Sweers et al. Nanoscale Research Letters 2011, 6:270 http://www.nanoscalereslett.com/content/6/1/270 Page 6 of 10 Figure 6 Effective spring constant as a function of sample stiffness. (A) Force versus z piezo displacement curve in case of sample spring constant larger, the same or lower compared to the spring constant of the cantilever. (B) Effective spring constant (keff, representing the slope of the force curves in A) as a function of the stiffness of the sample. From the slope of this curve it is clear that the maximum sensitivity is achieved when both spring constants are of the same order of magnitude. frequency of 1 kHz. These hydrodynamic forces acting on the cantilever are frequency-dependent [27,28]. Although we do not know how the Peakforce QNM software compensates for this, it is possible these effects in liquid could interfere with the measurements. Scan- ning with stiffer cantilevers with nominal spring con- stant 2.8 N/m yielded reproducible results. Finally, in addition to choosing the optimal cantilever stiffness, it is also important to ensure that the reso- nance frequency for Peakforce QNM imaging is above 10 kHz, in order not to interfere with the 1 kHz ramping. Calibration The calibration of all three methods is difficult and con- sists of several steps. For all methods one needs the deflec- tion sensitivity, the spring constant of the cantilever and the tip radius. For the SPI experiments the tip radius can be determined afterwards. Both surface mapping methods need the tip radius as an input parameter before measur- ing. For HarmoniX, in addition to this tip radius, some additional parameters, such as the torsional frequency, are needed. An alternative way of calibration of the surface mapping methods was done with the reference sample (see “Methods” section). In this study, this reference sam- ple is only used in the HarmoniX measurements. Analysis of results Error analysis All three techniques use a contact mechanics model which is based on assumptions and parameters which can only be determined with a limited accuracy. The first assump- tion starts with the Poisson ratio for these protein fibrils. For small biological samples this ratio between lateral strain and axial strain is not known. The theoretical upper limit is 0.5 and concrete as a material has a value between 0.1 and 0.2. In this study we used 0.3, because we assumed the fibrils to be in the same range as polymers [29]. This Poisson ratio has only a small influence on the actual modulus of elasticity values (Poisson ratio change from 0.3 to 0.4 gives a 5% change in modulus of elasticity). The tip radius has, compared to the Poisson ratio and fibril radius, a large impact on the results. It is therefore important to measure the tip radius after the experi- ments. The tip radius is in our experience in practice always larger than the manufacturer specification, both before and after the experiment. Figure 7 shows the impact of the tip radius on the results of the SPI mea- surements on the a-synuclein fibrils when all the other parameters are kept constant. The dependence is less significant at larger tip radii. Figure 7 Dependence of modulus of elasticity in tip radius. The force curve data obtained with SPI measurements are used to calculate the modulus of elasticity with variable tip radii while all other parameters are kept constant.