A method for simulating protein conformational changes based on vectorial elastic network dynamics

Abstract

The application discloses a protein conformation change simulation method based on vector elastic network dynamics, and belongs to the cross field of biophysical simulation and computational mechanics. Protein atom structure is discretized into a coarse-grained particle elastic network model; a particle dynamics control equation is established; a path unit concept is introduced to perform time domain incremental linearization processing on a simulation process; particle displacement is solved based on a central difference method; virtual reverse motion is used to decouple rigid body displacement and pure deformation of the particle; internal force vectors in a local coordinate system are solved based on a virtual work principle; the internal force is returned to a global coordinate system through a coordinate conversion matrix and the particle state is updated; external loads are applied, and continuous dynamics trajectories of the protein are iteratively calculated and output. The application solves the problems that traditional elastic network models cannot process large-scale nonlinear conformation changes of proteins and molecular dynamics simulation is low in efficiency, and can accurately capture non-harmonic motion and transient response of the protein when performing a biological function.

Description

Technical Field

[0001] This invention relates to the interdisciplinary field of biophysical simulation and computational mechanics, specifically to a protein dynamics simulation method based on Vector Elastic Network Dynamics (VEND). Background Technology

[0002] Proteins perform their biological functions (such as enzyme catalysis, signal transduction, ion channel gating, and protein folding) often with large-scale conformational rearrangements. These movements often span displacements of several nanometers and involve complex rotational and translational couplings, exhibiting significant geometrical nonlinearity.

[0003] Among existing simulation techniques, all-atomic molecular dynamics (MD) faces a huge computational cost bottleneck when dealing with large-scale conformational transitions over long timescales (above microseconds) due to its extremely high degree of computational freedom. Traditional elastic network models (ENM), based on the assumption of simple harmonic motion with small deformations, describe dynamics by solving steady-state modes. However, they cannot accurately handle nonlinear large deformation processes far from equilibrium, and it is also difficult to introduce complex external force fields that vary with time.

[0004] Vector finite element method (VFIFE) theory decomposes structural motion into particle displacements and uses inverse motion decoupling techniques to handle geometric nonlinearities, and has been applied in aerospace and architectural large deformation analysis. Introducing this theory into biological macromolecular systems to construct a simulation method that can balance atomic-level topological constraints with the ability to handle large macroscopic mechanical deformations has significant theoretical and applied value for revealing the dynamic functional mechanisms of proteins. Summary of the Invention

[0005] This invention provides a method for simulating protein conformational changes based on vector elastic network dynamics, aiming to achieve efficient and accurate simulation of large-scale, aharmonic, and non-equilibrium deformation during protein functional conformational changes.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for simulating protein conformational changes based on vector elastic network dynamics includes the following steps: Step 1: Obtain the initial three-dimensional structure of the protein and discretize it into a coarse-grained particle elastic network model with amino acid residues as particles and elastic connection units established between particles according to a preset distance threshold. Step 2: Establish the governing equations for particle dynamics, which include mass, velocity damping, internal force, and external force terms. Step 3: Discretize the simulation time domain into a series of continuous path units, each path unit being a very small time step, thereby transforming the continuous nonlinear conformation trajectory into an incremental linearization problem within the time step; Step 4: Solve the governing equations of particle dynamics based on the central difference method, and calculate the displacement of the particle in the next time step based on the current time step and the displacement of the particle in the previous time step. Step 5: Within each time step, perform virtual reverse motion on each elastic connection unit. First, perform translation correction to make the unit endpoints coincide, and then perform rotation correction to align its current configuration with the reference configuration, thereby decoupling the pure deformation of the elastic connection unit. Step 6: In the local coordinate system after the virtual reverse motion, solve for the internal forces generated by the elastic connection unit based on the pure deformation. Step 7: Transform the interior in the local coordinate system obtained in Step 6 to the global coordinate system and superimpose it on the force vector of the corresponding mass point to update the force state of the mass point. Step 8: Repeat steps 4 to 7 until all time steps are traversed, and update the external load in the iterative loop, finally outputting the continuous conformational dynamics trajectory of the protein.

[0007] Furthermore, the damping coefficient of the velocity damping term described in step 2 is used to simulate the viscous resistance and energy dissipation between protein residues and the surrounding water molecules or lipid environment.

[0008] Furthermore, the process of solving the governing equations of particle dynamics based on the central difference method in step 4 does not require assembling a global stiffness matrix, and each calculation step depends only on the force and displacement state at the previous moment.

[0009] Furthermore, the rotation correction described in step 5 specifically includes: The rotation angle is obtained by calculating the dot product of the direction vector of the elastic element at the current moment and the corresponding direction vector in the reference configuration, and then performing the reverse rotation based on the angle.

[0010] Furthermore, in step 6, based on the principle of virtual work, the relationship between internal force and deformation energy is established, and the internal force is calculated based on the pure deformation using a linear elastic or nonlinear elastic potential energy function.

[0011] Furthermore, the updated external load described in step 8 includes constant force, periodic oscillating force, and linearly increasing force.

[0012] Furthermore, the protein is a membrane protein, a soluble globulin, a polypeptide, or a multimeric protein complex.

[0013] The beneficial effects of this invention are: (1) This invention introduces the concept of path unit to perform incremental linearization of the time domain and uses virtual inverse motion technology to precisely decouple rigid body displacement and pure deformation in each path unit, thereby being able to stably handle large-angle rotation and large-displacement translation generated by proteins during allosteric regulation or folding, and making up for the failure of traditional elastic network models in the nonlinear region.

[0014] (2) The explicit integration algorithm is adopted, which eliminates the need to assemble and invert the computationally intensive global stiffness matrix. The computational workload is linearly related to the system size, making it suitable for long-term simulation of large-scale protein complexes.

[0015] (3) Compared with static modal analysis, this method supports the application of external forces that vary with time or location at any time, which can more realistically simulate the stress environment in the body.

[0016] (4) Based on the laws of classical mechanics and the principle of virtual work, the simulation results have clear energy and mechanical meanings, which facilitates quantitative comparison with the experimental results of single-molecule mechanics. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the calculation process of the VEND method of this invention.

[0018] Figure 2 This is a Piezo1 ion channel protein dot model according to an embodiment of the present invention.

[0019] Figure 3 This is the initial conformation of the Piezo1 ion channel protein in an embodiment of the present invention.

[0020] Figure 4 This is the modified configuration of the Piezo1 ion channel protein according to an embodiment of the present invention. Detailed Implementation

[0021] The present invention will be further described and illustrated below with reference to specific embodiments. The embodiments described are merely examples of the content of this disclosure and do not limit the scope of the invention. The technical features of each embodiment in the present invention can be combined accordingly, provided that there is no mutual conflict.

[0022] The accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. Some of the block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0023] The flowchart shown in the attached diagram is merely an illustrative example and does not necessarily include all steps. For example, some steps may be broken down, while others may be combined or partially combined; therefore, the actual execution order may change depending on the specific circumstances.

[0024] like Figure 1 As shown, the present invention proposes a method for simulating protein conformational changes based on vector elastic network dynamics, which mainly includes the following steps: Step 1: Construct a coarse-grained particle elastic network model of the protein.

[0025] The initial three-dimensional atomic structure of the protein is obtained and simplified into a particle system with each amino acid residue as a node. Based on the spatial topological relationship between residues, elastic unit connections are established within a preset cutoff distance to construct a discrete coarse-grained particle elastic network model that retains the overall topological characteristics of the protein.

[0026] Step 2: Establish the governing equations for particle dynamics.

[0027] This step is for each particle. i The dynamic governing equations are established, and a velocity-dependent damping term is introduced to simulate the dissipation effect of the biofluid environment. This term fully includes mass, velocity damping, internal force, and external force terms. The dynamic governing equations are as follows: in, Let the mass of particle i be... Let be the damping coefficient of mass i. Let i be the internal force vector generated by the interaction of particle i within the protein. Let i be the external environmental load vector of mass i. Let be the velocity and acceleration of particle i, respectively.

[0028] Step 3: Time-domain incremental linearization processing.

[0029] By introducing the concept of path elements, complex nonlinear conformation trajectories are discretized into a series of extremely small time steps. Within each such path element, the motion can approximately satisfy the linear mechanics assumption. Therefore, by applying the linear mechanics assumption within each step and capturing the global nonlinear behavior through continuous state updates between steps, the continuous nonlinear conformation trajectory is transformed into an incremental linearization problem within time steps.

[0030] Step 4: Solve using explicit time integration.

[0031] Based on the discretization framework of step 3, the central difference method is used to solve the dynamic equations established in step 2, directly based on the particle's position in the system. and Displacement at time t, calculation The displacement, thus directly updating explicitly. Displacement of the particle at time t: in, The damping factor, To calculate the step size, For the current moment, For the displacement at the next time step, and They are the particles in and The displacement at time step. This calculation process does not require assembling and inverting the computationally intensive global stiffness matrix, and the computational efficiency is approximately linearly related to the system size, making it particularly suitable for large-scale protein systems.

[0032] Step 5: Decouple rigid body displacement and pure deformation through virtual inverse motion.

[0033] Within each path cell, a fictitious reverse motion is performed on the elastic cell: first, translation correction is performed to make the cell endpoints coincide, and then rotation correction is performed by calculating the direction cosines of the current vector and the reference vector. This step filters out pseudo-deformation caused by the overall rotation and translation of the protein, and accurately extracts the pure deformation components that truly generate internal forces, caused only by elastic stretching and bending.

[0034] Specifically, translation correction involves translating the entire element after displacement so that one of its endpoints coincides with the corresponding endpoint in the reference configuration. Rotation correction, on the other hand, determines the spatial rotation angle by calculating the direction cosine between the current element's direction vector and the reference vector, and then performs the corresponding inverse rotation.

[0035] In this invention, the reference configuration refers to the initial three-dimensional spatial form of the protein at the start of the simulation, before it is subjected to external forces; it is the baseline state for the entire dynamic simulation. During the simulation, the real-time three-dimensional spatial form of the protein after being subjected to both external loads and internal forces at the current moment is defined as the current configuration.

[0036] Step 6: Solving for local internal forces and coordinate transformation.

[0037] In the decoupled local coordinate system, internal forces are calculated using the pure deformation of the element. Then, a coordinate transformation matrix is ​​used to map the internal forces from the local coordinate system to the global coordinate system, and these forces are superimposed onto the resultant force vector of the corresponding mass point. In this process, the equations of motion for the next time step are used as input. Step 7: Load application and dynamic evolution.

[0038] Depending on the specific simulation scenario, external loads that simulate the physical environment and change over time are applied to specific residues or regions. Factors such as membrane tension, ligand binding force, or shear force are considered. By iteratively executing steps 4 to 6, the load, position, force, and velocity are dynamically updated, ultimately obtaining the continuous conformational motion trajectory of the protein under complex conditions. The simulation method of this invention is described in detail below with specific parameters and examples.

[0039] Example 1: Reconstruction of the dynamic gating trajectory of Piezo1 ion channel protein under simulated membrane tension This embodiment demonstrates the application of the method of the present invention to simulate the conformational change trajectory of the mechanosensitive ion channel protein Piezo1 under membrane tension.

[0040] Step 1: Construction of coarse-grained elastic network model A high-resolution cryo-electron microscopy structure (PDBID: 6B3R) of the Piezo1 protein was obtained. The protein was discretized into a particle system containing 4,554 particle nodes, with each amino acid residue representing a node. Cutoff distances were set based on spatial topological relationships. Å, elastic units based on harmonic potential are established between any two nodes within this distance, thereby constructing a coarse-grained elastic network model that preserves the overall topological characteristics of the protein, such as... Figure 2 As shown.

[0041] Step 2: Initialize dynamic parameters Assigning equivalent mass to each particle Introducing a normalized damping coefficient It is used to consume the excess kinetic energy generated by external forces during the calculation process, so that the structure can smoothly tend to the transient equilibrium configuration under non-equilibrium state.

[0042] Step 3: Determine the total computation time and time step. The total simulation duration is set to 100 ps, ​​with the first 50 ps being the loading phase and the last 50 ps being the unloading phase. Calculation step size. Set to the minimum value that satisfies the CFL stability condition (e.g.) ps), to ensure the numerical accuracy of explicit integrals.

[0043] Step 4: Apply external mechanical load Synchronous, horizontally radial external forces were applied to the transmembrane helical region surrounding the three helical blades of the Piezo1 protein. The load amplitude increased linearly with time, with a peak value set at 155 pN. This load distribution simulated the process by which cell membrane tension acts on channel proteins through the lipid-protein interface.

[0044] Step 5: Start the simulation cycle by solving the dynamics and decoupling the nonlinearity. Initiate iterative computation and perform the following operations at each time step: Using the central difference method, based on the node displacements at the current and previous moments, the displacements of all nodes at the next moment are explicitly solved; For each elastic unit Perform virtual reverse motion: first, deform the configuration of the unit. The entire node is translated. Coincident with the starting point i; then calculate the rotation angle using the vector dot product. And perform a reverse rotation, where It is a reference configuration. This is the current configuration; After the above operations, the pure deformation caused solely by stretching is extracted. ,in, It is the elastic unit of the reference configuration The original length under the reference configuration, It is an elastic unit The length after decoupling the rigid body displacement through virtual reverse motion in the current configuration.

[0045] In the decoupled local coordinate system, based on the pure deformation... Using Hooke's Law to calculate local internal forces ; The internal forces are transformed to the global coordinate system using a transformation matrix and then superimposed onto the corresponding nodes i and j. In the vector, the resultant force is used for calculation in the next time step.

[0046] Step 6: Output Results and Verification Simulation Results Display Through the above iterations, the continuous gated trajectory of Piezo1 under membrane tension was successfully reconstructed. The key results are as follows: Geometric response: At the start of the simulation (t=0 ps), the initial configuration of piezo1 is as follows Figure 3 As shown, at 42 ps (corresponding to a load of approximately 130 pN), the Piezo1 blade exhibits significant radial expansion, as... Figure 4 As shown, the diameter increases by approximately 9.5 nm; at the same time, the vertical height of the channel shrinks by 2.4 nm from the initial state.

[0047] Energy assessment: The total work performed by the system on external forces peaks at 46 ps, approximately 58.4 ps. This is consistent with the Piezo1 flattening energy barrier (approximately 50) measured by high-speed atomic microscopy (HS-AFM). The results showed extremely high consistency, confirming the accuracy of the simulated energy.

[0048] Stiffness characteristics: The effective mechanical stiffness of Piezo1 was estimated to be approximately 9.1 pN / nm by using the slope of the displacement-load curve.

[0049] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for simulating protein conformational changes based on vector elastic network dynamics, characterized in that, Includes the following steps: Step 1: Obtain the initial three-dimensional structure of the protein and discretize it into a coarse-grained particle elastic network model with amino acid residues as particles and elastic connection units established between particles according to a preset distance threshold. Step 2: Establish the governing equations for particle dynamics, which include mass, velocity damping, internal force, and external force terms. Step 3: Discretize the simulation time domain into a series of continuous path units, each path unit being a very small time step, thereby transforming the continuous nonlinear conformation trajectory into an incremental linearization problem within the time step; Step 4: Solve the governing equations of particle dynamics based on the central difference method, and calculate the displacement of the particle in the next time step based on the current time step and the displacement of the particle in the previous time step. Step 5: Within each time step, perform virtual reverse motion on each elastic connection unit. First, perform translation correction to make the unit endpoints coincide, and then perform rotation correction to align its current configuration with the reference configuration, thereby decoupling the pure deformation of the elastic connection unit. Step 6: In the local coordinate system after the virtual reverse motion, solve for the internal forces generated by the elastic connection unit based on the pure deformation. Step 7: Transform the interior in the local coordinate system obtained in Step 6 to the global coordinate system and superimpose it on the force vector of the corresponding mass point to update the force state of the mass point. Step 8: Repeat steps 4 to 7 until all time steps are traversed, and update the external load in the iterative loop, finally outputting the continuous conformational dynamics trajectory of the protein.

2. The method for simulating protein conformational changes based on vector elastic network dynamics according to claim 1, characterized in that, The damping coefficient of the velocity damping term described in step 2 is used to simulate the viscous resistance and energy dissipation between protein residues and the surrounding water molecules or lipid environment.

3. The method for simulating protein conformational changes based on vector elastic network dynamics according to claim 1, characterized in that, Step 4 describes solving the governing equations of particle dynamics based on the central difference method. The calculation process does not require assembling a global stiffness matrix, and each calculation step depends only on the force and displacement state at the previous moment.

4. The method for simulating protein conformational changes based on vector elastic network dynamics according to claim 1, characterized in that, The rotation correction mentioned in step 5 specifically refers to: The rotation angle is obtained by calculating the dot product of the direction vector of the elastic element at the current moment and the corresponding direction vector in the reference configuration, and then performing the reverse rotation based on the angle.

5. The method for simulating protein conformational changes based on vector elastic network dynamics according to claim 1, characterized in that, In step 6, based on the principle of virtual work, the relationship between internal force and deformation energy is established, and the internal force is calculated based on the pure deformation using linear elastic or nonlinear elastic potential energy functions.

6. The method for simulating protein conformational changes based on vector elastic network dynamics according to claim 1, characterized in that, The updated external load described in step 8 includes constant force, periodic oscillating force, and linearly increasing force.

7. The method for simulating protein conformational changes based on vector elastic network dynamics according to claim 1, characterized in that, The protein is a membrane protein, a soluble globulin, a polypeptide, or a multimeric protein complex.

Images