2 coefficient D is cm /s from our experimental measurement discussed above, which gives the roughness of the singlemolecule CaM protein folding free energy barrier ε of 3.8kT; k is the Boltzmann constant and T is the temperature. Compared with the hydrogen bonding (~2-12 kT), this value of free energy barrier roughness is at the scale of hydrogen bonding interaction energy in a protein folding process associating with breaking and forming of a number of hydrogen bonds. On the other hand, the height of the free energy barrier is estimated by using Kramer’s barrier-crossing theory. We first estimate the actual folding time of CaM by using τ = 2 2 0.5 /(3D) to be 0.89s in which () is experimental value measured by EFRET 6.1 ± 0.8 nm and D is experimental value measured by the time bunching effect of single-molecule CaM folding process. Since the single-molecule CaM folding-unfolding conformational fluctuation motion diffusion coefficient D is determined from our single-molecule experimental measurements. We move further to use Kramer’s theory to estimate the empirical free energy barrier of single-molecule protein folding process. Kramer’s theory assumes that the dynamic process of protein folding can be described as a onedimensional diffusion along a reaction coordinate, and the minimum and maximum of the free energy surface are parabolic. From Kramer’s theory, τfolding = 2πτlimit exp(ΔG/kT)

(8)

τfolding is the folding time of single-molecule CaM measured in our experiment. τlimit is the theoretical upper bound of sin-

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gle-molecule CaM folding time. ΔG Is the free energy barrier and k is the Boltzmann’s constant T is the temperature. The height of the free energy barrier ΔG is estimated to be 11kT, which is consistent with previous optical tweezers measurement for CaM. Our measurement yields an free energy barrier slightly lower than optical tweezers measurements, this difference is likely due to the distinct structure involved in the measurement assays using different denature methods resulting in slightly different energetic feature of energy landscape. Nevertheless, our analysis reveals

Figure 6. The scatter plot we constructed with number of steps involved in each of the dynamic process vs. conformational diffusion coefficient. The folding-unfolding dynamics pattern naturally clustered into separated domains. Subsequently, a CaM folding energy landscape can be extracted, and a distribution of the folding paths with distinct probability assigned to each of them can be achieved. A Cartoon Showing Folding Process. A cartoon showing a combination of molecular scale effects lead to protein unfolding under buffer condition. Such molecular crowding effects leading to a protein unfolding can be seen as a concerted effect of solvation and macromolecular crowding. that instead of a two-state dynamic scheme our study shows a more complex and higher dimensional dynamic process on a multiple-pathway multiple-state energy landscape. By recording detailed fluctuation dynamics at the thermodynamic equilibrium under the condition of 2M GdmCl, we characterize such unique dynamic feature via a conformational diffusional modeling of single-molecule CaM folding-unfolding conformational dynamic process. We have analyzed approximately 30 trajectories under different crowding conditions to acquire a distribution of such dynamic processes on the energy landscape. For each of them, we simulate the number of steps involved in the overall protein folding-unfolding dynamic process, and we also calculate the folding-unfolding conformational motion diffusion coefficient. A two-dimensional scatter plot is constructed with conformational diffusion coefficient vs. number of steps (Figure 6). Remarkably, the folding-unfolding trajectories with same number of steps and similar conformational motion diffusion coefficient cluster together. This cluster behavior is clearly a manifestation of an energy landscape with distinct folding pathways. Moreover, these various folding pathways have a distribution with distinct probabilities. To better present this observation, we convert the two-dimensional scatter plot to be a two dimensional energy landscape plot with color arrow indicating different folding pathways. Our results suggest four different folding pathways of CaM molecule folding process both in the crowding enhancing and diminishing regions. In summary, from our single-molecule studies, inspirations drawn from polymer solution theory, we propose a


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brand new perspectives on the protein conformational dynamics under crowding, stress and strain force fluctuations. It is a new way of looking at all these concepts of condensed phase dynamics and draw connections. We demonstrate single-molecule protein foldingunfolding conformational dynamics in the presence of molecular crowding effect provided by Ficoll 70. In our singlemolecule FRET experiment, we observe large heterogeneity of EFRET which is a clear evidence of single-molecule protein refolding and unfolding processes. Such remarkable detailed information of conformational dynamics eludes ensembleaveraged experiments due to averaging. The enhanced folding process is entropic driven process which stabilizes single protein molecules and refolds proteins into native states. However, at higher concentration of crowding reagent Ficoll 70, we observe unfolding of single protein molecules which are a combined process of polymer-polymer interaction, entropic and solvation mechanism. Utilizing polymer solution theory, we show such unfolding process can be understood as an isotropic force exerted on single-molecule protein solely due to the existence of host polymers. Subtle conformational fluctuation dynamics can be readily observed and studied by single-molecule techniques. The longer folding conformational fluctuation time indicates an enthalpic trap provided by the presence of molecular crowding reagents. In other words, extensive polymerpolymer interactions slow down folding conformational fluctuations by favoring the unfolded states of single-molecule proteins. By our dynamic modeling, we observe a converged folding pathway due to normal crowding reagents as a result of entropic effect. Simply, the existence of polymer provides excluded volume which decreases the sampling conformations available for protein molecules. However, in concentrated regime of polymer solutions, such entropic effect is out-favored by polymer-polymer interaction and solvation effect which destabilize single-protein molecules. The unfolding process due to molecular crowding is highly heterogeneous, which is a manifestation of complex, cooperative mechanisms. We observe single-molecule protein spontaneous folding-unfolding conformational fluctuation dynamics in crowded environment. We, for the first time, report a detailed molecular scale, mechanistic study of protein spontaneous folding and unfolding conformational dynamics under a progressively rowdiness conditions. By incorporating ideas and insights from single-molecule spectroscopy, condensed phase dynamics and polymer theoretical modeling, the characteristic protein folding dynamic pattern, time scale, length scale and molecular force scale are probed in great detail. Furthermore, our study is a prototypical study serving as the first step to initiate molecular scale study of diseases caused by protein overexpression and aggregation beyond ensembleaveraged traditional methods. Using artificial polymer, we achieved simulated crowded intracellular condition. The intermolecular distance in our study is within ~2nm averagely, in a statistical perspective, which is, for example, closely related to real structure of cross-β spine (1.4nm), a leading toxic structure, ubiquitous in pathological intracellular environment. Our extensive study of this fundamental process involved in protein folding dynamic pattern, time scale, length scale and molecular force scale provides insights on mechanistic understanding of human diseases related with molecular folding-unfolding under crowdedness molecular environments, such as diseases associated with molecular

crowding, protein aggregation, protein fibril formation, and gene translational regulations. The Supporting Information is available free of charge on the ACS Publications website. ACKNOWLEDGMENT We acknowledge the support of the Ohio Eminent Scholar endowment and Sigma Graduate Scholarship.

REFERENCES 1. Lu, H. P.; Xun, L.; Xie, X. S., Single-molecule enzymatic dynamics. Science 1998, 282 (5395), 1877-82. 2. Schuler, B.; Lipman, E. A.; Eaton, W. A., Probing the free-energy surface for protein folding with single-molecule fluorescence spectroscopy. Nature 2002, 419 (6908), 743-7. 3. Lu, H. P.; Iakoucheva, L. M.; Ackerman, E. J., Singlemolecule conformational dynamics of fluctuating noncovalent DNA-protein interactions in DNA damage recognition. J. Am. Chem. Soc. 2001, 123 (37), 9184-5. 4. Ha, T.; Ting, A. Y.; Liang, J.; Caldwell, W. B.; Deniz, A. A.; Chemla, D. S.; Schultz, P. G.; Weiss, S., Single-molecule fluorescence spectroscopy of enzyme conformational dynamics and cleavage mechanism. Proc. Natl. Acad. Sci. U.S.A. 1999, 96 (3), 893-8. 5. Zimmerman, S. B.; Minton, A. P., Macromolecular crowding: biochemical, biophysical, and physiological consequences. Annu. Rev. Biophys. Biomol. Struct. 1993, 22, 27-65. 6. van den Berg, B.; Ellis, R. J.; Dobson, C. M., Effects of macromolecular crowding on protein folding and aggregation. EMBO J. 1999, 18 (24), 6927-33. 7. Benton, L. A.; Smith, A. E.; Young, G. B.; Pielak, G. J., Unexpected Effects of Macromolecular Crowding on Protein Stability. Biochemistry 2012, 51 (49), 9773-9775. 8. Biswas, S.; Kundu, J.; Mukherjee, S. K.; Chowdhury, P. K., Mixed Macromolecular Crowding: A Protein and Solvent Perspective. ACS Omega 2018, 3 (4), 4316-4330. 9. Singh, P.; Chowdhury, P. K., Unravelling the Intricacy of the Crowded Environment through Tryptophan Quenching in Lysozyme. J. Phys. Chem. B 2017, 121 (18), 4687-4699. 10. Minton, A. P., Implications of macromolecular crowding for protein assembly. Curr. Opin. Struct. Biol. 2000, 10 (1), 349. 11. Minton, A. P.; Lewis, M. S., Self-association in highly concentrated solutions of myoglobin: a novel analysis of sedimentation equilibrium of highly nonideal solutions. Biophys. Chem. 1981, 14 (4), 317-24. 12. Minton, A. P.; Wilf, J., Effect of macromolecular crowding upon the structure and function of an enzyme: glyceraldehyde-3-phosphate dehydrogenase. Biochemistry 1981, 20 (17), 4821-6. 13. Matthes, D.; Daebel, V.; Meyenberg, K.; Riedel, D.; Heim, G.; Diederichsen, U.; Lange, A.; de Groot, B. L., Spontaneous aggregation of the insulin-derived steric zipper peptide VEALYL results in different aggregation forms with common features. J. Mol. Biol. 2014, 426 (2), 362-76. 14. Aguzzi, A.; O'Connor, T., Protein aggregation diseases: pathogenicity and therapeutic perspectives. Nature Reviews. Drug Discovery 2010, 9 (3), 237-48. 15. Ross, C. A.; Poirier, M. A., Protein aggregation and neurodegenerative disease. Nature Medicine 2004, 10 Suppl, S107.



16. Chowdhury, S. R.; Cao, J.; He, Y.; Lu, H. P., Revealing Abrupt and Spontaneous Ruptures of Protein Native Structure under picoNewton Compressive Force Manipulation. ACS Nano 2018, 12 (3), 2448-2454. 17. Chowdhury, S. R.; Lu, H. P., Probing Activated and Non-Activated Single Calmodulin Molecules under a Piconewton Compressive Force. Biochemistry 2018, 57 (13), 1945–1948. 18. Lu, H. P., Single-molecule study of protein-protein and protein-DNA interaction dynamics. Methods in molecular biology 2005, 305, 385-414. 19. Chung, H. S.; Louis, J. M.; Eaton, W. A., Experimental determination of upper bound for transition path times in protein folding from single-molecule photon-by-photon trajectories. Proc. Natl. Acad. Sci. U.S.A. 2009, 106 (29), 11837-11844. 20. Chung, H. S.; McHale, K.; Louis, J. M.; Eaton, W. A., Single-Molecule Fluorescence Experiments Determine Protein Folding Transition Path Times. Science 2012, 335 (6071), 981984. 21. Haran, G., How, when and why proteins collapse: the relation to folding. Curr. Opin. Struct. Biol. 2012, 22 (1), 14-20. 22. Sherman, E.; Haran, G., Coil-globule transition in the denatured state of a small protein. Proc. Natl. Acad. Sci. U.S.A. 2006, 103 (31), 11539-11543. 23. Slaughter, B. D.; Unruh, J. R.; Price, E. S.; Huynh, J. L.; Bieber Urbauer, R. J.; Johnson, C. K., Sampling Unfolding Intermediates in Calmodulin by Single-Molecule Spectroscopy. J. Am. Chem. Soc. 2005, 127 (34), 12107-12114. 24. Deniz, A. A.; Laurence, T. A.; Beligere, G. S.; Dahan, M.; Martin, A. B.; Chemla, D. S.; Dawson, P. E.; Schultz, P. G.; Weiss, S., Single-molecule protein folding: Diffusion fluorescence resonance energy transfer studies of the denaturation of chymotrypsin inhibitor 2. Proc. Natl. Acad. Sci. U.S.A. 2000, 97 (10), 5179-5184. 25. Dill, K. A.; Chan, H. S., From Levinthal to pathways to funnels. Nature Structural Biology 1997, 4, 10-19. 26. Nettels, D.; Hoffmann, A.; Schuler, B., Unfolded Protein and Peptide Dynamics Investigated with Single-Molecule FRET and Correlation Spectroscopy from Picoseconds to Seconds. J. Phys. Chem. B 2008, 112 (19), 6137-6146. 27. Onuchic, J. N.; and, Z. L.-S.; Wolynes, P. G., THEORY OF PROTEIN FOLDING: The Energy Landscape Perspective. Annu. Rev. Phys. Chem. 1997, 48 (1), 545-600. 28. Socci, N. D.; Onuchic, J. N.; Wolynes, P. G., Diffusive dynamics of the reaction coordinate for protein folding funnels. J. Chem. Phys. 1996, 104 (15), 5860-5868. 29. Zwanzig, R., Diffusion in a rough potential. Proc. Natl. Acad. Sci. U.S.A. 1988, 85 (7), 2029-2030. 30. Wang, Z.; Lu, H. P., Probing single-molecule protein spontaneous folding-unfolding conformational fluctuation dynamics: the multiple-state and multiple-pathway energy landscape. J. Phys. Chem.. B 2015, 119 (21), 6366-78. 31. James, P.; Vorherr, T.; Carafoli, E., Calmodulin-binding domains: just two faced or multi-faceted? Trends in biochemical sciences 1995, 20 (1), 38-42. 32. Chin, D.; Means, A. R., Calmodulin: a prototypical calcium sensor. Trends in cell biology 2000, 10 (8), 322-8. 33. Chattopadhyaya, R.; Meador, W. E.; Means, A. R.; Quiocho, F. A., Calmodulin structure refined at 1.7 A resolution. J. Mol. Biol. 1992, 228 (4), 1177-92. 34. Babu, Y. S.; Sack, J. S.; Greenhough, T. J.; Bugg, C. E.; Means, A. R.; Cook, W. J., Three-dimensional structure of calmodulin. Nature 1985, 315 (6014), 37-40. 35. Slaughter, B. D.; Unruh, J. R.; Price, E. S.; Huynh, J. L.; Bieber Urbauer, R. J.; Johnson, C. K., Sampling unfolding intermediates in calmodulin by single-molecule spectroscopy. J. Am. Chem. Soc. 2005, 127 (34), 12107-14.

Page 8 of 16

36. Liu, R.; Hu, D.; Tan, X.; Lu, H. P., Revealing two-state protein-protein interactions of calmodulin by single-molecule spectroscopy. J. Am. Chem. Soc. 2006, 128 (31), 10034-42. 37. Bhaganna, P.; Volkers, R. J. M.; Bell, A. N. W.; Kluge, K.; Timson, D. J.; McGrath, J. W.; Ruijssenaars, H. J.; Hallsworth, J. E., Hydrophobic substances induce water stress in microbial cells. Microbial Biotechnology 2010, 3 (6), 701-716. 38. Collins, K. D., Charge density-dependent strength of hydration and biological structure. Biophys. J. 1997, 72 (1), 6576. 39. He, Y.; Li, Y.; Mukherjee, S.; Wu, Y.; Yan, H.; Lu, H. P., Probing single-molecule enzyme active-site conformational state intermittent coherence. J. Am. Chem. Soc. 2011, 133 (36), 14389-95. 40. Arakawa, T.; Timasheff, S. N., Protein stabilization and destabilization by guanidinium salts. Biochemistry 1984, 23 (25), 5924-5929. 41. Lee, J. C.; Timasheff, S. N., Partial specific volumes and interactions with solvent components of proteins in guanidine hydrochloride. Biochemistry 1974, 13 (2), 257-265. 42. Makhatadze, G. I.; Privalov, P. L., Protein interactions with urea and guanidinium chloride: A calorimetric study. J. Mol. Biol. 1992, 226 (2), 491-505. 43. Wang, X.; Lu, H. P., 2D regional correlation analysis of single-molecule time trajectories. J. Phys. Chem. B 2008, 112 (47), 14920-6. 44. Zhou, Y.; Zhang, C.; Stell, G.; Wang, J., Temperature Dependence of the Distribution of the First Passage Time: Results from Discontinuous Molecular Dynamics Simulations of an All-Atom Model of the Second β-Hairpin Fragment of Protein G. J. Am. Chem. Soc. 2003, 125 (20), 6300-6305. 45. Wang, J., Statistics, pathways and dynamics of single molecule protein folding. J. Chem. Phys. 2003, 118 (2), 952-958. 46. Leite, V. B. P.; Onuchic, J. N.; Stell, G.; Wang, J., Probing the Kinetics of Single Molecule Protein Folding. Biophys. J. 2004, 87 (6), 3633-3641. 47. Wang, J., The Complex Kinetics of Protein Folding in Wide Temperature Ranges. Biophys. J. 2004, 87 (4), 2164-2171. 48. Wang, Y.; Lu, H. P., Bunching effect in single-molecule T4 lysozyme nonequilibrium conformational dynamics under enzymatic reactions. J. Phys. Chem. B 2010, 114 (19), 6669-74. 49. Thirumalai, D.; Klimov, D. K., Deciphering the timescales and mechanisms of protein folding using minimal offlattice models. Curr. Opin. Struct. Biol. 1999, 9 (2), 197-207. 50. Stigler, J.; Ziegler, F.; Gieseke, A.; Gebhardt, J. C.; Rief, M., The complex folding network of single calmodulin molecules. Science 2011, 334 (6055), 512-6. 51. Chen, Y.; Hu, D.; Vorpagel, E. R.; Lu, H. P., Probing Single-Molecule T4 Lysozyme Conformational Dynamics by Intramolecular Fluorescence Energy Transfer. J. Phys. Chem. B 2003, 107 (31), 7947-7956. 52. Gennes, P.-G. d., Scaling concepts in polymer physics. Cornell University Press: Ithaca, N.Y., 1979; p324 . 53. Des Cloizeaux, J.; Jannink, G. r., Polymers in solution : their modelling and structure. Clarendon Press ; Oxford University Press: Oxford, New York, 1990; p xlvi, 895 p. 54. Ziv, G.; Thirumalai, D.; Haran, G., Collapse transition in proteins. Phys. Chem. Chem. Phys. 2009, 11 (1), 83-93. 55. Puchner, E. M.; Franzen, G.; Gautel, M.; Gaub, H. E., Comparing proteins by their unfolding pattern. Biophys. J. 2008, 95 (1), 426-434. 56. Sedlak, S. M.; Bauer, M. S.; Kluger, C.; Schendel, L. C.; Milles, L. F.; Pippig, D. A.; Gaub, H. E., Monodisperse measurement of the biotin-streptavidin interaction strength in a welldefined pulling geometry. Plos One 2017, 12 (12), e0188722. 57. Valle-Orero, J.; Rivas-Pardo, J. A.; Tapia-Rojo, R.; Popa, I.; Echelman, D. J.; Haldar, S.; Fernandez, J. M., Mechani-


Page 9 of 16 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


cal Deformation Accelerates Protein Ageing. Angew. Chem. Int. Ed. 2017, 56 (33), 9741-9746. 58. Zoldak, G.; Rief, M., Force as a single molecule probe of multidimensional protein energy landscapes. Curr. Opin. Struct. Biol. 2013, 23 (1), 48-57. 59. Schuler, B., Single-molecule fluorescence spectroscopy of protein folding. Chemphyschem 2005, 6 (7), 1206-1220. 60. Thirumalai, D.; Hyeon, C., RNA and Protein Folding: Common Themes and Variations. Biochemistry 2005, 44 (13), 4957-4970. 61. Yamakawa, H., Modern Theory of Polymer Solutions. Harper & Row: 1971. 62. Khokhlov, A. R.; Grosberg, A. Y.; Pande, V. S., Statistical Physics of Macromolecules (Polymers and Complex Materials) American Institute of Physics: New York, 1994.


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Single-Molecule Spectroscopy Study of Crowding-Induced Protein

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