Subscriber access provided by Kaohsiung Medical University
Biological and Medical Applications of Materials and Interfaces
Stabilization of Immobilized Enzymes via the Chaperone-like Activity of Mixed Lipid Bilayers Andres F Chaparro Sosa, Daniel F Kienle, Rebecca M Falatach, Jessica Flanagan, Joel L Kaar, and Daniel K Schwartz ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b05523 • Publication Date (Web): 16 May 2018 Downloaded from http://pubs.acs.org on May 16, 2018
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 33 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
ACS Applied Materials & Interfaces
Stabilization of Immobilized Enzymes via the Chaperonelike Activity of Mixed Lipid Bilayers Andres F. Chaparro Sosa, Daniel F. Kienle, Rebecca M. Falatach, Jessica Flanagan, Joel L. Kaar*, Daniel K. Schwartz* Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309
*
Corresponding Authors: Joel L. Kaar University of Colorado Boulder Department of Chemical and Biological Engineering Campus Box 596 Boulder, CO 80309 Tel: (303) 492-6031 Fax: (303) 492-4341 Email:
[email protected] Daniel K. Schwartz University of Colorado Boulder Department of Chemical and Biological Engineering Campus Box 596 Boulder, CO 80309 Tel: (303) 735-0240 Fax: (303) 492-4341 Email:
[email protected] KEYWORDS: Lipid bilayers, Enzyme immobilization, Enzyme stability, Single-molecule Förster resonance energy transfer, Nitroreductase
1 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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
Abstract Biomimetic lipid bilayers represent intriguing materials for enzyme immobilization, which is critical for many biotechnological applications. Here, through the creation of mixed lipid bilayers, the retention of immobilized enzyme structure and catalytic activity are dramatically enhanced. The enhancement in the retention of enzyme structure, which correlated with an increase in enzyme activity, is observed using dynamic single-molecule (SM) fluorescence methods. The results of SM analysis specifically show that lipid bilayers composed of mixtures of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) and 1,2-dioleoyl-sn-glycero-3-phospho(1'-rac-glycerol) (DOPG) stabilize the folded state of nitroreductase (NfsB) increasing the rate of re-folding relative to unfolding of enzyme molecules on the bilayer surface. Remarkably, for optimal compositions with 15-50% DOPG, over 95% of NfsB remains folded while the activity of the enzyme is increased as much as two-times over that in solution. Within this range of DOPG, the strength of the interaction of folded and unfolded NfsB with the bilayer surface was also significantly altered, which was evident by the change in the diffusion of folded and unfolded NfsB in the bilayer. Ultimately, these findings provide direct evidence for the chaperone-like activity of mixed DOPG/DOPC lipid bilayers, which can be controlled by tuning the fraction of DOPG in the bilayer.
2 ACS Paragon Plus Environment
Page 2 of 33
Page 3 of 33 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
ACS Applied Materials & Interfaces
Introduction Surface tethering of enzymes is fundamental in many areas of biotechnology, including biosensing,1,2 biocatalysis,3,4 bioelectronics,5–7 bioremediation,8,9 and tissue engineering.10–13 Enzymes are often tethered to surfaces to improve their reusability, which offsets the cost of enzyme preparation and purification. The immobilization of enzymes also enables sophisticated functions that impart biocatalytic activity to the immobilization support. However, because surface-tethering is often accompanied by a significant loss of enzyme structure and activity, the full technological potential of immobilized enzymes has not been realized.14,15 The loss of structure and activity of enzymes upon immobilization may be attributed to the vastly different environment, and potentially perturbative, interactions near a synthetic surface compared to the native environment of enzymes inside of cells.16 For example, it has been reported that near hydrophobic interfaces, amino acids in the hydrophobic core of an enzyme may experience strong interactions with the surface, which destabilize the folded state leading to denaturation and inactivation.17,18 Additionally, the formation of hydrogen bonds and electrostatic interactions between chemical groups on the enzyme and surface can lead to the loss of protein structure.19,20 Such interactions may also inactivate enzymes by restricting dynamics (e.g., the opening of a lid domain that covers the active site cleft) that are critical to the catalytic mechanism. While the design of synthetic materials to control denaturing interactions between enzymes and surfaces has, to date, remained elusive, there are a plethora of examples from nature from which we can learn about biointerfaces at which enzymes, and proteins in general, are stable. For example, many proteins, including enzymes, are in frequent contact with biomembranes and other lipid-containing structures, with minimal loss of structure and function.
3 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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
Of specific interest, enzymes are frequently tethered to membrane surfaces and involved in critical metabolic functions, including signal transduction and membrane trafficking. As such, there has been considerable interest in using supported lipid bilayers (SLBs) as artificial biomimetic surfaces for enzyme immobilization in many applications. In nearly all cases, the enzyme has been immobilized on homogeneous SLBs consisting of lipids with a phosphatidylcholine (PC) head group, which is commonly found in eukaryotic and bacterial cell membranes.21,22 For example, Wicklein and co-workers23 reported that the immobilization of urease and cholesterol oxidase on silicate sepiolite modified with SLBs comprising a cocktail of PC-containing lipids resulted in a significant increase in activity as well as improved storage stability and reusability compared to immobilization on bare sepiolite. A similar increase in activity and stability over to that of the enzyme in solution was observed for glucose oxidase that when immobilized on 1,2-dimyristoyl-sn-glycero-3-PC.24 Studies have suggested that the apparent increase in stability of enzymes on SLBs is due to a chaperone-like effect, whereby SLBs may promote re-folding of denatured enzyme molecules.25–28 Although never directly shown, it has been hypothesized that denatured enzyme molecules may specifically re-fold within the hydrophobic acyl region of the SLB. In the case of such a mechanism, one would expect the putative chaperone-like activity to be highly sensitive to the structure, composition, and dynamics of the SLB. However, the effect of tuning such properties on the re-folding of enzymes on SLBs has yet to be systematically studied and, at best, remains poorly understood. As a method to characterize the structure and stability of enzymes on SLBs, dynamic single-molecule (SM) tracking has several advantages. Specifically, using dynamic SM tracking, the folding state of surface immobilized enzymes may be characterized in situ while capturing various heterogeneities, including dynamic, spatial, and population heterogeneities, which are
4 ACS Paragon Plus Environment
Page 4 of 33
Page 5 of 33 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
ACS Applied Materials & Interfaces
masked by traditional ensemble-averaging techniques. Additionally, through large-scale multivariate analysis, structural and dynamic behavior (e.g., diffusion, folding and unfolding) of enzymes may be directly correlated on a molecule-by-molecule basis. In previous work, we demonstrated the utility of combining dynamic SM tracking with intramolecular Förster resonance energy transfer (FRET) to elucidate the influence of surface environments on protein structure and dynamic behavior.29,30 This approach involves using total internal reflection fluorescence (TIRF) microscopy to monitor the FRET signature of protein molecules as they diffuse and undergo conformational changes on the surface in a high-throughput manner, which permits the analysis of 103-105 molecules per experiment. Here, dynamic SM-FRET tracking was used to investigate the impact of lipid composition on the structure, apparent unfolding and re-folding kinetics, and diffusion of enzymes tethered to SLBs. Specifically, using this approach, the structure and dynamics of the Escherichia coli nitroreductase NfsB on SLBs composed of 1,2-dioleoyl-sn-glycero-3phosphocholine (DOPC), 1,2-dioleoyl-sn-glycero-3-phospho-(1'-rac-glycerol) (DOPG), and mixtures of DOPC and DOPG, was characterized. The results from SM studies were further correlated with ensemble activity measurements of NfsB tethered to unilamellar lipid vesicles. Our results provide unprecedented insight into the role of SLB heterogeneity on immobilized enzyme structure and activity as well as evidence into the chaperone-like activity of SLBs.
Results and Discussion Preparation of FRET Active NfsB Construct Site-specifically labeled NfsB was initially prepared by introducing p-azidophenylalanine (AzF) and a Cys residue at amino acid positions 89 and 315, respectively, in a Cys-free form of the enzyme. To enable the attachment of a single donor and acceptor fluorophore, a construct 5 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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
was used in which the monomeric subunits of NfsB, which is a native homodimer, were genetically fused. This construct, moreover, enabled control of the tethering location to a single uniform site (i.e., the N-terminus) via a hexa-histidine motif, which doubled as an affinity tag for purification as well as a capture sequence through which the enzyme could be anchored to an NTA ligand. Notably, amino acid positions 89 and 315 were chosen for labeling based on solvent accessibility and close proximity in the tertiary structure (2.7 nm), but large separation in the primary sequence (Figure 1A). Following expression in E. coli, NfsB was reacted with dibenzocyclooctyne-Alexa Fluor (AF) 488 and maleimide-CF633, resulting in the labeling of AzF89 with AF488 (donor) and Cys315 with CF633 (acceptor). Conjugation of the AF488 and CF633 to the engineered NfsB construct was confirmed by in-gel fluorescence imaging (Figure S1). Additionally, characterization of the NfsB construct used for labeling indicated that the Ala89AzF and Ala315Cys mutations had a negligible effect on the structure and activity of the fused NfsB (Figure S2). To confirm that the FRET efficiency of the labeled NfsB construct was sensitive to unfolding, changes in FRET efficiency of NfsB upon denaturation with urea were measured in solution. Figure 1B shows that, in solution, FRET efficiency of NfsB decreased strongly with increasing denaturant concentration, demonstrating the folded and unfolded states could be distinguished by FRET.
6 ACS Paragon Plus Environment
Page 6 of 33
Page 7 of 33 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
ACS Applied Materials & Interfaces
Figure 1. A) Structure of NfsB-FRET. The mutated sites Ala89AzF and Ala315Cys are shown as blue and red spheres, respectively. Residue numbers correspond to those of full-length NfsB. The purple spheres indicate the location of the N-terminus, which contained a hexa-histidine tag for tethering to the bilayer. The distance between the labeling sites in the crystal structure (PDB ID: 1DS7) of the NfsB is 2.7 nm. B) Denaturation of FRET-labeled NfsB in solution as a function of urea concentration, showing the change in ensemble-average FRET efficiency between the folded and unfolded state of NfsB. Error bars represent standard deviation from three different measurements.
7 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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
NfsB Conformation on SLBs The impact of lipid composition on NfsB stability on SLBs was determined by preparing SLBs composed of DOPC, DOPG, and DOPC/DOPG mixtures (with 15%, 25%, 35%, 50%, 75% DOPG, respectively) on fused silica surfaces via vesicle fusion. Following vesicle fusion, the continuity of the SLBs was characterized by fluorescence recovery after photo-bleaching (FRAP). For FRAP analysis, the mobile fraction of rhodamine-labeled 1,2-dioleoyl-sn-glycero3-phosphoethanolamine (DOPE-LR), which was added to the SLB, was quantified without tethered NfsB. Results of FRAP analysis showed that the mean mobile fraction of DOPE-LR in SLBs containing 0-50% DOPG was greater than 0.9 (Table S1), indicating that the continuity of the SLBs was high. Additionally, the FRAP-determined diffusion coefficients of the SLBs ( = 1.2 µm2 s-1 on DOPC, and = ~0.8 µm2 s-1 on 15-50% DOPG) were consistent with that reported previously for SLBs of similar compositions.31 For SLBs with greater than 50% DOPG, the mean mobile fraction of the SLBs was negligible, which was also consistent with previous reports.32,33 The negligible mobile fraction on these SLBs suggested that the vesicles, although apparently covering the silica surface as indicated by uniform fluorescence images (Figure S3), did not fuse laterally to form a continuous bilayer. For SM studies, NfsB was tethered to the SLB through the interaction of an N-terminal hexa-histidine tag and lipid-NTA-nickel inter-dispersed within the bilayer. The lipid-tethered NfsB, which was immobilized at concentrations suitable to monitor individual molecules, was subsequently illuminated via alternating-laser TIRF excitation. Excited molecules were monitored via wide-field imaging using spectrally separated channels to capture donor and acceptor emission, which were spatially aligned on the lipid surface. Alternating-laser excitation allowed for accurate identification of correctly labeled NfsB enzymes containing active donor and acceptor fluorophores, and prevented incorrect state assignments that could arise due to 8 ACS Paragon Plus Environment
Page 8 of 33
Page 9 of 33 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
ACS Applied Materials & Interfaces
photo-bleaching or mislabeling. Heat maps of the intensities of the donor (FD) and acceptor (FA) fluorophores were created from the accumulated trajectories (~2000) for the tethered NfsB on each SLB. Figure 2 shows heat maps of all observations on each surface where two distinct populations were observed. The population with high FA and low FD was representative of folded NfsB whereas the fraction with low FA and high FD was representative of unfolded NfsB. For each time-step in the trajectory, a folded or unfolded state was assigned based on the location of that time-step on the heat map relative to a dividing line, which was positioned to split the folded and unfolded populations as shown in Figure 2. The dividing line was chosen to minimize the integrated values of the heat map along the line, which passed approximately through a saddle point between the folded and unfolded populations. Additionally, sample movies showing raw data from the SM experiments on 25% DOPG and 100% DOPG are shown in the supporting information (Movie S1 and S2).
9 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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
Figure 2. Heat maps of the donor (FD) and acceptor (FA) intensities from SM-FRET imaging of NfsB on SLBs composed of A) 0%, B) 15%, C) 25%, D) 35%, E) 50%, F) 75%, and G) 100% DOPG, as well as H) fused silica. Two distinct populations were observed and separated by a linear threshold (white dashed lines) that minimized the integrated map values along the dividing line. The population with higher acceptor intensity and lower donor intensity (below the dividing line with peak represented by an asterisk) corresponded to the folded fraction, while the population above the dividing line corresponded to the unfolded fraction (with peak represented by a diamond). The total number of observations in the heat maps were 11,619, 3,920, 10,326, 9,014, 8,101, 2,390, 5,804, and 2,466 for panels A-H, respectively. The intensities in the heat maps were normalized to the total number of observations for each condition such that the relative differences of folded and unfolded populations cold be compared.
The results of SM analysis showed that, while the tethered enzyme was highly stable on all of the SLB surfaces, an optimum in the stability of NfsB was observed on the 25% DOPG
10 ACS Paragon Plus Environment
Page 10 of 33
Page 11 of 33 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
ACS Applied Materials & Interfaces
(75% DOPC) surface (Figure 3A). Specifically, on the 25% DOPG surface, the folded fraction value of NfsB (Pfolded) was 0.98, suggesting that virtually all of the enzyme tethered to the surface was folded. The value of Pfolded decreased systematically for surfaces with higher and lower fractions of DOPG, with the lowest Pfolded values observed on the 75% (Pfolded = 0.63) and 100% (Pfolded = 0.51) DOPG surfaces. A potential reason for the decreased stability on the 75% and 100% DOPG surfaces could be the hypothetical presence of exposed fused silica defect regions due to discontinuities within the SLB. Notably, NfsB was almost entirely unfolded on fused silica (Pfolded = 0.07). However, as shown below, the activity of NfsB tethered to dispersed DOPC/DOPG vesicles followed a nearly identical trend as that observed for the structural stability on SLBs, suggesting that lipid composition was the dominant factor. Overall, the stability of tethered NfsB on the SLBs was striking given that the folded fraction of proteins in contact with other surfaces, including putatively biocompatible oligoethylene glycol selfassembled monolayers and polyethylene glycol brushes, was previously measured to be less than 0.6 using SM-FRET methods.29,34–36 The observed trend in folded fraction with fraction of DOPG was subsequently compared with the trends for ensemble activity of NfsB anchored to lipid vesicles (Figure 3B) and the rate constants for the unfolded and re-folding of NfsB on SLBs (Figure 3C) with DOPG fraction. Details of the analysis of ensemble activity on lipid vesicles and the rate constants for the unfolded and re-folding of NfsB on SLBs is discussed below.
11 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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
Figure 3. A) Folded fraction (Pfolded) of NfsB as a function of SLB composition. The error bars represent the standard deviation of calculated Pfolded using a sub-sampling method (see experimental section for details). B) Relative specific activity of NfsB tethered to unilamellar lipid vesicles with varying DOPG concentration, which mimic the SLBs used in SM experiments. The activity of tethered NfsB at each condition was normalized to the maximum activity, which was observed for the vesicles with 25% DOPG. For comparison, the activity of free NfsB in solution relative to the activity of tethered NfsB on vesicles with 25% DOPG was 0.51 ± 0.02 as indicated by the horizontal dotted line. The error bars represent the standard error of the specific activity of NfsB for three independent replicate experiments. C) Rate constants of folding (kf; red squares) and unfolding (ku; blue circles) of NfsB enzymes as a function of SLB composition from SM-FRET analysis. The error bars represent the standard error estimated by propagating the uncertainty of the transition probabilities through the calculation of the rate constants. The uncertainty in the transition probabilities was estimated as the square-root of the Cramèr–Rao lower bound.
12 ACS Paragon Plus Environment
Page 12 of 33
Page 13 of 33 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
ACS Applied Materials & Interfaces
NfsB Activity on Lipid Vesicles To complement the SM-FRET observations of NfsB conformation when tethered to SLBs, NfsB was tethered to the surface of dispersed unilamellar lipid vesicles using the same tethering approach (i.e., through the hexa-histidine tag), and the enzymatic activities of these dispersions were measured. Remarkably, a similar trend was observed for tethered enzyme activity as a function of vesicle lipid composition (Figure 3B) as was observed above for NfsB conformational stability on SLBs (Figure 3A). In particular, a maximum of the enzymatic activity was observed on vesicles containing 25% DOPG, where tethered NfsB had roughly two times more activity than free (i.e., untethered) NfsB in solution. The activity of tethered NfsB decreased systematically for vesicles having lower or higher DOPG content, with the lowest activity of tethered NfsB observed at 100% DOPG. However, even on 100% DOPG vesicles, the activity of NfsB was higher (59% of the maximum relative activity) when tethered compared to untethered NfsB in the absence of vesicles (51% of the maximum relative activity). Although it is interesting that the activity of NfsB on the vesicles was greater than that for untethered NfsB in the absence of vesicles, the mechanism for this increase in activity is unclear. For example, while it is plausible the higher activity on the vesicles was due to a higher fraction of folded enzymes on the vesicles than in solution due to refolding, such an increase may also be due to partitioning effects of the substrate as well as changes in local pH and/or electrostatic environment around the enzyme upon immobilization. One cannot also rule out that immobilization resulted in the enzyme adopting a structure that was more active than the native structure of NfsB. Nonetheless, the consistency of the folded fraction and activity results demonstrate the direct relationship between SM-FRET measurements of enzyme structure on SLBs and enzymatic activity on unilamellar vesicles.
13 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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
Impact of DOPG Fraction on the Kinetics of NfsB Unfolding and Re-folding on SLBs The results from SM-FRET and activity measurements suggest that DOPG fraction had a marked impact on enzyme stability, which also translated directly to activity. To develop a more mechanistic view of the role of lipid bilayers on the stability of NfsB, the FRET trajectories were analyzed to determine the apparent rate constants associated with tethered NfsB unfolding (ku) and apparent re-folding (kf) on the different SLBs. A maximum likelihood approach was implemented, using the simplest possible model that adequately described the data, assuming homogeneous folding, unfolding and bleaching of the tethered enzymes in each experiment. That is, the model assumed that each enzyme in a given experiment obeyed the same rate constants, ignoring potential complications due to heterogeneity. This model was sufficient to describe the conformational time series data. The results (Figure 3C) showed a maximum in the apparent folding rate constant (kf = 8.6 s-1) at the same lipid composition (25% DOPG) where the folded fraction and enzymatic activity were also maximized, suggesting that the re-folding of NfsB was facilitated the most on this SLB composition. The value of kf decreased systematically for NfsB tethered to SLBs with higher and lower fractions of DOPG, with the lowest kf value observed at 100% DOPG, where kf (0.71 s-1) was 12 times lower than at 25% DOPG. Interestingly, an opposite (although less dramatic) trend was observed for the unfolding rate constants (ku), which was minimized for NfsB tethered to SLBs containing 25% DOPG and exhibited a maximum on 100% DOPG SLBs. The more subtle changes in ku as a function of DOPG fraction, compared to the changes in kf, indicated that the influence of lipid composition on re-folding was the main driving force for NfsB stability on SLBs composed of 25% DOPG. These observations support previous suggestions that LBs stabilize tethered proteins via a chaperone-like re-folding mechanism,25,27 and, in particular, the results presented here
14 ACS Paragon Plus Environment
Page 14 of 33
Page 15 of 33 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
ACS Applied Materials & Interfaces
demonstrate that this putative chaperone activity is strongly related to the details of the SLB structure and composition. Connection of NfsB Conformation and Diffusion on SLBs As described above, the dependence of kf and ku on SLB composition generally supports a hypothetical chaperone-like mechanism where the re-folding of proteins is mediated by interactions with lipid bilayers. Previous work has shown that interactions between tethered proteins and lipid bilayers are reflected in the diffusive motion of the proteins, where stronger interactions result in slower diffusion deriving from increased friction due to protein associations with a larger number of lipid molecules.37–39 Thus, an apparent instantaneous diffusion coefficient of NfsB can be used as a proxy for the interaction strength with lipids in the proximal bilayer. Differences in the interaction of folded and unfolded NfsB with the SLBs was elucidated by examining the mobility of NfsB on the SLBs as a function of enzyme conformation. On average, the frame-to-frame displacements of folded NfsB were significantly higher than those of unfolded NfsB. This was consistent with the fact that enzyme denaturation often leads to increased surface area, and thus, more points of contact with the SLB. Moreover, changes in conformation, determined from FRET efficiency, often coincided with changes in the step sizes for individual molecular trajectories. Figure 4A shows a representative trajectory undergoing two conformational changes, starting with the enzyme initially in an unfolded state. Notably, the step displacement increased when the enzyme underwent an apparent re-folding transition, and decreased when the enzyme unfolded. This behavior is further illustrated by the representative trajectories shown in Figure 4B, where the conformational state is indicated by color-coding, and folded (red) steps are visually longer than unfolded (blue) steps.
15 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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
Figure 4. A) Representative temporal trajectory of NfsB on SLBs showing changes in FD and FA as well as simultaneous measurement of diffusive step sizes. Changes in the diffusive step size correlate strongly with changes in conformational state. B) Representative spatial trajectories of folded (red) and unfolded (blue) NfsB with lengths between 10 and 15 frames. C) Complementary cumulative square displacement distributions of folded (red) and unfolded (blue) NfsB tethered to 100% DOPC for a time interval of 60 ms. Error bars represent a 68% confidence interval of each data point obtained from 100 sub-samples of the data using a
16 ACS Paragon Plus Environment
Page 16 of 33
Page 17 of 33 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
ACS Applied Materials & Interfaces
bootstrap method with replacement. Solid black lines represent the fitting function associated with a Gaussian mixture model. To quantify the difference in the mobility of folded and unfolded NfsB on SLBs, complementary cumulative squared displacement distributions (CCSDDs), for time intervals of 60 or 70 ms, were calculated. Figure 4C shows CCSDD plots for NfsB on 100% DOPC, where folded NfsB diffused faster than unfolded NfsB as indicated by a higher probability for larger step displacements. From the CCSDD plots, weighted average diffusion coefficients (D̅w) were calculated by fitting the distributions to a Gaussian mixture model. Values of D̅w determined in this way represent effective short-time diffusion coefficients, in contrast with , which represents effective diffusion for long times, which can be influenced by anomalous diffusion (e.g. sub-diffusive behavior).
Moreover, in SM tracking, unlike FRAP, anomalously slow
diffusing objects (e.g., aggregates or rare contaminants) were identified and removed from the analysis. As has been previous reported,40,41 these effects result in systematically larger absolute values of diffusion coefficients measured from SM tracking as compared to FRAP. Based on analysis of SM tracking data, folded enzymes diffused more rapidly than unfolded enzymes. For example, for the SLB composition shown in Figure 4C (100% DOPC), the folded enzymes (D̅w=2.8 µm2 s-1) diffused 2.3 times faster than the unfolded enzymes (D̅w=1.2 µm2 s-1). This behavior was observed in all SLB compositions, where, on average, folded enzymes diffused 1.8 times faster than unfolded enzymes (Figure 5), suggesting that unfolded enzymes interacted more strongly with the lipid bilayers. From a more careful analysis of trajectories like those shown in Figure 4C, and the statistical fitting of the squared displacement distributions (Table S2), two diffusive modes (fast and slow) were observed for both folded and unfolded molecules. The physical meaning of this observation is that both folded and unfolded NfsB molecules could switch dynamically between
17 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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
the two diffusing modes; however folded molecules were more likely to be found in the “fast” mode compared to unfolded molecules. The average apparent diffusion coefficient associated with the slow mode ( = 0.24 µm2 s-1) was roughly 17 times slower than individual lipids in the fast mode ( = 4.2 µm2 s-1 as shown in Figure 5), which is consistent with a conformational state in which molecules were in contact with multiple lipids.38,39 In the fast mode, the diffusion of both folded ( = 3.9 µm2 s-1) and unfolded ( = 3.5 µm2 s-1) molecules closely resembled that of individual lipids, suggesting minimal interaction with lipids other than the single lipid to which the enzyme was tethered. While molecules in both conformational states switched between the two diffusing modes, folded molecules spent an average of 83% of the time in the fast mode, while unfolded molecules spent on average only 48% of the time in this mode. As such, the frequency with which molecules interacted strongly with the underlying SLB was greater for unfolded molecules relative to folded molecules.
Impact of SLB Composition on the Diffusion of Folded and Unfolded NfsB on SLBs To test the hypothesis that the chaperone-like activity of SLBs was dependent on lipid composition, the diffusivity of folded and unfolded NfsB as a function of DOPG fraction was compared. As above, D̅w of folded and unfolded NfsB were used as a proxy for the strength of the interaction of the respective folding state with the SLB. For both folding states, slower diffusion coefficients were observed for NfsB tethered to 100% DOPC SLBs compared to those on mixed lipid bilayers with 15-50% DOPG (Figure 5). Specifically, the value of D̅w for folded NfsB was the lowest on 100% DOPC (2.75 µm2 s-1), while on 15-50% DOPG the average D̅w values of folded enzymes (3.4 µm2 s-1) approached those of individual lipids (3.7 µm2 s-1). Similarly, the lowest value of D̅w for unfolded enzymes was observed on 100% DOPC (1.2 µm2 s-1), and monotonically increased with DOPG content (to values as high as 2.3 µm2 s-1 on 35% 18 ACS Paragon Plus Environment
Page 18 of 33
Page 19 of 33 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
ACS Applied Materials & Interfaces
and 50% DOPG). These combined results implied that NfsB had the strongest affinity for the 100% DOPC bilayer, and that this affinity decreased as a function of DOPG content. Notably, due to the presence of discontinuous bilayers, D̅w for folded and unfolded NfsB on the 75 % and 100 % DOPG surfaces could not be calculated.
Figure 5. Value of D̅w of fluorescently labeled lipids (black squares), folded NfsB (red circles) and unfolded NfsB (blue triangles) molecules as a function of the fraction of DOPG in the SLB. Error bars represent standard deviations of fitting 100 sub-samples of the data using a bootstrap method with replacement. We hypothesize that the higher D̅w observed with increasing DOPG fraction reflect increasing repulsive forces between NfsB, which has a pI of 5.8 and is thus negatively-charged at the pH used in SM experiments (pH 8.0), and DOPG in the SLB, which is also negatively charged at pH 8.0. Interestingly, the lipid composition for which the bilayer-mediated re-folding activity was most efficient (25% DOPG) corresponded not to the conditions where diffusion was the slowest or fastest (i.e., the strongest or weakest enzyme-bilayer interactions, respectively), but under conditions where the diffusion coefficient and interactions were intermediate. Thus, it is possible that NfsB re-folding was hindered at high interaction strengths (i.e., on 100% DOPC) while, at low interaction strengths (i.e., on 75 % and 100 % DOPG), the interaction of NsfB with 19 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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
the bilayer was too weak to promote re-folding. This phenomenon would be similar to the Sabatier principle (i.e., a so-called “Volcano plot”) often observed in catalysis, where, in an optimum case, reactants bind to a catalyst with an intermediate strength, allowing for both activation of the reactants and release of the products.42 Accordingly, our results suggest that the mechanism of SLB-mediated re-folding of NfsB is analogous to that by which traditional catalysts accelerate chemical reactions. This mechanism is consistent with chaperones themselves being catalysts, which catalyze the re-folding of proteins inside of cells. Although the results from the SM-FRET analysis support the hypothesis that the SLBs mediated the re-folding of NfsB, and that this process can be optimized by changing the extent of the enzyme-lipid interactions through the modification of the bilayer composition, it is possible that other phenomena may be responsible for the observed trends. For example, an alternative hypothesis is that the folding state, and, in turn, activity, of tethered NfsB was impacted by changes in pH at the SLB-water interface as a result of varying DOPG fraction. Notably, increasing the fraction of phosphatidylglycerol in a SLB can reduce the pH at the SLB-water interface by as much as 1.5 pH units relative to the pH of the solution above the SLB.43 Based on this, and given that the pH of the buffer used in our SM experiments was pH 8, the pH at the SLB-water interface, which would be lowest for the 100% DOPG surfaces, could, in theory, be as low as 6.5. To determine if such a change in pH correlated with the observed changes in Pfolded, the pH-dependence of the activity of NfsB in solution was measured (Figure S4). Based on the pH-dependence of NfsB activity in solution, where NfsB activity was the highest at pH 6.5, one would expect that the value of Pfolded would be highest on the 100% DOPG. However, this is inconsistent with our findings from SM-FRET analysis, which showed that Pfolded was lowest on the 100% DOPG surface. As such, any changes in pH of the SLB-water interface
20 ACS Paragon Plus Environment
Page 20 of 33
Page 21 of 33 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
ACS Applied Materials & Interfaces
arising from variations in the fraction of DOPG were not responsible for the apparent trend in Pfolded with DOPG fraction in SM studies.
Conclusions In summary, we have shown that introducing chemical heterogeneity within lipid bilayers can stabilize immobilized enzymes through a chaperone-like mechanism. Specifically, our findings suggest that mixed lipid bilayers may stabilize immobilized enzymes by increasing the rate of re-folding relative to unfolding of enzyme molecules on the bilayer surface. The extent of stabilization was strongly dependent on the fraction of DOPG in the bilayer, which differentially mediated the interaction between the bilayer and folded and unfolded NfsB. Importantly, these observations were enabled via exploiting SM methods that enable enzyme structure, dynamics, and diffusivity on the bilayer surface to be directly measured and correlated. Notably, the observations from SM analysis were also consistent with the results of ensemble activity measurements, which showed that mixed lipid bilayers supported higher NfsB activity. To the best of our knowledge, this is the first report of direct evidence of the differential interaction of lipid bilayers with folded and unfolded enzyme or protein molecules, thereby illuminating the mechanism of the chaperone-like activity of lipid bilayers. Ultimately, these findings have important practical implications in the design of novel lipid-containing surfaces and surface coatings that enhance the stabilization and activity of immobilized enzymes for use in biotechnological applications. Of further interest is exploring the extent to which this enhancement in stability and activity is general to other enzymes that have varying surface properties (e.g., charge) and native environments within cells (i.e., membrane versus nonmembrane associated). Related to this, it is interesting to consider how the optimum mixture of lipids correlates with enzyme properties. 21 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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
Materials and Methods Preparation and Labeling of Recombinant NfsB Plasmid DNA encoding for the dimeric fusion of NfsB from E. coli, which was mutated at residues 89 (to AzF) and 315 (to Cys) for site-specific FRET labeling, was kindly provided by Neil Marsh (University of Michigan). The NfsB plasmid along with pDule2 pCNF RS (from Ryan Mehl, Oregon State University) were co-transformed in BL21 (DE3) E. coli and expressed in Luria Broth containing AzF (1 mM; Chem-Impex International). Cells, which were allowed to grow to an optical density of 0.6, were induced with isopropyl β-D-1-thiogalactopyranoside at 18 °C for 20 h. After expression, NfsB, which contained an N-terminal hexa-histidine tag, was purified under UV-free conditions from clarified cell lysate via affinity chromatography using a nickel-charged Bio-Scale mini column (Bio-Rad). Purified NfsB containing AzF and Cys at amino acid positions 89 and 315 was dialyzed against a sodium phosphate (50 mM) buffer (pH 7.6) containing sodium chloride (100mM) at 4 °C and subsequently reacted with dibenzocyclooctybne-AF 488 (donor; Life Technologies) and maleimide-CF633 (acceptor; Biotium) using a 10:1 molar ratio of each fluorophore-to-enzyme. The labeling reaction was allowed to proceed for 18 h at room temperature in the dark with a total reaction volume of 100 µL and enzyme concentration of 40 µM. Labeled NfsB was separated from unreacted fluorophore via repetitive washing using 40k MWCO Zebra spin desalting columns (Thermo Fisher). Labeling efficiencies were determined using the molar extinction coefficient for each dye (73,000 M-1 cm-1 for AF 488 at 495 nm and 100,000 M-1 cm-1 for CF633 at 630 nm), and the theoretical adsorption coefficient of NfsB at 280 nm (51,900 M-1 cm-1). Correcting for absorbance of the dyes at 280 nm, the labeling efficiencies for AF 488 and CF633 were 73% and
22 ACS Paragon Plus Environment
Page 22 of 33
Page 23 of 33 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
ACS Applied Materials & Interfaces
23%, respectively. For activity assays, wild-type NfsB was prepared the same way except without inclusion of the pDule2 pCNF RS during expression.
Preparation of DOPC, DOPG, and Mixed DOPC/DOPG SLBs Separate solutions of DOPC (Sigma Aldrich) and DOPG (Sigma Aldrich) in chloroform were mixed to form solutions with varying lipid composition (0%, 15%, 25%, 35%, 50%, 75%, and 100% DOPG with balance DOPC) and a total lipid concentration of 3 mM. DGS-NTA-Ni (0.3 nM; Avanti Polar Lipids) was added to each mixture to provide specific enzyme binding sites. Unilamellar vesicles with diameter of 50 nm were prepared as described previously using a rehydration buffer containing sodium phosphate (10 mM) and sodium chloride (800 mM) at a pH of 8.0.37 After unilamellar vesicle formation, dual-labeled NfsB was added to the lipid solution at a molar ratio of 1:100 NfsB-to-DGS-NTA-Ni, which was found to repeatedly form bilayers with a concentration of labeled NfsB suitable for SM tracking. The solution containing dual-labled NfsB and vesicles was incubated for 1 h at room temperature to allow complex formation between the N-terminal hexa-histidine tag on NfsB and the DGS-NTA-Ni. Fused silica wafers (Mark Optic) were cleaned as described previously.30 Briefly, wafers were washed with a 2% Micro-90 (International Product Corporation) solution and thoroughly rinsed with ultrapure 18 MΩ-cm water. The wafers were then submersed in piranha solution (70% hydrochloric acid, 30% hydrogen peroxide) for 1 h and subsequently rinsed with ultrapure water and dried with nitrogen. Immediately afterwards, the wafers were treated with UV-ozone for 1 h. After the UV-ozone treatment, wafers were placed in a custom-built flow cell (internal volume 0.24 mL),44 and exposed to a solution of NfsB-bound vesicles. Enzyme-tethered vesicles were incubated with the surface for 30 min, allowing fusion with the silica wafer. Any remaining
23 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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
vesicles and NfsB molecules in solution were removed by purging the flow cell with 1 mL of buffer containing 10 mM sodium phosphate (pH of 8.0) without sodium chloride, at a rate of 0.1 mL min-1 using a syringe pump (NE-1000, New Era Pump Systems, Inc.). The modified surfaces were equilibrated with the solutions for 20 mins prior to imaging. To confirm vesicle fusion and formation of SLBs, mobile fractions and lateral diffusion coefficients were determined through FRAP experiments (details in the supporting information).
Alternating-laser Excitation Imaging The samples were imaged using alternating-laser excitation at SM resolution using a custom-built prism TIRF system with a Nikon TE-2000 microscope and a 60x water immersion objective.44 To enable alternating-laser excitation, high-speed shutters (LS2T2, Vincent Associates) were synchronized with the camera readout using a NIDAQ (National Instruments PCI6723) card controlled by Nikon NIS-Elements Triggered Device Control software. Alternating illumination by 491 nm and 640 nm lasers was used to directly excite the AF488 donor label and CF633 acceptor label, respectively. Emissions from the donor and acceptor fluorophores were separated by wavelength into a donor and acceptor 2-channel image using an Optosplit III beam splitter (Cairn Research) containing a 610 nm dichroic mirror (T610LPXR, Chroma). To decrease bleed-through of the donor emission into the acceptor channel image and remove residual excitation light from the image, the spectrum from each channel was further filtered with 90% transmission 528/30 and 685/40 bandpass filters (Semrock) for the donor and acceptor emissions, respectively. The fluorescent emission during the donor excitation was used to quantify the FRET efficiency between the donor and acceptor labels on individual NfsB molecules, providing information about the conformation of the enzymes. The emission during
24 ACS Paragon Plus Environment
Page 24 of 33
Page 25 of 33 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
ACS Applied Materials & Interfaces
acceptor excitation was used to detect mislabeled enzymes and photo-bleached acceptor labels, which were removed during image processing. Finally, images were collected with an Andor iXon3 888 EMCCD camera with acquisition times of 60 or 70 ms.
Image Processing and Data Analysis Objects in each channel were located and tracked using Matlab-based software written in house. The two imaging channels were initially aligned using a constant translational offset which was determined by maximizing the cross correlation of the two images from a selected frame. The object locations were determined by fitting the point-spread function (PSF) of each object to a linearized circular Gaussian, and the intensities were estimates by summing background-subtracted pixel intensities within a user-defined radius of each object location, which was chosen to encompass the entire PSF. For the donor excitation data, where fluorescence is expected in both channels due to FRET, the objects from either channel were colocalized. Detailed algorithms for object detection, localization, quantification of intensities and inter-channel co-localization was previously.45 Trajectories were then defined by linking objects in consecutive red-excited frames (every 2nd frame) that were located within a user defined tracking radius (in this case 8 pixels or 1.8 µm). Finally, the objects identified during either excitation were also co-localized. Objects were considered co-localized if the positions of an object during two consecutive frames (one from each excitation) were within the tracking radius multiplied by 1/√2, which corrects for the reduced inter-frame time. Each trajectory was truncated at the first pair of excitations where complimentary objects were not found, ending the trajectory when the first label photo-bleaches and preventing misinterpretation of bleaching events as state changes. At this point, the acceptor-excited data was discarded, leaving only
25 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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
correctly labeled, non-bleached objects whose donor and acceptor intensities are decided by FRET. Data was further filtered to remove anomalously slow diffusing objects (e.g., aggregates or rare contaminants), which is described in the supporting information.
Analysis of FRET Efficiency and State Assignments of Dual-labled NfsB on SLBs The intensity data from each channel was used to generate 2-dimentional heat maps showing FD vs FA for every observation as shown in Figure 2. From these maps, two distinct populations at high and low FRET efficiency, = / + , corresponding to folded and unfolded NfsB populations were identified. A linear threshold dividing the 2 populations was defined by determining the slope and intercept that minimized the integrated map values along the dividing line. This was used to assign folding states base on the donor and acceptor emission of the objects. To reduce to probability of interpreting noise in the intensities as state changes, a state change was only assigned if both FD and FA crossed the dividing line by more than the uncertainty of corresponding intensity. This criterion was not applied to the initial state of each trajectory. To estimate the uncertainty of Pfolded, the state assignment algorithm was successively performed (300 iterations) on sub-samples of trajectory data, which were assembled by randomly sampling 9 of every 10 trajectories without replacement. For each sub-sample, the folded fraction was calculated from the state assignments, and the uncertainty was defined as the standard deviation of the collection of subs-sample folded fractions.
Calculation of Transition Rate Constants To estimate the folding and unfolding transition rate constants, a Markov-Chain model was required because the turn-off rate constant (rate at which trajectories end via desorption,
26 ACS Paragon Plus Environment
Page 26 of 33
Page 27 of 33 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
ACS Applied Materials & Interfaces
photo-bleaching or premature loss of trajectory) was greater than either of the folding or unfolding rates such that the fraction of the population that underwent state-transitions (changed from folded to unfolded and vice-versa in two consecutive frames) was not representative of the whole population. This model assumes that folding, unfolding and turn-off kinetics are homogeneous properties of the population and are well described as a Markov process. As these assumptions may be important, we present this as a first approximation that is primarily useful for comparative purposes. Maximum likelihood estimates of kf and ku were = where
,
,
log
,
and
,
and =
log
(Equation 1),
are the total number of times any object unfolds, remain folded,
folds, or remains unfolded, respectively, between successive frames, and ! is the frame
acquisition time. Additional details of the determination of and are in the supporting
information.
Analysis of Diffusion Coefficients of Dual-labeled NfsB on SLBs and Fluorescently Labeled Lipids Apparent diffusion coefficients were determined by creating CCSDDs of the tethered NfsB molecules and fitting them to a Gaussian mixture model.46 Briefly, the CCSDD is fit to a function of the square displacements of molecules in consecutive frames and the image acquisition time, " # $ , &'. This cumulative distribution represents the estimated probability that
a molecule moves a distance greater than # in the time interval, &'. To estimate the uncertainty of each CCSDD’s data point, a bootstrap with replacement method was used to select 100 subsamples, which were assembled by randomly selecting n step displacement data points at each condition (e.g. folded, unfolded), where n=original sample size. CCSDDs were created for each 27 ACS Paragon Plus Environment
ACS Applied Materials & Interfaces 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
subsample, and the standard deviations at each x axis value was calculated. To account for multiple modes of diffusion, CCSDDs were modeled using the Gaussian mixture model, " # $ , &' = ∑+ *+ ,-./3401 ∆78, with fitting parameters *+ and 9+ , where *+ represents the 5
2
fraction of molecules with diffusion coefficient 9+ in the corresponding :'ℎ mode. To calculate the errors in the diffusion coefficients, each of the 100 sub-samples was fitted to the gaussian mixture model, and the standard deviation of the fits was calculated as the error. The mean