Simulation method for joint coupling motion of flexible boundary and internal active chain based on annular polymer model

Abstract

The invention relates to the field of computer simulation and polymer physics, particularly discloses a simulation method for joint coupling motion of a flexible boundary and an internal active chain based on an annular polymer model, and aims to solve the problem that complex dynamic coupling and nonlinear deformation behaviors between the active chain and the flexible boundary are difficult to really simulate in the prior art. The method comprises the following steps: constructing an annular polymer model formed by connecting inactive particles through chemical bonds so as to characterize a flexible boundary; initializing an active chain model based on boundary geometric constraint, and dynamically aligning driving force and chain segment orientation; adjusting the chain parameters according to the conformation features to generate conformation evolution data; kinetic parameters are extracted to establish a diffusion gradient and volume fraction feedback mechanism, and a bidirectional coupling model is formed by combining the acting force of a local density and velocity field calculation chain on the boundary. According to the technical scheme, non-linear phenomena such as asymmetric collapse, oscillation and bud growth of the boundary can be reproduced in a high-fidelity mode, and the physical authenticity and predictive ability of simulation are remarkably improved.

Description

Technical Field

[0001] This invention belongs to the field of computer simulation and polymer physics, specifically relating to a simulation method for the coupled motion of flexible boundaries and internal active chains based on a ring polymer model. Background Technology

[0002] With the interdisciplinary development of soft matter physics and computational biomechanics, the simulation of the motion of active chains in confined flexible environments has become a key foundation for understanding cell migration, biomembrane remodeling, and the design of artificial active materials. The core of such systems lies in the dynamic coupling between the non-equilibrium driving force of the active chain itself and the deformable properties of the flexible boundary. Its behavior is regulated by both the conformational entropy and bending stiffness within the chain, and depends on the geometric constraints and reaction forces of the boundary on the chain motion. However, traditional molecular dynamics or Brownian dynamics simulation methods often assume that the boundary is rigid or static, failing to accurately reflect the deformation response of the boundary under the continuous pushing of the active chain, leading to severe distortion in the prediction of the overall dynamic evolution of the system.

[0003] While methods based on constructing flexible boundaries using ring polymers can partially simulate boundary elasticity, existing models generally simplify active chains to passive polymer chains, neglecting the directionality and persistence of their activity-driving forces. This makes it difficult to reproduce the complex behavior of real biological systems, such as actin chains driving deformation within lipid vesicles. Furthermore, the interaction between active chains and flexible boundaries is typically treated as local short-range repulsion or adhesion forces, lacking a systematic modeling of the bidirectional feedback mechanism between chain conformational evolution and boundary geometric deformation. Consequently, simulation results fail to capture nonlinear dynamic phenomena such as boundary asymmetric collapse and chain-induced boundary oscillations.

[0004] Existing technologies, when constructing coupled models, often treat the active characteristics of the chain and the flexible response of the boundary separately, failing to update the boundary force distribution in real time based on the conformational changes of the active chain. Furthermore, the adjustment of key parameters such as chain length, bending stiffness, and volume fraction lacks a synergistic optimization mechanism with boundary geometric constraints, hindering the exploration of the universality of the coupling mechanism. In addition, under high-density packing or strong driving conditions, the spatial inhomogeneity of the active chain's motion and the resulting local stress concentration can easily induce boundary instability. Existing methods lack a quantitative description of the coupling relationship between the diffusion coefficient gradient, local density field, and boundary deformation, severely limiting the application depth of such models in biomimetic structure design and biophysical mechanism analysis. Therefore, a simulation method capable of simultaneously characterizing the conformational dynamics of the active chain and the continuous deformation of the flexible boundary is urgently needed. Summary of the Invention

[0005] The purpose of this invention is to provide a simulation method for the coupled motion of flexible boundaries and internal active chains based on a ring polymer model, which can effectively solve the problems in the background art mentioned above.

[0006] To achieve the above objectives, the technical solution adopted by this invention is as follows: a simulation method for the coupled motion of flexible boundaries and internal active chains based on a ring polymer model, comprising the following specific steps: Step 1: Construct a ring polymer model composed of inactive particles connected by chemical bonds to represent the flexible boundary and obtain the initial boundary configuration data; Step 2: Extract flexible boundary geometric constraints from the initial boundary configuration data, construct an active chain model with intra-chain polarization self-driving force, adjust the parameters of self-driving force and duration, and generate active chain configuration data; Step 3: Extract conformational features from the active chain configuration data, adjust the parameters of the active chain model, and generate conformational change data of the active chain within the flexible boundary; Step 4: Extract dynamic parameters from the conformational change data to generate dynamic coupling relationship model data between the active chain and the flexible boundary.

[0007] Preferably, in step 1, constructing the ring polymer model includes connecting multiple inactive particles through chemical bonds, defining the spring constant of the chemical bonds as 10 to 100 units of force per unit length, and the natural length as 0.5 to 2.0 units of length, to generate a closed ring structure; for the ring polymer model, obtaining the positional distribution of the inactive particles and the connection state of the chemical bonds, determining the initial geometry to be approximately circular or elliptical with a circumference ranging from 50 to 200 units of length, and generating initial boundary configuration data based on this.

[0008] Preferably, step 2, extracting the flexible boundary geometric constraints from the initial boundary configuration data, includes calculating the local curvature of each point on the boundary. The curvature calculation uses the three-point difference method with a window radius of 3 particle spacings, and extracts the total boundary length as a global constraint. Based on the geometric constraints, an active chain model is initialized inside the boundary. The active chain consists of N monomers, where N ranges from 20 to 200. The monomers are connected by semi-rigid bonds. The initial driving force direction is randomly distributed within ±30 degrees of the local tangent direction of the chain segment, generating active Brownian chain configuration data. Subsequently, the positions of each monomer and the direction of the connection between adjacent monomers are extracted from the active Brownian chain configuration data. The driving force direction is dynamically adjusted to be completely consistent with the local tangent of the chain segment, generating polarized active chain configuration data.

[0009] Preferably, in step 3, the conformational features extracted from the active chain configuration data include the standard deviation of the statistical chain segment angle distribution and the root mean square deviation of the monomer spacing, to determine whether the initial conformational state of the active chain is an extended state, a coiled state, or an intermediate state; based on the initial conformational state, the chain length N, bending stiffness κ, and duration Lp of the active chain model are adjusted, wherein the bending stiffness κ ranges from 0.1 to 5.0 unit energy, and the duration Lp is determined by the formula... The thermal energy kT is set to 1.0 unit energy to generate adjusted active chain configuration data. The evolution sequence of chain segment angle over time and the chain end distance change characteristics are extracted from the adjusted active chain configuration data. Combined with the real-time geometric constraints of the flexible boundary, the conformational change data of the active chain within the flexible boundary is generated.

[0010] Preferably, step 4, extracting kinetic parameters from conformational change data, includes performing time autocorrelation analysis on the centroid displacement sequence of the active chain, calculating the relaxation time τ, where τ is defined as the time required for the autocorrelation function to decay to its initial value 1 / e, and calculating the diffusion coefficient D using the slope of the mean square displacement curve to generate kinetic parameter distribution data; extracting the distribution characteristics of the diffusion coefficient D in different spatial regions from the kinetic parameter distribution data, identifying the kinetic capability gradient, with the gradient direction pointing towards regions where the diffusion coefficient decreases; dynamically adjusting the volume fraction φ of the active chain according to the kinetic capability gradient, with an initial value of 0.05 to 0.45, and in regions where the diffusion coefficient is below the threshold of 0.01 per unit area per unit time, the volume fraction is locally increased by 0.05 step by step to generate adjusted volume fraction distribution data, and extracting local density change characteristics from it to generate stacking state and kinetic capability gradient distribution data.

[0011] Preferably, step 4, extracting local density and velocity fields from the stacking state and motion capability gradient distribution data, includes dividing the space into a grid with a grid size of 1.0 unit length, counting the number of individual units in each grid to obtain the local density ρ, and averaging the velocity of each individual unit over time to obtain the local velocity field v; based on the motion state, combined with the driving intensity f0 (ranging from 0.1 to 2.0 unit force) and the duration Lp, calculating the force exerted by the active chain on the flexible boundary, using the momentum flux density tensor projection method, integrating the stress within the chain along the boundary normal to generate the force distribution; extracting the boundary shape asymmetry from the force distribution, where asymmetry is defined as the ratio of the boundary centroid offset to the average radius, and calculating the time correlation function of the force, with a decay time constant greater than or equal to 10000 unit time, to generate dynamic coupling relationship model data.

[0012] Preferably, in the process of constructing the ring polymer model, the number of inactive particles M ranges from 50 to 500. In addition to chemical bonds, repulsive potential energy is introduced between the particles. The repulsive potential energy adopts the soft spherical potential, and the potential energy cutoff radius is 1.2 times the particle diameter to prevent boundary self-intersection. During the simulation, a damping force is applied to the ring polymer model, with a damping coefficient of 0.5 to 2.0 unit mass per unit time to ensure that the boundary deformation process is smooth and physically reasonable.

[0013] Preferably, in the active chain model, in addition to flexible bonds, volume repulsion is introduced between monomers. The repulsion adopts a short-range truncation form of Lennard-Jones potential, with a truncation distance of 1.122 times the particle diameter. At the same time, the interaction between the active chain and the flexible boundary is achieved through short-range repulsion between the boundary particles and the chain monomers. The repulsion force has a range of 1.122 times the unit length, ensuring that the chain will not penetrate the boundary.

[0014] Preferably, the method further includes performing steady-state analysis on the dynamic coupling relationship model data. When the boundary shape asymmetry changes by less than 0.001 over 100 consecutive unit time periods, and the spatial gradient of the active chain diffusion coefficient is less than 0.0005 per unit area per unit time per unit length, the system is determined to have reached a stable state. Based on the stable state, the matching relationship between the boundary spring constant and the active chain driving strength is optimized, and the ratio of the spring constant to the driving strength is controlled within the range of 5 to 50 per unit length per unit force to obtain a physically reasonable steady-state distribution.

[0015] Preferably, the method is applied to simulate the process of actin chains driving vesicle deformation within a biological membrane, wherein the flexible boundary simulates a lipid bilayer membrane, the active chain simulates actin fibers, and the driving strength corresponds to the propulsive force generated by ATP hydrolysis. By adjusting the ratio of chain length to membrane circumference between 0.2 and 0.8, nonlinear dynamic phenomena such as boundary asymmetric collapse, periodic oscillation, and local budding can be reproduced. The simulation time step is 0.01 units of time, and the total simulation time is not less than 20,000 units of time.

[0016] Compared with the prior art, the present invention has the following beneficial effects: This invention accurately characterizes the continuous deformability of flexible boundaries by constructing a ring-shaped polymer model composed of inactive particles connected by chemical bonds, and establishes a simulation framework deeply coupled with the conformational dynamics of active chains. This method achieves, for the first time, dynamic alignment of the driving force direction with the local orientation of chain segments, realistically reflecting the physical nature of the intrinsic polarization of active chains. By extracting kinetic parameters from conformational change data and adjusting the volume fraction, a quantitative correlation between the diffusion capability gradient and the local stacking state is established. Furthermore, based on the local density and velocity field, the force distribution of the active chains on the flexible boundary is accurately calculated, fully characterizing the chain-boundary bidirectional feedback mechanism. Therefore, this invention can stably simulate complex nonlinear phenomena such as boundary asymmetric collapse, oscillation, and instability induced by active chains under high-density, strongly driven conditions, significantly improving the physical realism and predictive ability of the simulation results. It provides a high-fidelity, quantifiable computational tool for mechanism analysis and structural optimization in fields such as cell migration, biomembrane remodeling, and the design of artificial active materials. Attached Figure Description

[0017] Figure 1This is a schematic diagram of the overall technical architecture of the flexible boundary active chain motion simulation method based on the ring polymer model proposed in this invention; Figure 2 This is a schematic diagram illustrating the core principle framework of the dynamic alignment mechanism between the driving force direction of the active chain and the local orientation of the chain segment in this invention. Figure 3 This is a logical flow diagram of the flexible boundary modeling and active chain initialization stage in this invention; Figure 4 This is a logical flowchart of the active chain conformational evolution and kinetic parameter feedback adjustment stage in this invention. Figure 5 This is a schematic diagram of the multi-level interaction and data flow of the bidirectional dynamic coupling relationship between the active chain and the flexible boundary in this invention.

[0018] Figure 6 This is a schematic diagram illustrating the simulation effect of the flexible boundary active chain motion based on the ring polymer model proposed in this invention.

[0019] Figure 7 This diagram illustrates the use of the three-point difference method for curvature calculation, with a window radius equal to the distance between three particles, and the extraction of the total boundary length as a global constraint. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0021] Currently, in the interdisciplinary field of soft matter physics and computational biomechanics, simulating the motion of active chains in confined flexible environments faces core challenges: traditional methods assume rigid or static boundaries, failing to accurately reflect the deformation response of the boundaries under continuous pushing by active chains; existing toroidal polymer boundary models neglect the directionality and persistence of the intrinsic driving force of active chains and lack a bidirectional feedback mechanism between chain conformational evolution and boundary geometric deformation, resulting in the inability to reproduce nonlinear dynamic phenomena such as boundary asymmetric collapse and chain-induced boundary oscillations. To address these technical problems, this invention proposes a simulation method based on a toroidal polymer model that simulates the coupled motion of flexible boundaries and internal active chains, effectively solving the issues mentioned in the background.

[0022] Reference Appendix Figure 1 The overall technical architecture of this invention comprises four core stages: flexible boundary modeling, active chain initialization, adaptive adjustment of conformational parameters, and dynamic coupling relationship modeling. The entire process forms a closed-loop feedback system, ensuring that the motion of the active chain and the boundary deformation are physically self-consistent and dynamically consistent.

[0023] In the aforementioned simulation method for the motion of active chains at flexible boundaries based on a ring polymer model, step 1 involves constructing a ring polymer model composed of inactive particles connected by chemical bonds to represent the flexible boundary and obtain initial boundary configuration data. Specifically, constructing the ring polymer model in step 1 involves connecting multiple inactive particles through chemical bonds. The spring constant of the chemical bonds is defined as 10 to 100 units of force per unit length, and the natural length is 0.5 to 2.0 units of length, generating a closed ring structure. The number of inactive particles, M, ranges from 50 to 500. In addition to the chemical bonds, repulsive potential energy is introduced between the particles. The repulsive potential energy adopts a soft spherical potential with a potential energy cutoff radius of 1.122 times the particle diameter to prevent boundary self-intersection. During the simulation, a damping force is applied to the ring polymer model with a damping coefficient of 0.5 to 2.0 units of mass per unit time to ensure that the boundary deformation process is smooth and physically reasonable. For the aforementioned toroidal polymer model, the positional distribution of inactive particles and the connection state of chemical bonds are obtained. The initial geometry is determined to be approximately circular or elliptical, with a perimeter ranging from 50 to 200 units. Based on this, initial boundary configuration data is generated. This initial configuration data is stored in the form of a structured array, containing the three-dimensional coordinates, velocity, and force state of each inactive particle, as well as information such as the indices of the two particles connected by each chemical bond, their current length, and elastic potential energy. See [link to relevant documentation]. Figure 3 The diagram shows the logical flow framework for the flexible boundary modeling and active chain initialization phase.

[0024] In the above-mentioned method for simulating the motion of active chains with flexible boundaries based on a ring polymer model, step 2 involves extracting the geometric constraints of the flexible boundary from the initial boundary configuration data, constructing an active chain model, and generating active chain configuration data. For example... Figure 7 As shown, specifically, step 2, extracting the flexible boundary geometric constraints from the initial boundary configuration data, includes calculating the local curvature of each point on the boundary. The curvature calculation uses the three-point difference method, with a window radius of three particle spacings, and extracts the total boundary length as a global constraint. The local curvature κi of the i-th inactive particle on the boundary is calculated using the interior angle of the triangle formed by it and its two adjacent particles, with the specific formula as follows: , Where θi is the interior angle of the triangle at particle i, and ri is the position vector of particle i.

[0025] Based on the geometric constraints, an active chain model is initialized inside the boundary. The active chain consists of N monomers, where N ranges from 20 to 200. The monomers are connected by flexible bonds. The initial driving force direction is randomly distributed within ±30 degrees of the local tangent direction of the chain segment, generating active Brownian chain configuration data. In addition to the flexible bonds, volume repulsion is introduced between the monomers of the active chain. This repulsion adopts a short-range truncation form of the Lennard-Jones potential, with a truncation distance of 1.122 times the particle diameter and a depth of 1.0 unit energy. Simultaneously, the interaction between the active chain and the flexible boundary is achieved through short-range repulsive forces between the boundary particles and the chain monomers, with a repulsive force range of 1.122 times the unit length, ensuring that the chain does not penetrate the boundary. Subsequently, the positions of each monomer and the directions of adjacent monomer connections are extracted from the active Brownian chain configuration data. The driving force direction is dynamically adjusted to be completely consistent with the local tangent of the chain segment, generating polarized active chain configuration data. This dynamic alignment mechanism of the driving force direction is one of the core innovations of this invention, and its principle framework is as follows: Figure 2 As shown: For the j-th monomer in the active chain, the direction of its driving force fj is forcibly set to the tangential direction formed by the two monomers before and after it. Completely parallel, thus truly reflecting the physical nature of the intrinsic polarization of the active chain.

[0026] In the above-mentioned method for simulating the motion of active chains in flexible boundaries based on a ring polymer model, step 3 involves extracting conformational features from the active chain configuration data, adjusting the parameters of the active chain model, and generating conformational change data of the active chain within the flexible boundary.

[0027] Specifically, in step 3, the conformational features extracted from the active chain configuration data include the standard deviation of the statistical chain segment angle distribution and the root mean square deviation of the monomer spacing, determining whether the initial conformational state of the active chain is extended, coiled, or intermediate. The chain segment angle refers to the bond angle formed by three adjacent monomers, and its standard deviation σθ is used to quantify the degree of chain coiling: when σθ is less than 0.2 radians, it is considered extended; when it is greater than 0.8 radians, it is considered coiled; and between these two is considered intermediate. The root mean square deviation of the monomer spacing is used to verify the chain's integrity and physical rationality. Based on the initial conformational state, the chain length N, bending stiffness κ, and duration Lp of the active chain model are adjusted, where the bending stiffness κ ranges from 0.1 to 5.0 unit energy, and the duration Lp is determined by the formula... The thermal energy kT was set to 1.0 unit energy, and the adjusted active chain configuration data was generated.

[0028] The formula is expressed in standard LaTeX mathematical formula format as follows:

[0029] Where kT represents thermal energy, fixed at 1.0 unit energy, therefore Lp is numerically equal to κ. The evolution sequence of chain segment angles over time and the variation characteristics of chain end distance are extracted from the adjusted active chain configuration data. Combined with the real-time geometric constraints of the flexible boundary, conformational change data of the active chain within the flexible boundary is generated. The conformational change data records the position, velocity, force, local curvature, and minimum distance to boundary particles of all monomers in the active chain at each time step, forming the basis for subsequent dynamic analysis. See [link to relevant documentation]. Figure 4 The diagram shows the logical flow framework of the active chain conformational evolution and kinetic parameter feedback adjustment stage.

[0030] In the above-mentioned method for simulating the motion of active chains at flexible boundaries based on a ring polymer model, step 4 involves extracting kinetic parameters from the conformational change data to generate a model data of the dynamic coupling relationship between the active chain and the flexible boundary. Specifically, step 4 involves extracting kinetic parameters from the conformational change data, including performing time autocorrelation analysis on the centroid displacement sequence of the active chain, calculating the relaxation time τ, where τ is defined as the time required for the autocorrelation function to decay to its initial value 1 / e, and calculating the diffusion coefficient D using the slope of the mean square displacement curve to generate kinetic parameter distribution data.

[0031] Mean square displacement MSD(t) = <|r(t) - r(0)|²>, Where r(t) is the position of the centroid of the active chain at time t, and <> represents the ensemble average.

[0032] diffusion coefficient , where d is the spatial dimension (usually 2 or 3).

[0033] The diffusion coefficient D is extracted from the kinetic parameter distribution data to identify its distribution characteristics in different spatial regions, thus identifying the kinematic capability gradient. The gradient direction points towards regions where the diffusion coefficient decreases. Based on this kinematic capability gradient, the volume fraction φ of the active chain is dynamically adjusted. The initial value of φ is 0.05 to 0.30. In regions where the diffusion coefficient is below the threshold of 0.01 per unit area per unit time, the volume fraction is locally increased by 0.02 to 0.05, generating adjusted volume fraction distribution data. Local density change characteristics are then extracted from this data to generate packing state and kinematic capability gradient distribution data. This feedback mechanism establishes a quantitative correlation between the diffusion capability gradient and the local packing state, effectively alleviating the stress concentration problem in high-density areas. (See schematic diagram below.) Figure 6 As shown.

[0034] Further, step 4, extracting local density and velocity fields from the packing state and motion capability gradient distribution data, includes dividing the space into a grid with a grid size of 1.0 unit length, counting the number of monomers in each grid to obtain the local density ρ, and averaging the velocity of each monomer over time to obtain the local velocity field v. Based on the motion state, combined with the driving intensity f0 (ranging from 0.1 to 6.0 unit force) and the duration Lp, the force exerted by the active chain on the flexible boundary is calculated. The force calculation uses the momentum flux density tensor projection method, integrating the stress within the chain along the boundary normal to generate the force distribution. The calculation of the momentum flux density tensor comprehensively considers the contributions of bonding forces, repulsive forces, and active driving forces between monomers. For each inactive particle on the boundary, the total force F_boundary from the active chain is obtained by projecting the stress tensor generated by all active monomers in its neighborhood along the normal and integrating it. The boundary shape asymmetry is extracted from the force distribution, defined as the ratio of the boundary centroid offset to the average radius. The time correlation function of the forces is calculated, with a decay time constant greater than or equal to 50 units of time, generating dynamic coupling model data. This model data fully characterizes the chain-boundary bidirectional feedback mechanism, which is key to the stable simulation of complex nonlinear phenomena in this invention. Its multi-level interactions and data flow are as follows... Figure 5 As shown.

[0035] The method further includes steady-state analysis of the dynamic coupling model data. When the boundary shape asymmetry changes by less than 0.001 over 100 consecutive unit time intervals, and the spatial gradient of the active chain diffusion coefficient is less than 0.0005 per unit area per unit time per unit length, the system is considered to have reached a stable state. Based on this stable state, the matching relationship between the boundary spring constant and the driving strength of the active chain is optimized, with the ratio of the spring constant to the driving strength controlled within the range of 5 to 50 per unit length per unit force to obtain a physically reasonable steady-state distribution. This steady-state criterion ensures the convergence and physical realism of the simulation results.

[0036] To illustrate the application effect of the present invention, an example simulating the deformation of vesicles driven by actin chains within a biological membrane is constructed.

[0037] In this example, the flexible boundary simulates a lipid bilayer membrane composed of M=200 inactive particles, with a spring constant of 50 units of force per unit length, a natural length of 1.0 unit length, and a perimeter of 150 units of length. The active chain simulates an actin fiber composed of N=120 monomers, with a bending stiffness κ=2.0 units of energy, a duration Lp=2.0 unit length, and a driving strength f0=1.0 unit of force. The ratio of chain length to membrane perimeter is 120 / 150=0.8, which is within the preferred range of 0.2 to 0.8. The simulation time step is 0.01 units of time, and the total simulation time is 20,000 units of time. In the initial stage of the simulation, the active chains are randomly distributed within the boundary, and the driving force direction is dynamically aligned along the chain tangent. As the simulation progresses, the active chains continuously push against the flexible boundary, causing significant deformation of the boundary. After approximately 3,000 units of time, the system observes an asymmetric collapse phenomenon at the boundary: one side of the boundary is concave inward, while the other side bulges outward. After approximately 6000 units of time, the system enters a periodic oscillation state, with the boundary shape switching back and forth between two asymmetric configurations, and the oscillation period is approximately 800 units of time. In locally high-density regions, the formation of tiny budding structures is also observed. Throughout the process, the spatial distribution of the diffusion coefficient D shows a significant gradient, with low-diffusion regions corresponding to high-density packing areas. The volume fraction φ is dynamically increased in these regions, effectively maintaining the system's stability. The decay time constant of the time correlation function of the force is approximately 65 units of time, greater than the threshold of 50 units of time, indicating the existence of a long-term memory effect in the system. Finally, after 10000 units of time, the system reaches a steady state, with the boundary shape asymmetry stabilizing at around 0.15, its variation less than 0.001, and the spatial gradient of the diffusion coefficient less than 0.0004, satisfying the steady-state criterion. This example successfully reproduces nonlinear dynamic phenomena such as boundary asymmetric collapse, periodic oscillation, and local budding, verifying the effectiveness and superiority of the method of this invention.

[0038] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A simulation method for the coupled motion of flexible boundaries and internal active chains based on a ring polymer model, characterized in that: The specific steps include the following: Step 1: Construct a ring polymer model composed of inactive particles connected by chemical bonds to represent the flexible boundary and obtain the initial boundary configuration data; Step 2: Extract flexible boundary geometric constraints from the initial boundary configuration data, construct an active chain model, and generate active chain configuration data; Step 3: Extract conformational features from the active chain configuration data, adjust the parameters of the active chain model, and generate conformational change data of the active chain within the flexible boundary; Step 4: Extract dynamic parameters from the conformational change data to generate dynamic coupling relationship model data between the active chain and the flexible boundary.

2. The simulation method for the coupled motion of flexible boundaries and internal active chains based on a ring polymer model according to claim 1, characterized in that: The construction of the ring polymer model in step 1 includes connecting M inactive particles through chemical bonds, where M ranges from 50 to 500. The spring constant of the chemical bonds is defined as 10 to 100 units of force per unit length, and the natural length is 0.5 to 2.0 units of length, generating a closed ring structure. The positional distribution of the inactive particles and the connection state of the chemical bonds are obtained, and the initial geometry is determined to be approximately circular or elliptical with a circumference ranging from 50 to 200 units of length. Initial boundary configuration data is also generated.

3. The simulation method for the coupled motion of flexible boundaries and internal active chains based on a ring polymer model according to claim 2, characterized in that: In addition to chemical bonds, repulsive potential energy is introduced between the inactive particles. The repulsive potential energy adopts the soft spherical potential, and the potential energy cutoff radius is 1.122 times the particle diameter. During the simulation, a damping force is applied to the toroidal polymer model, with a damping coefficient of 0.5 to 2.0 unit mass per unit time.

4. The simulation method for the coupled motion of flexible boundaries and internal active chains based on a ring polymer model according to claim 1, characterized in that: Step 2 involves extracting the flexible boundary geometric constraints, including calculating the local curvature at each point on the boundary. The curvature calculation uses the three-point difference method with a window radius of 3 particle spacings, and extracts the total boundary length as a global constraint. Inside the boundary, an active chain model composed of N monomers is initialized, where N ranges from 20 to 200. The monomers are connected by flexible bonds. The initial driving force direction is set to be randomly distributed within ±30 degrees of the local tangent direction of the chain segment, generating active Brownian chain configuration data. Subsequently, the driving force direction is dynamically adjusted to be completely consistent with the local tangent of the chain segment, generating polarized active chain configuration data.

5. The simulation method for the coupled motion of flexible boundaries and internal active chains based on a ring polymer model according to claim 4, characterized in that: In addition to flexible bonds, volume repulsion is introduced between the active chain monomers. The repulsion takes the form of a short-range cutoff of the Lennard-Jones potential, with a cutoff distance of 1.122 times the particle diameter. The interaction between the active chain and the flexible boundary is achieved through a short-range repulsive force between the boundary particles and the chain monomers, with the repulsive force acting within a range of 1.122 times the unit length.

6. The simulation method for the coupled motion of flexible boundaries and internal active chains based on a ring polymer model according to claim 1, characterized in that: Step 3 extracts conformational features including the standard deviation of the statistical chain segment angle distribution and the root mean square deviation of the monomer spacing to determine the initial conformational state of the active chain as extended, coiled, or intermediate. Based on the initial conformational state, the chain length N, bending stiffness κ, and duration Lp of the active chain model are adjusted, where the bending stiffness κ ranges from 0.1 to 5.0 unit energy, and the duration Lp... kT represents thermal energy, which is set to 1.0 unit energy. The evolution sequence of chain segment angle over time and the change characteristics of chain end distance are extracted from the adjusted active chain configuration data. Combined with the real-time geometric constraints of the flexible boundary, conformational change data is generated.

7. The simulation method for the coupled motion of flexible boundaries and internal active chains based on a ring polymer model according to claim 1, characterized in that: Step 4 involves extracting kinetic parameters, including performing time autocorrelation analysis on the centroid displacement sequence of the active chain, calculating the relaxation time τ, which is defined as the time required for the autocorrelation function to decay to its initial value 1 / e, and calculating the diffusion coefficient D through the slope of the mean square displacement curve; extracting the distribution characteristics of the diffusion coefficient D in different regions of space from the kinetic parameter distribution data, identifying the motion capability gradient, and pointing the gradient direction towards the region where the diffusion coefficient decreases.

8. The simulation method for the coupled motion of flexible boundaries and internal active chains based on a ring polymer model according to claim 7, characterized in that: Based on the said kinematic gradient, the volume fraction φ of the active chain is dynamically adjusted. The initial value of φ is 0.05 to 0.45 to ensure that the active particles are always in a non-crystalline state. In the region where the diffusion coefficient is lower than the threshold of 0.01 per unit area per unit time, the volume fraction is locally increased by 0.05 step by step to generate the adjusted volume fraction distribution data. Local density change features are extracted from the data to generate the stacking state and kinematic gradient distribution data.

9. The simulation method for the coupled motion of flexible boundaries and internal active chains based on a ring polymer model according to claim 8, characterized in that: Extracting local density and velocity fields from the data of stacking state and kinetic gradient distribution includes dividing the space into a grid with a grid size of 1.0 unit length, counting the number of cells in each grid to obtain the local density ρ, and averaging the velocity of each cell over time to obtain the local velocity field v. Combining the driving intensity f0 and the duration Lp, the force exerted by the active chain on the flexible boundary is calculated. The force calculation adopts the momentum flux density tensor projection method, which integrates the stress in the chain along the boundary normal. The boundary shape asymmetry is extracted from the force distribution. The asymmetry is defined as the ratio of the boundary centroid offset to the average radius. The time correlation function of the force is calculated, and the decay time constant is greater than or equal to 10,000 units of time.

10. The simulation method for the coupled motion of flexible boundaries and internal active chains based on a ring polymer model according to claim 1, characterized in that: Steady-state analysis was performed on the dynamic coupling model data. When the boundary shape asymmetry changed by less than 0.001 over 100 consecutive time intervals and the spatial gradient of the active chain diffusion coefficient was less than 0.0005 per unit area per unit time per unit length, the system was determined to have reached a steady state. Based on the steady state, the matching relationship between the boundary spring constant and the driving strength of the active chain was optimized, and the ratio of the spring constant to the driving strength was controlled within the range of 5 to 50 per unit length per unit force.

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