Titin Measurements Using the MFP-1D

Titin is a giant protein found in muscle tissue. It provided one of the first spectacular examples of the utility of cantilever-based "Force Pulling" for studying the mechanical properties of domains in proteins.^1,2

The MFP-1D is being used by researchers Dr. J. Clarke, Susan Fowler and Annette Steward of Cambridge University, UK to study domains in synthetic molecules constructed from tandem repeats of a single Titin domain.² Pictured are Dr. Jason Cleveland, Chairman of Asylum Research, and Dr. Jane Clarke, the first MFP-1D user.

Figure 1 shows a force curve made with a Titin molecule tethered between the cantilever tip and a gold substrate. As the cantilever retracted from the surface, the force on the molecule increased until a domain unfolded. When this happened there was a sudden decrease in the cantilever deflection. The cantilever continued to retract, gradually increasing the force until another domain popped. The purple curves on the plot show sequential Worm-like Chain model fits.¹

Figure 2 shows a a plot of the contour lengths from the WLC fitting in Figure 1. The slope of the contour length vs. peak index gives a value of 29.2nm, consistent with the contour length of an individual Titin domain.

The MFP-1D uses powerful software based on IGOR Pro from Wavemetrics. In addition to providing flexible control of the data acquisition, IGOR has many built in features for data analysis and presentation, some of which are shown in the above analysis.

Spring Constant Calibration Using the Thermal Method
The cantilever used to obtain the protein data shown in Figure 1 was calibrated using the thermal method.³ For a comparison of cantilever calibration methods, see the Cantilever Calibration Technical Notes.

Briefly, the thermal method relies on fitting a thermal spectrum of the cantilever motion to a simple harmonic oscillator model. Within that model, once the thermal spectrum has been parameterized, the spring constant follows from the equipartition theorem. We obtained the thermal spectrum by digitizing the cantilever deflection signal. An example of cantilever deflection versus time data acquired with the MFP is shown in Figure 3. This data was acquired at a sampling frequency of 200kHz. The sampling speed is an important factor to consider when measuring thermal noise because of the Nyquist theorem (see for example Nyquist Link or reference 4). Simply put, to get information about the 100kHz behavior of the cantilever, it is necessary to sample the cantilever deflection at a rate twice as fast, 200kHz. Once the data has been sampled, it can be Fourier Transformed to give the power spectrum, shown in Figure 4.

The power spectrum was fit to a simple harmonic oscillator model (see the blue solid line).Through the use of the equipartition function, the model parameters provide a quantitative measure of the spring constant.For this fit, the measured spring constant was 0.050 nN/nm, the quality factor was 0.73 and the resonant frequency was 3859 Hz The measurement was made in fluid so the first resonance of the cantilever was very heavily damped.The uncertainty in thermal calibration is on the order of 10%.More information on this procedure is available in reference 5.

Thermal Noise Limited Force Measurements
One measure of the quality of a force measurement is the noise level. In general, it is desirable to be limited by the thermal noise of the cantilever, rather than by some electronic, optical or vibrational noise in the force measuring instrument. The thermal force noise within the context of the simple harmonic oscillator model is easy to calculate and is given by:⁶

D F is the rms force noise	kc is the spring constant
B is the measurement bandwidth	T is the absolute temperature
kB is the Boltzmann's constant	Q is the quality factor
w0 is the resonant frequency

The Titin measurements shown at the top of this page were made using a 2 kHz bandwidth, in other words, sampling the cantilever position twice each millisecond. Assuming the measurements were made at a temperature of 300K and inserting the fit value of the spring constant (0.050 nN/nm), the quality factor (0.73) and the resonant frequency of the cantilever (3870 Hz) into the above equation yields a thermal force noise level of 9.8 picoNewtons rms. The measured noise levels from the data shown in Figure 1 was 9.7 picoNewtons rms, allowing us to conclude that our signal was limited by the thermal motion of the cantilever.

Dr. Clarke's full paper can be found in the October 2001 issue of the Biophysical Journal ⁷ .

References:

1 M. Rief, M. Gautel, F. Oesterhelt, J. M. Fernandez and H. E. Gaub, Science, 276, 1109 (1997)

2 M. Carrion-Vasquez, A. F. Oberhauser, S. B. Fowler, P. E. Marszalek, S. E. Broedel, J. Clarke and J. M. Fernandez, Proceedings of National Academy of Sciences, 96, 3694 (1999).

3 J.L Hutter and J. Bechhoefer, The Review of Scientific Instruments, 64(7), 1868, (1993).

4. Numerical Recipes in C by W. Press, S. A. Teukolsky, W. Vetterling and B. Flannery, Cambridge University Press, p. 500

5 D. Walters, J. Cleveland, N. H. Thomson, P. K. Hansma, M. A. Wendman, G. Gurley and V. Elings, The Review of Scientific Instruments, 67(10), 3583 (1996).

6. See, for example, Scanning Force Microscopy by D. Sarid, Oxford University Press, p. 48.

7. R.Best, B. Li, A. Steward, V. Daggett, and J. Clarke. Can Non-Mechanical Proteins Withstand Force? Stretching Barnase by Atomic Force Microscopy and Moleculare Dynamics Simulation, Biophysical Journal, 81, 2344, (2001)

Figure 1: Titin pulls

Figure 2: Contour lengths vs peak index for unzipping curves.

Figure 3: Cantilever deflection
signal acquired at 200kHz.

Figure 4: Power Spectrum.