A method for constructing a cell nucleus model based on abaqus-python

Abstract

This invention discloses a method for constructing a cell nucleus model based on Abaqus-Python, relating to the field of cell stress analysis technology. This method utilizes Abaqus finite element software to draw a cell nucleus model and analyze its mechanical properties. Simultaneously, it employs Python for secondary development, simplifying the model drawing process through scripting and improving the efficiency and accuracy of model creation. This model can be used to calculate the stress distribution of the cell nucleus's main structures—the nuclear membrane and nuclear lamina—during the process of nanoneedles penetrating the cell nucleus, and to optimize nanoneedle parameters by analyzing the stress concentration of the nuclear membrane during penetration.

Description

Technical Field

[0001] This invention relates to the field of cell stress analysis technology, specifically to a method for constructing a cell nucleus model based on abaqus-python and its mechanical analysis. Background Technology

[0002] Gene delivery is a technique that introduces exogenous DNA into cells, and it can be used in gene therapy, cell reprogramming, vaccine development, and other fields. Currently, many gene delivery technologies have been developed, such as chemical transfection, electroporation, and virus-mediated delivery. However, these technologies have many limitations, such as low efficiency, cytotoxicity, and DNA damage. In recent years, nanoneedle insertion into the cell nucleus has gradually become an emerging gene delivery technology. Nanoneedles are nanostructures composed of nanoscale channels that can directly inject exogenous DNA into the cell nucleus without damaging the cell. Nanoneedles have advantages such as high efficiency, selectivity, and safety, and therefore have broad application prospects in gene therapy, cell reprogramming, and other fields. Gene delivery and nanoneedle insertion into the cell nucleus provide researchers with a promising tool that is expected to make significant contributions to disease treatment and improving the level of biological research. However, currently, commercially available nanoprobes only achieve a 30% penetration rate into the cell nuclear membrane. This invention can analyze the stress distribution in the cell nucleus during nanoneedle insertion through simulation, optimize nanoneedle parameters, and promote nanoneedle insertion.

[0003] In 2009, Cheng Qin et al. from Chongqing University constructed a three-dimensional cell model subjected to shear force using the finite element method (FEM) platform, analyzing the stress relaxation of a single cell at different locations. The cell nucleus was analyzed as a single cell component. Most FEM models treat the cell nucleus as a whole, ignoring its internal structure. In 2021, Khunsaraki et al. discretized the nuclear skeleton, establishing a tensile overall structure of the cell and simplifying the nuclear lamina as beams, reflecting its supporting structural function. However, they neglected parameters such as type and density, failing to analyze the influence of different nuclear lamina structures on the mechanical properties of the cell nucleus. Most existing finite element models of the cell nucleus can only analyze the stress distribution under small-scale deformation. However, the cell nucleus undergoes significant deformation during nanoneedle insertion. Therefore, this invention proposes a multi-structure finite element model of the cell nucleus that can represent the orthogonal network characteristics of the nuclear lamina and produce large deformations. This model can be used to analyze the stress concentration of the nuclear membrane during nanoneedle insertion and optimize nanoneedle parameters. Summary of the Invention

[0004] The purpose of this invention is to provide a method for constructing cell nucleus models based on abaqus-python, analyze the mechanical properties of cell nuclei, and determine the optimal needle insertion speed and probe thickness for various cell nuclei.

[0005] The technical solution of this invention is: a method for constructing a cell nucleus model based on abaqus-python, comprising the following steps:

[0006] Step 1: Based on the mechanical properties of the cell nucleus, the cell nucleus structure is divided into four parts, from the outside to the inside: nuclear membrane, nuclear lamina A, nuclear lamina B, and nucleoplasm. Nuclear lamina A and nuclear lamina B together form the nuclear lamina, which are independent networks connected by linker proteins. Based on the actual dimensions, geometric models of each part of the cell nucleus are created in the part module of the ABAQUS software and assembled according to their positional distribution. A rigid plane is created to represent a glass slide, which is tangent to the bottom of the cell nucleus model. Simultaneously, nanoneedles of different sizes are created to achieve the insertion action.

[0007] Step 1.1: Create the nuclear membrane;

[0008] A hollow sphere with an inner diameter of 2500 nm and an outer diameter of 2550 nm was used as the core membrane;

[0009] Step 1.2: Create the core fiber layer;

[0010] Orthogonal network thin layers are used as core fiber layers. The radius of core fiber layer A is 2450 nm and the spacing of the orthogonal network fibers is 150 nm; the radius of core fiber layer B is 2500 nm and the spacing of the orthogonal network fibers is 250 nm.

[0011] Step 1.3: Create the glass slide and nanoneedles;

[0012] The shapes of the glass slide and nanoneedles are created according to their actual shapes. The nanoneedles are 1 to 2 micrometers long and 50 to 400 nanometers in diameter. The glass slide is a disk with a radius of 5000 nm and a thickness of 50 nm.

[0013] Step 2: Based on the material properties of the cell nucleus's mechanical structure, create material and cross-sectional properties for the nuclear membrane and nuclear lamina;

[0014] Step 3: Assemble according to the position of each component: The cell nucleus part consists of nuclear lamina A, nuclear lamina B, and nuclear membrane from the inside out, and the three are assembled concentrically; the glass slide is located below the cell nucleus, and the upper surface of the glass slide is in contact with the bottom of the nuclear membrane; the nanoneedles are vertically located above the cell nucleus, and the distance between the needle tip and the upper surface of the nuclear membrane is set as needed, here it is set to 100nm;

[0015] Step 4: Define the analysis step in abaqus-python, set it to a dynamic display analysis step, and set the analysis step duration to 0.15s;

[0016] Step 5: Define the interaction relationships between the components, including: using connectors to represent the connection between the nuclear membrane and nuclear fiber layer A or nuclear fiber layer B, with hinges between nodes; the nucleus and cytoplasm are represented by fluid cavities in the interaction;

[0017] Define the surface-to-surface interaction between the base of the cell nucleus and the rigid glass slide, and the surface-to-surface interaction between the tip surface of the nanoneedle and the contact surface of the nuclear membrane;

[0018] Step 6: Add loads and boundary conditions to the three-dimensional finite element model of the cell nucleus mechanical structure. Here, the glass slide is fixed and displacement load is applied to the nanoneedle to simulate the needle insertion process.

[0019] Step 7: Divide the cell nucleus into a grid, where the nuclear membrane is a solid unit, nuclear fiber layer B is a beam unit, nuclear fiber layer A is a truss unit, and the glass slide and nanoneedles are discrete rigid units.

[0020] Step 8: Select double precision to perform mechanical response calculations on the cell nucleus's mechanical structure.

[0021] Based on the Abaqus finite element software, the model includes structures such as the nuclear membrane, nuclear lamina A, nuclear lamina B, and nucleoplasm. The nucleoplasm is represented by fluid cavities with interactions, the nuclear membrane is a solid, nuclear lamina B is a beam, and nuclear lamina A is a truss. Therefore, the model has the ability to analyze the mechanical properties of specific structures, such as the stress distribution of the nuclear membrane or nuclear lamina.

[0022] Python-based parametric modeling enables rapid modeling and batch connections, improving modeling efficiency and accuracy.

[0023] The structures of nuclear layer A and nuclear layer B are orthogonal, and their discretization model is closer to the real structure of the nuclear layer. Furthermore, the discretization model can be used to analyze the influence of the density of the nuclear layer on the mechanical properties of the nuclear membrane.

[0024] This model can be used to analyze the influence of nanoneedle parameters (such as nanoneedle diameter and nanoneedle insertion rate) on the stress distribution of the cell nucleus, and optimize the nanoneedle parameters through simulation results to improve the efficiency of nanoneedle insertion into the cell nucleus. Attached Figure Description

[0025] Figure 1 To model the overall process flow;

[0026] Figure 2 Flowchart for building a geometric model using a Python script;

[0027] Figure 3 Flowchart for batch building of Python script connectors;

[0028] Figure 4This is a Python script with a GUI interface.

[0029] Figure 5 This is a diagram of the nuclear membrane structure.

[0030] Figure 6 Diagram of the core fiber layer construction process;

[0031] Figure 7 This is the overall assembly drawing;

[0032] Figure 8 Fluorescent images of nanoneedles penetrating the cell nucleus in situ;

[0033] Figure 9 Displacement contour maps of the whole and its components. (a) Overall displacement contour map; (b) Overall displacement contour map of the nuclear membrane; (c) Displacement contour map of nuclear layer B; (d) Displacement contour map of nuclear layer A;

[0034] Figure 10 Stress cloud diagrams for the whole system and its components. (a) Overall stress cloud diagram; (b) Core membrane stress cloud diagram; (c) Core fiber layer stress cloud diagram;

[0035] Figure 11 The diagram shows the stress distribution of the nuclear membrane under different needle tip diameters;

[0036] Figure 12 The distribution of nuclear membrane stress along the path under different needle tip diameters;

[0037] Figure 13 The distribution of nuclear membrane stress along the path under different needle tip velocities;

[0038] Figure 14 The diagram shows the displacement deformation under different needle tip diameters (left) and the nuclear membrane stress distribution (right).

[0039] Specific implementation steps

[0040] This method utilizes Abaqus finite element software to construct a mouse bone marrow mesenchymal stem cell nucleus model and analyze its mechanical properties. Furthermore, it employs Python for secondary development, simplifying the model construction process through scripts and improving its efficiency and accuracy. This model can be used to calculate the stress distribution of the main structures of the nucleus—the nuclear membrane and nuclear lamina—during the insertion of nanoneedles into the cell nucleus. The stress concentration of the nuclear membrane during insertion is used to optimize the nanoneedle parameters. 1. Model Construction and Material Settings: As shown in the overall modeling flowchart, the construction of the geometric model and material settings can be achieved through Python script one. Therefore, in operation, only script one needs to be run, and the corresponding parameters input in the GUI interface. The GUI interface of script one is shown below. Figure 4 As shown, the flowchart for this step is as follows: Figure 2As shown, the specific operations implemented in the script are as follows: Open the ABAQUS software, and in the part module, create components based on the actual dimensions of each structure of the cell nucleus insertion model. These components consist of the nuclear membrane, nuclear lamina A, nuclear lamina B, glass slide, and nanoneedles.

[0041] Step 1: The construction method of the nuclear membrane is as follows: Since the main focus here is on analyzing the properties of the membrane, and the thickness of the nuclear membrane is relatively small compared to the overall cell nucleus, it is represented by a hollow sphere with a thickness of 50. Concentric semicircles with an inner diameter of 2500 and an outer diameter of 2550 are created, connected at the endpoints, and rotated 360° around the axis of symmetry to obtain the deformable solid component of the nuclear membrane, as shown below. Figure 5 As shown.

[0042] Step 2: Construction method of uniform core fiber network: In practice, the core fiber layer is a uniformly dense orthogonal network thin layer. The spacing between the orthogonal network fibers varies from 50nm to 400nm depending on the density distribution. The average spacing of core fiber layer B is greater than that of core fiber layer A. In this model, the spacing of core fiber layer B is set to 250nm, and the spacing of core fiber layer A is set to 150nm. First, draw a circular wireframe according to the diameter of the core fiber layer. In the assembly interface, array the wireframe around two orthogonal axes respectively, with the number of arrays being... An instance of a merged array is a component; by trimming the component, only components with uniform meshes remain. Partially, the uniform grid section is rotated and arrayed into 6 sections to form a complete mesh sphere. The arrayed components are then merged to obtain a core fiber layer component with a uniform grid, such as... Figure 6 As shown.

[0043] Step 3: Construction of glass slide and nanoneedles: Both nanoneedles and glass slides are discrete rigid bodies. After being constructed into solids according to their shapes, they are transformed into shells. The needle tips are cylinders with a length of 1-2 micrometers and a diameter of 50-400 nanometers. The glass slide is a disk with a radius of 5000 and a thickness of 50.

[0044] Step 4: Assembly: As shown in the figure, assemble according to the position of each component. Assemble the nuclear fiber layer and nuclear membrane concentrically. The nanoneedle is located above the cell nucleus, with the needle tip 75 degrees away from the cell nucleus. The glass slide is located at the bottom of the cell membrane and is tangent to the cell nucleus. Figure 7 The image shown is a model assembly diagram.

[0045] Step 5: Assign cross-sectional properties: Define the materials of each component according to the material properties in Table 1, and assign cross-sectional properties. Among them, the core fiber layer B mainly plays a supporting role in the cell nucleus and is assigned as a beam, while the core fiber layer A mainly maintains the stiffness of the cell nucleus and is assigned as a truss.

[0046] 2. Mesh generation: Membrane approximates global size 47, assigns mesh control attribute hexahedral sweep advanced algorithm, assigns element type C3D8R; laminaA truss element type is T3D2, laminaB beam element type is [missing information], slide element type is R3D4.

[0047] 3. Define the analysis step: Create step1, the dynamic display step, with a time step of 0.001 and enable geometric nonlinearity.

[0048] 4. Define the interaction relationships: The interaction relationships include: 1) The nucleus and cytoplasm are represented by a fluid cavity, with appropriate fluid density and bulk modulus selected. 2) The nuclear lamina and nuclear membrane are connected by connectors, and the connection method is hinged. Due to the large number of connection points between the nuclear lamina and nuclear membrane, this is implemented through script two. The flowchart of the implementation is as follows: Figure 3 As shown. 3) Contact settings: frictionless universal contact.

[0049] 5. Set load and boundary conditions: The displacement load is applied to the reference point of the nanoneedle tip, and the glass slide reference point is set with fixed boundary conditions.

[0050] 6. Submit assignment: Select double precision to perform mechanical response calculation and analysis on the mechanical structure of the cell nucleus.

[0051] Case Analysis:

[0052] 1) Comparison of simulation results and experimental images

[0053] One advantage of the cell nucleus model in this invention is that it can demonstrate the large deformation of the cell nucleus. Figure 8 Images show the experimental process of Liu et al. using nanoneedles to penetrate cells. From top to bottom, the three stages are: the nanoneedle begins to press down, the nanoneedle is pressed to the middle position, and the nanoneedle retracts. Figure 8 (b) Shows the deformation of the cell nucleus during the downward pressure process. Figure 9 The model is shown in the overall displacement contour plot and the displacement contour plot of each component. Figure 9 (a) is a cross-section of the deformed assembly diagram, and... Figure 9 (b) The deformation state at the needle tip is basically the same.

[0054] 2) Selection of nanoneedle diameter

[0055] The diameter of nanoneedles generally ranges from 10 nm to 500 nm. The smaller the diameter of the nanoneedle tip, the more difficult it is to manufacture. Here, we analyzed six different nanoneedle tip diameters as variables to perform penetration analysis on a standard cell nucleus model.

[0056] The six sets of variables are nanoneedle diameters D1 = 50 nm, D2 = 100 nm, D3 = 150 nm, D4 = 200 nm, D5 = 250 nm, and D6 = 300 nm. The stress distribution of the nuclear membrane under the action of these six diameter needle tips is as follows: Figure 11 As shown, with the increase of the needle tip diameter, the stress distribution on the nuclear membrane becomes increasingly dispersed, and the maximum stress gradually decreases. To more clearly illustrate the stress magnitude relationship in the stress concentration area, the stress magnitude along the upper half of the path in the cell nucleus cross-section was measured, as shown below. Figure 12 The red highlighted area in the upper right corner is the path for measuring stress magnitude. Figure 12 The diagram shows a broken line graph illustrating the stress distribution along the path of the nuclear membrane as the tip diameter changes. The graph shows that the maximum stress gradually decreases with increasing tip diameter. When the nanoneedle diameter reaches 200 nm, the stress distribution at the nanoneedle tip exhibits a decline. This is because, once the tip diameter reaches a certain size, the stress concentrates at the tip edge rather than the tip itself, thus dispersing the stress distribution. Therefore, when selecting the tip diameter, it is advisable to choose a size smaller than 200 nm to increase the stress concentration effect at the contact area.

[0057] 3) Effect of nanoneedle loading rate

[0058] Besides the diameter, another important parameter is the nanoneedle loading speed. When analyzing the nanoneedle insertion speed, six different speeds were selected for analysis: v1 = 0.5 μm / s, v2 = 2 μm / s, v3 = 10 μm / s, v4 = 20 μm / s, v5 = 100 μm / s, and v6 = 200 μm / s. The speed variation gradient is large, resulting in a large difference in the deformation of the cell nucleus. The deformation of the cell nucleus, the stress magnitude, and the distribution are analyzed below.

[0059] like Figure 10 As shown, the higher the speed of the nanoneedles, the greater the stress on the nuclear membrane, and the greater the concentration of stress distribution on the nuclear membrane. This can be seen from... Figure 13 peak and Figure 14 (Right) Top view showing stress distribution. However, from... Figure 11The displacement deformation diagram in (left) shows that the displacement load applied by the needle tip is consistent across the five velocities. When the needle tip applies loads of v1, v2, and v3, the overall deformation of the cell nucleus is concentrated near the needle tip. However, as the velocity increases to v4 and v5, the deformation of the cell nucleus gradually distributes throughout the entire nucleus. This indicates that once the velocity reaches a certain value, the deformation of the cell nucleus diffuses throughout the entire nucleus and is no longer concentrated near the needle tip. Since the cell nucleus is relatively fragile, large deformations can have detrimental effects. Therefore, unnecessary deformation must be avoided during the needle tip compression process. The deformation results suggest that the suitable velocity for nanoneedle compression should be less than 20 μm / s. Furthermore, the deformation diagram shows that the model with the most concentrated overall deformation distribution of the cell nucleus is a velocity of 10 μm / s. Therefore, the optimal velocity should be around v2.

[0060] In summary, this invention optimizes the parameters for nanoneedle insertion, proposing that when selecting the needle tip diameter, a diameter less than 200 nm should be chosen to increase the stress concentration effect; at the same time, the downward speed of the nanoneedle should be less than 20 μm / s, and the optimal speed should be around 10 μm / s with a v2 value.

Claims

1. A method for constructing a cell nucleus model based on abaqus-python, comprising the following steps: Step 1: Based on the mechanical properties of the cell nucleus, the cell nucleus structure is divided into four parts, from the outside to the inside: nuclear membrane, nuclear lamina A, nuclear lamina B, and nucleoplasm. Nuclear lamina A and nuclear lamina B together form the nuclear lamina, which are independent networks connected by linker proteins. Based on the actual dimensions, geometric models of each part of the cell nucleus are created in the part module of the ABAQUS software and assembled according to their positional distribution. A rigid plane is created to represent a glass slide, which is tangent to the bottom of the cell nucleus model. Simultaneously, nanoneedles of different sizes are created to achieve the insertion action. Step 1.1: Create the nuclear membrane; A hollow sphere with an inner diameter of 2500 nm and an outer diameter of 2550 nm was used as the core membrane; Step 1.2: Create the core fiber layer; Orthogonal network thin layers are used as core fiber layers. The radius of core fiber layer A is 2450 nm and the spacing of the orthogonal network fibers is 150 nm; the radius of core fiber layer B is 2500 nm and the spacing of the orthogonal network fibers is 250 nm. Step 1.3: Create the glass slide and nanoneedles; The shapes of the glass slide and nanoneedles are created according to their actual shapes. The nanoneedles are 1-2 micrometers long and 50-400 nanometers in diameter. The glass slide is a disk with a radius of 5000 nm and a thickness of 50 nm. Step 2: Based on the material properties of the cell nucleus's mechanical structure, create material and cross-sectional properties for the nuclear membrane and nuclear lamina; Step 3: Assemble according to the position of each component: The cell nucleus part consists of nuclear lamina A, nuclear lamina B, and nuclear membrane from the inside out, and the three are assembled concentrically; the glass slide is located below the cell nucleus, and the upper surface of the glass slide is in contact with the bottom of the nuclear membrane; the nanoneedles are vertically located above the cell nucleus, and the distance between the needle tip and the upper surface of the nuclear membrane is set as needed, here it is set to 100nm; Step 4: Define the analysis step in abaqus-python, set it to a dynamic display analysis step, and set the analysis step duration to 0.15s; Step 5: Define the interaction relationships between the components, including: using connectors to represent the connection between the nuclear membrane and nuclear fiber layer A or nuclear fiber layer B, with hinges between nodes; the nucleus and cytoplasm are represented by fluid cavities in the interaction; Define the surface-to-surface interaction between the base of the cell nucleus and the rigid glass slide, and the surface-to-surface interaction between the tip surface of the nanoneedle and the contact surface of the nuclear membrane; Step 6: Add loads and boundary conditions to the three-dimensional finite element model of the cell nucleus mechanical structure. Here, the glass slide is fixed and displacement load is applied to the nanoneedle to simulate the needle insertion process. Step 7: Divide the cell nucleus into a grid, where the nuclear membrane is a solid unit, nuclear fiber layer B is a beam unit, nuclear fiber layer A is a truss unit, and the glass slide and nanoneedles are discrete rigid units. Step 8: Select double precision to perform mechanical response calculations on the cell nucleus's mechanical structure; The model is based on the Abaqus finite element software and includes structures such as the nuclear membrane, nuclear lamina A, nuclear lamina B, and nucleoplasm. The nucleoplasm is represented by fluid cavities with interaction relationships, the nuclear membrane is a solid, nuclear lamina B is a beam, and nuclear lamina A is a truss. Python-based parametric modeling can achieve fast modeling and batch connection, improve modeling efficiency and accuracy; The orthogonal structure of the A and B lamina structures is closer to the real structure of the lamina, and the discrete model can be used to analyze the influence of the density of the lamina on the mechanical properties of the nuclear membrane.

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