CN114112808B - Characterization method of cytoplasmic mechanical properties - Google Patents
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Abstract
The invention provides a characterization method of cytoplasmic mechanical properties, which is a multi-parameter characterization method of cell physical properties of a cellular porous structure by considering the tension effect of a cell membrane, and has a cytoskeletal network modulus E of cytoplasm S Apparent viscosity eta of cytoplasm and intrinsic diffusion coefficient D of cell fluid p Characterization was performed and described in E S Eta and D p The physical characteristics of the cells are visually characterized in the three-dimensional space as a reference. The characterization result of cytoplasm is distributed on the curved surface D, which is proved by both theoretical and experimental data p ＝αE S Near/eta. The method has great promotion effect on the research of single cell mechanics.
Description
Technical Field
The invention relates to nano science and biophysics, in particular to a method for characterizing cytoplasmic mechanical properties.
Background
Existing models for characterizing the physical properties of biological materials such as cells can be broadly classified into linear elastic models, nonlinear elastic models, viscoelastic models, porous medium models, and plastic models. In the process of characterizing physical properties of cells, only one or several parameters of the cells are often concerned and numerical distributions are respectively given, but the description method cannot intuitively characterize the comprehensive properties of the cells.
(1) Acquisition of cell force relaxation curves for analysis of cell mesoporous elasticity
As shown in FIG. 1, the AFM probe was allowed to apply a force of about 3.5-6nN to the cells for about 35ms and to generate a penetration depth of about 1 μm for a period of time, and the changes in penetration depth and loading force during this process were collected to obtain the force relaxation curve shown in FIG. 2.
As shown in FIG. 2, during the force relaxation, the loading force of the AFM probe is reduced by about 35%, while the indentation depth is increased by only less than 5%. This means that this process is almost a constant strain process. The Moeendarbary E et al used the method described above to obtain force curves using a JPK Nanowizard-I atomic force microscope and performed mesoporous elastic analysis by MATLAB.
(2) Mesoporous elastic theory
Based on the previous study, moeendarbary E et al (Moeendarbary E, valon L, fritzsche M, et al cytoplasm of living cells behaves as a poroelastic material [ J ]. Nat Mater,2013,12 (3): 253-61) set the theory of mesoporous elasticity when a spherical probe acts on cells.
The force profile during the relaxation phase satisfies the following formula:
wherein τ=d p t/Rδ。F i Is the magnitude of the force at the beginning of the relaxation phase, F f Is the force magnitude at the end of the relaxation phase, and F (t) is the force magnitude at the time t of the relaxation phase. D (D) p Is the intrinsic diffusion coefficient of the cell, R is the radius of the sphere probe, and δ is the depth of indentation. Fitting the above formula with force relaxation curve to obtain intrinsic diffusion coefficient D of cell p This is also the most important parameter of the mesoporous elastic model.
Hu Y et al give the mesoporous elastic model force relaxation equation for differently shaped probes according to AFM experiments on hydrogels (Hu Y, zhao X, vlassak J J, et al using indentation to characterize the poroelasticity of gels [ J ]. Appl Phys Lett,2011,96 (12): 37). In the case of a tapered probe pin,
τ＝D p tπ 2 /4δ 2 tan 2 θ
where θ is the half-open angle of the tapered probe.
Similarly, the force relaxation curve of the tapered probe is fitted to the corresponding equation to obtain the intrinsic cell diffusion coefficient D when the probe is tapered p 。
The mesoporous elastic theory is that cells are regarded as a liquid-containing porous medium structure consisting of a solid skeleton network and cell liquid filled in the solid skeleton network. Moeendarbary E et al gives the following formula on this basis:
wherein E is C Is the elastic modulus of the solid skeleton network, zeta is the pore size of the porous structure, and mu is the viscosity of the cell sap.
(3) Cell fluid viscosity
Darling E M et al treat cells as viscoelastic materials and give an expression for the force relaxation curve of the spherical probe (Darling E M, zauscher S, guilak F. Viscoelastics properties of zonal articular chondrocytes measured by atomic force microscopy [ J ]. Osteoarthritis Cartilage,2006,14 (6): 571-9):
wherein F is the interaction force between the probe and the cell, delta is the indentation depth, delta 0 Is the depth of indentation at the beginning of the relaxation phase (i.e. at t=0), E R For the relaxation modulus, v is the Poisson's ratio (as per Moeendarbary E et al, 0.3 should be taken), τ σ And τ σ The constant force and the constant change relaxation time constants, respectively, are obtained by analyzing the force relaxation curve obtained by the method of "(1) obtaining a cell force relaxation curve for analyzing cell mesoporous elasticity" by the above formula, and E can be obtained R ，τ σ And τ σ Is a value of (2). Whereas the apparent viscosity η of a cell may be based on η=e R (τ σ -τ σ ) Obtained.
Moeendarbary E et al believe that there is a relationship between the apparent cell viscosity η and the cell fluid viscosity μ as follows:
where L is the characteristic constant of the backbone network.
(4) Young's modulus of cells
Young's modulus of cellsObtained from the well-known Hertz model (Hertz H. Ueberdie Beru hrung fester elastischer)[J]Journal Tu r Die Reine Und Angewandte Mathematik,2006,1882 (92): 156-71). The Hertz model treats cells as pure elastomers, and thus only focuses on the force profile of the cell during the needle insertion phase.
According to the Hertz elastic indentation theory, when the probe is spherical, the following relationship exists between the loading force and the indentation depth:
wherein R is the radius of the spherical probe.
When the probe is tapered, there is a relationship between loading force and indentation depth as follows:
in the prior art, the cell is regarded as a porous medium structure as a whole in the process of measuring the mesoporous elastic characteristics of the cell, and the effect of the cell membrane and the influence of the cell membrane on the cell are not considered.
In the course of apparent viscosity measurement of cells, darling E M et al only gives quantitative solutions for spherical probes, but does not give corresponding analytical formulae for conical probes, and the derivation process of Darling E M et al has a careless leak and needs to be re-derived.
For each parameter involved in the cell model, previous studies often only give solutions for each parameter, and the interrelation between them is not intuitively presented.
Disclosure of Invention
The invention aims to provide a method for characterizing cytoplasmic mechanical properties, which combines a cell membrane tension model with a cytoplasmic porous medium model, characterizes physical properties of cytoplasm by utilizing an atomic force microscope, and presents the physical properties of cytoplasm in a three-dimensional space in a three-dimensional visual way.
In order to achieve the object of the invention, the invention provides a method for characterizing cytoplasmic mechanical properties, which comprises the following steps:
(1) Obtaining single cell force relaxation signal data based on an AFM nanoindentation experiment;
(2) Calculating the interaction force F (t) between the AFM probe and the cell under a viscoelastic model;
(3) Cytoskeletal network modulus E for cytoplasm S Apparent viscosity eta of cytoplasm and intrinsic diffusion coefficient D of cell fluid p Three parameters are characterized;
(4) Using three parameters E in step (3) S Eta and D p The cytoplasmic mechanical properties were characterized.
In the step (2) for the spherical probe,
wherein F (t) represents the interaction force between the probe and the cell at time t of the relaxation phase; r is the radius of the spherical probe, delta is the pressing depth, E R For the relaxation modulus, v is poisson's ratio, τ σ Is a constant force time constant, τ ε Is a constant time constant;
in the case of a tapered probe pin,
wherein F (t) is the interaction force between the probe and the cell; θ is half open angle, δ is press depth, E R For the relaxation modulus, v is poisson's ratio, τ σ Is a constant force time constant, τ ε Is a constant time constant;
dividing the interaction force F (t) between the probe and the cell into two parts, one part being the force F provided by the cytoplasm C (t) the other part is the force F provided by the curvature of the cell membrane and the surface tension M I.e. F (t) =f M +F C (t); and for three parameters E S Eta and D p Characterizing;
in the step (3) for the spherical probe,
wherein F is C (t) a force provided by the cytoplasm; r is the radius of the spherical probe, delta is the pressing depth, E S Is the network modulus of the cytoskeleton, v is the Poisson's ratio, τ σ Is a constant force time constant, τ ε Is a constant time constant;
E S is the cytoskeletal network modulus of the cytoplasm, η is the apparent viscosity of the cytoplasm, η=e S (τ σ -τ ε )；
F M ＝2γπδ
Wherein F is M Force provided by curvature of cell membrane and surface tension; gamma is the surface tension and delta is the indentation depth;
wherein F (++) is the loading force of the AFM probe after the relaxation stage is stable, R is the spherical probe radius, δ is the indentation depth, E S Is the network modulus of the cytoskeleton, v is the Poisson's ratio, τ σ Is a constant force time constant, τ ε Is a constant time constant;
in the case of a tapered probe pin,
F M ＝4γδsinθ
wherein F is M Force provided by curvature of cell membrane and surface tension; gamma is surface tension, is pressing depth, and theta is half open angle of the conical probe;
wherein F is C (t) a force provided by the cytoplasm; θ is the half-open angle of the conical probe, δ is the depth of penetration, E S Is the network modulus of the cytoskeleton, v is the Poisson's ratio, τ σ Is a constant force time constant, τ ε Is a constant time constant;
wherein F (++) is the loading force of the AFM probe after the relaxation stage is stable, θ is the half-open angle of the tapered probe, δ is the indentation depth, E S Is the network modulus of the cytoskeleton, v is the Poisson's ratio, τ σ Is a constant force time constant, τ ε Is a constant time constant;
in the case of a ball-shaped probe,
τ＝D p t/Rδ
wherein D is p Is the intrinsic diffusion coefficient of the cell fluid; r is the radius of the spherical probe, and delta is the pressing depth;
in the case of a tapered probe pin,
τ＝D p tπ 2 /4δ 2 tan 2 θ
wherein D is p Is the intrinsic diffusion coefficient of the cell fluid; θ is the half-open angle of the conical probe, and δ is the press-in depth;
in the step (4), the step of (c),
wherein D is p Is the intrinsic diffusion coefficient of the cell fluid; v s Is the poisson's ratio of the dry skeletal network,is porosity, κ is a constant taking into account pore irregularities, connectivity and bendability, E S Is the network modulus of the cytoskeleton, xi is the pore size of the porous structure of the cytoplasm, and mu is the viscosity of the 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 porous structure of the cytoplasm;
then
Wherein D is p Is the intrinsic diffusion coefficient of the cell fluid; v s Is the poisson's ratio of the dry skeletal network,is the porosity, L is the characteristic constant of the backbone network, κ is a constant taking into account pore irregularities, connectivity and bendability, E S Is the network modulus of the cytoskeleton, eta is the apparent viscosity of the cytoplasm,
then
Wherein α is a structural correlation coefficient.
Further, for a sphere probe, step (1) includes: after the AFM system brought the probe into contact with the single cell surface, the probe was lifted off the cell to 5-7 μm above the surface and allowed to stand for 1s, then the AFM probe tip was brought close to the cell surface at a rate of 15-20 μm/s, producing indentations with a depth of 500-1000 nm, and then allowed to stand for 5-10 s until the cell force relaxation signal was gradually stabilized, and the distance, time and force data of the whole process were recorded. Preferably, after the AFM system has brought the probe into contact with the single cell surface, the probe is lifted off the cell to 7 μm above the surface and allowed to stand for 1s, after which the AFM probe tip is brought into proximity to the cell surface at a rate of 20 μm/s, making indentations with a depth of 500nm, and then allowed to stand for 5s until the cell force relaxation signal becomes gradually stable, and the distance, time and force data for the entire process are recorded.
For a tapered probe, step (1) includes: after the AFM system brought the probe into contact with the single cell surface, the probe was lifted off the cell to 5-7 μm above the surface and allowed to stand for 1s, then the AFM probe tip was brought close to the cell surface at a rate of 15-20 μm/s, producing indentations with a depth of 500-1000 nm, and then allowed to stand for 5-10 s until the cell force relaxation signal was gradually stabilized, and the distance, time and force data of the whole process were recorded.
In the invention, a conical probe used in an AFM nanoindentation 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 prepared from silicon nitride needleless cantilever (TL-CONT, nanosensors) with force constant of 0.095N/m and SiO with diameter of 10 μm 2 AFM probe composed of microsphere.
The cell types for which the method is applicable are living adherent cells having an intact membrane structure.
By means of the technical scheme, the invention has at least the following advantages and beneficial effects:
the invention relates to a new method for three-dimensional space characterization of physical properties of cytoplasm by utilizing an atomic force microscope, which relates three physical parameters of cells in three-dimensional space through coefficients under the premise of considering cell membrane action, thus realizing the display of visual three-dimensional space distribution of physical properties of cytoplasm for the first time.
The method can intuitively perform three-dimensional characterization on physical characteristics of the cells. At E S Eta and D p The physical characteristics of the cells are intuitively displayed in a three-dimensional space formed by three basic dimensions. Meanwhile, unlike the previous method for characterizing the mesoporous elasticity of the cells, the method not only regards the cells as porous media, but also considers the effect of cell membranes in the process of characterizing the mesoporous elastic mechanical properties of the cells. On the basis, the physical characteristics of cytoplasm can be more accurately represented, and the method has great promotion effect on the study of single cell mechanics.
Based on the porous medium model containing liquid, the invention considers the intrinsic structure of cells, and firstly provides a method for intuitively characterizing the physical properties of cytoplasm in a three-dimensional space. By using 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 more intuitively given.
And thirdly, the invention considers the functions of cell membrane tension and cytoplasmic mesoporous elasticity, and can deduce each parameter related to the cytoplasmic mesoporous elasticity by utilizing a corresponding physical model, thereby realizing multi-parameter three-dimensional space characterization of cytoplasmic mechanical properties.
Drawings
FIG. 1 is a flow chart of a prior AFM acquisition force relaxation curve. Wherein, (I) is the stage of probe needle insertion, (II) is the stage of probe force relaxation, and (IV) is the state after probe and cell force are stable.
FIG. 2 is a graph showing the prior art force relaxation curve and mesoporous elasticity analysis. Wherein, (I) is a graph of normalized indentation depth and force variation with time, and (II) is a fitting analysis of force relaxation curve by using mesoporous elastic model.
FIG. 3 is a flow chart illustrating the AFM force curve acquisition in a preferred embodiment of the invention.
FIG. 4 is a schematic representation of the 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 the clustering analysis of cells by the method of the present invention with the conventional method. Wherein a is a clustering analysis result of the method; b is the result of traditional mesoporous elastic clustering analysis without considering the action of cell membranes.
Detailed Description
The following examples are illustrative of the invention and are not intended to limit the scope of the invention. Unless otherwise indicated, the technical means used in the examples are conventional means well known to those skilled in the art, and all raw materials used are commercially available.
The AFM system used in the examples below was an AFM (Agilent 5500) system with an inverted fluorescence microscope (Nikon Eclipse Ti) available from Agilent corporation.
Example 1 method for three-dimensional spatial characterization of physical properties of cytoplasm using atomic force microscope
1. AFM nanoindentation experiment and acquisition/acquisition of force relaxation curve
As shown in FIG. 3, taking 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 allowed to stand for 1s, after which the AFM probe tip was brought into proximity with the cell surface at a rate of 20 μm/s, making an indentation with a depth of about 500nm, followed by allowing to stand for 5s until the force relaxation signal was gradually stabilized. Distance, time and force data of the whole process are recorded.
In fig. 3, the whole curve comprises four phases: a needle withdrawal stage, a standing stage, a needle insertion stage and a relaxation stage. The probe is first moved from Z 0 At position T 1 Elevation d in time 0 Distance to Z 1 Position, makeThe probe and the cell transition from a contacted state to a separated state. Then let the probe at Z 1 Position standing T 2 And (5) time, the cells are restored to the normal state as much as possible. Subsequently, the probe is controlled from Z 1 At position T 3 Drop d in time 1 Height reaches Z 2 The position is such that a certain depth of impression is produced, this needle insertion speed being typically above 10 μm/s. Finally, the probe is set at Z 2 Position holding T 4 The relaxation of the force was observed until the AFM loading force was almost completely stabilized.
2. Re-derivation of viscoelastic formulas
The basic equation for elasticity is:
σ＝2E(T)ε
σ＝2G(t)(1+v)ε
converting it into the laplace domain:
the basic equation for viscoelasticity is:
converting it into the laplace domain:
there is a case where the number of the group,
due to the shear modulus G and Young's modulus E Y There is a relationship between:
the young's modulus in the laplace domain can thus be described as:
in this example, as observed by Emoeendarbary E et al, the degree of strain change is much less during the relaxation experiments in which AFM acts on cells. Thus, this process can be approximated as a constant-change process.
During stress relaxation (constant condition), F (t) is represented by the Heaviside step-over function H (t):
in the case of a ball-shaped probe,
in the case of a tapered probe pin,
turning it to the Laplace domain is:
in the case of a ball-shaped probe,
in the case of a tapered probe pin,
and then respectively converting the two into time domain space, wherein the following steps are as follows:
in the case of a ball-shaped probe,
wherein F (t) represents the interaction force between the probe and the cell at time t of the relaxation phase; r is the radius of the spherical probe, delta is the pressing depth, E R For the relaxation modulus, v is poisson's ratio, τ σ Is a constant force time constant, τ ε Is a constant time constant;
in the case of a tapered probe pin,
wherein F (t) is the interaction force between the probe and the cell; θ is half open angle, δ is press depth, E R For the relaxation modulus, v is poisson's ratio, τ σ Is a constant force time constant, τ ε Is a constant time constant;
respectively correspond to the expressions of the force change of the spherical probe and the conical probe with time under the viscoelastic model.
3. Characterization of cytoskeletal network modulus and apparent cytoplasmic viscosity taking into account membrane tension
Considering the influence of membrane tension, the force acting on the probe (i.e. the interaction force between the probe and the cell) can be broken down into two parts F, one part being the force F provided by the cytoplasm C (t) the other part is the force F provided by the curvature of the cell membrane and the surface tension M . In this process, cell membrane tension is considered constant because of F M Is constant. And F provided by cytoplasm C (t) may change over time during relaxation.
Based on the theoretical results of Darling et al, the force relaxation curve formula after the cytoplasm is indented by the sphere probe is deduced:
wherein F is C (t) a force provided by the cytoplasm; r is the radius of the spherical probe, delta is the pressing depth, E S Is the network modulus of the cytoskeleton, v is the Poisson's ratio, τ σ Is a constant force time constant, τ ε Is a constant time constant;
E S for the elastic modulus of the cytoskeletal network, apparent viscosity η=e S (τ σ -τ ε )。
F M ＝2γπδ
Wherein F is M Force provided by curvature of cell membrane and surface tension; gamma is the surface tension and delta is the indentation depth;
wherein F (++) is the loading force of the AFM probe after the relaxation stage is stable, R is the spherical probe radius, δ is the indentation depth, E S Is the network modulus of the cytoskeleton, v is the Poisson's ratio, τ σ Is a constant force time constant, τ ε Is a constant time constant;
fitting the above with the force relaxation curve to obtain E S ，τ σ And τ ε Is a value of (2).
Similarly, for a tapered probe,
F M ＝4γδsinθ
wherein F is M Force provided by curvature of cell membrane and surface tension; gamma is surface tension, is pressing depth, and theta is half open angle of the conical probe;
wherein F is C (t) a force provided by the cytoplasm; θ is the half-open angle of the conical probe, δ is the depth of penetration, E S Is the network modulus of the cytoskeleton, v is the Poisson's ratio, τ σ Is a constant force time constant, τ ε Is a constant time constant;
wherein F (++) is the loading force of the AFM probe after the relaxation stage is stable, θ is the half-open angle of the tapered probe, δ is the indentation depth, E S Is the network modulus of the cytoskeleton, v is the Poisson's ratio, τ σ Is a constant force time constant, τ ε Is a constant time constant;
fitting the above with force curve to obtain E S ，τ σ And τ ε Is a value of (2). According to the formula η=e S (τ σ -τ ε ) The value of apparent viscosity can also be obtained.
4. Characterization of intrinsic diffusion coefficient of cell sap
As previously mentioned, if a cell is considered as a structure of a liquid-containing porous medium surrounded by a cell membrane, then the theory of mesoporous elasticity is applicable only to the cytoplasm and should not contain the cell membrane. Thus, there should be the following mechanical relationship for the cytoplasm:
in the case of a ball-shaped probe,
τ＝D p t/Rδ
wherein D is p Is the intrinsic diffusion coefficient of the cell fluid; r is the radius of the spherical probe, deltaIs the pressing depth;
similarly, for a tapered probe,
τ＝D p tπ 2 /4δ 2 tan 2 θ
wherein D is p Is the intrinsic diffusion coefficient of the cell fluid; θ is the half-open angle of the conical probe, and δ is the press-in depth;
5. three-dimensional spatial characterization of cytoplasmic physical properties
According to the above-described experiment and analysis method, D can be obtained p η and E s Is a value of (2). According to the theory of porous media:
wherein D is p Is the intrinsic diffusion coefficient of the cell fluid; v s Is the poisson's ratio of the dry skeletal network,is porosity, κ is a constant taking into account pore irregularities, connectivity and bendability, E S Is the network modulus of the cytoskeleton, xi is the pore size of the porous structure of the cytoplasm, and mu is the viscosity of the 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 porous structure of the cytoplasm;
then
Wherein D is p Is the intrinsic diffusion coefficient of the cell fluid; v s Is the poisson's ratio of the dry skeletal network,is the porosity, L is the characteristic constant of the backbone network, κ is a constant taking into account pore irregularities, connectivity and bendability, E S Is the network modulus of the cytoskeleton, eta is the apparent viscosity of the cytoplasm,
then
We refer to α as the structure correlation coefficient.
The above determines, η and D p Three parameters are spatially distributed on the curved surface D p ＝αE s Around/η, the physical properties of the cytoplasm can be intuitively characterized.
FIG. 4 is a schematic diagram of a three-dimensional visual characterization of the physical properties of the cytoplasm, giving a three-dimensional scattergram of a multi-parameter characterization of the cytomechanics, giving a corresponding fitted surface D p ＝αE S And/η, a curved surface-scatter plot of the multi-parameter characterization of the cell mechanics is given. The value of alpha determines the distribution position of the three-dimensional curved surface in space, and the measured value of each parameter determines the specific range of the distribution of a certain cell mechanical parameter in three-dimensional space. In the invention, E is S And η "average ± standard deviation" as a constraint condition of the distribution range of the curved surface.
The method can intuitively perform three-dimensional characterization on physical characteristics of the cells. At E S Eta and D p The physical characteristics of the cells are intuitively displayed in a three-dimensional space formed by three basic dimensions. Meanwhile, unlike the previous method for characterizing the mesoporous elasticity of cells, the cell is not only regarded as a porous medium, but also the effect of a cell membrane in the process of characterizing the mesoporous elastic mechanical property of the cells is considered. On the basis, the physical characteristics of cytoplasm can be more accurately represented, and the research on single-cell mechanics is greatly promoted.
It is a great innovation of the present invention to characterize the mesoporous elastic properties of cells in view of the role of the cell membrane therein. Another innovation point 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 a great promotion effect on the mechanical characterization of single cells.
The conventional mesoporous elasticity has a disadvantage in that the effect of the cell membrane is not considered, and the whole cell is regarded as a porous medium. The invention originally distinguishes cytoplasm from cell membranes, and on the basis, cells are regarded as porous media materials of membrane encapsulation. As shown in fig. 5, 15 cells were selected, and these 15 cell lines were divided into 9 normal cells, i.e., DCs (mouse bone marrow derived dendritic cells); 3T3 (mouse embryonic fibroblasts); l929 (mouse fibroblasts); RCFB (rabbit eye corneal fibroblasts, rabbit eye corneal fibroblast); PTMC (porcine trabecular meshwork epithelial cells, porcine trabecular meshwork cell); LSEC (liver sinus endothelial cells, 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 mammary cancer cells); 4T1 (mouse breast cancer cells); HELA (human cervical cancer cells); CASKI (human cervical cancer 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 porous medium structure of the present invention, which regards cells as membrane-coated cells, can correctly classify these 15 cells into two groups (normal cell group and cancer cell group), whereas the conventional method, which regards cells as porous medium structure as a whole, can misclassify part of cells (HELA, DC and NRK are misclassify) during classification.
While the invention has been described in detail in the foregoing general description and with reference to specific embodiments thereof, it will be apparent to one skilled in the art that modifications and improvements can be made thereto. Accordingly, such modifications or improvements may be made without departing from the spirit of the invention and are intended to be within the scope of the invention as claimed.
Claims (4)
1. A method for characterizing cytoplasmic mechanical properties, comprising the steps of:
(1) Obtaining single cell force relaxation signal data based on an AFM nanoindentation experiment;
(2) Calculating the interaction force F (t) between the AFM probe and the cell under a viscoelastic model;
(3) Cytoskeletal network modulus E for cytoplasm S Apparent viscosity eta of cytoplasm and intrinsic diffusion coefficient D of cell fluid p Three parameters are characterized;
(4) Using three parameters E in step (3) S Eta and D p Characterizing the mechanical properties of cytoplasm;
in the step (2) for the spherical probe,
wherein F (t) represents the interaction force between the probe and the cell at time t of the relaxation phase; r is the radius of the spherical probe, delta is the pressing depth, E R For the relaxation modulus, v is poisson's ratio, τ σ Is a constant force time constant, τ ε Is a constant time constant;
in the case of a tapered probe pin,
wherein F (t) is the interaction force between the probe and the cell; θ is half open angle, δ is press depth, E R For the relaxation modulus, v is poisson's ratio, τ σ Is a constant force time constant, τ ε Is a constant time constant;
dividing the interaction force F (t) between the probe and the cell into two parts, one part being the force F provided by the cytoplasm C (t) the other part is the force F provided by the curvature of the cell membrane and the surface tension M I.e. F (t) =f M +F C (t); and for three parameters E S Eta and D p Characterizing;
in the step (3) for the spherical probe,
wherein F is C (t) a force provided by the cytoplasm; r is the radius of the spherical probe, delta is the pressing depth, E S Is the network modulus of the cytoskeleton, v is the Poisson's ratio, τ σ Is a constant force time constant, τ ε Is a constant time constant;
E S is the cytoskeletal network modulus of the cytoplasm, η is the apparent viscosity of the cytoplasm, η=e S (τ σ -τ ε )；
F M ＝2γπδ
Wherein F is M Force provided by curvature of cell membrane and surface tension; gamma is the surface tension and delta is the indentation depth;
wherein F (+) is after the relaxation stage is stableThe loading force of the AFM probe, R is the radius of the spherical probe, delta is the pressing depth, E S Is the network modulus of the cytoskeleton, v is the Poisson's ratio, τ σ Is a constant force time constant, τ ε Is a constant time constant;
in the case of a tapered probe pin,
F M ＝4γδsinθ
wherein F is M Force provided by curvature of cell membrane and surface tension; gamma is surface tension, is pressing depth, and theta is half open angle of the conical probe;
wherein F is C (t) a force provided by the cytoplasm; θ is the half-open angle of the conical probe, δ is the depth of penetration, E S Is the network modulus of the cytoskeleton, v is the Poisson's ratio, τ σ Is a constant force time constant, τ ε Is a constant time constant;
wherein F (++) is the loading force of the AFM probe after the relaxation stage is stable, θ is the half-open angle of the tapered probe, δ is the indentation depth, E S Is the network modulus of the cytoskeleton, v is the Poisson's ratio, τ σ Is a constant force time constant, τ ε Is a constant time constant;
in the case of a ball-shaped probe,
τ＝D p t/Rδ
wherein D is p Is the intrinsic diffusion coefficient of the cell fluid; r is the radius of the spherical probe, and delta is the pressing depth;
in the case of a tapered probe pin,
τ＝D p tπ 2 /4δ 2 tan 2 θ
wherein D is p Is the intrinsic diffusion coefficient of the cell fluid; θ is the half-open angle of the conical probe, and δ is the press-in depth;
in the step (4), the step of (c),
wherein D is p Is the intrinsic diffusion coefficient of the cell fluid; v s Is the poisson's ratio of the dry skeletal network,is porosity, κ is a constant taking into account pore irregularities, connectivity and bendability, E S Is the network modulus of the cytoskeleton, xi is the pore size of the porous structure of the cytoplasm, and mu is the viscosity of the 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 porous structure of the cytoplasm;
wherein D is p Is the intrinsic diffusion coefficient of the cell fluid; vs is the poisson's ratio of the dry skeletal network,is the porosity, L is the characteristic constant of the backbone network, κ is a constant taking into account pore irregularities, connectivity and bendability, E S Is the cytoskeletal network modulus, η is the apparent viscosity of the cytoplasm;
then
Wherein α is a structural correlation coefficient.
2. The method of claim 1, wherein for a sphere probe, step (1) comprises: after the AFM system makes the probe contact with the surface of single cell, the probe is lifted from the cell to 5-7 mu m above the surface and kept stand for 1s, then the tip of the probe is made to approach the surface of the cell at a speed of 15-20 mu m/s to generate an indentation with a depth of 500-1000 nm, and then kept stand for 5-10 s until the relaxation signal of the cell force is gradually stabilized, and the distance, time and acting force data of the whole process are recorded;
for a tapered probe, step (1) includes: after the AFM system brought the probe into contact with the single cell surface, the probe was lifted off the cell to 5-7 μm above the surface and allowed to stand for 1s, then the probe tip was brought into proximity with the cell surface at a rate of 15-20 μm/s, an indentation was produced with a depth of 500-1000 nm, and then allowed to stand for 5-10 s until the cell force relaxation signal was gradually stabilized, and the distance, time and force data of the whole process were recorded.
3. The method according to claim 2, wherein the conical probe used in the AFM nanoindentation test is a silicon nitride probe 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 needleless cantilever with a force constant of 0.095N/m and SiO with a diameter of 10 μm 2 AFM probe composed of microsphere.
4. A method according to any one of claims 1 to 3, wherein the cell type to which the method is applicable is a living adherent cell having an intact membrane structure.
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