Single molecule microscopic imaging industrial camera imaging system and imaging method

Abstract

The invention discloses a single molecule microscopic imaging industrial camera imaging system and imaging method. The system comprises an inverted fluorescence microscope, a laser light source, a coupler, a light source adjusting device, an optical filter, an objective lens, a CMOS camera, a microcomputer processing system and an image enhancement device. The inverted fluorescence microscope is used for laser scanning confocal microscopic imaging or single molecule PALM microscopic imaging; the laser light source is used for providing incident light for the camera system; the coupler is used for obtaining high-power excitation and activation laser to enter the microscope system; the light source adjusting device is used for switching light sources; the optical filter is used for collecting the maximum fluorescence signal and blocking the exciting light at the same time; the objective lens is used for total internal reflection of light beams on the sample surface; the CMOS camera is used for photographing to obtain an image; the image intensifier is used for intensifying the image. And the microcomputer processing system carries out picture synthesis and result output through a preset correction algorithm. According to the invention, the living cell single-molecule trajectory detection efficiency can be improved.

Description

Technical Field

[0001] The present application relates to the technical field of industrial cameras, and in particular to an imaging system and an imaging method of a single-molecule microscopic imaging industrial camera. Background Art

[0002] Microscopic optical imaging, also commonly known as "optical microscopic imaging" or "optical microscopy" (Optical Microscopy, or Light Microscopy), refers to the technology that can obtain a magnified image of a tiny sample after the visible light passes through the sample or is reflected from the sample through one or more lenses. The resulting image can be directly observed by the eyepiece. At present, microscopy technology generally uses photosensitive plates or digital image detectors such as CCD and CMOS for recording to avoid distortion of the results after long-term exposure to bright light. Finally, the resulting photos are displayed and analyzed on the computer.

[0003] Ordinary optical microscopy using bright field illumination usually has three limitations: first, it can only image dark samples (transmission type) or strongly reflective samples (reflection type); second, the optical diffraction limit limits the maximum resolution of this technology to about 200nm; third, out-of-focus information will reduce image contrast. Fluorescence microscopy, which is based on the excitation and fluorescence emission of (exogenous or endogenous) fluorescent molecules in the sample, can overcome the limitation of being unable to image transparent samples, but the problems of limited resolution and out-of-focus interference still need to be solved by other measures.

[0004] In the prior art, patent application CN202220349466.2 discloses a detection device that relies on adding lenses and combining lenses. The device mainly performs multiple lenses to jointly magnify. Although the volume of the equipment is not increased, the improvement effect is still limited to the size and specifications of the lenses, and it cannot be further processed on the computer. Although the efficiency is improved, it is impossible to perform further calculations and reduce errors, and this error will not change due to the innovation of this device; in addition, patent application CN202111074871.4 discloses an optical layer that rapidly and continuously rotates the sample. The present invention discloses a microscopic imaging system and method, which uses optical tweezers made of linear polarized light to capture and rotate samples. By generating a single-beam gradient force well, microparticles or cells can be constrained near the focus in three-dimensional space, and anisotropic polarization in the sample is caused, thereby generating a torque that depends on the angle between the birefringence polarization direction and the electric field direction, thereby being able to control the captured object to rotate synchronously with the polarization direction of the light field. The invention may change the properties of the sample itself, cause physical changes, and change the state of the substance itself, so it can only be used for substances that are particularly stable in nature and are insensitive to optical tweezers.

[0005] To address the above issues, there is an urgent need for a microscopic imaging system that can capture single molecules in living cells. Summary of the invention

[0006] The purpose of this application is to provide a single-molecule microscopy industrial camera imaging system and imaging method, which can improve the efficiency of single-molecule trajectory detection in living cells, reduce the interference of manual operations, and ensure that the original state of the sample can be detected to the greatest extent.

[0007] The present application provides a single-molecule microscopy industrial camera imaging system, comprising:

[0008] Inverted fluorescence microscope, laser light source, coupler, light source adjustment device, filter, objective lens, CMOS camera, microcomputer processing system and image intensification device;

[0009] The inverted fluorescence microscope is used for laser scanning confocal microscopy or single molecule PALM microscopy;

[0010] The laser light source is used to provide incident light for the camera system;

[0011] The coupler is used to obtain high-power excitation and activation lasers into the microscope system;

[0012] The light source adjustment device is used to switch the light source;

[0013] The filter is used to collect the maximum fluorescence signal while blocking the excitation light;

[0014] The objective lens is used to make the light beam undergo total internal reflection on the sample surface;

[0015] The CMOS camera is used to take pictures and acquire images;

[0016] The image intensifier is used to enhance the image.

[0017] The microcomputer processing system synthesizes the pictures and outputs the results through a preset correction algorithm.

[0018] In this solution, the laser light source includes: an activation light laser and an excitation light laser.

[0019] In this solution, the coupler is a free space or optical fiber multi-wavelength coupler.

[0020] In this solution, the filters include: an excitation filter, a dichroic filter, and a long-pass filter.

[0021] In this solution, the objective lens is a total internal reflection fluorescence microscope, and the numerical aperture of the objective lens is greater than a set threshold.

[0022] In this solution, the image intensifier adopts the third generation GaAsP photocathode material, and the quantum efficiency at 570nm is 40%.

[0023] The second aspect of the present application provides a single-molecule microscopic imaging industrial camera imaging method, which is applied to the single-molecule microscopic imaging industrial camera system, comprising the following steps:

[0024] Adjust the camera system to a horizontal state and adjust the laser light source;

[0025] Place the sample and make sure the sample is positioned and the field of view is centered;

[0026] Select the laser light source and take a photo;

[0027] The trajectory is extracted and drawn according to the picture obtained by taking pictures to obtain the trajectory picture.

[0028] In this solution, the extraction of trajectories and drawing of images specifically include: detecting single-molecule fluorescent spots, determining the positions of the single-molecule fluorescent spots in the image, and linking the positions to generate trajectories.

[0029] In this scheme, detecting single-molecule fluorescent spots, determining the positions of the single-molecule fluorescent spots in an image, and linking the positions to generate a trajectory include:

[0030] Each fluorescent spot in the image was detected and its position determined using an in-house computer program based on a spatial cross-correlation matrix, and the spot position (x, y coordinates) was determined as follows;

[0031] First, the centroid of the cross-correlation matrix was calculated, and then a circular area with a diameter of 830 nm, whose center was located at the centroid, was determined as the area of ​​the fluorescence spot intensity distribution. Second, the intensity distribution in the circular area was fitted to a symmetrical two-dimensional Gaussian PSF using the following formula to determine the spot position:

[0032]

[0033] Wherein, A: amplitude of Gaussian peak, (x0, y0) represents the pixel center position of the light spot, SXY: standard deviation of Gaussian peak, and B: background offset, i.e. background signal intensity divided by the number of pixels.

[0034] In this protocol, trajectories extraction and image drawing also include single molecule trajectory quantitative analysis based on MSD-Δt graph. The specific steps are as follows:

[0035] For each single-molecule trajectory, the one-dimensional MSD (x or y) in the x or y direction at each time interval was calculated according to the following formula:

[0036]

[0037] 其中， δt: is the frame time, (x(jδt+nδt) and y(jδt+nδt)) describe: the position of the fluorescent molecule after a time interval nδt from the position (x(jδt), y(jδt)), N represents the total number of frames in the sequence, where n and j are positive integers, n ： Time increment.

[0038] As can be seen from the above, the single-molecule microscopic imaging industrial camera imaging system and imaging method disclosed in the present invention include: an inverted fluorescence microscope, a laser light source, a coupler, a light source adjustment device, a filter, an objective lens, a CMOS camera, a microcomputer processing system and an image enhancement device; the inverted fluorescence microscope is used for laser scanning confocal microscopic imaging or single-molecule PALM microscopic imaging; the laser light source is used to provide incident light for the camera system; the coupler is used to obtain high-power excitation and activation lasers to enter the microscope system; the light source adjustment device is used to switch the light source; the filter is used to collect the maximum fluorescence signal and block the excitation light at the same time; the objective lens is used to make the light beam undergo total internal reflection on the sample surface; the CMOS camera is used to take pictures to obtain images; the image intensifier is used to enhance the image. The microcomputer processing system synthesizes the picture and outputs the results through a preset correction algorithm. The present invention can improve the efficiency of single-molecule trajectory detection in living cells, reduce the interference of manual operations, and ensure that the original state of the sample can be detected to the greatest extent.

[0039] Other features and advantages of the present application will be described in the following description, and partly become apparent from the description, or be understood by practicing the embodiments of the present application. The purpose and other advantages of the present application can be realized and obtained by the structures specifically pointed out in the written description, claims, and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments of the present application will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0041] Figure 1 Schematic diagram of a single-molecule microscopic imaging industrial camera imaging system provided in an embodiment of the present application;

[0042] Figure 2 A schematic diagram of the structure of a single-molecule microscopic imaging industrial camera imaging system provided in an embodiment of the present application;

[0043] Figure 3 Flowchart of the single-molecule microscopy imaging industrial camera imaging method provided in an embodiment of the present application. DETAILED DESCRIPTION

[0044] The technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. The components of the embodiments of the present application described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the application claimed for protection, but merely represents the selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without making creative work belong to the scope of protection of the present application.

[0045] It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. At the same time, in the description of this application, the terms "first", "second", etc. are only used to distinguish the description and cannot be understood as indicating or implying relative importance.

[0046] Please refer to Figure 1-Figure 2 , is a schematic diagram of a single-molecule microscopic imaging industrial camera imaging system in some embodiments of the present application. The single-molecule microscopic imaging industrial camera imaging system includes:

[0047] Inverted fluorescence microscope, laser light source, coupler, light source adjustment device, filter, objective lens, CMOS camera, microcomputer processing system and image intensification device;

[0048] The inverted fluorescence microscope is used for laser scanning confocal microscopy or single-molecule PALM microscopy; the laser light source is used to provide incident light for the camera system; the coupler is used to obtain high-power excitation and activation lasers into the microscope system; the light source adjustment device is used to switch the light source; the filter is used to collect the maximum fluorescence signal and block the excitation light at the same time; the objective lens is used to make the light beam undergo total internal reflection on the sample surface; the CMOS camera is used to take pictures to obtain images; the image intensifier is used to enhance the image. The microcomputer processing system synthesizes the pictures and outputs the results through a preset correction algorithm.

[0049] It should be noted that the purpose of this technology is to provide a single-molecule microscopic imaging industrial camera imaging system, including: an inverted fluorescence microscope, a laser light source, a coupler, a light source adjustment device, a filter, an objective lens, a CMOS camera, a microcomputer processing system and an image enhancement device; the inverted fluorescence microscope is used for laser scanning confocal microscopic imaging or single-molecule PALM microscopic imaging; the laser light source is used to provide incident light for the camera system; the coupler is used to obtain high-power excitation and activation lasers to enter the microscope system; the light source adjustment device is used to switch the light source; the filter is used to collect the maximum fluorescence signal and block the excitation light at the same time; the objective lens is used to make the light beam undergo total internal reflection on the sample surface; the CMOS camera is used to take pictures to obtain images; the image intensifier is used to enhance the image. The microcomputer processing system synthesizes the picture and outputs the results through a preset correction algorithm.

[0050] The present invention uses the light source signal amplification system of the industrial camera and the unique background noise suppression technology to take pictures of single molecules in chronological order, and finally connects the trajectories of multiple pictures to ultimately form a single molecule trajectory motion picture.

[0051] This application adds a signal amplification device to the light source system, which can effectively eliminate background noise and restore the real picture, reduce the subsequent amount of calculation, and can quickly detect. This application can reduce the exposure time of single molecules under laser, and does not require very time-consuming manual parameter adjustment for background elimination. Once set, multiple subsequent samples can be detected, ensuring that the original state of the sample can be detected to the greatest extent.

[0052] Finally, the system can still be upgraded and customized, and different testing standards can be formulated based on the different samples being tested.

[0053] In this solution, the laser light source includes: an activation light laser and an excitation light laser.

[0054] It should be noted that, in a specific embodiment, a 405nm laser is used as activation light, and a 561nm laser is used as excitation light. The selection of the laser wavelength is related to the characteristics of the photoactivated protein used. The laser wavelengths used to excite fluorescence generally include 488, 561, 594, and 635nm. The laser power is generally 50-200mW. In order to facilitate the adjustment of the optical path, the laser output spot quality is generally required to be good.

[0055] In this solution, the coupler is a free space or optical fiber multi-wavelength coupler.

[0056] It should be noted that free-space couplers can allow higher-power excitation and activation lasers to enter the microscope system, making the imaging process faster.

[0057] According to an embodiment of the present invention, the light source adjustment device may be an acousto-optic tunable filter, which functions to switch the activation light and the excitation light so that the activation light and the excitation light are sequentially irradiated on the sample to achieve the purpose of fast optical switching. Before the spatial light is input into the microscope, the use of an AOTF can maximize the light intensity entering the microscope.

[0058] According to an embodiment of the present invention, the filter includes: an excitation filter, a dichroic filter, and a long-pass filter.

[0059] It should be noted that the filter is used to collect the maximum fluorescence signal while blocking the excitation light to ensure the signal-to-noise ratio and eliminate residual light and autofluorescence.

[0060] According to an embodiment of the present invention, the objective lens is a total internal reflection fluorescence microscope, and the numerical aperture of the objective lens is greater than a set threshold.

[0061] It should be noted that the role of the objective lens is to make the light beam undergo total internal reflection on the sample surface to improve the signal-to-noise ratio of the image. At the same time, the numerical aperture of the TIRF objective lens is relatively large, which will have a better photon collection efficiency.

[0062] According to the embodiment of the present invention, the CMOS camera should have high quantum efficiency, high frame rate and low noise in the visible light range. The camera in this application is a customized camera with the following specific parameters: For a frame size of 14×14μm 2 The resolution of 100 μs (10 kHz frame rate) and the localization accuracy of 20 nm (256 × 256 pixels) were achieved for single molecules, and the resolution was 33 μs (30 kHz frame rate), the localization accuracy was 34 nm, and the frame size was 7.1 × 6.2 μm. 2 (128×112 pixels). These frame rates are 330 times and 1,000 times faster than normal video rates (30 Hz).

[0063] According to an embodiment of the present invention, the image intensifier adopts the third generation GaAsP photocathode material, and the quantum efficiency at 570nm is 40%.

[0064] Figure 3 A flow chart of a single-molecule microscopy imaging industrial camera imaging method is shown.

[0065] The second aspect of the present application provides a single-molecule microscopic imaging industrial camera imaging method, which is applied to the single-molecule microscopic imaging industrial camera system, comprising the following steps:

[0066] S101: Adjust the camera system to a horizontal state and adjust the laser light source;

[0067] S102 places the sample and determines the sample position and the center of the field of view;

[0068] S103: Select a laser light source and take a photo;

[0069] S104: Extracting the trajectory according to the image obtained by taking photos and drawing the image to obtain a trajectory image.

[0070] It should be noted that, in a specific embodiment, the system needs to be calibrated first. Before use, the system must be adjusted to a horizontal state using a level meter, and the system's light source must be adjusted to an appropriate brightness of white light. The eyepiece is used to observe whether the light from the light source is blocked and whether the light spot refracted by the light source is complete. If not, the objective lens and eyepiece need to be cleaned until the shape of the light spot can be seen completely.

[0071] Secondly, the sample to be observed is placed on the stage, and ordinary white light observation is first used to find the position of the cell. Then the system's excitation filter, dichroic filter, and long-pass filter are used to excite the fluorescence of the sample cell, so as to start tracking the trajectory on the screen and finally draw the changes of the fluorescent substance in the cell. We checked the suitability of the camera system for observing fast molecular motion in the PM of living cells by testing whether it can detect the jump diffusion of Cy3-labeled single molecules, phospholipids, and the transmembrane protein transferrin receptor (TfR).

[0072] According to an embodiment of the present invention, the extraction of the trajectory and drawing of the image specifically includes: detecting single-molecule fluorescent spots, determining positions of the single-molecule fluorescent spots in the image, and linking the positions to generate the trajectory.

[0073] According to an embodiment of the present invention, detecting a single-molecule fluorescent spot, determining a position of the single-molecule fluorescent spot in an image, and linking the position to generate a trajectory includes:

[0074] Each fluorescent spot in the image was detected and its position determined using an in-house computer program based on a spatial cross-correlation matrix, and the spot position (x, y coordinates) was determined as follows;

[0075] First, the centroid of the cross-correlation matrix was calculated, and then a circular area with a diameter of 830 nm, whose center was located at the centroid, was determined as the area of ​​the fluorescence spot intensity distribution. Second, the intensity distribution in the circular area was fitted to a symmetrical two-dimensional Gaussian PSF using the following formula to determine the spot position:

[0076]

[0077] Wherein, A: amplitude of Gaussian peak, (x0, y0) represents the pixel center position of the light spot, SXY: standard deviation of Gaussian peak, and B: background offset, i.e. background signal intensity divided by the number of pixels.

[0078] In this protocol, trajectories extraction and image drawing also include single molecule trajectory quantitative analysis based on MSD-Δt graph. The specific steps are as follows:

[0079] For each single-molecule trajectory, the one-dimensional MSD (x or y) in the x or y direction at each time interval was calculated according to the following formula:

[0080]

[0081] 其中， δt: is the frame time, (x(jδt+nδt) and y(jδt+nδt)) describe: the position of the fluorescent molecule after a time interval nδt from the position (x(jδt), y(jδt)), N represents the total number of frames in the sequence, where n and j are positive integers, n ： Time increment.

[0082] The single-molecule microscopic imaging industrial camera imaging system and imaging method disclosed in the present invention include: an inverted fluorescence microscope, a laser light source, a coupler, a light source adjustment device, a filter, an objective lens, a CMOS camera, a microcomputer processing system and an image enhancement device; the inverted fluorescence microscope is used for laser scanning confocal microscopic imaging or single-molecule PALM microscopic imaging; the laser light source is used for the camera system to provide incident light; the coupler is used to obtain high-power excitation and activation lasers to enter the microscope system; the light source adjustment device is used to switch the light source; the filter is used to collect the maximum fluorescence signal and block the excitation light at the same time; the objective lens is used to make the light beam undergo total internal reflection on the sample surface; the CMOS camera is used to take pictures to obtain images; the image intensifier is used to enhance the image. The microcomputer processing system synthesizes the picture and outputs the result through a preset correction algorithm. The present invention can improve the efficiency of single-molecule trajectory detection in living cells, reduce the interference of manual operation, and ensure that the original state of the sample can be detected to the greatest extent.

[0083] In the several embodiments provided in the present application, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are only schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation, such as: multiple units or components can be combined, or can be integrated into another system, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the components shown or discussed can be through some interfaces, and the indirect coupling or communication connection of the devices or units can be electrical, mechanical or other forms.

[0084] The units described above as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units; they may be located in one place or distributed on multiple network units; some or all of the units may be selected according to actual needs to achieve the purpose of the present embodiment.

[0085] In addition, all functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may be separately used as a unit, or two or more units may be integrated into one unit; the above-mentioned integrated units may be implemented in the form of hardware or in the form of hardware plus software functional units.

[0086] Those skilled in the art can understand that: all or part of the steps of implementing the above method embodiments can be completed by hardware related to program instructions, and the aforementioned program can be stored in a readable storage medium. When the program is executed, it executes the steps of the above method embodiments; and the aforementioned storage medium includes: mobile storage devices, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), disks or optical disks, and other media that can store program codes.

[0087] Alternatively, if the above-mentioned integrated unit of the present invention is implemented in the form of a software function module and sold or used as an independent product, it can also be stored in a readable storage medium. Based on this understanding, the technical solution of the embodiment of the present invention can be essentially or partly reflected in the form of a software product that contributes to the prior art. The software product is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the methods described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as mobile storage devices, ROM, RAM, magnetic disks or optical disks.

Claims

1. A single-molecule microscopic imaging industrial camera system, characterized in that: include: Inverted fluorescence microscope, laser light source, coupler, light source adjustment device, filter, objective lens, CMOS camera, microcomputer processing system and image intensification device; The inverted fluorescence microscope is used for laser scanning confocal microscopy or single molecule PALM microscopy; The laser light source is used to provide incident light for the camera system; The coupler is used to obtain high-power excitation and activation lasers into the microscope system; The light source adjustment device is used to switch the light source; The filter is used to collect the maximum fluorescence signal while blocking the excitation light; The objective lens is used to make the light beam undergo total internal reflection on the sample surface; The CMOS camera is used to take pictures and acquire images; The image intensifier is used to enhance the image. The microcomputer processing system synthesizes the pictures and outputs the results through a preset correction algorithm.

2. A single-molecule microscopic imaging industrial camera system according to claim 1, characterized in that: The laser light source includes: an activation light laser and an excitation light laser.

3. A single-molecule microscopic imaging industrial camera system according to claim 2, characterized in that: The coupler is a free space or optical fiber multi-wavelength coupler.

4. A single-molecule microscopic imaging industrial camera system according to claim 1, characterized in that: The optical filters include: an excitation filter, a dichroic filter, and a long-pass filter.

5. A single-molecule microscopic imaging industrial camera system according to claim 4, characterized in that: The objective lens is a total internal reflection fluorescence microscope, and the numerical aperture of the objective lens is greater than a set threshold.

6. A single-molecule microscopic imaging industrial camera system according to claim 1, characterized in that: The image intensifier adopts the third generation GaAsP photocathode material, and the quantum efficiency at 570nm is 40%.

7. A single-molecule microscopic imaging industrial camera imaging method, the method is applied to the single-molecule microscopic imaging industrial camera system according to any one of claims 1 to 6, characterized in that: The following steps are involved: Adjust the camera system to a horizontal state and adjust the laser light source; Place the sample and make sure the sample is positioned and the field of view is centered; Select the laser light source and take a photo; The trajectory is extracted and drawn according to the picture obtained by taking pictures to obtain the trajectory picture.

8. The single-molecule microscopy industrial camera imaging method according to claim 7, characterized in that: The extraction of the trajectory and drawing of the image specifically includes: detecting single-molecule fluorescent spots, determining the positions of the single-molecule fluorescent spots in the image, and linking the positions to generate the trajectory.

9. The single-molecule microscopy industrial camera imaging method according to claim 7, characterized in that: Detecting single-molecule fluorescent spots, determining positions of the single-molecule fluorescent spots in an image, and correlating the positions to generate trajectories, including: Each fluorescent spot in the image was detected and its position determined using an in-house computer program based on a spatial cross-correlation matrix, and the spot position (x, y) was determined as follows; First, the centroid of the cross-correlation matrix was calculated, and then a circular area with a diameter of 830 nm was determined, with its center at the centroid, as the area of ​​the fluorescence spot intensity distribution; second, the intensity distribution in the circular area was fitted to a symmetrical two-dimensional Gaussian PSF using the following formula to determine the spot position: Wherein, A represents the amplitude of the Gaussian peak, (x0, y0) represents the pixel center position of the light spot, SXY represents the standard deviation of the Gaussian peak, and B represents the background offset, that is, the background signal intensity divided by the number of pixels.

10. The single-molecule microscopy industrial camera imaging method according to claim 9, characterized in that: Extracting trajectories and drawing pictures also includes quantitative analysis of single-molecule trajectories based on MSD-Δt graphs. The specific steps are as follows: For each single-molecule trajectory, the one-dimensional MSD (x or y) in the x or y direction at each time interval was calculated according to the following formula: Where δt is the frame time, (x(jδt+nδt) and y(jδt+nδt)) describe the position of the fluorescent molecule after a time interval nδt from the position (x(jδt), y(jδt)), and N represents the total number of frames in the sequence, where n and j are positive integers, n ： Time increment.

Images