METHOD TO LABEL AS DEFECTIVE A MEASURE OF AN OPTICAL TRAP FORCE EXERTED ON A TRAPPED PARTICLE BY A TRAPPING LIGHT BEAM

Abstract

A method to label as defective a measure of an optical-trap force, that is exerted on a trapped particle located inside a living, dispersive, viscoelastic medium, including operations of: (i) determining a calibration constant between the optical trap forces and the sensed voltages; (ii) determining a first calibration function of the frequency of the particle oscillation with the active-passive procedure; (iii) computing a second calibration function of the frequency as the quotient between the calibration constant and the first calibration function; (iv) computing an energy function of the frequency as the product of the thermal energy of the trapped particle and the second calibration function; (v) checking whether the energy function converges to the thermal energy of the trapped particle as the frequency increases; (vi) if there is no such convergence, then label as defective the measure of the optical-trap force.

Claims

1. A method to label as defective a measure of an optical-trap force exerted on a trapped particle by a trapping light beam, the particle being located inside a viscoelastic medium, the method comprising the operations of: determining a calibration constant with the known macroscopic direct procedure; determining a first calibration function of the frequency of the trapped particle oscillation with the known active-passive procedure, the first calibration function including the thermal energy of the trapped particle as a multiplicative factor; computing a second calibration function of the frequency of the trapped particle oscillation as the quotient between the calibration constant and the first calibration function; computing an energy function of the frequency of the trapped particle oscillation as the product of the thermal energy of the trapped particle and the second calibration function; checking whether the energy function converges to the thermal energy of the trapped particle as the frequency of the oscillation thereof increases; if there is no such convergence, then labelling as defective the measure of the optical-trap force.

2. The method of claim 1, the optical trap being a single-beam optical tweezers.

3. The method of claim 1, the particle being located within a biological tissue.

4. The method of claim 3, the particle being located within a cell.

5. The method of claim 4, the particle being located within a cell cytoplasm.

6. The method of claim 2, the particle being located within a cell.

7. The method of claim 6, the particle being located within a cell cytoplasm.

8. The method of claim 1, the setup to determine the calibration constant comprising a photodetector, and the calibration constant being derived from one or more of the photodetector radius and other parameters.

9. The method of claim 8, the calibration constant being derived from one or more of the transmittance of said setup and other parameters.

10. The method of claim 2, the setup to determine the calibration constant comprising a photodetector, and the calibration constant is derived from one or more of the photodetector radius and other parameters.

11. The method of claim 10, the calibration constant being derived from one or more of the transmittance of said setup and other parameters.

12. The method of claim 1, comprising an operation that is prior to the stated operations, said prior operation including limiting the stage drifts below a threshold that renders significant the non-equilibrium effects.

13. The method of claim 2, comprising an operation that is prior to the stated operations, said prior operation including limiting the stage drifts below a threshold that renders significant the non-equilibrium effects.

14. The method of claim 1, comprising an operation that is prior to the stated operations, said prior operation including limiting the laser pointing fluctuations below a threshold that renders significant the non-equilibrium effects.

15. The method of claim 2, comprising an operation that is prior to the stated operations, said prior operation including limiting the laser pointing fluctuations below a threshold that renders significant the non-equilibrium effects.

16. A method to reveal the presence of disrupting out-of-focus tissue structures when a measurement of an optical-trap force exerted by a trapping light beam on a trapped particle is performed, comprising the operations of: determining a calibration constant with the known macroscopic direct procedure; determining a first calibration function of the frequency of the trapped particle oscillation with the known active-passive procedure, the first calibration function including the thermal energy of the trapped particle as a multiplicative factor; computing a second calibration function of the frequency of the trapped particle oscillation as the quotient between the calibration constant and the first calibration function; computing an energy function of the frequency of the trapped particle oscillation as the product of the thermal energy of the trapped particle and the second calibration function; checking whether the energy function converges to the thermal energy of the trapped particle as the frequency of the oscillation thereof increases; if there is no such convergence, then mark the presence of disrupting out-of-focus tissue structures that scatter the light beam.

17. An apparatus to perform the method of claim 1, comprising a photodetector.

18. The apparatus of claim 17, comprising a single laser source to emit the trapping light beam.

19. The apparatus of claim 17, comprising a back-focal-plane interferometer.

20. The apparatus of claim 18, comprising a back-focal-plane interferometer.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Non-limiting examples of the present disclosure will be described in the following, with reference to the appended drawings, in which the sole FIGURE, the FIGURE, is a graph that plots the effective energy against the frequency of the particle oscillations.

DETAILED DESCRIPTION OF EXAMPLES

[0034] Taking advantage of the difference in nature of the two aforementioned calibrations (the macroscopic direct calibration and the microscopic active-passive calibration), herein disclosed are methods to determine the presence of the out-of-focus scattering that is fairly typical in dispersive samples. The integration of the macroscopic and microscopic approaches provides for detection of the existence of beam momentum changes outside the trapping region.

[0035] The methods exploit the complementarity between the two approaches using each one as a benchmark for the other one. On the one hand, the sensitivity of the active-passive calibration to the specific conditions of the experiment allows for identifying and quantifying the biological activity at low frequencies (<100 Hz, approx.) so as to have evidence of the reliability of the calibration. On the other hand, the validated robustness of the sensor's momentum response in the packed cytoplasm of cells provides a reference for the in situ calibrations at high frequencies (>100 Hz, approx.). Both approaches combined together give a procedure to discard results affected by out-of-focus momentum changes.

[0036] The methods may include the following operations: [0037] 1. A first operation may involve reducing the sources of noise, such as stage drifts or laser pointing fluctuations, below a critical limit where non-equilibrium effects may become noticeable (i.e. significant). [0038] 2. Macroscopic direct calibration (momentum procedure): calibration constant .sub.sensor (force=.sub.sensor.Math.Voltage). [0039] 3. Active-passive calibration: calibrate .sub.trap() as

[00001]$\frac{2.Math.k_B.Math.T}{.Math..Math.P^V\left(\right)}.Math.{\mathrm{Im}\left({\tilde{V}}_{\mathrm{dr}}/{\tilde{x}}_s\right)}_{}$

for different frequencies fin the range 1 Hz-1 kHz (or at least 1-100 Hz or 1-200 Hz) with the same trapped particle, where is the angular frequency 2f, T is the absolute temperature, V.sub.dr and X.sub.s are the Fourier transform of the recorded output voltage and the stage displacement, respectively, and P.sup.V is the power spectral density of the passive motion of the sample as measured by the detection system. If oscillations of the particle are induced by the motion of the trap, X.sub.S is replaced by X.sub.L, the Fourier transform of the laser displacement, and the preceding equation includes a minus () sign. By using the equation, the force calibration can be obtained even if the sample is outside the linear region of the force. If necessary, one just needs to measure the position-voltage curve and multiply the calibration by (.sub.dr/.sub.P).sup.2, where represents the position calibrations for the driving signal and for passive spectrum, respectively. [0040] 4. Compute the non-equilibrium activity through the effective energy obtained as E.sub.eff (f)=E.sub.therm.Math.(.sub.sensor/.sub.trap(), where E.sub.therm=k.sub.BT. [0041] 5. Plot E.sub.eff (f) as a function of frequency (see the FIGURE). Its value should be several times that of E.sub.therm in the range of 1-10 Hz and decrease monotonically until approximately 100-200 Hz, where it should converge to E.sub.therm. [0042] 6. If this convergence does not show up, the force measurements may be contaminated by out-of-focus structures and should be discarded.

[0043] Although only a number of examples have been disclosed herein, other alternatives, modifications, uses and/or equivalents thereof are possible. Furthermore, all possible combinations of the described examples are also covered. Thus, the scope of the present disclosure should not be limited by particular examples, but should be determined only by a fair reading of the claims that follow. If reference signs related to drawings are placed in parentheses in a claim, they are solely for attempting to increase the intelligibility of the claim, and shall not be construed as limiting the scope of the claim.