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BioTechnological Center, University of Technology, 01307 Dresden, Germany
Correspondence: Address reprint requests and inquiries to Harald Janovjak, Tel.: 49-351-463-40331; Fax: 49-351-463-40342; E-mail: harald.janovjak{at}biotec.tu-dresden.de.
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ABSTRACT |
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). Here, we apply two independent methods in combination with Monte Carlo simulations to analyze the unfolding of 
-helices E and D of bacteriorhodopsin (BR). We show that correlation analysis of unfolding forces is very sensitive to errors in force calibration of the instrument. In contrast, a comparison of relative forces provides a robust measure for the stability of unfolding intermediates. The proposed approach detects three energetically different states of -helices E and D in trimeric BR. These states are not observed for monomeric BR and indicate that substantial information is hidden in forced unfolding experiments of single proteins.
The past few years have seen a dramatic increase in our understanding of the processes that stabilize single proteins (2). Atomic force microscopy (AFM) unfolding experiments, where an external pulling force plays the role of the denaturant, revealed the unfolding pathways and kinetics of individual water-soluble (1,3) and membrane proteins (4,5). It was found that many water-soluble and membrane proteins unfold in a well-defined sequence of one or several partly unfolded intermediates (1,4,5). Until very recently it was assumed that unfolding transitions from the native state to the intermediate(s) and from the intermediate(s) to the fully unfolded state occur independently from each other. Interestingly, Li and co-workers lately reported a linear correlation between the unfolding force of the native state and the intermediate in fibronectin (Fn) (1). This correlation suggests either the presence of multiple hidden unfolding pathways or a molecular memory in Fn.
As proposed by Li and co-workers (1), we have used linear regression analysis to look for a correlation between the unfolding forces of -helices E and D of bacteriorhodopsin (BR) (Fig. 1), which represent stable mechanical unfolding intermediates of the membrane protein (6). On plotting the unfolding force of -helix D against that of -helix E for each single molecule (Fig. 1 A), we found linear correlation coefficients (R-values) between 0.043 and 0.636 depending on the pulling speed (Fig. 1 B). R-values as large as 0.636 could indicate a significant linear correlation for unfolding of the two -helices. However, we observed that the R-values are scattered heavily and show no clear tendency with pulling speed. Because one would expect constant (or increasing) correlation with pulling speed the scattering suggests a different, other than molecular, origin for the observed correlation between -helix E and D.
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). The most commonly applied method to determine spring constants, thermal fluctuation analysis, is known to be associated with an error of at least 10% (8). Due to this systematic error, unfolding forces measured in the same experiment will have either a bit smaller or a bit larger values than an ideally calibrated reference. Therefore, these data sets tend to cluster in a plot such as shown in Fig. 1 A. Consequently, if data recorded in different experiments are pooled, this clustering might result in a (linear) correlation. To estimate the influence of error in force calibration on linear correlation analysis we performed Monte Carlo (MC) simulations for unfolding -helices E and D (9,10). MC simulations are well suited as a reference because consecutive elements unfold independently (no memory) and a single unfolding pathway exists (1,9). At all pulling speeds, we observed R-values near zero suggesting no correlation of the simulated unfolding forces (Fig. 1 B, open symbols). Fig. 1 C shows the result of a typical simulation where 1000 force pairs have been computed (red symbols). To simulate a typical experimental situation (five experiments, ±10% error in spring constant determination), we added an error of 10%, 5%, 0, –5%, and –10% each to a fifth of these force pairs. Remarkably, linear correlation analysis now yields an R-value of 0.391 (Fig. 1 C, blue dots) showing that uncertainities in spring constant calibration could be responsible for the correlations observed in Fig. 1 B. This effect might also have implications for the recent observation in Fn (1).
Because a comparison of absolute forces is sensitive to inevitable errors in force calibration, we propose an alternative analysis method based on force ratios. Here, we define force ratio as the normalized unfolding force of -helix D obtained by dividing it by the unfolding force of -helix E for each protein. This approach yields a population of force ratios near 1 and is insensitive to errors in force calibration. An easy yet powerful way for analyzing this population is to compile it as a histogram because this allows immediate access to the distribution of the force ratios. Fig. 2 A shows the force ratio histogram compiled from unfolding data determined on native (trimeric) BR. Three peaks are visible in the histogram that can be well described with three Gaussian fits. This indicates that, in the trimeric BR, -helices E and D coexist in three distinct states, which differ in the relative strength of the -helices. Surprisingly this is not observed for the simulated data (Fig. 2 A, inset) or monomeric BR (T. K. Sapra, H. Besir, D. Oesterhelt, and D. J. Müller, unpublished data) (Fig. 2 B). In latter cases, -helices E and D unfold at a fixed force ratio as indicated by a single peak in the histograms. Detecting an increased energetic complexity of -helices E and D in trimeric BR may not be a surprising finding if one considers that these -helices, in combination with certain lipid molecules, are responsible for intermonomer contacts (11).
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Submitted on January 20, 2005; accepted for publication March 21, 2005.
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REFERENCES |
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2 Zhuang, X., and M. Rief. 2003. Single-molecule folding. Curr. Opin. Struct. Biol. 13:88–97.[CrossRef][Medline]
3 Rief, M., M. Gautel, F. Oesterhelt, J. M. Fernandez, and H. E. Gaub. 1997. Reversible unfolding of individual titin immunoglobulin domains by AFM. Science. 276:1109–1112.
4 Oesterhelt, F., D. Oesterhelt, M. Pfeiffer, A. Engel, H. E. Gaub, and D. J. Müller. 2000. Unfolding pathways of individual bacteriorhodopsins. Science. 288:143–146.
5 Kedrov, A., C. Ziegler, H. Janovjak, W. Kühlbrandt, and D. J. Müller. 2004. Controlled unfolding and refolding of a single sodium-proton antiporter using atomic force microscopy. J. Mol. Biol. 340:1143–1152.[CrossRef][Medline]
6 Janovjak, H., J. Struckmeier, M. Hubain, A. Kedrov, M. Kessler, and D. J. Müller. 2004. Probing the energy landscape of the membrane protein bacteriorhodopsin. Structure. 12:871–879.[Medline]
7 Florin, E. L., M. Rief, H. Lehmann, M. Ludwig, C. Dornmair, V. T. Moy, and H. E. Gaub. 1995. Sensing specific molecular-interactions with the atomic force microscope. Biosensors. Bioelectr. 10:895–901.[CrossRef]
8 Proksch, R., T. E. Schäffer, J. P. Cleveland, R. C. Callahan, and M. B. Viani. 2004. Finite optical spot size and position corrections in thermal spring constant calibration. Nanotechnology. 15:1344–1350.[CrossRef]
9 Rief, M., J. M. Fernandez, and H. E. Gaub. 1998. Elastically coupled two-level systems as a model for biopolymer extensibility. Phys. Rev. Lett. 81:4764–4767.[CrossRef]
10 For MC simulations, we used published kinetic parameters: -helix E, xu = 4.6 Å, ku = 1.1 x 10–4 s–1; -helix D, xu = 7.7 Å, ku = 1.5 x 10–6 s–1 (6).
11 Müller, D. J., J. B. Heymann, F. Oesterhelt, C. Moller, H. Gaub, G. Buldt, and A. Engel. 2000. Atomic force microscopy of native purple membrane. Biochim. Biophys. Acta. 1460:27–38.[Medline]
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