CN114112808A - Method for characterizing cytoplasmic mechanical properties - Google Patents
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Abstract
The invention provides a method for characterizing the mechanical property of cytoplasm, which is a method for characterizing the physical characteristics of cells by simultaneously considering the tension effect of cell membranes and the porous structure of cytoplasm and has a cell skeleton network modulus E of cytoplasmSThe apparent viscosity eta of the cytoplasm and the intrinsic diffusion coefficient D of the cytosolpCharacterized by the fact thatSEta and DpAnd carrying out visual representation in the three-dimensional space for the physical characteristics of the cells in the three-dimensional space of the benchmark. The results of characterization of cytoplasm are shown to be distributed on the curved surface D in both theory and experimental datap＝αESNear/η. The method has great promotion effect on the research of single cell mechanics.
Description
Technical Field
The invention relates to the nanometer science and the biophysics, in particular to a characterization method of cytoplasmic mechanical properties.
Background
Existing models for characterizing physical properties of biological materials such as cells can be roughly classified into linear elastic models, nonlinear elastic models, viscoelastic models, porous medium models, and plastic models. In the process of characterizing the physical characteristics of cells, only one or a few parameters of the cells are often focused and respectively given a numerical distribution, but the description method cannot intuitively characterize the comprehensive characteristics of the cells.
Acquisition of cell force relaxation curve for analyzing mesoporous elasticity of cells
As shown in FIG. 1, force relaxation curves as shown in FIG. 2 can be obtained by applying a force of about 3.5-6nN to the cell with an AFM probe in about 35ms and creating an indentation depth of about 1 μm for a period of time, and collecting the variation in indentation depth and loading force during this process.
As shown in fig. 2, the loading force of the AFM probe decreased by about 35% during the force relaxation, while the penetration depth increased only by less than 5%. This means that the process is almost a constant strain process. Moeendarbary E et al used the above method to obtain a force curve using a JPK Nanowizard-I atomic force microscope and performed mesoporous elastic analysis using MATLAB.
Theory of mesoporous elasticity
On the basis of previous studies, Moeendarbary E et al (Moeendarbary E, Valon L, Fritzsche M, et al. the cytoplasms of living cells as a porous material [ J ] Nat Mater,2013,12(3):253-61) gave the theory of elasticity of mesopores when a set of spherical probes were applied to cells.
The force curve during the relaxation phase satisfies the following formula:
wherein τ ═ Dpt/Rδ。FiIs the magnitude of the force at the beginning of the relaxation phase, FfIs the magnitude of the force at the end of the relaxation phase, and f (t) is the magnitude of the force at time t of the relaxation phase. DpIs the intrinsic diffusion coefficient of the cell, R is the size of the radius of the spherical probe, and δ is the size of the depth of indentation. Fitting the formula with a force relaxation curve to obtain the intrinsic diffusion coefficient D of the cellpThis is also one of the most important parameters of the mesoporous elastic model.
Hu Y et al, based on AFM experiments on hydrogels, gave the mesoporous elastic model force relaxation formula for different shaped probes (Hu Y, Zhao X, Vlassak J, et al, use indication to characteristics of the pore elasticity of gels [ J ]. Appl Phys Lett,2011,96(12): 37). In the case of a tapered probe, the probe,
τ＝Dptπ2/4δ2tan2θ
where θ is the half-open angle of the tapered probe.
Similarly, the intrinsic cell diffusion coefficient D of the probe in the tapered shape can be obtained by fitting the force relaxation curve of the tapered probe to the corresponding equationp。
The theory of mesoporous elasticity is that cells are regarded as a liquid-containing porous medium structure consisting of a solid skeleton network and cell sap filled in the solid skeleton network. On this basis, moeendarbry E et al give the following formula:
wherein E isCIs the elastic modulus of the solid skeleton network, xi is the pore size of the porous structure, and mu is the viscosity of the cell sap.
③ viscosity of cell fluid
Darling E M et al consider cells as viscoelastic materials and give an expression of the force relaxation curve for spherical probes (Darling E M, Zauscher S, Guilak F. viscoelastic properties of spherical probes measured by atomic force for microscopy [ J ]. Osteoarthritis Carticage, 2006,14(6): 571-9):
where F is the interaction force between the probe and the cell, δ is the depth of penetration, δ0Is the depth of penetration at the beginning of the relaxation phase (i.e., when t is 0), ERFor relaxation of the modulus, v is the Poisson's ratio (which should be taken to be 0.3 according to Moeendarbary E et al), τσAnd τσRespectively constant force and constant change relaxation time constant, and analyzing the force relaxation curve acquired by the method in the step of acquiring the cell force relaxation curve for analyzing the mesoporous elasticity of the cells by using the formula to obtain the product ER，τσAnd τσThe value of (c). And the apparent viscosity η of the cell can be determined according to η ═ ER(τσ-τσ) Thus obtaining the product.
Moeendarbary E et al believe that the following relationship exists between the apparent viscosity η of the cells and the viscosity μ of the cytosol:
where L is the characteristic constant of the skeletal network.
Young's modulus of cell
Young's modulus of cells was obtained by the well-known Hertz model (Hertz H.Ueber die Berlung fester elastscher)
[J]Journal fur Die rein Und Angewandte Mathimatik, 2006,1882(92): 156-71). The Hertz model treats cells as pure elastomers and therefore only focuses on the force curve at the stage of cell insertion.
According to the elastic indentation theory of Hertz, when the probe is spherical, the following relationship exists between the loading force and the depth of penetration:
wherein R is the radius of the spherical probe.
When the probe is tapered, the following relationship exists between the loading force and the penetration depth:
in the process of measuring the mesoporous elastic characteristics of cells in the prior art, the whole cells are regarded as a porous medium structure, and the action of cell membranes and the influence of the cell membranes on the porous medium structure are not considered.
In the process of measuring the apparent viscosity of the cells, Darling E M et al only gives a quantitative solution of the spherical probe, and does not give a corresponding analytical formula for the conical probe, and the derivation process of Darling E M et al is careless and needs to be deduced again.
For each parameter involved in the cell model, previous researches often only give a solution of each parameter, and the mutual relation among the solutions is not intuitively presented.
Disclosure of Invention
The invention aims to provide a method for representing mechanical properties of cytoplasm, which combines a cell membrane tension model with a cytoplasm porous medium model, represents physical characteristics of cytoplasm by using an atomic force microscope, and represents the cytoplasm in a three-dimensional space in a three-dimensional visual manner.
In order to achieve the object of the present invention, the present invention provides a method for characterizing cytoplasmic mechanical properties, comprising the steps of:
(1) obtaining single cell force relaxation signal data based on AFM nano indentation experiment;
(2) calculating the interaction force F (t) between the AFM probe and the cell under a viscoelastic model;
(3) modulus of cytoskeletal network to cytoplasm ESThe apparent viscosity eta of the cytoplasm and the intrinsic diffusion coefficient D of the cytosolpThree parameters are characterized;
(4) utilizing the three parameters E in step (3)SEta and DpAnd characterizing the mechanical property of cytoplasm.
In the step (2), for the spherical probe,
wherein, F (t) represents the interaction force between the probe and the cell at the moment t of the relaxation stage; r is the spherical probe radius, delta is the penetration depth, ERFor the relaxation of the modulus, v is the Poisson's ratio, τσIs a constant force time constant, τεIs a constant time constant;
in the case of a tapered probe, the probe,
wherein, F (t) is the interaction force between the probe and the cell; theta is the half-open angle, delta is the penetration depth, ERFor the relaxation of the modulus, v is the Poisson's ratio, τσIs a constant force time constant, τεIs a constant time constant;
the interaction force F (t) between the probe and the cell is divided into two parts, one part being the force F provided by the cytoplasmC(t), the other part is the force F provided by the curvature and surface tension of the cell membraneMI.e. F (t) ═ FM+FC(t); and for three parameters ESEta and DpCarrying out characterization;
in the step (3), for the spherical probe,
wherein, FC(t) force provided by cytoplasm; r is the spherical probe radius, delta is the penetration depth, ESIs the cytoskeletal network modulus, v is the Poisson's ratio, τσIs a constant force time constant, τεIs a constant time constant;
ESis the modulus of the cytoskeletal network of the cytoplasm, η is the apparent viscosity of the cytoplasm, η ═ ES(τσ-τε)；
FM＝2γπδ
Wherein, FMThe force provided by the curvature and surface tension of the cell membrane; gamma is the surface tension and delta is the penetration depth;
wherein F (∞) is the loading force of the AFM probe after stabilization of the relaxation phase, and R is sphericalRadius of the probe, delta press-in depth, ESIs the cytoskeletal network modulus, v is the Poisson's ratio, τσIs a constant force time constant, τεIs a constant time constant;
in the case of a tapered probe, the probe,
FM＝4γδsinθ
wherein, FMThe force provided by the curvature and surface tension of the cell membrane; gamma is surface tension, pressing depth and theta is half-open angle of the conical probe;
wherein, FC(t) force provided by cytoplasm; theta is the half-open angle of the tapered probe, delta is the penetration depth, ESIs the cytoskeletal network modulus, v is the Poisson's ratio, τσIs a constant force time constant, τεIs a constant time constant;
where F (∞) is the loading force of the AFM probe after the relaxation phase has stabilized, θ is the half-open angle of the tapered probe, δ is the penetration depth, E is the depth of penetrationSIs the cytoskeletal network modulus, v is the Poisson's ratio, τσIs a constant force time constant, τεIs a constant time constant;
in the case of a spherical probe, the probe is,
τ＝Dpt/Rδ
wherein D ispIs the intrinsic diffusion coefficient of the cell sap; r is a spherical probeRadius, δ is the penetration depth;
in the case of a tapered probe, the probe,
τ＝Dptπ2/4δ2tan2θ
wherein D ispIs the intrinsic diffusion coefficient of the cell sap; theta is the half-open angle of the conical probe, and delta is the pressing depth;
in the step (4), the step (c),
wherein D ispIs the intrinsic diffusion coefficient of the cell sap; v. ofsIs the poisson's ratio of the dry skeletal network,
is porosity,. kappa.is a constant taking into account the irregularity, connectivity and flexibility of the pores, ESIs the modulus of cytoskeleton network, xi is the pore size of the porous structure of cytoplasm, and mu is the viscosity of cell sap;
wherein η is the apparent viscosity of the cytoplasm; mu is the viscosity of the cell sap, L is the characteristic constant of the skeleton network, and xi is the pore size of the cytoplasmic porous structure;
then
Wherein D ispIs the intrinsic diffusion coefficient of the cell sap; v. ofsIs the poisson's ratio of the dry skeletal network,
is the porosity, L is the characteristic constant of the framework network, κ is a constant taking into account the irregularity, connectivity and flexibility of the pores, ESIs the modulus of the cytoskeletal network, η is the apparent viscosity of the cytoplasm,
then
Wherein α is a structural correlation coefficient.
Further, for the spherical probe, the step (1) includes: after the probe is contacted with the surface of the single cell by an AFM system, lifting the probe away from the cell to a position 5-7 microns above the surface and standing for 1s, then enabling the probe tip of the AFM to approach the surface of the cell at a speed of 15-20 microns/s, generating an indentation with the depth of 500-1000 nm, then standing for 5-10 s until a cell force relaxation signal is gradually stabilized, and recording distance, time and acting force data of the whole process. Preferably, after the AFM system brought the probe into contact with the surface of the single cell, the probe was lifted off the cell 7 μm above the surface and left for 1s, then the AFM probe tip was brought into proximity with the cell surface at a rate of 20 μm/s, creating an indentation with a depth of 500nm, then left for 5s until the cell force relaxation signal gradually stabilized, and the distance, time and force data were recorded for the entire process.
For a tapered probe, step (1) comprises: after the probe is contacted with the surface of the single cell by an AFM system, lifting the probe away from the cell to a position 5-7 microns above the surface and standing for 1s, then enabling the probe tip of the AFM to approach the surface of the cell at a speed of 15-20 microns/s, generating an indentation with the depth of 500-1000 nm, then standing for 5-10 s until a cell force relaxation signal is gradually stabilized, and recording distance, time and acting force data of the whole process.
In the invention, the conical probe used in the AFM nano-indentation experiment is a silicon nitride probe (MSCT-C, Bruker) with a half-open angle of 18 degrees and a force constant of 0.01N/m; the spherical probe is composed of a silicon nitride needle-free cantilever (TL-CONT, nanosensor) with force constant of 0.095N/m and SiO with diameter of 10 μm2AFM probe composed of microspheres.
The cell type to which the method is applied is a live adherent cell with an intact membrane structure.
By the technical scheme, the invention at least has the following advantages and beneficial effects:
the invention relates to a novel method for carrying out three-dimensional space representation on physical characteristics of cytoplasm by utilizing an atomic force microscope, which correlates three physical parameters of cells in a three-dimensional space through coefficients under the premise of considering the action of cell membranes, and realizes the visual display of the physical characteristics of the cytoplasm in three-dimensional space distribution for the first time.
The method can intuitively carry out three-dimensional characterization on the physical characteristics of the cells. In the presence of ESEta and DpPhysical properties of cells are visually displayed in a three-dimensional space formed by three basic dimensions. Meanwhile, different from the traditional method for performing mesoporous elastic characterization on cells, the method not only considers the cells as porous media, but also considers the effect of cell membranes in the process of performing mesoporous elastic mechanical property characterization on the cells. On the basis, the physical characteristics of cytoplasm can be more accurately represented, and the research on single cell mechanics is greatly promoted.
The invention provides a method for visually representing physical characteristics of cytoplasm in three-dimensional space for the first time on the basis of a liquid-containing porous medium model and in consideration of the essential structure of cells. By utilizing the method, the physical characteristics of cytoplasm can be effectively expressed in a visual three-dimensional space, and the difference between the physical characteristics of different cells can be given more visually.
And thirdly, the invention simultaneously considers the functions of cell membrane tension and cytoplasmic mesoporous elasticity, and can deduce each parameter related to the cytoplasmic mesoporous elasticity by using a corresponding physical model, thereby realizing multi-parameter three-dimensional space representation of the cytoplasmic mechanical property.
Drawings
FIG. 1 is a flow chart of a conventional AFM acquisition force relaxation curve. Wherein, the probe inserting stage (I), the probe indentation stage (II), the force relaxation stage (III) and the force stabilization state (IV) are respectively carried out on the probe and the cell.
FIG. 2 shows a conventional force relaxation curve and mesoporous elasticity analysis. Wherein, the (I) is a graph for normalizing the variation of the indentation depth and the force along with the time, and the (II) is a fitting analysis for a force relaxation curve by using a mesoporous elastic model.
FIG. 3 is a flow chart of AFM force curve acquisition in a preferred embodiment of the present invention.
FIG. 4 is a schematic diagram of three-dimensional characterization of physical properties of cells in accordance with a preferred embodiment of the present invention.
FIG. 5 is a graph comparing the results of clustering of cells according to the method of the present invention with those of the conventional method. Wherein a is a clustering analysis result of the method; b is the traditional mesoporous elastic clustering analysis result without considering the cell membrane effect.
Detailed Description
The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention. Unless otherwise specified, the technical means used in the examples are conventional means well known to those skilled in the art, and the raw materials used are commercially available products.
The AFM system used in the following examples is an AFM (Agilent 5500) system with an inverted fluorescence microscope (Nikon Eclipse Ti) from Agilent.
Example 1 method for three-dimensional spatial characterization of physical characteristics of cytoplasm using atomic force microscope
1. AFM nanoindentation experiment and collection/acquisition of force relaxation curve
As shown in FIG. 3, using a spherical probe as an example, after the AFM system brought the probe into contact with the cell surface, the probe was lifted off the cell to 7 μm above the surface and left to stand for 1s, then the AFM probe tip was brought close to the cell surface at a rate of 20 μm/s, creating an indentation with a depth of about 500nm, and then left to stand for 5s until the force relaxation signal gradually stabilized. Distance, time and force data were recorded for the entire procedure.
In fig. 3, the entire curve contains four phases: needle withdrawing stage, standing stage, needle inserting stage and relaxation stage. First the probe is moved from Z0At position T1Elevation in time d0Reach Z1And (c) a position to transition the probe and the cell from a contact state to a detached state. Then let the probe at Z1Position standing T2For a period of time sufficient to restore the cells to normal conditions. Subsequently, the probe is controlled from Z1At position T3Decrease in time d1Height reaches Z2At a position to produce a certain indentation depth, this needle insertion speed is usually above 10 μm/s. Finally, the probe is brought to Z2Position holding T4Time, force relaxation was observed until the AFM loading force was almost completely stabilized.
2. Re-derivation of visco-elastic equations
The basic equation for elasticity is:
σ＝2E(T)ε
σ＝2G(t)(1+v)ε
converting it to the laplace domain:
the basic equation for viscoelasticity is:
converting it to the laplace domain:
then there is a change in the number of,
due to shear modulus G and Young's modulus EYThere is the following relationship between:
the young's modulus can therefore be described in the laplace domain as:
in this embodiment, as observed by Emoeendarbary E, the degree of strain change is much smaller than the degree of stress change during the relaxation experiment of AFM on cells. Thus, this process can be approximated as a constant process.
During stress relaxation (constant condition), f (t) is expressed by a Heaviside step function h (t):
in the case of a spherical probe, the probe is,
in the case of a tapered probe, the probe,
turning it to the laplacian domain is:
in the case of a spherical probe, the probe is,
in the case of a tapered probe, the probe,
then, the time domain space is respectively converted back to the time domain space, and the following steps are carried out:
in the case of a spherical probe, the probe is,
wherein, F (t) represents the interaction force between the probe and the cell at the moment t of the relaxation stage; r is the spherical probe radius, delta is the penetration depth, ERFor the relaxation of the modulus, v is the Poisson's ratio, τσIs a constant force time constant, τεIs a constant time constant;
in the case of a tapered probe, the probe,
wherein, F (t) is the interaction force between the probe and the cell; theta is the half-open angle, delta is the penetration depth, ERFor the relaxation of the modulus, v is the Poisson's ratio, τσIs a constant force time constant, τεIs a constant time constant;
the expressions respectively correspond to the changes of the force of the spherical probe and the force of the conical probe along with time under the viscoelastic model.
3. Characterization of cytoskeletal network modulus and cytoplasmic apparent viscosity taking into account membrane tension
Considering the influence of the membrane tension, the force acting on the probe (i.e., the interaction force between the probe and the cell) can be decomposed into two parts F, one of which is fineForce F provided by the cytoplasmC(t), the other part is the force F provided by the curvature and surface tension of the cell membraneM. In this process, the cell membrane tension is considered constant, since FMIs constant. And F provided by cytoplasmC(t) will vary with time during relaxation.
Based on the theoretical results of Darling et al, the force relaxation curve formula after indentation of the cytoplasm by the spherical probe was derived:
wherein, FC(t) force provided by cytoplasm; r is the spherical probe radius, delta is the penetration depth, ESIs the cytoskeletal network modulus, v is the Poisson's ratio, τσIs a constant force time constant, τεIs a constant time constant;
ESis the elastic modulus of the cytoskeletal network, apparent viscosity eta ═ ES(τσ-τε)。
FM＝2γπδ
Wherein, FMThe force provided by the curvature and surface tension of the cell membrane; gamma is the surface tension and delta is the penetration depth;
wherein F (∞) is the loading force of the AFM probe after stabilization of the relaxation phase, R is the spherical probe radius, δ is the penetration depth, ESIs the cytoskeletal network modulus, v is the Poisson's ratio, τσIs a constant force time constant, τεIs a constant time constant;
fitting the above formula with a force relaxation curve to obtainTo ES，τσAnd τεThe value of (c).
Similarly, for a tapered probe, the probe,
FM＝4γδsinθ
wherein, FMThe force provided by the curvature and surface tension of the cell membrane; gamma is surface tension, pressing depth and theta is half-open angle of the conical probe;
wherein, FC(t) force provided by cytoplasm; theta is the half-open angle of the tapered probe, delta is the penetration depth, ESIs the cytoskeletal network modulus, v is the Poisson's ratio, τσIs a constant force time constant, τεIs a constant time constant;
where F (∞) is the loading force of the AFM probe after the relaxation phase has stabilized, θ is the half-open angle of the tapered probe, δ is the penetration depth, E is the depth of penetrationSIs the cytoskeletal network modulus, v is the Poisson's ratio, τσIs a constant force time constant, τεIs a constant time constant;
fitting the above formula to a force curve to obtain ES，τσAnd τεThe value of (c). According to the formula eta ═ ES(τσ-τε) Values for apparent viscosity can also be obtained.
4. Characterization of the intrinsic diffusion coefficient of the cell fluid
As mentioned before, if the cell is considered to be a liquid-containing porous medium structure surrounded by cell membranes, the theory of mesoporous elasticity applies only to the cytoplasm and should not contain cell membranes. Therefore, the following mechanical relationship should be given for the cytoplasm:
in the case of a spherical probe, the probe is,
τ＝Dpt/Rδ
wherein D ispIs the intrinsic diffusion coefficient of the cell sap; r is the radius of the spherical probe, and delta is the pressing depth;
similarly, for a tapered probe, the probe,
τ＝Dptπ2/4δ2tan2θ
wherein D ispIs the intrinsic diffusion coefficient of the cell sap; theta is the half-open angle of the conical probe, and delta is the pressing depth;
5. three-dimensional spatial characterization of cytoplasmic physical properties
D can be obtained according to the experimental and analytical methods described abovepEta and EsThe value of (c). According to the porous medium theory:
wherein D ispIs the intrinsic diffusion coefficient of the cell sap; v. ofsIs the poisson's ratio of the dry skeletal network,
is porosity,. kappa.is a constant taking into account the irregularity, connectivity and flexibility of the pores, ESIs the cytoskeletal network modulus, xi is the cellThe pore size of the porous structure is small, and mu is the viscosity of cell sap;
wherein η is the apparent viscosity of the cytoplasm; mu is the viscosity of the cell sap, L is the characteristic constant of the skeleton network, and xi is the pore size of the cytoplasmic porous structure;
then
Wherein D ispIs the intrinsic diffusion coefficient of the cell sap; v. ofsIs the poisson's ratio of the dry skeletal network,
is the porosity, L is the characteristic constant of the framework network, κ is a constant taking into account the irregularity, connectivity and flexibility of the pores, ESIs the modulus of the cytoskeletal network, η is the apparent viscosity of the cytoplasm,
then
We refer to α as the structural correlation coefficient.
The above formula determines [ ] eta and DpThree parameters are spatially distributed on the curved surface Dp＝αEsNear/η, physical characteristics of the cytoplasm can be visually characterized.
FIG. 4 is a schematic diagram of visual three-dimensional characterization of physical properties of cytoplasm, giving a three-dimensional scattergram of multi-parameter characterization of cell mechanics, and giving a corresponding fitted surface Dp＝αESAnd eta, providing a curved surface-scatter diagram of the multi-parameter characterization of the cell mechanics. The value of alpha determines the distribution position of the three-dimensional curved surface in the space, and the measured value of each parameter determines the specific range of the distribution of a certain cell mechanics parameter in the three-dimensional space. In the present invention, with ESThe "mean ± standard deviation" of η is used as a limiting condition for the distribution range of the curved surface.
The method can intuitively carry out three-dimensional characterization on the physical characteristics of the cells. In the presence of ESEta and DpPhysical properties of cells are visually displayed in a three-dimensional space formed by three basic dimensions. Meanwhile, different from the previous method for performing mesoporous elastic characterization on cells, the method not only considers the cells as porous media, but also considers the effect of cell membranes in the process of performing mesoporous elastic mechanical property characterization on the cells. On the basis, physical characteristics of cytoplasm can be more accurately characterized, and the method has a great promoting effect on the research of single cell mechanics.
The process of characterizing the mesoporous elastic characteristics of the cells, which takes the cell membrane into consideration to play a role therein, is a great innovation point of the invention. Another innovation of the invention is that three-dimensional visual description and characterization of physical characteristics of cells are realized for the first time. The characterization method has great promotion effect on the mechanical characterization of single cells.
The conventional mesoporous elasticity has a defect that the function of a cell membrane is not considered, and the whole cell is regarded as a porous medium. The invention creatively distinguishes cytoplasm from cell membrane, and on the basis of the cytoplasm, the cell is regarded as a porous medium material wrapped by the membrane. As shown in FIG. 5, 15 cells were selected, and these 15 cell lines were classified into 9 normal cells, namely DCs (mouse bone marrow-derived dendritic cells); 3T3 (mouse embryonic fibroblasts); l929 (mouse fibroblasts); RCFB (rabbit eye corneal fibroblast ); PTMC (porcine trabecular mesheath cell); LSEC (liver sinusoidal endothelial cells); NRK (rat kidney cells); HC11 (mouse mammary epithelial cells) and MCF-10A (human mammary epithelial cells)) and 6 cancer cells (i.e., MCF-7 (human breast cancer cells); 4T1 (mouse breast cancer cells); HELA (human cervical cancer cells); CASKI (human cervical carcinoma epithelial cells); B16F10 (mouse skin melanoma cells) and SHG-44 (human glioma cells).
As shown in fig. 5, the multi-parameter characterization method of the present invention, which considers the cells as the membrane-wrapped porous medium structure, can correctly classify the 15 cells into two groups (normal cell group and cancer cell group), while the traditional method, which considers the cells as the porous medium structure as a whole, can misclassify part of the cells during the classification (HELA, DC and NRK are misclassified).
Although the invention has been described in detail hereinabove with respect to a general description and specific embodiments thereof, it will be apparent to those skilled in the art that modifications or improvements may be made thereto based on the invention. Accordingly, such modifications and improvements are intended to be within the scope of the invention as claimed.
Claims (4)
1. Method for characterizing the mechanical properties of cytoplasm, characterized in that it comprises the following steps:
(1) obtaining single cell force relaxation signal data based on AFM nano indentation experiment;
(2) calculating the interaction force F (t) between the AFM probe and the cell under a viscoelastic model;
(3) modulus of cytoskeletal network to cytoplasm ESThe apparent viscosity eta of the cytoplasm and the intrinsic diffusion coefficient D of the cytosolpThree parameters are characterized;
(4) utilizing the three parameters E in step (3)SEta and DpCharacterizing the mechanical property of cytoplasm;
in the step (2), for the spherical probe,
wherein F (t) represents the probe at the moment t of the relaxation phaseInteraction with cells; r is the spherical probe radius, delta is the penetration depth, ERFor the relaxation of the modulus, v is the Poisson's ratio, τσIs a constant force time constant, τεIs a constant time constant;
in the case of a tapered probe, the probe,
wherein, F (t) is the interaction force between the probe and the cell; theta is the half-open angle, delta is the penetration depth, ERFor the relaxation of the modulus, v is the Poisson's ratio, τσIs a constant force time constant, τεIs a constant time constant;
the interaction force F (t) between the probe and the cell is divided into two parts, one part being the force F provided by the cytoplasmC(t), the other part is the force F provided by the curvature and surface tension of the cell membraneMI.e. F (t) ═ FM+FC(t); and for three parameters ESEta and DpCarrying out characterization;
in the step (3), for the spherical probe,
wherein, FC(t) force provided by cytoplasm; r is the spherical probe radius, delta is the penetration depth, ESIs the cytoskeletal network modulus, v is the Poisson's ratio, τσIs a constant force time constant, τεIs a constant time constant;
ESis the modulus of the cytoskeletal network of the cytoplasm, η is the apparent viscosity of the cytoplasm, η ═ ES(τσ-τε)；
FM＝2γπδ
Wherein, FMThe force provided by the curvature and surface tension of the cell membrane; gamma is the surface tension and delta is the penetration depth;
wherein F (∞) is the loading force of the AFM probe after stabilization of the relaxation phase, R is the spherical probe radius, δ is the penetration depth, ESIs the cytoskeletal network modulus, v is the Poisson's ratio, τσIs a constant force time constant, τεIs a constant time constant;
in the case of a tapered probe, the probe,
FM＝4γδsinθ
wherein, FMThe force provided by the curvature and surface tension of the cell membrane; gamma is surface tension, pressing depth and theta is half-open angle of the conical probe;
wherein, FC(t) force provided by cytoplasm; theta is the half-open angle of the tapered probe, delta is the penetration depth, ESIs the cytoskeletal network modulus, v is the Poisson's ratio, τσIs a constant force time constant, τεIs a constant time constant;
where F (∞) is the loading force of the AFM probe after the relaxation phase has stabilized, θ is the half-open angle of the tapered probe, δ is the penetration depth, E is the depth of penetrationSIs the cytoskeletal network modulus, v is the Poisson's ratio, τσIs a constant force time constant, τεIs a constant time constant;
in the case of a spherical probe, the probe is,
τ＝Dpt/Rδ
wherein D ispIs the intrinsic diffusion coefficient of the cell sap; r is the radius of the spherical probe, and delta is the pressing depth;
in the case of a tapered probe, the probe,
τ＝Dptπ2/4δ2tan2θ
wherein D ispIs the intrinsic diffusion coefficient of the cell sap; theta is the half-open angle of the conical probe, and delta is the pressing depth;
in the step (4), the step (c),
wherein D ispIs the intrinsic diffusion coefficient of the cell sap; v. ofsIs the poisson's ratio of the dry skeletal network,
is porosity,. kappa.is a constant taking into account the irregularity, connectivity and flexibility of the pores, ESIs the modulus of cytoskeleton network, xi is the pore size of the porous structure of cytoplasm, and mu is the viscosity of cell sap;
wherein η is the apparent viscosity of the cytoplasm; mu is the viscosity of the cell sap, L is the characteristic constant of the skeleton network, and xi is the pore size of the cytoplasmic porous structure;
wherein D ispIs the intrinsic diffusion coefficient of the cell sap; vs is the poisson's ratio of the dry skeleton network,
is the porosity, L is the characteristic constant of the framework network, κ is a constant taking into account the irregularity, connectivity and flexibility of the pores, ESIs the cytoskeletal network modulus, η is the apparent viscosity of the cytoplasm;
then
Wherein α is a structural correlation coefficient.
2. The method according to claim 1, wherein, for the spherical probe, the step (1) comprises: after the probe is contacted with the surface of the single cell by an AFM system, lifting the probe away from the cell to a position 5-7 microns above the surface and standing for 1s, then enabling the probe tip to approach the surface of the cell at a speed of 15-20 microns/s to generate an indentation with a depth of 500-1000 nm, then standing for 5-10 s until a cell force relaxation signal is gradually stabilized, and recording distance, time and acting force data in the whole process;
for a tapered probe, step (1) comprises: after the probe is contacted with the surface of the single cell by an AFM system, lifting the probe away from the cell to a position 5-7 microns above the surface and standing for 1s, then enabling the probe tip to approach the surface of the cell at a speed of 15-20 microns/s, generating an indentation with the depth of 500-1000 nm, then standing for 5-10 s until a cell force relaxation signal is gradually stabilized, and recording distance, time and acting force data of the whole process.
3. The method according to claim 2, wherein the conical probe used in the AFM nanoindentation experiment is a silicon nitride probe with a half-open angle of 18 ° and a force constant of 0.01N/m; the spherical probe is made of silicon nitride with force constant of 0.095N/m, no sharp cantilever and SiO with diameter of 10 μm2AFM probe composed of microspheres.
4. The method of any one of claims 1 to 3, wherein the cell type to which the method is applied is a viable adherent cell with intact membrane structure.
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