Transfección del sistema CRISPR/Cas

In both static and dynamic cases, the main aim of the identification method is to convert the vertical force and the rod displacement signals into viscoelastic modules: E’, E’’ and tan(δ). The above described Kelvin- Voigt model will be considered as reference and its stiffness and damping parameters will be identified. As described in the previous Paragraph A.3.5, the equations (A.11) has been used to convert and to and respectively.

An optimization method has been introduced and the mean square deviation between the predicted and the measured characteristics is minimized. To determine the quality of the optimization results, the root mean square error RMSE% in percent is calculated, as shown below:

√∑ 𝑦 𝑦̂ (A.12)

whereas n corresponds to the number of values, 𝑦̂ to the measured and y to the calculated value.

This approach has been considered for the calculation of the loss modulus E”, storage modulus E’ and loss factor tan(δ), based on the Kelvin-Voigt mathematical model described in the Chapter 2. The algorithm is based on some sub sections that are listed below:

1. importing section of the raw data; 2. filtering with a low-pass filter;

3. extracting the fundamental frequency;

4. identification of stiffness and damping compliances of the rubber through the Matlab function “lsqcurvefit”, normally used to solve nonlinear data-fitting problems in least-squares sense.

The calculation of the stiffness and damping values have been taken directly from the raw data. We can divide the process in 2 phases, with the Phase 1 as shown in Figure A-17.

Figure A-17 - Phase1: estimation of stiffness and damping of the Kelvin-Voigt model.

The two parameters and are the measured displacement and force, respectively. The Phase 2 is dedicated to the validation of the identified model, as shown in Figure A-18.

Appendix

Figure A-18 - Phase 2: validation of the identified model parameters.

For the validation of the proposed method, the obtained vertical force results (of the optimization process), are used as input signals for the viscoelastic model: therefore, it has been considered the comparison between the displacement values obtained from optimization process and those ones obtain from measurements (Figure A-19).

Figure A-19 - Validation of the Kelvin-Voigt model with the identified parameters.

No boundary conditions have been considered for the setup of the “lsqcurvefit” Matlab function. In the following figures results about the E’, E’’ and tan(δ) are shown.

The DMA analysis, provided by the rubber company, have been considered at different frequencies and strain values, as shown in Table A-2 below.

Table A-2 – Frequency and Strain of the DMA for A, B and C rubber samples.

Frequency [Hz] Strain [%]

0.1 0.1

1.0 0.1

In the following Figure A-20, A-21 and A-22 the estimated storage modulus, los modulus and loss tangent are compared with the DMA data of the same rubber slabs.

Figure A-20 – Storage modulus comparison between DMA at different frequencies and strains and V-ELA results with the 2 studied methods. Normalized data.

Figure A-21 – Loss modulus comparison between DMA at different frequencies and strains and V-ELA results with the 2 studied methods. Normalized data.

Appendix

Figure A-22 - Loss tangent comparison between DMA at different frequencies and strains and V-ELA results with the 2 studied methods.

The graph in Figure A-22 above are showing the results of the optimization, based on Kelvin-Voigt model. The points (related to Identification method, explained in this paragraph), can show a similar trend with respect to the DMA analysis of the same slabs. Regarding the test performed with V-ELA, the only frequency that has been possible to reach was around and 0.7 Hz.

Figure A-23 – Quadratic fitting of the DMA data in the Temperature range [0; 40°C], at = 1 Hz and strain = 0.1%.

In the Figure A-23, quadratic fitting of the DMA data has been done in the temperature range [0; 40°C]. The quadratic equation is shown below:

where , and are the estimated coefficients. This range has been chosen because it can be defined as the more reliable one due to the difficult control of temperature at very low and high values. Because of it, the estimated stiffness and damping parameters could show higher errors with respect to the range that has been considered for the current assessment.

Figure A-24 – Fitting of the experimental data and comparison with the DMA results.

In Figure A-24 it can be observed that there is a good correlation between DMA and V-ELA in terms of trends of loss factor. Probably this is due to the fact that in the interval [0; 40°C], the temperature condition was more efficiently kept during the test, it is then expected that the results can be more reliable. The absolute values are not directly comparable, it could depend on several reason:

 the applied frequency is not always the same;

 the strain values are not comparable because of the nature of the indentation approach is different from the one used for DMA test (traction of the rubber sample);

 the limitation of the instrument to allow micro or nanoindentations.

Regarding the last point, the strain percentage could be considered around 20%, if it is assumed that the average indentation depth is 1,20 mm and the thickness of the slab is 5 mm. The indentation depth has been calculated by considering the RMS of the harmonic displacement signal.

The future development of this instrument will expect the improvement of the following points: temperature conditioning, correlating the 2 different kind of strains (which cannot be considered directly comparable with DMA, because of the 2 different test procedures) and automating the harmonic displacement signal.